1. Introduction
In recent years, excessive energy consumption has caused problems such as ecological environment deterioration and depletion of non-renewable energy sources. Worldwide, populations have begun to seek a new energy development path to gradually replace traditional fossil fuels with renewable energy [
1]. Solar energy is valued because of its safety, efficiency, economy, and environmental friendliness. New energy grid-connected power generation, represented by photovoltaic power generation, is integral to future power systems [
2]. In 2022, the global photovoltaic installed capacity reached 230 GW, and the cumulative installed capacity will reach 1156 GW, with a year-on-year growth of 35.3%. The output power of PV systems exhibits a high degree of randomness and volatility due to meteorological factors such as solar radiation [
3,
4]. When the grid is connected to a high proportion of PV, the complexity of large-scale grid scheduling increases, and the stability and reliability of the power system operation are threatened.
PV power prediction has become one of the vital fundamental technologies used to improve operation quality and ensure the stable operation of PV power generation. Accurate prediction of the power output of PV systems in the ultra-short-term is essential for extending the life of storage devices such as batteries, helping dispatchers to develop rational scheduling plans, improving system reliability, and deploying PV power on a large scale. In addition, it helps to reduce the uncertainty of PV generation on the power system, coordinate with other conventional power sources, improve grid scheduling, and increase the utilization of PV generation. In addition, PV power generation prediction is also utilized to enable online PV array fault diagnosis, which allows for the rapid detection of faults or anomalies due to corrosion, high winds, heavy rains, hailstorms, dirt, UV irradiation, thermal cycling, etc. [
5]. Therefore, accurate ultra-short-term PV power prediction is an important research area [
6].
Various prediction methods have been proposed for PV power prediction [
7]. There are four time periods for PV power prediction: long-term prediction is from one month to one year, medium-term prediction is from one week to one month, short-term prediction is from one week or less, and very short-term or ultra-short-term prediction is from one minute to a few minutes. Long-term forecasting is used for planning and decision-making for PV generation, transmission, and distribution and guarantees reliable power system operation. For medium-term forecasting, a model can be used for medium-term decision support for power system dispatches. Short-term forecasts are essential for day-ahead generation planning and improving the power system reliability. Ultra-short-term forecasts are used to guide real-time grid scheduling and battery storage control to ensure the safe operation of the grid. In addition, this method helps improve the quality of the information and make real-time corrections to short-term PV power forecast data. Forecasting methods can be classified into physical, statistical, and machine learning-based methods [
8].
The physical approach is based on the principle of PV power generation. It uses mathematical models of solar radiation, temperature, humidity, cloud cover, barometric pressure, and wind speed obtained from numerical weather prediction (NWP). Physical forecasts are based on detailed site geographic information, accurate weather data, and complete PV information. Historical data are not required. However, since the meteorological environment limits solar resources, the complexity of the atmospheric environment will directly lead to a dramatic increase in model complexity. Therefore, simulation and prediction of PV output using physical models cannot provide accurate and meaningful predictions reflecting reality under extremely severe weather conditions [
9]. They are not universal, cannot be adapted to changing meteorological conditions, and can only be used for short-term forecasting.
Statistical forecasting methods include time series methods [
10], regression analysis [
11], gray theory [
12], fuzzy theory [
13], multi-source data-driven methods [
14], and spatio–temporal correlation [
15]. Statistical methods include curve fitting, parameter estimation, and correlation analysis of historical data such as solar radiation and PV power generation. Predicting future PV power generation is achieved by establishing a correlation mapping relationship between input and output data. Compared to physical methods, there is no need to have a clear and complete understanding of the complex photovoltaic conversion relationships of PV systems [
16]. Therefore, it is characterized by the simplicity of modeling and generalizability across different regions compared to physical methods. However, the premise of the implementation of statistical methods is that a large amount of correct historical data needs to be processed, and there are difficulties in data collection and calculation during the implementation process. Due to the need for a large number of numerical calculations in the forecasting process, the general computer forecasting time is long. Meeting the requirements of forecasting speed (especially at the minute level) is difficult for ultra-short-term PV power forecasting. In addition, the prediction quality of statistical methods is closely related to the data quality and the degree of historical data retention. Therefore, screening and elimination of spurious data have a significant impact on forecast accuracy. Prediction accuracy relies on high-dimensional computation for effectiveness, which increases the computational effort and reduces the prediction speed.
Machine learning can efficiently extract high-dimensional complex nonlinear features and map them directly to the output. Taking advantage of this, machine learning-based forecasting methods have become one of the most widely used methods for predicting different time series [
17]. In recent years, deep learning models represented artificial neural networks (ANN), recurrent neural networks (RNN), gated recurrent unit neural networks (GRU), and so on, which have been widely used in the field of PV power prediction [
18,
19].
The LSSVM model has proven to be an effective advanced prediction model, which has been increasingly used in solving prediction problems to minimize the sum-of-squares error and marginal error of the training data [
20,
21]. A previous study [
22] proposed a hybrid prediction model combining variable mode decomposition (VMD), particle swarm optimization (PSO), and least squares support vector regression (LSSVM), which improves the accuracy of day-ahead prediction by at least 19% compared to the best RecMO strategy. A previous study [
23] developed an evolutionary seasonal decomposition LSSVM model to predict the PV power generation in the current month while using a genetic algorithm to optimize the parameters of the LSSVM, and the results showed that the prediction system has better prediction accuracy. Another study [
24] used a hybrid prediction model combining wavelet transform, particle swarm optimization, and support vector machine for day-ahead power generation prediction of real microgrid PV systems with a daily average MAPE of 4.2% and NMAE of 0.4%. Although the LSSVM model performs well in solving the prediction problem, it has some limitations. First, the LSSVM model may face the challenge of high computational complexity for large-scale datasets, leading to longer training time or an inability to handle large-scale data. Second, LSSVM models are more sensitive to selecting data features and adjusting parameters, which need to be carefully designed and adjusted to obtain good performance. In addition, the predictive performance of LSSVM models is affected by data noise and outliers, which may require additional processing steps to enhance the robustness of the model. However, traditional optimization algorithms also have some limitations in optimizing the parameters of the LSSVM model, and these algorithms may converge slowly, tend to fall into local optimal solutions, or need help dealing with high-dimensional complex datasets.
PV power output is highly volatile, especially in unstable weather. In this case, a combined prediction model based on signal decomposition is often used, which mainly decomposes the PV power sequence into several sub-sequences, models the prediction, and superimposes the prediction results. Classic decomposition techniques include wavelet transform (WT) [
25], empirical mode decomposition (EMD) [
26], and ensemble empirical mode decomposition (EEMD) [
27]. However, both EMD and its improved methods exhibit apparent modal overlapping phenomena, which affect the prediction performance of the model to a certain extent. Compared with EEMD and WT, intrinsic computing-expressive empirical mode decomposition with adaptive noise (ICEEMDAN) best decomposes sequences [
28]. The frequencies of the decomposed components fluctuate with significant frequency differences, representing different information at different timescales within the time series. However, the direct use of a single model to predict all of the components and superimpose the results will cause some errors.
Changes in weather conditions can make PV power generation stochastic and volatile. Utilizing all historical data as training samples, especially those day-by-day records with significant variations in weather conditions, will prolong the model training time and reduce the forecasting accuracy. Therefore, it is necessary to divide the large amount of historical power data by weather type and train them separately [
29]. A similar day selection method based on the Levy–Flight Beetle antenna search algorithm was proposed in the literature [
30]. Considering the global horizontal radiation (GHR) trend, GHR fluctuations, and other weather factors, similar days are selected as training samples and better prediction results are achieved. Currently, many short-term PV power prediction studies focus on improving model accuracy, often ignoring the impact of weather factors on PV power generation [
31]. In order to improve the prediction accuracy of the short-term PV power prediction model, it is necessary to effectively extract the relevant data from the massive data, avoid data redundancy, and reduce the non-stationarity of the PV power series. In this paper, the advantages of various models are synthesized and an ultra-short-term PV prediction model is constructed. The model considers weather factor feature selection, similar day clustering, signal decomposition, and hybrid deep learning. The main contents of this paper are as follows:
- (1)
A similar day clustering model is proposed. The K-means clustering method is applied to the historical data to accurately classify the weather conditions into sunny, cloudy, and rainy days. This concise and targeted classification strategy effectively avoids data clutter and redundancy, dramatically enhances the relevance and reliability of the training data, and lays a solid foundation for the accurate construction of the subsequent ultra-short-term PV prediction model.
- (2)
To improve the algorithm’s optimization ability, a multi-strategy improved snow ablation optimizer (MISAO) combining cyclic chaotic mapping initialization strategies, Gaussian diffusion strategies, and random follower search strategies is proposed. The parameters of ICEEMDAN are optimized using MISAO. The model decomposes the fluctuating stochastic raw PV power series into multiple subsequences, each with unique frequencies and features, thus reducing the non-stationarity and complexity of the PV power series.
- (3)
Constructing the multivariate prediction model extends the available data dimensions and enhances the model’s predictability. Meteorological factors have a more significant impact on the PV power system, and adding the influence of meteorological factors to the model and building a multivariate prediction model can provide more practical prediction results and more credible data support for relevant information users.
- (4)
A hybrid model for ultra-short-term PV power prediction integrating MISAO-ICEEMDAN-WLSSVM is proposed to improve the prediction accuracy of PV power. MISAO can search for the optimal hyperparameter combinations of the WLSSVM, which improves the model’s prediction accuracy.
- (5)
To determine the models’ reliability and robustness, the various models’ prediction results were compared with the MISAO-ICEEMDAN-WLSSVM. Simulation experiments were conducted on three significantly different weather-type datasets.
5. Experiment and Result Analysis
This study selected data from a 20 MW photovoltaic power plant in Hebei, China, as the research object to verify the accuracy of the model. Meteorological and power data from 1 July 2018 to 31 December 2018, including global irradiance, diffuse irradiance, temperature, wind speed, wind direction, and atmospheric pressure, were selected. A time interval of 15 min was selected, from 07:00 to 19:00. The predicted step length was one. The time step of the input data was determined to be 10 by utilizing a trial-and-error approach.
5.1. Data Sets and Data Preprocessing
The training, testing, and validation sets were divided into 60%, 20%, and 20% of the total dataset. Normalization was conducted in this study to address the different magnitudes among the data. We adopted the min–max normalization method (Equation (25)):
Min–max normalization can map the data clearly and directly to the [0, 1] interval, which can prominently exhibit the data’s relative magnitudes and distribution characteristics. It allows the differences and relationships of the data to be presented more intuitively and clearly, facilitating our understanding and analysis of the data. In contrast, mean normalization is mainly adjusted based on the mean of the data and may not fully reflect the extreme values and distribution range of the data in some cases. Although z-score normalization can standardize the data, it is less intuitive and direct than min–max normalization in emphasizing the data’s relative magnitudes and original distribution characteristics. Considering the data’s characteristics and the analysis requirements in this study, min–max normalization can serve our research purposes and data processing requirements more effectively.
5.2. Model Evaluation Indicators
In this study, the mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage of error (MAPE) were selected to evaluate the accuracy of the prediction of each model, which was calculated as:
where
is the number of predicted outcomes,
is the actual value, and
is the model-predicted value.
5.3. Parameter Optimization Results
The MISAO parameters were set as follows: the number of populations was 30, the maximum number of iterations was 30, the optimization range of parameter was [0.1, 1000], and the optimization range of parameter was [0.01, 100]. The search range was [0.15, 0.6], the search range was [50, 600], and the minimum average envelope entropy was used as the fitness function. The optimized values of and were [0.461, 452], [0.180, 236], and [0.241, 197] for sunny, cloudy, and rainy weather, respectively.
5.4. Weather Clustering and Data Decomposition
Clustering the data using the K-means algorithm yielded 94, 49, and 41 days of sunny, cloudy, and rainy weather, respectively. Taking sunny weather as an example,
Figure 7 shows the power components obtained by the MISAO-ICEEMDAN algorithm for a sunny day. From the figure, it is clear that 12 IMF components and one RES component are obtained from the ICEEMDAN decomposition, and each sequence is arranged according to the frequency from high to low. Among them, IMF1, as the dominant component, has a smooth and relatively stable curve, which can characterize the trend of the original PV power signal well. In contrast, the remaining components accurately show the local characteristics of the power data. Through in-depth analysis, it is found that the fluctuations of different frequency series have a certain regularity. The high-frequency IMF components usually reflect short-term rapid fluctuations, which are likely to be related to transient changes in local meteorology (e.g., short-term cloud cover) or transient responses of the equipment. In contrast, the low-frequency IMF and RES components are more indicative of long-term trends and overall energy levels, which are closely related to the cyclical changes in solar radiation as well as the inherent characteristics of the system. Each mode is independent of the other, effectively avoiding the problem of mode mixing. At the same time, the residuals of the RES component are gradually stabilized, which means that after the ICEEMDAN decomposition, the remaining unexplained part of the IMF component is close to the stable random noise, which strongly verifies the effectiveness of the decomposition. In the prediction model, each power component is set as an output series, and its corresponding meteorological data are used as an input series, which is finally superimposed to obtain the prediction results.
5.5. Result Analysis
To further verify the prediction effect of the proposed model, a total of six comparison models were set up in this study: Temporal Convolution Networks (TCN), Gate Recurrent Unit (GRU), SVM, WLSSVM, SAO-WLSSVM, and MISAO-WLSSVM. The prediction model was visualized and analyzed for three days selected for three weather types, namely sunny, cloudy, and rainy, while keeping the parameters constant, as shown in
Figure 8,
Figure 9 and
Figure 10.
Figure 8 shows the predicted results under sunny conditions. The power variation during sunny weather was moderate, and the overall prediction effect was the best. The prediction results of the improved prediction model were closer to the actual values, and
Figure 9 shows the predicted results under cloudy conditions. Owing to continuous changes in cloud cover, solar irradiance also changes with both gentle and abrupt changes. In the abrupt changes, the model in this study performed well, proving its strong anti-interference ability.
Figure 10 shows the prediction results under rainy day conditions. The power amplitude is lower during rainy weather, and the power change is more evident owing to the long fluctuation period and significant volatility. The model prediction effect is reduced; however, this model still has some advantages in terms of prediction accuracy and stability.
Using three evaluation metrics (MAPE, RMSE, and MAE) on the prediction effect of the TCN, GRU, SVM, WLSSVM, SAO-WLSSVM, MISAO-WLSSVM, and MISAO-ICEEMDANWLSSVM prediction models for the three weather types, the calculation of the error yields the evaluation results as shown in
Table 7.
Table 7 shows that, in comparison to the individual TCN, GRU, SVM, and WLSSVM models, all of the combined prediction models outperform the single model in a variety of weather scenarios. This suggests that the WLSSVM network’s hyperparameters specifically need to be optimized. By comparing the prediction results of the SAO-WLSSVM and MISAO-WLSSVM models, it was found that all of the indicators of the MISAO-WLSSVM model were lower than those of the SAO-WLSSVM model, and the average absolute error percentage MAPE under different weather conditions decreased by 22.9%, 36.4%, and 20.9%, respectively. The average absolute error MAE percentage under different weather conditions decreased by 15.0% and 20.9%, respectively. MAE decreased by 15.7%, 24.8%, and 15.0%, respectively, and the root mean square error MASE decreased by 12.0%, 25.1%, and 13.9%, respectively, under different weather conditions, indicating that MISAO has a better ability to find the optimum and stability than SAO.
In addition, the MISAO-ICEEMDAN-WLSSVM hybrid model obtained the best value among all of the evaluation indicators, in which the indicator MAPE under different weather conditions decreased by 25.3%, 29.1%, and 32.8% compared to that of MISAO-WLSSVM, respectively; the indicator MAE under different weather conditions decreased by 39.0%, 17.8%, and 19.9%, respectively; under different weather conditions, the indicator RMSE decreased by 37.2%, 16.0%, and 13.3%, respectively. The prediction results show that the use of ICEEMDAN decomposition can effectively eliminate redundant noise, extract the main features of the historical PV data, and significantly improve the prediction accuracy of the model, which verifies the superiority and validity of the MISAO-ICEEMDAN modal decomposition.
In order to make a strong argument for the necessity of classifying PV forecasts according to different weather conditions, we selected the same models as in the previous experiment, i.e., TCN, GRU, SVM, WLSSVM, SAO-WLSSVM, MISAO-WLSSVM, and MISAO-ICEEMDAN-WLSSVM, and we started this experiment based on the data from 1 July to 15 July 2018. The experimental metrics are recorded in
Table 8, and the prediction results are displayed in
Figure 11.
The data in
Table 8 show that the key metrics such as MAE, MAPE, and RMSE are significantly higher when not categorized based on weather conditions compared to the previous experiments categorized based on weather.
Figure 11 visually presents the prediction result curves of each model in this unclassified experiment. It can be observed that the prediction curves in the unclassified case are more volatile and deviate from the actual values to a more significant extent than the relatively smooth and accurate prediction curves in the previous classification case. It is especially noteworthy that even under such unfavorable experimental conditions, the MISAO-ICEEMDAN-WLSSVM model proposed in this paper still shows relatively optimal performance. This result strongly supports the critical role of weather condition-based classification in improving the accuracy of PV forecasts. It demonstrates the robustness of the proposed model under different experimental settings.
6. Discussion
In order to fully assess the performance of the MISAO-ICEEMDAN-WLSSVM model, it was compared with three existing models, TVF-EMD-ELM (M1), WPD-LFABS-SDS-GRU (M2) and SSA-VMD-Informer (M3).
Table 9 describes the development process of the existing hybrid models.
Table 10 compares the mean values of the error results of the proposed model with the existing models for the three weather types under the dataset of this paper. The bold values represent the optimal forecasts among all the model’s predictions. As shown in
Table 10, the MAE of the proposed model is reduced by 36.25%, 14.82%, and 25.23% compared with M1, M2, and M3, respectively. The MAE of M1 is 1.7254, and its TVF-EMD method is more complicated in parameter selection and has the problem of manual selection, which may be needed to be able to achieve the best decomposition effect for different PV data. The ELM model, when dealing with complex data, finds it difficult to fully explore the deep features, resulting in limited prediction accuracy. The MAE of M3 is 1.4710, and there may be modal aliasing problems during the decomposition process, affecting the feature extraction accuracy. The MAE of M2 is 1.2912, and the wavelet packet transform is time-consuming in selecting the appropriate wavelet basis function and ineffective in dealing with the boundary data, which negatively affects the prediction results. In addition, the combination of multiple algorithms and strategies increases the model complexity and may affect the computational efficiency.
On the other hand, the proposed model adopts the ICEEMDAN method of adaptive decomposition, which avoids complex parameter selection. The similar day model is constructed by K-means clustering, which improves the data quality. The multi-strategy improved MISAO optimizes the model parameters, combining the multivariate prediction considering meteorological factors and the optimal hyperparameter search of WLSSVM, significantly improving the prediction accuracy and adaptability.
The comparative analysis proves that the MISAO-ICEEMDAN-WLSSVM model proposed in this paper performs better in ultra-short-term PV power prediction.
7. Conclusions
Photovoltaic (PV) power generation is greatly affected by external factors, and the output power is random and unstable. In order to improve the prediction accuracy of PV power generation and reduce the impact of PV grid connection on the power system, a new MISAO-ICEEMDAN-WLSSVM prediction model was established. The research results are as follows:
- (1)
A MISAO algorithm is proposed by improving the SAO optimization algorithm in three aspects. A series of numerical experiments were conducted using 30 CEC 2017 benchmark functions, and the results show that the MISAO algorithm has a better ability to find the optimal solution and jump out of the local optimal solution.
- (2)
The MISAO algorithm was used to optimize the parameters of the ICEEMDAN-WLSSVM model, and the MISAO-ICEEMDAN-WLSSVM prediction model was established.
- (3)
The MISAO-ICEEMDAN-WLSSVM model was validated using data from a photovoltaic (PV) power plant in Hebei Province, China, and the prediction results were compared with seven neural network models, including WLSSVM, ICEEMDAN-WLSSVM, and MISAO-ICEEMDAN-WLSSVM, for three different weather types. The results show that the prediction curve of the MISAO-ICEEMDAN-WLSSVM model is closer to the actual value curve with the smallest error.
- (4)
Three evaluation indexes, MAPE, MAE and RMSE, were used to evaluate the seven models. The MAPE values of the proposed model were reduced by at least 25.3%, 29.1% and 32.8%; the MAE values were reduced by at least 39.0%, 17.8% and 32.8%; and the RMSE values were reduced by at least 37.2%, 16.0% and 13.3%, respectively, under the three types of weather compared with the other six models. The results showed that the MISAO-ICEEMDAN-WLSSVM prediction model has high prediction accuracy and stability. The proposed prediction model is conducive to accurately predicting the PV output power, making full use of solar energy resources, reducing the impact of the grid-connected PV on the modern power grid power system, promoting the smooth operation of grid scheduling, and maintaining the security and stability of the power system.
Furthermore, there are certain limitations in the prediction aspect of this study. Currently, the one-step forecasting method is employed. One-step forecasting restricts the comprehensive understanding of the long-term variation trend of photovoltaic power and may not fully meet the precise prediction requirements for photovoltaic power changes over a more extended period in some complex scenarios. Future research efforts will be dedicated to exploring multi-step forecasting methods. Intensive study will advance prediction techniques and model architectures, integrate more valuable feature information, and optimize the model training strategies to enhance the accuracy and stability of multi-step forecasting, providing more reliable technical support for optimized management and efficient operation in the field of new energy.
The limitations of this study also include the varying prediction effects of the model under different weather types. Specifically, when it is cloudy and rainy, the forecasting effect is less than when it is sunny. A thorough analysis of how to enhance the impact of weather type on forecasting has yet to be conducted. Moreover, compared to periods of high-power generation, the prediction accuracy is lower in the morning or evening. It is necessary to investigate the enhancement of the forecasting efficacy throughout the day. Future research should examine the effects of different weather conditions on the generation of PV power in more detail.