**Short-Term Forecasting of Photovoltaic Solar Power Production Using Variational Auto-Encoder Driven Deep Learning Approach**

#### **Abdelkader Dairi 1,† , Fouzi Harrou 2, \* ,† , Ying Sun 2,† and Sofiane Khadraoui 3,†**


Received: 7 October 2020; Accepted: 19 November 2020; Published: 25 November 2020

**Abstract:** The accurate modeling and forecasting of the power output of photovoltaic (PV) systems are critical to efficiently managing their integration in smart grids, delivery, and storage. This paper intends to provide efficient short-term forecasting of solar power production using Variational AutoEncoder (VAE) model. Adopting the VAE-driven deep learning model is expected to improve forecasting accuracy because of its suitable performance in time-series modeling and flexible nonlinear approximation. Both single- and multi-step-ahead forecasts are investigated in this work. Data from two grid-connected plants (a 243 kW parking lot canopy array in the US and a 9 MW PV system in Algeria) are employed to show the investigated deep learning models' performance. Specifically, the forecasting outputs of the proposed VAE-based forecasting method have been compared with seven deep learning methods, namely recurrent neural network, Long short-term memory (LSTM), Bidirectional LSTM, Convolutional LSTM network, Gated recurrent units, stacked autoencoder, and restricted Boltzmann machine, and two commonly used machine learning methods, namely logistic regression and support vector regression. The results of this investigation demonstrate the satisfying performance of deep learning techniques to forecast solar power and point out that the VAE consistently performed better than the other methods. Also, results confirmed the superior performance of deep learning models compared to the two considered baseline machine learning models.

**Keywords:** photovoltaic power forecasting; data-driven; deep learning; variational autoencoders; RNN

#### **1. Introduction**

The accurate modeling and forecasting of solar power output in photovoltaic (PV) systems are certainly essential to improve their management and enable their integration in smart grids [1,2]. Namely, the output power of a PV system is highly correlated with the solar irradiation and the weather conditions that explain the intermittent nature of PV system power generation. Particularly, the characteristic of fluctuation and intermittent of the temperature and solar irradiance could impact solar power production [3]. In practice, a decrease of larger than 20% of power output can be recorded in PV plants [4]. Hence, the connected PV systems to the public power grid can impact the stability and the expected operation of the power plant [5]. Given reliable real-time solar power forecasting, the integration of PV systems into the power grid can be assured. Also, power forecasting becomes an

indispensable component of smart grids to efficiently manage power grid generation, storage, delivery, and energy market [6,7].

Long-and short-term forecasting methods are valuable tools for efficient power grid operations [8,9]. The success of integrating PV systems in smart grids depends largely on the accuracy of the implemented forecasting methods. Numerous models have been developed to enhance the accuracy of solar power forecasting, including autoregressive integrated moving average (ARIMA), and Holt-Winters methods. In Reference [10], a short term PV power forecasting based on the Holt-Winters algorithm (also called triple exponential smoothing method) has been introduced. This model is simple to construct and convenient to use. In Reference [11], different time series models including Moving average models, exponential smoothing, double exponential smoothing (DES), and triple exponential smoothing (TES) have been applied for short-term solar power forecasting. In Reference [12], a coupled strategy integrating discrete wavelet transform (DWT), random vector functional link neural network hybrid model (RVFL), and SARIMA has been proposed to a short-term forecast of solar PV power. This study showed that the use of the DWT negatively affects the accuracy of solar PV power forecasting under a clear sky. While the quality of the forecast model is improved when using DWT in cloudy and rainy sky weather. In addition, the coupled model showed superior forecasting performance in comparison to individuals models (i.e., SARIMA or RVFL). However, switching between two forecast models is not an easy task, particularly for real-time forecasting. In Reference [13], a hybrid model merging seasonal decomposition and least-square support vector regression was developed for forecasting monthly solar power output. Improved results have been obtained with this hybrid model compared to those obtained with ARIMA, SARIMA, and generalized regression neural network.

In recent years, shallow machine learning (ML) as non-parametric models, which are more flexible, have been widely exploited in improving solar PV forecasting. These models possess desirable characteristics and can model the complicated relationship between process variables and do not need an explicit model formulation to be specified, as is generally required. In Reference [14], a hybrid approach combining support vector regression (SVR) and improved adaptive genetic algorithm (IAGA) is developed for an hourly electricity demand forecasting. It has been shown that this hybrid approach outperformed the traditional feed-forward neural networks, the extreme learning machine (ELM) model, and the SVR model. In Reference [15], an approach for forecasting PV and wind-generated power using the higher-order multivariate Markov Chain. This approach considers the time-adaptive stochastic correlation between the wind and PV output power to achieve the 15-min ahead forecasting. The observation interval of the last measured samples are included to follow the pattern of PV/wind power fluctuations. In Reference [16], a univariate method is developed for multiple steps ahead of solar power forecasting by integrating a data re-sampling approach with machine learning procedures. Specifically, machine learning algorithms including Neural Networks (NNs), Support Vector Regression (SVR), Random Forest (RF), and Multiple Linear Regression (MLR) are applied to re-sampled time-series for computing multiple steps ahead predictions. However, this approach is designed only for univariate time series data. In Reference [17], a forecasting strategy combining the gradient boosting trees algorithm with feature engineering techniques is proposed to uncover information from a grid of numerical weather predictions (NWP) using both solar and wind data. Results indicate that appropriate features extraction from the raw NWP could improve the forecasting. In Reference [18], a modified ensemble approach based on an adaptive residual compensation (ARC) algorithm is introduced for solar power forecasting. In Reference [19], an analog method for day-ahead regional photovoltaic power forecasting is introduced based on meteorological data, and solar time and earth declination angle. This method exhibited better day-ahead regional power forecasting compared to the persistence model, System advisor model, and SVM model.

Over the last few years, deep learning has emerged as a promising research area both in academia and industry [20–24]. The deep learning technology has realized advancement in different areas, such as computer vision [25], natural language processing [26], speech recognition [27], renewable energy forecasting [4,28], anomaly detection [29–31], and reinforcement learning [32]. Owing to its data-driven approaches, deep learning has brought a paradigm shift in the way relevant information in time series data are extracted and analyzed. By concatenating multiple layers into the neural network structures, deep learning-driven methods enable flexible and efficient modeling of implicit interactions between process variables and automatic extraction of relevant information from a voluminous dataset with limited human instruction. Various deep techniques have been employed in the literature for improving solar power forecasting. For instance, in Reference [33], Recurrent Neural Networks (RNNs) is adopted for PV power forecasting. However, simple RNN is not suited to learn long-term evolution due to the vanishing gradient and exploding gradient. To bypass this limitation, several variants of RNN have been developed including Long Short-Term Memory Networks (LSTM) and gated recurrent unit (GRU) networks. Essentially, compared to a simple RNN model, LSTM and GRU models possess the superior capacity in modeling time-dependent data within a longer time span. In Reference [4], the LSTM model, which is a powerful tool in modeling time-dependent data, is applied to forecast solar power time series data. In Reference [34], a GRU network, which is an extended version of the LSTM model, has been applied to forecast short-term PV power. In Reference [35], at first, an LSTM recurrent neural network (LSTM-RNN) is applied for independent day-ahead PV power forecasting. Then, the forecasting results have been refined using a modification approach that takes into consideration the correlation of diverse PV power patterns. Results showed that the forecasting quality is improved by considering time correlation modification. In Reference [36], by using the LSTM model, a forecasting framework is introduced for residential load forecasting to address volatility problems, such as variability of resident's activities and individual residential loads. Results show that the forecasting accuracy could be enhanced by incorporating appliance measurements in the training data. In Reference [37], a hybrid forecasting approach is introduced by combining a convolutional neural network (CNN) and a salp swarm algorithm (SSA) for PV power output forecasting. After classifying the PV power data and associated weather information in five weather classes: rainy, heavy cloudy, cloudy, light cloudy, and sunny, the CNN is applied to predict the next day's weather type. To this end, five CNN models are constructed and SSA is applied to optimize each model. However, using several CNN models makes this hybrid approach not suitable for real-time forecasting. In Reference [38], a method combining deep convolutional neural network and wavelet transform technique is proposed for deterministic PV power forecasting. Then, the PV power uncertainty is quantified using quantile regression. Results demonstrated the deterministic model possesses reasonable forecasting stability and robustness. Of course, deep learning models possess the capacity to efficiently learn nonlinear features and pertinent information in time-series data that should be exploited in a wide range of applications.

This study offers a threefold contribution. Firstly, to the best of our knowledge, this the first study introducing a variational autoencoder (VAE) and Restricted Boltzmann Machine (RBM) methods to forecast PV power. Secondly, this study provides a comparison of forecasting outputs of eight deep learning models, including simple RNN, LSTM, ConvLSTM, Bidirectional LSTM (BiLSTM), GRUs, stacked autoencoders, VAE, and RBM, which takes into account temporal dependencies inherently and nonlinear characteristics. The eight deep learning methods and two commonly used machine learning methods, namely logistic regression (LR) and support vector regression (SVR), were applied to forecast PV power time-series data. Finally, for the guidance of short- and long-term operational strategies for PV systems, both single- and multi-step-ahead forecasting are examined and compared in this paper. Data sets from two grid-connected plants are adopted to assess the outputs of the deep learning-driven forecasting methods. Section 2 introduces the eight used deep learning methods. Section 3 describes the deep learning-based PV power forecasting strategy. Section 4 assesses the forecasting methods and compares their performance using two actual datasets. Finally, Section 5 concludes this study and sheds light on potential future research lines.

## **2. Methodologies**

Deep learning techniques, which possess good capabilities in automatically learning pertinent features embed in data, are examined in this study to forecast PV power output. Table 1, summarizes the pros and cons of the seven considered benchmark deep learning architectures: RNN [39], LSTM [40], GRU [41], Bi-LSTM [42], ConvLSTM [43], SAE [44], RBM [45,46], and VAE [20,47].


**Table 1.** The considered benchmark deep learning methods.


**Table 1.** *Cont.*

#### *Variational Autoencoders Model*

VAEs are an essential class of generative-based techniques that are efficient to automatically extract information from data in an unsupervised manner [20,47]. One desirable characteristic of VAEs is their ability for reducing the input dimensionality enabling them to compress large dimensional data into a compressed representation. Moreover, they are very effective for approximating complex data distributions using stochastic gradient descent [47]. There are two major advantages of VAEs compared the conventional autoencoders, one is they are efficient to solve the overfitting problem in the conventional autoencoders by using a regulation mechanism in the training phase, and the second advantage is that they have proved effective when handling various kinds of complex data in different applications, including handwritten digits, and urban networks modeling [48]. Here, VAE is adopted for solar PV production forecasting. Figure 1 shows a schematic diagram of the construction of a VAE.

**Figure 1.** Basic schematic illustration of a variational autoencoder (VAE).

Basically, the VAE, as a variant of autoencoders, contains two neural networks an encoder and a decoder, where the encoder mission is to encode a given observed set, **X** into a latent space *Z* as distribution, q (**z**|**x**). The latent (termed hidden) space dimension is decreased in comparison to the dimension of the observed set. Indeed, the encoder is built to compress the observed set toward this reduced dimensional space efficiently. Then, a sample is generated via, *z* ∼ q(**z**|**x**),using the learned probability distribution. On the other hand, the key purpose of the decoder, **p** (**x**|**z**), consists in generating the observation *x* based on the input *z*. It should be emphasized that the reconstruction of data using the decoder results in some deviation of reconstruction, which is calculated and backpropagated through the network. This error is minimized in the training phase of the VAE model by the minimization of the deviation between the observed set and the encoded-decoded set.

To summarize, the VAE encoder is gotten via an approximate posterior **q***<sup>θ</sup>* (**z**|**x**), and the decoder is obtained by a likelihood **p***<sup>φ</sup>* (**x**|**z**), where *θ* and *φ* refers respectively to the parameters of encoder and decoder. Here a neural network is constructed for learning *θ* and *φ*. Essentially, the VAE encoder's role is learning latent variable **z** based on gathered sensor data, and the decoder employs the learned latent variable **z** for recovering the input data. The deviation between the reconstructed data and the input data should be close to zero as possible. Notably, the learned latent variable **z** from the encoder is used for feature extraction based on the input data. Usually, the dimension of the output of the encoder is smaller than that of the original data, which leads to the dimensionality reduction of input data. Note that the encoder is trained by training the entire VAE comprising encoder and decoder.

It is worth pointing out that the loss function has an essential effect on feature extraction for training VAE. Assume that **X***<sup>t</sup>* = [*x*11, *x*2*<sup>t</sup>* , . . . , *xNt*] is the input data points of VAE at time point *t*, and **X** ′ *t* is the reconstructed data using the VAE model. Furthermore, it is assumed maximizing the marginal likelihood learning of parameters, expressed as [49]:

$$\log p\_{\boldsymbol{\theta}}(\mathbf{x}') = D\_{\text{KL}}\left[q\_{\boldsymbol{\theta}}(\mathbf{z}|\mathbf{x})\,\middle|\,\|p\_{\boldsymbol{\theta}}(\mathbf{x})\right] + \mathcal{L}(\boldsymbol{\theta},\boldsymbol{\phi};\mathbf{x}),\tag{1}$$

where *DKL*[.] denotes the Kulback-Leibler divergence, and L refers to the likelihood of the parameters of encoder and decoder (i.e., *θ* and *φ*). Hence, the loss can be expressed as

$$\mathcal{L}(\theta,\phi) = \underbrace{\mathbb{E}\_{\mathbf{z}\sim\mathbf{q}\_{\theta}(\mathbf{z}|\mathbf{x})}\Big(\log\mathfrak{p}(\mathbf{x}'|\mathbf{z})\Big)}\_{\text{Reconstruction term}} - \underbrace{D\_{\text{KL}}\big(\mathbf{q}\_{\theta}(\mathbf{z}|\mathbf{x})||\mathbf{p}\_{\theta}(\mathbf{z})\Big)}\_{\text{Regularization term}}.\tag{2}$$

The VAE's loss function is composed of two parts: the reconstruction loss and a regularizer. Reconstruction loss tries to get an efficient encoding-decoding procedure. In contrast, a regularizer part permits the regularization of the latent space construction to approximate the distributions out of the encoder as near as feasible to a prefixed distribution (e.g., Normal distribution). Figure 2 schematically summarizes the procedure for computing the loss function.

The term (2) permits reinforcing the decoder capacity to learn data reconstruction. Higher values of the reconstruction loss mean that the performed reconstruction is not suitable , while lower values mean that the model is converging. The regularizer is reported using the Kulback-Leibler (KL) divergence separating the distribution of the encoder function (q*<sup>θ</sup>* (**z**|**x**)) and of the latent variable prior (**z**, |p*φ*(**z**)). Indeed, KL is employed to compute the distance that separates two given probability distributions. The gradient descent method is used to minimize the loss function with respect to the encoder's parameters and decoder in the training phase. Overall, we minimize the loss function to ensure getting a regular latent space,*z*, and adequate sampling of new observation using **z** ∼ p*φ*(**z**) [50].

**Figure 2.** Reconstruction loss and Kulback-Leibler (KL) divergence to train VAE.

Let assume that *pφ*(**z**) = N (*z*; 0, *I*), we can write *q<sup>θ</sup>* (**z**|**x**) in the following form:

$$\log q\_{\theta}(\mathbf{z}|\mathbf{x}) = \log \mathcal{N}(\mathbf{z}; \mu, \sigma^2 I). \tag{3}$$

The mean and standard deviation of the approximate posterior are denoted by (*µ*, *σ*), respectively. Note here that a layer is dedicated to both of them. Moreover, the latent space *z* is constructed using a deterministic function *g* parameterized by *φ* and an auxiliary noise variable *ε* ∼ *p*(*ε*) or more specifically *ε* ∼ N (0, *I*).

$$z = \mathcal{g}\_{\Phi}(\mathfrak{x}, \mathfrak{e}) = \mathfrak{\mu} + \sigma \odot \mathfrak{e}.\tag{4}$$

The reconstruction error term can be expressed in the following form:

$$\mathcal{L}(\theta, \phi, \mathbf{x}) = \frac{1}{2} \sum\_{i} \left( 1 + \log((\sigma\_i)^2) - (\mu\_i)^2 - (\sigma\_i)^2 \right) + \frac{1}{L} \sum\_{l=1}^{L} \log(p\_\theta(\mathbf{x}|\mathbf{z}^{(l)})),\tag{5}$$

where the ⊙ denotes the element-wise product.

Overall, the encoder and decoder's parameters are obtained by minimizing the loss function, L(*θ*, *φ*), using the training observations. The VAE is trained using the procedure tabulated Algorithm 1.

#### **Algorithm 1:** VAE training algorithm.

**Input:** : Training dataset *X* = {*x* 1 , . . . , *x k*} **Output:** : {*θ*, *φ*} *θ* : Encoder parameters; *φ* : Decoder parameters; *M* : number of mini-batch (drawn from full dataset) ; {*θ*, *φ*} ←− Initialize model parameters randomly ; **repeat** *X<sup>m</sup>* ←− *RandomMinibatch*(*X*, *M*); Draw *L* samples from *ǫ* ∼ N (0, 1) ; *z* = *gφ*(*Xm*,*ε*) ; G = ∑ *j KL qj z*|*x* (*j*) ||*p* (*z*) + 1 *L* ∑ *L l*=1 *log*(*p*(*x* (*l*) |*z* (*i*,*l*) )); {*θ*, *φ*} ←− *OptimizerU pdate*(G, *θ*, *φ*); **until** *parameters convergence :* {*θ*, *φ*};

#### **3. Deep Learning-Based PV Power Forecasting**

The input data consists of PV power output that variates between 0 and the rated output power. Thus, when handling some large-value data with the RNN model, a gradient explosion can be occurred and negatively affects the performance of the RNN. Furthermore, the learning effectiveness of RNN will be reduced. To remedy this issue, the input data is normalized via min-max normalization within the interval [0, 1], and then used for constructing the deep learning models. The normalization of the original measurements, **y** is defined as:

$$
\tilde{y} = \frac{(y - y\_{\min})}{(y\_{\max} - y\_{\min})}' \tag{6}
$$

where *ymin* and *ymax* refer to the minimum and maximum of the raw PV power data, respectively. After getting forecasting outputs, we applied a reverse operation to ensure that the forecasted data match to the original PV power time-series data.

$$y = \tilde{y} \* (y\_{\max} - y\_{\min}) + y\_{\min}.\tag{7}$$

As discussed above, the generated PV power shows a high level of variability and volatility because of its high correlation with the weather conditions. Hence, for mitigating the influence of uncertainty on the accuracy of the PV power forecasting this work presents a deep-learning framework to forecast PV power output time-series. Essentially, deep learning models are an efficient tool to learn relevant features and process nonlinearity from complex datasets. In this study, a set of eight deep learning models have been investigated and compared for one-step and multiple steps ahead forecasting of solar PV power. The overall structure of the proposed forecasting procedures is depicted in Figure 3. As shown in Figure 3, solar PV power forecasting is accomplished in two phases: training and testing. The original PV power data is split into a training sub-data and a testing sub-data. At first, the raw data is normalized to build deep learning models. Adam optimizer is used to select the values of parameters of each model by minimizing the loss function based on training data. Once the models are constructed, they are exploited for PV power output forecasting. The quality of models are quantified using several statistical indexes including the Coefficient of determination (*R* 2 ), explained variance (EV), mean absolute error (MAE), Root Mean Square Error (RMSE), and normalized RMSE (NRMSE).

**Figure 3.** Schematic presentation of deep learning-based photovoltaic (PV) power forecasting.

Essentially, the deep learning-driven forecasting methods learn the temporal correlation hidden on the PV power output data and expected to uncover and captures the sequential features in the PV power time series. The main objective of this study is to investigate the capability of learning models namely RNN, LSTM, BiLSTM, ConvLSTM, GRU, RBM, SAE, and VAE for one-step and multiple-steps ahead solar PV power forecasting.

#### *3.1. Training Procedure*

The eight models investigated in this study can be categorized into two classes: autoencoders and recurrent neural networks. The autoencoders represented include RBM, VAE, and SAEs while the RNN-based models contain RNN, LSTM, GRU, BiLSTM, and ConvLSTM. The dataset used for training and testing are normalized first, and more data preprocessing is needed for the autoencoder models. For instance, data reshaping is needed to transform the univariate PV power time-series data to a two-dimension matrix to be used as input for the autoencoders including the SAE, VAE, and RBM. The main difference between the two classes in the training phase is the learning way, the RNNs are entirely supervised trained while the auto-encoders are first pre-trained in an unsupervised manner and then the training is completed based on supervised learning. Specifically, RNNs models are trained in a supervised way by using a subset of training as input sequence (X = *x*1, . . . , *x<sup>k</sup>* ) and an output variable Y = *xk*+<sup>1</sup> . The sequence length *l*, called the lag, is a crucial parameter used in the data preparation phase. The mapping sequence to the next value is constructed using a window sliding algorithm. The value of *l* is determined using the Grid Search approach [51]. Here, the value of *l* is chosen 6, which is the lowest value that maximizes the overall performance of the proposed approach.

RNN—based models are trained to learn the mapping function from the input to the output. After that, these trained models are used to forecast new data that complete the sequence. On the other hand, the greedy layer-wise unsupervised plus fine-tuning were applied to RBM, VAE, and SAES. It should be noted that PV power output forecasting based on autoencoder is accomplished as a dimensionality reduction. That is these models do not have the possibility to discover time dependencies or model time series data. Hinton [44] shows that a greedy layerwise unsupervised learning for each layer followed by a fine-tuning improves the features extraction and learning process of the neural networks dedicated to prediction problems or for dimensionality reduction like autoencoders. The VAE-driven forecasting procedure including the pretreatment step is illustrated in Figure 4.

**Figure 4.** VAE-driven procedure.

#### *3.2. Measurements of Effectiveness*

The deep learning-driven forecasting methods will be evaluated using the following metrics: *R* 2 , RMSE, MAE, EV, and NRMSE.

$$R^2 = \frac{\sum\_{i=1}^{n} [(y\_i - \bar{y}) \cdot (\mathfrak{g}\_i - \bar{\mathfrak{g}})]^2}{\sqrt{\sum\_{i=1}^{n} (y\_i - \bar{y})^2} \cdot \sqrt{\sum\_{i=1}^{n} (\mathfrak{g}\_i - \bar{\mathfrak{g}})^2}},\tag{8}$$

$$RMSE = \sqrt{\frac{1}{n} \sum\_{t=1}^{n} (y\_t - \hat{y}\_t)^2},\tag{9}$$

$$MAE = \frac{\sum\_{t=1}^{n} |y\_t - \hat{y}\_t|}{n} \,\tag{10}$$

$$EV = 1 - \frac{\text{Var}(\hat{\mathbf{y}} - \mathbf{y})}{\text{Var}(\mathbf{y})},\tag{11}$$

$$\text{NRMSE} = \left(1 - \sqrt{\frac{\sum\_{i=1}^{N} (y\_i - \mathfrak{Y})^2}{\sum\_{i=1}^{N} (y\_i - \overline{y})^2}}\right) . 100\% \tag{12}$$

where *y<sup>t</sup>* are the actual values, *y* ˆ*<sup>t</sup>* are the corresponding estimated values, *y* is the mean of measured power data points, and *n* is the number of measurements. Instead of using RMSE that relies on the range of the measured values, the benefit of using NRMSE as the statistical indicator is that it does not rely on the range of the measured values. NRMSE metric indicates how well the forecasted model response matches the measurement data. A value of 100% for NRMSE denotes perfect forecasting and lower values characterize the poor forecasting performance. Lower RMSE and MAE values and EV and R2 closer to 1 are an indicator of accurate forecasting.

#### **4. Results and Discussion**

## *4.1. Data Description*

In this study, solar PV power data from two PV systems are adopted to verify the performance of the eight deep learning-driven forecasting methods.


**Figure 5.** (**a**) distribution of solar PV power output from Parking Lot Canopy Array dataset. (**b**) Hourly distribution of solar PV power output from January to December 2018.

Figure 6 depicts the boxplots of DC power output (Data Set 1 and Data Set 2) in Figure 5 to show the distribution of DC power in the daytime. The maximum power is generated around mid-day.

**Figure 6.** Boxplots of PV power output during daytime hours: (**a**) Data Set 1 and (**b**) Data Set 2.

#### *4.2. Forecasting Results*

Accurate short-term forecasting of PV power output gives pertinent information for maintaining the desired power grid production delivery and storage [7,53]. This section assesses the eight models (i.e., RNN, GRU, LSTM, BiLSTM, ConvLSTM, RBM, AE, and VAE) and compares their forecasting performance using PV power output collected from two different PV systems. Towards this ends, we first build each to capture the maximum variance in training data and then use them to forecast the future trend of PV power output. The training data in Data Set 1 consists of one-minute power data collected from 1 January 2017 to 29 June 2017. The training data in Data Set 2 is collected from 1 January 2018 to 19 October 2018. The hyper-parameters of the built deep learning methods based on training datasets are tabulated in Table 2. For all models, we used the cross-entropy as loss function and Rmsprop as an optimizer in training.


**Table 2.** Tuned parameters in the considered methods.

#### 4.2.1. Forecasting Results Based on Data Set 1: Parking Lot Canopy Array Datasets

The principal feature of the PV power output is its intermittency. This unpredicted fluctuation in solar PV power could lead to many challenges including power generation control and storage management. Essentially, it is crucial to appropriately forecast PV power output to guarantee reliable operation and economic integration in the power grid. In the first case study, the above-trained models will be evaluated using the testing solar PV power output starting from 30 June to 6 July 2017 collected from Parking lot canopy array. Forecasting outputs using the eight deep learning models using test measurements are displayed in Figure 7. These results illustrate the goodness of deep learning models for PV power forecasting.

Also, to show clearly the accordance of the measured and the forecast outputs from the investigated deep learning models, the scatter plots are presented in Figure 8. Figure 8 shows that the forecasted data from RBM and SAE models are moderately correlated with the actual PV power output. The forecasting with ConvLSTM is relatively weakly correlated with the measured power data. On the other hand, the forecasted power with RNN-based models and the VAE model are strongly correlated with the measured PV power.

**Figure 7.** Forecasting results from the eight models using the testing datasets: (**a**) Long Short-Term Memory Networks (LSTM), (**b**) gated recurrent unit (GRU), (**c**) recurrent neural network (RNN), (**d**) Bidirectional LSTM (BiLSTM), (**e**) Convolutional LSTM (ConvLSTM), (**f**) Restricted Boltzmann Machine (RBM), (**g**) stacked autoencoder (SAE) and (**h**) VAE.

**Figure 8.** Scatter graphs of PV power forecasting and measurements using the eight models: (**a**) LSTM, (**b**) GRU, (**c**) RNN, (**d**) BiLSTM, (**e**) ConvLSTM, (**f**) RBM, (**g**) SAE, and (**h**) VAE.

Now, to quantitatively evaluate the forecasting accuracy of the eight considered models based on the testing data, five statistical indexes are computed and listed in Table 3. Also, we compared the eight the forecasting results of the ten deep learning models with two baseline machine learning models: LR and SVR (Table 3). For this application, ConvLSTM performs poorly in terms of the forecasting accuracy compared to the other models and cannot track well the variability of PV power and does not describe the most variance in the data (i.e., EV = 0.832). Moderate forecasting performance are obtained using RBM and SAE by explaining respectively 0.929 and 0.932 of the total variance in the testing PV power data. The results of this investigation exhibit also that the VAE model provides accurate forecast in comparison to the other models by achieving PV power forecast with lower RMSE, MAE, and higher NRMSE (%) as well as the highest R2, EV values closer to 1 that means that most of the variance in the data is captured by the VAE model. Specifically, the VAE model achieved the highest R2 of 0.992 and the lower RMSE (6.891) and MAE (5.595). We highlight that this is the first time that the VAE model is used for solar PV power output forecasting. This application showed that the VAE method for PV power forecasting has superior performance. Also, it is noticed that RNN and its extended variants LSTM, BiLSTM, and GRU achieve slightly comparable performance to the VAE in terms of the statistical indexes (RMSE, RMSE, MAE, EV, and NRMSE). Table 3 indicates that deep learning models exhibited improved forecasting performance compared to the baseline methods (i.e., LR and SVR).


**Table 3.** Forecasting performance of the eight models based on testing data of the first dataset.

#### 4.2.2. Forecasting Results Based on Data Set 2: Algerian PV Array Datasets

Now, the effectiveness of the eight methods will be tested based on power output data collected from the 9 MWp PV plant in Algeria (Data Set 2). In this experiment, the above-trained models will be evaluated using the testing solar PV power output collected from 20 October to 31 December 2018. The measured test set together with model forecasts are charted in Figure 9. Similar conclusions are also valid for these datasets. One major reason is that RNN-based models have a strong capability to describe time dependents data and can better model the complicated relationship between historical and future PV power output data than other methods. The RNN-based models and the VAE model again confirm the superior forecasting performance of PV power output as shown by the scatter plots in Figure 9. The ConvLSTM model shows poor forecasting performance results (Figure 9).

And then, the statistical indicators are computed to compare the forecasting performance between the eight models, and baseline machine learning models: LR and SVR based on testing datasets (Table 4). It is worth noting that the RNN-based models (i.e., RNN, LSTM, BiLSTM, ConvLSTM, and GRU) and the VAE model show the improved forecasting performance compared to the RBM, and SAE.

Results in Figure 9 and Table 4 indicate that using RNN-based models and VAE method has led to improved forecasting performance. Furthermore, the error analysis highlights that the forecasting accuracy obtained by these models can satisfy practical needs and can be useful for PV power management. It should be noted that the VAE model is trained in an unsupervised manner in order to forecast solar PV power. This means that the forecast is based only on the information from past data. However, the other models are trained in a supervised way by using a subset of training as input sequence (*x*1, . . . , *x<sup>k</sup>* ) and an output variable *x<sup>k</sup>* and we train RNN-based models to learn the mapping function from the input to the output. After that, these trained models are used to forecast new data. Even if the VAE model is trained in an unsupervised way, it can provide comparable forecasting performance to those obtained by the supervised RNN-based models. Accordingly, the VAE-based forecasting approach is a more flexible and powerful tool to be used in real-time PV power forecasting.

**Figure 9.** Scatter graphs of PV power forecasting and measurements using the eight models: (**a**) LSTM, (**b**) GRU, (**c**) RNN, (**d**) BiLSTM, (**e**) ConvLSTM, (**f**) RBM, (**g**) SAE, and (**h**) VAE.


**Table 4.** Forecasting performance of the eight methods using the test set of the second dataset.

Overall, the NRMSE (%) quantifies the quality of power forecasting between the measured and forecasted PV power output time-series data, where the larger value indicates a better prediction performance. A visual display of the NRMSE (%) derived with the eight considered deep learning methods based on the testing datasets from the two PV systems is displayed in Figure 10. The first dataset is with a one-minute resolution and the second dataset is with fifteen minutes resolution. The VAE model achieves better PV power flow forecast performance compared to the RBM and SAE models and RNN-based models. Furthermore, the results show that VAE models are efficient in capturing the linear and nonlinear features in PV power data with different time resolutions.

**Figure 10.** NRMSE by method based on the testing datasets from the two considered PV systems.

#### *4.3. Multi-Step Ahead PV Power Forecasts*

Precise multi-step forecasts are essential to managing the operation of PV systems appropriately. Now, we assess the capability of the eight methods for multi-step ahead forecasting of PV power output using data from Data Set 1 (a 243 kW parking lot canopy array in the US) and Data Set 2 (a 9 MW PV system in Algeria). Based on the past measurements, *x* = [*x*1, *x*2, . . . , *x<sup>l</sup>* ], the computed single-, two-, and multistep-ahead forecast are respectively *xl*+<sup>1</sup> , *xl*+<sup>2</sup> , and *xl*+*n*. The 5, 10, 15 steps-ahead forecastings of PV power data based on the testing data of the Parking lot canopy array dataset and the Adrar PV system are tabulated in Table 5.


**Table 5.** Validation metrics for multistep-step-ahead forecasts.

We can easily observe that, for all data sets, except BiLSTM and ConvLSTM, the other models performed consistently reasonable forecasting results five-, ten-, fifteen-step-ahead forecasting. For instance, the VAE model achieved R2 values of 0.902,0.873, 0.856 for five-, ten-, fifteen-step-ahead forecasting when using the first for Data Set 1, R2 values of 0.951,0.877, 0.818 for Data Set 2. The RNN, GRU, RBM, SAE, and VAE models performed about equally in terms of R2, MAPE, and RMSE in all cases.

For Data Set 1, the five-step-ahead forecasting R2's for all models except ConvLSTM is around 0.90 (Table 5). Results in Table 5 show that for five-steps ahead forecasting based Data Set 2 almost all models provide relatively good forecasting accuracy in terms of *R*2 which is around 0.94. It is worthwhile noticing that for a ten-step -ahead forecast, the accuracy of all models starts to decrease and achieve *R*<sup>2</sup> values around 0.86. In the fifteen-step -ahead forecasting, we observed that LSTM, BiLSTM, and ConvLSTM achieved poor forecasting performance. The other models are still providing acceptable forecasting accuracy. We notice that the SAE model outperforms slightly the other models with higher *R*<sup>2</sup> and lowest forecasting errors. The overall forecasting performance of the RNN, GRU, RBM, SAE, and VAE model was satisfying, and they can maintain a reasonable forecasting performance to forecast solar PV power output as the number of steps increases. The error for the second dataset is large compared to the first one. The first dataset is 15 min time resolution recorded for one year, while the second data is of one-minute time resolution recorded for three years. Moreover, we used 90% of data for both datasets for training and 10% for testing. The one-minute data is very dynamic, which explains the large error compared to the first dataset.

It is challenging to tell which models were absolutely superior on the basis of the R2, MAPE, and RMSE values. The results of this study show that RNN, GRU, and VAE performs slightly better on average than the other models in most cases for one- and multi-step-ahead forecasting. The obtained results demonstrate that both RNNs with supervised learning and VAE with unsupervised learning can perform a one-step and multi-step forecasting accurately. Overall, the VAE deep learning model gives an effective way to model and forecast PV power output, and it has emerged as a serious competitor to the RNN-driven models (i.e., RNN, GRU, and LSTM).

#### **5. Conclusions**

PV power output possesses high volatility and intermittency because of its great dependency on environmental factors. Hence, a reliable forecast of solar PV power output is indispensable for efficient operations of energy management systems. This paper compares eight deep learning-driven forecasting methods for solar PV power output modeling and forecasting. The considered models can be categorized into two categories: supervised deep learning methods, including RNN, LSTM, BiLSTM, GRU, and ConvLSTM, and unsupervised methods, including AE, VAE, and RBM. We also compared the performance of the deep learning methods with two baseline machine learning models (i.e., LR and SVR). It is worth highlighting that this study introduced the VAE and RBM methods to forecast PV power. For efficiently managing the PV system, both single- and multi-step-ahead forecasts are considered. The forecasting accuracy of the ten models has been evaluated using two real-world datasets collected from two different PV systems. Results show the domination of the VAE-based forecasting methods due to its ability to learn higher-level features that permit good forecasting accuracy.

To further enhance the forecasting performance, in future study, we plan to consider multivariate forecasting by incorporating weather data. Also, these deep learning models can be applied and compared using data from other renewable energy systems, such as forecasting the power generated by wind turbines. Further, it will be interesting to conduct comparative studies to investigate the impacts of data from different technologies, such as monocrystalline, and polycrystalline.

**Author Contributions:** A.D.: Conceptualization, Formal analysis, Investigation, Methodology, Software, Writing-original draft, Writing-review & editing F.H.: Conceptualization, Formal analysis, Investigation, Methodology, Software, Supervision, Writing-original draft, Writing-review & editing Y.S.: Investigation, Conceptualization, Formal analysis, Methodology, Writing-review & editing, Funding acquisition, Supervision. S.K.: Investigation, Conceptualization, Formal analysis, Methodology, Writing- original draft. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by funding from King Abdullah University of Science and Technology (KAUST), Office of Sponsored Research (OSR) under Award No: OSR-2019-CRG7-3800.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Solar Power System Assessments Using ANN and Hybrid Boost Converter Based MPPT Algorithm**

**Imran Haseeb 1 , Ammar Armghan 2 , Wakeel Khan 3 , Fayadh Alenezi 2 , Norah Alnaim <sup>4</sup> , Farman Ali 1, \* , Fazal Muhammad 5 , Fahad R. Albogamy 6, \* and Nasim Ullah 7**


**Abstract:** The load pressure on electrical power system is increased during last decade. The installation of new power generators (PGs) take huge time and cost. Therefore, to manage current power demands, the solar plants are considered a fruitful solution. However, critical caring and balance output power in solar plants are the highlighted issues. Which needs a proper procedure in order to minimize balance output power and caring issues in solar plants. This paper investigates artificial neural network (ANN) and hybrid boost converter (HBC) based MPPT for improving the output power of solar plants. The proposed model is analyzed in two steps, the offline step and the online step. Where the offline status is used for training various terms of ANNs in terms of structure and algorithm while in the online step, the online procedure is applied with optimum ANN for maximum power point tracking (MPPT) using traditional converter and hybrid converter in solar plants. Moreover, a detail analytical framework is studied for both proposed steps. The mathematical and simulation approaches show that the presented model efficiently regulate the output of solar plants. This technique is applicable for current installed solar plants which reduces the cost per generation.

**Keywords:** artificial neural network based MPPT; hybrid boost converter; renewable energies; solar power system

#### **1. Introduction**

The electrical energy plays a key role in the economic development of a country. From last decade, rapid increase in consumption of electricity and demand is recorded [1,2]. In order to fulfill power demands, installation of new power plants are time consumption and high expensive procedures [3]. The renewable energies, such as wind and solar, appear to be appropriate solutions to cover energy demand while reducing environmental pollution and toxic materials [4]. Furthermore, the renewable energy resources are followed by many countries, which comes from geothermal heat, tides, rain, wind, and sunlight. Major remote sites in each country of the globe utilizing renewable energy [5].

**Citation:** Haseeb, I.; Armghan, A.; Khan, W.; Alenezi, F.; Alnaim, N.; Ali, F.; Muhammad, F.; Albogamy, F.R.; Ullah, N. Solar Power System Assessments Using ANN and Hybrid Boost Converter Based MPPT Algorithm. *Appl. Sci.* **2021**, *11*, 11332. https://doi.org/10.3390/app112311332

Academic Editors: Luis Hernández-Callejo, Maria del Carmen Alonso García and Sara Gallardo Saavedra

Received: 5 October 2021 Accepted: 26 November 2021 Published: 30 November 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

The renewable energy generated power depends on site selection and climate condition. Furthermore, there is a need of storage system power induced by renewable energy to insure the continuity of available power [6]. Various types of resources are existed in the entire globe, however, among of all these resources solar energy is considered economical, inexhaustible, and sustainable energy. Photovoltaic (PV) cells mostly use for bulk and small power and gradually increased day by day [7]. The output of PV depends on different factor such as temperature, weather conditions, module materials, and is used in different applications, i.e., light sources, battery charging, water pumping, space, satellite power system, remote islanded power system, etc. This work explores the applications of artificial neural network (ANN) and hybrid boost converter (HBC) for enhancing the efficiency for MPPT to increase the smoothness of solar power system. The deep learning based ANN mechanism has key features to optimize the input data and produce the purified desire outcomes. Furthermore, currently the ANN approach is widely used in several fields for the purpose of optimizing structure complexity and predict the expected outputs. For example, in [8] the ANN technique is utilized for predicting droughts, in [9] the ANN method is studied for accurately measure the wind speed and predict its results, in [10] the particular matter is discussed for the Ankara city through ANN and similarly, in the field of solar system the ANN is applied in [11] for forecasting the generation of solar system. Thus, in this proposed work the ANN mechanism is estimated for optimize the output of MPPT and HBC.

#### *1.1. Major Contribution*

The use of MPPT has increased the performance of solar power system and now the demand of solar plant installation is enhanced. The efficiency of the MPPT based solar system can be further improved applying ANN and HBC. Thus, this paper studies the contributions of ANN and HBC based MPPT in the solar system. The major contributions of this work are discussed as follows.


#### *1.2. Organization of Paper*

The rest of the paper is organized as follows: Section 2 explains the proposed framework; Section 3 investigates the analytical approach; Section 4 defines the result and discussions; similarly, Section 5 presents the conclusion.

#### *1.3. Related Work*

As it has been shown that solar energy is a cost effective solution for managing current electric load demands, a number of research work have been carried out so far, which are analyzed as follows:

In [12,13], the authors have discussed the two artificial based mechanisms in term of variable and fixed step load. The theoretical and simulation analysis are investigation for MPPT controller, and simulation. In [14], authors have proposed the MPPT technique which is based on enhanced neural network (ENN). The proposed ENN based control have the ability to adjust the step size to track MPPT automatically and it can improve the dynamic and steady performance of PV panels. The proposed ENN technique can easily be implemented because of less constructed data. In [15], authors have proposed a MPPT

converter using online learning neural network (OLNN) and perturbation and observation technique. The proposed work can improve the fast tracking of the solar panels when the radiation is changing constantly. The simulation results show improved output when the radiation is changing rapidly. In [16], authors have investigated an optimal power operating point (OPOP) using photovoltaic and thermal neural network (PV/TNN). The NN has been used to calculate the OPOP. The OPOP computes the optimum flow rate of PV/T for maximum electrical and thermal power. The results show that this technique can hold fast and accurate PV/T flow rate control. In [17], authors have presented the super twisting sliding mode MPPT controller (ST-SMC) with ANN. The robust sliding mode controller is used against disturbance and parametric variations while the ANN controls the peak power voltage for the efficiency of MPPT. The simulation results show the improved performance in terms of dynamic response and robustness. In [18], authors have suggested the two fast and digital MPPT techniques for fast changing environment. They approximate the MPP locus by using piecewise line segment or cubic equation. The MPP locus parameters are found with the help of NN based program. The results show that the proposed research required less computation requirement, high static, and dynamic tracking and fast speed. In [19], authors have proposed the different intelligence technique, i.e., neural network (NN), fuzzy logic (FL), genetic algorithm (GA), and neuro-fuzzy and their possible implementation into a field programmable gate array (FPGA). The authors have developed intelligent MPP controller using simulink/MATLAB and then different step to design and implement the controller into FPGA. The best controller among all these is tested in real time using FPGA Virtex 5. The comparative study of all controllers describe that the effectiveness of developed intelligence technique in term of accuracy, quick response, power consumption, flexibility, and simplicity. In [20], authors have presented the two techniques ANN and Fuzzy logic controller (FLC) for MPPT of PV cell. They investigate the proposed work using MATLAB/Simulink. The results show that the efficiency and response under variable irradiation conditions are satisfactory. In [21], authors have investigated the new combined method that is established by a three point comparing method and an ANN based PV model method. During the fast variations of solar irradiance, the exact MPP is searched by three point comparison and ANN methods. The results show that the proposed method search the exact and fast MPP under different irradiance condition with feedback voltage and current. In [22], authors have proposed the ANN method for the non-linear and time-varying output of PV panels. ANN is the suitable solution for non-linear outputs. The results also denote that the ANN algorithm have better MPPT characteristics as compared with the traditional perturbation and observation technique. In [23], authors have suggested the intelligent MPPT method for a standalone PV system using ANN and fuzzy logic controller (FLC). The ANN is used for different solar irradiance and temperature to find MPP voltage. FLC uses MPP voltage as a reference voltage to generate a control signal for the DC-DC converter. The results explain good performance of ANN-FLC as compared to traditional incremental conductance (IC). In [24], authors have investigated the method to achieve acceptable tracking time and less power oscillation by adjusting the changing step size of Flyback inverter. Solar irradiance is adopted as an input of ANN which is used to appropriate modulation step size. The simulation results show that for any solar irradiance ANN based Flyback inverter can find appropriate step size. In [25], authors have presented the MPPT using ANN, and the hysteresis current controlled inverter with fixed band and variation of load value is determined with output current total harmonic distraction (THD) is lower than 5%. The results confirm that the efficiency of controller and flexibility of inverter is satisfactory. In [26], authors have proposed the MPPT of a grid connected 20 kW neuro-fuzzy network based PV system. The neuro-fuzzy system consists of fuzzy based classifier and three multilayered feed forwarded ANN. The inputs of ANN are irradiance and temperature, and, after the estimation process, output is the reference voltage. The reference voltage guarantees the optimal power transfer between PV generator and the main utility grid. The simulation results proved the best efficiency as compared to conventional single ANN and perturb

and observe (P&O) algorithm. The study in [27] reveals the performance of ANN based different algorithms, i.e., Levenberg–Marquardt (LM), Bayesian regularization (BR), and scaled conjugate gradient (SCG) algorithms are used in MPPT energy harvesting in solar photovoltaic system. The simulated results show that SCG algorithm reveal superior performance compared to LM and BR algorithms. However, the LM algorithm performs better in the correlation between input–output, dataset training, and error. A fuzzy logic, particle swarm optimization (PSO), and imperialist competitive algorithm are proposed in [28], where it is declared that the fuzzy logic is less complicated, faster, more accurate, and more stability then the other three algorithms. The authors have explored a hybrid shuffled frog leaping and pattern search (HSFL–PS) algorithm in [29] for optimizing ANNbased MPPT in a grid-tied PV system. The simulation results show that the performance of MPPT is improved in comparison with the conventional MPP methods. A novel ANN-ACO MPPT controller is developed by authors in [30] based on an ant colony optimization (ACO) algorithm which is useful to train the developed ANN. The ANN-ACO technique has improved the MPPT and reduced the drawbacks in conventional MPPT. The authors have also improved the power quality and distortion free signal to the grid. The simulation and experimental results show that ANN-ACO controller can track the MPP rapidly and robustness with a minimum steady-state oscillation than the conventional INC method. ANN based controller is used in [31] to control the converter fed by an autonomous photovoltaic generator (PVG) instead of classical MPPT algorithms such as perturb and observe (P&O). The results present that the ANN based PVG provide low oscillation and better performance.

#### **2. Proposed ANN Based MPPT and Hybrid Boost Converter Model**

Figure 1 explains the HBC and ANN based MPPT presented model for minimizing the solar power system critical caring and balancing output power issues. The output of PV is attained by ANN based MPPT in order to improve the performance of solar power system. The neural network technique consist of major amount of interconnected processors called neurons. Each neuron includes a huge number of weighted links for transforming signals. Thus, it has potential to manage the difficult task of data processing and interpretation. In this proposed model, the feed forward back propagation ANN is installed which contains logsig purelin and purelin activation functions based hidden layers, as depicted in Figure 2. In case of offline step the ANN training is performed in terms of activation function structure and training algorithm. On the other side for online step the trained ANN based MPPT is applied to track the MPP. The output of PV array voltage derivation (dv) and power derivation (dp) is given to ANN based MPPT which depends on solar radiation and temperature conditions. Table 1 summarizes the basic principle of ANN based MPPT which output is corresponding normalized increasing or decreasing duty cycle (+1, 0, −1).

Table 1 explains the basic mechanism of ANN based MPPT controller.


**Table 1.** ANN based MPPT controller basic principle.

**Figure 1.** Proposed framework using ANN MPPT and enhanced hybrid boost converter.

**Hidden Layer**

**Figure 2.** Internal structure of ANN based MPPT .

#### **3. Analytical Approach**

#### *3.1. Analytical Model of PV Module*

The main background of the presented approach is discussed in Section 2. This section elaborates the mathematical mechanism for the modern MPPT based ANN system, considering the array of PVs at input side and utility grid at the receiving end. The description of used symbols are declared in Table 2. The circuitry of the PV cell contain diode for paralleling current as shown in Figure 3, which can be mathematically [32–34] defined as

$$
\dot{\mathbf{i}}\_{\text{total}} = \dot{\mathbf{i}}\_{\text{sc}} - \dot{\mathbf{i}}\_{\text{diode}} \tag{1}
$$

where *idiode* is the diode current, *isc* is the current through the parallel resistor. The *idiode* is further explained as

$$i\_{diode} = i\_o(e^{\frac{cv\_d}{\eta KT\_c}} - 1) \tag{2}$$

So, the Equation (1) can be modified with Equation (2) the total current from PV cell is measured as

*i*

$$i\_{total} = i\_{sc} - i\_o(e^{\frac{\epsilon v\_d}{\eta kT\_c}} - 1) \tag{3}$$

Parallel resistance *R<sup>p</sup>* and series resistance *R<sup>s</sup>* is also considered for the dynamic behavior of PV cell, however, for the proposed PV cell simulation there is computational limitation if taking both series and parallel resistance. Therefore, parallel resistance is usually neglected in PV systems bibliography. For the proposed PV cell simulation series resistance is considered and the PV cell total current is mathematically written as [35,36]

$$\dot{\mathbf{i}}\_{total} = \dot{\mathbf{i}}\_{\mathbf{sc}} - \dot{\mathbf{i}}\_o \{ \exp(\frac{e(\upsilon + \dot{\mathbf{i}}\_{total} \mathbf{R}\_s)}{\eta K T\_\varepsilon}) \} - \mathbf{1} \tag{4}$$

The PV system consist of *N* numbers of branches in parallel and each parallel branch consist of N number of PV cells in series. So, the total current from PV module under constant weather condition is

$$i\_{\rm sc}^{N} = i\_{\rm sc}^{N} [1 - \exp(\frac{V^{m} - V\_{\rm oc}^{m} + R\_{\rm s}^{N} \cdot i^{N}}{N\_{\rm s} \cdot V\_{T}^{\rm c}})] \tag{5}$$

The module current depends on some different parameters of the cell. Each variable depends on different parameters of each cell. The module short circuit current depends on number of branches and short circuit of the cell [37,38].

$$\mathbf{^M\_{sc}} = \mathbf{N\_p} \cdot \mathbf{i\_{sc}^c} \tag{6}$$

The open circuit voltage of the module depends on the number of cells in series and the open circuit voltage of the cell.

*i*

$$V\_{\rm oc}^{\rm m} = \mathbf{N}\_{\rm s} \times V\_{\rm oc}^{\rm c} \tag{7}$$

The thermal voltage of the semiconductor in the module depends on Boltzmann's constant, cell temperature and the charge of electron, i.e., 1.602 <sup>×</sup> <sup>10</sup>−<sup>19</sup> [39].

$$V\_T^c = \frac{mKT\_c}{e} \tag{8}$$

The equivalent series resistant of the module depends on series resistance of the cell, number of parallel branches in the module and the number of cell in series in each branch.

$$R\_s^M = \frac{R\_s^c \cdot N\_p}{N\_s} \tag{9}$$

Assume that all the cell in PV system are same, so the power, voltage, and current under standard condition are

$$P\_{\text{max}}^{\text{c}} = \frac{P\_{\text{max}}^{M}}{N\_{\text{s}} \cdot N\_{p}} \tag{10}$$

$$V\_{oco}^c = \frac{V\_{oco}^M}{N\_s} \tag{11}$$

$$\stackrel{c}{\}\_{\rm sco}} = \frac{\dot{\imath}\_{\rm sco}^{\rm M}}{\mathcal{N}\_p} \tag{12}$$

Now the instantaneous series resistance of the PV cell can be expressed as

*i*

$$R\_s^c = (1 - \frac{FF}{\frac{P\_{\text{max}}^c}{V\_{\text{oco}}^c i\_{\text{xo}}^c}}) \frac{V\_{\text{oco}}^c}{I\_{\text{sco}}^c} \tag{13}$$

Fill factor is denoted with FF and is given as

$$FF = \frac{\frac{V\_{\text{oou}}^c}{V\_{\text{To}}^c} - L\_{\text{ll}}(\frac{V\_{\text{oou}}^c}{V\_{\text{To}}^c} + 0.72)}{\frac{V\_{\text{oou}}^c}{V\_{\text{To}}^c} + 1} \tag{14}$$

The short circuit current of the cell itself depends on the irradiance and can be expressed as

$$\dot{i}\_{\rm sc}^{\rm c} = \frac{\dot{i}\_{\rm sco}^{\rm c} G\_{\rm a}}{G\_{\rm ao}} \tag{15}$$

The open circuit voltage of the cell depends on the nominal open circuit and the actual weather condition, i.e., ambient temperature, temperature of cell, and irradiance. The open circuit voltage is expressed [40,41] as

$$V\_{oc}^{c} = V\_{oco}^{c} + 0.03(T\_a + 0.03 \cdot G\_a - T\_{co}) \tag{16}$$

Now the current generated from the PV module in term of all parameters, i.e., irradiance, temperature, voltage, etc., is

$$\dot{\mathbf{u}}^{M} = \mathbf{N}\_{p} \cdot \dot{\mathbf{t}}\_{\text{sc}}^{\text{c}} [1 - \exp(\frac{V^{m} - \mathbf{N}\_{\text{s}} V\_{\text{oc}}^{\text{c}} + \dot{\mathbf{t}}^{m} \mathbf{R}\_{\text{s}}^{\text{c}} \frac{\mathbf{N}\_{\text{s}}}{N\_{T}}}{N\_{\text{s}} V\_{T}^{\text{c}}})] \tag{17}$$

Now assume the case that PV array consist of *B* number of parallel branches and each branch contain *M* number of module so, the array current will be equal to *I* = ∑ *N<sup>B</sup> i*=1 . If we consider all the panels are same and under same temperature and irradiance then the output current will be

$$
\dot{a}\_{total} = \mathbf{N}\_B \cdot \dot{\mathbf{r}}^M \tag{18}
$$


**Table 2.** List of symbols used for analytical model.

**Figure 3.** Equivalent circuit of photovoltaic cell.

#### *3.2. Analytical Modeling of a Traditional Boost Converter*

The electrical MPPT can be achieved through a DC to DC converter inserted between the photovoltaic module and the load.The DC to DC converter ensures the matching of load resistance with the varying source resistance. The converter is basically used to transfer maximum energy from source to load.

The framework of traditional boost converter is represented in Figure 4 which transfers maximum energy by adjusting the PV module output voltage to the reference voltage. The traditional boost converter has two controllable variables: Voltage *Vpu* and the inductor current *iL*. The mathematical model that describe the voltage and inductor current relation is

$$\begin{cases} V\_m \\ i\_L \end{cases} = (1 - D) \begin{cases} V\_m \\ i\_L \end{cases} \tag{19}$$

where *D* is the duty cycle of the boost converter, which is expressed as

$$D = \frac{T\_{on}}{T\_{total}} = T\_{on} f\_{\text{s}} \tag{20}$$

where *f<sup>s</sup>* is the frequency of switching of converter's switch and *Ttotal* is the total time and *TON* is the on time of the switch.

$$\frac{dI\_L}{T} = \frac{1}{L\_{pu}}(V\_m - V\_{pu}) - \frac{P\_{pu}}{L\_{pu}}\tag{21}$$

where *Vpu* is the reference voltage generated by the ANN based MPPT.

$$\frac{dV\_{pu}}{dt} = \frac{(I\_L - I\_{pu})}{Pu} \tag{22}$$

By using Equation (21) we obtain the reference inductor current

$$i\_L^\* = (V\_{pu}^\* - V\_{pu}) + I\_{pu} \tag{23}$$

The optimal switching voltage can be expressed by using the Equations (22) and (23)

$$V\_m^\* = PI(V\_{pu}^\* - V\_{pu}) + Vpu + \frac{R\_{pu}}{L\_{pu}}I\_L \tag{24}$$

while the boost converter command is obtained by the conversion of Equation (19)

$$D^\* = 1 - \frac{V\_m^\*}{V\_{\rm DC}} \tag{25}$$

The DC link capacitor at the output play a key role to ensure energy balance between the PV module and the power injected into the system. The DC link capacitor charge and discharge that oscillate between two levels depending on actual weather condition and power injection.

**Figure 4.** Traditional boost converter.

#### *3.3. Analytical Modelling of Enhanced Single Phase Hybrid Boost Converter*

Figure 4 shows the traditional boost converter that theoretically, voltage gain is very high at very high duty ratio near 100% but practically, traditional boost converter cannot work efficiently at 100% duty cycle because of diodes, equivalent resistance of inductor and capacitor, and the saturation of both capacitor and inductor [40,41]. In this paper, enhanced single phase HBC is introduced which has replaced the inductor in traditional

boost converter into two inductors and 3 diodes, this structure provides high gain and efficiency. The gain of proposed converter is also increased than the traditional boost converter by a factor of (d + 1). Figure 5 shows the enhanced single phase HBC, for the mathematical modeling, we assumed that all the components are lossless and the outputs and the inputs are pure DC signals. For these consideration voltage across the inductor depends on input and output voltages. The voltage across the inductor during ON and OFF time are estimated as

$$T\_{\rm ON} : V\_L = V\_{\rm IN} \tag{26}$$

$$T\_{OFF}: V\_L = -\frac{V\_{OUT} - V\_{IN}}{2} \tag{27}$$

The above formula indicates that during the switch is at ON state the voltage across the inductor is positive and at OFF state voltage will be negative. The positive and negative area of the voltage of the inductor will be same. With the above condition the output voltage is calculated as

$$V\_{OUT} = \frac{1+d}{1-d}. V\_{IN} \text{ with} \quad d = \frac{T\_{ON}}{T\_P}, \; 1-d = \frac{T\_{OFF}}{T\_P} \tag{28}$$

The average inductor current is the function of input current from the solar module and the duty cycle of the switch

$$I\_{LAV} = \frac{I\_{IN}}{1+d} \tag{29}$$

To find the appropriate inductor and capacitor value in the circuit we need to know the output and input voltage of the converter and the rated power which should be transferred to the output. With these known parameters input current and average inductor current can be calculated and assumed that the average inductor current is the max current in the circuit. To find the inductor value in the circuit the input and output voltage is considered and the duty cycle is measured as

$$L\_1 = L\_2 = \frac{V\_{IN} \cdot T\_{ON}}{\triangle I\_L} \tag{30}$$

$$L\_1 = L\_2 = \frac{V\_{OUT} \cdot T\_P}{\triangle I\_L} \cdot \frac{d.(1 - d)}{1 + d} \tag{31}$$

The AC voltage is produced in the capacitor which overlaps with DC voltage so, because of this reason voltage variation is the key factor in capacity dimension of capacitor.

$$\mathcal{C}\_{IN} = \frac{I\_{\mathcal{C}} \cdot T\_{ON}}{\triangle \cdot V\_{\mathcal{C}}} \tag{32}$$

$$\mathcal{C}\_{IN} = \frac{I\_{LAV} \cdot T\_P}{\triangle \cdot V\_{INmax}} \cdot d \cdot (1 - d) \tag{33}$$

To design the capacitor for boost converter the RMS current of the load is the important factor. Duty cycle of the average inductor current and the maximum current variation are used for the capacitor current, which are defined as

$$I\_{\rm INC} = I\_{\rm LAV} \sqrt{d \cdot (1 - d) + \left(\frac{\triangle \cdot I\_{\rm Lmax}}{I\_{\rm LAV}}\right)^2 \cdot \frac{d^2 \cdot (1 - d)^2 \cdot (1 + 3 \cdot d)}{12 \cdot (1 + d)^2 (3 - 2 \cdot \sqrt{2})}} \tag{34}$$

The maximum voltage variation that is acceptable for the capacitor is important for the selection of output capacitor. The current time area of capacitor is the function of duty cycle and output current, which are calculated as

$$\mathcal{C}\_{OUT} = \frac{I\_{OUT} \cdot T\_P \cdot d}{\triangle V\_{OUT\max}} \tag{35}$$

$$\mathcal{C}\_{OUT} = \frac{I\_{LAV} \cdot T\_P}{\triangle V\_{OUT\max}} \cdot d \cdot (1 - d) \tag{36}$$

Practically, acceptable voltage variation for capacitor is less than 1% of the output voltage so the output capacitor dimension is calculated is given as

$$\mathcal{C}\_{OUT} = \frac{I\_{LAV\,R} \cdot T\_P}{4 \,\triangle\,V\_{OUT\,max}} \quad \text{with} \quad \triangle\,V\_{OUT\,max} \le 0.01 \cdot V\_{out\,R} \tag{37}$$

The output current across the capacitor is the function of duty cycle for an average inductor current and maximum inductive current variation. So the output current will be

$$I\_{INC} = I\_{LAV} \sqrt{d \cdot (1 - d) + \left(\frac{\triangle \cdot I\_{L\max}}{I\_{LAV}}\right)^2 \cdot \frac{d^2 \cdot (1 - d)^3}{12 \cdot (1 + d)^2 (3 - 2 \cdot \sqrt{2})}}\tag{38}$$

**Figure 5.** Enhanced single phase hybrid boost converter.

#### **4. Results and Discussion**

In the presented model, the ANN and HBC based MPPT is used for enhancing the productivity and performance. The results of the proposed model are compared among ANN based traditional boost converter and ANN based proposed HBC. The results of the proposed model present that the ANN based HBC MPPT give smooth output powers as compare to traditional boost converter. The proposed model is analyzed using MATLAB simulation software. The data are collected in terms of short circuit current, maximum current, open circuit voltage, maximum voltage, current temperature and voltage temperature, standard irradiance, standard temperature, maximum current of the given irradiance and temperature, maximum voltage of the given irradiance and temperature, and maximum power of the given irradiance and temperature. The temperature and irradiance are applied as input variables while the MPP voltage is used as a output of the ANN

model. The current and power of the MPPT are estimated using V-! characteristics and multiplication of obtained current and voltage, respectively. The collected data are divided among training and testing for ANN approach. Table 3 explains the list of elements used for calculating the simulation results. Whereas the flow chart of applied algorithm is depicted in Figure 6. Figure 7 presents the correlation among tradition boost converter and proposed HBC, which clarifies that HBC gain is several folds higher than traditional boost converter. Hence, with applying the proposed HBC the performance of ANN based MPPT is enhanced than without installed HBC MPPT system. Figure 8 shows the analysis of ANN based MPPT controller and advance hybrid converter in terms of power and time. Which declares that the irradiance level is instantly changed at 0 s, 0.04 s, 0.07 s, 0.11 s, and 0.15 s, and temperature is constant at 25 ◦C. At 0.04 s, the range of power is constant till 0.5 s. At 0.5 s the power jumped from 140 W to 220 where fluctuation is recorded. Similarly, this slight variations are continued in whole process as mentioned in Figure 8. Furthermore, it is depicted from Figure 8, that the ANN based MPPT has increased the smoothness of outcomes. The recorded instability in Figure 8 is highlighted in Figure 9, which shows that variation is increased from 0.0 to 0.2 s. The constant outcomes are gained at 0.04 s. Thus, Figure 9 defines that, in view of ANN and advance hybrid converter, the variation in generated power is optimized. The smoothness of the proposed induced power compared with conventional boost converter, which is illustrated in Figure 10 for power against time. Figure 10 clarifies that without the use of the proposed advance hybrid converter, the maximum variation in the produced power occurs. The signals achieve constant position after maximum delay. The alteration of the induced power mentioned in Figure 10 is zoomed out in Figure 11. Which explains that the fluctuations in generated power is larger than the proposed advance HBC and ANN based MPPT model. Another important term is the ripples in the output power during the constant irradiance, shown in Figure 12, which is 0.02 W in the proposed model. Figures 13 and 14 declare the relation among train, test, validation, and best data from the ANN approach in terms of means square error and epochs. Similarly, Figure 15 depicts the output results of the utilized AN as a function of time. The parameters like training target, training outputs, validation targets, validation outputs, test targets, test outputs, errors, and responses are evaluated in Figure 15. Figure 16a,b mention the outcomes of solar system excluding ANN and HBC based MPPT and including ANN and HBC based MPPT, respectively. In the last, the fruitful outcomes of the proposed ANN and advance hybrid boost converter based MPPT for enhancing the fidelity of the solar power system is compared with current work, as shown in Table 4.


**Table 3.** Parameter description used for evaluation the proposed model.

**Figure 6.** Flow chart description for proposed model.

**Figure 7.** Comparison of traditional and hybrid boost converters in terms of voltage gain and duty cycle.

**Figure 8.** ANN based MPPT controller with hybrid boost converter.

**Figure 9.** Zoom out portion of the ANN based MPPT controller with hybrid boost converter.

**Figure 10.** ANN based MPPT controller with traditional boost converter.

**Figure 11.** Analysis of varied area of the ANN based MPPT controller with traditional boost converter.

**Figure 12.** Power ripples of the ANN and hybrid boost converter based MPPT converter.

**Figure 13.** Maximum square error against epoch for evaluation the performance (41 Epochs).

**Figure 14.** Maximum square error against epoch for evaluation the performance (163 Epochs).

**Figure 15.** Measuring the output response in terms of error and output targets.

**Figure 16.** (**a**): Output results of the proposed model excluding ANN and HBC enabled MPPT, (**b**): Proposed model outcomes with ANN and HBC MPPT.


**Table 4.** Performance comparison with current published system.

#### **5. Conclusions**

The increase in electric load is recorded during last decade. Solar plants are the fruitful solution to minimize pressure on the main power grids. In this paper, load management is discussed using an ANN based MPPT and hybrid boost converter. Furthermore, to maintain output power smart transformer is installed before load distribution. The ANN based MPPT controller with hybrid converter have fast tracking and less fluctuations. The mechanism of ANN based is explained with mathematical background. The traditional and proposed HBC are compared theoretically and the features of HBC are highlighted. The results of proposed ANN and HBC based MPPT are evaluated in terms of power and time for using traditional boost converter with ANN and proposed HBC with ANN. The results show the superiority of solar power system with hybrid converter to improve the efficiency of solar power system. In this work, the performance and productivity of the solar power system are strengthened by utilizing the ANN and HBC based MPPT. However, in future the power generation can be further improved by using advance algorithms and machine learning methodologies, such as the flower pollination algorithm (PFA), optical swarm optimization (PSO), convolution neural network (CNN), and coyote optimization algorithm (COA). In addition, for forecasting the solar power system condition the hybrid based ANN and adaptive neural-fuzzy inference system (ANFIS) using hybrid whale optimization and pattern search (HWO-PS) algorithm can be evaluated.

**Author Contributions:** Conceptualization, I.H., F.A. (Farman Ali), and A.A.; methodology, F.A. (Farman Ali), and I.H.; software, F.A. (Farman Ali), and A.M., F.A. (Fayadh Alenezi); validation, F.M., F.A. (Farman Ali) and N.A.; formal analysis, F.M., F.A. (Farman Ali), A.M., F.A. (Fayadh Alemezi); investigation, A.M., F.A. (Fayadh Alenezi), A.A. and N.A. data analysis, F.A. (Farman Ali), I.H.; writing—original draft preparation, I.H.; writing—review and editing, W.K., F.A. (Fayadh Alenezi); and A.A.; visualization, F.M., F.A. (Fayadh Alenezi); supervision, F.A. (Farman Ali), A.A.; project administration, F.A. (Farman Ali); funding acquisition, W.K., N.U., F.R.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** The authors would like to acknowledge the support from Taif University Researchers Supporting Project Number(TURSP-2020/331), Taif University, Taif, Saudi Arabia.

**Institutional Review Board Statement:** Not applicable

**Informed Consent Statement:** Not applicable

**Data Availability Statement:** Data will be available as per request.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


## *Article* **Online Distributed Measurement of Dark I-V Curves in Photovoltaic Plants**

**José Ignacio Morales-Aragonés 1 , María del Carmen Alonso-García 2 , Sara Gallardo-Saavedra 1 , Víctor Alonso-Gómez 1 , José Lorenzo Balenzategui 2 , Alberto Redondo-Plaza <sup>1</sup> and Luis Hernández-Callejo 1, \***


**Abstract:** The inspection techniques for defects in photovoltaic modules are diverse. Among them, the inspection with measurements using current–voltage (I-V) curves is one of the most outstanding. I-V curves, which can be carried under illumination or in dark conditions, are widely used to detect certain defects in photovoltaic modules. In a traditional way, these measurements are carried out by disconnecting the photovoltaic module from the string inside the photovoltaic plant. In this work, the researchers propose a methodology to perform online dark I-V curves of modules in photovoltaic plants without the need of disconnecting them from the string. For this, a combination of electronic boards in the photovoltaic modules and a bidirectional inverter are employed. The results are highly promising, and this methodology could be widely used in upcoming photovoltaic plants.

**Keywords:** dark I-V curves; bidirectional power inverter; online distributed measurement of dark I-V curves

### **1. Introduction**

Solar photovoltaic (PV) energy is a reliable renewable energy source that has increased its cumulative installed capacity up to 633.7 GW by the end of 2019 [1,2]. This means an increase of 23% from the 516.8 GW achieved in 2018 and represents a progression by almost 400 times the installed capacity at the beginning of the century. In terms of annual installed capacity, the 116.9 GW installed in 2019 reflects a growth of 13% with respect to 2018, and it positions solar photovoltaic as the champion power generation source installed in 2019, with 48% of annual share [1]. The COVID-19 pandemic and its associated crisis slowed down the progression of PV solar energy in 2020. A recent study of the International Energy Agency analyzes different consequences of the pandemic and accordingly proposes several scenarios of possible energy futures. In all scenarios analyzed, renewable energies will grow rapidly, with solar in the lead of this new era of electricity generation [3].

Therefore, solar PV energy is a key factor in the diversification of energy sources that promotes a gradual decarbonation and encourages the large-scale implementation of energy models free of greenhouse gas emissions. The reason for the spectacular growth and prospect of this energy source lays in the constant development of the technology and its high reliability. This has made possible a drastic reduction of costs, which has favored its large-scale implementation. Moreover, PV applications have a variety of configurations and power levels, ranging from a few watts for consumer products or small home applications to large utility-scale power plants. These power plants have represented the largest share in the solar market in preceding years, with great expectations to keep this trend in next years [3]. In these high-power applications, the long-term reliability of the plant results in

**Citation:** Morales-Aragonés, J.I.; Alonso-García, M.d.C.; Gallardo-Saavedra, S.; Alonso-Gómez, V.; Balenzategui, J.L.; Redondo-Plaza, A.; Hernández-Callejo, L. Online Distributed Measurement of Dark I-V Curves in Photovoltaic Plants. *Appl. Sci.* **2021**, *11*, 1924. https:// doi.org/10.3390/app11041924

Academic Editor: Francesco Calise

Received: 20 January 2021 Accepted: 19 February 2021 Published: 22 February 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

the recovery of the investment and the profit of the plant. In order to ensure this long-term reliability and a return on investment, the components of a PV plant, and the plant itself, are subjected to careful control procedures before, during, and after their construction. There exists a large collection of quality control mechanisms and international standards to asseverate the guaranty of the PV systems, being one of most widely used the ones issued by Technical Committee 82 of the International Electrotechnical Commission [4].

Ensuring energy production is a key factor in warranting plant profitability, and this has forced the design of increasingly intelligent and advanced operation and maintenance (O&M) strategies [5–8]. The maintenance operation included in most O&M PV power plant contracts can be divided into Preventive, Corrective, and Predictive. While corrective maintenance is performed after some failure has been detected, preventive and predictive seek to anticipate the fault. Both need specialized personnel to perform the tasks and to analyze the data, and the second one requires "intelligent" equipment for the monitoring that can supply information about the state of the plant, allowing the evaluation of subtle trends that could be unnoticed in regular inspections.

Among the advanced operation and maintenance techniques that provide information about the PV modules, infrared thermography (IRT), electroluminescence (EL), and string current–voltage (I-V) curve measurement can be highlighted.

IRT has been widely used to detect failures in PV modules and plants [9–15]. It has the advantage of being non-intrusive, and it can be done while the plant is in operation. EL, on the other hand, is an excellent technique for the detection of failures such as cracks, interconnection defects, broken cell fingers, or other cell and string issues [16,17]. It can be used at the laboratory level in PV modules [18,19] or in PV plants where bigger areas can be analyzed with ground-mounted or aerial equipment [20]. To perform EL analysis, it is necessary to forward bias the module or array. This implies disconnecting the module or array and the use of an electronic load or an external power supply to bias the module or string.

Finally, I-V curve measurement gives more comprehensive information about the state of a PV module or string. The main characteristic parameters of the device are obtained from the I-V curve. Some of them are inferred directly from the measurement and give information about the performance: short circuit current (*Isc*), open circuit voltage (*Voc*), and maximum power point (*Pmax*) with its associate current (*Impp*) and voltage (*Vmpp*). Others give information about the physical properties of the device under study, and they are obtained from the I-V curve by applying models. The most widely used are the double or single diode models [21–23], which supply the parameters: photogenerated current *IL*, series resistance *R<sup>s</sup>* , shunt resistance *Rsh*, diode saturation current *I0*, and ideality factor m. By analyzing the magnitude and evolution of these parameters, the degradation of a PV device can be quantified. There are several techniques and devices used to measure the I-V curve of PV devices in the field. An excellent review can be found elsewhere [24]. In addition, some authors developed a mobile laboratory to perform I-V curve measurements of PV modules in the plant at standard test conditions according to IEC standard [25,26]. This has the advantage of ensuring uniform environmental conditions during the tests and it allows a precise quality control of selected PV modules throughout their shelf life.

The measurement of the I-V curve of PV modules or strings in a PV plant under illumination implies in most of the cases the disconnection of the module/array in order to sweep the operating point from *Isc* to *Voc*. This has the drawback, on the one hand, of requiring the disconnection of the plant and thus production, and on the other, the high voltages and/or currents when strings are measured, which forces taking rigorous personal security measures. In recent times, electronic boards to be installed in photovoltaic modules and inverters have been developed, from which it is possible to make I-V traces without disconnecting the photovoltaic modules. For example, in [27], the authors present two I-V tracing strategies at the photovoltaic module level without the need to disconnect them. One strategy uses electronic boards at the photovoltaic module level, while the second strategy combines electronic boards at the photovoltaic module level together with an

electronic string card (common for all photovoltaic modules). In both cases, the measures are of high quality, and the strategies have low costs.

The measurement at dark conditions has the clear advantage that it is performed when the plant is not in operation. While the normal operating mode of a plant or PV modules is under illumination, the dark curve gives very important information about the characteristics of the device, and it allows analyzing various failure modes. It has been used for many years to determine solar cell parameters [21,28,29] and as a diagnosis to detect certain defects such as mismatch, handling, soldering, or lamination problems in module manufacturing [30]. More recent works propose the use of a dark I-V curve alone or in combination with a light I-V curve for the identification of several failure modes. In [31], complementary analysis of dark and light current voltage characteristic is used to characterize failure modes such as degradation of the electrical circuit of the PV module, mechanical damage to the solar cells, and potential-induced degradation (PID). In [32], the analysis of a dark I-V curve to in situ monitor the degradation of PV modules undergoing thermal cycling and mechanical loading stress testing is proposed. The same group proposes an extension of their method to analyze in situ the temperature dependence of power loss estimations in PID experiments [33].

In this paper, we go a step further and propose the use of the developed technology to measure online distributed dark I-V curves of the PV modules in the plant. The online measurement refers to the acquisition without the need to disconnect the PV module from the string to which it is connected. It is a distributed strategy, since all the electronics required for the I-V measurement are located in the PV modules. Therefore, the proposed strategy implies the automatic acquisition of dark I-V curves by the developed electronic device, which is included in the PV modules, without the need for the onsite disconnection of any component in the plant. This is especially interesting for PV plant operators, who can obtain the dark I-V curves of the modules, which give relevant information of the individual modules, as has been outlined (characteristics of the device, to analyze various failure modes, to determine solar cell parameters, for monitoring the degradation of modules,, to diagnosis or characterize certain defects and failure modes) with the advantage of online measures, significantly reducing the onsite workforce, acquisition time, and costs. The paper has been structured as follows: it starts with an introduction to the research in Section 1, followed by the materials and method presented in Section 2, the results and their discussion in Section 3, and the main conclusions in Section 4.

#### **2. Materials and Method**

This section presents the materials and method used in the research performed. It has been divided in five subsections. The first one revises the dark I-V curves, highlighting their importance in PV inspections; the second and the third subsections explain the bidirectional inverter and the electronic board used in the research, respectively. Both have been developed by this research group. In the fourth subsection, the main characteristics of the PV modules tested are detailed. Finally, subsection five describes the methodology followed in the research proposed in this article.

#### *2.1. Dark I-V Curves*

Solar PV cells convert sunlight into electricity. All potential combinations of current and voltage pairs of points of the PV device under certain conditions of irradiance and temperature are represented in an I-V curve. There are different models that describe the electrical behavior of the I-V curve of a PV device. The one exponential model is widely used and it includes the series and shunt resistances, as detailed in the following Equation (1) [10,21]. Figure 1 shows the equivalent circuit of the one-diode model of a PV cell under illumination conditions (a) and dark conditions (b).

$$I = \left[ I\_L - I\_0 \left[ \exp\left(\frac{V + I \ R\_s}{n \ v\_l}\right) - 1 \right] - \left( \frac{V + I \ R\_s}{R\_{sh}} \right) \right] \tag{1}$$

0

**Figure 1.** One-diode model of a photovoltaic (PV) cell under illumination conditions (**a**) and dark conditions (**b**), including the series and shunt resistances.

In Equation (1), *I<sup>L</sup>* is the photogenerated current, *I<sup>0</sup>* is the saturation current of the diode, *n* is the diode ideality factor, *R<sup>s</sup>* is the series resistance, *Rsh* is the shunt resistance, and *v<sup>t</sup>* is the thermal voltage (*K T/e*) with *k* as the Boltzmann constant, *e* as the electron charge, and T as the temperature in Kelvin. In the dark conditions model circuit, as the photogenerated current *I<sup>L</sup>* due to illumination is zero, the current generator is missing. In Figure 2, there is a common I-V curve under illumination represented in the fourth quadrant, which overlaps the dark diode current with the photogenerated current due to illumination and the dark I-V curve in the first quadrant. The main characteristic points of the curve in illumination are marked in this figure. The criteria that have been considered in this research are that the current is negative when the PV device is generating power (fourth quadrant).

0

exp 1

exp 1

**Figure 2.** Illuminated and dark current–voltage (I-V) curves with their characteristic points.

As it has been remarked in the introduction, the measurement at dark conditions has the clear advantage that it is performed when the plant is not in operation, giving very important information about the characteristics of the device. It allows analyzing various failure modes, determining solar cell parameters, and monitoring the degradation of modules and it is used as a diagnosis to detect or characterize certain defects and failure modes. The application of the model of Equation (1) with the calculation of the parameters for the dark I-V curve can give information about the changes of a PV module performance, indicating that some failure or degradation has occurred. To illustrate how the variation of the parameters affect the dark I-V curve, Figure 3a,b show the changes in the dark I-V curve of a standard PV cell in which each one of the model parameters of Equation (1) has been changed one at a time. Parameters are expressed in relation to the area for being more comparable, so current is presented in mA/cm<sup>2</sup> , and *J*<sup>0</sup> represents the diode saturation current density. The reference curve corresponds to a standard cell with the following parameters: *J*<sup>0</sup> = 1.5 \* 10−<sup>9</sup> A/cm<sup>2</sup> , *n* = 1.5, *R<sup>s</sup>* = 0.6 Ω cm<sup>2</sup> , and *Rsh* = 60.000 Ω cm<sup>2</sup> . From

these initial values, parameters have been changed to simulate worse device behavior by increasing *R<sup>s</sup>* , *J*0, and *n*, and decreasing *Rsh*. The graph has been split into two parts to better appreciate the modifications that the change of each parameter introduces in the I-V curve. For the case of variations in "*n*" and *Rsh*, the graph is presented in logarithm scale to better distinguish its influence and the voltage area in which these changes produce their effect.

− − **Figure 3.** Simulated dark I-V curves by introducing changes in one of the exponential parameters. Reference curve: *<sup>J</sup>*<sup>0</sup> = 1.5 <sup>×</sup> <sup>10</sup>−<sup>9</sup> A/cm<sup>2</sup> , *n* = 1.5, *R<sup>s</sup>* = 0.6 Ω cm<sup>2</sup> , and *Rsh* = 60.000 Ω cm<sup>2</sup> , (**a**) increase in *R<sup>s</sup>* from 0.6 to 2.5 Ω cm<sup>2</sup> and *J*<sup>0</sup> from 1.5 <sup>×</sup> <sup>10</sup>−<sup>9</sup> to 5 <sup>×</sup> <sup>10</sup>−<sup>8</sup> A/cm<sup>2</sup> ; (**b**) increase in n from 1.5 to 1.9 and decrease in *Rsh* from 60,000 to 500 Ω cm<sup>2</sup> . Graph (**b**) is presented in logarithm scale.

The variations of the curves presented in Figure 3 can be indicative of certain degradation modes. For example, the degradation of the electrical circuit of a PV module usually contributes to the increasing of series resistance [31], which is appreciated in the highvoltage area of the I-V curve. Mechanical damage would contribute also to the increase of series resistance, but it will also increase recombination and shunt losses [31], as appreciated by the changes in *J*<sup>0</sup> and *Rsh*. Shunting losses are visible in the low-voltage region. These types of analysis through the dark I-V curve have been shown to be especially interesting to detect degradation provoked by PID [31,34,35].

An additional way to evaluate the performance of a PV device through the dark I-V curve is by obtaining the parameters of the dark curve equivalent to the illuminated one by transposing the dark I-V curve to the short circuit current of the illuminated one and calculating the *fill factor dark (FFD*) [31,34,35]. A decrease in this *FF<sup>D</sup>* implies degradation in the performance of the PV device.

In a common arrangement, it is necessary to forward bias the module with an external power supply in order to perform dark I-V curves. As a novel approach, a power inverter with bidirectional power flow capability has been used in this work for biasing the modules instead of the external power supply by applying the procedure explained in the following subsections [36].

#### *2.2. Power Inverter with Bidirectional Power Flow Capability*

Nowadays, common solar inverters used in PV plants only have the capability to invert the electricity produced in the solar panels to lately be injected to the grid. However, the use of a power inverter with bidirectional power flow capability is proposed in recent research [36] as a novel system that extremely facilitates the operation and maintenance of PV plants, allowing the on-site outdoor EL and IRT inspections [10]. In this scenario, this

device is suitable for the acquisition of dark I-V curves, as permits the current injection to the modules (I quadrant).

The 3 kW bidirectional inverter pilot presented in [36] has been used in this research. In the DC input side, the PV string voltage can be set between 330 and 550 V. The bidirectional inverter allows fixing ten different levels of current injection to the string of modules, from 10% of *Isc* to 100% of *Isc* in steps of 10% of *Isc*. For the dark I-V curves tracing presented in this paper, the bidirectional inverter has been set to 100% of *Isc*, and the electronic board is in charge of tracing the curve, as it is explained in the following section. Although the leakage current is dependent on the voltage, the temperature, and the humidity conditions, at low temperatures (< 25◦C), the influence of the voltage in the leakage current is minor [37]. Therefore, achieving slightly higher values of voltage in defective modules during outdoor dark I-V curve measurement, in which the temperature is low and the acquisition time is rapid (40 ms) should not affect the leakage current. As well, the authors in [38] proved how injecting current for long periods does not degrade the panel. Hence, the degradation of the panels should be insignificant during a 40 ms measurement. That is why the maximum limit of 100% of *Isc* has been selected, obtaining complete dark I-V curves. However, the maximum current limit can be set in the bidirectional inverter if desired in any specific case.

This bidirectional inverter allows EL to be done at night in individual modules or in the string with this system, without the need for an external source. The current set point, sent from the computer to the inverter, is controlled by means of the PV side voltage. Figure 4 shows the power inverter with bidirectional power flow capability used in on-site measurements.

**Figure 4.** Bidirectional power inverter of the Campus Duques de Soria of the University of Valladolid.

#### *2.3. Electronic Board Integrated in Photovoltaic Modules*

For the local measurements over each PV module, an electronic board has been designed to be installed within the module connecting box. In order to obtain a full I-V curve of the PV module under dark conditions, it is necessary to sweep the forward current injected from the bidirectional inverter explained above between zero and its maximum value (100% of *Isc*). This way, a set of module current values and their corresponding voltage values can be measured and stored as points of the I-V curve.

It is possible to perform this sweep controlling the current supplied by the bidirectional inverter, but if a good resolution in the current values is needed, it will require a

precise regulation of string voltages of some hundreds of volts, increasing the complexity of the bidirectional inverter, and in addition, a communications system between the inverter and the module electronics will be required to synchronize the sweep with the measurements. For these reasons, we have opted for a local sweeping electronics integrated in the PV module.

Figure 5 shows the schematic of the PV module electronic board. An 8-bit microcontroller is the heart of the circuit as it stores and executes the firmware for generating all the necessary signals that perform the I-V tracing process. For the measurement of current and voltage values, two of the microcontroller pins (labelled as V and I in Figure 5) can be configured as analog inputs for an internal analog-to-digital converter (ADC) of 10-bits. The module voltage analog input (V) is fed from the positive module terminal through a voltage divider. The resistive values of the voltage divider are much greater than the PV module *Rsh;* therefore, they do not alter the module parallel resistance. This divider reduces the module voltage for a full-scale matching with the positive reference of the ADC (5 V). Consequently, the resolution of the 10-bits ADC is 5 mV (5 V/1024), which corresponds with the full scale of the I-V curve measurement, which results in a resolution of 50 mV (50V/1024) in voltage measurements.

The module current is measured with an AMR (Anisotropic Magnetoresistance) sensor (*Is*), which outputs a voltage proportional to the current with a 5 volts swing for a current value from zero to 5 Amps, so it can be connected directly to the 10 bit ADC input (*I*). This setup allows for a current resolution of 5 mA (5 Amps/1024). The MOSFET transistor M1 will be responsible for the local current sweeping process. The M1 gate is driven directly by the microcontroller pin (Cm), which is configured as an analog output from an internal digital-to-analog converter (DAC). For a smooth and as linear as possible sweep, a closed control loop has been implemented in firmware, where the current and voltage values sampled by the ADC are used as a feedback for adjusting the gate voltage of M1. This strategy allows for the tuning of the control loop by simply changing some parameters in the firmware (as delay or gain).

The power supply for the entire system is provided by the voltage module established when the forward current from the bidirectional inverter flows along the string, via a DC/DC converter that outputs the 5 volts needed by the electronics. Since during the I-V tracing, the current sweep forces the module to different operating points, including the zero voltage, a power supply holding circuit has been implemented in order to keep the supply voltage at the input of the DC/DC converter high enough during the time that the I-V tracing is performed. This circuit is composed by the capacitor (C) and the diode (D) in such a way that capacitor (C) is charged up to the module voltage when the circuit is idle. When during an I-V tracing the module voltage drops, the diode (D) is reverse biased, avoiding the capacitor discharge over the module, and this capacitor can then supply the energy to the circuit until the I-V tracing is finished.

For the experiments, the communications with the microcontroller for tracing demand or data download have been implemented using the serial port integrated in it, which is connected to an external computer that send the commands for starting the measurements and receives the numerical data of the I-V curves.

The process applied for I-V curve tracing is based on these consecutive steps:


module voltage returns to its maximum, and the I-V tracing is finished. The maximum current value is the one fixed initially in the bidirectional inverter (*Isc).*

• The microcontroller sends the data corresponding to the I-V curve to the external computer, and the circuit returns to the idle mode.

(**b**)

**Figure 5.** Schematic of the module electronic board (**a**) and a real picture of the card (**b**).

#### *2.4. Tested Modules*

On-site outdoor tests have been performed in the PV installation in the School of Forestry, Agronomic, and Bioenergy Industry Engineering (EIFAB) of the University of Valladolid, in Soria, Spain. It is shown in the upper row of PV modules in Figure 6. It is

composed by eleven mono-crystalline PV modules with different kinds of defects. Their main characteristics are presented in Table 1. The area of each cell is 156.25 cm<sup>2</sup> .

**Figure 6.** Photovoltaic (PV) installation in Campus Duques de Soria.



#### *2.5. Method*

As it has been introduced, the objective of the research presented in this paper is the use of the developed electronic board integrated in photovoltaic modules presented in Section 2.3 to measure the online distributed dark I-V curves of the PV modules in the plant. To obtain and validate the dark I-V curves, the followed methodology has been used: firstly, the dark I-V curves of all the modules presented are measured with the developed device, and secondly, the main parameters of the curves are extracted to draw some conclusions on the state of the analyzed PV modules.

I-V curve measurements are carried out after sunset. It is not necessary to cover the panels, since the influence of the moon is completely negligible, 3.916 \* 10−<sup>3</sup> W/m<sup>2</sup> (perigee, perihelion) for a full moon [37]. For the I-V curves acquisition, 100% of the *Isc* setpoint is selected in a computer connected to the bidirectional inverter, which gives the order. The eleven PV modules under analysis are all connected in series to the bidirectional inverter (which is unique for the entire string). To make the dark I-V curve measurements, each module has one electronic board integrated (the developed card presented). In order, one of the cards makes a short circuit in the module, so that the rest of the modules of the string remain connected in series to the inverter while the card makes the dark I-V curve of that first module. When the acquisition of the curve ends, the card re-integrates the first module measured in the string. Successively, the measurements of all the modules are made. The time it takes to acquire the I-V curve of each module is 40 ms. A better definition, reliability, and low disturbance in the low-current region of the I-V curve can be obtained, if required, by the acquisition of several I-V curves and averaging [39], but at the expense of a longer time of exploration. For installations with a large number of PV modules, a balance between total time of measurement and curve definition should be considered.

Ambient and module temperatures in the I-V curve acquisition moment have been measured and will be presented within the results. The temperatures were measured using an external PT1000 temperature probe, as this electronic board prototype does not have any temperature nor irradiance sensor incorporated. The temperature probe has been attached to a healthy cell in the middle of the PV module. A schema of the system is presented in Figure 7, showing the global operating diagram, where it is possible to see the bidirectional inverter, as well as the electronic boards installed in each photovoltaic module. The injection of current in dark conditions will allow the realization of the dark I-V curve.

**Figure 7.** Global operating diagram of the system.

Once the dark I-V curves are captured, the main parameters of the one exponential model (single-diode model) of each module are obtained using the 2/3 Diode Fit software [40] with the objective of drawing some conclusions on the state of the analyzed PV modules. The free software 2/3 Diode Fit permits calculating model parameters for PV devices using a 1-diode model, 2-diode model, and other more complex options. The software provides initial guesses of the parameters, calculating the slopes and applying conditions in the areas in which each parameter has more influence. From these starting parameters, optimized ones are obtained through an iterative procedure, in which it is possible to select the precision and stopping criteria. The algorithm to calculate the I-V curve is described in detail in [41], and all program functionalities and a comprehensive explanation of the equations and options available can be found in the program manual available at [40]. As it has been detailed, these parameters are extremely useful for analyzing the appearance of different failure modes, monitoring the degradation of modules, and detecting or characterizing certain defects, among others.

#### **3. Results and Discussion**

#### *3.1. Dark I-V Curves Onsite Measurements*

The following Table 2 shows the ambient temperature and the temperature of the photovoltaic cell for the measurements performed.

**⁰ ⁰**



Figure 8 shows the I-V curves in darkness for all photovoltaic modules. These measurements have been taken at the temperature values indicated in Table 2. Each I-V curve has been presented at the cell temperature at which it has been captured. Conversion to 25 ◦C cell temperature has not been performed, as PV modules with different kinds of defects have been used, and the nominal conversion parameters (alpha, beta, and gamma) could have changed over the years associated with the degradation of the modules.

**Figure 8.** Dark I-V curves of the eleven modules measured with the developed device at the PV installation in Campus Duques de Soria.

#### *3.2. Extraction of Solar Module Parameters from the Measured Dark I-V Curves*

Once the dark I-V curves onsite measurements have been presented, the main parameters of the one exponential model (single-diode model) of each module are obtained using the 2/3 Diode Fit software. These results are presented in Table 3. In order to have comparative results between the different modules, parameters are presented in relation to the area. With the objective of drawing some conclusions on the state of the analyzed PV modules and for comparison purposes, all dark I-V curves have been presented in the same graph in Figure 8 and are analyzed together with their main parameters in this subsection.

**Ω**

**Ω Ω Ω**

Ω Ω

**Table 3.** Absolute and referred to unit area main parameters of the one exponential model (singlediode model) of each module obtained using the 2/3 Diode Fit software. The values referred to unit area correspond to the cell current density *J*<sup>0</sup> [A/cm2] and cell shunt *<sup>R</sup>sh* [kΩ·cm<sup>2</sup> ] and series *R<sup>s</sup>* [Ω cm<sup>2</sup> ] resistances. The absolute values of current and resistance included in the table correspond to the module parameters, and they have been obtained from the cell values referred to unit area.


First, it can be observed from Figure 8 is that there is one curve—number 10 from module 10—that has different characteristics from the rest. This is reflected in the extremely high value of the saturation current that, combined with the high value of the diode factor, dominates the rest of the model parameters.

For the curves that belong to the same module type (1, 2, 3, 4, 5, 7, 8, and 9), some differences can also be appreciated. If we fix a current equivalent to *Isc*, we find that different voltages are found for the I-V characteristics. Given that all the curves are measured at approximately the same temperature, these variations would indicate different degradation in these modules. Furthermore, changes in the slope in the high-voltage area indicate changes in series resistance (higher slope, lower series resistance). It has to be taken into account that these modules have a lot of damages, some of them appreciated by the naked eye (see the upper row of modules in Figure 6), and various degradation modes are mixed, influencing the measured dark I-V curves. Higher series resistance modules indicate degradation in the module electrical circuit (modules 1, 3, and 7). High series resistance, combined with lower shunt resistance and diode saturation current could inform about mechanical damage [31] (for example, module 3).

It is also observed that some modules, especially those numbered 7, 8, and 2 present a very low value of shunt resistance (see Table 3). This low value of shunt resistance is also found in the other EOPLLY module (165W type), and in the number 10 module, which presents high degradation in all parameters. These low values of shunt resistance would imply shunting loses in the module. The combination of a lower *Rsh* and higher *J*<sup>0</sup> in modules 2 and 8 would indicate that the recombination losses are also enhanced in these modules.

With reference to the I-V curves presented, other interesting ideas can be pointed out. Differences between curves (in the 35–50 V range) are a consequence of the combination of parameters that can have opposite effects (for example, *J*<sup>0</sup> and *n*), so it is very difficult to grasp differences among the degradation states of several modules by solely comparing their I-V curves in a certain moment (except for cases as that of module 10), one to each other. In this case, the rightmost curve corresponds to module 1 (*J*<sup>0</sup> = 7.87 <sup>×</sup> <sup>10</sup>–9 A/cm<sup>2</sup> and *<sup>n</sup>* = 1.73), while the leftmost is of module 7 (*J*<sup>0</sup> = 3.98 <sup>×</sup> <sup>10</sup>–12 A/cm<sup>2</sup> and *<sup>n</sup>* = 1.04). The important point is also to compare the I-V curves of the same module in different periods along its life, because a check of possible shifts or changes in the curves or in the extracted parameters along time could reveal degradation processes being started or affecting the performance of the module.

#### **4. Conclusions**

This work demonstrates the possibility of tracing dark I-V curves in the modules of a PV plant without disconnecting them from the string. This is a breakthrough, as the dark I-V curve gives important information about the PV device and certain defects. These measures have been possible thanks to the combination of a bidirectional inverter and the developed electronic boards installed at the PV module level.

The results of the measurements have been satisfactory, and this allows obtaining the values of *R<sup>s</sup>* and *Rsh*, among others, of the different PV modules of a plant online, without disconnection. The values obtained for *R<sup>s</sup>* and *Rsh,* adjusted with the 2/3 Diode Fit software perfectly fit to the PV module installed.

With regard to future work, the authors will research the combination of dark and light I-V curve measurements. All measurements will be carried out without disconnection in the PV plant when combined with the bidirectional inverter. In addition, these measures will be managed and controlled through a low-cost communications system based on power line communications. In addition, with the measurements carried out, this research group will work with models based on artificial intelligence to locate defects in modules and cells, with the aim of keeping the performance of the photovoltaic plant high. Advances in O&M are key for this research team. Models based on artificial intelligence will work with images (electroluminescence and thermography) and I-V curves (light and dark).

**Author Contributions:** Conceptualization, L.H-C. and J.I.M.-A.; methodology, L.H-C., J.I.M.-A., S.G-S., M.d.C.A.-G., V.A-G., and J.L.B.; software, J.I.M.-A. and A.R-P.; validation, L.H-C., J.I.M.-A., S.G-S., M.d.C.A.-G., V.A-G., and J.L.B.; formal analysis, L.H-C. and J.I.M.-A.; investigation, L.H-C., J.I.M.-A., S.G-S., M.d.C.A.-G., and V.A-G.; resources, L.H-C. and V.A-G.; data curation, J.I.M.-A., S.G-S., M.d.C.A.-G., and A.R-P.; writing—original draft preparation, L.H-C., J.I.M.-A., S.G-S., M.d.C.A.-G., and J.L.B.; writing—review and editing, L.H-C., J.I.M.-A., S.G-S., M.d.C.A.-G., V.A-G., J.L.B., and A.R-P.; visualization, L.H-C., J.I.M.-A., S.G-S., M.d.C.A.-G., and V.A-G.; supervision, L.H-C., M.d.C.A.-G., and V.A-G.; project administration, L.H-C.; funding acquisition, L.H-C. and V.A-G. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the "Ministerio de Industria, Economía y Competitividad" grant number "RTC-2017-6712-3" with name "Desarrollo de herramientas Optimizadas de operaCión y manTenimientO pRedictivo de Plantas fotovoltaicas—DOCTOR-PV".

**Data Availability Statement:** To request the data, please, contact the corresponding author

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


## *Article* **A Study on the Improvement of Efficiency by Detection Solar Module Faults in Deteriorated Photovoltaic Power Plants**

**Myeong-Hwan Hwang 1,2 , Young-Gon Kim <sup>1</sup> , Hae-Sol Lee 1,3 , Young-Dae Kim <sup>4</sup> and Hyun-Rok Cha 1,3, \***


**Abstract:** In recent years, photovoltaic (PV) power generation has attracted considerable attention as a new eco-friendly and renewable energy generation technology. With the recent development of semiconductor manufacturing technologies, PV power generation is gradually increasing. In this paper, we analyze the types of defects that form in PV power generation panels and propose a method for enhancing the productivity and efficiency of PV power stations by determining the defects of aging PV modules based on their temperature, power output, and panel images. The method proposed in the paper allows the replacement of individual panels that are experiencing a malfunction, thereby reducing the output loss of solar power generation plants. The aim is to develop a method that enables users to immediately check the type of failures among the six failure types that frequently occur in aging PV panels—namely, hotspot, panel breakage, connector breakage, busbar breakage, panel cell overheating, and diode failure—based on thermal images by using the failure detection system. By comparing the data acquired in the study with the thermal images of a PV power station, efficiency is increased by detecting solar module faults in deteriorated photovoltaic power plants.

**Keywords:** photovoltaic module; defect detection; power plant; efficiency; thermal image; photovoltaic aging

#### **1. Introduction**

In recent years, photovoltaic (PV) power has been receiving considerable attention as an alternative renewable energy source. Numerous studies on PV systems have attempted to improve the electrical performance of PV panels and have proposed maximum power estimation techniques and advanced power conversion techniques [1,2].

Owing to their environmental friendliness and good productivity, PV modules have been installed in various areas, including building rooftops, forests, and open fields. According to the "Korea Renewable Energy 2030 Plan", Korea should increase the proportion of renewable energy production from the current value of 4% to 20% by 2030. However, the amount of waste from spent PV modules is expected to exceed 1900 tons in 2030 (the target year of the 2030 Plan) and 85,000 tons in 2040. Therefore, it is necessary to develop a method for the disposal of solar equipment in preparation for the end-of-life management of PV modules, understand the environmental and social issues of PV modules, and reduce the cost of PV power generation [3–5].

PV modules have a lifespan of approximately 20 years when exposed to the outside environment, and they can be used as semipermanent systems with low maintenance

**Citation:** Hwang, M.-H.; Kim, Y.-G.; Lee, H.-S.; Kim, Y.-D.; Cha, H.-R. A Study on the Improvement of Efficiency by Detection Solar Module Faults in Deteriorated Photovoltaic Power Plants. *Appl. Sci.* **2021**, *11*, 727. https://doi.org/10.3390/app11020727

Received: 21 December 2020 Accepted: 7 January 2021 Published: 13 January 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

costs [6]. Further, it was reported that the electrical performance of systems operated for a long time in more technologically advanced countries degraded significantly because of the degradation of the electrical characteristics and discoloration of the buffer materials, such as ethylene-vinyl acetate, in addition to physical damage [7].

In general, defect diagnosis of an aging PV panel is performed by comparing its system status and output with that of a normally operating PV system. The defects of the system can be evaluated by measuring the voltage and current of the PV panel terminals. In a previous study, ZigBee communication models were used to identify the types of PV panel defects, and it is expected that these models can be used to obtain thermal imaging data of the PV panels that are determined to be defective through their voltage drops [8].

For the accurate localization of the defects and determination of the causes of the efficiency decrease in PV panels, a system that thoroughly reflects the natural environment should be developed to compare the PV panel output under various control conditions and to obtain experimental data, including thermal images for each failure type. When implementing an actual system with traditional models or electrical performance-based failure diagnosis techniques, errors and inaccuracies in the identification of the defects may be experienced since the system status, and the output contains random signal components. To reduce such errors, in this paper, a system has been proposed that detects the failures and malfunctions of aging PV panels based on image data [9–12].

Furthermore, it is necessary to develop a method for the detection of PV panel failures at a minimum cost and avoid replacing all the panels in a PV power station. To accelerate the defect detection in PV panels, in this study, we first designed and fabricated an environmental chamber for accelerated life tests to simulate the actual natural environment by controlling key variables, such as temperature, lighting irradiation (illumination intensity), humidity, and vibration. Further, the fabricated chamber was used to conduct artificial tests and analyze the key factors affecting the normal PV panel output through the Taguchi method. Subsequently, an aging PV panel failure detection system was developed by analyzing images of frequently occurring failure types.

Ultimately, the aim was to develop a method that enables users to immediately check the type of failures among the six failure types that frequently occur in aging PV panels—namely, hotspot, panel breakage, connector breakage, busbar breakage, panel cell overheating, and diode failure—based on thermal images by using the failure detection system. To this end, we first checked the output of a normally operating PV panel and then induced various failures on the panels to obtain image data by failure type through output comparison and thermal image capturing process. Subsequently, we checked whether the same image is generated when images are captured after establishing a small-scale power generation facility using the normal panels and faulty panels.

It is expected that the proposed method will enable efficient operation of PV power generation facilities by standardizing the thermal images that are used indiscriminately and allowing easy detection of failure types. Additionally, the method will also contribute to reducing the maintenance cost as it will enable users to determine which panel is producing the lowest output in the power generation facility. Further, we propose a detection system that enables easy detection of failure types by standardizing thermal images for each failure type after capturing PV panel images with a thermal imaging camera. In addition, a method that can increase the output in the PV power generation facility by detecting whether the output is the highest or lowest in the failure types and replacing the faulty panels in a timely manner is presented.

#### **2. Structure of PV Panel and Causes of Power Loss**

#### *2.1. Structure of a PV Panel*

Once the photons from sunlight enter the semiconductor composed of a P–N junction, the electrons separated by the internal electric field accumulate in the N-type silicon, generating a charge; a path is formed to enable current to flow in the direction opposite to electron flow [13–15].

In a typical PV power generation system, several solar cells are wired in series to form a panel-type module. Then, several modules are wired in series and parallel. Depending on the type of light-absorbing material, solar cells can be classified into three types: silicon-based, compound semiconductor-based, and organic semiconductor-based. Further, the order of commercialization is as follows: first-generation cells (crystalline silicon), second-generation cells (amorphous silicon, copper indium gallium selenide (CIGS), and cadmium telluride (CdTe)), third-generation cells (dye-sensitized and organic cells), and next-generation cells (quantum dots and plasmons).

Among these materials, crystalline silicon solar cells were the first to be commercialized, and they currently account for more than 90% of the solar cells on the world market. Further, thin-film solar cells (CdTe, CIGS, etc.) account for approximately 8% of the world market. Dye-sensitized solar cells and organic solar cells are attracting interest owing to their potential implementation in a variety of applications, such as building-integrated PV and mobile devices. In recent years, perovskite solar cells have been widely studied as potential alternatives to silicon solar cells [16].

#### *2.2. Power-Loss Factors of PV Panels*

Excluding manufacturing errors and deterioration, the factors that affect the power loss in PV panels can be categorized into three types: mismatch effect due to shading or dirt that occurs when panels are connected in series and parallel to increase the output, changes in solar altitude, and temperature increases. These three types of factors that affect the power loss in PV panels are described in detail in the following subsections.

#### 2.2.1. Module Mismatch Losses and Application of Inverters

The required output of PV panels is generated by arranging them into strings, i.e., connecting several panels in series or parallel (arrays), rather than using the panels individually. During operation, shading effects due to obstruction factors such as clouds or fallen leaves may cause mismatch losses, which could lead to a decrease in the power output. Several methods to decrease the module mismatch losses have been developed, including the use of built-in module inverters, string inverters, and module built-in DC–DC converters [17–21]. However, these methods require a separate circuit for compensating for the voltage loss due to shadowed strings. For the implementation of these methods, the cost of the additional modules to be installed, and the power losses due to the presence of these modules should be analyzed.

#### 2.2.2. Power Loss Caused by Solar Altitude Change and Tracking System

The altitude of the sun changes from sunrise to sunset and over different seasons. PV panels are most efficient when they are positioned perpendicular to the position of the sun; thus, it is efficient to use a solar tracking system. The methods for positioning panels at the optimal angle include tracking the sun through a software program, utilizing an optical sensor, or employing both methods. In a previous study, the use of a tracking system for one month led to an increase in the output power of a 100 W panel of approximately 18% compared to a case where no tracking system was used. Nevertheless, the implementation of the corresponding systems required additional structures and power systems and incurred maintenance costs and additional power consumption.

#### *2.3. Power-Loss Factors of PV Panels*

Excluding manufacturing errors and deterioration, the factors that affect the power loss in PV panels can be categorized into three types: mismatch effect due to shading or dirt that occurs when panels are connected in series and parallel to increase the output, changes in solar altitude, and temperature increases. These three types of factors that affect the power loss in PV panels are described in detail in the following subsections.

#### 2.3.1. Module Mismatch Losses and Application of Inverters

The required output of PV panels is generated by arranging them into strings, i.e., connecting several panels in series or parallel (arrays), rather than using the panels individually. During operation, shading effects due to obstruction factors such as clouds or fallen leaves may cause mismatch losses, which could lead to a decrease in the power output. Several methods to decrease the module mismatch losses have been developed, including the use of built-in module inverters, string inverters, and module built-in DC–DC converters [16–20]. However, these methods require a separate circuit for compensating for the voltage loss due to shadowed strings. For the implementation of these methods, the cost of the additional modules to be installed, and the power losses due to the presence of these modules should be analyzed.

#### 2.3.2. Power Loss Caused by Solar Altitude Change and Tracking System

The altitude of the sun changes from sunrise to sunset and over different seasons. PV panels are most efficient when they are positioned perpendicular to the position of the sun; thus, it is efficient to use a solar tracking system. The methods for positioning panels at the optimal angle include tracking the sun through a software program, utilizing an optical sensor, or employing both methods. In a previous study, the use of a tracking system for one month led to an increase in the output power of a 100 W panel of approximately 18% compared to a case where no tracking system was used [21]. Nevertheless, the implementation of the corresponding systems required additional structures and power systems and incurred maintenance costs and additional power consumption.

#### **3. Methods and Materials**

#### *3.1. Analysis of Aging PV Panel Failure Types*

There are two main types of PV panel failure modes: corrosion and solar cell or connection problems. However, corrosion problems are usually caused by reactions such as those occurring when a metal is exposed to oxygen, solutions such as water, and other microscopic organisms. Thus, corrosion can be neglected because it is rare and insignificant in most cases; thus, only solar cell and connection problems are analyzed. Table 1 summarizes the various solar cell failure mode types analyzed in this study. Among the failure modes presented in Table 1, the most critical is the hotspot type.


**Table 1.** Solar cell failure types.

#### *3.2. Specifications of Experimental PV Panels*

Three PV panel models with different outputs and sizes were selected for the PV panel output comparison test; their parameters are presented in Table 2. The panel shown in the fourth column of the table was selected to analyze whether the failure types can be found in the panel.

**Table 2.** Photovoltaic (PV) panel output and specifications.


#### *3.3. Configuration of the Environmental Chamber*

Figure 1 shows photographs of the interior and exterior of the experimental chamber constructed in this study. The chamber had an external size of 3000 (W) × 4500 (D) × 2800 (H) mm, rated power of 4800 W, a correlated color temperature of 5500 K, and lamp luminous flux of 180,000 Lm. (PV panel experimental chamber, Korea) The interior of the experimental chamber was sealed and designed to allow the control of the temperature and humidity using a thermohygrostat and induce vertical vibrations through a vibrator installed on the support structure area. Additionally, xenon lamps with a wavelength and light irradiation similar to those of the sun were installed on top of the chamber to irradiate the PV panel. Specifically, a total of six xenon lamps with a power of 1 kW (total: 6 kW) were installed inside the chamber, along with three 220 V power supplies. (UXL Xenon Short-Arc Lamps, UXL-16SB, Germany).

#### *3.4. PV Panel Performance Test Method*

The cells constituting the PV module generate heat during electricity generation. The cells display 100% of their normal starting efficiency when the temperature is maintained at 25 ◦C, and for every temperature increase of 1 ◦C, the efficiency decreases by 0.5%. Thus, it can be inferred that PV panels are sensitive to the temperature and that higher cell temperatures cause output degradation. Accordingly, the experiment was conducted by acquiring thermal images of the PV panel failures and considering the output decrease when the temperature increases in certain areas of the PV panels.

Assuming that the panel output degrades when a specific area of the panel heats up, the types of failure can be determined by taking a wide range of images of the power station with a drone equipped with a thermal imaging camera.

Table 3 summarizes the image acquisition methods for the most frequently occurring failure types. The thermal images used to determine the failure types can serve as a basis for reducing the maintenance cost of power generation stations by allowing only partial replacement of power generation equipment.

Figure 2 shows photographs of typical PV modules with different failure types. In figure, a total of six images are secured on failures by panel breakage, diode failure, connector degradation, hotspot, busbar breakage, and panel cell overheating to obtain thermal images that can immediately differentiate the type of failure in an aging PV panel.


**Table 3.** Panel image acquisition method for different panel failure types.

**Figure 2.** Photographs of PV panels with different failure types: (**a**) panel breakage, (**b**) diode failure, (**c**) connector breakage, (**d**) hotspot, (**e**) busbar, and (**f**) overheating of panel cells.

#### *3.5. Method for Securing PV Panel Failure Images by Constructing a Small-Scale Power Generation Facility*

We established a small-scale power generation facility composed of normal and faulty panels using the failure types of Figure 2 and detected the images by failure type. The facility was equipped with a total of 32 panels, comprising two parallel modules, each composed of 16 panels connected in series. As each module generated 1.7 kW output, the facility was designed to generate a total of 3.4 kW when the two modules were connected. Additionally, the small-scale power generation facility was arranged so that the images of normal and faulty panel types could be analyzed. In this study, the PV panel images were analyzed after capturing them using a drone equipped with a thermal imaging camera. Table 4 shows Normal and faulty panel placement layout in the small-scale power generation facility.


**Table 4.** Normal and faulty panel placement layout in the small-scale power generation facility.

#### **4. Results**

#### *4.1. Key Factors of PV Module Output*

Figure 3 shows the key factors affecting the PV module output obtained using the Taguchi experimental design method. In addition to the four main influential factors, the operator and maintenance time factors were analyzed. The operator factor was categorized as either professional or nonprofessional, denoted as U0 and U1, respectively; the maintenance time factor was set to 1 or 3 h, denoted as V0 and V1, respectively.



**Figure 3.** Key factors affecting PV module output obtained using the Taguchi experimental design method.

From Figure 4, it can be seen that the level of influence of the factors was ranked based on signal-to-noise ratio and mean. Temperature and lighting have a high ranking in terms of both the signal-to-noise ratio and mean. It can be seen that the factors with higher response ranks were more likely to be recognized as key influential factors.

Figure 4 shows the analysis results of the main effects of the signal-to-noise ratio. Similar to the response tables, the temperature and lighting factors show a greater influence (steeper slope) than the other factors.

**Figure 4.** Analysis results of the main effects of the signal-to-noise ratio.

#### *4.2. Image Analysis According to Failure Type*

We imaged the failures of twenty 35 W panels, twenty 220 W panels, and ten 365 W panels, for a total of 50 panels. Because the 35 W panels did not contain diodes, a total of five images were acquired for the failures of panel breakage, connector degradation, hotspots, busbars, and cell overheating. Furthermore, because the 220 and 365 W panels contain diodes, a total of six images, including the diode failure, were acquired for each panel type.

#### *4.3. Analysis of the 365 W PV Panel*

Table 5 presents the power output of the 365 W PV panel measured before and after different failure types. From the table, it can be seen that before failure, the output of the 365 W panel is 355.79 W, and after failure, it decreased by at least 10% in all cases.


**Table 5.** Power output of the 365 W PV panel after different failure types.

Figure 5 shows photographs and thermal images of the 365 W PV panel after different types of failure. From the figure, it can be seen that overheating occurs in a certain part of the panel in the case of the hotspot problem. Furthermore, sporadic heat generation is observed in the case of diode malfunction. In the case of connector failure, heat generation is observed at the edges of the panel. In the case of cell overheating, heat generation is observed throughout the damaged areas. Lastly, in the case of busbar failure, overheating is observed in the area where the busbar is located.

**Figure 5.** Photographs (left) and thermal images (right) of the 365 W panel with different failure types: (**a**) hotspot, (**b**) diode failure, (**c**) connector breakage, (**d**) panel breakage, (**e**) busbar, and (**f**) overheating of panel cells.

#### *4.4. Analysis of the 220 W PV Panel*

Table 6 presents the power output of the 220 W PV panel measured before and after different failure types. From the table, it can be seen that before failure, the output of the panel is 175.10 W. After diode failure, connector breakage, and cell overheating, the panel output is 0 W.


**Table 6.** Power output of the 220 W PV panel after different failure types.

Figure 6 shows photographs and thermal images of the 220 W PV panel after different types of failures. It can be seen that the thermal images of the 220 W PV panels after different types of failures are similar to those of the 365 W PV panels.

**Figure 6.** *Cont.*

(**a**)

(**b**)

(**c**)

(**d**)

(**e**)

**Figure 6.** Photographs (left) and thermal images (right) of the 220 W panel with different failure types: (**a**) hotspot, (**b**) diode failure, (**c**) connector breakage, (**d**) panel breakage, (**e**) busbar, and (**f**) overheating of panel cells.

#### *4.5. Analysis of the 35 W PV Panel*

Table 7 presents the power output of the 35 W PV panel measured before and after different failure types (excluding diode failure because low-output power panels do not contain diodes). After connector breakage and cell overheating, the panel output is 0 W.


**Table 7.** Power output of the 35 W PV panel after different failure types.

Figure 7 shows photographs and thermal images of the 35 W PV panel after different types of failures. It can be seen that the thermal images of the 35 W PV panels after different types of failures are similar to those of the 365 and 220 W PV panels.

(**a**)

(**b**)

**Figure 7.** *Cont.*

**Figure 7.** Photographs (left) and thermal images (right) of the 35 W panel with different failure types: (**a**) hotspot, (**b**) connector breakage, (**c**) panel breakage, (**d**) busbar, and (**e**) overheating of panel cells.

#### *4.6. PV Panel Thermal Image Analysis Results*

Figure 8 shows thermal images of the investigated panels with different failure types. From figure, it can be seen that most of the failure images are similar. It can be concluded that by photographing a PV power station with a drone equipped with a thermal imaging camera, malfunctions in the panels can be discovered immediately. As a result, faulty panels can be replaced, enhancing the power output and efficiency of the station.

**Figure 8.** *Cont.*

**Figure 8.** Thermal images of the 365 W (left), 220 W (middle), and 35 W (right) panels after different failure types: (**a**) hotspot, (**b**) diode failure, (**c**) connector breakage, (**d**) panel breakage, (**e**) busbar, and (**f**) overheating of panel cells.

#### *4.7. Output Data Comparison Analysis by Failure Type in the 365 W, 220 W, and 35 W Panels*

As the output of the PV panels varies by size, failure types were generated on a total of 50 panels composed of 365 W, 220 W, and 35 W PV panels to compare the output data. Figure 5 illustrates failure images of a 365 W panel by failure type, while Figures 6 and 7 illustrate failure images of a 220 W panel and a 35 W panel, respectively. Figure 8 shows combined thermal images for each output. The important factor here is to analyze the changes in the output in each failure type and propose a method for increasing the efficiency of the power generation facility by prioritizing replacement of the PV panels having the lowest output among the failure types.

Figure 9 compares the output values of each PV panel by failure type. In the figure, (a) to (f) indicate the following failure types: (a) hotspot, (b) diode failure, (c) connector breakage, (d) panel breakage, (e) busbar, and (f) overheating of panel cells. The failure type yielding the lowest panel output was analyzed as the (c) connector breakage, followed by (d) panel breakage, (b) diode failure, (e) busbar, (f) overheating of panel cells, and (a) hotspot. When the connector breakage was detected through PV panel imaging, the corresponding panel was analyzed as the panel requiring a priority in replacement. It is inferred that the panel that requires immediate replacement can be derived based on the images obtained using a thermal imaging camera and the panel output data.

**Figure 9.** Output comparison of each PV panel by failure type.

#### *4.8. Thermal Image Results of Small-Scale Power Generation Facility*

Based on the panel placement layout shown in Table 4, the PV panels were arranged using normal and faulty panels. The panels were arranged in parallel modules, with each module comprising16 panels in series. Further, a thermal imaging camera was attached to a drone to obtain the images of the normal and faulty PV panels. The images were captured during clear weather, and the drone was set to fly at the height of about 20 m from the ground.

Figure 10. Faulty panel images acquired using a thermal imaging camera. While panels #1, 3, 9, 11, 17, 19, 25, and 27 were normal panels without any failure shown in the thermal images, it can be seen that the rest of the panels other than the normal ones showed overheating of cells in certain areas of the panel as a result of taking images with a thermal imaging camera for each failure type, thereby generating various images. As for the connector breakage, it was possible to detect the failure with only the image analysis as severe overheating is generated throughout the PV panel. In the connector breakage, which yields the lowest output, the phenomenon in which the cells encounter overheating throughout the panels is observed. Through this image analysis, it was possible to check the results of image data for panels requiring immediate replacement by acquiring images of connector breakage, which displays the lowest panel output among the failure types.

**Figure 10.** Faulty panel images acquired using a thermal imaging camera.

#### **5. Conclusions**

In this study, we analyzed the power output of PV panels after different types of failure. To this end, we designed and fabricated an experimental chamber and placed PV panels inside the chamber. Xenon lamps were used to simulate sunlight irradiation. After generating different types of damage to PV panels with power outputs of 365, 220 and 35 W and irradiating these in the experimental chamber, failure images were acquired using a thermal imaging camera to analyze the damaged PV panels. Many similarities were found in the thermal images of the PV panels with different failures.

By comparing the data acquired in this study with the thermal images of a PV power station, PV panels experiencing malfunction could be identified, and the power output loss due to the defects could be calculated.

In the future, more failure images of panels in PV power stations should be captured using drones. By analyzing these images in real time, panel failures can be discovered, improving the efficiency of PV power stations.

Based on the experiment results of this study, it was possible to obtain images of PV panels showing the lowest output and overheating throughout the panels by conducting analysis on the thermal images of a PV power generation facility captured using a drone. While the output can be increased by replacing the entire panel when failure types occur, if the replacement priority is given on the connector breakage failure type that yields the lowest output among all failure types in consideration of the cost aspect, the output of the power generation facility can be improved, and the maintenance cost can be minimized as proposed in this study.

**Author Contributions:** Conceptualization, M.-H.H. and H.-S.L.; data curation, H.-S.L.; formal analysis, Y.-G.K.; methodology, Y.-D.K.; supervision, H.-R.C.; validation, H.-R.C. and M.-H.H.; visualization, H.-S.L.; writing—original draft, M.-H.H.; writing—review and editing, Y.-G.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This study was conducted with the support of the Korea Institute of Energy Technology Evaluation and Planning as "Developing image big data based real time detection system for detecting defective module applied to solar power plant (KETEP 20183010014230)."

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**Andrés Pérez-González \* , Álvaro Jaramillo-Duque and Juan Bernardo Cano-Quintero**

Research Group in Efficient Energy Management (GIMEL), Electrical Engineering Department, Universidad de Antioquia, Calle 67 No. 53-108, Medellín 050010, Colombia; alvaro.jaramillod@udea.edu.co (Á.J.-D.); bernardo.cano@udea.edu.co (J.B.C.-Q.)

**\*** Correspondence: afernando.perez@udea.edu.co; Tel.: +57-322-639-7758

**Abstract:** Nowadays, the world is in a transition towards renewable energy solar being one of the most promising sources used today. However, Solar Photovoltaic (PV) systems present great challenges for their proper performance such as dirt and environmental conditions that may reduce the output energy of the PV plants. For this reason, inspection and periodic maintenance are essential to extend useful life. The use of unmanned aerial vehicles (UAV) for inspection and maintenance of PV plants favor a timely diagnosis. UAV path planning algorithm over a PV facility is required to better perform this task. Therefore, it is necessary to explore how to extract the boundary of PV facilities with some techniques. This research work focuses on an automatic boundary extraction method of PV plants from imagery using a deep neural network model with a U-net structure. The results obtained were evaluated by comparing them with other reported works. Additionally, to achieve the boundary extraction processes, the standard metrics Intersection over Union (*IoU*) and the Dice Coefficient (*DC*) were considered to make a better conclusion among all methods. The experimental results evaluated on the Amir dataset show that the proposed approach can significantly improve the boundary and segmentation performance in the test stage up to 90.42% and 91.42% as calculated by *IoU* and *DC* metrics, respectively. Furthermore, the training period was faster. Consequently, it is envisaged that the proposed U-Net model will be an advantage in remote sensing image segmentation.

**Keywords:** deep learning (DL); unmanned aerial vehicle (UAV); photovoltaic (PV) systems; imageprocessing; image segmentation; semantic segmentation

#### **1. Introduction**

In the last decade, the world began the transition towards renewable energy the harvesting of solar energy one of the most promising sources used today. Photovoltaic (PV) energy production is a fast-growing market: The Compound Annual Growth Rate (CAGR) of cumulative PV plants was 35% from year 2010 to 2019. The main reasons for this accelerated growth are: production cost of PV panels have decreased, return on investment ranging from 0.7 to 1.5 years. Some countries offer economic benefits for new facilities and the performance ratio (which informs how energy-efficient and reliable PV plants are against its theoretical production) is better nowadays. Before 2000 it was 70%, today performance ranges from 80% to 90% [1,2].

Nonetheless, PV plants present some challenges for maintaining proper performance with failures and defects being the most common ones. In general, failures on PV systems are more concentrated in the inverters and PV modules. In the PV modules, because of dirty equipment, environmental conditions, or manufacturing problems the PV plant energy output can be reduced by 31% [3–5]. To detect these problems, it is necessary to consider that the PV systems are commonly located on roofs, rooftops, and farms. Therefore the access, maintenance, and detection of possible problems in the panels should be carried out by trained and qualified personnel working at heights to detect these problems. These

**Citation:** Pérez-González, A.; Jaramillo-Duque, Á.; Cano-Quintero, J.B. Automatic Boundary Extraction for Photovoltaic Plants Using the Deep Learning U-Net Model. *Appl. Sci.* **2021**, *11*, 6524. https://doi.org/ 10.3390/app11146524

Academic Editors: Luis Hernández-Callejo, Maria del Carmen Alonso García and Sara Gallardo Saavedra

Received: 2 June 2021 Accepted: 13 July 2021 Published: 15 July 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

procedures can put the integrity of people, equipment, and PV Plants at risk [6]. Manual inspection can take up to 8 h/MW, depending on the number of test modules. This period can be more than double for rooftop systems, depending on the characteristics of the installation [7].

As an alternative to use trained personnel for maintenance, the use of an Unmanned Aerial Vehicle (UAV) has many advantages: it reduces the risks in maintenance labours, increases reliability, and increases effectiveness of PV plants. As a result, research teams are currently working on developing equipment that can automatically inspect and clean PV systems, as shown in [8,9].

Compared to traditional methods, UAVs could perform an automatic inspection and monitoring with lower costs, cover larger areas, and achieve faster detection. The cameras installed on UAVs take photos [10], and through image processing, the area of the PV systems can be identified in a process called boundary extraction [11]. Once the area is identified, the ground control station calculates the Coverage Path Planning (CPP) that guides the UAV in the automatic plant inspection. Any faults are detected with the inspection, the required maintenance is scheduled.

This work focused on the boundary extraction of PV systems which is a key aspect for UAVs to conduct autonomous inspections and enhance Operation and Maintenance (O&M) [11].

Several inspections and defect detection methods have been proposed in the literature. Lately, UAVs have been used for the inspection of different PV plants, to identify the correlation between altitude and the PV panel defects detection as: shape, size, location, color, among others [12–16]. Many attempts have been committed to developing a reliable and cost-effective aerial robot with optimum efficiency over PV plant inspection [10,17–19]. For autonomous inspection, large volumes of information or big data are required from PV systems. These datasets improve the inspection by means of automatic learning algorithms during the O&M process [7]. The O&M process of photovoltaic plants is an important aspect for the profitability of investors. Autonomous inspection of PV systems is a technology with great potential, mainly for large PV plants, roofs, facades and where manual techniques have notable restrictions in terms of human risk, performance, time and cost.

Traditional Image Processing (TIP) has been used extensively by other authors. In this study [13,20–24], the authors used TIP to defect recognition in the inspection of photovoltaic plants. Furthermore, using HSV transformation, color filtering and segmentation, techniques have been implemented in many projects, especially for defect detection [25], to enumerate photovoltaic modules [20,26] and identification of limits [27]. This technique has a restriction for unsupervised procedures; the user should assist in the image processing by adjusting the filter to the particular color of each target the technique aims to find. Therefore, TIP is not a proper method for autonomous aerial inspection of photovoltaic plants.

The boundary extraction is referred to as an image segmentation technique. This technique divides an image into a set of regions, and it is performed by dividing the image histogram into optimal threshold values [28,29]. The aim is to substitute the representation of an image into something easily analyzable to obtain detailed information on the region of interest in an image and aid to annotate the scene of the object [30]. Image segmentation is necessary to identify the content of the photo. Accordingly, edge detection is an essential tool for image segmentation [31] and can be achieved by means of traditional image processing techniques [27,32] or through artificial vision techniques [33].

The image segmentation techniques with TIP were developed to identify objects such as the area of PV Plants out of an orthophoto [10,34,35]. Later, the Machine Learning (ML) and Deep Learning (DL) image segmentation techniques, also known as semantic segmentation, were proposed [36,37]. In semantic segmentation each pixel is labeled with the class of its enclosing object or region [33]. Convolutional Neural Networks have been used for semantic segmentation , such as the Fully Convolutional Network (FCN) model [33], and U-Net network model [38], which drastically enhances the segmentation certainty compared with TIP method results, and ML technique results [36,37].

The convolutional neural networks are used for extracting dense semantic representations from input images and to predict labels at the pixel level. To perform this task, it is necessary to obtain or create a dataset, perform a pre-processing of the data, select an appropriate model and train it based on metrics, and then evaluate the results as shown in [11]. This is a fundamental challenge in computer vision with wide applications in scene interpretation, medical imaging, robot vision, etc. [39]. Once the segmentation is done, the next step is to obtain the automatic Coverage Path Planning (CPP).

Although advances in GPS systems have improved and accuracy is around 10 cm in low-cost Real Time Kinematics (RTK) GPS systems [40]. Most of the projects use software tools that provide companies like Mission Planner [41] or development groups as Qground-Control [42]. These tools are based on simple polygonal coverage areas and a coverage pattern of zigzag path. They require time when the area is of complex geometry, or when the plant is in continuous expansion. Additionally, the programmer preloads waypoints without optimal coverage. As a consequence, to develop a real-time path-planning algorithm for an autonomous monitoring system, it is a hard task in this platform. Therefore, it is first necessary to determine the boundary of the PV plant. By taking out the boundaries of PV plants, aerial photogrammetry and mapping can be faster, effective, economical and customizable [27], they motivate to make this work.

The key contributions of this work are as follows:


This paper is structured as follows. In Section 2, the necessary definitions and techniques to obtain the results are described. In Section 3, the three techniques implemented for boundary extraction are compared to show the best method. Finally, in Section 4 some conclusions are shown.

#### **2. Materials and Methods**

#### *2.1. Samples Collection*

Before the segmentation, training samples were collected, based on the orthoimage and PV plant on-farm, rooftop, and roof photos. The samples collected to cover the spectral variability of each class of PV panel and consider the lighting variation in the scene, also in different parts of the world. For CNN, the samples were converted in a tagged image file format (.jpg) file and mask image file format (.png) with a shape of 240 × 320. The total of this dataset was found in the Amir dataset [43].

#### *2.2. Boundary Extraction Procedure*

UAVs must have a precise set of coordinates to define the coverage path planning correctly and thus fly over the total area of PV Plants in the inspection mission. To achieve this task automatically, it is necessary to explore how to extract the boundary of photovoltaic facilities with some techniques. There is a process called semantic segmentation, where each pixel is labeled with the class of its enclosing object or region, which can extract the PV Plants as a particular object in an image [11], but with the constraints that this work addresses. Two techniques have been implemented so far: Traditional Image Processing (TIP) [10] and Deep Learning (DL) [11]. Figure 1 shows the steps followed to reach that result by TIP and DL-based techniques.

**Figure 1.** Steps of boundary extraction by image analysis with two techniques.

#### *2.3. Traditional Image Processing (TIP)*

The process to obtain the boundary pixels of a target can be achieved by means of traditional image processing techniques with functions that extract, increase, filter, and detect the features of an image and obtain its segmentation [27,32]. The main stages were used to remove the borders of PV plants out of an image, as shown in Figure 1 [10]. In the first stage, the original image was filtered using "filter2D" function from OpenCV, that is a convolution filter with 5 × 5 averaging filter kernel, as shown at Algorithm 1. This filter is compound with various Low-Pass Filters (LPF) and High-Pass Filters (HPF). LPF helps in removing noise, blurring images. HPF filters help in finding edges in images.

In the second stage, the filtered image is transformed into the HSV (hue, saturation, and value) representation. The transformation lessens reflection caused by environmental light during aerial image collection. Furthermore, this transformation helps in the colorbased segmentation required in the next stages.

In the third stage, each channel was processed separately to extract the area of the PV plants. This was achieved by applying thresholding operations on the HSV image. To extract the PV blue color out of the image, the HSV range limits for thresholding where determined: from (50, 0, 0) to (110, 255, 255). Thresholding was implementing using the inRange function of OpenCV.

At the fourth stage, two morphological operators were applied: the "erode" and "dilate" functions. Together these operations helps to reduce noise and to better define the boundaries of the PV devices, the application of erosion followed by dilation is also known as opening operation. Erosion and dilation requires an structuring element (also known as kernel) to be applied to the images. In this case, a rectangular kernel of 2 × 2 pixels (MORPH\_RECT,(2, 2)) was used for both operations. Lines 13, 14 and 15 from Algorithm 1 show the creation of the structuring element and the successive use of the erode and dilate functions.

Then, the "findCountours" function was used to help in extracting the contours from the image. The contour can be defined as a curve joining all the continuous points in the boundary of the PV installation. The input parameters for this function are: the image (dilated image from previous stage), the type of contour to be extracted (in this case only the external contours, RETR\_EXTERNAL) and the contour approximation method (in this case not approximation, CHAIN\_APPROX\_NONE). Finally the area was recognized using a multi-stage algorithm to detect a wide range of edges in images, known as the Canny edge detection "Canny" [44].

The pseudo-code of the Traditional Image Processing is shown in Algorithm 1, and was implemented in Python 3 using OpenCV library.

#### **Algorithm 1:** TIP algorithms


#### *2.4. Deep Learning*

Another approach to ascertain the boundaries of PV plants uses a DL-based technique which consists of several steps:

#### 2.4.1. Data Specifications

The first step is to select the data for training the Neural Networks. The parameters to take into account are: PV Plants in orthophotos and aerial images with the respective masks for each image [11].

#### 2.4.2. Data Understanding

The data preparation phase can be subdivided, into at least four steps. The first step is data selection inside the dataset. The second step involves correcting the individual data, which are assumed to be noisy, apparently incorrect, or absent. The third step involves resizing the data as needed. Finally, most of the available implementations assume that the data are given in a single table, so if the data are in several tables, they must be parsed together in a single one [45].

#### 2.4.3. Modeling

In the literature, the semantic segmentation task has many existing models that can be selected for the desired task. In this work, two methods based on deep learning have been selected, taking into account the following criteria: the most competent for the type of task, the amount of data to be processed, the execution time, and the ease of implementation to predict each label for each pixel. The methods were selected according to [11,46–49]. The FCN model was the first one selected, which was proposed by [33] and used by [11]. The network architecture is delineated in Figure 2. The second one is the U-Net model, first

proposed by [38] and selected for this project. The network architecture is illustrated in Figure 3.

(a). Fully Convolutional Network (FCN) model: This model has two blocks. The first block is a series of 13 layers in order to create a modified version of a VGG16 backbone Figure 2, which was introduced for the first time by [50]. The VGG16 backbone has 16 convolutional layers and its creators belong to the team "Visual Geometry Group", hence its name VGG16. The backbone is the network that takes the image as input and

extracts the feature map upon which the rest of the network is based. The second block consists of a series of deconvolutional layers that simply reverses the forward and backward passes of convolution. The last layer uses a softmax function to predict the probability of the category as shown in Figure 2. As a result, the input of FCN model is an RGB image, and the output is the predicted mask of the PV plants. For more details, read [33]. The parameters for the training process were depicted in Table 1.

(b). The U-net network model: This model has two blocks: a decreasing path and an increasing path, respectively, which gives it the u-shaped architecture or horizontal hourglass shape [51]. The decreasing path is a typical convolutional network that consists of repeated application of convolutions, each followed by a rectified linear unit (ReLU) and a max-pooling operation. During the decrease, the spatial information is reduced whereas feature information is increased. The increasing pathway combines the feature and spatial information through a sequence of upsampling layers followed by two layers of transposed convolution for each step [38,52], as illustrated in Figure 3. The parameters for the training process were depicted in Table 1. Its architecture is shown in Table 2. The platform used for FCN and Unet models by this work was Tensorflow with Keras backend [53]. The U-net model had never been used for this kind of application so far.

**Table 1.** Summary of the FCN and U-net model parameters for the training process.


The FCN and U-net models additionally have a binary cross-entropy function (*Hp*) to calculate the loss in the process of training the neuronal network [54]. As the problem at hand is a semantic segmentation task, Equation (1) is used. This function examines each pixel and compares the binary-predicted values vector with the binary-encoded target vector.

$$H\_p(q) = -\frac{1}{N} \sum\_{i=1}^{N} y\_i \cdot \log(p(y\_i)) + (1 - y\_i) \cdot \log(1 - p(y\_i)) \tag{1}$$

where *y* is the label of each pixel, it takes the value of 1 for the PV plants area and 0 to indicate other areas or elements, and *p*(*y*) is the probability of the pixel belonging to the PV plants area for all *N* points. The Adam optimization function is used to optimize the models [55]. Because semantic segmentation is the task at hand, it is essential to implement metrics to ensure the model performs well.

**Table 2.** Architecture of the U-net.




#### 2.4.4. Metrics

The metrics evaluate the similarities between the predicted mask (N) and the original mask (S). Such similarity assessment can be performed by considering spatial overlapping information, that is, by computing the true positives (TP), false positives (FP) and false negatives (FN) given by *TP* =|*N* ∩ *S*|, *FP* = *N* \ *S* , and *FN* = *S* \ *N* , respectively.

There are three standard metrics commonly employed to evaluate the effectiveness of the proposed semantic segmentation technique [29,48,49,56]. The three metrics, namely, pixel accuracy (Acc), region Intersection over Union (*IoU*), and Dice Coefficient (*DC*).

Pixel accuracy is the ratio of correctly classified PV plants pixels to the total number of PV plants pixels in the original mask image [57], which can be mathematically represented as Equation (2).

$$Accuracy = \frac{TP}{TP + FN} \tag{2}$$

The *IoU* metric (the Jaccard index) is defined by Equation (3). This equation is a ratio between the intersection of the predicted mask *N*, and the original mask *S* and the union of both. More details can be found in [58].

$$IoU(N, S) = \frac{|N \cap S|}{|N \cup S|} = \frac{TP}{TP + FP + FN} \tag{3}$$

The *DC* metric [56,58,59] is expressed as Equation (4). This equation divides the intersection of the predicted mask *N*, and the original mask *S* times two by the sum of *N* and *S*.

$$D\mathbb{C}(N,\mathbb{S}) = \frac{2.|N \cap \mathbb{S}|}{|N| + |\mathbb{S}|} = \frac{2.TP}{2.TP + FP + FN} \tag{4}$$

To validate the results of the techniques described above, the FCN and U-net models were trained and their performance was evaluated by validating and testing samples of the Amir dataset [43]. The next section describes such results and compares the models in detail.

#### **3. Results and Discussion**

#### *3.1. Database Specification*

For this work, the DeepSolar [60], Google Sun-Roof [61], OpenPV [62], and Amir's databases were accessed [43]. Only the last database met the established parameters. It contained PV plants in orthophotos and aerial images with their respective masks. Furthermore, the PV plants images were from different countries around the world. Therefore, the "Amir" dataset was selected.

#### *3.2. Results with TIP Technique*

The results obtained in this work were compared with the results obtained in previous investigations where the TIP and the deep learning techniques were used alongside the FCN model [11].

The stages to obtain the results are shown in Figure 4. In the First Stage, a 2D filter was applied, depicted in Figure 4a. In the second stage, the filtered image is transformed into the HSV representation, Figure 4b. In the third stage, the blue color was filtered out, Figure 4c. At the fourth stage, the opening function was used, as seen in Figure 4d. Finally, the area was recognized using the canny method illustrated in Figure 4e. The results were satisfactory and can be modified depending on the environment.

The results are shown in Table 3. The TIP technique was obtained by randomly selecting images out of the test dataset, then applying the functions described in the methodology section (Section 2), and finally comparing the mask obtained with the original mask. The *IoU* metric obtained was 71.62% and the *DC* was 71.62%.

**Figure 4.** Steps of boundary extraction by TIP.

#### *3.3. Results with DL-Based Techniques*

The training data consisted of 2864 aerial images selected at random: 90% of the training dataset in the Amir database. The validation data were the remaining 10% of the same training dataset. Figure 5a shows the loss function and *IoU* metric of the FCN model during the training and validation process. The general trend of the two curves is consistent, showing that the network converges rapidly and is stable at iteration 30, and the loss value tends to 0.04%. Figure 5b shows the *DC* metric of the model during the training and validation stage. The general trend of the two curves is consistent at iteration 30.

On the other hand, using the same metrics, the U-net model proposed in this work shows a better performance. Figure 6a shows the loss function and *IoU* metric of the model during the training and validation stage. The common trend of the two curves shows the network converges quickly and is stable at iteration 16, and the loss value tends to 0.03%. Figure 6b shows the *DC* metric of the model all along the training and validation phase. The prevalent trend of the two curves is consistent and in iteration 16.

**Figure 5.** Performance and metrics of the FCN model using the training and validation sets.

**Figure 6.** Performance and metrics of the U-net model obtained using the training and validation sets.

In the evaluation stage, 716 images were used along with the trained FCN model for PV plant detection. Some relevant results are shown in Figure 7. In this figure, the columns correspond to different PV plants. The first row contains the original images; the second row, the original masks; and, the third one, the predicted masks. The images used were taken in deserted regions and vegetation zones. The FCN model detects the PV plants in vegetation zones with some false positives. As an example, the second and third predictions of Figure 7 identify a lake and vegetation as part of the PV plants. In deserted regions, PV plants are detected more precisely. Although these images have very high precision, their predicted shape does not fully correspond to the original mask. Hence, it was necessary to review the performance metrics of the algorithm [63].

The segmentation results in the evaluation stage, using the same 716 images and the trained U-Net model, are shown in Figure 8. The arrangement is the same as in the previous Figure 7. It is noteworthy that this model correctly segments the photovoltaic plant while the other model does not achieve this result, as can be seen in the second and third predictions in Figure 8.


**Figure 7.** Evaluation with test data FCN Model.

**Figure 8.** Evaluation with test data U-net Model.

Afterwards, the trained model tested 716 samples. Table 3 shows the results and comparison among the TIP technique, the U-net proposed model and the FCN model used by [11], which was replicated in this study. The FCN and the proposed U-net models were

compared. The accuracies obtained for the FCN model in the stages of training and testing were 97.99% and 94.16% respectively [11]. For U-Net proposed, the accuracy obtained in the stages of training and testing were 97.07% and 95.44%, respectively. Both results can be seen in Table 3.

To compare the FCN model proposed by Amir [11], and the U-net model proposed in this work, the two most used metrics in semantic segmentation problems were used. The FCN model was implemented with the standard *IoU* metric, whose result for the training stage was 94.13%,and the validation stage was 90.91% and for test stage was 87.47%. The *DC* metric of the validation 92.96% and test 89.61% which deviates a little from the training 95.10%. However, using the same metrics the U-net model proposed in this work shows a better performance. The *IoU* metric obtained was 93.57% in the training stage, 93.51% in the validation stage, and 91.42% in the test stage. The *DC* metric of the validation 94.44% was almost the same as that of the training 94.03% which deviates a little from the test 91.42%. Table 3 shows these results. Due to this, a difference was found between the FCN and U-net model for the first metric of 2.95% and for the second metric used of 1.81% difference was calculated. All files and logs from the experiments are available at GitHub in [64].


**Table 3.** Comparison between three techniques.

#### *3.4. Discussion*

The U-net model proposed reconstructs the segmented image and protects the original image shape characteristics by storing the grouping indices of the max-pooling layer, a process that is not done in the FCN model.

The training and testing accuracy is the percentage of pixels in the image that are classified correctly and cannot be taken as indicators of how similar the predicted PV plants and the original mask are [65]. For the purpose of comparing the similarity in the results, the *IoU* metric was used. This metric varies from 0 to 1 (0–100%) with 0 meaning no similarity and 1 meaning total similarity between original and predicted masks [63].

The U-net model proposed in this work aimed to obtain a value closer to 1 in the *IoU* metric. The iteration times show the model used is faster and therefore reliable for the training and processing stages obtaining results virtually in real time [66]. The *DC* is the other metric used in this work. This metric also ranges from 0 to 1, with 1 signifying the greatest similarity between the predicted and original masks [63]. Both metrics were used to determine if the U-net model was better than the FCN model in the validation and test stages. The values of the *IoU* and Dice metrics in Table 3 showed the U-net model had a better performance when compared to the FCN model. This work was implemented with VGG16 as an encoder because it was the encoder used by Amir [11], which is a comparison work, but in future work, it is possible to use other encoders like ResNet, AlexNet, etc. [37].

Finally, the results obtained with the TIP and FCN model agree with the results obtained by other authors [11,13]. The authors mentioned they did not use the standard metrics for these kinds of problems and the bias in the results were expected. On the contrary, this work did take these metrics into account and found satisfactory results. The U-net network increased the processing speed, veracity in the segmentation process, and the overall performance of the model.

#### **4. Conclusions**

This work used three techniques, namely, the TIP technique, the DL-based FCN and U-net models. This work applied the U-net model to PV plants. All the models were used for the extraction of the PV plants boundaries out of an image. As a consequence, the TIP technique can be very precise but requires constant adjustment depending on the image, whereas the FCN and U-net network models are more useful when it comes to unknown PV plants.

The U-net network model is novel for this kind of problem. It allows greater processing speeds and performance when predicting the area of PV plants, also better features. The results obtained open the door for further investigation of this model in this problem.

The U-net technique turned out to be satisfactory compared to the TIP technique and the FCN model used in previous studies. The values obtained in the implemented metrics guarantee that the areas predicted for the PV plants are similar to the real ones. The results also help to predict possible false positives, such as lakes in the vicinity of photovoltaic plants. The relevant features of an object can be obtained using this technique while using the FCN technique is not possible.

**Author Contributions:** Conceptualization, A.P.-G., Á.J.-D. and J.B.C.-Q.; methodology, A.P.-G.; software, A.P.-G.; validation, A.P.-G.; formal analysis, A.P.-G.; investigation, A.P.-G.; resources, A.P.-G., Á.J.-D. and J.B.C.-Q.; data curation, A.P.-G.; writing—original draft preparation, A.P.-G.; writing—review and editing, A.P.-G., Á.J.-D. and J.B.C.-Q.; visualization, A.P.-G.; supervision, Á.J.-D. and J.B.C.-Q.; project administration, Á.J.-D. and J.B.C.-Q.; funding acquisition, A.P.-G., Á.J.-D. and J.B.C.-Q. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Colombia Scientific Program within the framework of the so-called Ecosistema Científico (Contract No. FP44842-218-2018).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The models used in the computational experiment are available at GitHub in [64].

**Acknowledgments:** The authors gratefully acknowledge the support from the Colombia Scientific Program within the framework of the call Ecosistema Científico (Contract No. FP44842-218-2018). The authors also want to acknowledge Universidad de Antioquia for its support through the project "estrategia de sostenibilidad".

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **List of Symbols**


#### **Abbreviations**

The following abbreviations are used in this manuscript:


#### **References**


## *Article* **Generation of Data-Driven Expected Energy Models for Photovoltaic Systems**

**Michael W. Hopwood 1,2 and Thushara Gunda 1, \***


**\*** Correspondence: tgunda@sandia.gov

**Abstract:** Although unique expected energy models can be generated for a given photovoltaic (PV) site, a standardized model is also needed to facilitate performance comparisons across fleets. Current standardized expected energy models for PV work well with sparse data, but they have demonstrated significant over-estimations, which impacts accurate diagnoses of field operations and maintenance issues. This research addresses this issue by using machine learning to develop a data-driven expected energy model that can more accurately generate inferences for energy production of PV systems. Irradiance and system capacity information was used from 172 sites across the United States to train a series of models using Lasso linear regression. The trained models generally perform better than the commonly used expected energy model from international standard (IEC 61724-1), with the two highest performing models ranging in model complexity from a third-order polynomial with 10 parameters (*R* 2 *adj* = 0.994) to a simpler, second-order polynomial with 4 parameters (*R* 2 *adj* = 0.993), the latter of which is subject to further evaluation. Subsequently, the trained models provide a more robust basis for identifying potential energy anomalies for operations and maintenance activities as well as informing planning-related financial assessments. We conclude with directions for future research, such as using splines to improve model continuity and better capture systems with low (≤1000 kW DC) capacity.

**Keywords:** photovoltaic systems; expected energy models; fleet-scale; lasso regression; performance modeling; machine learning

#### **1. Introduction**

The increasing penetration of photovoltaic (PV) systems within the energy markets has established the need for evaluating and ensuring high system reliability. In particular, a large emphasis has been placed on monitoring algorithms that can contextualize observed energy generation at a site with information about how the system would have performed in a nominal state [1]. The latter are commonly estimated through expected energy models. Expected energy models are incorporated into many PV performance monitoring tasks, including anomaly detection [2–5], financial planning [6], fleet-level (site vs. site) comparisons [7], degradation analysis [7], and the evaluation of extreme weather effects [8]. The comparison of observed energy values to those derived from expected energy models serves as the basis for informing both tactical (i.e., short-term tasks such as field repair) and strategic (i.e., long-term activities such as site planning) operations and maintenance (O&M) activities.

Expected energy models can vary from asset-level to site-level estimates [9]. Assetlevel models typically focus on using parameters provided by the manufacturer (e.g., maximum power) [9,10]. However, such approaches do not always work well for in-field performance since the parameters were developed in standardized test conditions and thus do not reflect operational conditions [11]. In response to these limitations, empirical methods that use field observations and regression methods have emerged to derive parameters across non-standardized test conditions (e.g., [12,13]). At the site-level, most expected

**Citation:** Hopwood, M.W.; Gunda, T. Generation of Data-Driven Expected Energy Models for Photovoltaic Systems. *Appl. Sci.* **2022**, *12*, 1872. https://doi.org/10.3390/app12041872

Academic Editor: Giovanni Petrone

Received: 23 December 2021 Accepted: 31 January 2022 Published: 11 February 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

energy models leverage the correlation between power production and meteorological covariates [14,15]. For example, the standard expected energy model from the International Electrotechnical Commission (IEC) uses irradiance and site capacity information to develop an expected energy estimate [15]. Similarly, the PVUSA model trains a regression model for a given site by estimating power production using local irradiance, temperature, and wind speed conditions [16]. Industry research shows that most expected energy estimates tend to be overestimate production by a median of 3% but could be up to 20% [17]. Although the mismatch between observed and expected generation are well-recognized [18], limited attention has been given to date for improving the accuracy of expected energy models at the site-level, especially suited for fleet-level (i.e., site vs. site) comparisons.

This work aims to address this knowledge gap by generating a standardized, interpretable data-driven expected energy model that can be used for fleet-level comparisons. Although gradient-boosted and neural network-based methods have demonstrated significant successes for output performance [19–21], they often lack in model interpretability. In particular, models with high complexity can hide prediction biases or other vulnerabilities [22]. Thus for this work, we opted for more interpretable, regression-based models to increase the transparency of the implemented methods. In addition to identifying a more robust alternate for expected energy modeling, the associated publication of code used for training models (in the open source software pvOps) enables the extension of these methods to develop site-specific expected energy models for PV systems anywhere in the world or to other renewable energy systems. Such advancements in expected energy model estimates are needed to continue supporting better planning and field O&M activities, both of which ultimately influence the sustainability of PV sites. The following sections describes the data processing and model construction activities (Section 2), the performance of trained models (Section 3), and summarize primary findings (Section 4).

#### **2. Methodology**

The data-driven expected energy model training activities were supported by Sandia National Laboratories' PV Reliability, Operations, and Maintenance (PVROM) database [23]. Information about the PVROM database, as well as data processing, model training, and model evaluations, are described in the following Sections.

#### *2.1. Data*

The PVROM database contains 1.3 million data points of hourly production data across 176 sites in the United States [23], spanning multiple states (Figure 1) and generally ranging between 2017 and 2020. The database contains hourly measurements of expected energy in kiloWatt-hours (kWh), irradiance (Watts per square meter; <sup>W</sup> m<sup>2</sup> ), ambient temperature, and module temperature; site-level direct current (DC) capacity is provided by the industry partners. The DC capacity (*CDC*) for the sites within the database span from 37.8 kilowatts (kW) to 130,000 kW; a majority of the sites (140) are under 10,000 kW, with 67 of those sites under 1000 kW. A subset of the sites (100) contain industry-partner-provided expected energy estimates generated from proprietary models; these values serve as a basis for model validation activities (see Section 2.5).

**Figure 1.** Geographical coverage of sites within the PVROM database. A majority of the sites are located in California.

#### *2.2. Preprocessing*

Data quality issues stemming from measurement errors and system anomalous conditions (reflecting local field failures, such as communication loss) could introduce signal variations in field data that would hinder model performance. Problematic data convolute the relationships between features, making it more difficult to measure the true parameter estimates; these potential irreducible errors are decreased through numerous data quality filters (Figure 2). Missing values (i.e., NaN or None values) were removed prior to applying data quality filters. An evaluation of these missing values revealed that a majority of them (~88%) occurred during nighttime hours (~7 p.m. to 8 a.m.), indicating that some sites captured night-time entries as null (Figure 2). After removing these missing values, ~900 K data points remained, which were then subject to a series of data quality filtering steps.

**Figure 2.** Data preprocessing activities included both data quality- and anomaly-related filters. Data quality filters were conducted independently; only data points that passed all quality-based filters were subject to the anomaly-based filters.

Data were filtered to ensure they are within nominal sensor ranges, using thresholds following [24] and the IEC 61724-1 standard [15]. Specifically, we retained data that met the following criteria:


Wind speed was not consistently available from partners and thus was excluded from analysis. Although available temperature data were used in the preprocessing steps, they are not used as a predictor variable in the regression models, since they ate not included in current standard models [15].

Flatlining values—determined by periods where consecutive data changed by less than a threshold—were flagged for removal using the pecos package [25], which follows the IEC 61724-3 standard [26]. Specifically, four consecutive hours with either ∆*E* < 0.01% of the site's capacity or ∆*I* < 10 W <sup>m</sup><sup>2</sup> were filtered. Lastly, inverter clipping, which occurs when the DC energy surpasses an inverter's DC energy rating, was addressed by mathematically observing plateaus in the energy signal using the pvanalytics package [27]. Dropping energy measurements during inverter clipping, which manifest as a static value across high irradiance levels, would create a better linear fit. After data quality checks, 429 K data points across 150 sites remained (Figure 2).

Data points that passed all quality checks were also assessed for system-level anomalies. These anomalies likely reflect abnormal operating conditions (i.e., local failures) and thus require removal to ensure the trained baseline energy models reflect nominal system performance. Anomalous entries were detected using a comparison of observed energy to irradiance and site capacities (Figure 3). The comparison of observed energy and irradiance filter focuses on removing data where the E–I ratio (*λ*) is outside its nominal distribution by 3 standard deviations {*<sup>λ</sup>* : *<sup>λ</sup>* <sup>&</sup>lt; *<sup>µ</sup><sup>λ</sup>* <sup>−</sup> <sup>3</sup>*σ<sup>λ</sup>* <sup>∪</sup> *<sup>λ</sup>* <sup>&</sup>gt; *<sup>µ</sup><sup>λ</sup>* <sup>+</sup> <sup>3</sup>*σλ*}, where *<sup>µ</sup><sup>λ</sup>* and *<sup>σ</sup><sup>λ</sup>* are the mean and standard deviation of the E–I ratio, respectively [28]. This filter was implemented for each site separately to capture site-specific variations (including system capacity) and resulted in the removal of 70 K data points (Figure 2). The second system anomaly filter focused on removing sites with mismatches between observed energy and site capacity. Namely, if a site's maximum recorded energy was over 1.2 × *CDC* or under 0.7 × *CDC*, then all data points for that site were excluded from subsequent analysis. This method filtered 23 sites; 50%+ of these sites were under 1000 kW, and only 1 was over 10,000 kW. Approximately 26 K data points were removed with this filter, resulting in a final dataset that contained 332 K data points across 127 sites for model training and testing activities (Figure 2). The age of the sites within the final dataset ranged from newly installed sites up to 10 years, with a majority being less than 5 years in age (Figure A2).

**Figure 3.** An example of anomaly-based filter (energy production vs. irradiance) for a particular site. Anomalous data points (visualized as Xs) are often lower than non-anomalous values within the distribution-derived bands (red lines).

#### *2.3. Variable Standardization*

The specific inputs used for model training mimic commonly available parameters used in current expected energy models (e.g., [15]), such as irradiance and site capacity. However, with covariates at different scales (e.g., {0 W <sup>m</sup><sup>2</sup> <sup>&</sup>lt; *<sup>I</sup>* <sup>&</sup>lt; 1.2 <sup>×</sup> <sup>10</sup> 3 W <sup>m</sup><sup>2</sup> } while {1 × 10 <sup>2</sup> kW<sup>&</sup>lt; *<sup>C</sup>DC* <sup>&</sup>lt; 1.3 <sup>×</sup> <sup>10</sup> <sup>5</sup> kW}), variable standardization is required to reduce model sensitivity to parameter scales. In particular, without standardization, weights generated

for each parameter are more likely to reflect scalar nuances rather than the relative importance of the parameter to the outcome of interest. Variable standardization centers the data by subtracting data points in a feature from its associated mean value (*µ*) and then scales the data by dividing by the associated standard deviation (*σ*)—i.e., *Z* = *µ*−*µ*¯ *σX* . The resulting standardized variables have a mean of zero and a standard deviation of one. This process makes parameters easier to rank in terms of influence; the variable with the larger parameter holds a more important effect on the output response. Thus, variable standardization also aids in the interpretability of the derived parameters, especially when variable interactions (e.g., *I* × *CDC*) are introduced. The mean and standard deviation parameters used to standardize irradiance, capacity, and energy values are captured in Table 1.

**Table 1.** Mean and standard deviation (StDev) parameters used to standardize variables prior to training regression models.


#### *2.4. Model Design and Training*

Similar to other machine learning models, regression techniques leverage input data to learn relationships and use those relationships to predict unseen quantities. These relationships are generally contained in model parameters (*β*ˆ), which map predictors, as summarized in a design matrix **X**, to an output *Y*ˆ = **X***β*ˆ + *ǫ* with residual model error *ǫ*. Many different regression techniques exist; these techniques typically vary in the structure of the cost function, which quantifies the error between predicted and expected values. This cost function (*C*) is usually captured as a summation of loss functions (calculated on each data point) across the training set. The set *β*ˆ, which renders the smallest cost, is defined as the learned parameters, mathematically notated as:

$$
\hat{\boldsymbol{\beta}} = \underset{\boldsymbol{\theta}}{\arg\min} \,\mathsf{C}.\tag{1}
$$

A popular regression model is the ordinary least squares (OLS), which defines its best model (*β*ˆ*OLS* = *arg* min *θ SSE*) with an objective function equal to the sum of squared errors (*SSE*):

$$SSE = \sum\_{i=1}^{n} (y\_i - \hat{y}\_i)^2 = \sum\_{i=1}^{n} (y - \sum\_{j=0}^{p} \hat{\beta}\_j \mathbf{x}\_{ij})^2 \tag{2}$$

where *n* is the number of samples, *p* is the number of predictors, and *xij* is the *i th* value for the *j th* explanatory variable. As shown in the equation, the *SSE* sums the squared difference between each sample (*y*) and its associated model estimate (*y*ˆ). High emphasis is naturally placed on reducing high-error samples. Therefore, outliers can have a large effect on the learned parameters, so data preprocessing steps are required for robust model development. Additionally, OLS renders non-zero coefficients on all *β*ˆ, which can create small, insubstantial parameters which are likely components of the training dataset and therefore contribute to model overfitting and thus should be removed from the model.

Alternate approaches to OLS include the Theil–Sen regressor [29], which is robust against outliers since it chooses the median of the slopes of all lines between pairs of points, as well as techniques such as Lasso regression [30] that explicitly address model overfitting by reducing model complexity (i.e., the number of parameters used). For this analysis, the latter was selected since Lasso regression models are able to incorporate both parameter regularization and residual sum of squares into the loss function. The cost function for

Lasso regression *β*ˆ *lasso* = *arg* min *θ* (*SSE* + *α* ∑ *p j*=1 |*βj* |) incorporates an L1 regularization *p*

term *α* ∑ *j*=1 |*βj* |, which penalizes the magnitude of the *β* terms. This penalization tends to shrink coefficients to zero, rendering a more parsimonious model; we use an *α* = 0.003 for defining the impact of the regularization on the regression kernel. Specifically, the penalization acts as a bias, which in turn can reduce overall error due to the bias–variance tradeoff [31].

Standardized variables are passed into Lasso regression to learn a linear model, which relates the input variables to energy. Multiple combinations of input variables were used to train the regression models (more details below). For all models, a randomized (80–20%) split is utilized to partition the preprocessed, standardized data into train and test partitions, respectively.

In addition to individual parameter influences, interactions and temporal factors were incorporated as input features to capture nuances within the datasets. Interaction parameters, which allow the effect of one parameter on the response variable to be weighted by the value of another variable, are introduced by including terms which are the product of two or more predictor variables. For example, Figure 4 shows that the relationship between *E* and *I* does vary across *CDC*. Thus, the inclusion of an *I* and *CDC* interaction term may be helpful in predicting the generated energy. The suite of interaction combinations are instantiated using polynomial models up to the third order (i.e., degree *d* = 3). In a model with *d* = 2 and 2 covariates, the initiated regression model would take the following form:

$$y = \beta\_0 + \beta\_1 \mathbf{x}\_1^2 + \beta\_2 \mathbf{x}\_2^2 + \beta\_3 \mathbf{x}\_1 \mathbf{x}\_2 + \beta\_4 \mathbf{x}\_1 + \beta\_5 \mathbf{x}\_2. \tag{3}$$

Notice that a *d* = 2 also includes *d* = 1 parameters (i.e., *β*4*x*<sup>1</sup> and *β*5*x*2). This remains true for all values of the polynomial power (e.g., for a model initiated with *d* = 3, terms from *d* = 2 and *d* = 1 are also included). Two interaction polynomial orders are tested: a second-order (*d* = 2) and a third-order (*d* = 3) (Table 2). The particular interaction noted above (*I* × *CDC*) is captured in multiple models, including an additive model with a single interaction term (Table 2).

In addition to interactions, temporal factors are used to capture a variable's changing effect on the energy generated over time. For instance, the correlation between *I* and *E* changes over the course of the year due to spectral irradiance effects [32,33]. Therefore, allowing the model to capture time-variant nuances may be important for capturing such nonlinearities. Three temporal based conditions were explored: seasonal (four per year), monthly, and hourly. A model with two predictor variables and monthly temporal-based variable conditions would be instantiated as:

$$\begin{aligned} y &= a\_{\text{jan}} \mathbf{1}\_{t \in \text{jan}} \mathbf{x}\_1 + a\_{feb} \mathbf{1}\_{t \in feb} \mathbf{x}\_1 + \dots + a\_{dec} \mathbf{1}\_{t \in dec} \mathbf{x}\_1 \\ &+ b\_{\text{jan}} \mathbf{1}\_{t \in \text{jan}} \mathbf{x}\_2 + b\_{feb} \mathbf{1}\_{t \in feb} \mathbf{x}\_2 + \dots + b\_{dec} \mathbf{1}\_{t \in dec} \mathbf{x}\_{2\prime} \end{aligned} \tag{4}$$

where the *a* and *b* parameters are coefficients describing the effect of parameter *x*<sup>1</sup> and *x*2, respectively, when conditioned on a month of the year. For instance, *ajan* describes the effect of *x*<sup>1</sup> on the *y* response variable during the month of January. The indicator function 1*<sup>t</sup>* masks the predictor variable to ensure it is within its timeframe. With the various combinations of interactions and temporal conditions, a total of 13 regression kernels were evaluated (Table 2; see Appendix A for some of the mathematical formulations).

**Figure 4.** Correlation between energy production and irradiance for raw data (**a**) and preprocessed data (**b**) for different site capacities. Higher correlations in the preprocessed data indicate interaction between DC capacity and irradiance for energy production.

**Table 2.** Combinations of parameters used to initiate the 13 regression kernels evaluated in this study. The simple additive model attaches a parameter to each predictor variable to evaluate individual effects. \* For hourly temporal conditions, only 15 h are used to reflect daytime hours.


#### *2.5. Model Evaluation*

Three metrics were used to evaluate the performance of the trained expected energy models: logarithmic root mean squared error (log *RMSE*), coefficient of determination (*R* 2 ), and percent error (*δ*). Both partner-provided expected energy values and those calculated by the leading standardized expected energy model (i.e., IEC 61724) were used as reference values for model evaluations.

The root mean squared error (*RMSE*) is a common goodness-of-fit statistic used for model evaluation. The *RMSE* is expressed as:

$$RMSE = \sqrt{\frac{1}{n} \sum\_{i=1}^{n} (y\_i - \mathcal{y}\_i)^2}$$

where *y<sup>i</sup>* and *y*ˆ*<sup>i</sup>* are the measured and predicted values of the response variable, and *n* is the number of samples. *RMSE* is in the same units as the response variable (i.e., kWh). Lower *RMSE* values indicate a better, lower predicted error. Because the error can be quite large in magnitude (10<sup>0</sup> to 1010), a logarithmic transform is applied to facilitate evaluations. Because the magnitude of the error is closely connected to a site's capacity, the log *RMSE* cannot be used to compare model performance between sites unless the sites are similar in size.

The coefficient of determination (*R* 2 ), however, can be used to compare model performance across different site sizes. Specifically, *R* 2 is calculated as:

$$R^2 = 1 - \frac{\sum (y\_i - \mathcal{Y}\_i)^2}{\sum (y\_i - \mathcal{Y})^2},\tag{5}$$

where *y*¯ is the average of the *y* values. *R* <sup>2</sup> denotes the proportion of variability in the response explained by the model with a value of 1, indicating a perfect fit. *R* <sup>2</sup> was used to compare trained model outputs with partner-generated expected energy values, whose underlying model structures were unknown.

Generally, however, *R* 2 is not well-suited for comparing models across varying numbers of parameters. Thus, when comparing the 13 trained models to one another, we utilize an adjusted *R* 2 *adj* metric, which checks whether the added parameters contribute to the explanation of the predictor variable and penalizes models with unnecessary complexity [34]. Low-effect parameters (i.e., *β* ≈ 0) reduce the model's overall fit score. The adjusted *R* 2 *adj* is calculated as follows:

$$R\_{adj}^2 = 1 - (\frac{(1 - R^2)(n - 1)}{n - p - 1}),\tag{6}$$

where *n* is the number of samples, and *p* is the number of predictors.

Finally, *δ* was used to capture the directionality of error (i.e., overprediction vs. underprediction):

$$
\delta = 100 \times \frac{\mathcal{Y} - y}{y}. \tag{7}
$$

The log *RMSE* and *R* <sup>2</sup> were implemented to evaluate model performance at both site and fleet (i.e., across multiple sites) levels, while *δ* was only implemented at the fleet level; all metrics were reported on the test dataset. T-tests were used to evaluate significance in performance variations between the trained and reference values.

#### **3. Results and Discussion**

Data processing activities generally increased the correlations between the predictor variables (i.e., irradiance and capacity) and the response variable (i.e., energy) (Table A1). The processed data were inputted into a total of 13 trained models—ranging in model complexity (pre-lasso) from 3 parameters for the 'simple additive' model pre-lasso to 151 parameters for the 'third-order-hour' (see Table 3). Generally, the number of parameters were lower for all models post-lasso fit, except for the 'simple additive' and 'additive interaction' models, likely indicating the already sparse construction of these models.

**Table 3.** This table describes the parameterization and performance of all of the models evaluated in the results of this paper. Wins are summarized by showing the percentage of sites where a given model was the top performer according to the associated goodness-of-fit metric (Adj. *R* <sup>2</sup> or log *RMSE*); the IEC model was used as the reference value for log *RMSE* calculations. The thirdorder interactions model and basic model perform consistently well, a conclusion also found on the heatmaps (Figure 5). Additionally, because lasso regression was leveraged, the models decrease in size after training the model.


Initially, the various models were trained using data across all system sizes. However, this approach demonstrated systemic underperformance for low-capacity systems (<1000 kW DC capacity). Specifically, the best trained models (i.e., 'third-order interactions' and 'additive interaction') outperformed the IEC model in terms of log *RMSE* when tested on every single system above 1300 kW DC capacity; however, 12 of 34 systems below a 1300 kW DC capacity underperformed relative to the IEC model. This result likely reflects the varying relationships between the site DC capacity and the energy generated; systems of higher capacity tend to receive a higher maximum energy generated per DC capacity (Figure A1). To better deal with this varying linearity, two separate sets of models were trained: one for models under 1000 kW DC capacity and another over.

Across both high-capacity and low-capacity systems, models with the *I* × *CDC* interaction term perform better than those without the interaction term (i.e., 'hour', 'month', 'seasonal', and 'simple additive' models). For example, two of the top-performing models (across both high-capacity and low-capacity systems) are the 'simple additive' and the 'third-order interactions' models, both of which contain this interaction term (Table 3 and Figure 5). The 'additive interaction' trained (AIT) model has four parameters:

$$\hat{e} = \begin{cases} 0.07 + 0.69i + 0.65c + 0.42ic & \mathcal{C}\_{DC} < 1000 \text{ kW} \\ -0.06 + 0.29i + 0.76c + 0.40ic & \mathcal{C}\_{DC} \ge 1000 \text{ kW} \end{cases} \tag{8}$$

where *i* and *c* define the standardized irradiance and capacity variables, respectively, as defined in Table 1. The 'third-order interactions' model, on the other hand, contains these four terms as well as higher-order interactions (e.g., irradiance<sup>2</sup> <sup>×</sup> capacity, capacity<sup>3</sup> ). Although the variables within both of these two models are similar to the IEC standard, the inclusion of the interaction term, which highlights that the linear relationship between *I* and *E* is moderated by *CDC* (Figure 4), likely explains the superior performance of these models relative to that standard. The heatmaps of the log *RMSE* values highlight the evaluation metric's dependence on site capacity (Figure 5a,c), while the adjusted *R* <sup>2</sup> heatmaps show consistent performance across site capacity (Figure 5b,d). The vertical concentration of dark bars likely reflects data quality issues not addressed by data preprocessing steps. A comparison of the associated partner generated expected energy estimates to those predicted from models also demonstrates that the AIT-derived estimates have lower average percent errors than the other models and the IEC (Table A2). Further evaluation of 2 years of records at a single site demonstrates that the AIT-derived estimates have a lower standard deviation and do not overestimate as much as the IEC-derived estimates (Figure A3). Given its parsimonious nature, the AIT model is subjected to further evaluation for both highand low-capacity systems.

#### (**a**): Log RMSE for high-capacity systems:

(**c**): Log RMSE for low-capacity systems:

**Figure 5.** High-capacity (**a**,**b**) and low-capacity (**c**,**d**) site-level model evaluations with test data. Models with lighter colors (i.e., low values for log *RMSE* and values closer to 1 for adjusted *R* 2 ) indicate better performance.

#### *3.1. High-Capacity Systems*

For high-capacity systems, a significant (almost uniform) difference is found in both the log *RMSE* and *R* <sup>2</sup> values between the AIT and the IEC reference models (Figure 6a,b). Across the sites, the AIT model improves the goodness of fit by 0.42 in *R* 2 (IEC: 0.501; AIT: 0.93) and 1.16 in log *RMSE* (IEC: 6.99; AIT: 5.83). Generally, there are very few systems for which the IEC model performs better than the trained models (Table 3). The percent error (*δ*), on average, of the AIT model (3.65) is significantly lower than the IEC model (20.86) for high-capacity systems. An evaluation of percent error shows that the AIT generally

performs well (i.e., *δ* ≈ 0 and thinner standard deviation bars) for most irradiance levels, except at the two extremes (i.e., <200 and >1100 W m<sup>2</sup> ) (Figure 7).

The difference in performance relative to the IEC model is especially pronounced for larger system sizes (Figure 6a,b). Although the AIT model appears to show a small improvement over the partner-provided values (Figure 6a,b), a *t*-test concluded that the distributions of both the log *RMSE* (*p*-value: 0.78) and *R* 2 (*p*-value: 0.48) are not significantly different.

**Figure 6.** Model evaluation using log *RMSE* and *R* <sup>2</sup> metrics for high-capacity systems (**a**) and lowcapacity systems (**b**). Data points reflect site-level summaries of associated test data while dotted lines reflect best line fits to support visual pattern identification. The *R* <sup>2</sup> metric was used for this analysis (vs. adjusted *R* 2 ) since partner-provided model architectures are unknown. The 'additive interaction' regression model (in red) is comparable to the partner-provided proprietary values (green) and consistently performs better than the IEC standard (blue), especially at higher capacity values.

**Figure 7.** Percent error as a function of irradiance shows that the 'additive interaction' model outperforms the IEC standard across both high-capacity (**a**) and low-capacity (**b**) systems. Lines indicate mean values, while shaded region captures one standard deviation. The 'additive interaction' model performs best (*δ* ≈ 0) at 500–1100 W <sup>m</sup><sup>2</sup> and at 200–1000 W m<sup>2</sup> for high-capacity and low-capacity systems, respectively.

#### *3.2. Low-Capacity Systems*

The model performance of the AIT for low-capacity systems was generally comparable to that of high-capacity systems, although the improvements were not as high. Across all low-capacity sites, the AIT model's goodness of fit improved by 0.165 in *R* 2 (IEC: 0.74; AIT: 0.90) and 0.61 in log *RMSE* (IEC: 3.35; AIT: 2.75) (Figure 6a,b). Out of the 31 low-capacity sites (comprising 50K hours), the IEC-based model outperformed the trained models in 4 systems (Table 3). In some of the low-capacity systems, the measured energy is much higher than expected (Figure 5). The tendency of the IEC model to overpredict likely describes why this model performs better for some of the lower-capacity systems.

The *δ*, on average, is 4.42 and 15.37 for the AIT model and IEC model, respectively. Similar to the high-capacity system, the percent error values are greater at the extremes (Figure 7b). However, the standard error is generally higher in the low-capacity systems, as evidenced by wider standard deviation bars across the irradiance levels (Figure 7b).

#### *3.3. Limitations and Future Work*

The methodological approach of this analysis was strongly guided by available data. However, future work could extend these methods to consider: (1) energy generation at finer resolutions, (2) additional co-variates, and (3) alternate model formulations. For example, scaling could be used to consider alternate frequencies (beyond the hourly intervals considered in this study) post-evaluation. The methods used in this analysis explicitly omitted variables not included in current standard models (e.g., [15]). However, future assessments could more explicitly incorporate co-variates such as temperature, wind speed, and even age of the site. The latter would especially enable active consideration of degradation influence, which can influence long-term energy generation of PV sites [35]. Additional co-variates (such as type of inverters and modules) could also be included in subsequent iterations to capture more subtle impacts associated with differing site designs. Finally, future work could consider alternate model formulations (e.g., splines) to improve model continuity and better capture energy generation for smaller system sizes.

#### **4. Conclusions**

This work demonstrates the opportunities for leveraging data-driven, machine learning methods to generate more robust expected energy models. Generally, when compared to partner-provided values, the trained regression models outperform the IEC standard, especially in high-capacity systems. Detailed evaluation of the parsimonious AIT or 'additive interaction' model, in particular, demonstrated significant potential for use as a standardized, fleet-level expected energy model. The specific code used to train the regression models as well as the AIT model have been integrated with pvOps, an open source Python package which supports the evaluation of field data by PV researchers and operators; pvOps can be accessed at https://github.com/sandialabs/pvOps, accessed on 22 December 2021. Although this work presents findings specific to PV systems, the general methodologies can be applied to any domain that uses expected energy models to support site planning and O&M activities. Ongoing evaluations and improvements of these standardized expected energy models will continue to increase the accuracy and precision of site-level PV performance evaluations, which is critical to supporting reliability and economic assessments of PV operations and maintenance.

**Supplementary Materials:** The following supporting information can be downloaded at https: //www.mdpi.com/article/10.3390/app12041872/s1. The supplementary material also includes a subsection with mathematical models for top-performing trained models.

**Author Contributions:** Conceptualization, T.G.; methodology, M.W.H. and T.G.; software, M.W.H.; validation, M.W.H. and T.G.; data curation, M.W.H.; writing—original draft preparation, M.W.H.; writing—review and editing, T.G.; visualization, M.W.H.; supervision, T.G.; project administration, T.G.; funding acquisition, T.G. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by U.S. Department of Energy Solar Energy Technologies Office (Award No. 34172).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The raw data was procured under non-disclosure agreements and thus, cannot be shared. However, an anonymized version of the filtered dataset used in this study analysis can be found within the article and Supplementary Information.

**Acknowledgments:** The authors would like to thank our industry partners for sharing data in support of this analysis as well as Sam Gilletly for their assistance with reviewing an earlier version of this manuscript. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia LLC, a wholly owned subsidiary of Honeywell International Inc. for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525. The views expressed in the article do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**

The following abbreviations are used in this manuscript:


#### **Appendix A**

*Appendix A.1. Tables & Figures*

**Table A1.** Correlations with energy generation and regression model parameters pre- and post- data processing. Correlations with energy production are generally comparable with irradiance across raw and filtered data, while correlations for site capacity are significantly higher for the filtered data than the raw data.


**Table A2.** Summary of average percent errors for each of the trained models, using the partnergenerated values as the reference value.



**Table A2.** *Cont.*

**Figure A1.** Relationship between DC capacity (kW) and hourly generated energy (kWh). The blue dots show a site's DC capacity versus its maximum recorded energy generated in a single hour. Although the trends are largely linear, the slopes differ for sites smaller than 1000 kW (blue dashed lines) and sites larger than 1000 kW (orange dashed lines). Since slight deviations in slope can render large prediction error, we train two separate model based on site size.

**Figure A2.** Age of sites within the final dataset. A majority are less than five years of age.

**Figure A3.** A 2-year comparison of observed energy with expected energy estimates from the trained additive interaction trained (AIT) model and the IEC standard at a single site. The IEC-derived estimates overestimate much more so than AIT-derived estimates. Slightly higher values of AITderived estimates relative to observed values likely indicate local failures at the site.

#### *Appendix A.2. Top-Performing Trained Models*

Mathematical equations associated with the trained regression models. In general, these model formulations contain more parameters and do not perform as well as the additive interaction model. High-capacity refers to systems with greater than or equal to 1000 kW in *CDC* while low-capacity refers to systems smaller than 1000 kW in *CDC*.

High-capacity second-order seasonal:

$$\begin{aligned} e &= 0.309iI\_{\text{winter}} + 0.292iI\_{\text{spring}} + 0.281iI\_{\text{summer}} + 0.287iI\_{\text{fall}} \\ &+ 0.762cI\_{\text{winter}} + 0.734cI\_{\text{spring}} + 0.724cI\_{\text{summer}} + 0.730cI\_{\text{fall}} \\ &- 0.003i^2I\_{\text{spring}} - 0.009i^2I\_{\text{summer}} - 0.007i^2I\_{\text{fall}} + 0.430icI\_{\text{winter}} \\ &+ 0.397icI\_{\text{spring}} + 0.380icI\_{\text{summer}} + 0.384icI\_{\text{fall}} + 0.008c^2I\_{\text{winter}} \\ &+ 0.008c^2I\_{\text{spring}} - 0.003c^2I\_{\text{fall}} - 0.054 \end{aligned}$$

High-capacity third-order interactions:

$$e = 0.293i + 0.769c - 0.019i^2 + 0.394ic + 0.021i^2c + 0.004ic^2 + 0.001c^3 - 0.039i$$

High-capacity third-order seasonal:

$$\begin{aligned} e &= 0.265iI\_{\text{winter}} + 0.270iI\_{\text{spring}} + 0.252iI\_{\text{summer}} + 0.243iI\_{\text{fall}} \\ &+ 0.749cI\_{\text{winter}} + 0.740cI\_{\text{spring}} + 0.722cI\_{\text{summer}} + 0.730cI\_{\text{fall}} \\ &- 0.006i^2I\_{\text{summer}} - 0.388icI\_{\text{winter}} + 0.378icI\_{\text{spring}} + 0.365icI\_{\text{summer}} \\ &+ 0.346icI\_{\text{fall}} + 0.019c^2I\_{\text{winter}} + 0.005c^2I\_{\text{spring}} - 0.002c^2I\_{\text{fall}} \\ &+ 0.016i^3I\_{\text{winter}} + 0.008i^3I\_{\text{spring}} + 0.014i^3I\_{\text{summer}} + 0.017i^3I\_{\text{fall}} \\ &- 0.013ic^2I\_{\text{winter}} + 0.008ic^2I\_{\text{spring}} + 0.007ic^2I\_{\text{summer}} + 0.019ic^2I\_{\text{fall}} \\ &- 0.002c^3I\_{\text{winter}} - 0.054 \end{aligned}$$

High-capacity second-order interactions:

$$e = 0.295i + 0.745c - 0.018i^2 + 0.404ic + 0.004c^2 - 0.042i$$

Low-capacity second-order seasonal:

$$\begin{aligned} e &= 0.711iI\_{\text{winter}} + 0.686iI\_{\text{spring}} + 0.680iI\_{\text{summer}} + 0.714iI\_{\text{fall}} \\ &+ 0.617cI\_{\text{winter}} + 0.576cI\_{\text{spring}} + 0.605cI\_{\text{summer}} + 0.636cI\_{\text{fall}} \\ &- 0.046i^2I\_{\text{winter}} - 0.028i^2I\_{\text{spring}} - 0.046i^2I\_{\text{summer}} - 0.038i^2I\_{\text{fall}} \\ &+ 0.401icI\_{\text{winter}} + 0.381icI\_{\text{spring}} + 0.382icI\_{\text{summer}} + 0.427icI\_{\text{fall}} \\ &+ 0.001c^2I\_{\text{winter}} - 0.006c^2I\_{\text{summer}} - 0.104 \end{aligned}$$

Low-capacity third-order interactions:

$$e = 0.746i + 0.642c - 0.043i^2 + 0.426ic - 0.019i^3 - 0.034i^2c - 0.017c^3 + 0.115i$$

Low-capacity third-order seasonal:

$$\begin{aligned} e &= 0.757il\_{\text{winter}} + 0.684il\_{\text{spring}} + 0.667il\_{\text{surnmer}} + 0.712il\_{\text{fall}} \\ &+ 0.577cl\_{\text{winter}} + 0.486cl\_{\text{spring}} + 0.567il\_{\text{surnmer}} + 0.619cl\_{\text{fall}} \\ &- 0.023i^2l\_{\text{winter}} - 0.027i^2l\_{\text{spring}} - 0.050i^2l\_{\text{surnmer}} - 0.033i^2l\_{\text{fall}} \\ &+ 0.413icl\_{\text{winter}} + 0.382icl\_{\text{spring}} + 0.381icl\_{\text{surnmer}} + 0.428icl\_{\text{fall}} \\ &- 0.028i^3l\_{\text{winter}} - 0.007i^3l\_{\text{surnmer}} - 0.022i^2cl\_{\text{winter}} - 0.004i^2cl\_{\text{fall}} \\ &- 0.047c^3l\_{\text{winter}} + 0.068c^3l\_{\text{spring}} + 0.027c^3l\_{\text{surnmer}} + 0.016c^3l\_{\text{fall}} + 0.099 \end{aligned}$$

Low-capacity second-order interactions:

$$e = 0.719i + 0.630c - 0.063i^2 + 0.411ic - 0.124$$

#### **References**


## *Article* **SCADA-Compatible and Scaleable Visualization Tool for Corrosion Monitoring of Offshore Wind Turbine Structures**

**Joachim Verhelst 1, \* , Inge Coudron 1,2 and Agusmian Partogi Ompusunggu 1**


**\*** Correspondence: joachim.verhelst@flandersmake.be

#### **Featured Application: Structural corrosion monitoring for offshore wind turbines.**

**Abstract:** The exploitation of offshore windfarms (WFs) goes hand in hand with large capital expenditures (CAPEX) and operational expenditures (OPEX), as these mechanical installations operate continuously for multiple decades in harsh, saline conditions. OPEX can account for up to 30% of the levelised cost of energy (LCoE) for a deployed offshore wind farm. To maintain the costcompetitiveness of deployed offshore WFs versus other renewable energy sources, their LCoE has to be kept in check, both by minimising the OPEX and optimising the offshore wind energy production. As corrosion, in particular uniform corrosion, is a major cause of failure of offshore wind turbine structures, there is an urgent need for corrosion management systems for deployed offshore wind turbine structures (WTs). Despite the fact that initial corrosion protection solutions are already integrated on some critical structural components such as WT towers, WT transition pieces or WT sub-structure (fixed or floating platforms), these components can still be harshly damaged by the corrosive environmental offshore conditions. The traditional preventive maintenance strategy, in which regular manual inspections by experts are necessary, is widely implemented nowadays in wind farm applications. Unfortunately, for such challenging operating environments, regular human inspections have a significant cost, which eventually increase the OPEX. To minimise the OPEX, remote corrosion monitoring solutions combined with supporting software (SW) tools are thus necessary. This paper focuses on the development of a software (SW) tool for the visualisation of corrosion measurement data. To this end, criteria for efficient structural corrosion analysis were identified, namely a scaleable, SCADA-compatible, secure, web accessible tool that can visualise 3D relationships. In order to be effective, the SW tool requires a tight integration with decision support tools. This paper provides three insights: Firstly, through a literature study and non-exhaustive market study, it is shown that a combined visualisation and decision SW tool is currently non-existing in the market. This gap motivates a need for the development of a custom SW tool. Secondly, the capabilities of the developed custom software tool, consisting of a backend layer and visualisation browser designed for this task are demonstrated and discussed in this paper. This indicates that a SCADA-compatible visualisation software tool is possible, and can be a major stepping stone towards a semi-automated decision support toolchain for offshore wind turbine corrosion monitoring.

**Keywords:** SCADA; visualisation; software; wind-turbine; windfarm; cross-platform; HMI; GUI; corrosion; monitoring

#### **1. Introduction**

The renewable energy markets in the world have reached a mature state and continue growing at a significant rate [1,2]. Among others, wind-sourced electricity production has the potential to deliver a significant contribution to the electric energy portfolio of the world within the next decades. This attracts many new investors and augments market

**Citation:** Verhelst, J.; Coudron, I.; Ompusunggu, A.P. SCADA-Compatible and Scaleable Visualization Tool for Corrosion Monitoring of Offshore Wind Turbine Structures. *Appl. Sci.* **2022**, *12*, 1762. https://doi.org/10.3390/ app12031762

Academic Editors: Luis Hernández-Callejo, Maria del Carmen Alonso García and Sara Gallardo Saavedra

Received: 1 December 2021 Accepted: 29 January 2022 Published: 8 February 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

interactions, thereby increasing the importance of optimisation of operational costs and efficiency gains [1].

Europe is a leading player in this domain, notably for offshore wind turbine manufacturing, as (in 2015) European manufacturers produced around 41 to 50% of annually installed wind power installations worldwide. While this market share had increased up to 61% in 2017 [3], in the last five years, both China and USA have made an unprecedented comeback, partially driven by expiring government subsidies. In 2020 [4], the Chinese wind market dominated the global wind market, totalling 97 GW that year, with a share of 40% of the newly installed production capacity worldwide, both onshore and offshore.

As the world's landmass is rather limited and already under tremendous pressure, offshore installations are becoming ever more popular. The mean cost per produced energy unit for offshore exploitation is rapidly decreasing, thereby closing the gap compared to conventional energy generation methods and onshore wind farms; therefore, many large investors in the domain of windfarm operations move towards larger wind turbines and offshore windfarms. Some sources predict that the global offshore wind farm (WF) market size will continue to grow at a rate of 12% per year [5].

These off-shore investments currently result in a typical levelised cost of (produced) electricity (LCoE) in the range between USD 70 to USD 210 per MWh [2], with a mean around USD 90 per MWh, which is currently still higher than that of most onshore wind turbines estimates (USD 47–60 per MWh*produced*) [6]. These costs are mainly composed of three items: capital expenditures (CAPEX) for power production, conversion and transmission installations; operational expenses (OPEX) and the weighted average cost of capital (WACCs) for financing related costs, such as the cost of depth and risk premiums.

This market growth and shift of deployment area does have consequences: Weather conditions and corrosion effects are more severe in offshore and saline environments, making structural stability more critical, while decreasing maintenance time windows. This leads to increased costs for operation and maintenance (O&M) compared to onshore installations, signalling an economic opportunity for (data-driven or model based) optimisation of maintenance scheduling. Due to the unpredictable nature of corrosion, both for installations that are approaching the end of design lifetime and more recent deployments (which may be engineered with lower tolerances), regular inspection and preventive maintenance is crucial to monitor, track and predict the individual status of structural health of individual wind turbines. Moreover, near the end of the planned turbine lifetime, decommissioning should be scheduled and performed.

The scheduling of these maintenance tasks is a complex planning problem [7], wherein the two key bottlenecks of failure mode analysis are: the availability of suitable measurement data and expert insights to interpret the data correctly. In order to bridge this gap, further research is warranted.

The contributions of this paper are threefold:


In the following sections, the state-of-the-art of corrosion monitoring is presented (Section 2), together with a market analysis (Section 3.1) and a presentation of our custom software (SW) tool (Section 3.3.2) developed to tackle these specific needs.

#### **2. State-of-the-Art**

In order to analyse the needs and benchmark available software solutions for structural stability evaluation of wind turbines, objective criteria are needed. Several existing wind

farm operation market studies were taken as a guideline for this comparison [5,8,9], together with input from EU-project partners involved in the WATEREYE project [10].

In the case of offshore wind turbines, a large variety of support-structure types are used. The most prevalent design is a monopile structure mounted on the seabed floor, yet other structures such as a tripod structures, jacket type or gravity-based structures are used as well [11], while even floating turbines are in the research phase for the deployment of offshore wind turbines in deep waters. A few examples are given in Figure 1.

**Figure 1.** Some commercial offshore wind turbine structures: (**a**) monopile wind turbine; (**b**) floating wind turbine; (**c**) lattice type wind turbine. Images are courtesy of [12].

Therefore, especially for new, non-standard installations such as floating wind turbines, expert supervision for structural analysis will likely be required. Visualisation and decision support tools can assist them in this analysis. A breakdown of the needs for these roles, lead to the following standard practices and derived criteria for structural stability monitoring.

#### *2.1. Maturity of the Wind Turbine Market*

The collective world experience with regard to offshore wind turbine structural corrosion is rather limited: Most of the experience regarding corrosion of offshore wind turbine structures is condensed in Europe, especially in Denmark, the Netherlands, Germany and the UK, as 90% of the globally installed offshore installations (by capacity) were produced and installed by European companies [13].

The first offshore windfarm was constructed in 1991 (Ørsted), yet these demonstrators contained small wind turbines (0.5 to 2 MW each) installed in shallow water (3–5 m), whereas in the last decade, the trend is to go towards larger sizes and capacities per wind turbine (3 to 12 MW each), and with anchoring on ever deeper seabeds [13]. In the US, the first commercial offshore wind farm was only constructed in 2016, near Rhode Island. In China, the first commercial offshore windpark was deployed in 2010 [14].

#### *2.2. Standard Practices for Structural Stability Monitoring*

Most wind turbine manufacturers offer tools for operational management of their wind turbines; however, the focus of these tools is mostly on the rotating components (gearbox, generator, etc.), whereas the evaluation of structural stability of the wind turbine pylons are rarely addressed in these tools [15].

The default inspection mode for structural stability of offshore wind turbines, are visual (RGB-camera-based) inspections and flooded member detection. For submerged parts, this is traditionally performed by divers or remotely operated vehicles, with a frequency between one and five years. These types of inspections and full scale post construction impact evaluation campaigns [16]; however, can be costly in terms of vessel time, and involve hazards to personnel [17].

Therefore, in more recent constructions, manufacturers or operators often embed sensors to detect and quantify structural loading, flooding or corrosion effects, for example accelerometers, saline senors, displacement measurements or acoustic emission systems.

In this data-rich environment, it is not the data capture that is the main difficulty. Rather, the robustification of the measurements, the detection of all failure modes and the subsequent evaluation and analysis of the captured data is what leads to understanding and effective decision making.

#### *2.3. Criteria for Structural Analysis of WT*

From existing literature reviews and interviews, including [17–20], multiple features for structural analysis of wind turbines are extracted and subsequently condensed in criteria. A holistic SW tool for structural health monitoring of offshore WF should be:


These identified criteria are subsequently used to evaluate existing SW solutions in the market.

#### **3. Software Solutions**

*3.1. Existing Windfarm Visualisation Tools*

Both for wind-farm development [21] and for structural monitoring and maintenance planning, visualisation tools are indispensable. Dozens of software packages exist in the market for these applications. The scope of this review is not to be exhaustive, nor to provide a judgement or ranking. Rather, the aim is to classify a subset of existing software tools that are publicly advertised, according to the criteria presented in Section 2.

This exercise results in the non-exhaustive overview shown in Table 1. This table shows that there are multiple software providers; each offering unique, functional pieces of software; however, to the author's knowledge, none of these suppliers currently offer a holistic and tailored solution specifically for the structural monitoring of the windfarm market, including 3D corrosion visualisation and maintenance task planning.

#### *3.2. Existing Visualisation Tools in Other Industries (Oil and Gas)*

Beyond the domain of WF, it makes sense to extend the search into an other domain where metal structures are deployed in offshore, saline environments, where corrosion monitoring is important, namely, the offshore oil and gas industry.

Since the economic loss in these industries due to corrosion can be extremely high, monitoring and managing corrosion in the oil and gas industry is paramount importance; therefore, this industry has deployed and is inspecting and maintaining ten-thousands of offshore drilling platforms, undersea pipelines and supporting pylons.

Offshore oil drilling platforms have a long history: the first deep-sea oil-rig was erected in 1947 in the gulf of Mexico, whereas the first platform might have been built around 1890 (Grand Lake, St. Maris) [22].

A similar classification exercise was undertaken for this industry, using the same criteria as stipulated in Section 2.3, in order to carry over suitable approaches and frameworks (where available) to tackle monitoring of renewable energy projects.

Interested readers are directed to existing literature reviews in this field, including (among others) following book [23] and paper [24]. These authors describe common practices for design, maintenance and monitoring of offshore installations.


**Table 1.** Non-exhaustive list and classification of commercial wind turbine corrosion visualisation and maintenance planning software tools.

\* 1 Scaleability and Modularity.

Table 2 summarises our (non-exhaustive) market analysis of structural corrosion analysis tools used in the oil and gas industry. There are uncountable sources and software packages published online, that list multiple (hundreds) of software packages in this industry [25], that may be applied (with minimal modifications) to WF applications.

**Table 2.** Non-exhaustive list and classification of commercial oil and gas industry corrosion visualisation and maintenance planning software tools.


\* 1 Scaleability and Modularity.

From our investigation, most software packages offer one or more of the required functionalities of the listed criteria, yet to our knowledge, no single application offers a holistic solution fitting the needs of the WT structural corrosion monitoring. Furthermore, there is a need for adapting these solutions to the needs of the offshore windfarm industry. Even if one would fit all criteria, it is not certain that it is applicable in plug-and-play fashion to monitor the structural health of wind farms.

#### *3.3. Custom SW Tool*

#### 3.3.1. Custom Architecture

In offshore wind turbines, failures of structural components, caused by corrosion at tower including the "tower-platform" junction and the entire splash-zone can cause significant and critical down-times and subsequent loss of electricity production. As no holistic commercially available tool was identified, to the best of the authors' knowledge, in the framework of the ongoing WATEREYE research project [10], a custom SW demonstrator tool was developed. The initial concept and architecture of the custom SW tool was developed in our previous work [26]. In this paper, the concept and architecture are further refined and finally implemented into a demonstrable and deployable SW tool.

In the WATEREYE project [10], corrosion monitoring and O&M planning tools for offshore wind farms and turbine structures are developed and integrated in (a subsequent version of) the custom SW-tool. Further, in the scope of the WATEREYE project, technologies for monitoring, data analytics, modelling, and diagnosis and for wind turbine (WT) and wind farm (WF) O&M advanced control strategies have been investigated and implemented.

The analysis listed in Table 1, resulted in the design and development of an SW-tool that attempts to cover all criteria identified in Section 2.3. For the framework of this SW tool, Qt [27] was chosen. Because of its highly scaleable characteristics, it allows developers to build components that can run on embedded, desktop and mobile computers, and it supports graphical development (inclusion via widgets). Qt supports all of today's user interface paradigms, controls and behaviors, making it easy to design really attractive HMIs that users intuitively understand. Furthermore, Qt uses the latest SSL and TLS implementations to safely encrypt data communications for cyber-secure remote-access.

In order to leverage both web-based and SCADA-capabilities, pvbrowser [28] was chosen, which is an open source C++ GUI framework, built on top of Qt. This application framework provides a specialised browser for the client computer and an integrated development environment for creating servers that interact with data acquisition programs (daemons) for many SCADA protocols [28].

The stock architecture of pvbrowser is shown in Figure 2a. PvBrowser is available under the GPL v2 (program) and GNU LGPLv3 (library) licence frameworks.

**Figure 2.** (**a**) Original pvbrowser architecture [28] and (**b**) modified architecture and data flow, to support the WATEREYE project [10] needs.

For 3D-visualisation purposes, the visualisation toolkit (VTK) [29] was used. This C++ based open source toolbox is capable of filtering, processing and visualising large datasets, with numerous user and SCADA interaction capabilities. Pvbrowser provides some support for VTK, but the default browser does not support it out of the box. To setup the VTK-based Qt-widget and to streamline the interaction between the user and the widget, TCL-TK scripts (Graphical toolkit for TCL) were used, available under a BSD-type licence [30].

#### 3.3.2. Custom Visualisation SW Tool

In the WATEREYE project [10], measurements containing corrosion status information are generated using mobile and fixed sensors. These data are stored in a secure database, accessible through a Representational State Transfer application Programming interface (REST-API) . A visualisation tool is needed to support O&M experts to understand the status of an offshore wind turbine, based on gathered measurement data. To this end, a visualisation SW tool was developed according to the criteria developed defined in Section 2.

This framework was used to develop a custom web interface, which takes (maintenance staff) user input, queries a REST-datbase to fetch the measurement and prediction data from a windfarm database and subsequently presents the data on a custom pvdashboard. The user can interact with these data, either visually (in 3D or 2D), or by downloading the underlaying data and processing it offline.

This combination results in the following architecture, depicted in Figure 3. It was based on pvbrowser, but with modified architecture, as explained in Figure 2b. This SW tool is capable of:


**Figure 3.** Architecture of custom SW tool, with main components: QT-based (customised) pvserver (orange box) and VTK-enabled pvbrowser (blue box), fetching data from a database (grey box).

Through the browser client, the user can access and interact with the data, using a browser-like application. The user can use the software, agnostic of the architecture or changes at server side.

The server architecture allows us to centrally manage and adapt both the data and visualisation output from different windfarms and users.

Based on the chosen parameters, the server component makes a query to the dataserver, parses the data and presents them to the user in predefined widgets in the browser side (see Figure 4). There, the user can interact with the data (zoom, query, rotate) to increase his/her understanding of spatial and time relationships, or adapt the query for additional data.

The core functionalities of this SW tool are:


Any change in the parameters above, triggers the visualisation of:


**Figure 4.** Example of the browser window of our SW-tool. It consists of three areas: user input (red box), a 3D visualisation area (green box) and a 2D time series visualisation (blue box). All widgets are interactive and responsive, as explained in Section 3.3.2.

The user-friendliness and responsiveness of the tool is further enhanced by enabling 3D-panning, rotating and zooming, sensor highlighting, 2D-point picking and informational tooltips, as shown in Figure 5b,c.

**Figure 5.** (**a**) Example of the browser 3D window, with a large 3D wind turbine model. (**b**) Example of the browser 3D window, with 3D model, measurement location and status visualisation capability. (**c**) Example of the browser 2D window, with interaction and picking capability.

#### *3.4. Discussion*

The presented market analysis shows the potential and opportunities present in this growing market of structural monitoring of offshore wind turbine parks, both for applied research and further commercialisation of dedicated software solutions.

The technological readiness level (TRL) of the SW-tool presented here is relatively low (not production ready), as it is not deployed in the field yet, nor tested by a large userbase; however, it does form a profound starting point for further developments.

Paths toward industrial uptake could focus on security and robustness, as well as on an improved user-friendliness and modularity. Further research includes the extension of this SW-tool to stochastic estimates of corrosion processes and inclusion of risk-assessment and economic impact of different degradation scenarios. Moreover, with minimal effort it is possible to transition the SW tool to other fields where 3D visualisation of corrosion measurement data is relevant.

#### **4. Conclusions and Further Research**

Based on the insights presented in Section 2 and the existing tools identified in Section 3.3.2, it is clear that there currently is a lack of commercial tools that consider and address all the needs for corrosion monitoring of offshore wind turbine structures.

Furthermore, as corrosion is a slow, stochastic process influenced by multiple disturbances, it is very hard to quantify theoretically; therefore, data-based and risk aware maintenance planning is crucial to ensure the structural integrity of offshore wind assets throughout their intended service life. This improves the risk–return balance of CAPEX and OPEX, thereby further reducing the weighted average cost of capital (WACC).

The SCADA-compatible software tool presented here, can help wind turbine/wind farm operators to translate corrosion-related information to insights on the wind turbine structural degradation. Furthermore, it can assist the operators with the economic scheduling of preventive maintenance interventions.

**Author Contributions:** J.V.: Software, Methodology, Writing—original draft, Writing—review & editing; I.C.: Conceptualisation, Software, Methodology, Validation; A.P.O.: Conceptualisation, Supervision, Project administration, Funding acquisition, Writing—review & editing. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was carried within the WATEREYE project that has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No. 851207.

**Institutional Review Board Statement:** This study did not involve any testing on animals.

**Informed Consent Statement:** This study did not involve any testing on humans.

**Data Availability Statement:** The software described in this paper, developed in the framework of this H2020 WATEREYE project, is defined as a proprietary deliverable. Therefore, the source code of this software cannot be made open source or shared through open access.

**Acknowledgments:** The authors are grateful for the technical support of Stijn Helsen and Jia Wan during the development of the SW tool.

**Conflicts of Interest:** The authors declare no conflict of interest. The funding agencies had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

#### **References**


## *Article* **Ultrasound-Based Smart Corrosion Monitoring System for Offshore Wind Turbines**

**Upeksha Chathurani Thibbotuwa 1, \* , Ainhoa Cortés 1,2, \* and Andoni Irizar 1,2**


**Abstract:** The ultrasound technique is a well-known non-destructive and efficient testing method for on-line corrosion monitoring. Wall thickness loss rate is the major parameter that defines the corrosion process in this approach. This paper presents a smart corrosion monitoring system for offshore wind turbines based on the ultrasound pulse-echo technique. The solution is first developed as an ultrasound testbed with the aim of upgrading it into a low-cost and low-power miniaturized system to be deployed inside offshore wind turbines. This paper discusses different important stages of the presented monitoring system as design methodology, the precision of the measurements, and system performance verification. The obtained results during the testing of a variety of samples show meaningful information about the thickness loss due to corrosion. Furthermore, the developed system allows us to measure the Time-of-Flight (ToF) with high precision on steel samples of different thicknesses and on coated steel samples using the offshore standard coating NORSOK 7A.

**Keywords:** corrosion monitoring; FPGA; offshore wind turbines; ultrasound; thickness loss

#### **1. Introduction**

Wind energy plays a significant role as a renewable energy source, urging the need for cost-effective renewable energy sources. Compared to onshore wind energy, offshore wind turbines benefit from two main advantages: higher mean wind speeds (modest increases in wind speed can result in doubling the generated power) and steadier wind supply, which makes power generation more reliable. These two factors combined have a dramatic effect on the Return on Investment (RoI) of the farm [1].

In the last decade, we have witnessed a steady increase in the total installed capacity of offshore wind farms. By the end of 2019, 6.1 GW capacity has been newly installed. The total capacity installed by 2019, was 29.1 GW, which is a 10% increase with respect to 2018 [2]. Europe (UK, Germany, Denmark, Belgium) is leading by contributing 75% of total global offshore wind installation, as of the end of 2019, and Asian offshore wind energy production keeps growing significantly, lead by China and followed by Taiwan, Vietnam, Japan, and South Korea. Due to COVID-19, the overall expected wind capacity in 2020 was not met because of the challenges in project construction, execution activities, and investments. However, the Global Wind Energy Council (GWEC) has predicted that offshore wind energy will have a 20% of contribution to the global wind installation by the year 2025.

Offshore structures are installed in relatively deep water and exposed to the harsh marine environment. This leads to an increase of the cost of construction and deployment compared to onshore structures [3] and higher operation and Maintenance (O&M) costs of installations compared to land or coastal-based structures due to the limitations in accessibility, manpower, special equipment requirements, etc. [4]. The added costs in the construction and deployment of offshore turbines were mitigated at the beginning as the

**Citation:** Thibbotuwa, U.C.; Cortés, A.; Irizar, A. Ultrasound-Based Smart Corrosion Monitoring System for Offshore Wind Turbines. *Appl. Sci.* **2022**, *12*, 808. https://doi.org/ 10.3390/app12020808

Academic Editors: Luis Hernández-Callejo, Maria del Carmen Alonso García and Sara Gallardo Saavedra

Received: 10 December 2021 Accepted: 11 January 2022 Published: 13 January 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

turbines were installed mainly in coastal sites with shallow waters. In recent years, there has been a constant increase in the water depth and distance to shore for the offshore wind farms [5], as farms are located further away from shore (60 km) and as depth water reaches 200 m [6]. This leads to higher Capital Expenditure (CAPEX) and O&M costs that reduce the benefits of the farm [7]. Several foundations for wind turbines have been developed trying to reduce the construction and installation costs. Another key to the profitability of the wind farm is to improve the useful life of the wind turbines by maintaining the operational conditions of the towers to minimize the breakdowns or downtime of the turbines. Therefore, improving O&M models and tools and, at the same time, reducing costs have become key to maintain the profitability of offshore wind farms. Numerous research works providing different approaches that support directly or indirectly to improve O&M process of offshore wind turbines/farms have been discussed in Reference [8–12].

#### *1.1. Structural Health Monitoring of Wind Turbines: Corrosion Monitoring*

Structural Health Monitoring Systems (SHMSs) for Offshore Wind Turbines (OWTs) are used to detect damage in blades [13,14], tower, and support structure. Since the tower and foundation are two key elements of OWT that support the structural integrity, they must operate as much time as possible. Once the turbine is installed, it should sustain with associated loads, and their partial failure would carry catastrophic consequences. Not much progress has been made in developing robust applications regarding SHMs for operating WTs [15].

Corrosion is one of the main root causes that can produce offshore structural failure. Corrosion monitoring is the process of obtaining very frequent corrosion measures to evaluate the progress of corrosion within a specific environment. Corrosion inspections are done to evaluate the material condition at any given time based on a pre-scheduled routine or the available risks. Usually, inspections are performed much less frequently than corrosion monitoring. Frequent corrosion measures are always advantageous of early detecting the risks, repairing conditions, and, consequently, reducing the operational and maintenance cost associated with corrosion. The rust formation due to corrosion depends on the environment and the type of material, as well. Carbon steels corrode mostly by general corrosion (uniform corrosion), but localized types of corrosion can also take place, e.g., pitting, which usually are not considered in conventional corrosion analysis [16]. Different reasons can be identified behind the growth of corrosion process in an offshore structure, such as temperature, salinity, pH, and coating damage due to tidal fluctuations, dissolved oxygen, variable cyclic load due to wave and wind impact, etc. [17].

Even for a well-designed structure, with a long time of exposure to the harsh marine environment, corrosion causes the degradation of the metal leading to create corrosion fatigue cracks and, consequently, structural failure. This scenario increases the O&M cost because of the possibility of more frequent maintenance, repair activities, and any replacement if needed [18]. Therefore, a successful corrosion monitoring approach can potentially decrease the ongoing O&M cost of wind turbines directed at reducing economic losses and environmental damages. However, corrosion monitoring is one of the major challenges that an SHM system developed for an OWT faces, mainly due to the accessibility difficulties and the area the corrosion monitoring system must cover, which is very large even when one considers that some zones are more affected than others, e.g., the splash zone. Thinking about an automated solution, ideally, the corrosion sensor should work unattended 24/7 for several months or even years. This imposes very hard specifications that the monitoring system must meet. Therefore, prior to the selection of an appropriate corrosion monitoring technique and sensors, the zone of interest (splash zone, atmospheric zone, submerged zone) of the wind tower and the respective environmental conditions must be considered separately [19].

#### *1.2. Corrosion Inspection and Monitoring Techniques*

There are different types of corrosion inspection and monitoring techniques to find out the corrosion condition of metals, as is discussed and reviewed in Reference [20,21]. Figure 1 shows a detailed classification of these techniques based on the corrosion detection method and sensing parameters.

In general, corrosion detection measures can be direct measuring metal loss due to corrosion or corrosion rate or indirect measuring any parameter that may be a cause or consequence of the metal loss or corrosion. Some of these techniques need direct contact/exposure to the same corrosive fluids or to access the internal environment where the corrosion process takes place. They are known as intrusive techniques and can alter the corrosion process and create disturbances to the operation during installation and re-installation of measuring probes or inspection processes. Therefore, it is beneficial if corrosion testing can be performed from the outside of the test object. This is possible with non-intrusive techniques through detecting physical and geometry changes due to corrosion (mass loss, crack, or surface discontinuities), and there is no need for any direct contact to the same corrosive fluids or access to the internal environment. On the other hand, it is very important to perform corrosion detection activities in the field applications without destroying the engineering properties of the material and without affecting its long-term future performance during the inspection process. This kind of evaluation can be achieved by using Non-Destructive Testing (NDT) methods for material testing [22]. Among the techniques listed in Figure 1, if this condition is satisfied, they are known as an NDT method. Therefore, we can propose that the most appropriate corrosion detection technique for offshore wind turbines shall be both non-intrusive and non-destructive.

The main objective of this research work is to develop a smart ultrasound solution for corrosion monitoring in offshore wind turbines. Due to the harsh and distant environment they have been installed in, it is a challenge to find the most suitable corrosion detection technique. Based on the expected solution, we have identified the following design specifications to be achieved and feasible with the selected corrosion detection method.


The paper is structured as follows. In Section 2, a review of different ultrasound solutions for corrosion monitoring is introduced. Section 3 describes the concept of the presented approach for corrosion monitoring in offshore wind turbines. Section 4 provides the description of the ultrasound testbed and the design methodology followed to miniaturize the solution. In Section 5, the samples preparation and the experimental setup are presented. Section 6 shows the most relevant results we have obtained through our experiments. Finally, the conclusions are summarized in Section 7.

#### **2. Related Work**

In ultrasound techniques, a high-frequency ultrasound wave will travel along with a material that shows elastic properties. The frequency range of ultrasonic sound waves used for NDT of materials is generally 1 MHz to 15 MHz [23]. The velocity of the ultrasound wave propagation through a material is a function of the elastic modulus and density of the material [22,24]. Importantly, ultrasound waves are distinctly reflected at the boundaries when the acoustic impedance change due to a different material or medium properties. Based on that, the thickness loss due to corrosion will be given as a function of propagating velocity, frequency, and energy components [25]. The setup can be designed based on two common techniques [23,26]:


It can be said that the best technique for corrosion monitoring would be the pulseecho method as it gives the depth/location of the defect in comparison to the through transmission method.

Thus, current sensing methods using the ultrasound technique give valuable information about various forms of degradation that occur in all sorts of materials (cracks, deformations, thinning, corrosion, etc.), but, in general, they are classified as inspection devices, rather than monitoring devices. The inspection devices are usually "once-off" measurements that cover a given period of time (according to maintenance schedules), while the monitoring devices involve very frequent measurements that must detect small fluctuations in the advancement of corrosion in order to be used as input for a general assessment of corrosion [27]. Several previous works have been reported to assess corrosion in pipelines using ultrasounds [28].

Although not focused on corrosion detection, Ref. [13] proposes a novel walking robot-based system for NDT in wind turbines. Moreover, commercial systems based on ultrasounds exist in the market to monitor large structures. For example, Eddyfi Technologies has developed the Scorpion2 product [29] for ultrasonic tank shell inspections. To the best of our knowledge, it monitors wall thickness during the inspection using a dry-coupled, remote-access ultrasonic crawler that brings major efficiency and data

improvements to tank shell inspections. It scans the tank wall to get an image of the wall status with the aim of estimating the wall thickness. Among other NDT techniques, the walking robot offers ultrasonic testing, but it is aimed at identifying cracks, delamination, etc., in composites (e.g., in blades). Furthermore, this walking robot has already been used in onshore wind turbines.

Ultrasound is a technique with a lot of potentials to deploy a Wireless Sensor Network (WSN). Nodes can be housed in small devices with communication capabilities, drawing very little power from a battery and offering very good corrosion detection capabilities. However, this is not enough when referred to large structures (e.g., offshore WT) where corrosion may develop randomly at a given point. The continuous technological improvements of all kinds of unmanned vehicles (terrestrial, maritime, and aerial) during the last decade make this technology very attractive for many industries that require frequent and costly maintenance operations in areas where access is difficult. Ref. [30] proposes an autonomous ultrasonic inspection using UAVs. This research is very relevant since it demonstrates the influence of the accuracy of the measurements positioning and of the electrical noise produced by control electronics and the propeller motors into the thickness estimation. These uncertainties cause ultrasonic signal coupling issues. One of the main advantages of permanently installed ultrasound sensors is that they achieve a better repeatability since the coupling and probe-positioning errors are removed. Hence, in the case of mobile solutions, there are challenges to solve regarding probe alignment, more robust control strategies, enhanced positioning the accuracy, and novel ultrasonic angular coupling capabilities. The paper is focused on the improvement of the UAV design, and they do not show the accuracy obtained in the thickness estimation. Additionally, in this paper, they claim to detect the loss of thickness over non-coated aluminium samples (11 mm of thickness). It is well known that coating reduces accuracy of wall thickness estimations [31], and wind turbine walls are usually protected with standard coatings of different thicknesses and formulations. Therefore, coating affects the ultrasound signal response, and it is another key challenge to be solved, not only for ultrasound mobile solutions but also for fixed solutions. Another problem is that ultrasound monitoring employs liquid couplants, which makes it necessary to integrate a couplant dispenser into the UAV and a cleaning phase after the ultrasound measurement has been taken.

Corrosion is an extremely slow process, and corrosion rates between 0.1–0.2 mm/year are typical rates. Therefore, with a resolution of 1 µm, we will have to wait, on average, more than 4 days between consecutive measures to get statistically meaningful results. The work presented by References [32,33] proposes the use of curve fitting algorithms of a Gaussian echo model to estimate the time of arrival of ultrasound echoes. In order to improve the precision of the ToF measurements, it is necessary to compensate for temperature variations that affect both the thickness of the material and the speed of sound, digitally processing several back-wall echoes or using adaptive filtering techniques [34]. Other proposals rely on improving the Signal-to-Noise Ratio (SNR) and time resolution of the signals by employing the Wiener filter and spectral extrapolation [35]. An interesting idea to increase the SNR of the ultrasound system is to use coded excitation as in [36], which introduces a code gain in the signal's path. Finally, Ref. [37] proposes a non-standard approach based on cross-correlation, but, instead of performing the correlation with the transmitted signal, they correlate a back-wall echo with a reference signal that has been modified using an iterative algorithm that also involves cross-correlations. Thus, this approach achieves wall-thickness estimations (below 1 µm) on ultrasonic signals. However, this is at the expense of increased data processing complexity that will affect the power consumption and the cost of the solution.

To the best of our knowledge, none of the proposals in the literature develop a low-cost and low-power corrosion monitoring system based on ultrasound able to measure the thickness loss precisely showing that the solution can work for different thicknesses and mainly, for coated samples using the offshore standard coating NORSOK 7A. On top of that, the proposed approach aims to operate unattended inside offshore metallic towers.

#### **3. Corrosion Monitoring System Concept**

Our corrosion monitoring system design concept is focused on a novel and smart low-power and low-cost corrosion monitoring system for offshore wind turbines. The zones of interest are the splash zone and the atmospheric zone. The splash zone is the area that is intermittently exposed to seawater due to the action of tide or waves or both. This intermittence produces the highest level of corrosion. The atmospheric zone is the zone that is permanently exposed to marine air conditions. Therefore, the level of corrosion is also very high. Our approach includes two types of deployment, namely (i) a fixed and (ii) a mobile solution. In the case of the splash zone, the fixed sensors are attached to the structure due to the difficulties to access by a mobile platform. However, the atmospheric zone is covered by the mobile solution based on a drone flying inside the tower. Therefore, the main requirements to be achieved by our corrosion monitoring solution can be highlighted as follows.


#### **4. Smart Ultrasound Sensor Design**

Being aware of developing a reliable corrosion monitoring solution to decrease the cost of the maintenance and the downtimes during operation in the offshore wind sector, this paper presents a smart and robust corrosion monitoring system based on ultrasound technology and ToF technique that is capable of operating unattended inside an offshore metallic tower. With that aim, a prototype of the ultrasound test device has been designed. This is the Ultrasound Testbed (UT) with the capability of upgrading into a miniaturized solution that can be placed and operate inside of the wind turbine. UT is developed with the aim of performing frequent ultrasound measurements and analyzing the ultrasound responses. More details about sensor selection, excitation signals, and design methodology of the UT system are discussed in the following subsections.

#### *4.1. Probe Selection*

The selection of ultrasound probe or transducer needs to be done by considering the sensor characteristics, such as sensor dimensions, weight, dead zone duration, waveform duration, and peak frequency. The transducer operating frequency spectrum and the waveform duration are often provided by the manufacturer. The peak frequency of the transducer controls the penetrating power that affects the possible inspection thickness of test material, e.g., high-frequency ultrasound has low penetration power and might almost attenuate within the material. As at a fixed velocity in a perfectly elastic material the wavelength and frequency are inversely proportional, a change in the probe frequency will affect the sensitivity and the resolution to detect flaws in the material. Due to the diffraction of ultrasonic, the sensitivity is about half of the corresponding wavelength [38]. Thus, sensitivity and resolution are increased when probe frequency increases. The dead zone duration is the interval following the initial pulse where the transducer ringing

prevents detection or interpretation of reflected echoes. This is a constraint with thinner size samples as it is better that the time interval between back-to-back echoes has to be out of the dead zone.

As we are going to measure 5 mm thick samples, it is important to check the dead-zone of the selected probe. A 5 mm thick steel sample will introduce a delay between backto-back echoes of 2 <sup>×</sup> 5/5.9 <sup>×</sup> <sup>10</sup><sup>6</sup> <sup>=</sup> 1.69 µs (the speed of sound in steel is approximately 5.9 <sup>×</sup> <sup>10</sup><sup>6</sup> mm/s). This is the expected value of the ToF before corrosion takes place. This value is important when considering the dead zone of an ultrasonic probe. Dead zone value is highly dependent on the test conditions and instrumentation used. It is not normally given in the technical documentation of the probe and needs to be determined experimentally. The values shown on Table 1 correspond to the time when the ultrasound signal has almost completely settled (see Figure 2). However, it must be noted that the dead zone does not entirely invalidate the ultrasound data received on that interval. By proper filtering, and with the appropriate receiver's gain, it would be possible to extract echoes within the dead zone of the piezo.

**Figure 2.** Dead Zone of an ultrasound probe.



A comparative analysis of the performance specifications of three sensors has been done to select the most suitable one for the UT system as given in Table 2. As a result, V111 from Olympus [39] has been selected as the most suitable ultrasound probe for our system, specifically prioritizing its lower waveform duration (higher bandwidth) and sound pressure power. Having a higher dead zone compared to the other two sensors will not be a constraint in the real scenario as the system is designed for testing thickness around 40 mm.


**Table 2.** Applicability to the US system.

#### *4.2. Excitation Signal*

The conventional method is using a square wave as the excitation signal. The frequency response of the V111 peaks at 8.44 MHz; therefore, the frequency of the pulse must be similar in order to resonate and optimize the received signal's strength. Adding more pulses increases the signal's strength but at the expense of a larger pulse duration that deteriorates the time resolution of the ToF estimation. In our system, the period and the rise and fall times of the square wave can be controlled using a 125 MHz clock. The square wave pulse is bipolar (±15 V), and the generated frequency is obtained by dividing the clock frequency by an even integer 125/16 = 7.8 MHz to guarantee a 50% duty cycle for positive and negative pulses.

#### *4.3. Signal Processing and Time-of-Flight Estimation*

Based on ultrasound waves, corrosion is evaluated by estimating the wall thickness loss that happens due to corrosion. The proposed approach is based on the Time of Flight (ToF) technique, which estimates the thickness of the test object by measuring the elapsed time between two consecutive echoes of the ultrasound response. This is based on the reflection of the ultrasound waves in different acoustic impedance conditions. This way, the effect of the couplant is greatly reduced because no changes in the couplant are expected in the time period of a ToF (in our case, less than 5 µs). The main drawback is the additional attenuation of the second echo that reduces the SNR of the signal and, therefore, the quality of the estimation. The determination of the time is done using the cross-correlation operation.

A block diagram of the signal processing operations performed to complete the ToF estimation in our approach is given in Figure 3. To have an accurate time base, it is important that both the ultrasound signal generator (US Generator) and the signal acquisition circuit (ADC Read) work with the same clock input. The filter removes unwanted frequencies components outside the bandwidth of the probe. The Echo Windowing block determines the location and size of the echo signals that will be cross-correlated. Some signal quality measurements are performed on the echo signals (signal level, signal width, echo amplitude and decay rate, separation between echoes, etc.). These measurements will help to detect low-quality signals and discard those ToF measurements in advance. Finally, cross-correlation between two consecutive echoes, as well as peak detection and analysis, produce the ToF result.

**Figure 3.** Block diagram of the signal processing chain.

#### *4.4. Design Methodology*

The design of a highly integrated monitoring system involves the collaboration between several design teams: analog circuits, digital signal processing, FPGA and microcontroller development, PCB prototyping and design, validation, etc. To coordinate the efforts from different teams, it is very important to have a system design methodology that takes you from the conceptual design to the final device to be deployed.

We have used a prototype-based design methodology in which the system is first designed from large building blocks that allow us to define the system using high-level abstraction languages, such as MATLAB or C/C++. As can be seen in Figure 4, the main blocks of the system prototype include a PC/Laptop and an Ultrasound Testbed. The latter is composed of a high-performance embedded processor that is able to generate and acquire ultrasound signals. The embedded processor runs a Linux system with the Debian distribution and includes an SD card for mass storage, Ethernet and Wi-Fi connections, and access to an internal FPGA that serves the purpose of buffering the ultrasound data from a high-speed 14-bit ADC. The Ultrasound Analog Front End (AFE) is composed of a pulser generator, adaptation circuitry, and a variable gain amplifier.

The system prototype permits us first to set up an experiment and gather raw ultrasound data for a variety of steel samples with different coatings, to test different piezo sensors, and change the experiment conditions, such as temperature, signal frequency, number of pulses, etc. The raw data is stored as a JSON file in a data repository that can be accessed from MATLAB to design and test signal processing and detection algorithms with the aim of estimating the time-of-flight from the ultrasound response.

Secondly, thanks to the embedded system, it is possible to run a C/C++ implementation of the algorithm in the Red Pitaya microprocessor and test it for quantization effects. In this case, the embedded system is responsible for estimating the time-of-flight, and the data obtained can also be uploaded to the data repository as a JSON file.

The hardware architecture of the final implementation is designed by analyzing the computing requirements of the algorithms designed in the prototype phase. We have chosen an architecture that includes a low-power Cortex-M4-based microcontroller (µC), an FPGA that interfaces with the µC using an SPI link and the AFE devices. The µC is in charge of supervising the system, i.e., powering on and off the different devices (FPGA, AFE, memories), launching measurements and gathering the results and raw data from the FPGA using the SPI interface and providing communication interfaces with the external world (UART and wireless communications). The high-speed sampling of the ultrasound signals has called for the use of an FPGA. Ultrasound signal generation is also handled by

the FPGA to produce synchronized signals for the pulser. The processing of ultrasound data requires intensive computation that is more efficiently performed in the FPGA.

**Figure 4.** System design methodology.

By having models of the processing of ultrasound signals at different abstraction levels (MATLAB, C/C++, and FPGA), it is possible to perform validations at different stages of the design process as it advances towards the final implementation using the raw data stored in the data repository (see Figure 4). In this way, we can feed the MATLAB model with the real data from the miniaturized system and compare the ToF results obtained for verification.

Finally, after validating the ultrasound test method and algorithm implemented in UT, it has been migrated to a miniaturized system, as shown in Figure 5 (right), being able to place it inside a wind turbine to conduct ultrasound tests in the real scenario. The performance specifications of the miniaturized solution are given in Table 3.

**Table 3.** Miniaturized ultrasound system performance.


**Figure 5.** Pictures of the UT (**left**) and miniaturized solution (**right**).

#### **5. Sample Preparation and Experimental Setup**

#### *5.1. Sample Preparation*

Two types of S355 structural steel samples have been used for the system performance validation as reference samples and test samples. Reference samples have been used mainly to verify the test method and evaluate the precision of the measurements during the algorithm development. On the other hand, test samples have been used to test the long-term system performance. The dimensions of the reference and test samples are shown in Table 4.

**Table 4.** Reference and test sample dimensions.


The real thickness of a wind turbine tower is around 40 mm. However, the test samples have been used only with 5 mm thickness due to the practical difficulties in transportation and handling of the samples during the frequent experiments.

Coating layers are applied to protect the substrate from reacting with its environment so that it will not engage in an electrochemical process and corrode. Coatings provide protection against moisture, dissolved gases, acids, and other reactants in the environment. The test coated samples with applied standard coating NORSOK 7A (see Figure 6) were tested by our ultrasound system to observe the changes in the characteristics of the ultrasound signal and to analyze the performance of the developed signal processing algorithm.

Corrosion is a very slow process, and it takes a long time to induce corrosion on coated samples. Therefore, in order to observe a measurable thickness loss with time, the corrosion process has been accelerated by producing a 2 mm-wide and 50 mm-long scribe, cut completely through the coating, which is made in the coated samples, as can be seen in Figure 6. This scribe emulates in some way a coating defect or failure. The prepared coated samples were exposed and conditioned based on cyclic aging resistance processes (cyclic processes of exposure to UV, neutral salt spray, and low-temperature exposure) in agreement with EN ISO 12944-9. The test method consists of 25 cycles of 4200 h of exposure: over three days, the samples are exposed to UV/condensation according to EN ISO 16474-3; during the following three days, the samples are exposed to neutral salt spray according to EN ISO 9227; during the next day, the samples are exposed to low temperature at (−20 ± 2 °C).

In order to observe and measure the corrosion process, the coated samples have been exposed to cyclic aging resistance process for different time durations as 1 month, 3 months (see Figure 6 (bottom)), and 6 months. Testings of coated samples have been performed in three different layers as: on scribe, no-scribe bottom layer, and no-scribe top layer, to get an indication of thickness loss due to corrosion under cyclic aging process.

#### *5.2. Experimental Setup*

The developed Ultrasound Testbed (UT) prototype is shown in Figure 5 (left). It consists of a low-noise amplifier, pulser, piezoelectric transducer, and FPGA controller with high-frequency ADC and DAC conversion. The UT system is capable of performing frequent ultrasound testings. In the purpose of performing tests and analyzing results, the UT is connected to a PC/Laptop with MATLAB via Wi-Fi or Ethernet, and the experiments are launched and controlled via PC/Laptop. The main advantages of the UT system are that it allows the user to perform frequent tests, to visualize and compare the results easily, and to develop, analyze, and update the signal processing algorithms for better ToF estimations.

The ultrasound test is performed by placing the sensor on the sample using a couplant applied as shown in Figure 7. Olympus D12-gel, that is recommended for rough surfaces, has been used as the couplant to perform the ultrasound tests. Each test is performed by launching 25 excitation signals in a row and collecting the corresponding response from the test sample. Therefore, the ToF value calculated for a particular location is an average

of 25 measures, and this helps to minimize the uncertainty of the results. In addition to that, the precision is calculated as the standard deviation of those 25 measurements.

**Figure 7.** Non-exposed coated sample: on scribe measurements.

Ultrasonic couplant is used to make good contact between transducer and test piece, facilitating quality sound energy transmission. In NDT, the couplant is used because they do not transmit effectively through air. Even so, the applied couplant layer still can affect to ultrasonic velocity and attenuation of the back wall echoes from the test piece. This depends on the acoustic impedance of the couplant being used and how good the contact is made between the test surface and the transducer. On the other hand, if the amount of couplant is excessive, a couplant layer can act as a wedge and alter the direction of the sound wave affecting the final result.

The measurement of ToF in ultrasound signals propagating through steel is directly related to the variation of the speed of sound with temperature and, to a lesser extent, to thermal expansion. Therefore, we need to measure the temperature of the steel to compensate for the temperature effect in the measurement of ToF. However, all the measures performed using UT were made at room temperature. Therefore, no temperature compensation is needed at this point.

The value of Time of Flight depends on the speed of the sound through the target material. The speed of sound in steel is approximately 5900 m/s [40]. To increase the accuracy of the measurements, the speed of sound has been calculated for the selected steel material (S355J2G3) using the 5 mm reference samples. In the process of calculating the speed of sound, the reference bare steel sample surface was divided into 8 zones, and the average thickness of each zone was measured using a digital micrometer. Considering it as the thickness reference, the average speed of sound for each zone was calculated using Equation (1), based on 5 ToF measures performed by using the UT on each zone. Accordingly, the final calculated average speed of sound at room temperature for bare steel reference samples is 5950 m/s. This value has been set as the speed of sound in steel for the rest of the test samples measured by the ultrasound solution.

$$\text{Speed of sound [m/s]} = \frac{2 \times 10^3 \times \text{Reference thickness of sample [mm]}}{\text{Time of flight (ToF) [ns]}}.\tag{1}$$

The UT test approach has been validated by comparing the results from UT and micrometer measures from reference samples of both 5 mm and 40 mm thickness. The results showed a good agreement between the thickness estimations done by the UT and by conventional methods, such as using a caliper or a micrometer.

#### **6. Results and Discussion**

#### *6.1. Test Samples Measurements*

Though the test method of UT system has been validated using reference samples, the long-term system performance has been analyzed by measuring the test samples, as explained in Section 5.1. The following subsections discuss the results obtained by the UT system for non-exposed and exposed coated test samples.

#### 6.1.1. Measurements Precision of Non-Exposed Test Samples

The time response of an ultrasound sensor collected from a test object shows the characteristic behavior of echoes bouncing back and forth the wall's boundaries.

As discussed in Section 4.3, after ADC reading follows a filtering process that includes a bandpass filter that is used to remove the unwanted frequency components from the signal. Figure 8 presents the bandpass filtering results obtained for non-exposed bare steel and coated samples. Figure 8 (top) shows the ultrasound response from the bandpass filter for a bare steel sample that has a well separated and small echo duration, which facilitates the separation of the consecutive echoes for the ToF calculation. In addition, compared with Figure 8 (bottom), it can be seen that the echo duration is longer for coated samples compared to the bare steel samples. This fact makes the echo separation more difficult in the case of coated samples. The estimated echo durations for bare steel and coated samples are around 0.7–0.9 µs and 1.3–1.5 µs, respectively.

The precision of the ultrasound measures gives important information about the system's performance. Having a good precision allows us to take more frequent corrosion measurements, which can potentially be used to estimate the corrosion rate at any instant by using a derivative FIR filter. The latency of the corrosion rate measurements using this method will be in the range of a few hours which, in practical terms, can be considered a real-time signal for an O&M operator. Figure 9 shows the data plotted between the obtained ToF precision (*σToF*) and the signal level (SL) for both non-exposed bare steel and coated samples. Here, the SL refers to the Root Mean Square (RMS) value of the first detected echo measured after the amplifier. This value is calculated digitally after the bandpass filter mentioned above. Because of this, SL is an indication of the SNR of the digitized signal after bandpass filtering.

The precision of ToF values we are plotting here is the standard deviation of 25 measures launched at one location, as discussed in Section 5.2. The data points of the graph for non-exposed coated samples in Figure 9 are related to both on scribe and no-scribe areas. It has been clearly observed, in the Figure 9, that the SL of ultrasound measures has considerable variations, depending on the position of the piezo, and, when the signal level decreases, the precision obtained for those respective measures gets worse.

The data points of signal level versus ToF precision were best fitted with an exponential decay function (*σToF* = *A* · *e* −*SL*/*B* ). Each fitted curve is represented over the signal level range of 35 mV to 250 mV. Considering the decay constant coefficient associated with each fitted curve (parameter *B* in mV indicates the increase in SL necessary for a 63% reduction in *σToF*), the ToF precision versus SL behavior is almost the same for the bare steel and coated samples. Both bare and coated samples have good ToF precision results, but the obtained SLs are slightly better in coated samples. The reason behind this behavior may be that the quality of contact made between the transducer and the coated samples was better than in the case of the bare steel samples. Furthermore, the results do not show any significant reduction of the signal level due to the coating layer.

**Figure 8.** Bandpass filter results for bare steel sample (**top**) and coated sample (**bottom**).

**Figure 9.** Non-exposed samples: signal level versus precision.

#### 6.1.2. Measurements Precision of Exposed Test Coated Samples

Different sets of numbered coated samples have been exposed to a controlled corrosive environment under the cyclic aging test after 1 month, 3 months (see Figure 6 (bottom)), and 6 months exposure. After the completion of the exposure time, each sample has been tested using the UT. The ultrasound thickness measures have been performed in both on scribe and no-scribe locations of the coated samples, as discussed in Section 5.1.

The precision of measures obtained for the test coated samples exposed under cyclic aging test for different time durations with respect to the signal level has been plotted in Figure 10. Here, also, the SL refers to the Root Mean Square (RMS) value of the first detected echo measured after the amplifier, and precision refers to the standard deviation of 25 measures performed in the same location (*σToF*). Comparing the precision of ToF measures between on scribe and no-scribe areas, it can be seen that, in order to obtain similar precisions in Scribe and Non-Scribe areas, we must increase the SL by ∼75 mV (see the *B* parameter of fitting curve) when measuring Scribe areas.

**Figure 10.** Exposed coated samples: signal level versus precision.

Furthermore, in the case of the on scribe area, it can be observed that the most lower signal level data points belong to the samples with higher exposition time. This may be caused due to the non-uniformity of the corrosion layer developed on the scribe area. In general, we are obtaining a good precision for both bare and coated samples. The ToF precision computed here is the standard deviation of ToF values of 25 measures at the same sensor position (as discussed in Section 5.2). If we place the sensor on different locations of the same sample and calculate the standard deviation of ToF measures, the obtained precision is lower than the given values here. This is because the thickness at different locations of the same sample varies, even for the non-exposed bare steel samples. These small thickness variations (at µm level) are due to the common existing imperfections during the sample production. Therefore, in order to have a good precision of ToF measures, the positioning of the sensor on the same location is very important. As discussed in Section 3, from the two modes of operation (fixed and mobile), the positioning accuracy can be a constraint for the mobile solution, which we have to address in future work.

#### 6.1.3. Thickness Loss Measurements on Exposed Test Coated Samples

Each exposed coated sample has been measured using UT, as mentioned in Section 5.1. Figure 11 shows the thickness measures on scribe and no-scribe locations of coated samples

for different exposed time durations. Considering the fact that no significant difference has been observed between the no-scribe bottom and no-scribe top layer thickness measures, only an average of no-scribe top and bottom layer measures has been used as the noscribe measures.

**Figure 11.** Coated samples: thickness versus exposed time in months.

The detected thickness differences between the scribe and no-scribe locations of the same sample are indicated by the arrows. With the scribe made in the coated samples, the corrosion process has been accelerated and initiated along with the scribe. Apparently, the results show that the thickness losses are higher on the scribe area than on the no-scribe area when the exposure time is sufficient to produce a significant thickness loss due to corrosion, as is the case of 6 months exposure.

#### **7. Conclusions**

In this paper, we present a corrosion monitoring system based on ultrasound technology. The size, weight, and other performance parameters, such as precision in thickness loss measurements, power consumption, and wireless connectivity, make the proposed solution very suitable for unattended deployment in offshore wind turbines or installed in mobile platforms, such as drones operating inside the tower, to cover easily large structures. This mobile solution would be able to detect earlier critical failures due to corrosion and, consequently, plan better maintenance actions.

The system design was developed using an Ultrasound Testbed (UT) that allows us to assess the performance of the detection and measuring algorithms in MATLAB and C/C++. The UT can launch ultrasound experiments with different parameters (frequency, waveform duration, gain, etc.) in order to find the optimal values. As a result, we created a large database of ultrasound raw signals that were later used to validate the algorithms implemented in the final miniaturized system. After validation, the UT system has been successfully migrated into a miniaturized system with low power, low cost, and size of 110 × 60 × 15 mm.

All the measurements presented in the paper were done using the UT and analyzed under a MATLAB development environment for test samples of 75 × 150 × 5 mm. However, the system was validated for reference samples of 75 × 150 × 40 mm, as well, demonstrating that the solution is flexible enough to work with different thicknesses closer to a

realistic scenario. Further large-scale validation of the proposed solution mainly for sensor placement and alignment in the case of the mobile solution will be done in the near future. Related to that, and taking into account the harsh conditions of these offshore platforms, we pay special attention to the batteries and sensor probe with the aim of reducing the number of replacements and to facilitate those replacements when needed.

Considering the results obtained in this research work, the signal level (SL) and ToF precision measurements show a similar exponential decaying relation for both bare steel and coated samples. In general, we could observe that the signal level is slightly higher for coated samples than for bare samples and that precisions below 1 µm can readily be obtained for SL > 50 mV. The thickness loss could be estimated in the coated (NORSOK 7A system) samples as the difference in the sample thickness between the no-scribe and on scribe areas after running the cycling aging test for several months. The results show, as expected, a growing thickness loss as exposition time increases. The values of the thickness loss reported is an average of the difference between the thickness along the on scribe area and the thickness in many no-scribe areas of the same sample. Other observations are that SL in on scribe areas is normally worse than in no-scribe areas, SL deteriorates as exposition time increases, and ToF precisions are again below 1 µm for SL > 50 mV.

Therefore, the thickness estimation of coated samples exposed under the cyclic aging test shows meaningful information about thickness loss due to corrosion. The variable tolerance of the wall thickness at different locations of the same sample very well obliges sensor positioning for the mobile platform. However, this is not an issue for the fixed solution.

To sum up, it can be said that the main objectives related to achieve a miniaturized system, to get a precision of 1 µm, and to estimate the thickness loss with high precision have been accomplished, taking into account bare and coated samples. The obtained precision allows us to take several thickness measurements per day to estimate the value of the corrosion rate in real-time for practical purposes.

**Author Contributions:** Conceptualization, A.C. and A.I.; Formal analysis, A.I. and U.C.T.; Funding acquisition, A.C. and A.I.; Investigation, A.C., A.I. and U.C.T.; Methodology, A.I. and U.C.T.; Project administration, A.C.; Software, A.I. and U.C.T.; Supervision, A.C. and A.I.; Validation, A.I. and U.C.T.; Writing—Original draft, U.C.T.; Writing—Review & editing, A.C. and A.I. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the WATEREYE project, which has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No. 851207.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** This work has been possible thanks to the cooperation of CEIT with all the WATEREYE partners, especially in this case with SINTEF Industry, who is responsible for producing the samples, measuring the samples through conventional methods, and corroding the samples in lab.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**

The following abbreviations are used in this manuscript:


#### **References**


## *Article* **Diagnosis of Broken Bars in Wind Turbine Squirrel Cage Induction Generator: Approach Based on Current Signal and Generative Adversarial Networks**

**Yuri Merizalde Zamora 1 , Luis Hernández-Callejo 2, \* , Oscar Duque-Pérez <sup>3</sup> and Víctor Alonso-Gómez 4**


**Abstract:** To ensure the profitability of the wind industry, one of the most important objectives is to minimize maintenance costs. For this reason, the components of wind turbines are continuously monitored to detect any type of failure by analyzing the signals measured by the sensors included in the condition monitoring system. Most of the proposals for the detection and diagnosis of faults based on signal processing and artificial intelligence models use a fault-free signal and a signal acquired on a system in which a fault has been provoked; however, when the failures are incipient, the frequency components associated with the failures are very close to the fundamental component and there are incomplete data, the detection and diagnosis of failures is difficult. Therefore, the purpose of this research is to detect and diagnose failures of the electric generator of wind turbines in operation, using the current signal and applying generative adversarial networks to obtain synthetic data that allow for counteracting the problem of an unbalanced dataset. The proposal is useful for the detection of broken bars in squirrel cage induction generators, which, according to the control system, were in a healthy state.

**Keywords:** wind turbine; faults diagnostic; artificial intelligence; unbalanced datasets; synthetic data

#### **1. Introduction. Fault Diagnosis in Wind Turbines by Means of the Current Signal**

Due to the remote locations where wind farms are installed and the considerable height of the wind turbines (WTs), condition-based maintenance predominates in the wind industry [1–3]. The detection and diagnosis of failures of WT components is usually performed using signal processing techniques applied to the vibration signal [4]. However, according to [5], the vibration signal has some disadvantages that can be overcome using the current signal, since with this signal it is possible to detect not only electrical faults, but also mechanical faults.

When a current flows through the stator of the induction machine, a flux is created in the air gap that depends on the design parameters of the motor. This flux induces currents in the rotor bars, which will create their own field. According to [6], when the rotor is in good condition, there is only one field that rotates in the same direction as the rotor, at the slip frequency. However, when there is an asymmetry in the rotor, a current and a field appear in the opposite direction of the normal current. The electromotive force due to the fault current induces a current in the stator, whose frequency is given by *fbb* = (1 − 2*ks*)*f* Hz [7].

**Citation:** Zamora, Y.M.;

Hernández-Callejo, L.; Duque-Pérez, O.; Alonso-Gómez, V. Diagnosis of Broken Bars in Wind Turbine Squirrel Cage Induction Generator: Approach Based on Current Signal and Generative Adversarial Networks. *Appl. Sci.* **2021**, *11*, 6942. https:// doi.org/10.3390/app11156942

Academic Editor: Daniel Villanueva Torres

Received: 28 June 2021 Accepted: 26 July 2021 Published: 28 July 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

The broken rotor bar causes a torque pulsation at twice the slip frequency (2*sf*), in addition to a speed oscillation that is also a function of the inertia of the rotor. The speed oscillation can reduce the magnitude of the sideband (1 − 2*s*)*f*, but instead an upper sideband current component is induced at (1 + 2*s*)*f* in the stator winding, which is reinforced by the magnetic core nonlinearity, that is, as a summary it can be said that the failure due to broken bars or other oscillations induces additional frequencies in the stator current given by Equation (1).

$$f\_{bb} = [(1 \pm 2ks)]f\tag{1}$$

Equation (1) is what is known as a double slip frequency sideband due to broken rotor bars, which modulates the amplitude and phase of the line current. According to [8], as the oscillations of the load torque are also manifested in the spectrum around the fundamental frequency, the components of Equation (1) would not be useful to diagnose broken bars. For this, it is necessary to use the higher order components given by Equation (2).

$$f\_{bb} = \left[ \left( \frac{k}{p} \right) (1 - s) \pm s \right] f \tag{2}$$

Having analyzed the way in which the components associated with failures are produced, such as broken bars, now the problem is to find the appropriate method for their detection and diagnosis. For the detection and diagnosis of faults in rotating electrical machines, the prevalent approach is based on working in the frequency domain, identifying the frequency components of failure in the vibration spectrum. Although many proposals in this regard can be found in the specialized literature, there are still challenges to overcome, especially in the detection of incipient faults and in operation at low load. Besides, if the slip varies due to change in speed, load, or grid instability, there is no constant spectrum, and signal processing techniques must be applied, such as: time-frequency transforms, filtering techniques to eliminate the components that are not of interest, and algorithms to obtain the spectrum corresponding to a specific speed [9,10].

Thus, in relation specifically to the use of the current signal for the fault detection of the electric generator of WTs and prime mover coupled to its shaft, some examples can be mentioned. In [11], the faulty gears of the gearbox are detected using power spectrum density (PSD), [12] proposes a model that allows for detecting the broken teeth of gears applying fast Fourier transform (FFT), [13] also detects the broken teeth of gears, using FFT prior to the application of SVM, [14] uses PSD to extract the characteristics of the signal that, after passing through a model called particle filtering, feeds an adaptive neuro Fuzzy inference System (ANFIS) capable of detecting broken teeth in gears, [15] proposes the use of a multiphase imbalance separation technique (EMIST) together with FFT to detect faults in the inner and outer race bearings of a gearbox, [16] proposes the detection of roughness in bearings, decomposing the current signal by means of wavelets. In [17], faults of the stator and rotor windings are detected by analyzing the spectrum obtained with the FFT. Through a comparative study, [18] determined that, to detect bearing failures, broken bars, and eccentricity, the wavelet-based methodology is superior to the Welch periodagram, PSD and Short Time Fourier Transform (STFT), while according to [19], Hilbert transform (HT) is superior to Park transform and Teager energy operator when it comes to detecting generator bearing failures. As a summary, once the signal processing techniques have been applied, the identification of the components associated with the failures is done according to the equations, such as those included in Table 1.

**Table 1.** Frequency components associated with faults [5].


From a historical point of view, methodologies based on signal processing techniques were the first to be used regarding the detection and diagnosis of faults in rotating electrical machines. After the appearance of the AI models, it would not take long before they were applied to the diagnosis and detection of faults in rotating induction machines. At present, signal processing techniques constitute a previous step for the application of AI models.

AI has been the subject of a huge number of publications and research papers, which have allowed for the construction of sophisticated equipment to control, monitor and detect the presence of faults, especially using ANN, Fuzzy logic and Neuro-Fuzzy systems [20] and [21]. As an example of the basic methodology used, we can mention the publication made by [22], approximately twenty-two years ago. According to this proposal, the frequency components that are relevant for the diagnosis depend on the slip or speed, so it is necessary to make two measurements, a sampling at high frequencies to determine the slip by means of the harmonic of the first slot and another sampling of greater duration at low frequencies to find the components associated with the faults. The inference machine of an expert system compares the spectrum obtained with a database containing the components associated with different types of faults and filters out the part of the spectrum that is not of interest. A simple way to carry out the diagnosis is by comparing the values obtained against a previously established threshold. The other alternative is through ANFIS with a Sugeno-type first-order inference system. The set of faults obtained are the input of the membership functions that form the adaptive nodes of the first layer of a multilayer neural network fed forward. The first layer is associated with the membership functions of linguistic variables (small, medium, and large), while the last layer provides the diagnosis expressed as: no failure, incipient failure, one broken bar, and two broken bars. To diagnose broken bars, the input variables are the components associated with these faults, whilst the negative and positive sequence components are used to detect short circuits between turns.

According to [21], as the ANFIS model only has one output, it can detect only one fault. For this reason, [21] proposes the co-active ANFIS (CANFIS) model capable of detecting several faults at the same time. The previously filtered and demodulated signal is decomposed by wavelet transform to obtain the coefficients that are affected by the faults. These coefficients are the input of the CANFIS model, which by having multiple outputs, can detect several faults at the same time. For [23,24], when fault diagnosis is done applying wavelet transform, it is not necessary to use slip. However, according to [25], as wavelets have the drawback of energy loss and edge distortion, it is preferable to use empirical mode decomposition (EMD) to obtain intrinsic mode functions (IMF). Each IMF represents a frequency band in which a type of failure can be found using Support Vector Machines (SVM), but after the optimization of the parameters by means of a genetic immune algorithm.

Although most of the proposals are based on models that have been previously trained with data containing the faults to be detected, according to the proposal of [26], this requirement would not be necessary. According to [27,28], the diagnosis can be made based only on data from systems such as Supervisory Control and Data Acquisition (SCADA). In [29], the signal is filtered to obtain the root mean square (RMS), kurtosis, skewness, standard deviation and crest factor. These parameters are the input data of a neural network trained with the Bayesian Regularization algorithm; the ANN has a hidden layer with 46 neurons and for the output layer it uses the tan-sigmoid transfer function.

According to [30], once the rotor current signal of a doubly fed induction generator (DFIG) has been sampled, the instantaneous rotation frequency of the shaft is obtained and the signal is demodulated using HT to obtain its envelope, but as the speed and shaft rotation frequency are not constant, an angular resampling algorithm is applied to obtain a constant envelope. Once this constant envelope is obtained, its PSD can be obtained to detect faults. In each phase, the amplitudes of the rotation frequencies corresponding to the input shaft, pinion and output shaft are obtained, plus RMS, kurtosis, peak value, and signal-to-noise ratio (SNR). These variables become the input of a deep learning model

called a stacked autoencoder. Finally, the characteristics obtained from the learning of the ANN feed an SVM algorithm that classifies the failures. In [13], the frequency components that correspond to the faults are derived as a function of the interaction between the rotor and stator currents. When the gearbox suffers a failure, the vibration produces a torque on the shaft, Equation (3), altering its speed and frequency, which will be reflected in the current spectrum. Thus, when the FFT is applied to rotor and stator signals, characteristic frequencies of gearbox failures can be detected. In total, 16 variables of the rotor and 9 of the stator are extracted, of which 19 are in the frequency domain and 6 are in the time domain (RMS, kurtosis, and peak value of both signals). These variables feed an SVM whose output offers a diagnosis of the failures expressed in probability form, unlike the traditional SVM model that only classifies the failures.

$$T = T\_0 + \sum T\_l \cos(2\pi f\_l t + \varphi\_l) \tag{3}$$

Another way to visualize the state of a component is by means of its remaining useful life (RUL), as applied in [14] to analyze the state of the bearings of a gearbox. According to this study, whilst gears cause torsional vibrations, bearings do so radially. For this reason, in a healthy state the phase current will contain the fundamental component *f* and sidebands *fi* caused by the normal vibrations of the gearbox. However, as the faults will be reflected in the amplitude of the frequency components, if there are bearings with localized faults, new components will appear in the current signal, according to Equation (4). Once the signal has been sampled and before obtaining the PSD, the high frequency noise is eliminated by means of a forward-backward filter. The variable used to predict the state of the multiplier and its RUL is the SNR calculated according to Equation (5). The SNR values are the input of a five-layer ANFIS model, with an inference system formed by a set of 16 Fuzzy rules of the IF-THEM form based on a first order Sugeno model and optimizing the parameters using an ANN.

$$\begin{split} i\_{\rm sd} &= i\_{\rm sT0} \cos(2\pi f t) + \sum\_{i} \frac{1}{2} A\_{\rm sT\_i} [\cos(2\pi (f - f\_{\rm i})t - \varphi\_{\rm Ti}) + \cos(2\pi (f + f\_{\rm i})t + \varphi\_{\rm Ti})] \\ &+ \sum\_{j} \frac{1}{2} A\_{\rm sT\_j} [\cos(2\pi (f - f\_{\rm j})t - \varphi\_{\rm Ti}) + \cos(2\pi (f + f\_{\rm j})t + \varphi\_{\rm Ti})] \end{split} \tag{4}$$

$$NSR = \frac{P\_{noise}}{P\_{signal}} = \frac{P\_{total} - P\_{signal}}{P\_{signal}} \tag{5}$$

According to [31], although the rotor imbalance is manifested in the amplitude of the lateral harmonics of the fundamental frequency, the FFT and STFT fail to detect faults when the SNR is low, and the speed is not constant. As a single ANN would not be sufficient to cover the entire range of the electric generator speed, the authors propose dividing the interval in which the speed varies by several ranges and using one ANN for each range. The variables used correspond to wind speed, wind direction, pitch angle, turning speed and power output for one year, all of them obtained from the SCADA. To test the proposal, [31] simulates in Simulink a WT whose current signal is sampled at 5 kHz for 300 s. Applying FFT to 2 s signal segments, the spectrum formed by 250 components that become the input of the ANN is obtained. Having trained the model first with the signal in a healthy state and then with the signal containing the fault, the author states that it is possible to detect the frequency components associated with rotor eccentricity, which according to classical spectral analysis are given by Equation (6).

$$f\_{\text{ecc}} = [1 \pm (2k - 1/p)]f\tag{6}$$

In [32], through the equations that relate voltage, current, flux, mutual inductance and torque between stator and rotor, a WT with DFIG is simulated in Matlab, but unlike [31], the faults studied are the one-phase fault and the inter-turns short circuit of the stator, while the model used is Fuzzy logic. The current signals from the three phases of the stator feed the Fuzzy system, which interprets them as linguistic variables (zero, small, medium, and large). From the database obtained with the measurements, the membership functions and 14 Fuzzy rules are built. In another simulation proposed in [33], the current signal from a DFIG and ANN are used to monitor islanding events of WTs that are part of a wind farm connected to the grid. Other models used include the detection of broken bars and inter-turns short circuits, using equations from Table 1 [34].

In relation to the publications on the monitoring, detection, and diagnosis of failures in induction motors, using current signal and AI models, there is less research that deals with WTs. Some proposals are shown in Table 2. The components that have received the most attention are: bearings, gearbox, blades and electric generator. It can also be observed that among the models used, the following predominate: SVM, ANN, fuzzy logic and ANFIS. However, at the time of writing this research, only the works of [15,35–37] deal with the use of the current signal based on data from WTs in operation, although none of them apply AI models. By way of summary, it can also be stated that:


In most of the proposals, the AI model used is trained with the signal from the faultfree machine, to later use a sample of the signal that contains some type of failure caused on purpose (so the type of failure is known in advance). In these conditions, diagnosis is relatively easy, but due to the related costs, in the wind industry it would be very difficult to proceed in this way, so only the signal during the WT operation is available. However, if we only have the signal from the electric generator of TWs during its operation, the diagnosis process is complicated, since, in this case, and assuming that there are few faults or the faults are in an incipient state, the data are unbalanced. Since the efficiency of generative adversarial networks (GANs) is so high that it is difficult to distinguish between real and synthetic data, samples obtained by GANs could be used to compensate for unbalanced datasets.

Considering what has been stated previously, the main objectives of this work are to investigate the detection and diagnosis of faults of the SCIG installed in an operating WT (on which there are very few field studies), using electrical current signal and GANs, which is a methodology little explored thus far. The rest of this investigation is organized as follows: in Section Two, a brief conceptual analysis is made on the use of the current signal and GANs for fault detection and diagnosis in WTs. Section Three includes the methods and materials. In Section Four, the results obtained when applying the proposed methodology are shown and discussed. Conclusions and recommendations are included in Section Five.


**Table 2.** Proposals on fault detection in WTs using current signal and AI models.

#### **2. Fault Diagnosis by Means of GANs**

From a computational point of view, there are several methods to improve the efficiency of AI models trained with an unbalanced dataset, [39]. However, according to [40], statistical, regression, clustering and reconstruction models are not efficient when it comes to unbalanced datasets with very few outliers. Non-parametric models require large amounts of data and computational resources, while proximity-based models are affected by the volume and dimensionality of the data. Therefore, to overcome the drawbacks of unbalanced datasets and the lack of information caused by the course of dimensionality, [40] proposes Artificially Generating Potential Outliers (AGPO), whose main idea is to apply generative adversarial networks (GANs) to detect outliers of unbalanced datasets.

Among the most widely used AI models are those called generative modeling, whose main objective is to learn the exact distribution of the data with which they are trained, so that new data similar to the original can be generated, simulated or predicted. Although the main application of these models has been the treatment of images, they have also been used in the field of video games, cinema, graphic design, audio analysis and body language. However, the main difficulty has been finding the function that allows modeling the input data, and for this purpose, these models use the Monte Carlo method based on Markov chains, which is computationally very expensive. To overcome this drawback, several proposals, such as the Variational Autoencoders (VAEs) model have incorporated the use of ANNs capable of obtaining a powerful approximation function, through backpropagation. VAEs obtain the probability function using Bayesian statistics and two generative networks. The first ANN generates a probability function and random values on the studied phenomenon. The second ANN performs the discriminator function and provides a model only for the variables labeled conditional on the observed variables [41].

Until a few years ago, VAEs were among the most powerful and popular models used for the unsupervised autonomous learning of complicated distributions; however, they have the drawback that to determine probability distributions, they use Bayesian networks and Markov chains. However, in 2014, Ian Goodfellow [42] proposed the GANs, which is a model composed of two multilayer perceptron (MLP) ANNs. The first ANN

plays the role of generator (NNG), since, after obtaining the distribution function of the dataset, it is capable of generating synthetic data very similar to the originals. The second ANN works as a discriminator (NND), because it determines whether a sample is real or is generated by the NNG. The two ANNs compete with each other until they find the Nash equilibrium for the non-cooperative game between two players trying to minimize their cost function. When the optimal point has been reached, the synthetic samples are so similar to the real ones that the NNG is not able to determine if a sample is real or fake. All this is achieved without using Markov chains and inference systems, and both ANNs are trained simultaneously with the same dataset, unlike models such as VAE, in which the NNG and NND are trained separately, [42].

According to [43], the minimization technique based on the gradient to lower the cost of each player simultaneously, which is used in [42], fails in convergence, so it is preferable to train the generator to match the value that it should have for an intermediate layer of the discriminator. This strategy, called GAN coincident characteristic, is excellent as a semi-supervised learning classifier, since, according to [40], its strength is based on the fact that: "*Instead of directly maximizing the output of the discriminator, the new objective requires the generator to generate data that matches the statistics of the real data, where we use the discriminator only to specify the statistics that we think are worth matching*."

Currently, one of the most recent alternatives to solve the problem of classifying outliers from an unbalanced dataset is to generate synthetic data using semi-supervised and unsupervised models based on GANs [44]. The applications of GANs are no longer limited to image processing, but they are also applied to tabular data. In addition, to improve efficiency, proposals can be found that combine GANs with other models [45], while other investigations even modify the structure of the original GANs proposal. In [40], the Single-Objective Generative Adversarial Active Learning (SO-GAAL) algorithm is proposed to detect outliers from an unbalanced tabular dataset. The SO-GAAL model, which is based on the Generative Adversarial Active Learning (GAAL) proposed by [46], is basically a GAN that performs the classification when the NND separates the real data from those potential synthetic outliers generated by NNG. However, as the training progresses and the min-max game reaches Nash equilibrium, the information about the potential outliers is too close to the real data and the NND fails to distinguish between real data and outliers, causing the accuracy of SO -GAAL to drop dramatically.

The SO-GAAL model is unable to obtain a distribution function that represents the whole dataset and fails to detect the outliers because it does not stop the training when the outliers provide the necessary information, and this is due to fact that the GAN proposed by [42] has no prior information. To correct this problem, [40] proposes to modify the structure of the GANs, adding multiple NNGs with different objectives (MO-GAAL). The real data are divided into subsets of affine samples and each subset will feed an NNG, which will learn to generate outliers similar to the real data. In this way, a set of distributions is obtained that represents the whole dataset, which allows the NND to classify the outliers.

Regarding the detection and diagnosis of faults in rotating electrical machines, based on unbalanced datasets, several approaches are available, such as: [47], which proposes the Adaptive Boosting (AdaBoost) method to detect broken bars, and [48], which proposes a multiclass support vector machine (SVM) based on the one-vs-one strategy to detect broken bars in the case of speeds close to synchronism. In general, it can be said that, when it comes to fault detection and diagnosis, proposals based on an unbalanced dataset combine various statistical and AI models, but there is no standardized methodology. The application of GANs is still limited and there are not many references: [49] uses the current signal and synthetic data generated by GANs to correct the overtraining of a deep neural network used to detect the faults of an induction motor, while, to detect incipient faults in a gearbox, [50] obtains a synthetic dataset through GANs that are added to the original dataset to properly train a Stacked Denoising Autoencoder (SDAE) using the vibration signal. In general, it can be said that no references have been found on the use of the current signal together with GANs for fault detection in WTs, and especially in

squirrel cage induction generators (SCIG) of WTs. Furthermore, the mentioned proposals for induction motors have been demonstrated on test benches and using small power electric motors. The GANs could also be applied to other types of signals, in such a way that the results can be compared with other proposals, such as [51].

#### **3. Materials and Methods**

For this study, measurements were made in a wind farm located in the region of Castilla y León, Spain. The wind farm has 33 WTs (NEG Micon brand) that use two winding SCIG, one of 750 kW that operates when the wind speed exceeds 6.5 m/s and another 200 kW winding for wind speeds between 3 and 6.5 m/s (see Table 3). As it is necessary to turn off the WTs to install the measurement equipment, permission was only obtained to perform the measurements at four WTs (WT-3, WT-4, WT-16 and WT-25). It must also be noted that the tests were done on the highest power winding, since the wind speed was relatively high at the time the signal was sampled.

**Table 3.** Technical characteristics of the SCIG.


For measurements, three Fluke i3000s FLEX-36 current clamps (one for each phase) were connected to the main panel of the WT. The other end of the current clamp was connected to a PicoScope® 4424, which must necessarily be connected to a computer where the software has previously been installed to configure the acquisition of the signal (see Figure 1). Although generally to obtain a good resolution in the frequency domain the sampling rate used fluctuates between 2 and 5 kHz, in this work a 10 kHz sampling rate was applied, since the frequencies that could be found were unknown. The total measurement time in each WT was approximately 8.5 min and to reduce the effects of spectrum variation, the sampled signal is recorded every two seconds. The software to sample the signal simultaneously records a file in *mat* format for each phase. Under these conditions and considering the four WTs, a total of 1006 signal files are obtained for each phase and 3018 files if the three phases are considered.

The signal records are processed in Matlab to obtain the power spectral density. The difference in magnitude between the fundamental frequency and its sidebands is then calculated, and depending on the magnitude of this difference, the data are labeled as 0 (healthy) or 1 (broken bars) [52]. Through Equation (2), the lateral components of the fifth, seventh, eleventh and thirteenth harmonics are also obtained.

**Figure 1.** Generator electrical signal sampling.

According to what was seen in Section Two, the identification of the frequency components associated with the faults must be done at a fixed speed and slip. However, as the wind speed has a stochastic behavior, the spectrum of the generator will vary, and it is necessary to apply a method that allows the analysis in the frequency range at which the faults occur [53]. To solve the inconvenience described, one of the most accepted alternatives is the wavelet transform, since it allows for analyzing the signal in both the time and frequency domain [23]. Using the wavelet transform, a signal can be represented as a sum of small waves or wavelets throughout the time domain, which is known as a continuous wavelet transform (CWT). Each wavelet is a wavelet function that represents the original signal but scaled and shifted. However, as CWT involves too many calculations, another alternative is to apply the discrete wavelet transform (DWT), which can be seen as a downsampling process to decompose a signal into two sequences called *cA<sup>1</sup>* (approximation coefficients) and *cD<sup>1</sup>* (detail coefficients). *cA<sup>1</sup>* corresponds to the lower frequency range, while *cD<sup>1</sup>* consists of the high-frequency noise of the original signal. If we decompose *cA1*, a second level of decomposition formed by *cA<sup>2</sup>* and *cD<sup>2</sup>* will be obtained. Decomposing *cA2,* we will obtain *cA<sup>3</sup>* with *cD3*, and so on until the frequency level we are trying to analyze is reached [54].

Applying Equation (1) for broken bars, a frequency component of 49.33 Hz is obtained. Then, following the methodology proposed in [55], the signal is decomposed using discrete wavelet transform (DWT) in 8 levels (see Figure 2). Since the 49.33 Hz frequency is contained within the frequency range of level *d8* (38-78.16 Hz), signal power is obtained from level d8. In addition, the maximum and minimum values of the signal power are obtained, as well as the median, mean, mode, standard deviation, and variance. With all these data obtained in Matlab, a file type *csv* is created, which becomes the dataframe to

work in Python and tensorflow. The data are scaled to the range 0 to 1 for the best behavior of the neural networks.

**Figure 2.** Signal decomposition using DWT, [55,56].

In Python, Kmeans is first applied to obtain three clusters, in such a way that the dataset is separated into healthy and faulty samples. Once the failure samples have been identified, and because they are relatively few, then the GANs are used to generate synthetic samples with faults which can compensate the unbalanced dataset. The synthetic data obtained in this way are put together with the original samples to retrain an ANN (see Figure 3).

**Figure 3.** General scheme of the proposed model.

The GANs are MLP with backward propagation and are fed with the same variables used to apply Kmeans but are from the samples with failures. The structure of the ANNs is:


The hyper-parameters of the ANNs are: 100 training cycles (epochs) and the samples presented to the network each time are 10 (batch size). Accuracy is defined as the initial results metric. To guarantee the independence of the training and test data, ANNs are trained using 5-fold CrossValidation. The implementation of the ANN models was done with tensorflow and Keras. The computer used was the same one that was used to sample the signal, that is, a Toshiba laptop with an Intel Core i3-3120M processor, 2.50 GHz, 8 GB of RAM and an Intel HD Graphics 4000 graphics card.

To compare the results obtained with the proposed procedure, the proposal of [40] is applied, in which, in addition to generating synthetic data using GANs to compensate unbalanced tabular data, it is also proposed to use several generating neural networks (GNN), instead of a single GNN that is used in the original proposal of GANs. The research code from [40] is available in the GitHub repository, but since it is written in previous versions of Python and Tensorflow, it is necessary to create another virtual environment in Anaconda Powershell.

#### **4. Results and Discussion**

Applying some basic AI models, it can be observed that for all the models, the convergence is excellent, the RMSE is very small, and the accuracy value is very high (see Table 4 and Figure 4). The same does not happen with the Presiccion, Recall and F1 metrics, since the uniformity of the data and the existence of very few outliers make it difficult to identify the outliers. Applying kmeans and segmenting the dataset into three clusters (see Figure 5), the uniformity of the data can be appreciated, but also in one of the clusters the dispersion of the outliers can be observed. Outliers reduce the effectiveness of kmeans, as can be seen in the confusion matrix in Figure 6.

**Table 4.** Root mean square (RMSE) error for AI models trained with real data.


Out of 3018 samples, 2953 are free of faults and only 65, approximately 2% of samples, have any indications of a fault. The distribution of the asymmetries found according to each WT is summarized in Table 5, where 78% of the failures indicated correspond to WT-3 and WT-4. The small number of samples which have failures causes the set of data available to train the AI model to be unbalanced, which would also likely cause the metrics of the first Kmeans model to be improved.

The low number of outliers (incomplete dataset) reduces the efficiency of the AI models. So, to improve the quality of the prediction, we apply the strategy of generating synthetic data using GANs. First, we tested with the methodology proposed by [40]. When the SCIG signal is processed using the algorithm proposed to generate synthetic samples using GANs with only one GNN, the precision in the detection of outliers is shown in Figure 7a and the area under the curve (AUC) is 0.52. When the GANs model with multiple GNNs is used, which according to [40] is superior to models such as: kNN, FastABOD, Parzen and k-means, the precision in the detection of outliers improves considerably (see Figure 7b) and the value AUC increases to 0.84.

**Figure 4.** ANN convergence trained with real data.

**Figure 5.** Kmeans (k = 3) model trained with real data.

**Figure 6.** Confusion matrix obtained with original dataset and Kmeans.

**Table 5.** Number of samples with trace of failure.

**Figure 7.** Precision in the detection of broken bars of the SCIG, using the proposal of [40]. (**a**) GANs with one GNN; (**b**) GANs with multiple GNNs.

As can be seen in Figure 7, the ROC curves are very unstable and the predictions fall below the non-discrimination line, which means that the model has difficulties converg and is ineffective at predicting failures. When only one GNN is used, the instability of the model is maintained despite reaching 17,000 iterations (see Figure 7a), while, using several GNNs, the model stabilizes after 7000 iterations (see Figure 7b), and the sensitivity also improves markedly.

Applying the methodology proposed in this research, as described in the fourth section, with the samples showing signs of failure (see Table 5), we train the GANs to generate 100 synthetic data, which is added to the original data, to retrain a neural network. Proceeding in this way, the Receiver Operating Characteristics (ROC) curve (see Figure 8) and the value of 0.95 for the AUC are obtained. Compared with the ROC curve obtained by applying the proposal of [40] (see Figure 7), the ROC curve in Figure 8 is much smoother and indicates a better convergence of the models used in this research. In fact, the AUC is also higher.

Another way to visualize the efficiency of the proposed model is through the confusion matrix (see Figure 9). From t 9 it can be seen that the proposed model is capable of appropriately classifying the synthetic data and in this way improves the accuracy of the prediction.

**Figure 8.** Receiver Operating Characteristic curve of the K-means model trained with data generated by GANs.

**Figure 9.** Confusion matrix of the ANN trained with synthetic data.

#### **5. Conclusions**

The signal processing techniques have represented an important advance regarding the detection and diagnosis of faults; however, in many cases they are not enough and must be combined with other mathematical models that generally assume some idealizations. Another alternative is artificial intelligence (AI) models, which from a conceptual point of view are characterized by their ability to adapt to uncertainty and to work with incomplete data. These AI models are used individually or together with signal processing techniques; however, when only the current signal of a WT in operation is available, but the signal has not been previously sampled in a healthy state or with some type of fault, the detection and diagnosis is complicated. It must also be noted that when failures are incipient and there are few failure records, the efficiency of AI models will be reduced.

In the usual procedures, the diagnosis algorithms are trained using data from tests with healthy equipment and with equipment in which failures have been caused. However, these situations may not be extrapolated to real situations, in addition to decreasing the performance of the classification algorithms when working with unbalanced datasets.

To improve the efficiency of AI models and wind turbine fault diagnosis procedures in cases of unbalanced data, this research proposes generating synthetic data using GANs. The methodology has shown its effectiveness for the early detection of failures due to broken bars in SCIG, in addition to allowing for improving the metrics of the AI model used.

Although this study has focused on broken bars, the proposed model could be applied to detect other faults. At the output of the proposed model, another model based on ANN or Fuzzy logic could be added to obtain a more precise diagnosis of the failure studied (half section broken bar, one broken bar, two broken bars, many broken bars). It would also be advisable to continue with the research trying to build GANs, not only with MLP, but also with other AI models, and to use GANs not to generate a synthetic dataset, but to carry out the diagnosis exclusively through GANs. In this study, tabular data have been used; however, the proposed methodology could be tested with images. In addition, other types of signals could also be used, such as: vibration, acoustic and thermal.

**Author Contributions:** Conceptualization, Y.M.Z. and L.H.-C. methodology, Y.M.Z.; validation, Y.M.Z., L.H.-C. and O.D.-P.; formal analysis, Y.M.Z., L.H.-C. and O.D.-P.; resources, Y.M.Z. and L.H.- C.; writing—original draft preparation, Y.M.Z.; writing—review and editing, L.H.-C. and O.D.-P.; visualization, V.A.-G.; supervision, L.H.-C.; project administration, O.D.-P. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by University of Guayaquil and CETASA.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors would like to thank the University of Valladolid and University of Guayaquil for the assistance in the preparation of this research. We would also like to thank the company CETASA for allowing the acquisition of the signals and providing the necessary equipment. Thanks also to the anonymous reviewer for their assistance in the improvement of the study.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Nomenclature**


#### **References**


**Claudio Risso 1, \* and Gustavo Guerberoff 2**


**Abstract:** The increasing rate of penetration of non-conventional renewable energies is affecting the traditional assumption of controllability over energy sources. Power dispatch scheduling methods need to integrate the intrinsic randomness of some new sources, among which, wind energy is particularly difficult to treat. This work aims at the optimal construction of energy bands around wind energy forecasts. Complementarily, a remarkable fact of the proposed technique is that it can be extended to integrate multiple forecasts into a single one, whose band width is narrower at the same level of confidence. The work is based upon a real-world application case, developed for the Uruguayan Electricity Market, a world leader in the penetration of renewable energies.

**Keywords:** wind power; non-conventional renewable energy; forecasting; energy bands; combinatorial optimization

#### **1. Introduction**

Whether due to economic pressure or environmental concerns, the rate of penetration of non-conventional renewable energies has been increasing rapidly over recent years, and it is expected to grow even faster in the years to come. Short-term operation and maintenance of electrical systems relies on optimal power dispatch scheduling methods.

Either renewable or not, conventional energy sources are dispatchable on request, i.e., authorities can control when and how much power will be provided from each source. Conversely, non-conventional renewable energies are not controllable, are intermittent and uncertain, even within a few hours period ahead. The intrinsic stochastic nature of the new energy sources turns out the short-term dispatch of the grid into a much harder challenge, which necessarily must coexist with randomness coming from significant portions of the installed power plant. This work regards with the optimal crafting of wind-energy bands (in a sense precisely defined in Section 3). It is based on an application case of Uruguay, a worldwide leader in the usage of renewable energies. The Uruguayan case was chosen as reference because: (i) Uruguay is the country of these authors, so the case is very proximate to our research group; (ii) the country counts an immense relative penetration of renewable generation of diverse sources; and (iii) there is plenty of open access information available. Although this document is guided by that reference application case, the methodology is general and its results extendable, so it can be ported to another system or country.

#### *1.1. Literature Overview*

In the context of forecast of daily scenarios there exist a vast literature and plenty of methods proposed to accurately predict a likely behavior for the stochastic process involved. Several of them use purely statistics techniques—parametric, semi-parametric and nonparametric—to infer forecasts. Particularly, there are standard and well-known techniques coming from the analysis of time series for the daily forecasting electricity prices and electricity demand (see [1]) that can be adapted to wind power inference. Statistical methods like those, perform well to forecast time series without very strong fluctuations,

**Citation:** Risso, C.; Guerberoff, G. A Learning-Based Methodology to Optimally Fit Short-Term Wind-Energy Bands. *Appl. Sci.* **2021**, *11*, 5137. https://doi.org/10.3390/ app11115137

Academic Editor: Luis Hernández-Callejo

Received: 21 April 2021 Accepted: 18 May 2021 Published: 31 May 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

like: electricity prices, electrical demand time series, hydraulic contributions to water reservoirs, or even to forecast mid and long-term availability of wind power. When the application regards with short-term wind power generation, the accuracy of such statistical methods degrades notably, even over short periods of time that range from a few hours till two or three days ahead. This is because wind power is much more volatile than electricity prices and electrical demand time series (and the other examples mentioned before).

Complementarily, there are approaches for short-term wind power forecasting based on numerical simulations of atmosphere's wind flows (see [2,3]). For a couple of days ahead period, or even larger time windows, numerical simulations are usually more accurate than purely statistical models. Such models are deterministic, while the underlying physical phenomena is chaotic by nature. So, they perform better than purely statistical methods to follow the process whereabouts at early stages but are far from being trustworthy in what respects to the construction of likely scenarios at larger times. Summarizing: the scheduling of short-term dispatch must coexist with randomness, so, even though wind simulations provide valuable information, they must be enriched in order to account the intrinsic stochasticity of the process.

In the last decade, the concept of prediction interval associated to probabilistic forecasts was introduced (see [4]). The construction is based on a nonparametric approach to estimate—at once, for all instant of time within a selected grid over a forecast horizon- the interdependent quantiles for the (unknown) distribution probability of the wind power process. For each time, the corresponding prediction interval provides an estimate of the expected accuracy of predictions with respect to what the actual value of the wind power will be. Therefore, this technique crafts bands inside which the wind power process is expected to stay with a given probability (the nominal coverage rate [5,6]). Complementing the previous line of work, in [7] other methods that also use deterministic forecasts as input are introduced, and through a subtle analysis that involves historical data to estimate nonparametric forecast error densities, for some relevant times chosen appropriately, the authors have succeeded in generating wind power scenarios with their respective probabilities.

Referred to the construction of confidence bands, several papers have been issued. In other works (see [8]), parametric processes guided by stochastic differential equations (SDEs) are studied. These processes involve a drift term, which acts as a force that tends to attract the trajectories towards the forecast (which is known as an input), and also involve a diffusive term modulated by a Wiener process factor as usual. Different parametric models are studied by considering specific forms for the drift and diffusion terms. The basic idea of the mentioned work consists in approximate these parametric non-Gaussian stochastic processes by Gaussian processes with the same mean, variance and covariance structure. Such approximations allow the estimation of the parameters through maximum likelihood techniques. Following the ideas of these authors and using the same data set for wind power in Uruguay as in the present work, the article [9] synthesizes multiple realizations of the calibrated process in order to build confidence bands. As a subsequent and tightly coupled step towards tackling the crafting of stochastic optimal short-term dispatches schedules of the grid, the previous research team uses those SDEs as supply for a Continuous-Time Stochastic Optimal Control (CTSOC) [10], with very promising results. However, scalable numerical techniques to solve optimal control problems derive from dynamical programming [11], what limits the number of state variables to integrate to the problem. The reference [10] is a pretty good example of what can be done when the number of states is manageable, but many times, the intrinsic structure of the problem makes it untreatable through such approaches. Some practical applications inevitably require crafting scenarios to use other optimization techniques, where the availability of wind-energy bands is essential.

Energy bands crafted in this article were used as a supply for an optimal short-term dispatch problem for the reference application case, which combines generation units with complex commitments, temporal dependencies among them, and other intrinsic characteristics that makes the problem too hard to be tackled when approached with dynamical programming or related techniques. We suggest [12] as an illustrative reference for practical applications of this work.

In recent years a considerable effort was put into controlling strong variability of weather conditions through the incorporation of what is called in the literature Ensemble Weather Forecasting (see for instance [13], focused on wind-power predictions in Japan); a strategy significantly different from that present in Section 4 of this paper. Methodologies aside, objectives are in fact quite similar: to control rare events, in that case through numerical studies over an area-averaged, added to a rigorous probabilistic analysis. Of course, the particularities of the Uruguayan case are notably different to the Japanese case due to the frequent existence in the eastern Pacific region of strong climatic anomalies as the passing of extratropical cyclones, that the authors called wind ramp events. Their probabilistic wind-power prediction achieved a good statistical reliably through confidence interval for the wind-power variability. Numerical Weather Predictions and Ensemble Weather Forecasting are also used in [14].

Finally, researchers from South Korea introduce an interesting ensemble [15] through different machine learning techniques, combining multilayer perceptron (MLP), support vector regression (SVR), and CatBoost to improve power forecasting of renewable sources. As we see later on, the article here presented focuses upon wind energy rather than power forecasts, and in fact, uses power forecasts as a supply. Furthermore, instead of using existing learning techniques as in [15], this work introduces a novel one, conceptually simpler, and yet promising according on its results.

#### *1.2. Particulars of the Reference Application Case*

As we previously mentioned, the methodology elaborated in this work is general and it can be applied to other cases. However, practical relevance of these results relies upon the magnitude and diversity of renewable energy sources in the particular application. Uruguay is one the countries of the world with highest penetration of renewable energies. Nowadays, over 98% of the annual energy consumed by the country or exported to neighbors (i.e., Argentina and Brazil) comes from renewable sources. Table 1 presents the installed power plant and annual generation by type of energy source (Information regarding capacity and energy is available at: https://portal.ute.com.uy/composicionenergetica-y-potencias while geographic distribution is in: https://www.ute.com.uy/ institucional/infraestructura/fuentes-de-generacion Other historical or real-time data is available at: https://www.adme.com.uy and https://adme.com.uy/mmee/infanual.php. A few years ago, when data of this work was acquired, that fraction was 96%, slightly lower but still remarkable high.


**Table 1.** Details of the installed power plant and energy by type of source [ADME: 2019, UTE: 2019].

Figure 1 on the other hand shows the geographical distribution of renewable units.

**Figure 1.** Geographical distribution of renewable sources. Leftmost: wind-power (blue), solar-photovoltaic (yellow) and biomass thermal units (red). Rightmost: hydroelectric dams. [source UTE: 2019 and [12]].

The information previously presented is public and accessible through the provided URLs. Detailed historic information about actual wind-power and related forecasts was also public by the time this work was realized, but unfortunately is no longer so.

#### *1.3. Main Goals of This Work*

Regardless of the technique used to narrow uncertainty with bands, those works mentioned in Section 1.1 share a common characteristic: the electric-power is the magnitude to be captured. For some applications and/or contexts, the *energy* coming from wind sources—which is a derivative of the wind's power anyway—is an important magnitude itself, and since it is the outcome of integrating the previous, results less noisy and easy to capture. This work aims on crafting bands representative of the energy to be produced along some periods, rather than focusing on accurate measures of the instant power. It is worth mentioning that since both magnitudes are strictly dependent, a fitted powerprocess cannot be outside energy-bands for too long. Thus, though this kind of bands could resemble the other in their shape, strictly speaking, they are different.

Regarding the process to craft such wind-energy bands, the idea goes by designing a learning model that is fed from: wind-power forecasts as a mainstream of what to expect for the days to come, and actual wind-power data to incorporate information related to the historical deviations of the process. The area inside the band is a measure of the quality of such calibration. The smaller the area, the better the quality of the fitting. So, crafting energy-bands of minimal area is our objective. Assuming persistent behavior, an optimal fitting over a training set is expected to replicate reasonably well over other independent instance, so a historical calibration could be used to estimate energy-bands in the near future.

Summarizing, our interest is not focused on particular power trajectories and their probabilities but aims on crafting optimal area energy-bands around wind-power forecasts, in such a way that the energy outside those bands be bounded. At this respect, our article presents a novel approach. The method is purely nonparametric, since it makes no assumptions on the physical phenomena, nor any hypothesis about the involved random processes (conditions on homogeneity in time, seasonal behavior of the temporal series or any kind of markovian hypotheses, are not necessary for this work). Our proposal is based

upon a mixed integer optimization problem, which aims on getting the narrowest average band around a set of forecasts, or a combination of forecasts, that keeps the off-band aggregated energy below a given threshold. As an innovation, to allow the optimization to go as farther as possible, the model enables to discard up to a given percentage of training samples that are treated as *atypical profiles*.

At first glance this last feature might look risky, in the sense that, in advance, one cannot tell whether the day to come will match or not an atypical profile. However, as we see later, when the method is trained with more than one forecast, whenever they are conditionally independent or weakly dependent, a combination of those forecasts and their bands allows to regain the lost confidence; the result is a more accurate band than those of constructions computed by separate. This is another remarkable point of the present work, since it helps to improve band's quality by taking the best of more than one forecasts provider.

#### *1.4. Structure of This Document*

This work uses data coming from two independent wind-power forecast providers for the Uruguayan Electricity Market: Garrad Hassan and Meteológica, which was available during the period. Complementarily, a third and purely probabilistic forecast was constructed up from historical wind-power realizations, by closely following other documented ideas (see [16]). Regarding actual wind-process realizations, we also have used power records measured over the Uruguayan grid. Therefore, the experimental evaluation here presented for training and test sets is based upon real-world data.

The structure of this article matches the stages of the novel technique. In Section 2 we describe the main characteristics of wind-power in Uruguay, together with the forecasts used as supplies for computations and analysis. Section 3 presents the optimization model to create likely bands of minimum width as well as results from experimental evaluation; while Section 4 shows how after filtering atypical days, a combination of bands calibrated up from independent forecasts performs better than any of them by separate. Finally, Section 5 summarizes the main results and possible applications.

#### **2. Wind-Power Uncertainty and the Use of Forecasts**

This section shows how variable wind-power is -when described as a stochastic process—and it presents the forecasts that are used to anticipate power realizations. The historical of wind-power data in Uruguay has a few years and along this period the installed power plant has been firmly growing. So, instead of expressing power in term of MW, we use the Plant Load Factor (PLF), which corresponds to the actual power generated at each time divided by the sum of the installed power capacity of each wind turbine in the system at that moment (i.e., the wind-power plant). Therefore, PLF is a dimensionless quantity that takes values between 0 and 1. Over an hour time-slot basis we consider the average PLF, i.e., the average power along each hour divided by the power plant; this is the main variable we use along this work. In this way the information is normalized, and we can disregard of changes in the installed capacity during the period of analysis. In what follows we present a summary of the behavior of wind-power in Uruguay. The data sample used involves around 730 days of the years 2014 to 2016. We decided to use this period as reference because of the homogeneity of forecast providers and the availability of open data sources.

#### *2.1. Seasonal Regularity*

Figure 2 shows the average energy and relative deviations of the daily PLF with respect to the historical mean. Daily PLF is the cumulated value of hourly PLFs over a day, so it ranges from 0 to 24. The temporal horizon varies from 1 day to 730 days ahead.

**Figure 2.** Total and relative deviations of actual PLF with respect to the historical average (leftmost horizontal blue line) as a function of the horizon (730 days).

The intermediate rebound in the deviation is due to a seasonal phenomenon; this effect decreases considerably if the records are limited to a single season. For instance, Figure 3 shows the equivalent plot when only summer days of the same period are considered.

**Figure 3.** Total and relative deviations of actual PLF with respect to the historical average for summer season (leftmost horizontal blue line).

The previous figure shows how after a week or two, the process goes inside the 10% error band, respect to the average value for that season. We must conclude that wind-power is fairly regular when used in medium-term planning. For shorter periods of time, the situation is quite the opposite.

#### *2.2. Changing Daily Behavior*

Managing the electric grid of a country is a challenging task that must be carried out carefully and optimally. To accomplish that, multiple problems are to be solved, spanning different scales of time and components. Medium-term planning usually refers to the valuation of intangible resources, such as the height of the lake in an electric dam accounted as an economic asset. Seasonal regularity as that observed in Section 2.1 is an advisable characteristic to develop mid-term optimization planning models. Short-term planning consists in crafting optimal dispatch schedules for some days ahead, and its aim is upon efficiently coordinate the usage of available resources. The object of this work is on suppling energy-bands for the short-term power dispatch of the Uruguayan grid, whose outcome sets the prices of energy in the electricity market. Due to its short scale of time (a few days ahead) and time-step (of an hour each) short-term planning requires accurate PLF estimations hour-by-hour over some days to come.

A histogram of daily cumulated PLFs along the available two years of samples is shown over the leftmost of Figure 4. Observe that many days within the period have daily cumulated PLFs below 5 (which is approximately 20% of the power plant). The number of samples whose cumulated PLFs are above 19 (80% of the power plant) are lesser, and yet there are days where the average wind-power was pretty close to the power plant. To get an insight about hourly behavior, the rightmost of Figure 4 shows the hour-by-hour mean marked with asterisks. The mean PLF is around 20% higher in the night hours compared with the hours of sun. Complementarily, the rightmost image plots actual wind-power samples, concretely those 30% with higher distance (||.||2) respect to the average over the first year. Observe how divergent are these samples when compared with the mean trajectory. We are not going further in the direction of standard statistical descriptive, since it exposes the predictions of wind-power to important errors and thus is seldom used.

**Figure 4.** Histogram of daily wind energy samples [daily PLF upon the leftmost] and 30% most atypical realizations for Uruguayan wind-power over a year [rightmost].

#### *2.3. Additional Accuracy Coming from Numerical Forecasts*

This section experimentally analyzes the benefits of using short-term wind-power forecastings based on numerical simulations of atmosphere's wind flows. As a measure of the error incurred we use the ||.||<sup>1</sup> distance between forecasts and actual realizations. Hence, the total energy error for the period starting on day *d* (denoted *err<sup>d</sup>* ) is computed as: *err<sup>d</sup>* = ∑ *T t*=1 |*w d <sup>t</sup>* − *p d t* |, being *w d t* and *p d t* , respectively, the actual power (PLF) for the day *d* as seen *t* hours ahead and its corresponding forecasted value. On the other hand, *T* is the time horizon of the forecasts: 72 h in our examples. In Section 3 we explain the convenience of using such an error measure.

This work used information for the Uruguayan grid, which was of public domain by the time computations were realized. Two independent forecast providers are considered: Garrad Hassan and Meteológica. Their common samples span around 300 days, starting in early 2016. A third forecast -about which we elaborate later on—that uses a purely statistics analysis (following PSF ideas [16]) is built to benchmark statistical and numerical forecast. In spite of its lower performance as an isolated technique, we see in Section 4 that this final forecast (referred to as PSF44) increases the overall quality of a convex combinations of filtered forecasts.

Regarding statistical moments of the series, the mean value of the PLF error samples is 6.80 for Garrad Hassan and 5.99 for Meteológica, with respective variances of values 2.48 and 2.21. On the other hand, those figures for the PSF44 are: 13.99 and 4.52; notoriously worse than numerical forecasts. Complementarily, histograms in Figure 5 represent error distributions for each case, reinforcing the idea that Meteológica's forecast slightly outperforms Garrad Hassan's, while both are much better than PSF44.

**Figure 5.** Histograms for total deviations of forecasts within a horizon of 72 h ahead. Red and blue areas concentrate 50% of probability in all cases [leftmost: Garrad Hassan, center: Meteológica, rightmost: PSF44].

#### *2.4. PSF-Like Forecast*

Pattern Sequence-based Forecasting algorithm (PSF) is a novel nonparametric approach to infer forecasts. This method has provided promising results when applied to an assortment of time series forecasting in several international markets, at a horizon of one or a few days ahead. The main idea of the PSF algorithm -and more recent variants- involves three parts working sequentially:


A remarkable advantage of the PSF method is its reduced number of parameters. There are only two main parameters to adjust: the number of clusters *K* and the historical time window *W*.

Figure 6 shows the centroids computed over the actual wind-power data-set when using different numbers of clusters. For example purposes, assume *K* = 3 and *W* = 4; so, a sequence of *D* days translates into a sequence {*sd*} (*d* ∈ *D*) of digits, with *s<sup>d</sup>* ∈ {1, 2, 3}. Here, *s<sup>d</sup>* is the index of the closest centroid to the realization of the day *d*.

**Figure 6.** Centroids of actual wind-power samples for different number of clusters.

Within such sequence, we aim now on finding subsequences with *W* = 4 symbols, for instance, the sequence 1231 (we are assuming that current day belongs to cluster 1, given by the last symbol in this sequence). Figure 7 shows examples where that subsequence could be found. The outcome of this predictor (one day ahead) is the average of the actual PLF realizations, among those samples immediately following the subsequences registered. To extend the construction to a two-days ahead forecast, one could repeat the

process seeking for the subsequence composed of the previous *W* − 1 days plus the new forecasted one, and so on.

**Figure 7.** Example of matching subsequences within a historical of symbols.

The purpose behind the development of this forecast is not devaluating statistical methods. On the contrary, this work shows an example of how such a simple method, may contribute to the overall quality when combined with forecasts coming from complementary techniques.

#### **3. Optimization of Wind-Energy Bands**

Optimization of wind-energy bands is in the core of this framework. We provide an expression to compute a band around any forecast, and, for that concrete formula, we seek for the narrowest band that satisfies a set of constraints, which imposes limits to the actual process in its deviations in accordance with the historical behavior. A traditional approach would go the way of setting constraints to keep the power deviation under certain boundaries. Conversely, this work aims on minimizing the expected off-band energy.

The previous is explained by the particulars of the Uruguayan electricity installed plant, but it is also justified by trends of new technologies. Around 98% of the electricity annually consumed in this country comes from renewable sources (see [17]). In average, 50% is from hydroelectric sources, while 35% is from wind-power. All of the hydroelectric dams in Uruguayan have water reservoirs; two of them (Bonete and Salto Grande, see Figure 1) are particularly huge. Almost 40% of the hydroelectric capacity is located after the greater lake (Bonete's), which would take 5 months to empty at full-power. Therefore, in fact, the hydroelectric plant also constitutes an accumulator, i.e., a kind of battery that can plenty compensate short-term fluctuations of the power coming from wind turbines. Hence, regarding Uruguayan short-term planning concerns, an accurate prediction of energy boundaries is more convenient than a power forecast of limited punctual quality. In a complementary manner, smart-grids capabilities are rapidly advancing towards active applications, capable of dynamically adjusting portions of the demand to adapt them to fit system needs (see [18]), while electricity storage units based on batteries are just around the corner (read [19] and also see the "Neoen & Tesla Motors" project in Australia). Therefore, in the near future, this work could be a useful experience for other countries.

The information required to determine an instance of our optimization problem comprises the following data sets. At first place, we need a historical of wind-power forecasts. We consider a collection P of deterministc registers that involves short-term point forecasts over a horizon of a few days ahead; i.e., a family of vectors *p <sup>d</sup>* <sup>∈</sup> [0, 1] *T* , with fixed *T*, which is set by the number of samples along the time horizon. Here, *d* is the index for each day on which the construction of a band begins; *d* ∈ *D*, being *D* the set of indices for days with historical observations. Wind-power forecasts usually span from one up to three days, i.e., from 24 to 72 h, and time is discretized at a rate of one sample per hour. Let *T* − 1 be the limit of hours ahead available for each forecast. We assume that all forecasts share the same time horizon, and that in *t* = 0 the current power is the only data known for sure. As we mentioned earlier, for simplicity the wind-power is expressed as the PLF, which corresponds to the actual power generated divided by the sum of the installed power capacity of wind turbines in the system at each moment. Thus *p d <sup>t</sup>* ∈ [0, 1] is the normalized point forecast of the wind-power *t* hours ahead, within the vector associated to the forecast issued on the day *d*.

The second part of the input data set comprises the actual historical wind-power time series samples, grouped into a collection: W, whose elements *w <sup>d</sup>* <sup>∈</sup> [0, 1] *<sup>T</sup>* are also assumed normalized. Hence, *w d <sup>t</sup>* ∈ [0, 1] is the actual PLF measured *t* hours after the beginning of the day *d*. For consistency, since the current state can be measured rather than forecasted, *p d* <sup>0</sup> = *w d* 0 for each day *d*. Observe that the set W usually has duplicated records, for instance: *w d* <sup>24</sup> = *w d*+1 0 . Despite that, we have chosen this format to simplify those expressions that link with forecast information. Regarding forecasts, however, the previous equality doesn't hold. In fact, *p d* <sup>24</sup> (a sample, forecasted 24 h ahead) is different from *p d*+1 0 (the actual value measured a day later).

It is clear that, given any two bands containing the real process inside of them at the same instants, the narrower band is of better quality. Wind-power generation is a process hard to anticipate, and violations to computed bands is a fact we must coexist with. However, not every violation has the same severity in terms of its impact to the power grid. In the context of the short-term energy dispatch, how much cumulated energy falls down outside the band is a convenient metric to assess the confidence of the pair: forecast plus computed band. In this work, we define the following expression as a metric for the reliability (The expression on the right hand side corresponds precisely to the anti-reliability, which of course is the complement of the reliability; hence the notation for the left hand side) <sup>R</sup>*<sup>d</sup>* , of a band around a given forecast *p d* :

$$1 - \mathcal{R}^d(w, lb, ub) = \frac{1}{T} \sum\_{t=0}^{T-1} \max\left[w(t) - ub\left(p^d, t\right), 0\right] + \frac{1}{T} \sum\_{t=0}^{T-1} \max\left[lb\left(p^d, t\right) - w(t), 0\right] \tag{1}$$

where *ub* and *lb* respectively are the functions that determine upper and lower limits for the bands along the forecasted period, and *w* is the actual generation, unknown until the near future where reality is revealed. Functions *lb* and *ub* take a forecast (*p d* ) and an instant (*t*) as their inputs, while their outputs are the respective bounds to expect.

As mentioned, the feasible region of the optimization model imposes limits to the severity of violations to the band. Besides, in order to improve the quality as further as possible, the model allows to discard up to a limit of elements in the training set, which are *atypical*, specially bad forecasts that whether included would either: deteriorate the accuracy of the result, or force us to use too broad bands. So, to complete an instance we must set values to those quantities. The parameter *θ* ∈ [0, 1] limits the amount of energy allowed to fall down outside the band along the optimization horizon. The parameter *λ* ∈ [0, 1] sets a minimum fraction of *regular* (i.e., not atypical) forecasts to be used in the effective training set or, in other terms, (1 − *λ*) is the maximum fraction of atypical days allowed to be discarded. It is worth mentioning that the limit for off-band energy only accounts over regular forecasts.

#### *3.1. Minimal Relative Width of Bands*

This work considers those bands defined by relative deviations with respect to forecasted values, which are simple to calculate and optimize, and yet lead to accurate results. Let {*x<sup>t</sup>* ≥ 0} be a set of coefficients associated to the time series analyzed, which delimits the width of the band. That is, for any instant *t* within the time horizon of the forecast issued on day *d*, we take *p d t* and compute the lower and upper limits of the band using the expressions *lb<sup>d</sup> <sup>t</sup>* <sup>=</sup> max<sup>h</sup> 0,(1 − *xt*)*p d t* i and *ub<sup>d</sup> <sup>t</sup>* <sup>=</sup> min<sup>h</sup> 1,(1 + *xt*)*p d t* i respectively. Hence, {*x<sup>t</sup>* : 0 ≤ *t* ≤ *T* − 1} comprises the first set of control variables that modulates the relative width of the band for a given forecast *p <sup>d</sup>* ∈ P. Figure 8 sketches about how these variables and derivatives are related, through a hypothetical forecast (centroid of the band, highlighted in blue), its correspondent energy-band (shaded in grey), and the actual power-process registered afterwards (red curve).

**Figure 8.** A wind-power band (grey) crafted after a forecast (blue), for some day *d*, and the actual process (red).

The objective function of this optimization is ∑ *T*−1 *<sup>t</sup>*=<sup>0</sup> *w*ˆ*tx<sup>t</sup>* , where *<sup>w</sup>*ˆ*<sup>t</sup>* = (∑*d*∈*<sup>D</sup> <sup>w</sup> d t* )/|*D*| is the average PLF at time *t* over a historical record of observations *D*, eventually different from that of the training set. In other words, *w*ˆ*<sup>t</sup>* corresponds to the sequence of asterisks in the rightmost of Figure 4, while ∑ *T*−1 *<sup>t</sup>*=<sup>0</sup> *w*ˆ*tx<sup>t</sup>* matches the average grey area in Figure 8. Whenever forecasts are statistically reliable, the objective function corresponds with the expected absolute PLF area of the band along the period *T*.

Defined so, the optimization is not instant-to-instant greedy, in the sense that it could deteriorate the performance at some points in order to surpass the overall performance by gaining more in others. That differentiates this work from related ones (like [7]), whose intention is to track power rather than energy. In fact, this model doesn't need conventional hypotheses about stochastic processes, such as homogeneity or markovianity.

The second group of control variables is composed by those who determine which are the regular forecasts. The variable *y<sup>d</sup>* ∈ {0, 1} indicates whether the forecast issued on day *d* should be considered regular (*y<sup>d</sup>* = 1), or atypical (*y<sup>d</sup>* = 0). Unlike the {*xt*} variables, these new ones are boolean. We denote *D* to the set of days for which the optimization problem is implemented (i.e., the training-set). The complete combinatorial optimization model is that in (2).

$$\begin{aligned} \min & \sum\_{t=0}^{T-1} \psi\_{l} \mathbf{x}\_{t} \\ & p\_{t}^{d} \mathbf{x}\_{t} - y\_{d} + z\_{t}^{d} \ge |w\_{t}^{d} - p\_{t}^{d}| - 1, 0 \le t \le T - 1, d \in D, \\ & \sum\_{t=0}^{T-1} z\_{t}^{d} \le T(\theta + 1 - y\_{d}), \ d \in D, \end{aligned} \tag{2}$$

$$\sum\_{d \in D} y\_d \ge \lambda D,\tag{iii}$$

$$y\_d \in \{0, 1\}, \; 0 \le x\_t, 0 \le z\_t^d \le 1.$$

The auxiliary variables (*z d t* ) account by how much power the process (*w d t* ) violates the band around the forecast (*p d t* ), either at the top or the bottom, for those days classified as regular (i.e., when *y<sup>d</sup>* = 1). For instance, if *y<sup>d</sup>* = 1 and *w d <sup>t</sup>* ≥ *p d t* (1 + *xt*), then it must be held *z d <sup>t</sup>* ≥ *w d <sup>t</sup>* − *p d t* (1 + *xt*) ≥ 0 to satisfy equation (*i*) in (2) for that day *d* at time *t*. When *y<sup>d</sup>* = 1 and *w d <sup>t</sup>* ≤ *p d t* (1 − *xt*), then *z d t* should verify *z d <sup>t</sup>* ≥ *p d t* (1 − *xt*) − *w d <sup>t</sup>* ≥ 0 to satisfy equation (*i*). For a graphical reference about both situations, please see Figure 8. The optimization process pushes down the *z d t* values, which ultimately are to be set to

max<sup>h</sup> 0, *w d <sup>t</sup>* − *p d t* (1 + *xt*), *p d t* (1 − *xt*) − *w d t* i , the anti-reliability of (1). That equation is always satisfied when *y<sup>d</sup>* = 0 simply by choosing *z d <sup>t</sup>* = 0 for every *t*; therefore, atypical days are disregarded for violations.

Given any day *d*, when *y<sup>d</sup>* = 1 (an effective day of the training set), the second equation guarantees that the time-normalized cumulated off-band energy along the forecasted period *<sup>T</sup>* is below *<sup>θ</sup>*. That is, in terms of the reliability: 1 − R*<sup>d</sup>* = (<sup>∑</sup> *T*−1 *t*=0 *z d t* )/*T* ≤ *θ*; so *θ* bounds the energy that lies outside the band to a fraction of the installed power plant. As it happens with (*i*), equation (*ii*) is automatically satisfied when *y<sup>d</sup>* = 0. Coming back to Figure 8 as a reference instance, by combining equations (*i*) and (*ii*) inside an optimization process, we are forcing the total off-band energy (the result of adding up both yellow areas) to be under a desired threshold. Finally, equation (*iii*) forces the problem to select at least *λD* days to be regular, which combined with the persistence hypothesis conveys likelihood to the result.

#### *3.2. Experimental Evaluation*

The experimental evaluation of this work is based upon a later open data from the Uruguayan Electricity Market. From that past repository, we chose two independent forecast sources: Garrad Hassan and Meteológica. The data were pre-processed using a power assimilation methodology, which fits forecasts along the first 6 h in order to match the starting state (*w d* 0 ). The exact process is described in paper [3]. The used forecasts from Garrad Hassan were those issued at 1AM between 5 April 2016, and 10 March 2017. Within this period there are 302 days where both, forecast and actual data, are complete. Regarding the other provider (Meteológica), the number of complete records is 394, with dates of issue ranging from 1 January 2016, to 10 March 2017. Regarding our own forecast (PSF44), synthesized up from a series of actual power registers, we used the same 730 days of between years 2014 to 2016 that were used upon the first part of Section 2.1. Best performance was found by using *K* = 4 and *W* = 4 (acronym PSF44 refers to those parameters).

Throughout this work, we relied upon IBM(R) ILOG(R) CPLEX(R) Interactive Optimizer12.6.3 as the optimization solver. The server was an HP ProLiant DL385 G7, with 24 AMD Opteron(tm) Processor 6172 with 64 GB of RAM. After running model (2) over a training set comprising around 30% of Meteológica's days, we find bands like those sketched in Figure 9.

**Figure 9.** Wind-energy bands for three random days within Meteológica's training set [*λ* = 1, *θ* = 0.05].

The x-axis represents the number of hours ahead for each forecast, while the y-axis corresponds to the PLF. Blue curves are associated with power forecasts while red ones are the actual values. Finally, the grey area represents the wind-power band for *θ* = 0.05 and *λ* = 1. Since *λ* equals 1, every day within the training set must be effectively included; that is, *y<sup>d</sup>* = 1 for each *d* ∈ *D*, so all days are treated as regular. Furthermore, when *λ* = 1 then (2) turns out to be a pure linear programing problem, and running times are within

the second. Fixing *λ* to 1, it is of interest to explore how *θ* modifies the bands. Figure 10 shows the result over the same training set when *θ* = 0.01.

**Figure 10.** Wind-energy bands for the same days when *θ* = 0.01 instead of *θ* = 0.05 [*λ* = 1].

Observe that bands in Figure 10 are wider than in Figure 9, which is expected since we are less tolerant respect to how much energy lies outside those bands. In order to balance reliability and thickness, it is of interest to compute how much area do bands cover as we change *θ* while keeping *λ* = 1.

The training in all of the previous cases was performed over a set *D* of 120 randomly selected days out of a set of 300 days in common for all providers. The common complement, i.e., the set of (180) days shared by these three forecasts and not being in the *training-set*, is used as the *test-set*. The calibration of PSF44 was crafted using the set of 430 contiguous days previous to those of training and test sets. Experimental evaluation (see leftmost of Figure 11) verifies that the average width of the bands, when trained over the entire training set of forecasts (*λ* = 1), falls down rapidly to 0, which is reached upon both companies when *θ* is close to 0.2. Although similar, Meteológica's bands (blue) are always better than Garrad Hassan's (red). PSF44 (green) requires much wider bands to achieve the same grades of reliability. The middle plot shows the relative difference between widths of original bands (those of the training set), and widths computed over the test-set using the corresponding *x* vector found for each *θ*. It is worth mentioning that widths are always similar (divergence is low), so the objetive function in (2) when evaluated over the training set is representative of what happens outside it. This is sustained even for relatively higher *θ* values right below 0.2, where widths tend to zero and the relative deviation makes no sense to be accounted.

**Figure 11.** Average width of bands found for the training set as *θ* changes while *λ* is fixed in 1 [leftmost], relative deviation between average widths register for training and testing sets [middle], and violations of off-band energy limits over testing set. [red samples correspond to Garrad Hassan, blue ones to Meteológica and green to PSF44].

Regarding off-band energy violations to the limit *θ* when computed over the test-set (they do not happen in the training-set because of (2)(*ii*)), the rightmost of Figure 11 shows the fraction of those violations, i.e., the fraction of samples where the off-band energy surpasses *Tθ*. They are also low for all forecasts and are particularly lower as values of *θ* get apart from zero. The previous exercise experimentally justifies the persistence hypothesis this technique is based on.

The goal of this work is providing stochastic short-term optimal power dispatch schedulers, with accurate wind-energy bands, in the context of the Uruguayan Electricity Market. In particular, our interest is keeping off-band energy below 10% of the average PLF, which is around 0.35; so we consider *θ* = 0.035. In Uruguay, 35% of electricity comes from wind-power sources, thus that value of *θ* corresponds to 1.23% of the average energy consumed, what is ambitious. That value is used as reference during this work.

The other parameter to consider is *λ* which attends to the fact that, whatever accurate a family of forecasts may be, there will always be samples that degrade the overall quality of the whole. Table 2 shows how some attributes of the bands change as *λ* decreases from 1 to 0.6, while *θ* remains fixed in 0.035 (our target off-band violation).

**Table 2.** Experimentally estimated attributes for confidence *θ* = 0.035 bands as *λ* decreases.


The first three four columns correspond to Meteológica forecasts, the second part does to Garrad Hassan's and the last one to PSF44 forecasts. These metrics were computed over the test-set by using optimal *x* coefficients for each *λ* over the samples in the training-set. Columns labeled as *%anomalous* indicate the percentage of the samples, in each case, whose off-band energies surpasses the 0.035 of the total plant factor (*Tθ*). We decided to use different adjetives to distinguish between *atypical days*: samples intentionally excluded from the training-set, and *anomalous days*: samples in the testing-set that by chance surpass the off-band energy limit. The columns *BW* and %*BW* respectively show the average absolute and relative areas of the wind-power bands over the test set, using 72 as the full plant factor for the time horizon. Finally, the number of seconds spent by the solver to find the optimal solution for each case appears in the column labeled as *t(s)*. Observe that as *λ* decreases so it does the expected width for energy bands, because the solver is allowed to select down to *λD* days during the training, and the optimization ends up by crafting bands for the best subset with a *λ* fraction of the original number of days. Computation times ascend, because (2) becomes combinatorial for *λ* < 1. Conversely, the percentage of *anomalous days* (i.e., those whose off-band energy falls outside the limit) increases, since the calibration performed over a partial/elite training-set is no longer representative over the complement (i.e., the test-set). A second goal of this work is keeping the percentage of *anomalous days* below 10%, which translates into attaining the target *θ* at least 90% of the times. The final goal is over the allowed variance for wind-power. Until now, we have focused upon energy rather than power. Keeping the process within narrower bands

is equivalent to expect lower power variations. According to official sources, the total electricity produced by Uruguay during 2017 (to meet internal demand plus energy exports to Argentina and Brazil) was of 12,600 GWh. The equivalent hourly average power is 1438 MW. The total wind-power plant by late 2017 was of 1437 MW (the fact these final figures match is just a coincidence). Hence, aiming on having energy bands whose relative width is below 20% is equivalent to expect average power fluctuations (either upwards or downwards the centroid) below 10% of the installed wind-power plant, which matches the average power consumption. In summary, our targets are: *θ* ≤ 0.035, %*BW* ≤ 20% and *%anomalous* ≤ 10%. Observe that no record in Table 2 fulfills all these goals simultaneously. Along Section 4 we see how to deal with that issue.

#### **4. Combining Forecasts**

At first sight, we might think that a convex combination of forecasts and their bands would inherit the width of each one, and that we cannot improve bands quality by means of combining them. The only mechanism we have seen that can get narrower bands goes by reducing *λ*. As a drawback, this also increases the percentage of anomalous days. However, we might regain confidence if anomalous days -for the different forecasts- were somehow independent, since a combination of anomalous situations in all bands would be rarer than in any of them by separate. That's the idea behind this section. To check the consistency of this idea we analyze how independent anomalous days are, by its correlation matrices. Table 3 recapitulates figures of anomalous days for different values of *λ* with *θ* = 0.035.


**Table 3.** Correlation matrices for anomalous days for different *λ*'s and *θ* = 0.035.

These numbers were computed over the test-set for Bernoulli's random variables, *Mt*(*d*), *Gt*(*d*) and *Pt*(*d*), indicator of the event of finding an anomalous day: they evaluate to 1 (respectively 0) if and only if the forecast for day *d* of the respective corresponding -Metológica, Garrad Hassan and PSF44- classifies as anomalous (resp. regular). From these correlation values, we infer that anomalous days of Metológica and Garrad Hassan are positively but weakly correlated. By running simple simulations with two sets of dependent Bernoulli's random variables with the same expected value, we observe that the correlations values of the table appeared when 1 out of between 3 to 4 samples of one set copy the value

of the other. PSF44 is basically independent of the others providers, and in fact can either be positively or negatively correlated with them.

Given the three sets of forecasts: P*mt*, P*gh* and P*ps*, and their corresponding functions to compute bands (lower and upper bounds): *bdMTλ*(*p*) → [0, 1] *T*×2 , *bdGHλ*(*p*) → [0, 1] *<sup>T</sup>*×<sup>2</sup> and *bdPSλ*(*p*) <sup>→</sup> [0, 1] *T*×2 , we explore convex combinations of them: *bdMX* = *α* · *bdMTλ*<sup>1</sup> + *β* · *bdGHλ*<sup>2</sup> + (1 − *α* − *β*) · *bdPSλ*<sup>3</sup> , with 0 ≤ *α*, *β* ≤ *α* + *β* ≤ 1, for different combinations of *λ*'s. The goal is on finding the combination that is closest to satisfy the targets: *θ* ≤ 0.035, %*BW* ≤ 20% and *%anomalous*≤10%. This second stage of training was performed over the half of the test-set (90 days). The other half remains as the definite test-set to check results. The most convenient combination over the new training-set was found for values: *α* = 0.66, *β* = 0.25, *γ* = 0.09, *λ*<sup>1</sup> = 0.85, *λ*<sup>2</sup> = 0.70 and *λ*<sup>3</sup> = 0.65. After checking over the now reduced test-set we verify that for *θ* = 0.035 as limit for off-band energy, 8.9% of the days fall into the anomalous condition, while the value for the average bandwidth is %*BW* = 21.7%. This final figure does not attain our original goal (i.e., 20%), but it is pretty close to it.

#### *Performance of Optimally Combined Bands*

The lecture of the previos figures indicates that the most performant family of forecasts (Metológica) contributes with 66% of the weight when is calibrated using 85% of its better forecast samples. Despite having similar performance (recall Figures 5 and 11), Garrad Hassan's forecasts only contributes with 25% of the weight, and that is after filtering 30% of its samples. Unexpectedly, being the worst by far, PSF44 contributes with almost 10% to the final result, although after purging 35% of its samples. Probably, the higher weight of PSF44 comes from its almost independence (small correlation) with respect to the other forecasts, rather than its quality.

To analyze the performance of the combined band we present qualitative and quantitive evidence. Figure 12 sketches random bands, its centroid and the corresponding actual power over six days within the test-set. The last two figures (middle and rightmost plots in the bottom row) correspond to two of the eight anomalous days found. Although the off-band energy surpasses the *Tθ* limit, overall, the performance of those bands doesn't look that bad either.

**Figure 12.** Hybrid bands for six random days in the test-set [blue is the centroid, the red one is the actual power].

Figure 13 shows other group of six random bands. This case does not include anomalous samples, but there are a couple of samples where the area of the band is above the target value. The most notorious case is that on the leftmost of the bottom row.

**Figure 13.** Hybrid bands for six random days in the test-set [blue is the centroid, the red one is the actual power].

It is worth wandering how much energy lies outside the band when violations happen, and how narrow confidence bands are. The residual test-set is so small (90 samples) that, although biased, we decided to use the old one to craft histograms. Figure 14 shows histograms computed up from the original (180 samples) test-set. The leftmost corresponds to the distribution of the off-band energy normalized by the total PLF along the period (72). It is observed that no sample disagrees in more than 7.3%, while in 50% of the samples (those colored with red) that percentage is lower than 1.6%. The rightmost represents the distribution of normalized widths (%*BW*). As in the previous case, samples colored in red add up to 50% and all of them are lower than 14.6%.

**Figure 14.** Histograms for relative off-band energy and widths of the bands.

Complementing the previous figure, Figure 15 marks with green the quantiles where the values of either: off-band energy [leftmost] or normalized widths [rightmost] satisfy original targets. The cumulated probability of samples in the first totalizes 90.17%, while those over the rightmost add up to 79.8%. These results reflect the quality of the forecasts and bands computed by this method. We conclude then, that the result is not only satisfactory regarding our initial average performance goals (*θ* ≤ 0.035, { but it is pretty good in terms of the overall quality of the bands and specially in terms of the energy confidence of them.

**Figure 15.** Histograms for relative off-band energy and widths of the bands.

#### **5. Conclusions and Future Work**

In this work we introduce a novel learning technique for crafting wind energy bands around forecasts of wind-power generation over a horizon of 72 h ahead. The analysis is based on a historical data set provided by the Uruguayan Electricity Market. The technique allows to discard a portion of atypical days in the training-set, while controls the average cumulated energy that lies outside bands. With an appropriate choice of the parameters involved in the analysis, the model has succeeded in providing bands satisfying natural requirements on confidence and width.

A remarkable conclusion of this work is that the use of an optimal convex combination of conditionally independent (or weakly dependent) forecasts and its corresponding bands improves significantly the performance of the model. For instance, the experimental evaluation of Section 3 suggests that Meteológica forecasts performs, in average, better than Garrad Hassan's and PSF44. However, an appropriate convex combination of all of them (even when the performance of PSF44 is rather bad) provides better results. While most of the weight of the combination goes to Meteológica, the inclusion of Garrad Hassan and PSF44 forecasts conveys stability to the result, compensating the fact that some anomalous days for one forecast are regular according to the others. This idea could be extended of course including more forecasts providers.

A drawback of the analysis that we mention here is that the available data set at the moment this work was developed was not too large (around 300 days). Regarding the quality of bands, we expect the performance of the technique will work even better with a more extensive data-set, perhaps spanning a few years. Nevertheless, this size introduces a challenge: increasing the training-set significantly increases computation times. Notice that after adding up computation times reported in Table 2, the total time is above 6 h, which is pretty good for the purposes of these experiments. However, those times are expected to be much higher as the training data-set increases in size, so, in such situations is necessary the introduction of specific algorithms to solve the optimization problem in (2), i.e., not to rely upon standard solvers. A line of future work precisely goes the way of experimenting with other exact methods or derivatives thereof and the exploration of Metaheuristics, in order to find more efficient algorithms to tackle the problem.

Complementarily, the current model uses a single set of *x*'s variables to delimit bands around forecasts, which results in symmetric widths either upwards or downwards. It is worth testing this hypothesis by including two sets of *x*'s, on per each direction, and letting the optimization to find solutions over a larger search space. A previous clusterization of forecasts might also improve the performance. Since the training-set indistinguishably comprises both: samples for windy and not-windy days, the relative deviation at a time *t* necessary to reposition the process within a band shall be greater for forecasts of low prospected energy than the necessary for high energy ones. The previous over-penalizes widths of bands in forecasts with higher expected energy. Training different bands for different seasons might also improve the quality. Most of these ideas however, require historical data sets much larger than the one currently available.

Regarding the application of bands as those developed in this work. They may be particularly important to craft scenarios in stochastic optimization problems where the complexity of state variables does not allow using other techniques, such as dynamical programming. Examples of such situations arise from a combination of: generation units with complex commitments (limit to minimum power, a slow starting/stopping process, a minimum uptime operation once started); temporal correlation between generation units (e.g., dam water reservoirs where water influxes come from another hydroelectric dam); control deferrable consumption (e.g., electrical residential water heating that must be accounted within certain time windows); large scale energy storage to be later returned to the grid; among others. That results in a wide spectrum of potential application cases.

**Author Contributions:** Both authors have contribute equally. Both authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** None.

**Informed Consent Statement:** None.

**Data Availability Statement:** None.

**Acknowledgments:** This work was partially supported by PEDECIBA-Informática and PEDECIBA-Matemática (Uruguay), by the STIC-AMSUD project 15STIC-07 DAT (joint project Chile-France-Uruguay), and by ANII (Agencia Nacional de Investigación e Innovación, Uruguay)-Fondo Sectorial de Energía 2015, ANII-FSE\_110454.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


## *Article* **Use of Ecofriendly Glass Powder Concrete in Construction of Wind Farms**

**Eva M. García del Toro 1, \*, Daniel Alcala-Gonzalez 1 , María Isabel Más-López 2 , Sara García-Salgado 1 and Santiago Pindado 3**


**Abstract:** Silicon is the main element in the composition of glass and it has been seen that it can be used as a partial replacement for cement in the manufacture of concrete. Different dosages of glass powder and cement were applied to manufacture the concrete mixes. Initially, the characteristics of fresh concrete were studied, such as consistency, air content, apparent density and workability. Secondly, compressive strength tests were performed on the different concrete mixtures produced. The consistency tests allowed us to classify these concretes within the group of fluids. The air content of these concretes increased with the rate of substitution of cement by glass powder, resulting in lighter concretes. Density tests showed that this parameter decreased as the rate of substitution of cement increased. A coefficient *k* has been calculated for the substitution of glass powder by cement in the binder, using the Bolomey formula. Also, a mathematical model has been proposed to further analyze the experimental data. Major contributions of this work were to study the possible application of this concrete in different dispersions as a surface protection layer against the action of corrosion, in wind turbine foundations as well as the stabilization of the wind farm roads.

**Keywords:** sustainability; compressive strength; Bolomey formula; sustainable concrete; glass powder

#### **1. Introduction**

By designing the 2030 Agenda, the United Nations (UN) established 17 primary global objectives, the so-called SDGs (Sustainable Development Goals) [1], mainly focusing on eradicating poverty, protecting the planet by fighting climate change and defending the environment. It is a commitment and a challenge that must be addressed jointly, seriously and responsibly from all areas of society. Since ancient times, civil engineering has promoted the development of society through the construction of different types of infrastructures [2]. However, this development has caused severe environmental damage due to the large amount of natural resources demanded, as well as the pollution produced [3]. Current trends in the field of civil engineering are aimed at adapting to the SDGs by achieving resilient and sustainable infrastructures that contribute in some way to the circular economy, where the value of products and materials is kept as long as possible. Waste and the use of resources are minimized, as these resources are kept within the economy when a product has reached the end of its useful life in order to be repeatedly reused and continue creating value [4], and contributing to achieve innovative products that represent an economic benefit and a higher quality of life for people [5]. Therefore, it is important to carry out an evaluation of the efficiency and sustainability of the works to determine the degree of efficiency of the materials and construction methods [6].

**Citation:** García del Toro, E.M.; Alcala-Gonzalez, D.; Más-López, M.I.; García-Salgado, S.; Pindado, S. Use of Ecofriendly Glass Powder Concrete in Construction of Wind Farms. *Appl. Sci.* **2021**, *11*, 3050. https:// doi.org/10.3390/app11073050

Academic Editors:

Luis Hernández-Callejo, Maria del Carmen Alonso García and Sara Gallardo Saavedra

Received: 27 February 2021 Accepted: 24 March 2021 Published: 29 March 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Within the framework of the circular economy, the role of glass is worth highlighting [7]. Glass is a material that is easily recyclable due to its physical-chemical characteristics [7]. All types of glass waste are used in the recycling process, coming from the selective recovery of containers and packaging from the glass and ceramic industry [8].

Although in most industrialized countries the percentage of annually recycled glass is increasing, there is still a high percentage of glass that is disposed in landfill [9], which involves an important problem due to the accumulation of non-degradable waste, especially in highly populated areas [10].

Some of the problems to increase the recycling rate of glass waste come from the combination of different colors of glass waste, as well as difficulties in removing dirt, paper or other contaminants from glass products [11]. These wastes that cannot be recycled will be reused for certain uses.

Currently, there are many studies that show the good properties of glass waste, which cannot be recycled, as substitutes for certain materials in the preparation of mortars and concrete. They are considered indeed one of the most suitable substitutes for sand and cement, due to their physical characteristics and chemical composition [12–14]. This reuse of waste materials becomes a viable strategy to reduce the use of Portland cement and natural aggregates in the preparation of mortars and concretes, reducing environmental and energy impacts. Among these, the reduction of CO<sup>2</sup> emissions is significant [14,15], as well as of areas destined for controlled landfills [13,16]. In this context, the so-called eco-efficient concretes arise, which comply with the characteristics outlined, but, in some cases, they have some worse properties, such as compressive strength or durability, when compared to those made with natural materials [16].

The use of finely grinded glass powder in the manufacture of mortars and concretes has been widely studied, especially the optimum particle size. Most of the studies have focused on assessing how the properties of concrete vary depending on the substitution percentage of cement by glass powder, as well as its particle size, which has been shown to play a vital role in the alkali–silica reaction (ASR) [17–19]. At this regard, and according to Idir et al. [19], with a particle size between 0.9 and 1 mm and a substitution percentage of 20% with glass powder, the classic contractions due to ASR do not occur. Corinaldesi et al. [20] stated that up to a substitution percentage of the aggregates by glass powder of 70% can be reached, provided that a particle size between 36 and 50 µm is used. This showed that by reducing the particle size of glass powder, the pozzolanic properties of the binders manufactured increase. In addition, a greater long-term strength resistance of the pastes manufactured with this type of cement was obtained, due to the higher presence of C-S-H gels [19,20]. Also, these gels have a self-repairing property when they are used in the stabilization of rolling track soils by prolonging their setting over time [21].

Liu [22] reported that self-compacting concrete produced with 10% glass powder to replace cement had good properties when fresh. They indicated that workability decreased as the glass powder content of the concrete increased due to the geometry of the glass dust. In the same line, Parghi et al. [13] indicated that the sharper edge and the more angular shape of the glass powder (GP) particles reduced the fluidity of the cement mortars and concretes.

Nassar and Soroushian [23] reported pozzolanic activity when glass powder with a particle size of 13 µm was used as a fractional replacement for cement in concrete. Schwarz et al. [24] studied the properties of ground glass powder and reported that up to a certain percentage substituting ground glass for cement was a viable solution for fabrication in concrete.

Studies carried out by Sahyan et al. [25] have shown that at constant water-to-binder mass ratio, the addition of 20% of glass powder significantly reduced the chloride ion permeability of concrete, which was confirmed by Schawrz et al. [21]. This property confers protective properties against corrosion to concretes made with glass powder and cement.

Shaoa et al. [23] observed an increase in compressive strength of 120% at the cure age from 3 to 90 days, when concrete was produced with ground glass powder with particle size up to 38 µm.

According to Pengwei et al. [24], in the traditional concrete used in civil construction that is generally subjected to large changes in temperature, its durability is clearly affected, and in extreme cases can leave the concrete out of service. To avoid these consequences in traditional concretes, air-entraining additives are incorporated into the mix. In the case of concrete made with glass powder as a binder, the higher the percentage of substitution of glass powder for cement, the higher the air content, so it is not necessary to include additives.

In 1935, Bolomey gave a formula to predict the compressive strength of cement mortar, which expresses a linear relationship between the water–cement ratio and compressive strength. This expression indicates that compressive strength of cement-based materials is mainly dependent on the water–cement ratio among all the other factors. Therefore, it is seen as a mathematical form of water–cement ratio law. In this regard, based on Fernández Cánovas studies [25], a calculation of theoretical compressive strengths at 28 and 90 days was reported using Bolomey's dosage, introducing a coefficient *k* that represented the replacement of cement CEM I52.5 R by glass powder.

Considering all the above-mentioned points, our initial research hypothesis was that the glass powder used in this work, with its characteristics and particle size, will allow us to produce an ecofriendly concrete, whose mechanical properties will not be adequate to use it as a structural concrete, but it may be useful as a surface protection layer to avoid or reduce corrosion phenomenon. Therefore, the aim of this work consisted of studying the compressive strength of cements produced with different substitution percentages of a certain glass powder. A mathematical model has been proposed to fit the experimental compressive strength results. Also, Bolomey's formula was applied for simulation of the relationship between the water–cement ratio and 28- and 90-day compressive strength.

In summary, major contributions of this work were to study the possible application of concrete made with cement and glass powder in different dispersions as a surface protection layer against the action of corrosion, in wind turbine foundations as well as the stabilization of the wind farm roads, since it is a sustainable and environmentally friendly material. On the other hand, the mathematical model developed has resulted in an appropriate simulation tool, since errors between real and simulated final stable values of compressive strength were lower than 3.3%. Finally, it has been proved that glass powder exerted an important activity in increasing the long-term compressive strength of concretes, according to results obtained by the application of Bolomey's formula. Also, the use of glass powder as a binder in the concrete would be beneficial from the point of view of the circular economy and environmental footprint because a final waste, which cannot be further recycled and whose destiny would be a landfill, may have another useful application.

#### **2. Materials and Methods**

#### *2.1. Materials*

CEM I 42.5-R Portland cement (Cementos Portland Valderrivas, Morata de Tajuña, Madrid, Spain) was used. This cement had a density of 3.12 g/cm<sup>3</sup> , a specific surface of 4.440 cm2/g and a green–gray color. Its chemical composition was as follows—CaO (65%), SiO<sup>2</sup> (19%), Al2O<sup>3</sup> (5.5%), Fe2O<sup>3</sup> (2.65%), SO<sup>3</sup> (2%), MgO (2%), Na2O (0.15%), K2O (0.7%).

The aggregate in mortar was essentially siliceous and non-reactive. It was sand with a granulometry <4 mm, gravel 4–12 mm and gravel 12–20 mm.

The glass powder used came from the grinding of waste from the ceramic industry, as well as from containers and packaging from the selective rubbish collection, which cannot be reused due to their characteristic (high percentage of paper, cork or plastic attached). They have been ground in a bar mill equipped with 15 bars of 3 different diameters and with different grinding times.

d50 glass powder of 16 µm was used (dimension of sample particles for which 50% of them have a diameter lower than a certain value) [8], which provides interesting mechanical results at a cost energy clearly lower than that necessary to obtain smaller granulometries of glass powder. This makes the use of this material more sustainable in the field of Civil Engineering [26].

Chemical composition of glass powder was given by the manufacturing company. It is composed by 71.00% SiO2, 11.80% Na2O, 11.28% CaO, 2.20% Al2O3, 1.60% Fe2O3, 1.40% MgO, 0.60% K2O, 0.10% MnO, 0.07% TiO<sup>2</sup> and 0.05% P2O5, with 0.90% volatile LF (lost of the Fire).

Physical and mechanical characteristics of the waste used were obtained by means of different analysis techniques—laser granulometry, X-ray Diffraction and Scanning Electron Microscopy. It should be noted that all the aforementioned ground glass powder comes from the same batch of waste. Only their granulometries vary.

#### *2.2. Characterization of Fresh Concrete*

Consistency tests were carried out using the UNE-EN 12350-5 standard [27], by means of the settlement test, which is sensitive when the mean settlement is between 10 and 200 mm. The air content of prepared concrete was determined by the UNE-EN 12350-7 standard [28] by pressure methods. The procedure followed for the calculation of density and porosity was based on the corresponding standard [29].

#### *2.3. Sample Preparation*

In order to evaluate the different characteristics of concrete, 6 series of test pieces were manufactured in accordance with the UNE-EN 12390-2 standard [30]. The only difference between these specimens was the amount of glass powder used to replace the CEM I 52.5 R cement, as described in Table 1.


**Table 1.** Summary of experimental conditions for the samples prepared.

All the mixtures were completely homogenized and poured into 10 × 30 cm cylindrical molds. They were compacted and after 24 h they were removed from the mold and kept in a humid curing chamber at 20 ◦C, for 2, 7, 28, 90 and 180 days. After this time, the test tubes were broken in accordance with the instructions of the UNE 83-304-84 standard [31], and the properties of compressive strength of manufactured concretes were determined.

#### **3. Results and Discussion**

#### *3.1. Characterization of Glass Powder*

Three grinding processes were carried out on the waste glass, each one for a different time, in order to obtain three samples of glass powders with different particle sizes.

Three dimensions have characterized the glass powders—d10, d50 and d90. They represent, respectively, the diameter of the sample particles for which 10%, 50% and 90% of the particles have a diameter smaller than that dimension, as can be seen in Table 2. In

this work, the value of d50 was used for the characterization of the different batches of ground glass.

—

—


The cumulative granulometric curves of the three samples (Figures 1 and 2) revealed considerable differences in the distribution of particle size.

**Figure 1.** Distribution of the accumulated granulometry of the 3 batches of glass powder [32].

**Figure 2.** Differential particle size distribution of the 3 batches of glass powder [32].

The glass powder subjected to X-ray diffraction tests resulted in a broad diffraction band between 15 and 45 degrees, which corresponded to its amorphous and disordered structure. The X-ray diffractogram of the glass powder of d50 = 16 µm is shown in Figure 3.

ray diffractogram of the glass powder of d50 = 16 μm. The dotted area shows the **Figure 3.** X-ray diffractogram of the glass powder of d50 = 16 µm. The dotted area shows the bulging of the baseline indicating the presence of amorphous phases [32]. ray diffractogram of the glass powder of d50 = 16 μm. The dotted area shows the

ctogram of the glass powder of d50 = 16 μm is shown in Figure

ctogram of the glass powder of d50 = 16 μm is shown in Figure

By means of the observation through the Scanning Electron Microscope (SEM), glass grains with particle size between 1 and 20 µm can be observed. These grains showed acicular shape and cone-shaped fractures. It should be noted the absence of fine elements attached to these glass particles and their low porosity. A frontal and side views of a glass powder particle, obtained by SEM, are shown in Figure 4.

**Figure 4.** View of a glass powder particle (scanning electron microscopy (SEM) cliche in secondary electrons). Frontal view (**left**) and side view (**right**) [32].

#### *3.2. Results of the Characterization of Concrete*

Results obtained for consistency, air content, apparent density and workability tests are shown in Table 3.


**Table 3.** Results obtained in the characterization of fresh concrete and concrete substituted by glass powder.

According to the results obtained for the consistency tests, carried out by means of a settlement test, concretes studied can be classified within the group of fluid concretes, regardless of their dosage. It can be observed that the penetration values decreased as the amount of glass powder added to the mixture increased, which is in agreement with the results obtained by Liu [22]. Regarding the air content, it varied from 3.9% to 7.5%, so air content increased with the substitution rate of the CEM I 52.5 R cement by glass powder. Therefore, it can be said that replacing cement with glass powder led to a higher air content. This phenomenon is caused by the retention of air bubbles by the surface energy of the glass, which is greater the finer the glass grains are. For this reason, the volumetric mass of the different concretes varied, decreasing when the substitution of cement for glass powder increased. In addition to air, a second cause intervened in the decrease in the volumetric mass of the concretes, which was the volumetric mass difference between glass and cement. This is because the substitutions of CEM I 52.5 R cement for glass powder were mass substitutions that were made without the volumetric corrections due to the presence of aggregates.

Workability decreased when the amount of glass powder in the binder increased, also in accordance with the tests carried out by Liu et al. [22].

The densities of the different concretes manufactured for this study were between 2351 and 2282 kg/m<sup>3</sup> , so density decreased as the rate of substitution of cement for glass powder increased. This is not in agreement with some authors, for example, Parghi et al. [13], who reported that the density was higher the higher the percentage of glass contained in the mixture was. This may be due to the volumetric mass of the cement used, which was 3.12 g/cm<sup>3</sup> , while that of the glass powder was 2.54 g/cm<sup>3</sup> .

Regarding workability, the results obtained for the manufactured concretes did not show significant changes. This result is in agreement with those obtained by Pereira-de-Oliveira et al. [33] and Taha et al. [34].

#### *3.3. Mechanical Properties of Concrete*

Table 4 presents the compressive strengths of manufactured concretes, with and without cement replacement with glass powder (see Table 1 for dosages), for all test ages (2, 7, 28, 90 and 180 days).

**Table 4.** Compressive strength of concrete manufactured with cement replaced by glass powder.


As can be observed, for concrete prepared with cement replaced by glass powder, the compressive strength of the concrete decreased when the quantity of glass powder in the

*τ*

binder increased. This can be attributed to the fact that glass powder has a low pozzolanic activity at the early ages. These results are in agreement with the results obtained by Tan et al. [35] and Mizahosseini et al. [36].

#### 3.3.1. Mathematical Analysis of the Experimental Results

A mathematical model has been proposed to further analyze the experimental data. The results obtained fit the following equation:

$$\text{Cs} = \text{Cs}\_0 \left( 1 - \exp\left(-\left(\frac{t}{\tau}\right)^n\right) \right) \tag{1}$$

close to the one that defines a first order system in classical mechanics (a similar model has been used by Fiol et al. [37] In the above equation, *Cs* is the compressive strength, *Cs*<sup>0</sup> is the final stable value of the compressive strength, *t* stands for the number of days after setting, *n* is a shape constant, and *τ* is a characteristic time that represents the time when the compressive strength reaches a 63% of its final value. The results of the fittings, together with the Root Mean Squared Error, RMSE: = <sup>0</sup> (1 − (− ( ) )) *τ*

$$\text{RMSE} = \sqrt{\frac{1}{N} \sum\_{i=1}^{N} (\text{Cs}|\_{\text{measured}} - \text{Cs}|\_{\text{calculated}})^2} \tag{2}$$

are presented in Table 5. The results of the modeling have been plotted in Figure 5 with dashed lines. =1

**Table 5.** Coefficients of Equation (1), *Cs*<sup>0</sup> , *τ*, and *n*, fitted to the measured values of the compressive strength, for each one of the studied cases (see Table 4), together with the Root Mean Squared Error (RMSE) of each fitting. *τ*


**Figure 5.** Evolution over time after setting of concrete compression strengths, *Cs*, for different cases studied (see Tables 1 and 4).

The model has proven to simulate quite well the results, as the errors were between 0.65% and 3.21% in relation to the calculated values of *Cs*0. Results of the model fitting to the G<sup>15</sup> sample were slightly different, as the shape of its curve seemed to detach from the general pattern shown by the curves fitted to the data from the other cases. In Figure 6, the coefficients of Equation (1) extracted from the different samples data are plotted in relation to the amount of glass powder used to replace the cement, *Gp*. The following equations were fitted to the results (see the dashed lines in graphs from Figure 5): = 2.8477 + 46.875 <sup>2</sup> + 73.28 4 = 0.3266 + 1.0277 2.172

$$\text{Cs}\_{0} = 41.54 - 38.06 \text{C}\_{s} \left( R^{2} = \, 0.967 \right) \tag{3}$$

$$
\pi = 2.8477 + 46.875 \text{C}\_s^2 + 73.28 \text{C}\_s^4 \left( \text{R}^2 = 0.986 \right) \tag{4}
$$

$$n = 0.3266 + 1.0277 \mathcal{C}\_s^{2.172} \left( R^2 = \ 0.857 \right) \tag{5}$$

<sup>0</sup> = 41.54 − 38.06

*τ* – **Figure 6.** Coefficients of Equation (1), *Cs*<sup>0</sup> , *τ*, and *n*, plotted in relation to the amount of glass powder used to replace the cement, *Gp*. The corresponding lines of tendency (Equations (3)–(5)) have been plotted as dashed lines.

Simulation by Bolomey's As previously mentioned, Bolomey's formula allows – ' From Figure 5, it can be seen that the coefficient *n* from the G<sup>15</sup> sample did not fit Equation (5), making the fitting of Equation (1) to this sample data (see Figure 5) slightly different from the general pattern. This might indicate that the normal errors present in the process of manufacturing the samples has larger effects for lower quantities of glass powder replacing the cement (that is, for lower values of *Gp*). Finally, with the coefficients extracted from the above equations for *Gp* = 15, the modeling of the sample G15 has been calculated and plotted in Figure 5 with a solid line. The fitting was worse to the experimental data than the one obtained from the direct fitting of Equation (1), with the error being larger (RMSE = 4.32%).

#### = × ( + + 3.3.2. Simulation by Bolomey's Formula

As previously mentioned, Bolomey's formula allows us to predict the compressive strength by means of a linear relationship between the water–cement ratio and compressive strength. According to Bolomey's law, by introducing a coefficient for a certain admixture, the compressive strength values of a concrete in which this admixture has been included as part of the binder can be estimated. From this equation, the effect of such addition on the compressive strengths of concrete can be measured:

− 0.5)

$$\text{Cs} = \text{Cs}m \times G \left( \frac{\text{C} + k + A}{V} - 0.5 \right) \tag{6}$$

where: *Cs*: Compressive strength of concrete (MPa); *Csm*: Compressive strength of a mortar of the same age (MPa); *G*: Granular coefficient; *C*: Amount of cement per m<sup>3</sup> of concrete (kg/m<sup>3</sup> ); *k*: additive coefficient; and *V*: volume of water per m<sup>3</sup> of concrete (l/m<sup>3</sup> )

Using the above Equation (6), the theoretical values, at 28 and 90 days, of the compressive strengths of concrete in which a part of the CEM I 52.5 R cement has been replaced by an inert additive (*k* = 0), were calculated. Table 6 shows the so-called 'Bolomey compressive strengths-Bolomey *Cs*' obtained. In this table, Bolomey's 'apparent' compressive strengths and 'apparent' coefficients of the additive correspond to values calculated without correcting for the secondary effect of air entrainment caused by glass dust. Bolomey's 'real' compressive strengths and 'real' coefficients of the additive indicate values calculated after correcting for this effect.

**Table 6.** Results of Bolomey's 'apparent' and 'real' compressive strengths.


Figure 7 shows the evolution over time of the compressive strengths of the concrete specimens, at a test age of 28 days, compared to Bolomey's 'apparent' and 'real' compressive strengths. As can be seen, the use of glass powder in the binder increased the compressive strengths of concrete in the long term, increasing their values slightly between 28 and 90 days. It seems that the particle size of glass powder was one important factor responsible for the increased reactivity in the long term [38].

Figure 8 shows the evolution over time of the compressive strengths of the concrete specimens, at a test age of 90 days, compared to Bolomey's 'apparent' and 'real' compressive strengths.

The differences between the 'apparent' and 'real' Bolomey compressive strengths (Figures 7 and 8) were due to the effect of air entrainment caused by glass powder. It is observed that the compressive strengths of concretes containing glass powder were clearly greater than those so-called Bolomey ones, whatever the amount of glass powder that the binder contained. It can be concluded, therefore, that glass dust exerted an important activity in increasing the long-term compressive strength of concretes. This activity can be represented by a coefficient *k*, at 28 and 90 days, shown in Figures 9 and 10, which present the evolution of the value of 'k apparent' and 'k real' depending on the amount of glass powder contained in the binder, respectively.

**Figure 7.** Compressive strength, *Cs*, 28 days after setting, with regard to the amount of glass powder used to replace the cement (*Gp*). The results are compared to the Bolomey (real and apparent) corresponding ones. The determination coefficients of the linear fittings are *R* <sup>2</sup> = 0.988 (*C<sup>S</sup>* 28); *R* <sup>2</sup> = 0.999 (*C<sup>S</sup>* apparent Bolomey); *R* <sup>2</sup> = 0.993 (*C<sup>S</sup>* real Bolomey). 's 'apparent' and 'real' com-

called 'Bolomey

' 'apparent' and 'real' com-

Bolomey Cs' obtained. In this table, ' 'apparent'

pressive strengths and 'apparent' coefficients of the additive correspond to values cal-

's 'real' compressive strengths and 'real' coefficients

Results of Bolomey's 'apparent' and 'real' compressive strengths.

**Figure 8.** Compressive strength, *Cs*, 90 days after setting, with regard to the amount of glass powder used to replace the cement (*Gp*). The results are compared to the Bolomey (real and apparent) corresponding ones. The determination coefficients of the linear fittings are *R* <sup>2</sup> = 0.973 (*C<sup>S</sup>* 90); *R* <sup>2</sup> = 0.993 (*C<sup>S</sup>* apparent Bolomey); *R* <sup>2</sup> = 0.999 (*C<sup>S</sup>* real Bolomey).

which present the evolution of the value of 'k apparent' and 'k real' depending on the

The differences between the 'apparent' and 'real' Bolomey compressive strengths

Evolution of the value of ' apparent' depending on the amount of glass powder con-**Figure 9.** Evolution of the value of '*k* apparent' depending on the amount of glass powder contained in the binder (*Gp*).

Evolution of the value of ' real' depending on the amount of glass powder contained in Evolution of the value of ' real' depending on the amount of glass powder contained in **Figure 10.** Evolution of the value of '*k* real' depending on the amount of glass powder contained in the binder (*Gp*).

Taking into account the precision of these measurements, two average values of ' ' Taking into account the precision of these measurements, two average values of ' ' Taking into account the precision of these measurements, two average values of '*k*' can be obtained, one for substitutions lower than 50% of CEM I 52.5 R cement for glass powder, and the other for substitutions higher than 50%.

In this way, it can be considered that '*k* apparent' was equal to 0.6, for replacements of cement for glass powder below 50%, and equal to 0.3 for those higher. Similarly, for '*k* real' a value of 0.4 can be considered for substitutions of cement for glass powder below 50%, and 0.3 for those higher. These results are interpreted so that if *k* was 0.6, for example, to

obtain the same compressive strength in a concrete produced with 60 kg of CEM I 52.5 R cement, it would be necessary to use 100 kg of glass powder.

By obtaining the so-called Bolomey coefficients, the percentage of cement that can be replaced for glass powder in concrete to obtain a certain compressive strength can be calculated. According to Figures 9 and 10, for up to 50% replacement of CEM I 52.5 R cement by glass powder, the compressive strength values of concretes are sufficiently important to classify these concretes in the group of building concretes. It was observed that the decrease in compressive strength occurred linearly as a function of the percentage of glass powder in the binder. In this way, from the experimental results, taking into account the percentage of glass powder contained in the binder and the compressive strength obtained in the control specimen, Equation (7) has been deduced. Such an equation makes it possible to predict the compressive strength of the concrete, at a certain setting time, according to the amount of glass powder used to replace the CEM I 52.5 cement:

$$\text{Cs} = -\mathfrak{Z}1V + \text{Cs}\_{\text{cell}} \tag{7}$$

where:

–

higher than Bolomey's

*V* is the percentage of glass powder contained in the binder; and *Cscem* is the compressive strength of the concrete whose binder is only CEM I 52.5 R.

Figure 11 shows the variation of compression strengths, for test ages of 2, 7, 28 and 90 days, of concrete manufactured with different replacement percentages of cement by glass powder. At above 50% replacement of CEM I 52.5 R cement by glass powder, the previous law is not applicable. The experimental values of compressive strength are lower than those obtained by this expression. From the values obtained for compressive strength, concretes studied can be classified in the group of concretes for paving roads and highways. Also, a possible use of concrete with a substitution percentage of glass powder for cement lower than 50% may be in the construction of wind farms, as a surface layer in foundations, since it may reduce the effects caused by corrosion because it significantly reduces the chloride ion permeability of concrete due to exposure to meteorological phenomena [25,26].

**Figure 11.** Variation of compression strengths, for test ages of 2, 7, 28 and 90 days, of concrete manufactured with different replacement percentages of cement by glass powder (*Gp*).

On the other hand, concretes manufactured with a replacement percentage higher than 50% of glass powder could be involved in the construction of park roads, especially in those located in areas with a high ecological value. From an environmental point of view, these concretes do not emit pollutant leachate [26] and adopt the color of the aggregate used, thereby minimizing the visual impact caused [32].

#### **4. Conclusions**

The results obtained in the tests carried out led us to confirm the initial research hypothesis, and the following conclusions:

On the properties of fresh concrete:


In terms of compressive strength:


**Author Contributions:** Conceptualization, E.M.G.d.T. and M.I.M.-L.; methodology, D.A.-G., E.M.G.d.T., M.I.M.-L., S.G.-S. and S.P.; software, M.I.M.-L.; validation, S.G.-S., E.M.G.d.T. and M.I.M.- L.; formal analysis, E.M.G.d.T., M.I.M.-L. and D.A.-G.; investigation, D.A.-G., E.M.G.d.T., M.I.M.-L., S.G.-S. and S.P.; data curation, E.M.G.d.T. and M.I.M.-L.; writing—original draft preparation, D.A.-G., E.M.G.d.T., S.G.-S., M.I.M.-L. and S.P.; writing—review and editing, E.M.G.d.T. and M.I.M.-L.; supervision, S.G.-S., M.I.M.-L. and S.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


*Article*
