A Review on Deep Learning Models for Forecasting Time Series Data of Solar Irradiance and Photovoltaic Power

Abstract

Presently, deep learning models are an alternative solution for predicting solar energy because of their accuracy. The present study reviews deep learning models for handling time-series data to predict solar irradiance and photovoltaic (PV) power. We selected three standalone models and one hybrid model for the discussion, namely, recurrent neural network (RNN), long short-term memory (LSTM), gated recurrent unit (GRU), and convolutional neural network-LSTM (CNN–LSTM). The selected models were compared based on the accuracy, input data, forecasting horizon, type of season and weather, and training time. The performance analysis shows that these models have their strengths and limitations in different conditions. Generally, for standalone models, LSTM shows the best performance regarding the root-mean-square error evaluation metric (RMSE). On the other hand, the hybrid model (CNN–LSTM) outperforms the three standalone models, although it requires longer training data time. The most significant finding is that the deep learning models of interest are more suitable for predicting solar irradiance and PV power than other conventional machine learning models. Additionally, we recommend using the relative RMSE as the representative evaluation metric to facilitate accuracy comparison between studies.

1. Introduction

Solar energy is a popular renewable energy source because it is abundant and environment-friendly. The amount of solar energy incident on the earth’s surface is approximately 1.5 × 1018 kW h/year, which is approximately 10,000 times the current annual energy consumption of the entire world [1]. Therefore, in recent years, solar photovoltaic (PV) has a significant role in electricity generation. A challenging issue associated with the solar PV is that its power output strongly depends on uncertain and uncontrollable meteorological factors, such as atmospheric temperature, wind, pressure, and humidity [2]. As the solar PV capacity increases, risks caused by the uncontrollable nature of PV power increase. Energy storage could mitigate such risks, but the drawbacks are the installation and management costs. However, solar irradiance forecasting is an inexpensive and immediate solution and effective in microgrid operation optimization such as peak shaving, uncertainty impact reduction, and economic dispatch problem in the power system [3].

Generally, solar irradiance can be forecast from very short terms (several minutes ahead) to long terms (several days ahead)—the requirement for the time horizon changes with applications. For the very short-term and short-term forecast horizons, sudden variations of solar irradiance, namely the ramp events, are of interest. Abrupt and severe variations of solar irradiance have the potential to degrade the reliability and quality of PV power. Hence, forecasting results for the short-term horizon are useful for estimating the largest PV power ramp rates [4]. Meanwhile, forecasting for the medium and long-term horizons helps operation optimization and market participation. For example, Husein et al. [3] demonstrated that day-ahead solar irradiance forecasting could increase annual energy savings for the operation of a commercial building microgrid. Therefore, solar energy forecasting should be targeted for a specific application, and accordingly, an appropriate forecasting method must be selected.

The solar irradiance and PV power forecasting methods are divided into physical and statistical models. The physical model mathematically or numerically manages the interaction of solar radiation in the atmosphere based on the laws of physics. It comprises numerical weather prediction, sky imagery, and satellite image models [5]. The statistical model finds a relationship between input and output variables and consists of conventional statistical models and machine learning models. Conventional statistical models include the fuzzy theory, Markov chain, autoregressive, and regression models. The machine learning model, also known as an artificial intelligence model, can efficiently extract high-dimensional complex nonlinear features and directly map input and output variables. In the past, the well-known machine learning models for predicting solar energy were the support vector machine (SVM), k-nearest neighbors, artificial neural network (ANN), naive Bayes, and random forest. These statistical models rely primarily on historical data to predict future time series. Therefore, the quantity and quality of historical data are essential for an accurate forecast.

Nowadays, the deep learning model becomes more popular in solar irradiance forecasting. The deep learning model, which is the subpart of the machine learning model, was developed to solve a complex problem with a large amount of data. The multiple layers in the deep learning structure automatically learn the abstract features directly from the raw data to discover useful representations

Deep learning models are distinctive from other machine learning models because they outperform as input data scale increases. Ng et al. [6] compared machine learning and deep learning models’ performance while changing the amount of input data. The result showed that deep learning models tend to increase their accuracy as the number of training data increases, whereas the traditional machine learning models stop improving at a certain amount of data.

The deep learning models specialized for handling sequential or time-series data such as text, speech, and image have been developed and have been successful. Recurrent neural network (RNN), long short-term memory (LSTM), gated recurrent unit (GRU), and convolutional neural network-LSTM (CNN–LSTM) models are typical. Because solar forecasting is intrinsically based on sequential data, such deep learning models were also applied for solar forecasting. For instance, Zang et al. [7] demonstrated that the accuracies of CNN–LSTM, LSTM, and CNN models are better than those of ANN and SVM in the short-term forecasting of global horizontal irradiance (GHI). Due to popularity and excellency, more applications of the deep learning model for solar forecasting are expected.

Outstanding review papers dedicated to machine learning can be found in solar forecasting literature [2,5,8,9]. However, they encompassed various machine learning models or paid little attention to deep learning models. Because the deep learning models suitable for sequential data and applied for solar forecasting have not been reviewed, the present study discusses basic principles of the RNN, LSTM, GRU, and CNN–LSTM selected as recently developed deep learning models and their comparative analyses. This paper is structured into six sections. Section 2 describes the solar irradiance variability for different time scales. Section 3 summarizes the theoretical background of the models, and Section 4 explains the evaluation metrics used to compare the performance of deep learning models. Then, Section 5 analyzes relevant studies in terms of features and accuracy. Finally, a summary of major findings in this study is presented in Section 6.

2. Solar Irradiance Variability

A single location on earth will experience a high degree of solar irradiance variability. The variability is highly dependent on local weather and atmospheric conditions as well as diurnal and seasonal cycles. The diurnal and seasonal variabilities due to the sun’s motion and the earth’s distance from the sun are fully predictable. However, the variability due to the moving clouds affected by local weather and atmospheric conditions has stochastic features and consequently is very difficult to predict.

The variability of solar irradiance depends on the time scale. A single datum represents a mean value of more frequent measurement records for a given time period. For instance, an hourly value of GHI may be acquired from 60 pyranometer records at the one-minute interval. Therefore, a long time interval results in the smoothing effect, and thus the variability lessens. Figure 1 shows the smoothing effect on the solar irradiance variability. The data were recorded every minute at Kookmin University, South Korea and presented by different time scales. The finest temporal resolution of one minute reveals a high degree of variability, but the variability smooths out with the time scale. It should be noticed that the smoothing effect also appears when a spatial averaging over a large area is applied.

The variability of solar irradiance directly affects solar PV power systems’ performance and more seriously disturbs grid stability. The grid typically absorbs power fluctuations at short time scales as fluctuations in frequency and voltage. Therefore, grid operators can control the power ramp rate by imposing a limit on PV plants; for instance, 10% of the nameplate capacity per minute. In addition, grid operators need to balance supply and demand while complying with power system regulations. If the power supply exceeds demand, curtailment can be applied to disconnect power delivery from PV plants with the grid. Solar irradiance or PV power forecasting can optimize the ramp rate control and schedule the load-following operation more effectively with an energy storage system.

Various solar forecasting techniques have their own applicable regimes in terms of time scale. Thus, depending on solar irradiance variability of interest, an appropriate technique must be selected. Figure 2 illustrates a guideline to select forecasting techniques. For time horizons less than one hour, sky-image-based techniques offer very good forecasting capability [10]. Satellite-image-based techniques are recommended for several hours ahead of forecasting with a spatial resolution around 1–5 km [11]. Numerical weather predictions (NWP) allows long-term forecasting over 1 day and up to 15 days ahead, but its time step and update interval are large. On the other hand, time series forecasting using statistical models covers many applications from short to long terms with fine time steps [12,13,14]. As an advanced version of statistical models, deep learning models for sequential data are anticipated to expand the regime.

3. Deep Learning Models

This section provides an overview of the theoretical background of the selected deep learning models. We describe a neural network and activation function because they are fundamental for all types of neural network algorithms, although ANN is not in the scope of this review.

3.1. Neural Network

The neural network is inspired by the structure of the human brain and significantly contributed to machine learning technology development. It is a simplified mathematical model to solve various nonlinear problems. In the past, researchers reviewed ANN models in predicting solar energy, such as Yadav et al. [15] for solar radiation prediction, Mellit et al. [16] for PV applications, and Cheon et al. [17] for solar energy forecasting. One conclusion from these studies is that the ANN model predicts solar radiation more accurately than other conventional models, such as the Angstrom, conventional, linear, nonlinear, and fuzzy logic models.

The neural network model comprises the input, hidden, and output layers with auxiliary components, such as neurons, weight, bias, and activation functions. Figure 3 shows the basic neural network architecture with a multilayer perceptron. The input layer receives input values, and the hidden layer analyzes the input values. The output layer collects the data from the hidden layer and decides the output. In the learning process, the neural network modifies its structure to get the same reference or set point as the supervisor. The training process will be repeated until the difference between the neural network output and the supervisor lies within an acceptable range [18].

The basic ANN mathematical formula can be expressed as

$$A_n={\displaystyle \sum _{j=1}^n(w_j}\cdot I_j)+b$$

(1)

where A_n is the output, n is the number of input, w_j is the weight, I_j is the input, and b is the bias.

The output value varies with the activation function. The activation function, also known as the transfer function, is a mathematical equation determining neurons’ output and can be divided into two types, namely, linear and nonlinear functions. A linear activation function generates the same linear result between the input and output layers. However, such a linear relationship is not enough for practical applications because the problems involve complex information and various parameters, such as image, video text, and sound. A neural network with a nonlinear activation function can tackle the limitations of the linear activation function. The commonly used activation functions are shown in

Table 1. Activation functions of the neural network.

Activation Function	Equation	Plot
Linear	$f\left(x\right)=x$
ReLU	$f\left(x\right)=\max \left(0,x\right)$
Leaky ReLU	$f\left(x\right)=\max \left(0.1\cdot x,x\right)$
Tanh	$f\left(x\right)=\tanh \left(x\right)$
Sigmoid	$f\left(x\right)=\frac{1}{1+e^{-x}}$

. Note that the rectified linear unit (ReLU) and leaky ReLU are examples of nonlinear activation function because the slope is not constant for all values. Especially for ReLU, the slope is always either 0 for negative values or 1 for positive values.

3.2. RNN

RNNs are specially designed for analyzing sequential data and have been successfully used in fields such as speech recognition, machine translation, and image captioning [19]. RNN processes sequence data by elements and preserves a state to represent the information at time steps [20]. A traditional neural network assumes that all units of the input vectors are independent. Consequently, the traditional neural network is ineffective for predicting using sequential data.

The architecture of RNN with three main components (input, hidden neuron, and activation function) is shown in Figure 4.

Previous hidden state (h_t) can be formulated as

$$h_t=\tanh \left(U\cdot x_t+W\cdot h_{t-1}\right)$$

(2)

where x_t is the input at time t, h_t is the hidden neuron at time t, U is the weight of the hidden layer, and W is the transition weights of the hidden layer. The input and previous hidden states are combined to produce information as the current and previous input go through the tanh function. Then, the output is the new hidden state, performing as the neural network memory because it holds information from the previous network.

Training regular RNNs can be challenging because of vanishing and exploding gradient problems. In the case of the exploding gradient, the problem can be solved after the backpropagation is closed at a certain point. However, the result is not optimal because all the weights are not updated. In the case of the vanishing gradient, it can be fixed by initializing the weights to reduce the possibility of vanishing gradient. However, an alternative treatment to solve the problem is to use LSTM, which we discuss later.

3.3. LSTM

LSTM is a time RNN proposed by Hochreiter et al. [21] to learn the long-term dependence of information. An LSTM has a similar flow as an RNN. The difference is the operation inside the cells. An LSTM unit comprises forget, input, and output gates (Figure 5). The forget gate categorizes the information that should be thrown away or kept. The input gate updated the cells, and the output gate decides the next hidden state. Furthermore, LSTM has an internal memory unit and gate mechanism to overcome both the vanishing gradient and explosion gradient problems in the training process of RNN [22].

The calculation formulas related to the LSTM structure in Figure 4 are as follows:

$$f_t=\sigma \left(W_f\cdot X_t+U_f\cdot h_{t-1}+b_f\right)$$

(3)

$$i_t=\sigma \left(W_i\cdot X_t+U_i\cdot h_{t-1}+b_i\right)$$

(4)

$$S_t=\tanh \left(W_c\cdot X_t+U_c\cdot h_{t-1}+b_c\right)$$

(5)

$$C_t=i_t\ast S_t+f_t\ast S_{t-1}$$

(6)

$$o_t=\sigma {\left(W_o\cdot X_t+U_o\cdot h_{t-1}+V_o\cdot C_t+b_o\right)}^{}$$

(7)

$$h_t=o_t\ast \tanh \left(C_t\right)$$

(8)

The mathematical symbols in the above equations are as follows:

• X_t is the input vector to the memory cell at time t.
• W_i, W_f, W_c, W_o, U_i, U_f, U_c, U_o, and V_o are weight matrices.
• b_i, b_f, b_c, and b_o are bias vectors.
• h_t is the value of the memory cell at time t.
• S_t and C_t are the values of the candidate state of the memory cell and the state of the memory cell at time t, respectively.
• σ and tanh are the activation functions.
• i_t, f_t, and o_t are values of the input gate, the forget gate, and the output gate at time t.

The forget gate (f_t), input gate (i_t), and output gate (o_t) in Equations (3), (4) and (7) have values from 0 to 1 through the sigmoid function (σ). A value of one means that all input information passes through the gate, but a value of 0 shows that no input information passes [23]. The values of the candidate state of the memory cells in Equation (6) calculate the new information at time t, and its output through the tanh function has a value between −1 and 1. The state of the memory at the cell, controlled by the forget and input gates, is calculated as variable C_t of time t (Equation (7)). The selected values are converted into output by multiplying them by o_t and output becomes h_t (Equation (8)).

3.4. GRU

Cho et al. [24] first proposed GRU as a simpler RNN architecture than LSTM, resulting in easier computation and implementation. GRU is similar to LSTM in terms of remembering valuable information and capturing long-term dependencies. The strength of GRU is that the computational time is more efficient with less complexity because of fewer parameters than LSTM [25]. GRU also only has two gates, namely, a reset and an update gate. The update gate is the same as the forget and input gate in LSTM because it selects what information should be stored or erased. Meanwhile, the reset gate decides the amount of information that must be forgotten. Therefore, the training time of GRU is faster than LSTM.

The structure of GRU is shown in Figure 6, and the relationship between the input and output for GRU can be written as:

$$r_t=\sigma \left(W_r\cdot X_t+U_r\cdot h_{t-1}+b_r\right)$$

(9)

$$Z_t=\sigma \left(W_z\cdot X_t+U_z\cdot h_{t-1}+b_z\right)$$

(10)

$$A_t=\tanh \left(W_h\cdot X_t+U_h\cdot \left(r_t\ast h_{t-1}\right)+b_h\right)$$

(11)

$$h_t=\left(1-Z_t\right)\ast h_{t-1}+Z_t\ast A_t$$

(12)

where r_t is the reset gate, Z_t is the update gate, A_t is the memory content, σ and tanh are the activation functions, and h_t is the final memory at the current time step. The reset (r_t) and update gate (Z_t) have values from 0 to 1 through the sigmoid function (σ) in Equations (9) and (10). Meanwhile, the memory content (A_t), using the rest gate to store the relevant information from the past, has a value between −1 and 1 through tanh.

3.5. The Hybrid Model (CNN–LSTM)

CNN is a deep learning algorithm by considering spatial inputs. Identical to other neural networks, CNN neurons have learnable weights and biases. However, CNN is mainly used for processing data with a grid topology, giving it a specific characteristic of its architecture [26].

CNN is a feedforward network because information flow occurs in one direction only, that is, from their inputs to their outputs [27]. The CNN model uses three main layers, namely, the convolutional, pooling, and fully connected layers (Figure 7). The convolutional and pooling layers are used to reduce the computational complexity. Meanwhile, the fully connected layer is the flattened layer connected to the output. Various pooling techniques are available in the architecture of CNN. However, max pooling is mostly used in CNN layers, where the pooling window contains the maximum value from each element [28].

CNN–LSTM was developed for visual time series prediction problems and generating textual descriptions from the sequences of images. The CNN–LSTM architecture uses CNN layers for feature extraction on input data and combines with LSTM to support sequence prediction. Specifically, CNN extracts the features from spatial inputs and uses them in the LSTM architecture to output the caption. The architecture of the CNN–LSTM model is illustrated in Figure 8.

The applications of this hybrid model have been used to solve many problems, such as rod pumping [29], particulate matter [30], waterworks [31], and heart rate signals [32]. Studies have demonstrated promising results; for example, Xingjian et al. [33] predicted the future rainfall intensity in a local region over a relatively short period. The experiments show that the CNN–LSTM network captures spatiotemporal correlations better and consistently outperforms the fully connected LSTM (FC-LSTM) model for precipitation forecasting.

4. Evaluation Metrics

Evaluation metrics are critical for explaining the forecast performance of deep learning models [34]. The metrics provide feedback regarding the accuracy of the forecasting to improve the models until a desirable accuracy is achieved. Various evaluation metrics are available for calculating the accuracy of prediction. The typical evaluation metrics for solar irradiance and PV power forecasting are summarized in

Table 2. Evaluation metrics.

Evaluation Metric	Equation
Error	$P_{pred}-P_{meas}$
Mean absolute error (MAE)	$\frac{1}{n}{\displaystyle \sum _{i=1}^n\left|P_{pred}-P_{meas}\right|}$
Mean absolute percentage error (MAPE)	$\frac{1}{n}{\displaystyle \sum _{i=1}^n\left|\frac{P_{pred}-P_{meas}}{P_{meas}}\right|}\cdot 100$
Mean bias error (MBE)	$\frac{1}{n}{\displaystyle \sum _{i=1}^n\left(P_{pred}-P_{meas}\right)}$
Relative Mean bias error (rMBE)	$\frac{{\displaystyle \sum _{i=1}^n\left(P_{pred}-P_{meas}\right)}}{{\displaystyle \sum _{i=1}^n{P}_{meas}}}\cdot 100$
rRMSE	$\frac{\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^n{\left(P_{pred}-P_{meas}\right)}^2}}}{\frac{1}{n}{\displaystyle \sum _{i=1}^n{P}_{meas}}}\cdot 100$
RMSE	$\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^n{\left(P_{pred}-P_{meas}\right)}^2}}$
Forecasting skill	$1-\frac{RMS{E}_{\mathrm{mod}el}}{RMS{E}_{persistence}}$

. Here, P_pred, P_meas, and n represent the forecasted values at each time, the measured values at each time, and the number of sample data for the period, respectively.

Mean absolute error (MAE) measures the average magnitude of error in a set of predictions using the absolute value. If the absolute sign is removed, the evaluation metric becomes MBE, capturing the average bias in the prediction, such that positive and negative values represent overprediction and underprediction, respectively. However, root-mean-square error evaluation metric (RMSE) measures the deviation from the measurement, and thus, the smaller, the better. When mean values vary with location or system, a direct comparison of evaluation metrics could lead to a misunderstanding. In such cases, the percentage or relative metrics such as Mean absolute percentage error (MAPE) and relative root-mean-square error (rRMSE) are more useful. Forecasting skill measures the forecasting model over the persistence model regarding RMSE, where the persistence model assumes that the atmospheric conditions are stationary. A positive forecasting skill value means that the model is outperforming the persistence model. Note that measurement data include uncertainty by nature, and thus, the true values are unknown. Hence, researchers prefer to use differences, such as root-mean-square difference (rRMSD) and relative mean bias difference (rMBD) [35].

5. Analysis of Past Studies

In this section, we present notable findings in forecasting solar irradiance and PV power after analyzing the published studies based on RNN, LSTM, GRU, and CNN–LSTM hybrid models. In total, 35 papers from 2005 to 2020 were collected and plotted by the publication year (Figure 9). From 2005 to 2017, only a few papers were published because these deep learning models were unpopular then. However, the number of publications increased dramatically since 2018. The number of publications grew by 250%, from 4 in 2018 to 14 in 2019. Meanwhile, only the publications until early 2020 were collected, and more publications are expected by the end of the year.

The proportion of publications by deep learning models for predicting solar irradiance and PV power individually is shown in Figure 10. In both cases, the LSTM accounts for most publications, with RNN and GRU following. Meanwhile, the CNN–LSTM hybrid model shows the lowest contribution. The popularity of the LSTM model is higher than that of the other standalone models because it provides promising accuracy in the case of solar energy forecasting. The CNN–LSTM also has a better performance than other models. However, the percentage of publications using this model is smaller than using other models because the CNN–LSTM is a new solar energy forecasting model.

It should be noted that we did an independent review for solar irradiance and PV power because the units and range values are different. Solar irradiance refers to the amount of solar radiation per unit area; meanwhile, PV power refers to the use of solar radiation as thermal energy through PV cells in the solar panel. The total solar radiation on the earth’s atmosphere is approximately 1360 W/m², called the solar constant. This value is attenuated to the earth’s surface through a complex series of reflections, absorptions, and remissions. Solar irradiance fluctuates because it is affected by several factors such as atmosphere condition, geographic location, season, and time of day. Although the amount of power generated by PV at a particular location depends on how much of the solar irradiance reaches it, the PV power output also relies on the solar panel’s size and efficiency. Therefore, it is essential to describe the specification of the solar panel for getting accurate PV output information.

5.1. Accuracy

The prediction accuracy is the most critical factor in selecting a forecast model. We chose RMSE as the basic evaluation metric because it is most popular in solar energy forecasting. Because the mean value of solar irradiance or PV power differs by factors such as location and system size, rRMSE is a better measure to compare the accuracy between studies. Unfortunately, only a few studies presented rRMSE. We selected the best accuracy out of all the studied cases.

Table 3. Solar irradiance forecasting.

Authors and Ref.	Forecast Horizon	Time Interval	Model	Input Parameter	Historical Data Description	RMSE (W/m2)
Cao et al. [38]	1 day	hourly	RNN	-Solar irradiance	1995–2000 (2192 days)	44.326
Niu et al. [37]	10 min ahead	every 10 min	RNN	-Global solar radiation -Dry bulb temperature -Relative humidity -Dew point -Wind speed	22–29 May 2016 (7 days)	118
	30 min ahead					121
	1 h ahead					195
Qing et al. [39]	1 day ahead	hourly	LSTM	-Temperature -Dew Point -Humidity -Visibility -Wind Speed	March 2011–August 2012 January 2013–December 2013 (30 months)	76.245
Wang et al. [25]	1 day ahead	every 15 min	CNN–LSTM	-Solar irradiance	2008–2012 2014–2017 (3013 days)	32.411
			LSTM			33.294
Aslam et al. [40]	1 h ahead	hourly	LSTM	-Solar irradiance	2007–2017 (10 years)	108.888
			GRU			99.722
			RNN			105.277
	1 day ahead		LSTM			55.277
			GRU			55.821
			RNN			63.125
Ghimire et al. [36]	1 day ahead	every 30 min	CNN–LSTM	-Solar irradiance	January 2006–August 2018	8.189
Husein et al. [3]	1 day ahead	hourly	LSTM	-Temperature -Humidity -Wind speed -Wind direction -Precipitation -Cloud cover	January 2003–December 2017	60.310
Hui et al. [41]	1 day ahead	hourly	LSTM	-Temperature -Relative humidity -Cloud cover -Wind speed -Pressure	2006–2015 (10 years)	62.540
Byung-ki et al. [42]	1 day head	hourly	LSTM	-Temperature -Humidity -Wind speed -Sky cover -Precipitation -Irradiance	(1825 days)	30.210
Wojtkiewicz et al. [43]	1 h ahead	hourly	GRU	-GHI -Solar zenith angle -Relative humidity -Air Temperature	January 2004–December 2014	67.290
			LSTM			66.570
Yu et al. [44]	1 h ahead	hourly	LSTM	-GHI -Cloud type -Dew point -Temperature -Precipitation -Relative humidity -Solar Zenith Angle -Wind speed -Wind direction	2013–2017	41.370
Yan et al. [45]	5 min ahead	every 1 min	LSTM	-Solar irradiance	2014	18.850
			GRU			20.750
	10 min ahead		LSTM			14.200
			GRU			15.200
	20 min ahead		LSTM			33.860
			GRU			29.580
	30 min ahead		LSTM			58.000
			GRU			55.290

and

Table 4. PV power forecasting.

Authors and Ref.	Forecast Horizon	Interval Data	Model	Input Variable	Historical Data Description	RMSE (kW)	PV Size
Vishnu et al. [49]	1 h ahead	hourly	CNN–LSTM	-Irradiation -Wind speed -Temperature	March 2012–December 2018	0.053	N/A
	1 day ahead					0.051
	1 w ahead					0.045
Gensler et al. [50]	1 day ahead	hourly	LSTM	-PV power	(990 days)	0.044	N/A
Wang et al. [51]	1 h ahead	hourly	GRU	-Total column liquid water -Total column ice water -Surface pressure -Relative humidity -Total cloud cover -Wind speed -Temperature -Total precipitation -Total net solar radiation -Surface solar radiation -Surface thermal radiation	April 2012–May 2014	68.300	N/A
Zhang et al. [34]	1 min ahead	every 1 min	LSTM	-Sky images -PV Power	2006	0.139	10 × 6 m2
Abdel-Nassar et al. [52]	1 h ahead	hourly	LSTM	-PV power	(12 months)	82.150	N/A
Lee et al. [53]	1 h ahead	hourly	LSTM	-PV power	June 2013–August 2016 (39 months)	0.563	N/A
Lee et al. [54]	1 h ahead	hourly	RNN	-Temperature -Relative humidity -Wind speed -Wind direction -Sky index -Precipitation -Solar altitude	June 2017–August 2018	0.160	N/A
Li et al. [55]	15 min ahead	N/A	RNN	-PV power	January 2015–January 2016	6970	N/A
			LSTM			8700
	30 min ahead		RNN			15,290
			LSTM			15,570
Li et al. [48]	1 h ahead	every 5 min	LSTM	-PV power	June 2014–June 2016 (743 days)	0.885	199.16 m2
			GRU			0.847
			RNN			0.888
Wang et al. [56]	5 min ahead	every 5 min	LSTM	-Current phase average -Wind speed -Temperature -Relative humidity -GHI -DHI -Wind direction	2014–2017 (4 years)	0.398	4 × 38.37 m2
			CNN–LSTM			0.343
Wen et al. [57]	1 h ahead	hourly	LSTM	-Temperature -Humidity -Wind speed -GHI -DHI	1 January–1 February 2018	7.536	N/A
Sharadga et al. [58]	1 h ahead	hourly	LSTM	-PV power	January–October 2010	841	N/A
	2 h ahead					1102
	3 h ahead					1824

list the accuracy of the papers, including forecast horizon, time interval, input parameters, and the size of PV systems in the case of PV forecasting.

Regarding solar irradiance forecasting in Table 3, the forecast horizon ranges from 5 min to 1 day ahead. Meanwhile, the time interval data vary from every 5 min to 1 h. Generally, the CNN–LSTM as the hybrid model performs better to predict solar irradiance for one day-ahead forecasting. Ghimire et al. [36] have the best performances of all the studies with RMSE values of 8.189 W/m². For LSTM and GRU, the best performance was the prediction of solar irradiance for 10 min ahead at 5 min intervals. However, RNN tends to result in lower accuracy than other models for day-ahead hourly forecasting.

In this case, the main factor causing changes in solar irradiation is the presence of clouds. Unfortunately, only some studies explained the condition of the sky. For example, Wang et al. [25] demonstrated that the CNN–LSTM hybrid outperformed the single LSTM to predict one day-ahead solar irradiation at 15 min intervals on sunny days, showing the small error where the RMSE value is less than 34 W/m². Meanwhile, Niu et al. [37] have the largest error in forecasting solar irradiance using the RNN model where the RMSE value is 195 W/m²; however, the sky conditions are not mentioned in the present study. Hence, further study regarding deep learning models to predict solar irradiance is required to create a concrete solution.

The performances for PV power forecasting are listed in Table 4. Most publications focused on predicting PV power in intra-hour forecast horizons. The RMSE reveals a wide variation from 0.044 to 15,290 kW because PV power generation is proportional to system size. Accuracy comparison is more difficult in PV power forecasting than in solar irradiance forecasting, suggesting an increasing need for evaluation based on rRMSE. For the LSTM models in references (Zhang et al. [46]; Wang et al. [47]; Li et al. [48]), the RMSE value increases as the PV size increases. The values are 0.139, 0.398, and 0.885 kW for the PV size of 60.00, 153.48, and 199.16 m², respectively.

5.2. Types of Input Data

The type of input data, endogenous and exogenous, can classify forecasting models. In the endogenous model, the type of input and output data is identical. That is, historical PV power data are used for forecasting future PV power. However, the exogenous model uses other data types, such as ambient temperature, humidity, wind speed, wind direction, and sun position, besides the type of output data. It should be noted that the cited references used historical data prediction as input rather than numerical weather prediction data. The time period of input data is also summarized in Table 3 and Table 4. The number of publications by exogenous and endogenous inputs, and the forecast horizon is illustrated in Figure 11. For the intra-hour and day-ahead forecast horizons, the endogenous model outnumbers the exogenous model.

Li et al. [55] presented RNN and LSTM models using endogenous inputs for predicting PV power output in the very short term. They used both PV power data from the previous day and previous forecasting data as the input. The results demonstrated that the average RMSE, MAPE, and MAE outperform the other models such as SVM, radial basis function (RBF), back propagation neural network (BPNN), and persistence in the 15 and 30 min forecasting horizons.

Husein et al. [3] proposed an LSTM model using exogenous inputs to forecast day-ahead solar irradiance. The models used dry bulb temperature, dewpoint temperature, and relative humidity as input from six locations. The results showed that LSTM outperforms the feedforward neural network (FFNN) for data from all locations. They also simulated a one-year operation of a commercial building microgrid using the actual and forecasted solar irradiance, and the results showed that using the forecasting approach increases the annual energy savings by 2% compared with FFNN.

We investigated the exogenous input parameters from 25 publications (Figure 12). The less frequently used parameters include visibility, sky images, column ice water, column liquid water, and pressure. However, it shows that temperature, humidity, and wind speed are used more frequently because they are easier to collect than other parameters.

The period of historical data also affects the performance of the prediction. If the time series is too short, it will lead to a lack of information for learning, and if the time series is too long, it will increase the complexity of the algorithm. However, the increase in time series data does not guarantee better performance. Wang et al. [47] compared the errors of the LSTM and CNN–LSTM according to input sequences (

Table 5. Root-mean-square error evaluation metric (RMSE) of LSTM vs. CNN–LSTM based on the input sequence.

Input Sequence (Years)	LSTM		CNN–LSTM (kW)
	RMSE (kW)	MAE (kW)	RMSE (kW)	MAE (kW)
0.5	1.244	0.654	1.161	0.559
1	1.393	0.616	1.434	0.628
1.5	1.533	0.599	1.248	0.529
2	1.320	0.457	0.941	0.397
2.5	0.945	0.389	0.426	0.198
3	0.398	0.181	0.343	0.126
3.5	1.150	0.455	0.991	0.384
4	1.465	0.565	0.886	0.405

). The results show that errors increase from 0.5 to 2 years of input time series data. The best accuracy was observed when three years of input sequences were used. Historical data of more than three years degraded performances, implying that the period of input data must be optimized.

5.3. Forecast Horizon

The forecast horizon is the length of time into the future for which a model can predict, and it strongly influences the performances and characteristics of the forecast. Forecasting horizons can be divided into four types [59]:

• Very short-term forecasting (1 min to several minutes ahead).
• Short-term forecasting (1 h or several hours ahead to 1 day or 1 week ahead).
• Medium-term forecasting (1 month to 1 year ahead).
• Long-term forecasting (1 to 10 years ahead).

Yan et al. [45] studied LSTM and GRU’s performance to predict solar irradiance for very short-term forecasting. The experiments were conducted in time ranges of 5, 10, 20, and 30 min and the four seasons. The RMSE in

Table 6. RMSE of LSTM and gated recurrent unit (GRU) for very short-term forecasting.

Forecast Horizon (min)	Model	Spring		Summer		Autumn		Winter
		RMSE	MAE	RMSE	MAE	RMSE	MAE	RMSE	MAE
		(W/m2)		(W/m2)		(W/m2)		(W/m2)
5	LSTM	36.67	26.95	89.91	59.20	18.85	13.13	44.24	21.58
	GRU	36.82	27.18	89.77	59.70	20.75	16.03	43.66	23.60
10	LSTM	41.02	29.65	42.23	32.96	53.01	33.62	14.20	11.09
	GRU	44.71	34.42	41.08	30.92	55.00	38.35	15.20	12.83
20	LSTM	56.22	49.09	46.31	40.58	33.86	28.11	43.54	39.10
	GRU	45.23	36.78	53.97	47.44	29.58	24.55	41.03	37.09
30	LSTM	58.77	47.54	58.00	47.82	81.75	59.08	61.68	52.29
	GRU	60.42	49.65	55.29	50.52	82.12	60.71	62.33	54.13

shows that LSTM and GRU’s smallest error occurred in winter for the 10 min forecast horizon. Generally, the two models showed a gradual increase of errors for the 10 to 30 min solar irradiance forecasting.

Ghimire et al. [36] used the CNN–LSTM hybrid model and three standalone models for solar irradiance forecasting. The forecasting errors for those models are listed in

Table 7. Evaluation of predictive model (RMSE and MAE) over multiple forecast horizons.

Model	RMSE (W/m2)				MAE (W/m2)
	1 Day	1 Week	2 Weeks	1 Month	1 Day	1 Week	2 Weeks	1 Month
CNN–LSTM	8.189	16.011	14.295	32.872	6.666	9.804	8.238	13.131
LSTM	21.055	18.879	16.327	33.387	18.339	11.275	10.750	14.307
RNN	20.177	18.113	15.494	41.511	18.206	11.387	10.492	26.858
GRU	14.289	21.464	19.207	57.589	11.320	15.658	14.005	39.716

. CNN–LSTM was used using 30 min interval data to predict solar irradiance for a 1 day up to 1-month forecast horizon, as measured by RMSE and MAE. Compared with RNN, LSTM, and GRU, the hybrid model outperforms other models to predict solar irradiance in all forecasting horizons.

5.4. Type of Season and Weather

The accuracy of deep learning models has been proven for the different seasons and types of weather. For example, Li et al. [48] used RNN, LSTM, and GRU models for short-term PV power forecasting. The performance evaluations of the different models for each season and types of weather are presented in

Table 8. RMSE of PV power prediction based on the type of weather (sunny, cloudy, and rainy).

Season	Type of Weather	LSTM (kW)	GRU (kW)	RNN (kW)
Winter	Sunny	1.2541	1.2399	1.2468
	Cloudy	1.1279	0.2206	0.2867
	Rainy	2.2336	2.0876	2.1223
Spring	Sunny	0.1643	0.2456	0.3431
	Cloudy	0.2759	0.6452	0.4222
	Rainy	0.8107	1.0036	0.8604
Summer	Sunny	0.9701	1.0748	0.8514
	Cloudy	0.8398	0.9323	0.8812
	Rainy	0.3009	0.5805	0.4993
Autumn	Sunny	0.7395	0.8029	0.7778
	Cloudy	1.0540	1.2110	1.1365
	Rainy	2.4216	2.3687	2.4275

. Except for winter, generally, the LSTM model outperforms the two other models. In winter, the GRU model is better than LSTM and RNN for all types of weather.

5.5. Training Time

Deep learning with many parameters requires distributed training, where training time is critical [60]. Training time is the product of the deep learning models that must be performed to reach the desired level of accuracy. Each deep learning model has a different training time to reach the best performance. Hence, in this section, we compared the training time for each model to know which model is more efficient in forecasting solar irradiation and PV power.

Wang et al. [25] conducted forecasting experiments for LSTM and GRU to experience information training time in the best, worst, and average cases. LSTM and GRU’s training times in the three cases are presented in

Table 9. The training time of LSTM vs. GRU.

Model	The Best Case/s	The Worst Case/s	The Average Case/s
LSTM	393.01	400.57	396.27
GRU	354.92	379.57	365.40

, proving that GRU is better than LSTM because the longest training time of GRU is shorter than the best training time of the LSTM.

The training times of LSTM and GRU in Seoul and Busan in 2016 and 2017 are shown in

Table 10. The training time of LSTM vs. GRU.

Region	Year	Hourly		Daily
		LSTM (s)	GRU (s)	LSTM (s)	GRU (s)
Seoul	2017	1251.23	1004.15	88.35	72.56
	2016	1060.82	832.63	77.98	64.12
Busan	2017	1269.21	1028.43	90.42	75.44
	2016	1023.27	830.54	75.99	64.29

. Aslam et al. [40] measured LSTM and GRU’s performance as training time in a system with an AMD Ryzen Thread ripper 2950X and 64 GB RAM. The mean values taken from 10 runs for accurate results were taken. GRU performed faster than LSTM in hourly and daily forecasting. For hourly prediction, the difference in training time is more than 200 s, and for daily forecasting, it is less than 20 s in each year and region.

The training times of LSTM and CNN–LSTM are compared in

Table 11. Performance of LSTM vs. CNN–LSTM.

Model	LSTM (s)	CNN–LSTM (s)
Training time	70.490	983.701

. The hybrid model has a longer training time than LSTM, which is 983.71 s because the hybrid model must extract both the temporal and spatial features of the data [47].

5.6. Comparison with Other Models

In this section, RNN, LSTM, GRU, and CNN–LSTM are compared in Table 11,

Table 12. Comparison between Recurrent neural network (RNN) and artificial neural network (ANN).

Forecast Horizon (min)	RMSE (W/m2)
	ANN	RNN
10	55.7	41.2
30	63.3	53.3
60	170.9	58.1

,

Table 13. Comparison between LSTM and other models.

Model	FFNN (W/m2)	SVR (W/m2)	LSTM (W/m2)
RMSE	0.160	0.110	0.086

,

Table 14. Comparison between CNN–LSTM and other models.

Model	RMSE (kW)
	With Weather Data	Without Weather Data
RFR	0.178	0.191
SVR	0.122	0.126
CNN–LSTM	0.098	0.140

and

Table 15. Comparison between GRU and multilayer perceptron (MLP).

Season	RMSE (kW)
	Winter	Spring	Summer	Autumn	Average
GRU	847	917	1238	1074	1035
MLP	916	1069	1263	1061	1086

with other machine learning models and deep learning models. Pang et al. [61] proposed a hierarchical approach to predict solar irradiance using ANN and RNN in Tuscaloosa, Alabama, USA. The data from 22 to 28 May 2016 were used to predict solar irradiance into three interval times (10, 30, and 60 min) (Table 12). Consequently, RNN outperformed ANN in forecasting horizon data sampling, and the best result for the forecast horizon is when the shortest horizon was considered.

In the case of LSTM, Alzahrani et al. [62] studied a machine learning approach in Chicago, USA, where the study compared various prediction models on a test dataset using FFNN and support vector regression (SVR). The data were collected over four days (24 March, 8 February, 8 October, and 12 August) and split into three parts, namely, data training, data testing, and data validation in portions of 70%, 15%, and 15%, respectively. The results in Table 13 show that LSTM has a better performance in achieving an RMSE of 0.086 W/m², whereas FFNN and SVR obtained 0.160 and 0.110 W/m², respectively.

Lee et al. [63] compared CNN–LSTM, random forest regression (RFR), and SVR. They considered two sets of inputs: a PV measurement incorporated with weather values from a nearby meteorological station and only past PV measurements. They collected 18,620 hourly data time series and divided the data training and data testing as 75% and 25%, respectively. The results in the first case show that CNN–LSTM has the lowest error metrics with an RMSE of 0.098 kW. However, the excluded weather data case shows that SVR is better than RFR and CNN–LSTM with 0.126 kW (Table 14).

Li et al. [48] presented their results for the comparison between GRU and multilayer perceptron (MLP) in a different season (Table 15). They collected the data in DKASC, Alice Springs, Australia. The generation of the PV system is 26.500 kW. In this case, they used the data from 1 June 2014 to 31 May 2015, as the training dataset, and the data for 12 June 2016, were used as the testing dataset. The results show that MLP has a better performance than GRU only in the autumn, with a value of 1061 kW. However, the average value of GRU has the most representative attributes of all the seasons compared with MLP.

6. Conclusions

This paper introduced deep learning models as techniques to predict solar irradiance and PV power generation. To represent a complete review of the models, the evaluation for the PV power and solar irradiance forecasting is made apart. The main reason because the output is different in terms of function, unit, and range value. Although the value fluctuates because it is affected by several factors such as atmosphere condition, geographic location, season, and time of day, the evaluation of solar irradiance forecasting is uncomplicated to understand. Radiation from the sun that reaches the earth’s surface is measured in power per unit area; hence it is possible to compare the solar irradiance at different locations. However, apart from the main factors, the PV power output relies on the solar panel’s size and efficiency. Therefore, in part of the review of PV power forecasting, the solar panel size is described to obtain accurate PV output information.

RNN, LSTM, GRU, and CNN–LSTM have become the topics of research interest because of their popularity in predicting solar energy. They also offer many advantages over other machine learning models, especially regarding time series data forecasting. Each model has its strengths and limitations to predict solar irradiance and PV power; therefore, it is challenging to decide which is the best among all the models. However, from the studies reviewed in this paper, we propose the following conclusions:

• In the case of the single model, most studies explain that LSTM and GRU show better performance than RNN in all conditions because LSTM and GRU have internal memory to overcome the vanishing gradient problems occurring in the RNN.
• The hybrid model (CNN–LSTM) outperforms the three standalone models in predicting solar irradiance. More specifically, the evaluation metrics for this hybrid model are substantially smaller than those of the standalone models. However, the CNN–LSTM model requires complex input data, such as images, because it has a CNN layer inside.
• The training time should be considered to recognize the performance of the models. This work reveals that the statistics of GRU are more efficient than that of LSTM in the case of computational time because the average time for LSTM to train the data is relatively longer than that for GRU. Therefore, considering training time and forecasting accuracy, the GRU model can generate a satisfactory result for forecasting PV power and solar irradiance.
• Comparisons between the deep learning models and other machine learning models conclude that these models were better used in predicting solar irradiance and PV power (Section 5.6). Most studies show that the accuracy of the proposed models is better than other models, such as ANN, FFNN, SVR, RFR, and MLP.