Power Forecasting for Photovoltaic Microgrid Based on MultiScale CNN-LSTM Network Models

Abstract

Photovoltaic (PV) microgrids comprise a multitude of small PV power stations distributed across a specific geographical area in a decentralized manner. Computational services for forecasting the output power of power stations are crucial for optimizing resource deployment. This paper proposes a deep-learning-based architecture for short-term prediction of PV power. Firstly, in order to make full use of the spatial information between different power stations, a spatio–temporal feature fusion method is proposed. This method is capable of exploiting both the power information of neighboring power stations with strong correlations and meteorological information with the PV feature data of the target power station. By using a multiscale convolutional neural network–long short-term memory (CNN-LSTM) network model, it is capable of generating a PV feature dataset containing spatio–temporal attributes that expand the data source and enhance the feature constraints. It is capable of predicting the output power sequences of power stations in PV microgrids with high model generalization and responsiveness. To validate the effectiveness of the proposed framework, an extensive numerical analysis is also conducted based on a real-world PV dataset.

1. Introduction

As an inexhaustible clean energy source, solar energy has been widely developed and utilized globally, and its utilization technology has been constantly innovated, which has become one of the most important conditions for solving the energy crisis, reducing carbon emissions and realizing sustainable socio–economic development [1]. However, photovoltaic (PV) power generation also faces challenges. The intermittent and fluctuating nature of PV output power means that the power generation of PV systems may fluctuate drastically within a short period of time. In addition, environmental factors such as terrain and climate, such as weather changes and cloud cover, can also have an impact on the efficiency and stability of PV power generation. With the advancement of distributed PV technology, the scale of the PV industry has been expanding, especially PV microgrids, which comprise a large number of distributed PV power plants deployed on the rooftops of buildings and have gradually evolved from off-grid operation to grid-connected operation with an increasing penetration rate. In order to reduce the impact of intermittent and fluctuating PV power on the grid and to ensure the stable operation of the large grid, PV power prediction research has become a hot topic nowadays [2].

PV power prediction refers to predicting PV power generation at a future point in time or over a period of time to assist grid enterprises with scientific scheduling and accurate management of power resources to adapt to dynamically changing weather conditions and power demand. Currently, the mainstream PV power prediction methods include physical methods, statistical methods, machine learning methods and deep learning methods. Among them, the physical method fits a mathematical model based on the physical characteristics of PV modules and meteorological data, which has a certain degree of accuracy, but it is difficult to accurately fit the mathematical model, and this method requires professional measurement equipment. Statistical methods use historical data to fit statistical models; they provide fast predictions but are less effective at dealing with nonlinear and nonstationary data [3]. In recent years, more and more studies have used artificial intelligence methods such as machine learning and deep learning to learn the features and trends of historical data and thus predict future PV power. Machine learning methods can automatically capture and analyze huge datasets and make predictions based on historical data and various features, and they perform well in dealing with complex feature relationships and nonlinear problems [4].

Dávid et al. [5] compared the performance of 24 machine learning models based on numerical weather prediction (NWP) for day-ahead PV power prediction, tested them against 2 years of data at 15 min time granularity for 16 distributed PV plants in Hungary, and analyzed the impact of the choice of predictor variables as well as the benefits of hyper-parameter tuning. Theocharides et al. [6] evaluated the performance of different machine learning models for day-ahead power prediction for PV systems under different supervised learning conditions and minimum input features to guide the design of aggregation schemes for intermittent distributed PV. Mayer et al. [7] proposed a hybrid physical and machine learning approach for solar irradiance conversion to validate the physical method in comparison with data-driven and hybrid methods for day-ahead power prediction performance. Pombo et al. [8] integrated a PV panel physical model with a machine learning model to predict PV power after several hours using historical data at a 5 min time granularity. The basic dataset consists of historical power data and meteorological monitoring data. The dataset was also expanded by introducing physical information to capture the relationship between meteorological conditions and PV system operating states.

Deep learning methods are able to uncover the implicit change patterns of PV power by building deep neural network models to mine complex spatio–temporal features, and they show strong potential in handling large-scale data and short-term and ultrashort-term prediction. Tang et al. [9] proposed a hybrid PV power prediction model that utilizes an attention-expanding convolutional neural network and a bi-directional long- and short-term memory network integration structure, and it solves the challenge of predicting the output power of new PV power plants (due to lack of training data for new PV power plants) through three key steps: input reconstruction, feature extraction and feature mapping. Abdel-Basset et al. [10] designed a new deep learning architecture called PV-Net for predicting PV power generation for the coming day. PV-Net utilizes convolutional layers to design gated recurrent units (GRUs) in gates (called Conv-GRU) to achieve efficient extraction of location and time features in PV power series. Qu et al. [11] proposed a hybrid model based on gated recurrent units that utilizes 3 min time-granularized local historical PV power data to train the model and subsequently predicts the future one-day distributed PV systems’ generation for distributed PV systems for the coming day.

From existing studies, distributed PV prediction approaches have been extensively discussed in many research articles [1,5,6,11]. However, most of them ignore the similarity in power output between different distributed power plants. Furthermore, deploying a forecasting system in every power station and updating the maintenance on time is a significant challenge. To address these issues, this paper proposes an innovative PV prediction method. Specifically, a spatio–temporal feature fusion method is introduced to enhance data quality. Correlation analyses can be utilized to merge PV power data from stations with similar output powers but different distributions, effectively enhancing the dataset’s data volume. This strategy is grounded in the idea that PV stations with comparable output power may demonstrate similar generation patterns, even with variations in data distribution. By conducting correlation analyses, these similarities can be recognized, and data from other stations can be incorporated to compensate for the data deficiency of the target station. This process enhances the dataset’s coverage and data volume, ultimately boosting the model’s generalization capability. Then, a multiscale convolutional neural network–long short-term memory (CNN-LSTM) network model is designed to extract the PV feature data from the temporal, spatial and scale dimensions. In addition, considering that solar irradiance has an essential effect on PV output power, a two-stage cascaded multiscale CNN-LSTM network model is designed to improve model performance. The main contributions are as follows: (1) This paper proposes a spatio–temporal feature fusion method for leveraging distributed PV data. Firstly, this study analyzes the key factors affecting PV output power. Then, the correlation between meteorological parameters and the output power of the target power station along with that of neighboring stations is calculated. Subsequently, highly correlated power and meteorological information from neighboring stations is fused with the PV feature data of the target station to obtain features that contain both temporal and spatial attributes, which is conducive to the neural network model to more quickly and better fit the feature data. (2) The output power of all power stations in the PV microgrid for the next time slot is predicted simultaneously using a multiscale CNN-LSTM structure to extract semantic information from the time, space, and scale dimensions, thus improving the model’s prediction performance. In addition, this architecture avoids deploying predictive models at all power stations, resulting in greater efficiency and cost savings. (3) A two-stage cascaded multiscale CNN-LSTM model is designed to enhance the model’s generalization capability. The first stage predicts the solar irradiance in the next time slot, which is spliced with the PV feature data, and the second stage utilizes a convolutional kernel to extract the multiscale semantic information in the state space to predict the output power of all the generating stations in the PV microgrid. This paper is organized as follows. In the subsequent section, Section 2, we explore relationship analyses in the context of power prediction. Section 3 delves into methodologies that involve multiscale CNN-LSTM architectures. Section 4 evaluates performance metrics and experimental outcomes. Finally, Section 5 consolidates the key findings and conclusions drawn from the study.

2. Correlation Studies

2.1. Correlation Analysis

The quality of the dataset directly impacts the performance of the prediction model. If there are missing, redundant, or noisy items in the dataset, these interference terms may fall outside the robust range of the model, leading to increased prediction error [12]. Correlation analysis aims to understand the degree of association between individual feature variables in the dataset as well as the associations between the feature variables and the target variables. Subsequently, appropriate features are selected for modeling, with the aim of reducing feature dimensionality and redundancy and thereby improving prediction accuracy and model fitting speed. Additionally, correlation analysis can help discover potential patterns and trends in the dataset, offering valuable insights for feature extraction [13].

It has been demonstrated that the output power of a photovoltaic power plant is positively correlated with the ambient temperature. In geographic areas with optimal light conditions, the output power increases as the ambient temperature rises. Conversely, factors such as humidity and cloud shading are negatively correlated with the output power, as they reduce the conversion efficiency of photovoltaic panels [14]. However, meteorological conditions typically exhibit regular changes over time. Moreover, in PV microgrids, the output power of a specific power station is not only impacted by local environmental changes but is also influenced by the similarities in power curves between neighboring power stations due to comparable meteorological and geographical conditions [15]. Therefore, analyzing and extracting the key spatio–temporal factors affecting the output power of PV power stations in order to enrich the dimensions and number of features can enhance the accuracy of PV power prediction.

The Pearson correlation coefficient (PCC) [16] is employed to quantify the degree of correlation between the feature sequences of distinct PV power stations. The calculation formula is as follows:

$${\rho }_{PCC}(x,y)={\displaystyle \frac{cov(x,y)}{var\left(x\right)var\left(y\right)}}$$

(1)

where x and y are two feature sequences; they include the output power sequences of the target generating station and neighboring generating stations as well as the data sequences of the selected meteorological parameter records. The covariance of the feature sequences x and y is denoted by $\mathrm{cov}(x,y)$. The standard deviations of the feature sequences x and y, respectively denoted by $\mathrm{var}\left(x\right)$ and $\mathrm{var}\left(y\right)$, are calculated as the square root of the variance of the two sequences.

2.2. Convolutional Neural Networks

Deep learning is one of the branches of machine learning that utilizes multilayer neural networks to learn abstract representations of data by mimicking the neural network structure of the human brain. In comparison with traditional machine learning, deep learning has more powerful representation and generalization capabilities. Convolutional neural networks (CNNs) [17] represent a significant development in the field of deep learning. In comparison to traditional neural networks, CNNs have the advantage of being able to effectively deal with lattice-pointed features and can significantly reduce the number of network parameters. The convolutional kernel adaptively adjusts its parameters during network training, and the size of the receptive field determines the coverage of the input features. The larger the receptive field, the more global the extracted features are. The utilization of multilayer convolutional kernels enables CNNs to more accurately recognize abstract semantic features within the state space, thus facilitating the efficient processing of input data. This approach has been widely employed in fields such as computer vision and natural language processing.

A CNN model comprises three main components: a convolutional layer, a pooling layer and a fully connected layer. These are illustrated in Figure 1. The convolution kernel is applied to the feature map in a series of unit steps, where each slide performs a dot-multiplication operation between the feature matrix in the sensory field and the weight matrix of the convolution kernel. The resulting products are then added together to obtain the result of the convolution operation. The pooling layer reduces the number of feature parameters by decreasing the size of the feature map, thus simplifying the network structure and preserving the semantic information of the original feature map. Pooling operations are typically performed in two ways: average pooling and maximum pooling. In the context of neural networks, average pooling is a mathematical operation that calculates the average value of all points within a specified field of view. This process helps to retain the local features of the feature map while also avoiding the excessive loss of semantic information. In contrast, maximum pooling is a mathematical operation that selects the maximum value within a specified area. This process is designed to focus on capturing the texture information present within the feature map. The fully connected layer is typically located at the end of the neural network and receives the distributed information transmitted from the preceding layer. This information is then mapped to the classification space through weight calculation, after which it is employed for classification or regression.

2.3. Long Short-Term Memory Network

A long short-term memory (LSTM) network [18] represents an enhanced recurrent neural network (RNN) [19] within the domain of deep learning. Primarily utilized for processing time series data, these networks have been extensively employed in the fields of natural language processing, automatic speech recognition and time series analysis. It is a widely used model. In comparison to a recurrent neural network (RNN) model, a long short-term memory (LSTM) network is more effective at processing long sequence data and is capable of overcoming the issues of gradient vanishing and gradient explosion.

The fundamental component of an LSTM network is its unique cell state and three gate structures: the forgetting gate, input gate and output gate. Collectively, these constitute the fundamental unit of the LSTM network and enable it to analyze long sequential data and efficiently capture long-term dependencies in time series with remarkable efficiency. By integrating the forgetting gate and input gate, the LSTM network is able to adaptively update the cell state, memorize historical information and apply it to the computation of the current time step. It is crucial to acknowledge that each gate structure within the LSTM network considers the gate structure data from the preceding time step or the current cell state unit. The cell state is updated through the synergy of the forgetting and input gates. This mechanism allows the LSTM network to effectively memorize historical information and flexibly apply it in the computation of the current time step.

Figure 2 shows $x^t$ and ${\widehat{y}}^t$, which denote the input and output information at time step t, respectively; $s^t$ denotes the state vector, which is a key part of the LSTM network and allows it to memorize historical information; ${\tilde{s}}^t$ denotes the candidate vector, which is used to update the state vector; $h^t$ and ${\widehat{y}}^t$ with the same, which is passed as the activation vector to the next LSTM network cell; $o_f^t,o_u^t,o_o^t$ denote the outputs of the forgetting gate, the input gate, and the output gate, respectively; $\sigma$ and the tanh functions of the activation operation are $\mathrm{sigmoid}\left(x\right)=1/(1+e^{-x})$ and $tanh\left(x\right)=(e^x-e^{-x})/(e^x+e^{-x})$, respectively.

3. Methodology

A CNN has powerful spatial feature extraction and generalization capabilities by sliding the convolutional kernel over the input space. In addition, CNNs can extract deeper spatial semantic features by stacking convolutional channels, while recurrent neural networks can fully exploit the temporal relationships within sequences by using the recurrent structure in the network. In order to fully utilize the spatio–temporal information of the feature data from different power plants in PV microgrids, obtain more dimensions and features that influence power prediction and expand the scale of the training data, this section introduces a PV microgrid power prediction framework based on a multiscale CNN-LSTM network model. As shown in Figure 3, The framework first performs a correlation analysis of feature data to extract spatio–temporal information with strong correlations, and then it expands the dimensionality and quantity of the dataset through splicing and fusion. Then, it trains and outputs the prediction results of the output power of all the generating stations in the PV microgrid simultaneously using a multiscale CNN-LSTM model. The overall process is as follows:

Stage 1. Feature correlation analysis: In Section 2.1, the correlation analysis PCC method is introduced. We find the key meteorological factors that affect the power output of target power plants based on PCC correlation scores, and then the PCC method is used to calculate the correlation between the power of the target power plant and the output power of neighboring power plants. Finally, meteorological features with high correlations are retained in the dataset. The neighboring power station with the strongest output power correlation is selected as the reference power station. Its solar irradiation features and output power sequence are added to the target power station dataset. These are jointly stitched together to become the spatio–temporal PV features.

Stage 2. Neural network training: A time series with a length of six is constructed for all PV power plants, and a corresponding neural network model is built for each power plant. Firstly, the PV features are input into a three-layer CNN network, and then the output feature maps of each layer are spliced and fused to obtain the multiscale features. Then, the temporal attributes in the data are fully extracted by an LSTM network, and finally, the power prediction results for all power stations are output by a fully connected layer.

3.1. Correlation Analysis and Feature Fusion

There are many factors affecting the output power of a target PV power plant, and in this paper, the influences of meteorological parameters such as solar irradiance, ambient temperature and wind speed are mainly considered; we analyze the degree of influence of different meteorological parameters on the PV output power in combination with the specific geographic location and meteorological conditions. Given that the power stations are situated in mountainous and hilly regions, it is possible for weather conditions to vary significantly between nearby stations. For instance, two power stations separated by a mountain may experience contrasting weather conditions, such as rain on one side and sunshine on the other. Conversely, power stations located far apart often experience similar weather and geographical conditions, resulting in comparable PV power generation. To enhance the dataset, spatial correlations are incorporated by including data not only from the target power station but also from stations with analogous weather and geographical conditions. For this reason, the key meteorological parameters affecting the output power of the target power station and the power data of neighboring power stations that have strong correlations with the target power station are first extracted by correlation analysis, and then they are spliced with the PV feature data of the target power station to expand the data dimensions and quantities through feature fusion. As the meteorological conditions and output power change over time, the meteorological data sequence and the output power sequence of each PV power station are segmented according to a certain interval of time slots, and they combined into a sequence of PV feature data for one forward calculation.

Figure 4 shows the phase schematic diagram for the correlation analysis and feature fusion, assuming that PV power station i is the target power station. First, the Pearson correlation coefficient ${\rho }_{PCC}(P_i,X_k)$ between the output power sequence $P_i$ of this power station and the selected meteorological parameter sequence $X_{\dot{\kappa }}$ and the Pearson correlation coefficient ${\rho }_{PCC}(P_i,P_d)$ between $P_i$ and the output power sequence of the neighboring power station $P_d$ are calculated. Here, $k=1,\cdots ,K,d=1,\cdots ,D$, where K is the number of selected meteorological parameters, and D is the number of neighboring power stations. Then, the meteorological parameter sequence with the strongest correlation and the neighboring power station output power sequence are selected from ${\rho }_{PCC}(P_i,X_k),k=1,\cdots ,K$ and ${\rho }_{PCC}(P_i,P_d),d=1,\cdots ,D$, respectively. Finally, $X_{\dot{\kappa }}^{*}$ and $P_d^{*}$ are spliced and fused with the target power station output power sequences $P_i$ to obtain a new PV feature sequence $\{P_i,P_d^{*},X_k^{*}\}$ with both temporal and spatial attributes. The semantic features of different dimensions combined with the powerful feature extraction and fitting ability of the deep learning model are conducive to improving the PV power prediction accuracy.

3.2. Framework of MultiScale CNN-LSTM

In PV microgrids, accurate and fast prediction of the output power of each PV power plant is conducive to real-time power resource allocation. Considering the spatial correlation between different power plants in a PV microgrid, a multiscale CNN-LSTM network architecture is designed to adapt to the spatial and temporal characteristics of different power plants and to simultaneously output the predicted power sequences of all power plants. Compared to building an independent prediction model for each power plant, this architecture fits the objective function across time, space and scale dimensions, and the prediction models for different power plants are constrained to each other, which improves the power prediction and the overall resilience of the PV microgrid. The multiscale CNN-LSTM network architecture is shown in Figure 5, and we assume the PV microgrid owns D distributed PV power stations. Firstly, the feature sequences obtained from each power station through correlation analysis and feature fusion are input into the corresponding CNN model, which adopts a three-layer one-dimensional CNN (1D-CNN) structure with convolution kernel sizes of $\{4,3,2\}$. The numbers of output channels are $\{16,32,64\}$, and the numbers of sliding steps are $\{1,1,1\}$. Due to the different convolutional kernel sizes of each CNN layer, semantic information in the state space can be extracted from different scales. In the forward propagation process, the output vectors ${\theta }_{m,d}$ of each layer of the CNNs from all the power stations are extracted separately and are spliced as ${\phi }_m=\{{\theta }_{m,1},\cdots ,{\theta }_{m,N}\}$, where ${\phi }_m,m=1,2,3$ is the splicing vector of the mth layer of the CNNs, ${\theta }_{m,d},d\in N$ is the output vector of the mth layer of the CNNs from the dth power station, and the final fusion features are represented as $\beta =\{{\phi }_1,{\phi }_2,{\phi }_3\}$. Then $\beta$ is fed into the LSTM network for feature extraction in the time dimension, and the model contains two hidden layers with 64 and 128 neurons, respectively. Finally, the predicted power sequences $P=\{P_1,\cdots ,P_D\}$ of all the power stations in the PV microgrid are output simultaneously through the fully connected layer with the ReLU activation function, and the number of neurons in the fully connected layer is the same as the number of power stations owned by the PV microgrid, i.e., D.

3.3. Two-Stage Cascaded Multiscale CNN-LSTM Architecture

The output power of a PV power plant is significantly influenced by solar irradiance. PV panels convert solar energy into electricity through the photovoltaic effect. Greater solar irradiation leads to a higher frequency of photons interacting with the PV panel material, increasing the likelihood of electron excitation and leading to the generation of more electricity.

To enhance prediction accuracy, a two-stage cascaded multiscale CNN-LSTM network model is proposed, as depicted in Figure 6. In the initial stage, the multiscale CNN-LSTM network predicts solar irradiance for the subsequent time period using historical meteorological data from the power station as input. Simultaneously, it generates a sequence of solar irradiance predictions for all power stations, denoted as $\sigma =\{{\sigma }_1,\cdots ,{\sigma }_N\}$, which is merged with the sequence of PV feature data obtained through correlation analysis and feature fusion. Subsequently, in the second stage, the PV feature data sequences are utilized to predict the power sequences of all power stations using another multiscale CNN-LSTM network model. Employing a multitask learning architecture to constrain the solar irradiance and power output from the multiscale CNN-LSTM network enhances feature extraction, accelerates model fitting and improves prediction accuracy.

3.4. Performance Evaluation Indicators

Two metrics are used to evaluate the prediction performance of the model: root mean squared error (RMSE) and mean absolute error (MAE). RMSE represents the sample standard deviation of the difference between the predicted and true values and is more sensitive to outliers in the data; MAE is a linear score that represents the mean absolute error between the predicted and true values. Compared to MAE, RMSE focuses more on penalizing higher variances [20].

RMSE and MAE are defined as follows:

$${\mathrm{RMSE}}_D=\sum _{d=1}^D{\mathrm{RMSE}}_d=\sum _{d=1}^D\sqrt{{\displaystyle \frac{1}{S}}\sum _{s=1}^S{(P_{d,s}-{\widehat{P}}_{d,s})}^2}$$

(2)

$${\mathrm{MAE}}_D=\sum _{d=1}^D{\mathrm{MAE}}_d=\sum _{d=1}^D{\displaystyle \frac{1}{S}}\sum _{s=1}^S\mid P_{d,s}-{\widehat{P}}_{d,s}\mid$$

(3)

where $P_{d,s}$ represents the real output power of PV power plant d, while ${\widehat{P}}_{d,s}$ represents the predicted output power; n is the number of samples selected for this PV power plant, and D is the number of power plants in the PV microgrid.

In training the multiscale CNN-LSTM network model for solar irradiance prediction, the loss function for one forward computation is set as ${\mathrm{loss}}_1={\alpha }_1·{\mathrm{RMSE}}_D+{\alpha }_2·{\mathrm{RMSE}}_{\sigma }$, where $RMS{E}_{\sigma }$ is the RMSE for solar irradiance prediction, and ${\alpha }_1,{\alpha }_2$ is the weighting factor, which is chosen empirically: here, ${\alpha }_1={\alpha }_2=0.5$. When training the multiscale CNN-LSTM network model for the output power prediction of all power stations, the loss function for one forward computation is set as ${\mathrm{loss}}_2={\mathrm{RMSE}}_D$.

4. Experimental Analysis

4.1. Experimental Setting

The experimental data were collected from a microgrid consisting of six distributed PV power stations, denoted as A, B, C, D, E and F, located in Shanxi Province, China. The straight-line distances between the power stations range from 10 to 100 km. The PV characterization data consist of eight meteorological parameters (e.g., solar irradiance, ambient temperature, wind speed, etc.), and the PV power output has a 5 min time granularity. Six consecutive data points were combined into one time series at half-hour intervals. Since PV power stations do not produce power output at night, data from 7 a.m. to 7 p.m. during the period of 7 November 2022 to 9 November 2023 were selected for the experiments. The dataset was cleaned to exclude anomalous data and null values using data cleaning methods. The final dataset consists of 9000 time series for each station, which were divided into a training set and a test set at a ratio of 9:1. The experiments were conducted using a PC with an Intel(R) i7 2.10 GHz CPU, 32.0 GB RAM, a GTX 4060 GPU and Windows 11 (64-bit) operating system. The experimental platform was PyCharm 2023.2.1, and the CNN and LSTM networks were built using PyTorch 2.0.1. The Adam optimizer was used to accelerate network convergence during training and had an initial learning rate of 0.01, a training period of 100 epochs, and a batch size of 32.

4.2. Correlation Analysis

To analyze the key meteorological parameters affecting the output power of the PV power plant, the correlations between each of the meteorological parameters and the PV output power was first calculated.

Since some meteorological parameters exhibit a negative correlation with PV output power, the absolute value of the Pearson’s correlation coefficient was used for analysis. The calculation results are shown in

Table 1. Correlations between meteorological parameters and PV output power.

Number	1	2	3	4	5	6	7	8
correlation coefficient	0.125	0.216	0.039	0.274	0.175	0.303	0.652	0.701

. Numbers 1–8 represent the wind speed, air humidity, atmospheric pressure, rainfall, cloud density, solar irradiation angle, temperature and solar irradiance, respectively. As expected, solar irradiance is the most critical factor affecting PV output power.

A correlation analysis was also conducted on the output powers of different PV power stations, and the results are presented in Figure 7. The analysis reveals certain degrees of correlation between the output powers of different stations due to the small geographical area and similar meteorological conditions.

The power station with the highest correlation to the target power station’s output power was selected as the reference power station. The output power sequence of the reference station and the solar irradiance sequence were then spliced into the PV feature data sequence of the target power station. This resulted in a spatio–temporal feature sequence with a dimension of 10. Equation (4) shows the feature structure of a neural network with one forward input.

$$\left[\begin{array}{ccccc}{x}_{1,1}& \cdots & x_{1,8}& s_1& p_1\\ ⋮& \ddots & ⋮& ⋮& ⋮\\ x_{6,1}& \cdots & x_{6,8}& s_6& p_6\end{array}\right]$$

(4)

where $x_{1,1}$ to $x_{1,8}$ denote the eight meteorological features of the first time series of the matrix—namely, wind speed, air humidity, atmospheric pressure, rainfall, cloud density, solar irradiation angle, temperature and solar irradiance, respectively—$x_{1,1}$ to $x_{6,1}$ represent six time series entered at a time with half-hour intervals, $s_1$ to $s_6$ indicate the solar irradiance sequence of the reference power station, and $p_1$ to $p_6$ is the historical power series of the reference power plant.

4.3. Experimental Results

To evaluate the effectiveness of the proposed CNN-LSTM (multiscale) and CNN-LSTM (cascade) models, comparative experiments were conducted on the test set against baseline models: CNN, LSTM and CNN-LSTM [21]. CNN-LSTM (multiscale) utilizes a multiscale architecture, while CNN-LSTM (cascade) employs a two-stage cascade multiscale architecture. The CNN and LSTM models utilize separate CNNs and LSTMs for feature extraction, respectively.

Figure 8 shows the prediction results for various models for a selection of power stations in the PV microgrid, demonstrating the ability of all models to capture the general trend of PV output power. However, our proposed CNN-LSTM (multiscale) and CNN-LSTM (cascade) models achieve predictions that are closer to the real values.

In addition, it can be observed from Figure 8 that the fluctuations in the predictions increase as the number of days progresses. This is because weather conditions become more variable and complex in the latter part of the forecast, particularly during rapid weather changes. These variations lead to greater fluctuations in the input feature data. Since deep learning models rely on patterns and regularities in the training data, significant fluctuations in input data can decrease the predictive accuracy of the models, resulting in increased prediction volatility. Therefore, the rapid changes in weather conditions are a primary factor in the reduced predictive capability of the models in the latter part of the forecast.

Table 2. Comparison of RMSE and MAE for different prediction models.

		CNN-LSTM (Cascade)	CNN-LSTM (Multiscale)	CNN	LSTM	CNN-LSTM
A	RMSE	0.2825	0.3241	0.3841	0.4647	0.4561
	MAE	0.1984	0.2415	0.2723	0.3985	0.3763
B	RMSE	0.2207	0.2744	0.3526	0.4027	0.4025
	MAE	0.1353	0.1879	0.2593	0.3082	0.2949
C	RMSE	0.2744	0.2856	0.4235	0.4736	0.4546
	MAE	0.1948	0.1994	0.3394	0.3990	0.3741
D	RMSE	0.2087	0.2674	0.3382	0.4485	0.3845
	MAE	0.1201	0.1859	0.2585	0.3684	0.2727
E	RMSE	0.2215	0.2813	0.3651	0.4176	0.4053
	MAE	0.1362	0.1974	0.2608	0.3351	0.3150
F	RMSE	0.2673	0.3049	0.4024	0.4586	0.4574
	MAE	0.1728	0.2014	0.2883	0.3772	0.3768
Total	RMSE	0.2423	0.2954	0.3834	0.4478	0.4251
	MAE	0.1510	0.2003	0.2697	0.3681	0.3427

compares the RMSE and MAE values of the different models for different power stations, highlighting the significant improvement in prediction accuracy achieved by both CNN-LSTM (multiscale) and CNN-LSTM (cascade) models.

As shown in Table 2, CNN-LSTM (multiscale) reduces the RMSE by about 29% compared to CNN, 34.03% compared to both LSTM and CNN-LSTM and 30.51% compared to single-scale CNN-LSTM for the average prediction results for all stations. Similarly, it achieves MAE reductions of approximately 29%, 34.03% and 30.51%, respectively. Furthermore, CNN-LSTM (cascade) shows superior performance, with reductions in RMSE and MAE of 17.98% and 29.61%, respectively, compared to CNN-LSTM (multiscale) due to the additional training data source. In addition, CNN-LSTM has much better performance than other models for all power stations.

5. Summary

In this paper, we aimed to build a trustworthy power prediction service for PV microgrids. The proposed method is capable of exploiting the correlations between meteorological parameters and output power among different power stations in a PV microgrid and fusing related spatio–temporal features to generate an expanded PV feature dataset. It takes the splicing power information and strongly correlated meteorological information of neighboring power stations with strong correlations as inputs and employs a multiscale CNN-LSTM network model for extracting temporal, spatial, and scale dimension information. For model validation purposes, numerical analyses were conducted based on real-world data from a PV microgrid consisting of six PV power stations in a county in Shanxi Province. The main numerical findings highlight that CNN-LSTM (multiscale) achieved reductions in RMSE and MAE of approximately 29% and 34.03% compared to CNN and LSTM models, and CNN-LSTM (cascade) shows superior performance, with RMSE and MAE reductions of 17.98% and 29.61% compared to CNN-LSTM (multiscale).