Solar Radiation Prediction Based on the Sparrow Search Algorithm, Convolutional Neural Networks, and Long Short-Term Memory Networks

Abstract

With the challenge of increasing global carbon emissions and climate change, the importance of solar energy as a clean energy source is becoming more pronounced. Accurate solar radiation prediction is crucial for planning and operating solar energy systems. However, the accurate measurement of solar radiation faces challenges due to the high cost of instruments, strict maintenance, and technical complexity. Therefore, this paper proposes a deep learning approach that integrates the Sparrow Search Algorithm (SSA), Convolutional Neural Networks (CNN), and Long Short-Term Memory (LSTM) networks for solar radiation forecasting. The study utilizes solar radiation data from Songjiang District, Shanghai, China, from 2019 to 2020 for empirical analysis. Initially, a correlation analysis was conducted to identify the main factors affecting the intensity of solar radiation, including temperature, clear-sky GHI, solar zenith angle, and relative humidity. Subsequently, the forecasting effectiveness of the model was compared on datasets of 10 min, 30 min, and 60 min, revealing that the model performed best on the 60 min dataset, with a determination coefficient (R²) of 0.96221, root mean square error (RMSE) of 65.9691, and mean absolute error (MAE) of 37.9306. Moreover, comparative experimental results show that the SSA-CNN-LSTM model outperforms traditional LSTM, BiLSTM, and CNN-LSTM models in forecasting accuracy, confirming the effectiveness of SSA in parameter optimization. Thus, the SSA-CNN-LSTM model provides a new and efficient tool for solar radiation forecasting, which is of significant importance for the design and management of solar energy systems.

1. Introduction

In recent years, global carbon emissions have grown exponentially, becoming one of the main factors causing climate change. According to the International Energy Agency (IEA) “CO₂ Emissions in 2023” report [1], global energy-related CO₂ emissions increased by 1.1%, adding 410 million tons to reach a record high of 37.4 billion tons in 2023. The global energy system still faces a severe reality in addressing climate challenges. Therefore, it is necessary to further intensify energy conservation and emission reduction efforts and to enhance the use of clean energy. As a form of clean energy, solar energy has attracted much attention, such as photovoltaic (PV) systems [2], solar thermal systems [3], and combined photovoltaic–thermal systems [4]. The solar radiation produced by the sun is the most important source for industrial applications, and the spatiotemporal variation in solar radiation is also a major driver of global climate change. Therefore, many disciplines and fields such as energy, meteorology, and industry all require accurate solar radiation information. However, due to the high cost of instruments, strict maintenance, and technical complexity, measuring solar radiation poses significant challenges. At the same time, the instability, intermittence, and randomness of solar irradiance also make it very difficult to accurately measure solar irradiance.

As artificial intelligence technology advances, solar radiation forecasting has become an extensively studied field [5,6,7]. The common methods for this forecasting can be categorized into physical methods [8,9], statistical methods [10,11,12], and artificial intelligence methods [13,14,15]. Physical methods primarily rely on measurements from radiation stations, which require high-precision instruments. Statistical methods are based on historical data, employing linear fitting and parameter estimation to build models. Artificial intelligence methods, especially deep learning, are widely and deeply researched for their ability to mine data. These methods train on raw sequence data to derive optimal parameters for prediction. Common approaches include time series models, neural network methods, and hybrid methods, among others. These studies and results are presented in

Table 1. Research on different methods.

Method	Application	Results	Accurate
Regression, ARIMA [16]	Analyzes solar radiation data in Mosul, Iraq	The study develops empirical equations for estimating solar radiation and successfully applies the ARIMA(2,1,1) model for predicting daily clearness indices, which can also be used for estimating monthly solar radiation values.	ARIMA(2,1,1): RMSE = 0.2714
ARIMA [17]	For solar radiation forecasting in Amman, Jordan, and Warsaw, Poland	The research finds that ARIMA models are suitable for solar radiation forecasting in different climatic conditions, with high predictive accuracy for both locations. The models performed better for hourly data during summer months and can support the planning and operation of energy systems. However, the study emphasizes the need to develop lo-cation-specific ARIMA models.	Amman: February: MSE = 2456.48, RMSE = 49.56, R2 = 98.3% August: MSE = 183.18, RMSE = 13.53, R2 = 99.9% Warsaw: February: MSE = 381.09, RMSE = 19.52, R2 = 82.2%. August: MSE = 2508.97, RMSE = 50.09, R2 = 97.9%
AGA-LSTM [18]	Forecasting GHI and DNI with forecast time steps of 5, 10, and 15 min	The experimental results show that under the three prediction scales, the prediction performance of the AGA-LSTM model is below 20%, which effectively improves the prediction accuracy compared with the continuous model and some public methods.	GHI prediction accuracy: 5 min: nRMSE = 6.35%, r = 0.9735 10 min: nRMSE = 8.99%, r = 0.9558 15 min: nRMSE = 11.28%, r = 0.9416 DNI prediction accuracy: 5 min: nRMSE = 12.68%, r = 0.9526 10 min: nRMSE = 11.63%, r = 0.9573 15 min: nRMSE = 16.57%, r = 9337
LSTM, RF, and SVR [19]	Predicting solar radiation using machine learning models, LSTM, RF, and SVR	The model outperforms ARIMA and LSTM, with better mean absolute error and mean square error, making it suitable for real-time solar power prediction and aiding the integration of solar energy into the grid.	LSTM: RMSE = 14.298, MAPE = 16.6% RF: RMSE = 16.840, MAPE = 20.1%; SVR: RMSE = 15.410, MAPE = 18.1%.
GBM [20]	An ensemble model using gradient boosting and developed for hourly global horizontal irradiance forecasting is proposed for the various climatic zones of India	The model outperforms ARIMA and LSTM, with better mean absolute error and mean square error, making it suitable for real-time solar power prediction and aiding the inte-gration of solar energy into the grid.	MSE = 1357.05 MAE = 20.97 R2 = 98.47
GA-BP [21]	An ultra-short-term solar radiation forecasting model for photovoltaic power stations	Experimental results show that the model’s prediction accuracy reaches 96%, which is a 5% improvement over models without cloud image feature information, particularly in cloudy weather conditions.	Accuracy: 96%
MRE-UNet [22]	Accurately forecasting solar radiation	The MRE-UNet model proposed in the article significantly improves the spatial-temporal prediction performance of solar radiation by combining 3D convolution, multi-scale feature convolution module and ConvLSTM. The model performs well in 1 h, 3 h, and 6 h ahead predictions with high mobility and robustness for solar radiation prediction in different regions.	1 h: MSE = 6.47 × 10−4 3 h: MSE = 1.38 × 10−3 6 h: MSE = 2.69 × 10−3
ANN [23]	Prediction of average monthly global solar radiation of Makurdi in order to improve the prediction accuracy	The ANN ensemble provided the most accurate predictions, with an R2 of 1.0 and MSE of 0.0139.	R2 = 1.0, MSE = 0.0139
SOM-OPEM [24]	Predicting global solar radiation	It employs three-time series strategies for multi-step-ahead forecasting and demonstrates improved accuracy over conventional methods like BP and ARIMA, making it significant for solar energy system design and management.	Rec-SOMOPELM: R2 = 0.960 Rir-SOMOPELM: R2 = 0.963 Mismo-SOMOPELM: R2 = 0.984

.

Those studies have successfully predicted solar radiation data. Still, due to the influence of spatial and environmental factors on solar radiation data, forecasting based on historical data for a single radiation can result in inaccurate predictions. Meanwhile, most deep-learning methods [15,25] use grid search for parameter optimization, which is not only slow but also not very accurate. To enhance the robustness of the algorithm and to address these issues, the article introduces a deep learning approach that employs a Sparrow Search Algorithm (SSA) to optimize a Convolutional Neural Network (CNN) with Long Short-Term Memory (LSTM) for both short- and long-term time series forecasting models for solar radiation forecasting. This algorithm not only overcomes the limitations of spatial and temporal dependence in processing data, but also achieves automated parameter optimization instead of manual grid search methods, thus significantly improving model efficiency.

The remainder of this article is organized as follows: Section 2 presents the methodology adopted to carry out the study. The discussion of the results is presented in Section 3. The conclusions end the paper in Section 4.

2. Methodology

In this section, we provide a detailed introduction to the application of the SSA-CNN-LSTM model in solar radiation prediction. This method employs CNN to efficiently extract key spatial features from solar radiation data, thereby providing a rich spatial context for subsequent time-series analysis. LSTM is then utilized to accurately capture the temporal periodicity within solar radiation data. The unique gating mechanism of LSTM effectively prevents issues of gradient vanishing and explosion, ensuring the stability and accuracy of the model when processing long sequences of data. Furthermore, the SSA is employed to optimize the parameters of the deep learning model, significantly reducing computational costs while greatly enhancing the accuracy of parameter optimization. This approach offers an efficient and reliable solution for solar radiation prediction, which can notably improve forecasting accuracy and provide robust support for the planning and operation management of solar energy systems.

2.1. Data Collection

The corresponding solar radiation data were found through the National Solar Radiation Database (NSRDB), managed by the National Renewable Energy Laboratory (NREL), as shown in Figure 1. It is capable of providing global solar radiation data, which includes the following indicators: Dew Point, Solar Zenith Angle, Wind Speed, Surface Albedo, Precipitable Water, Wind Direction, and GHI, among others. The data used in this article are located in Songjiang District, Shanghai (East Longitude 121°45′, North Latitude 31°), covering the period from 2019 to 2020, with solar radiation data collected every 10 min, 30 min, and 60 min.

2.2. Data Preprocessing

Data preprocessing methods include mean padding, manual filling, regression, cluster padding, and expectation maximization algorithms. In this paper, the expectation maximization algorithm [26] in SPSS 25.0 data analysis software is used to fill in the missing values of our data. The process of the expectation maximization algorithm is shown in Figure 2.

The principle of the expectation maximization (EM) algorithm is mainly based on the iterative optimization characteristics of the EM algorithm. It introduces latent variables to deal with the missing parts of the data, thereby enhancing the completeness and accuracy of the data.

Visualization of all data was conducted according to the processed 60 min data, as shown in Figure 3 and Figure 4. The graphs illustrate the variations over time in temperature, GHI, surface albedo, pressure, wind speed, clear-sky GHI and cloud type, solar zenith angle, relative humidity, and precipitable water.

The above graph shows that Global Horizontal Irradiance (GHI) varies over time, and other factors can also affect the variation in GHI. To more reasonably evaluate the rationality of the selected indicators, a correlation analysis is used to obtain the indicators of factors that have a greater impact on solar radiation, and these indicators are chosen as important indices for prediction.

The formula for the Pearson correlation coefficient [27] is as follows:

$$\rho ={\displaystyle \frac{\mathrm{cov}(x,y)}{{\sigma }_x{\sigma }_y}}={\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n(x_i-\stackrel{-}{x})(y_i-\stackrel{-}{y})}}{\sqrt{{\displaystyle {\sum }_{i=1}^n{(x_i-\stackrel{-}{x})}^2}}\sqrt{{\displaystyle {\sum }_{i=1}^n{(y_i-\stackrel{-}{y})}^2}}}}$$

(1)

$cov(x,y)$ represents the covariance of $x,y$, andthe standard deviation of the two variables. $\overline{x},\overline{y}$ represents the mean value of $x,y$, n represents the length of the input time series, and $\rho$ indicates the degree of correlation between the variables; a larger number indicates a higher correlation and a negative number indicates a negative correlation. Since the cloud type variable is categorical, its correlation with other variables is not meaningful; therefore, it is excluded from the correlation analysis. The correlation results are shown in Figure 5.

As the results of the correlation analysis show, the main factors related to solar radiation intensity are temperature, clear-sky GHI, solar zenith angle, and relative humidity. Among these, the solar angle and relative humidity have a negative correlation. Therefore, these four variables are selected as indicators for the correlation analysis.

2.3. Deep Learning Models

2.3.1. Sparrow Search Algorithm (SSA)

The SSA is an optimization algorithm proposed by Xue [28] in 2020. The design of the algorithm is inspired by the behavioral patterns of sparrows searching for food in their natural environment. The characteristics of social collaboration, spatial memory, and fast response to environmental changes demonstrated by sparrows during the foraging process are abstracted and transformed into operational steps in the algorithm for solving optimization problems. The flow chart is shown in Figure 6.

The SSA is designed to mimic the natural foraging behavior of sparrows by dividing the population into two distinct roles: discoverers and followers. Discoverers are assumed to have higher energy reserves within the population, which allows them to engage in more extensive searches for new food sources. Once a discoverer locates a food source, it shares this information with the rest of the flock, guiding other sparrows (followers) to areas with abundant resources. When building the model, the level of energy reserves for a discoverer is often determined by the individual sparrow’s fitness value. When a sparrow finds a predator, the individual sparrow signals an alarm. If the alarm value is higher than the safe value, the finder will take the follower to another safe place to forage. The roles of discoverers and followers are not fixed and can change throughout the algorithm. This dynamic interaction allows the algorithm to balance exploration (finding new solutions) with exploitation (refining existing solutions).

Discovery location updates are shown by Equation (2):

$$x_{i,d}^{+1}=\left\{\begin{array}{ll}{x}_{i,d}^{t}exp\left({\displaystyle \frac{-i}{aite{r}_{max}}}\right)& R_2<{\theta }_{ST}\\ & \\ x_{i,d}^t+QL& else\end{array}\right.$$

(2)

$x_{i,d}^t$ represents the position of the i-th sparrow in the d-th dimension at the t-th iteration. R₂ is the random number uniformly distributed in the range [0, 1]. Q is a random number drawn from a normal distribution. θ_ST is a predefined alert threshold value, typically set in the range [0.5, 1.0].

Follower position updates are shown by Equation (3):

$$x_{i,j}^{t+1}=\left\{\begin{array}{ll}Qexp\left({\displaystyle \frac{x_{worst}^t-x_{i,j}^t}{i^2}}\right)& if i>{\displaystyle \frac{n}{2}}\\ & \\ x_p^{t+1}+\mid x_{i,j}^t-x_p^{t+1}\mid A^{+}L& \mathit{else}\end{array}\right.$$

(3)

X_tp denotes the best position discovered by any sparrow at time t. X^t_worst represents the worst position (the current global worst solution) at time t. A is a 1 × d matrix; each element in matrix A is randomly assigned a value of either 1 or −1. In the algorithm, the index i represents the index of a particular sparrow within the population, and n is the total number of sparrows. When the index i is greater than half the population size n/2, it indicates that the sparrow is among the lower half of the population in terms of energy levels, suggesting that it has not been successful in finding food.

Detecting early warning behavior is shown by Equation (4):

$$x_{i,d}^{t+1}=\left\{\begin{array}{cc}x{b}_{i,d}^t+\beta \left(x_{i,d}^t-x{b}_{i,d}^t\right)& f_i\ne f_g\\ x_{i,d}^t+K({\displaystyle \frac{x_{i,d}^t-x{w}_{i,d}^t}{\left|f_i-f_w\right|+\epsilon }})& f_i=f_g\end{array}\right.$$

(4)

$x{b}_{i,d}^t$ represents the best position, $\beta$ is a random number that controls the step size a sparrow takes during its search, K is a random number that falls within the interval [0, 1], $f_i$ represents the quality or fitness of the current solution of an individual sparrow, $f_g$ is the fitness value corresponding to the global best position, while $f_w$ is the fitness value of the worst position in the population. When a sparrow’s fitness value $f_i$ equals the global best fitness $f_g$, it indicates that the sparrow is at the position of the best solution found so far. However, in the context of the SSA, this might also suggest that the sparrow is isolated and potentially vulnerable to predators. As a result, the sparrow may need to move closer to other sparrows to reduce the risk of predation.

2.3.2. Convolutional Neural Network (CNN)

The CNN [29] is a type of feedforward artificial neural network that significantly reduces the number of neuron connections through sparse connectivity and weight sharing. Each convolutional kernel extracts features from the data, and by increasing the size of the convolutional kernels, multi-dimensional features are obtained.

The structure includes input layer, hidden layer, and output layer, where the hidden layer is subdivided into a convolutional layer, a pooling layer, and a fully connected layer. The structure is shown in Figure 7.

2.3.3. Long- and Short-Term Memory (LSTM)

The LSTM [30] network is an improved RNN. Compared to the standard RNN, the LSTM network introduces gated units (input gate, output gate, and forget gate), which endow the LSTM with a memory function similar to the human brain. This allows the LSTM to store data information over extended periods on a timescale and to filter or retain data, better excavating the correlation between time and information. The emergence of the gated units addresses the shortcomings of RNN networks in processing long-time series, as well as the issues of gradient disappearance and gradient explosion. The structure is shown in Figure 8.

The relevant calculations are shown in Equation (5):

$$\begin{array}{c}{f}_t=\sigma \left(W_f \mathrm{\ast }\left[h_{t-1},x_t\right]+b_f\right)\\ i_t=\sigma \left(W_i \mathrm{\ast }\left[h_{t-1},x_t\right]+b_i\right)\\ g_t=\tanh \left(W_c \mathrm{\ast }\left[h_{t-1},x_t\right]+b_c\right)\\ C_t=f_t \mathrm{\ast } C_{t-1}+i_t \mathrm{\ast } g_t\\ {\mathrm{O}}_t=\sigma \left(W_o \mathrm{\ast }\left[h_{t-1},x_t\right]+b_o\right)\\ h_t={\mathrm{O}}_t \mathrm{\ast } \tanh \left(C_t\right)\end{array}$$

(5)

In the equation, $f_t$, $i_t$, and $O_{\mathrm{t}}$ represent the forget gate, input gate, and output gate, $\sigma$ is the activation function, $W_f$ is the weight vector of the forget gate, $\mathrm{\ast }$ denotes the convolution operation, and ${\mathrm{h}}_{\mathrm{t}-1}$ denotes the output of the memory cell at the previous time step t − 1. $b_f$ is the bias term associated with the forget gate; $W_i$ is the weight vector for the input gate; $b_i$ is the bias term for the input gate; $W_c$ is the weight vector for the output gate; $g_t$ is the candidate state of the memory cell; $b_c$ is the bias of the input gate candidate state; $W_o$ is the weight vector of the output gate; and $b_o$ is the bias of the output gate.

2.3.4. CNN-LSTM

The network structure is also very important for the prediction of solar radiation intensity using a CNN combined with the LSTM model. As shown in Figure 9, the CNN- LSTM combined model consists of the input, CNN, LSTM, and output. Firstly, the input layer ingests the multivariate time series data about solar radiation. Then, the data proceeds through the convolutional and pooling layers, adeptly executing feature extraction and dimensionality reduction. Next, the processed data are then seamlessly transferred to the LSTM, where a network of neurons engages in sophisticated time series computations to deduce the preliminary output values. Finally, the output layer calculates the output value of the previous layer to obtain the final prediction value.

2.3.5. SSA-CNN-LSTM

The SSA-CNN-LSTM algorithm for solar radiation forecasting is an integrated model that combines the SSA, CNN, and LSTM to predict solar radiation. The SSA is used to optimize the hyperparameters of the CNN-LSTM model. The CNN is capable of extracting spatial features from meteorological data, while the LSTM captures the temporal dynamics of solar radiation data. When employing the CNN-LSTM model [31,32], parameters are often selected manually through methods such as grid search, which is time-consuming and laborious, and it can be challenging to choose the most appropriate parameters. Therefore, utilizing the SSA to optimize parameters enhances the efficiency of the parameter selection process and improves accuracy. The combined model is as follows, as shown in Figure 10.

2.4. Model Evaluation

Mean Absolute Error and Root Mean Square Error [33] are common metrics used to evaluate the performance of predictive models. Here are their expressions:

2.4.1. Mean Absolute Error (MAE)

$$MAE={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n \left|y_i-{\hat{y}}_i\right|$$

(6)

where $y_i$ is the actual value of the i-th observation, ${\hat{y}}_i$ is the predicted value for the i-th observation, and n is the total number of observations.

2.4.2. Root Mean Square Error (RMSE)

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}{\sum }_{i=1}^n {\left(y_i-{\hat{y}}_i\right)}^2}$$

(7)

Both of these metrics measure the difference between the model’s predicted values and the actual observed values. MAE calculates the average absolute value of the prediction errors, while RMSE calculates the square root of the average of the squared prediction errors. RMSE is more sensitive to larger errors because it squares the differences before averaging, which serves to penalize larger errors. Typically, a good model should have low values for both MAE and RMSE.

2.4.3. Coefficient of Determination

The Coefficient of Determination [34], commonly denoted as R², reflects the model’s ability to explain the relationship between variables, that is, the degree of correlation between the model’s predicted values and the actual observed values. The formula for calculating R² is usually represented as

$$R^2=1-{\displaystyle \frac{S_{res}}{S_{tot}}}$$

(8)

$S_{res}$ is the sum of squared residuals; $S_{tot}$ is the total sum of squares. The value of R² ranges from 0 to 1; the higher the value of R², the stronger the model’s explanatory power and the higher the accuracy of the predictions.

3. Results and Discussion

3.1. Results

3.1.1. Model Parametric and Experimental Environment

In this paper, the parameters of the model are as follows (

Table 2. Model parameter.

Structure	Parametric
Iterations	100
CNN	Conv, Maxpooling, Relu
CNN kernel size	3 × 3
LSTM layers	2
Batch size	64
Initial learning rate	0.001

).

The experiments in this paper were carried out in the following hardware equipment parameters: Intel i9 CPU was selected, memory was 32 GB, and 3060 GPU was selected and programmed with matlab2022b application software using the self-contained function framework.

3.1.2. Results of the Experiment

Five parameters were optimized using SSA, learning rate, number of iterations, convolutional kernel size, number of convolutional kernels, and number of LSTM neurons. The parameters of the SSA are set as follows: Pop = 50, M = 100, ST = 0.8; in sparrow populations, 20% are producers. The article employs the SSA for parameter optimization. After iterations, the optimal fitness parameters are identified. The iterative process of the optimization search is as follows in Figure 11.

The figure shows the iterative process of the sparrow search algorithm; it can be seen that as the number of iteration defects increases, the fitness values reach stability at the 9th time and the optimal parameters are obtained.

The prediction of solar radiation data using SSA-CNN-LSTM is shown below in the training set (70%), test set (10%), and validation set (20%), and prediction results as shown in Figure 12.

In this figure, “True” refers to the historical solar radiation data, while “Prediction” represents the solar radiation data predicted using the algorithm proposed in this paper.

In Figure 12, the article employs a dataset with a 60 min interval for the study. The results show that the training set, testing set, and validation set all exhibit evident periodic variations. Further examination of the prediction results reveals that they also follow the periodic pattern. Given that solar radiation data has inherent periodic characteristics and that the sampling interval can influence the accuracy of the results, the study investigates the variations in datasets with 30 min and 10 min intervals. The results are shown in Figure 13 and Figure 14.

Figure 13 and Figure 14 illustrate the prediction results of the SSA-CNN-LSTM algorithm on the training set, testing set, and validation set, respectively. The results indicate that the algorithm achieves satisfactory prediction outcomes across datasets with different sampling intervals. However, it is important to note that the sampling interval significantly impacts the size of the dataset. The shorter the sampling time interval, the larger the volume of data. This not only increases the number of abnormal data points, thereby limiting the prediction accuracy, but also greatly increases the demand for computational resources. On the other hand, given the periodic nature of solar radiation data, an overly large sampling time interval will also reduce prediction accuracy. Therefore, based on the experimental comparisons, the 60 min dataset yields the best prediction results, with an R² of 0.96221, RMSE of 65.9691, and MAE of 37.9306.

3.1.3. Comparison Experiment

To verify the effectiveness of the designed model, comparative experiments were conducted using the same dataset and evaluation metrics. The LSTM [30], BiLSTM [35], CNN-LSTM [32], and SSA-CNN-LSTM algorithms were utilized to predict the solar radiation dataset. The predictive results are depicted in Figure 15.

Figure 15 presents the prediction results of four different algorithms. It can be seen from the figure that all these algorithms are capable of making periodic predictions of solar radiation. However, there are differences in the prediction accuracy among different methods. Therefore, in order to more accurately evaluate the performance of the algorithms, we further use MAE, RMSE, and R² to measure the accuracy of the algorithms.

The values of MAE, RMSE, and R² are shown below

Table 3. Evaluation under different algorithms.

Model	RMSE	MAE	R2
LSTM	88.1974	56.4279	0.94766
BiLSTM	81.2398	43.8849	0.95687
CNN-LSTM	78.6865	39.9251	0.95265
SSA-CNN-LSTM	65.9691	37.9306	0.96221

.

According to Table 3, it can be observed that the SSA-CNN-LSTM algorithm has lower MAE and RMSE compared to other algorithms. This is due to the use of the SSA, which facilitated the discovery of the optimal parameters. The R-squared (R²) value of the SSA-CNN-LSTM algorithm reached 0.96221, which is significantly higher in comparison.

3.2. Discussion

The SSA-CNN-LSTM model has demonstrated outstanding predictive performance across three temporal scales of datasets (10 min, 30 min, and 60 min intervals). Particularly noteworthy are its exceptional results on the high-temporal resolution 60 min dataset, R² of 0.96221, RMSE of 65.9691, and MAE of 37.9306, with all metrics outperforming traditional LSTM, BiLSTM and CNN-LSTM models. Furthermore, the SSA-CNN-LSTM demonstrates distinct advantages when compared with the different types of algorithms. For statistical models [16,17], it effectively resolves the inherent limitation of ARIMA models in capturing complex nonlinear relationships within solar radiation data. For neural network methods [20,21], the SSA-CNN-LSTM successfully overcomes the constraints of simple neural network models in handling spatial and temporal dependencies. For hybrid models [22,23], the SSA-CNN-LSTM replaces manual grid search approaches by achieving automated parameter optimization, thereby significantly enhancing model efficiency. Collectively, these comparative analyses confirm that our model achieves substantial improvements in both precision and accuracy over these existing approaches. Furthermore, the research results have a positive potential for enhancing smart grid stability and reducing operational costs at power stations.

4. Conclusions

This paper presents a deep learning approach for solar radiation forecasting that integrates the SSA, CNN, and LSTM. Empirical analysis using solar radiation data from Songjiang District, Shanghai, from 2019 to 2020, has verified the effectiveness of the proposed method.

The method takes into account the solar radiation data influenced by multi-scale factors, which have a broader scope compared to single radiation data. The choice of optimizing the CNN-LSTM model using SSA not only overcomes the traditional algorithms’ difficulties in dealing with the complex nonlinear relationships in solar radiation data but also achieves automatic parameter optimization, replacing the shortcomings of manual grid search. According to the experimental results, the model’s accuracy on the 60 min dataset far exceeds that of traditional algorithms such as LSTM, BiLSTM, and CNN-LSTM models, with an R² value reaching 0.96221, indicating its capability in capturing short-term fluctuations in solar radiation.

This study holds significant importance for improving the operational efficiency of power stations, optimizing energy storage, and facilitating resource allocation. Although the research has yielded promising results, it has certain limitations in exploring radiation data under different climatic conditions. Future research can further investigate the model’s applicability in various geographical locations and climatic conditions by altering the model structure, incorporating attention mechanisms, and integrating more meteorological factors to enhance the prediction’s universality.