Ultra-short-term Single-step Photovoltaic Power Prediction based on VMD-Attention-BiLSTM Combined Model

Ultra-short-term Single-step Photovoltaic Power Prediction based on VMD-Attention-BiLSTM Combined Model | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Ultra-short-term Single-step Photovoltaic Power Prediction based on VMD-Attention-BiLSTM Combined Model Haisheng Yu, Shenhui Song This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4909901/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Research on photovoltaic systems (PV) power prediction contributes to optimizing configurations, responding promptly to emergencies, reducing costs, and maintaining long-term system stability. This study proposes a VMD-Attention-BiLSTM model for predicting ultra-short-term photovoltaic power to further enhance prediction performance. Firstly, VMD decomposes historical photovoltaic power data into multiple sub-sequences with different frequencies, treating each sub-sequence as a separate input variable for data expansion. Secondly, the Attention mechanism calculates the correlation coefficients between variables and assigns corresponding weights based on the magnitude of the correlation coefficients between each input variable and the output variable. Finally, the BiLSTM model adopts a dual-layer LSTM structure to more accurately extract features. Experimental results show that compared to various advanced deep learning methods, the MAE of the VMD-Attention-BiLSTM combined model improves by at least 29%. Physical sciences/Energy science and technology/Renewable energy/Solar energy Physical sciences/Mathematics and computing/Statistics Photovoltaic Power Prediction Variational Mode Decomposition (VMD) Attention Mechanism Bidirectional Long Short-Term Memory model (BiLSTM) Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 1. Background Photovoltaic power generation is a form of clean energy, and accurate prediction of PV power generation can help power systems better plan and manage energy supply. By forecasting photovoltaic power generation, energy dispatch strategies can be adjusted in advance. Photovoltaic power prediction can be classified into long-term, medium-term 1 , short-term 2 , and ultra-short-term 3 prediction based on the prediction time scale 4 . This paper focuses on ultra-short-term 5 prediction of photovoltaic power 6 . 2. Research status In the field of photovoltaic power prediction 7 , some scholars have improved the prediction accuracy and model stability through methods such as combining models, data preprocessing, and algorithm improvements 8 . By setting control experiments to compare the predicted results of photovoltaic power generation under different scenarios, more targeted input features can be provided 9 . Combined models integrate multiple individual prediction models by selecting models with different prediction mechanisms and advantages 10 , which can improve the overall prediction accuracy and stability 11 . For example, combining the attention mechanism with multi-dimensional time series prediction models can capture long-term sequential relationships 12 . Improving algorithms involve optimizing existing algorithms or introducing new algorithmic ideas 13 , reflected in aspects such as improving model parameter learning, feature extraction, and prediction processes 14 . For instance, using Bayesian optimization algorithms to adjust the most relevant hyperparameters in the model 15 , a method for predicting daily photovoltaic power generation using Long Short-Term Memory (LSTM) 16 neural networks has been proposed 17 . Photovoltaic power generation is influenced by various spatio-temporal factors such as weather conditions 18 , geographical location, and seasonal variations 19 . By extracting spatio-temporal features related to photovoltaic power generation 20 , richer input information can be provided for prediction models 21 . Contrasting different scenarios, combining models, improving algorithms, and extracting spatio-temporal features are all important means to improve the accuracy of photovoltaic power prediction 22 , collectively driving the development and application of photovoltaic power prediction technology 23 . In the field of photovoltaic power generation forecasting, scholars face a series of challenges, including high computational costs, strong volatility and randomness, difficulties in data processing, high uncertainty, equipment group failures, and privacy security issues 24 . To reduce computational costs, scholars have designed efficient algorithms, such as upgrading data 25 , combining models with new environments 26 , and integrating artificial intelligence 27 . These methods maintain high prediction accuracy while having low computational complexity. Since photovoltaic power generation is volatile and random due to weather conditions 28 , scholars have combined multiple prediction models and introduced uncertainty quantification methods into the prediction models to capture the volatility and randomness of photovoltaic power generation 29 . To address the difficulties in data processing 30 , scholars have adopted methods such as data cleaning and preprocessing and the use of robust prediction models 31 . The strong uncertainty in photovoltaic power generation forecasting is reflected in variable weather conditions 32 , different energy storage, and inconsistent measurement conditions 33 . Scholars have used probabilistic forecasting methods and scenario analysis to simulate various possible future scenarios 34 . During the operation of photovoltaic equipment, equipment failures are inevitable 35 . Real-time monitoring of the operating status and performance parameters of photovoltaic equipment, as well as the introduction of redundant design and fault-tolerant mechanisms into the photovoltaic system 36 , help maintain the system's continuous power supply capability and reduce the impact of failures on power generation 37 . During data collection and processing, sensitive information involving user privacy is desensitized and anonymized to protect users' privacy rights 38 . In summary, scholars have effectively addressed these issues by adopting efficient algorithms, combined prediction models, data cleaning and preprocessing, probabilistic forecasting methods, fault prediction and health management, and privacy protection technologies. These solutions not only improve prediction accuracy and stability, but also provide strong support for the sustainable development of the photovoltaic industry. In the field of PV power prediction, various factors significantly influence the prediction results, which can be broadly categorized into natural and technical factors. Extracting spatiotemporal features from the data can also serve as a crucial factor in enhancing the accuracy of ultra-short-term and short-term PV power predictions 39 . Additionally, conducting experiments by setting variables such as parameters, meteorology, time periods 40 , temperature 41 , data sequence types 42 , and models allows for exploration through comparative analysis. The humanistic aspects of PV power prediction primarily manifest in its impact on the energy industry, environmental conservation, and socioeconomic factors 43 . In this study, we make the following main contributions: Firstly, we propose a novel VMD-Attention-BiLSTM combination model to enhance prediction accuracy. Through partial ablation experiments, we investigate the roles of each module in the combination model and their impact on prediction. Secondly, we utilize the VMD algorithm to decompose historical PV power data into several sub-sequences, thus increasing data dimensionality and volume. The Attention mechanism computes the correlation coefficients between variables, identifying variables strongly correlated with the output results and increasing the weight of such variables' predictions in the final results. In the empirical section, we conduct multiple experiments, including ablation experiments analyzing the effects of each part of the combination model on the results. Day-night comparisons demonstrate that removing invalid data enhances model accuracy, seasonal comparisons analyze the impact of seasonal variations on power generation, and stride comparisons explore the influence of sliding time window lengths on prediction results. Model comparisons validate the superiority of our proposed model. The arrangement of other sections is as follows: Section 3 elaborates on the improved methods and the overall framework flow of the combined model. Section 3 introduces the experimental results, including data preprocessing and multiple sets of comparative experiments on photovoltaic power generation prediction. Section 5 summarizes the research. In addition, the research framework proposed in this paper is shown in Fig. 1 . 3. Methodology In this section, we first introduce the Variational Mode Decomposition (VMD) algorithm and describe the role of the VMD algorithm module in the model. Next, we introduce the Attention mechanism and its role in the model. Then, we explain the basic mechanism and prediction principle of the proposed BiLSTM model. Finally, the overall architecture of the combined model consisting of these three modules is introduced. 3.1 Variational Mode Decomposition Variational Mode Decomposition (VMD) is an adaptive, completely non-recursive method for mode variation and signal processing. It uses iterative search to find the optimal solution of the variational model to determine the center frequency and bandwidth of each decomposed component, thereby decomposing the original signal into modal components with center frequencies and limited bandwidths to enhance robustness. Figure 2 shows the VMD decomposition process in this paper. The original input data consists of historical data of photovoltaic power generation and six conventional variables: total solar irradiance, direct normal irradiance, global horizontal irradiance, air temperature, atmospheric pressure, and relative humidity. To expand the data dimension and increase the proportion of historical data of photovoltaic power generation in the predictive variables, the VMD method is used to decompose the historical data of photovoltaic power generation into several sub-sequences. The center frequencies are calculated when the number of sub-sequences is from 1 to 10, and the number of sub-sequences with stable center frequencies is selected as the optimal number of sub-sequences, generating several sub-sequences. At this point, the input becomes six conventional variables and several sub-sequences of historical data of photovoltaic power generation. 3.2 Attention Mechanism The principle of the Attention mechanism is to allow the model to focus its attention on specific parts of the input text while ignoring others, thereby improving the performance and efficiency of the model. Figure 3 illustrates the process of the Attention mechanism. The input sequence processed by the VMD module is fed into the Attention mechanism. The embedded input is multiplied by the weight matrix obtained during the training process to calculate the query matrix Q, key matrix K, and value matrix V, which can be expressed as Equation. (1). The softmax function normalizes the attention weights, converting them into a probability distribution. Finally, the correlation coefficients between variables and the weights of each input variable's prediction results in the final output. $$Attention\left( {Q,K,V} \right)=soft\hbox{max} \left( {\frac{{Q{K^T}}}{{\sqrt {{d_k}} }}} \right)V$$ 1 3.3 Bidirectional Long Short-Term Memory model The BiLSTM model, short for Bidirectional Long Short-Term Memory model, is composed of both forward and backward LSTM units. By simultaneously processing the forward and backward information of sequences, BiLSTM can fully utilize the contextual information of sequences, thereby extracting more comprehensive and accurate features during modeling. Figure 4 depicts the framework of the BiLSTM model. The input data consists of six conventional variables and n subsequences processed by the VMD and Attention modules. With a time step of m, this forms a two-dimensional matrix of dimensions 6 + n by m. After assigning weights to variables, this matrix is fed into the LSTM model. The output is a two-dimensional matrix of dimensions 6 + n by 6 + n. This output is then separately input into two LSTM models, LSTM1 and LSTM2, for prediction. The results from these two models are merged in the fully connected layer. Subsequently, dimensionality reduction is performed on the merged results to generate the final output. 2.4 Improved Framework This paper proposes a multi-input single-output single-step prediction model based on VMD-Attention-BiLSTM. Figure 5 illustrates the flowchart of the VMD-Attention-BiLSTM combined model, while Fig. 6 depicts a schematic diagram of multi-input single-output single-step prediction. Figure 5 illustrates the flowchart of the VMD-Attention-BiLSTM combined model, comprising the VMD module, Attention mechanism module, and BiLSTM module in sequence. The VMD module decomposes PV power generation data into several sub-sequences based on different frequencies to extract data features. The Attention module computes the correlation coefficients among various variables (including three types of radiation, temperature, humidity, atmospheric conditions, historical power sequences, and current power generation), assigning different weights to input variables based on the magnitude of their correlation coefficients with the output variable. The BiLSTM module conducts predictions, using training set data for model learning, validating predictions with validation set data, adjusting model parameters based on results, and evaluating model performance using test set data. Figure 6 depicts a schematic diagram of multi-input single-output single-step prediction. Each row of data corresponds to the same time step, and each column corresponds to the same variable. The rightmost column represents the output, while the rest of the columns represent the inputs. The goal is to predict the value of the output variable at time step t using data from time steps t-m to t-1 of n input variables, as illustrated by the red box in Fig. 6 predicting the value inside the red circle. 4. Experiment This section covers the experimental part, including data preprocessing, introduction of evaluation metrics, and presentation of experimental results. 4.1 Data Set This subsection sequentially introduces the data source, handling of outliers, missing values, and invalid values, normalization method, data set division, and variable analysis. 4.1.1 Data Source The data used in this study are from the solar energy data of the renewable energy generation prediction competition held by the State Grid Corporation of China. The data set contains 7 variables, namely, total solar irradiance, direct normal irradiance, global horizontal irradiance, air temperature, atmospheric relative humidity, and photovoltaic power generation. The data collection period spans from January 1, 2019, 0:00 to December 31, 2020, 24:00, with data points collected at 15-minute intervals, totaling 70,176 data points. Each data point consists of measurements of 7 variables at a single time step. 4.1.2 Handling of Outliers, Missing Values, and Invalid Values Outliers in the data set, such as negative power generation or positive irradiance during nighttime, are identified based on environmental and time criteria and subsequently removed. The removed outliers are treated as missing values along with any existing missing values in the data set. Missing values are filled using linear interpolation, considering the low and nearly discontinuous missing rate in the data set and the continuous and small-scale trends in the data, as per Equation. (2). $$y={y_0}+\left( {x - {x_0}} \right)\frac{{{y_1} - {y_0}}}{{{x_1} - {x_0}}}$$ 2 Since photovoltaic power generation relies primarily on daylight, nighttime data where power generation is consistently zero are considered invalid and thus removed, while daytime data are retained. 4.1.3 Normalization The data are normalized to the [0,1] interval using the min-max normalization method. Normalization accelerates model speed, increases model stability, and enhances model accuracy, as described by Equation. (3). The data in which x is any data from dataset, \({x_{\hbox{max} }}\) is the maximum value in the dataset, \({x_{\hbox{min} }}\) is the minimum value in the dataset, and x' is the normalized value. 4.1.4 Data Set Division After the aforementioned steps, the new data set consists of 30,881 data points. The data set is divided into training, validation, and testing sets in a ratio of 7:2:1. The training set, comprising 70% of the data, is used to train the model, with a time span from January 1, 2019, 9:15 to June 4, 2020, 20:45. The validation set, comprising 20% of the data, is used for model adjustment and parameter optimization, with a time span from June 5, 2020, 6:15 to October 11, 2020, 12:15. The testing set, comprising 10% of the data, is used to evaluate model performance, with a time span from October 11, 2020, 12:30 to December 31, 2020, 18:15. 4.1.5 Variable Analysis Total solar irradiance: Represents the energy intensity of solar radiation reaching the Earth's surface in watts per square meter (W/m²). Higher total solar irradiance leads to increased stability in photovoltaic power output, while lower irradiance results in decreased output power. Direct normal irradiance: Refers to the radiation intensity of sunlight perpendicular to the Earth's surface in W/m². It directly affects the amount of solar energy received by photovoltaic panels. Increasing direct normal irradiance enhances photovoltaic power output, ensuring the stability of the system. Global horizontal irradiance: Represents the total irradiance of the sun on the Earth's horizontal plane in W/m². It determines the amount of solar radiation energy received by photovoltaic panels. Higher global horizontal irradiance leads to increased output power of photovoltaic systems. Air temperature: Affects photovoltaic power generation by influencing the operating temperature and efficiency of photovoltaic panels in degrees Celsius (°C). Beyond a certain range, temperature increase can decrease photovoltaic conversion efficiency, leading to panel aging and increased failure rates, thus reducing photovoltaic power output. Atmospheric pressure: Measured in hPa. Factors such as atmospheric clarity, cloud thickness, and weather conditions affect the intensity of sunlight reaching the ground and solar radiation. Particles and pollutants in the atmosphere absorb and scatter solar radiation, reducing the intensity of radiation received by photovoltaic components. Relative humidity: High humidity may cause surface water or condensation on photovoltaic components, reducing light transmittance and thus lowering photovoltaic conversion efficiency. Humidity also affects the heat dissipation of photovoltaic systems and exacerbates corrosion and aging of photovoltaic components. Historical data subseries of photovoltaic power generation: Data subseries at different frequencies reflect the operating characteristics of photovoltaic power stations at different time scales. High-frequency data capture instantaneous power fluctuations of photovoltaic power stations, suitable for real-time and short-term predictions, while low-frequency data reflect long-term operating trends, suitable for long-term predictions and trend analysis. Different frequency data subseries complement each other and can be used for mutual verification and supplementation. Table 1 Descriptive Information of Variables Variables Mean Maximum Minimum Std Skewness Kurtosis Total solar irradiance 560.64 1359.00 1.00 349.45 -0.05 1.66 Direct normal irradiance 209.33 980.00 1.00 257.25 1.11 2.94 Global horizontal irradiance 137.68 989.00 1.00 120.81 2.25 10.00 Air temperature 16.51 40.90 -17.20 14.30 -0.81 5.73 Atmosphere 911.56 936.30 894.00 32.12 -29.24 920.32 Relative humidity 1055.19 6553.50 0.00 2386.70 1.87 4.49 Power 20.46 48.32 0.00 13.41 0.07 1.75 Table 1 presents descriptive information for 7 variables. After data preprocessing, the minimum value of irradiance is 1, while the minimum values for relative humidity and photovoltaic power generation are 0. Due to the significant variation in irradiance throughout the day, following a timeline from 0 at sunrise, reaching a maximum, then decreasing back to 0 at sunset, the standard deviation of irradiance is large. Air temperature, atmospheric pressure, and relative humidity remain relatively stable. 4.2 Evaluation Metrics Evaluation of model predictive performance is conducted using Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and the coefficient of determination ( \({R^2}\) ). MAE measures the average absolute difference between predicted and actual values, intuitively reflecting the size of prediction errors and the precision of the model's predictions. MSE measures the average squared difference between predicted and actual values, reflecting the stability of the model's prediction results. A smaller RMSE indicates a stronger predictive ability of the model. The coefficient of determination measures the proportion of the variance in the output variable explained by the model, reflecting the degree to which the model fits the data. Its value ranges from 0 to 1, with a value closer to 1 indicating a better fit of the model to the data. The formulas for evaluation metrics are as follows: $$MAE=\frac{1}{n}\sum\limits_{{t=1}}^{n} {\left| {{{\hat {y}}_t} - {y_t}} \right|}$$ 4 $$MSE=\frac{1}{n}\sum\limits_{{t=1}}^{n} {{{\left( {{{\hat {y}}_t} - {y_t}} \right)}^2}}$$ 5 $$RMSE=\sqrt {\frac{1}{n}\sum\limits_{{t=1}}^{n} {{{\left( {{{\hat {y}}_t} - {y_t}} \right)}^2}} }$$ 6 $${R^2}=1 - \frac{{\sum\limits_{{t=1}}^{n} {{{\left( {{y_t} - {{\hat {y}}_t}} \right)}^2}} }}{{\sum\limits_{{t=1}}^{n} {{{\left( {{y_t} - {{\bar {y}}_t}} \right)}^2}} }}$$ 7 4.3 Subsequence Decomposition The photovoltaic power generation historical data was decomposed into subsequence counts ranging from 1 to 10, and the central frequency was calculated after each decomposition. It was determined that the central frequency was most stable when the subsequence count was 8, thus establishing the optimal subsequence decomposition count as 8. As shown in Fig. 7 , the top solid black line represents the original power data before decomposition, while the 8 rows of solid blue lines below represent the high, medium, and low-frequency components IMF1-IMF7. 4.4 Attention Mechanism Through the attention mechanism, correlations between 15 factors were calculated, including total solar irradiance, direct normal irradiance, global horizontal irradiance, air temperature, atmospheric relative humidity, 7 subsequences after decomposition of photovoltaic power generation historical data, and photovoltaic power generation. The first 14 are input variables, and the last one is the output variable. The correlation heat map between variables is illustrated in Fig. 8 . Figure 8 indicates that most variables exhibit weak positive correlations, with correlation coefficients around [0,0.4]. However, there are a few variables that show strong associations, such as total solar irradiance and the output variable, as well as the IMF7 and the output variable. This is because total solar irradiance represents sunlight intensity, and the frequency of the IMF7 occupies a significant proportion in the historical data of photovoltaic power generation, resulting in a strong positive correlation between them. Additionally, there are a few variables that show weak negative correlations, such as the IMF8 and temperature, and the direct normal irradiance and global horizontal irradiance, with correlation coefficients falling within the [-0.2,0] range. Table 2 Correlation coefficients Variable Correlation coefficient with output variable Output 1 Total Solar Irradiance 0.880215 IMF7 0.744364 IMF6 0.606838 RES 0.416276 Direct Normal Irradiance 0.401422 Global Horizontal Irradiance 0.357829 IMF5 0.32927 IMF4 0.196439 IMF3 0.12812 IMF2 0.095738 IMF1 0.075753 Relative Humidity 0.073687 Atmosphere 0.05432 Air Temperature 0.044742 Table 2 presents the correlation coefficients between each input variable and the photovoltaic power output variable, with variables sorted from top to bottom based on their correlation coefficients with the photovoltaic power output variable. From the data, it can be observed that the output variable has strong positive correlations with total solar irradiance, the IMF7, and the IMF6, with correlation coefficients of 0.880215, 0.744364, and 0.606838, respectively. This indicates that a surge in irradiance promotes a larger energy pool for photovoltaic cells to convert into electricity, thus increasing the power output. As the frequency decreases from IMF1 to IMF7, the correlation coefficients with the photovoltaic power output variable gradually decrease from 0.744364 to 0.075753. Higher-frequency subsequences, which have a higher proportion in the original sequence, exhibit larger correlation coefficients. Relative humidity, atmospheric pressure, and temperature show weak positive correlations with photovoltaic power generation, with coefficients of 0.073687, 0.05432, and 0.044742, respectively, all below 0.1. These nonlinear relationships among variables suggest that they do not directly impact photovoltaic power generation but rather indirectly influence electricity output by affecting other meteorological factors. 4.5 Ablation Experiment The ablation study is a scientific research method used to determine the impact of key components of a condition, parameter, or system on overall performance. This method involves systematically controlling or modifying specific parts of a system one by one to observe how these changes affect the system's functionality, performance, or behavior. Ablation experiments can enhance model transparency, optimize model performance, validate the effectiveness of specific functions or components, and enhance the integrity and credibility of research. This subsection sets up ablation experiments to explore the roles of various modules in the composite model and their contributions to improving model accuracy. The ablation experiment groups include four experimental groups: VMD-Attention-BiLSTM model, Attention-BiLSTM model, VMD-BiLSTM model, and VMD-Attention-LSTM model. In Fig. 9 , there are five solid lines representing the predicted results of the ablation experiment. They correspond to the true values of 50 samples taken throughout the day and the results under different models. The black solid line representing the true values appears relatively smooth and natural. However, the other four prediction curves exhibit varying degrees of fluctuation and curvature, indicating differences in the performance of these models at different time points. The samples are taken from 0 to 25 during the period from sunrise to midday. As the sunlight intensifies, the power generation increases. During this period, the predicted values of the four models are relatively close to each other, but deviate significantly from the true values. Among them, the VMD-Attention-LSTM experimental group and the VMD-BiLSTM experimental group have slightly higher accuracy compared to the other two groups. The samples taken from 25 to 50 are from midday to sunset, during which the solar irradiance decreases and the power generation decreases. During this period, the results of the four prediction experiments fluctuate in line with the changing trend of the true values, intertwining with each other. The true values are closest to the VMD-Attention-BiLSTM model. Table 3 Errors in ablation experiments Ablation experiments MAE MSE RMSE \({R^2}\) VMD-Attention-BiLSTM 0.1123 0.0207 0.1438 0.8835 Attention-BiLSTM 0.1516 0.0339 0.1840 0.7956 VMD-BiLSTM 0.1208 0.0238 0.1544 0.8641 VMD-Attention-LSTM 0.1132 0.0214 0.1464 0.8862 Table 3 presents the prediction results of the four experimental groups in the ablation experiment, comparing model performance using four evaluation metrics. Among them, the VMD-Attention-BiLSTM model has the lowest MAE, MSE, and RMSE, which are 0.1123, 0.0207, and 0.1438 respectively. The VMD-Attention-LSTM group has the highest \({R^2}\) of 0.8862. Arranging the metrics from lowest to highest, the sequence for MAE, MSE, and RMSE is: VMD-Attention-BiLSTM experimental group, VMD-Attention-LSTM experimental group, VMD-BiLSTM experimental group, and Attention-BiLSTM experimental group. This indicates that decomposing the sequence has the greatest impact on improving prediction accuracy, followed by allocating weights using attention mechanism, while the least impactful is the bidirectional structure of the LSTM model. Regarding \({R^2}\) , arranged from highest to lowest, the sequence is: VMD-Attention-LSTM experimental group, VMD-Attention-BiLSTM experimental group, VMD-BiLSTM experimental group, and Attention-BiLSTM experimental group. Moreover, the difference in \({R^2}\) between the VMD-Attention-LSTM experimental group and the VMD-Attention-BiLSTM experimental group is only 0.0027, suggesting that the bidirectional structure of the LSTM model has a minimal impact on data fitting in the combined model. 4.6 Comparative experiments This section establishes four sets of comparative experiments: day and night, seasons, step length, and models. Visualization graphs of prediction results and error tables of evaluation metrics are utilized to compare the performance of different datasets or models, exploring the effects of different variables, data processing methods, and environments on photovoltaic power prediction. 4.6.1 Day and night comparison The dataset is divided into daytime and full-day datasets based on sunlight hours. The full-day dataset includes data for all 24 hours of the day, including nighttime data when photovoltaic power is zero. The daytime dataset, on the other hand, is derived from the full-day dataset by removing all data points where photovoltaic power is zero. Both datasets undergo the same data preprocessing steps and are used for combined model predictions to investigate the impact of nighttime values on prediction. Figure 10 illustrates the comparison between the prediction results of the daytime dataset and the full-day dataset. The horizontal axis represents a time span of one week (7 days), with the black solid line indicating the trend of real values. Subplot (a) presents the comparison between the prediction results and real values of the daytime dataset, with 320 samples. The predicted values are depicted by the green solid line. Subplot (b) illustrates the comparison for the full-day dataset, containing 680 samples, with the predicted values shown by the red solid line. In subplot (a), the 3rd day is rainy, and the 7th day is cloudy, while the remaining 5 days are sunny. During sunny and cloudy days, the predicted values exhibit a significant deviation below the real values in the morning hours, but align closely with the real values in the afternoon, indicating good prediction accuracy. However, on rainy days, due to rapid power fluctuations caused by cloud cover, the prediction accuracy is slightly lower. In subplot (b), the 1st day is cloudy, and the remaining 6 days are sunny. The prediction for the cloudy day fails to capture the extreme peak in real values, while on sunny days, there is a lag between the predicted and real values, resulting in misalignment of the two curves. Additionally, the predicted values fail to simulate the peak in photovoltaic power generation during the strongest sunlight hours around noon, and they also lag behind in reaching zero at sunset compared to the real values. Table 4 Errors for the daytime dataset and the all-day dataset Dataset MAE MSE RMSE \({R^2}\) Daytime dataset 0.1123 0.0207 0.1438 0.8835 All-day dataset 0.1436 0.0325 0.1804 0.8386 Table 4 presents the errors for both the daytime and full-day datasets. From the table, it can be observed that the MAE, MSE, RMSE and \({R^2}\) of the daytime dataset are all better than those of the full-day dataset. This indicates that the prediction accuracy, stability, capability, and fitting degree are higher when using the daytime dataset, further suggesting that removing nighttime values can reduce data redundancy and make the dataset more refined and effective. 4.6.2 Seasonal comparisons The dataset is divided into spring, summer, autumn, and winter datasets based on seasonal variations, covering the periods from March to May, June to August, September to November, and December to February for the years 2019 and 2020, respectively. These four datasets undergo the same data preprocessing and combined model prediction to investigate the impact of seasonal changes on predictions. Figure 11 depicts the comparative forecast results of the seasonal dataset, comprising four subplots, each representing the prediction results for one week in the corresponding seasonal dataset. Subplot (a) shows that the trend of the predicted values is close to the actual values, but the predicted values fail to simulate peak changes when abrupt changes occur in the actual values. Subplot (b) illustrates that the variation in predicted values is synchronized with the actual values, with the two curves overlapping closely most of the time; however, the predicted values can only roughly simulate the numerical range when abrupt changes occur in the actual values, failing to accurately capture every short-term extreme change. In subplot (c), there are several peaks in the actual values on overcast days, while the predicted values can roughly simulate one peak. Subplot (d) shows that the predicted values almost coincide with the actual values, with slight discrepancies in numerical simulation when there are short-term abrupt changes in the actual values, indicating the best prediction performance. Table 5 Seasonal dataset errors Season MAE MSE RMSE \({R^2}\) Spring 0.2656 0.1153 0.3396 0.8375 Summer 0.2864 0.1310 0.3619 0.8468 Autumn 0.2673 0.1147 0.3386 0.8486 Winter 0.2477 0.1038 0.3222 0.8334 Table 5 presents the numerical values of four evaluation metrics corresponding to the four seasons. The MAE, MSE, and RMSE of the winter dataset are the lowest, at 0.2477, 0.1038, and 0.3222, respectively, while the \({R^2}\) of the autumn dataset is the highest, at 0.8486. The numerical values of MAE, MSE, and RMSE indicate that the overall prediction accuracy from highest to lowest is in the order of winter, autumn, spring, and summer. Winter experiences fewer cloudy days, relatively stable weather patterns, and abundant and stable sunlight. Conversely, summer exhibits significant weather fluctuations, more rainy days, and difficulties in accurately predicting cloud cover changes, which may lead to decreased output power of photovoltaic panels due to extremely high temperatures. 4.6.3 Comparison of step lengths By categorizing according to time step lengths, the four datasets can be divided into predicting the next time point value every 4, 8, 12, or 16 time steps. Since the data are collected every 15 minutes in the dataset, these four datasets use data from the previous 1, 2, 3, or 4 hours to predict the next time point data. Figure 12 presents a comparison of the prediction results for datasets with different time steps. Subplot (a) exhibits the highest overlap between actual values and predicted values, while subplots (b), (c), and (d) show varying degrees of deviation around the midday peak values. Table 6 Errors in the step size dataset Step size MAE MSE RMSE \({R^2}\) 4 0.1962 0.0616 0.2483 0.9297 8 0.2441 0.0976 0.3125 0.8598 12 0.2801 0.1212 0.3481 0.9097 16 0.2455 0.0942 0.3069 0.9272 Table 6 displays the error indicator data corresponding to different step lengths. Overall, when using data from the previous 4 time steps to predict the next time step, the MAE, MSE, RMSE, and \({R^2}\) are optimal, followed by using data from the previous 8 time steps, then 16 time steps, and finally 12 time steps. This is because in photovoltaic power generation forecasting, the operation of photovoltaic systems and weather conditions change minimally over short periods of time, and shorter time steps can more accurately capture the temporal correlation of the data. Longer time step models need to deal with more variables and uncertainties, which may lead to a decrease in prediction accuracy. As the prediction time step increases, errors may gradually accumulate, potentially significantly affecting the final prediction accuracy. 4.6.4 Comparison of models In this subsection, various prediction models, including the proposed VMD-Attention-BiLSTM composite model, and baseline models such as the LSTM model, CNN model, and RNN model, for forecasting the daytime dataset. The time step is uniformly set to 8, while the remaining model hyperparameters are set to their respective optimal configurations. Figure 13 illustrates the comparison of all models used in this section for predicting photovoltaic power generation on the dataset, which spans three consecutive days. Due to significant performance variations of the models at different time intervals, certain weather factors affect prediction accuracy. From the Fig., it can be observed that on the first day (samples 0–50), the CNN and RNN models predict values close to the ground truth in the morning, with none of the models predicting the peak value that appears at noon. In the afternoon, the prediction of each model is relatively close to the ground truth. On the second day (samples 51–110), overcast conditions in the midday result in insufficient sunlight and a decrease in power generation. The trend predicted by the proposed model in this paper is similar to the ground truth, while the other models still show clear weather predictions based on the morning trends of the second day. On the third day (samples 111–170), the predicted trends of all models are consistent, with slight numerical deviations. Table 7 Errors of the models Model MAE MSE RMSE \({R^2}\) Proposed 0.1123 0.0207 0.1438 0.8835 LSTM 0.2867 0.1274 0.3569 0.7910 CNN 0.1579 0.0520 0.2280 0.9258 RNN 0.2142 0.0787 0.2805 0.8956 Table 7 displays the performance metrics of prediction errors for each model. The proposed model exhibits the lowest MAE, MSE, and RMSE, with values of 0.1123, 0.0207, and 0.1438, respectively, while the CNN model shows the highest values, with an \({R^2}\) of 0.9258. From the perspective of MAE, MSE, and RMSE, the prediction accuracy decreases from our proposed model to the CNN model, RNN model, and LSTM model sequentially. The proposed model, which incorporates subsequence decomposition and weight allocation, effectively reduces prediction errors. In terms of fitting ability, the models rank from highest to lowest as CNN model, RNN model, our proposed model, and LSTM model. This indicates that the CNN model and RNN model exhibit higher short-term prediction fitting but lower long-term trend prediction ability compared to our proposed model. 5. Conclusion In order to enhance the accuracy of ultra-short-term photovoltaic power prediction, this study proposes a VMD-Attention-BiLSTM combined model and evaluates its performance. The main conclusions are as follows: Firstly, VMD decomposes the original time series data of photovoltaic power generation into multiple modal components with different frequency characteristics. This decomposition process helps refine the information in the original data, reduce data non-stationarity, and improve modeling accuracy. Secondly, the Attention mechanism plays a crucial role in the model by dynamically focusing on important parts of different modal components, further improving prediction accuracy. Lastly, BiLSTM, as the core part of the model, captures long-term dependencies in time series data. In summary, the VMD-Attention-BiLSTM combined model integrates the respective characteristics of VMD, Attention, and BiLSTM, enabling a more accurate description of the variation patterns of photovoltaic power generation and improving prediction accuracy. Additionally, this study conducts multiple control experiments, including ablation analysis of the modules in the combined model, day-night comparison experiments demonstrating the simplification of data by removing nighttime data, seasonal comparison experiments showing the influence of different seasonal features on power generation, stride comparison experiments indicating that appropriate time steps can improve prediction accuracy and avoid error accumulation, and model comparison experiments demonstrating the superiority of the proposed model in prediction accuracy and stability, as well as its adaptability in different prediction environments. Although the VMD-Attention-BiLSTM combined model exhibits high accuracy in single-step photovoltaic power prediction, there is room for improvement. Due to the large amount of data, the next step involves adding a data preprocessing step to simplify the data, facilitating the extraction of features as soon as possible. The hierarchical structure of the model results in long execution times, necessitating improvements to reduce runtime while maintaining result accuracy and stability. In summary, the VMD-Attention-BiLSTM combined model possesses many advantages in predicting photovoltaic power generation. By integrating the characteristics of VMD, Attention, and BiLSTM, it can more accurately describe the variation patterns of photovoltaic power generation and improve prediction accuracy. These advantages make the model widely applicable in the field of photovoltaic power generation prediction. Declarations Data availability The datasets analyzed during the current study are available from the corresponding author on reasonable request. Acknowledgments This work was supported by Social Science Planning Project of Shandong Province (22CSDJ13). Author contributions Haisheng Yu: Funding acquisition, Resources, Supervision, Writing – review and editing. Shenhui Song: Conceptualization, Data curation, Methodology, Software, Validation, Visualization, Writing – original draft. Competing interests The authors declare no competing interests. References Yu, C. et al. A new temporal frequency ensemble transformer for day-ahead photovoltaic power prediction. J. Clean. Prod. 448 , 141690. https://doi.org/10.1016/j.jclepro.2024.141690 (2024). liu, Q., li, Y., jiang, H., chen, Y. & zhang, J. Short-term photovoltaic power forecasting based on multiple mode decomposition and parallel bidirectional long short term combined with convolutional neural networks. Energy . 286 , 129580. https://doi.org/10.1016/j.energy.2023.129580 (2024). Liu, W. & Mao, Z. Short-term photovoltaic power forecasting with feature extraction and attention mechanisms. Renew. Energy . 226 , 120437. https://doi.org/10.1016/j.renene.2024.120437 (2024). Sabadus, A. et al. A cross-sectional survey of deterministic PV power forecasting: Progress and limitations in current approaches. Renew. Energy . 226 , 120385. https://doi.org/10.1016/j.renene.2024.120385 (2024). Zang, H. et al. Improving ultra-short-term photovoltaic power forecasting using a novel sky-image-based framework considering spatial-temporal feature interaction. Energy . 293 , 130538. https://doi.org/10.1016/j.energy.2024.130538 (2024). Khalil, I. U. & Haq ul Islam, N. A novel procedure for photovoltaic fault forecasting. Electr. Power Syst. Res. 226 , 109881. https://doi.org/10.1016/j.epsr.2023.109881 (2024). Zhou, S., Lu, W., Li, W. & Wang, S. Forecasting the temperature of a building-integrated photovoltaic panel equipped with phase change material using artificial neural network. Case Stud. Therm. Eng. 57 , 104355. https://doi.org/10.1016/j.csite.2024.104355 (2024). Li, G. et al. Research on a novel photovoltaic power forecasting model based on parallel long and short-term time series network. Energy . 293 , 130621. https://doi.org/10.1016/j.energy.2024.130621 (2024). Xu, S., Zhang, R., Ma, H., Ekanayake, C. & Cui, Y. On vision transformer for ultra-short-term forecasting of photovoltaic generation using sky images. Sol. Energy . 267 , 112203. https://doi.org/10.1016/j.solener.2023.112203 (2024). Hu, Z., Gao, Y., Ji, S., Mae, M. & Imaizumi, T. Improved multistep ahead photovoltaic power prediction model based on LSTM and self-attention with weather forecast data. Appl. Energy . 359 , 122709. https://doi.org/10.1016/j.apenergy.2024.122709 (2024). Lee, D. S., Lai, C. W. & Fu, S. K. A short- and medium-term forecasting model for roof PV systems with data pre-processing. Heliyon . 10 (6), e27752. https://doi.org/10.1016/j.heliyon.2024.e27752 (2024). Sakib, S. et al. Attention-Based Models for Multivariate Time Series Forecasting: Multi-step Solar Irradiation Prediction. Heliyon . 10, (6), e27795. (2024). https://doi.org/10.1016/j.heliyon.2024.e27795 Ait Mansour, A., Tilioua, A., Touzani, M. & Bi-LSTM GRU and 1D-CNN models for short-term photovoltaic panel efficiency forecasting case amorphous silicon grid-connected PV system. Results Eng. 21 , 101886. https://doi.org/10.1016/j.rineng.2024.101886 (2024). Liu, J. & Li, T. Multi-step power forecasting for regional photovoltaic plants based on ITDE-GAT model. Energy . 130468 https://doi.org/10.1016/j.energy.2024.130468 (2024). Shi, J., Wang, S., Qu, P. & Shao, J. Time series prediction model using LSTM-Transformer neural network for mine water inflow. Sci. Rep. 14 (1). https://doi.org/10.1038/s41598-024-69418-z (2024). Herrera Casanova, R. & Conde, A. Enhancement of LSTM models based on data pre-processing and optimization of Bayesian hyperparameters for day-ahead photovoltaic generation prediction. Comput. Electr. Eng. 116 , 109162. https://doi.org/10.1016/j.compeleceng.2024.109162 (2024). Hong, Y. Y. & Martinez, J. J. F. Forecasting solar irradiation using convolutional long short-term memory and feature selection of data from neighboring locations. Sustainable Energy Grids Networks . 38 , 101271. https://doi.org/10.1016/j.segan.2023.101271 (2024). Bai, M. et al. Spatial-temporal characteristics analysis of solar irradiance forecast errors in Europe and North America. Energy . 297 , 131187. https://doi.org/10.1016/j.energy.2024.131187 (2024). Bai, M. et al. Deep graph gated recurrent unit network-based spatial–temporal multi-task learning for intelligent information fusion of multiple sites with application in short-term spatial–temporal probabilistic forecast of photovoltaic power. Expert Syst. Appl. 240 , 122072. https://doi.org/10.1016/j.eswa.2023.122072 (2024). Nguyen-Duc, T., Nguyen-Trong, T., Nguyen-Hoang-Minh, G., Fujita, G. & Tran-Thanh, S. Spectral-temporal convolutional approach for PV systems output power forecasting: Case studies in single-site and multi-site. Sustainable Energy Grids Networks . 38 , 101357. https://doi.org/10.1016/j.segan.2024.101357 (2024). Zang, H. et al. Multi-site solar irradiance forecasting based on adaptive spatiotemporal graph convolutional network. Expert Syst. Appl. 236 , 121313. https://doi.org/10.1016/j.eswa.2023.121313 (2024). Long, H. et al. Defect monitoring method for Al-CFRTP UFSW based on BWO–VMD–HHT and ResNet. Scientific Reports . 14, (1). (2024). https://doi.org/10.1038/s41598-024-69596-w Abouzeid, A. F. et al. Experimental validation of a low-cost maximum power point tracking technique based on artificial neural network for photovoltaic systems. Scientific Reports . 14, (1). (2024). https://doi.org/10.1038/s41598-024-67306-0 Wang, H., Mao, L., Zhang, H. & Wu, Q. Multi-prediction of electric load and photovoltaic solar power in grid-connected photovoltaic system using state transition method. Appl. Energy . 353 , 122138. https://doi.org/10.1016/j.apenergy.2023.122138 (2024). Meng, X., Shi, X., Wang, W., Zhang, Y. & Gao, F. An upscaling minute-level regional photovoltaic power forecasting scheme. Int. J. Electr. Power Energy Syst. 155 , 109609. https://doi.org/10.1016/j.ijepes.2023.109609 (2024). Real, A. C., Luz, G. P., Sousa, J. M. C., Brito, M. C. & Vieira, S. M. Optimization of a photovoltaic-battery system using deep reinforcement learning and load forecasting. Energy AI . 16 , 100347. https://doi.org/10.1016/j.egyai.2024.100347 (2024). Díaz-Bello, D., Vargas-Salgado, C., Alcázar-Ortega, M. & Gómez-Navarro, T. Demand response of prosumers integrating storage system for optimizing grid-connected photovoltaics through time-pricing. J. Energy Storage . 88 , 111536. https://doi.org/10.1016/j.est.2024.111536 (2024). Li, M., Wang, W., He, Y. & Wang, Q. Deep learning model for short-term photovoltaic power forecasting based on variational mode decomposition and similar day clustering. Comput. Electr. Eng. 115 , 109116. https://doi.org/10.1016/j.compeleceng.2024.109116 (2024). Sareen, K., Panigrahi, B. K., Shikhola, T. & Nagdeve, R. Deep learning solar forecasting for green hydrogen production in India: A case study. Int. J. Hydrog. Energy . 50 , 334. https://doi.org/10.1016/j.ijhydene.2023.08.323 (2024). Tang, Y., Yang, K., Zhang, S. & Zhang, Z. Photovoltaic power forecasting: A dual-attention gated recurrent unit framework incorporating weather clustering and transfer learning strategy. Eng. Appl. Artif. Intell. 130 , 107691. https://doi.org/10.1016/j.engappai.2023.107691 (2024). Wang, X. & Ma, W. A hybrid deep learning model with an optimal strategy based on improved VMD and transformer for short-term photovoltaic power forecasting. Energy . 295 , 131071. https://doi.org/10.1016/j.energy.2024.131071 (2024). Ma, C. et al. Scenario-based ultra-short-term rolling optimal operation of a photovoltaic-energy storage system under forecast uncertainty. Appl. Energy . 356 , 122425. https://doi.org/10.1016/j.apenergy.2023.122425 (2024). Massidda, L., Bettio, F. & Marrocu, M. Probabilistic day-ahead prediction of PV generation. A comparative analysis of forecasting methodologies and of the factors influencing accuracy. Sol. Energy . 271 , 112422. https://doi.org/10.1016/j.solener.2024.112422 (2024). Matera, N., Longo, M. & Leva, S. Time-dependent photovoltaic performance assessment on a global scale using artificial neural networks. Sustainable Energy Grids Networks . 38 , 101337. https://doi.org/10.1016/j.segan.2024.101337 (2024). Yadav, A. K., Khargotra, R., Lee, D., Kumar, R. & Singh, T. Novel applications of various neural network models for prediction of photovoltaic system power under outdoor condition of mountainous region. Sustainable Energy Grids Networks . 38 , 101318. https://doi.org/10.1016/j.segan.2024.101318 (2024). Ding, Z. et al. Long-term operation rules of a hydro–wind–photovoltaic hybrid system considering forecast information. Energy . 288 , 129634. https://doi.org/10.1016/j.energy.2023.129634 (2024). Niu, Y. et al. Attend Next: A Mid-Term PV forecasting system with attention mechanism and encoder–decoder structure. Applied Energy . 353, 122169. (2024). https://doi.org/10.1016/j.apenergy.2023.122169 Varga, G., Gresina, F., Szeberényi, J., Gelencsér, A. & Rostási, Á. Effect of Saharan dust episodes on the accuracy of photovoltaic energy production forecast in Hungary (Central Europe). Renew. Sustain. Energy Rev. 193 , 114289. https://doi.org/10.1016/j.rser.2024.114289 (2024). Wang, J., Yu, Y., Zeng, B. & Lu, H. Hybrid ultra-short-term PV power forecasting system for deterministic forecasting and uncertainty analysis. Energy . 288 , 129898. https://doi.org/10.1016/j.energy.2023.129898 (2024). Perera, M., De Hoog, J., Bandara, K., Senanayake, D. & Halgamuge, S. Day-ahead regional solar power forecasting with hierarchical temporal convolutional neural networks using historical power generation and weather data. Appl. Energy . 361 , 122971. https://doi.org/10.1016/j.apenergy.2024.122971 (2024). Tziolis, G. et al. Direct short-term net load forecasting in renewable integrated microgrids using machine learning: A comparative assessment. Sustainable Energy Grids Networks . 37 , 101256. https://doi.org/10.1016/j.segan.2023.101256 (2024). Qamili, A. & Kapia, S. Evaluation and integration of photovoltaic (PV) systems in Albanian energy landscape. Solar Compass . 10 , 100070. https://doi.org/10.1016/j.solcom.2024.100070 (2024). Chen, Y. & Xu, J. Solar and wind power data from the Chinese State Grid Renewable Energy Generation Forecasting Competition. Sci. Data . 9 (1). https://doi.org/10.1038/s41597-022-01696-6 (2022). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4909901","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":354865935,"identity":"6a0816c8-e001-442a-ac95-70fd11d53edb","order_by":0,"name":"Haisheng 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dataset\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-4909901/v1/1aaa0d6b0e1a03a2b98ae831.png"},{"id":64910727,"identity":"e448c63a-3547-467e-a57a-d7582eb6e73d","added_by":"auto","created_at":"2024-09-20 09:42:32","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":114255,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of model predictions\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-4909901/v1/15615451609ffe9284f5ea00.png"},{"id":67629395,"identity":"c9d0811b-d725-41cf-ba98-30785d479e68","added_by":"auto","created_at":"2024-10-28 08:32:25","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2551200,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4909901/v1/f09001c4-ab3c-42b6-8b92-5758c3069b37.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Ultra-short-term Single-step Photovoltaic Power Prediction based on VMD-Attention-BiLSTM Combined Model","fulltext":[{"header":"1. Background","content":"\u003cp\u003ePhotovoltaic power generation is a form of clean energy, and accurate prediction of PV power generation can help power systems better plan and manage energy supply. By forecasting photovoltaic power generation, energy dispatch strategies can be adjusted in advance. Photovoltaic power prediction can be classified into long-term, medium-term\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e, short-term\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e, and ultra-short-term\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e prediction based on the prediction time scale\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. This paper focuses on ultra-short-term\u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e prediction of photovoltaic power\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e"},{"header":"2. Research status","content":"\u003cp\u003eIn the field of photovoltaic power prediction\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e, some scholars have improved the prediction accuracy and model stability through methods such as combining models, data preprocessing, and algorithm improvements\u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e. By setting control experiments to compare the predicted results of photovoltaic power generation under different scenarios, more targeted input features can be provided\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e. Combined models integrate multiple individual prediction models by selecting models with different prediction mechanisms and advantages\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e, which can improve the overall prediction accuracy and stability\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e. For example, combining the attention mechanism with multi-dimensional time series prediction models can capture long-term sequential relationships\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e. Improving algorithms involve optimizing existing algorithms or introducing new algorithmic ideas\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e, reflected in aspects such as improving model parameter learning, feature extraction, and prediction processes\u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e. For instance, using Bayesian optimization algorithms to adjust the most relevant hyperparameters in the model\u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e, a method for predicting daily photovoltaic power generation using Long Short-Term Memory (LSTM)\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e neural networks has been proposed\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. Photovoltaic power generation is influenced by various spatio-temporal factors such as weather conditions\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e, geographical location, and seasonal variations\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e. By extracting spatio-temporal features related to photovoltaic power generation\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e, richer input information can be provided for prediction models\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e. Contrasting different scenarios, combining models, improving algorithms, and extracting spatio-temporal features are all important means to improve the accuracy of photovoltaic power prediction\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e, collectively driving the development and application of photovoltaic power prediction technology\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eIn the field of photovoltaic power generation forecasting, scholars face a series of challenges, including high computational costs, strong volatility and randomness, difficulties in data processing, high uncertainty, equipment group failures, and privacy security issues\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e. To reduce computational costs, scholars have designed efficient algorithms, such as upgrading data\u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e, combining models with new environments\u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e, and integrating artificial intelligence\u003csup\u003e\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e. These methods maintain high prediction accuracy while having low computational complexity. Since photovoltaic power generation is volatile and random due to weather conditions\u003csup\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e, scholars have combined multiple prediction models and introduced uncertainty quantification methods into the prediction models to capture the volatility and randomness of photovoltaic power generation\u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e. To address the difficulties in data processing\u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e, scholars have adopted methods such as data cleaning and preprocessing and the use of robust prediction models\u003csup\u003e\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e. The strong uncertainty in photovoltaic power generation forecasting is reflected in variable weather conditions\u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e, different energy storage, and inconsistent measurement conditions\u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e. Scholars have used probabilistic forecasting methods and scenario analysis to simulate various possible future scenarios\u003csup\u003e\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e. During the operation of photovoltaic equipment, equipment failures are inevitable\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e. Real-time monitoring of the operating status and performance parameters of photovoltaic equipment, as well as the introduction of redundant design and fault-tolerant mechanisms into the photovoltaic system\u003csup\u003e\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e, help maintain the system's continuous power supply capability and reduce the impact of failures on power generation\u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e. During data collection and processing, sensitive information involving user privacy is desensitized and anonymized to protect users' privacy rights\u003csup\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e. In summary, scholars have effectively addressed these issues by adopting efficient algorithms, combined prediction models, data cleaning and preprocessing, probabilistic forecasting methods, fault prediction and health management, and privacy protection technologies. These solutions not only improve prediction accuracy and stability, but also provide strong support for the sustainable development of the photovoltaic industry.\u003c/p\u003e \u003cp\u003eIn the field of PV power prediction, various factors significantly influence the prediction results, which can be broadly categorized into natural and technical factors. Extracting spatiotemporal features from the data can also serve as a crucial factor in enhancing the accuracy of ultra-short-term and short-term PV power predictions\u003csup\u003e\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e. Additionally, conducting experiments by setting variables such as parameters, meteorology, time periods\u003csup\u003e\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e, temperature\u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e, data sequence types\u003csup\u003e\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e, and models allows for exploration through comparative analysis. The humanistic aspects of PV power prediction primarily manifest in its impact on the energy industry, environmental conservation, and socioeconomic factors\u003csup\u003e\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eIn this study, we make the following main contributions: Firstly, we propose a novel VMD-Attention-BiLSTM combination model to enhance prediction accuracy. Through partial ablation experiments, we investigate the roles of each module in the combination model and their impact on prediction. Secondly, we utilize the VMD algorithm to decompose historical PV power data into several sub-sequences, thus increasing data dimensionality and volume. The Attention mechanism computes the correlation coefficients between variables, identifying variables strongly correlated with the output results and increasing the weight of such variables' predictions in the final results. In the empirical section, we conduct multiple experiments, including ablation experiments analyzing the effects of each part of the combination model on the results. Day-night comparisons demonstrate that removing invalid data enhances model accuracy, seasonal comparisons analyze the impact of seasonal variations on power generation, and stride comparisons explore the influence of sliding time window lengths on prediction results. Model comparisons validate the superiority of our proposed model.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe arrangement of other sections is as follows: Section \u003cspan refid=\"Sec3\" class=\"InternalRef\"\u003e3\u003c/span\u003e elaborates on the improved methods and the overall framework flow of the combined model. Section \u003cspan refid=\"Sec3\" class=\"InternalRef\"\u003e3\u003c/span\u003e introduces the experimental results, including data preprocessing and multiple sets of comparative experiments on photovoltaic power generation prediction. Section \u003cspan refid=\"Sec24\" class=\"InternalRef\"\u003e5\u003c/span\u003e summarizes the research. In addition, the research framework proposed in this paper is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e"},{"header":"3. Methodology","content":" \u003cp\u003eIn this section, we first introduce the Variational Mode Decomposition (VMD) algorithm and describe the role of the VMD algorithm module in the model. Next, we introduce the Attention mechanism and its role in the model. Then, we explain the basic mechanism and prediction principle of the proposed BiLSTM model. Finally, the overall architecture of the combined model consisting of these three modules is introduced.\u003c/p\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Variational Mode Decomposition\u003c/h2\u003e \u003cp\u003eVariational Mode Decomposition (VMD) is an adaptive, completely non-recursive method for mode variation and signal processing. It uses iterative search to find the optimal solution of the variational model to determine the center frequency and bandwidth of each decomposed component, thereby decomposing the original signal into modal components with center frequencies and limited bandwidths to enhance robustness.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows the VMD decomposition process in this paper. The original input data consists of historical data of photovoltaic power generation and six conventional variables: total solar irradiance, direct normal irradiance, global horizontal irradiance, air temperature, atmospheric pressure, and relative humidity. To expand the data dimension and increase the proportion of historical data of photovoltaic power generation in the predictive variables, the VMD method is used to decompose the historical data of photovoltaic power generation into several sub-sequences. The center frequencies are calculated when the number of sub-sequences is from 1 to 10, and the number of sub-sequences with stable center frequencies is selected as the optimal number of sub-sequences, generating several sub-sequences. At this point, the input becomes six conventional variables and several sub-sequences of historical data of photovoltaic power generation.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Attention Mechanism\u003c/h2\u003e \u003cp\u003eThe principle of the Attention mechanism is to allow the model to focus its attention on specific parts of the input text while ignoring others, thereby improving the performance and efficiency of the model.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e illustrates the process of the Attention mechanism. The input sequence processed by the VMD module is fed into the Attention mechanism. The embedded input is multiplied by the weight matrix obtained during the training process to calculate the query matrix Q, key matrix K, and value matrix V, which can be expressed as Equation. (1). The softmax function normalizes the attention weights, converting them into a probability distribution. Finally, the correlation coefficients between variables and the weights of each input variable's prediction results in the final output.\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$Attention\\left( {Q,K,V} \\right)=soft\\hbox{max} \\left( {\\frac{{Q{K^T}}}{{\\sqrt {{d_k}} }}} \\right)V$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Bidirectional Long Short-Term Memory model\u003c/h2\u003e \u003cp\u003eThe BiLSTM model, short for Bidirectional Long Short-Term Memory model, is composed of both forward and backward LSTM units. By simultaneously processing the forward and backward information of sequences, BiLSTM can fully utilize the contextual information of sequences, thereby extracting more comprehensive and accurate features during modeling.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e depicts the framework of the BiLSTM model. The input data consists of six conventional variables and n subsequences processed by the VMD and Attention modules. With a time step of m, this forms a two-dimensional matrix of dimensions 6\u0026thinsp;+\u0026thinsp;n by m. After assigning weights to variables, this matrix is fed into the LSTM model. The output is a two-dimensional matrix of dimensions 6\u0026thinsp;+\u0026thinsp;n by 6\u0026thinsp;+\u0026thinsp;n. This output is then separately input into two LSTM models, LSTM1 and LSTM2, for prediction. The results from these two models are merged in the fully connected layer. Subsequently, dimensionality reduction is performed on the merged results to generate the final output.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Improved Framework\u003c/h2\u003e \u003cp\u003eThis paper proposes a multi-input single-output single-step prediction model based on VMD-Attention-BiLSTM. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e illustrates the flowchart of the VMD-Attention-BiLSTM combined model, while Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e depicts a schematic diagram of multi-input single-output single-step prediction.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e illustrates the flowchart of the VMD-Attention-BiLSTM combined model, comprising the VMD module, Attention mechanism module, and BiLSTM module in sequence. The VMD module decomposes PV power generation data into several sub-sequences based on different frequencies to extract data features. The Attention module computes the correlation coefficients among various variables (including three types of radiation, temperature, humidity, atmospheric conditions, historical power sequences, and current power generation), assigning different weights to input variables based on the magnitude of their correlation coefficients with the output variable. The BiLSTM module conducts predictions, using training set data for model learning, validating predictions with validation set data, adjusting model parameters based on results, and evaluating model performance using test set data.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e depicts a schematic diagram of multi-input single-output single-step prediction. Each row of data corresponds to the same time step, and each column corresponds to the same variable. The rightmost column represents the output, while the rest of the columns represent the inputs. The goal is to predict the value of the output variable at time step t using data from time steps t-m to t-1 of n input variables, as illustrated by the red box in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e predicting the value inside the red circle.\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Experiment","content":"\u003cp\u003eThis section covers the experimental part, including data preprocessing, introduction of evaluation metrics, and presentation of experimental results.\u003c/p\u003e\n\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\n \u003ch2\u003e4.1 Data Set\u003c/h2\u003e\n \u003cp\u003eThis subsection sequentially introduces the data source, handling of outliers, missing values, and invalid values, normalization method, data set division, and variable analysis.\u003c/p\u003e\n \u003cdiv id=\"Sec10\" class=\"Section3\"\u003e\n \u003ch2\u003e4.1.1 Data Source\u003c/h2\u003e\n \u003cp\u003eThe data used in this study are from the solar energy data of the renewable energy generation prediction competition held by the State Grid Corporation of China. The data set contains 7 variables, namely, total solar irradiance, direct normal irradiance, global horizontal irradiance, air temperature, atmospheric relative humidity, and photovoltaic power generation. The data collection period spans from January 1, 2019, 0:00 to December 31, 2020, 24:00, with data points collected at 15-minute intervals, totaling 70,176 data points. Each data point consists of measurements of 7 variables at a single time step.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec11\" class=\"Section3\"\u003e\n \u003ch2\u003e4.1.2 Handling of Outliers, Missing Values, and Invalid Values\u003c/h2\u003e\n \u003cp\u003eOutliers in the data set, such as negative power generation or positive irradiance during nighttime, are identified based on environmental and time criteria and subsequently removed. The removed outliers are treated as missing values along with any existing missing values in the data set.\u003c/p\u003e\n \u003cp\u003eMissing values are filled using linear interpolation, considering the low and nearly discontinuous missing rate in the data set and the continuous and small-scale trends in the data, as per Equation. (2).\u003c/p\u003e\n \u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e$$y={y_0}+\\left( {x - {x_0}} \\right)\\frac{{{y_1} - {y_0}}}{{{x_1} - {x_0}}}$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eSince photovoltaic power generation relies primarily on daylight, nighttime data where power generation is consistently zero are considered invalid and thus removed, while daytime data are retained.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec12\" class=\"Section3\"\u003e\n \u003ch2\u003e4.1.3 Normalization\u003c/h2\u003e\n \u003cp\u003eThe data are normalized to the [0,1] interval using the min-max normalization method. Normalization accelerates model speed, increases model stability, and enhances model accuracy, as described by Equation. (3).\u003c/p\u003e\n \u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"350\" height=\"51\"\u003e\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eThe data in which \u003cem\u003ex\u003c/em\u003e is any data from dataset, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x_{\\hbox{max} }}\\)\u003c/span\u003e\u003c/span\u003e is the maximum value in the dataset, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x_{\\hbox{min} }}\\)\u003c/span\u003e\u003c/span\u003eis the minimum value in the dataset, and \u003cem\u003ex\u0026apos;\u0026nbsp;\u003c/em\u003eis the normalized value.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec13\" class=\"Section3\"\u003e\n \u003ch2\u003e4.1.4 Data Set Division\u003c/h2\u003e\n \u003cp\u003eAfter the aforementioned steps, the new data set consists of 30,881 data points. The data set is divided into training, validation, and testing sets in a ratio of 7:2:1. The training set, comprising 70% of the data, is used to train the model, with a time span from January 1, 2019, 9:15 to June 4, 2020, 20:45. The validation set, comprising 20% of the data, is used for model adjustment and parameter optimization, with a time span from June 5, 2020, 6:15 to October 11, 2020, 12:15. The testing set, comprising 10% of the data, is used to evaluate model performance, with a time span from October 11, 2020, 12:30 to December 31, 2020, 18:15.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec14\" class=\"Section3\"\u003e\n \u003ch2\u003e4.1.5 Variable Analysis\u003c/h2\u003e\n \u003cp\u003eTotal solar irradiance: Represents the energy intensity of solar radiation reaching the Earth\u0026apos;s surface in watts per square meter (W/m\u0026sup2;). Higher total solar irradiance leads to increased stability in photovoltaic power output, while lower irradiance results in decreased output power.\u003c/p\u003e\n \u003cp\u003eDirect normal irradiance: Refers to the radiation intensity of sunlight perpendicular to the Earth\u0026apos;s surface in W/m\u0026sup2;. It directly affects the amount of solar energy received by photovoltaic panels. Increasing direct normal irradiance enhances photovoltaic power output, ensuring the stability of the system.\u003c/p\u003e\n \u003cp\u003eGlobal horizontal irradiance: Represents the total irradiance of the sun on the Earth\u0026apos;s horizontal plane in W/m\u0026sup2;. It determines the amount of solar radiation energy received by photovoltaic panels. Higher global horizontal irradiance leads to increased output power of photovoltaic systems.\u003c/p\u003e\n \u003cp\u003eAir temperature: Affects photovoltaic power generation by influencing the operating temperature and efficiency of photovoltaic panels in degrees Celsius (\u0026deg;C). Beyond a certain range, temperature increase can decrease photovoltaic conversion efficiency, leading to panel aging and increased failure rates, thus reducing photovoltaic power output.\u003c/p\u003e\n \u003cp\u003eAtmospheric pressure: Measured in hPa. Factors such as atmospheric clarity, cloud thickness, and weather conditions affect the intensity of sunlight reaching the ground and solar radiation. Particles and pollutants in the atmosphere absorb and scatter solar radiation, reducing the intensity of radiation received by photovoltaic components.\u003c/p\u003e\n \u003cp\u003eRelative humidity: High humidity may cause surface water or condensation on photovoltaic components, reducing light transmittance and thus lowering photovoltaic conversion efficiency. Humidity also affects the heat dissipation of photovoltaic systems and exacerbates corrosion and aging of photovoltaic components.\u003c/p\u003e\n \u003cp\u003eHistorical data subseries of photovoltaic power generation: Data subseries at different frequencies reflect the operating characteristics of photovoltaic power stations at different time scales. High-frequency data capture instantaneous power fluctuations of photovoltaic power stations, suitable for real-time and short-term predictions, while low-frequency data reflect long-term operating trends, suitable for long-term predictions and trend analysis. Different frequency data subseries complement each other and can be used for mutual verification and supplementation.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003ctable id=\"Tab1\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eDescriptive Information of Variables\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eVariables\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMean\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMaximum\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMinimum\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eStd\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSkewness\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eKurtosis\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTotal solar irradiance\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e560.64\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1359.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e349.45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.66\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDirect normal irradiance\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e209.33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e980.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e257.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.94\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGlobal horizontal irradiance\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e137.68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e989.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e120.81\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10.00\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAir temperature\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e16.51\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e40.90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-17.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e14.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.81\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.73\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAtmosphere\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e911.56\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e936.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e894.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e32.12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-29.24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e920.32\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRelative humidity\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1055.19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e6553.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2386.70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.87\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.49\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ePower\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e20.46\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e48.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e13.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.75\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eTable \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e presents descriptive information for 7 variables. After data preprocessing, the minimum value of irradiance is 1, while the minimum values for relative humidity and photovoltaic power generation are 0. Due to the significant variation in irradiance throughout the day, following a timeline from 0 at sunrise, reaching a maximum, then decreasing back to 0 at sunset, the standard deviation of irradiance is large. Air temperature, atmospheric pressure, and relative humidity remain relatively stable.\u003c/p\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\n \u003ch2\u003e4.2 Evaluation Metrics\u003c/h2\u003e\n \u003cp\u003eEvaluation of model predictive performance is conducted using Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and the coefficient of determination (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R^2}\\)\u003c/span\u003e\u003c/span\u003e). MAE measures the average absolute difference between predicted and actual values, intuitively reflecting the size of prediction errors and the precision of the model\u0026apos;s predictions. MSE measures the average squared difference between predicted and actual values, reflecting the stability of the model\u0026apos;s prediction results. A smaller RMSE indicates a stronger predictive ability of the model. The coefficient of determination measures the proportion of the variance in the output variable explained by the model, reflecting the degree to which the model fits the data. Its value ranges from 0 to 1, with a value closer to 1 indicating a better fit of the model to the data. The formulas for evaluation metrics are as follows:\u003c/p\u003e\n \u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e$$MAE=\\frac{1}{n}\\sum\\limits_{{t=1}}^{n} {\\left| {{{\\hat {y}}_t} - {y_t}} \\right|}$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e$$MSE=\\frac{1}{n}\\sum\\limits_{{t=1}}^{n} {{{\\left( {{{\\hat {y}}_t} - {y_t}} \\right)}^2}}$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e$$RMSE=\\sqrt {\\frac{1}{n}\\sum\\limits_{{t=1}}^{n} {{{\\left( {{{\\hat {y}}_t} - {y_t}} \\right)}^2}} }$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e$${R^2}=1 - \\frac{{\\sum\\limits_{{t=1}}^{n} {{{\\left( {{y_t} - {{\\hat {y}}_t}} \\right)}^2}} }}{{\\sum\\limits_{{t=1}}^{n} {{{\\left( {{y_t} - {{\\bar {y}}_t}} \\right)}^2}} }}$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec16\" class=\"Section2\"\u003e\n \u003ch2\u003e4.3 Subsequence Decomposition\u003c/h2\u003e\n \u003cp\u003eThe photovoltaic power generation historical data was decomposed into subsequence counts ranging from 1 to 10, and the central frequency was calculated after each decomposition. It was determined that the central frequency was most stable when the subsequence count was 8, thus establishing the optimal subsequence decomposition count as 8. As shown in Fig. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e, the top solid black line represents the original power data before decomposition, while the 8 rows of solid blue lines below represent the high, medium, and low-frequency components IMF1-IMF7.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec17\" class=\"Section2\"\u003e\n \u003ch2\u003e4.4 Attention Mechanism\u003c/h2\u003e\n \u003cp\u003eThrough the attention mechanism, correlations between 15 factors were calculated, including total solar irradiance, direct normal irradiance, global horizontal irradiance, air temperature, atmospheric relative humidity, 7 subsequences after decomposition of photovoltaic power generation historical data, and photovoltaic power generation. The first 14 are input variables, and the last one is the output variable. The correlation heat map between variables is illustrated in Fig. \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e indicates that most variables exhibit weak positive correlations, with correlation coefficients around [0,0.4]. However, there are a few variables that show strong associations, such as total solar irradiance and the output variable, as well as the IMF7 and the output variable. This is because total solar irradiance represents sunlight intensity, and the frequency of the IMF7 occupies a significant proportion in the historical data of photovoltaic power generation, resulting in a strong positive correlation between them. Additionally, there are a few variables that show weak negative correlations, such as the IMF8 and temperature, and the direct normal irradiance and global horizontal irradiance, with correlation coefficients falling within the [-0.2,0] range.\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003ctable id=\"Tab2\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eCorrelation coefficients\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eVariable\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCorrelation coefficient with output variable\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eOutput\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTotal Solar Irradiance\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.880215\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIMF7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.744364\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIMF6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.606838\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRES\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.416276\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDirect Normal Irradiance\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.401422\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGlobal Horizontal Irradiance\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.357829\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIMF5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.32927\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIMF4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.196439\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIMF3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.12812\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIMF2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.095738\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIMF1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.075753\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRelative Humidity\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.073687\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAtmosphere\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.05432\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAir Temperature\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.044742\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003eTable \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e presents the correlation coefficients between each input variable and the photovoltaic power output variable, with variables sorted from top to bottom based on their correlation coefficients with the photovoltaic power output variable. From the data, it can be observed that the output variable has strong positive correlations with total solar irradiance, the IMF7, and the IMF6, with correlation coefficients of 0.880215, 0.744364, and 0.606838, respectively. This indicates that a surge in irradiance promotes a larger energy pool for photovoltaic cells to convert into electricity, thus increasing the power output. As the frequency decreases from IMF1 to IMF7, the correlation coefficients with the photovoltaic power output variable gradually decrease from 0.744364 to 0.075753. Higher-frequency subsequences, which have a higher proportion in the original sequence, exhibit larger correlation coefficients. Relative humidity, atmospheric pressure, and temperature show weak positive correlations with photovoltaic power generation, with coefficients of 0.073687, 0.05432, and 0.044742, respectively, all below 0.1. These nonlinear relationships among variables suggest that they do not directly impact photovoltaic power generation but rather indirectly influence electricity output by affecting other meteorological factors.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec18\" class=\"Section2\"\u003e\n \u003ch2\u003e4.5 Ablation Experiment\u003c/h2\u003e\n \u003cp\u003eThe ablation study is a scientific research method used to determine the impact of key components of a condition, parameter, or system on overall performance. This method involves systematically controlling or modifying specific parts of a system one by one to observe how these changes affect the system\u0026apos;s functionality, performance, or behavior. Ablation experiments can enhance model transparency, optimize model performance, validate the effectiveness of specific functions or components, and enhance the integrity and credibility of research.\u003c/p\u003e\n \u003cp\u003eThis subsection sets up ablation experiments to explore the roles of various modules in the composite model and their contributions to improving model accuracy. The ablation experiment groups include four experimental groups: VMD-Attention-BiLSTM model, Attention-BiLSTM model, VMD-BiLSTM model, and VMD-Attention-LSTM model.\u003c/p\u003e\n \u003cp\u003eIn Fig. \u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e, there are five solid lines representing the predicted results of the ablation experiment. They correspond to the true values of 50 samples taken throughout the day and the results under different models. The black solid line representing the true values appears relatively smooth and natural. However, the other four prediction curves exhibit varying degrees of fluctuation and curvature, indicating differences in the performance of these models at different time points. The samples are taken from 0 to 25 during the period from sunrise to midday. As the sunlight intensifies, the power generation increases. During this period, the predicted values of the four models are relatively close to each other, but deviate significantly from the true values. Among them, the VMD-Attention-LSTM experimental group and the VMD-BiLSTM experimental group have slightly higher accuracy compared to the other two groups. The samples taken from 25 to 50 are from midday to sunset, during which the solar irradiance decreases and the power generation decreases. During this period, the results of the four prediction experiments fluctuate in line with the changing trend of the true values, intertwining with each other. The true values are closest to the VMD-Attention-BiLSTM model.\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003ctable id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eErrors in ablation experiments\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAblation experiments\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMAE\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMSE\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eRMSE\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R^2}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eVMD-Attention-BiLSTM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.1123\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.0207\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.1438\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.8835\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAttention-BiLSTM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1516\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0339\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1840\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.7956\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eVMD-BiLSTM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1208\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0238\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1544\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.8641\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eVMD-Attention-LSTM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1132\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0214\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1464\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.8862\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003eTable \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e presents the prediction results of the four experimental groups in the ablation experiment, comparing model performance using four evaluation metrics. Among them, the VMD-Attention-BiLSTM model has the lowest MAE, MSE, and RMSE, which are 0.1123, 0.0207, and 0.1438 respectively. The VMD-Attention-LSTM group has the highest \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R^2}\\)\u003c/span\u003e\u003c/span\u003eof 0.8862. Arranging the metrics from lowest to highest, the sequence for MAE, MSE, and RMSE is: VMD-Attention-BiLSTM experimental group, VMD-Attention-LSTM experimental group, VMD-BiLSTM experimental group, and Attention-BiLSTM experimental group. This indicates that decomposing the sequence has the greatest impact on improving prediction accuracy, followed by allocating weights using attention mechanism, while the least impactful is the bidirectional structure of the LSTM model. Regarding \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R^2}\\)\u003c/span\u003e\u003c/span\u003e, arranged from highest to lowest, the sequence is: VMD-Attention-LSTM experimental group, VMD-Attention-BiLSTM experimental group, VMD-BiLSTM experimental group, and Attention-BiLSTM experimental group. Moreover, the difference in\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R^2}\\)\u003c/span\u003e\u003c/span\u003ebetween the VMD-Attention-LSTM experimental group and the VMD-Attention-BiLSTM experimental group is only 0.0027, suggesting that the bidirectional structure of the LSTM model has a minimal impact on data fitting in the combined model.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec19\" class=\"Section2\"\u003e\n \u003ch2\u003e4.6 Comparative experiments\u003c/h2\u003e\n \u003cp\u003eThis section establishes four sets of comparative experiments: day and night, seasons, step length, and models. Visualization graphs of prediction results and error tables of evaluation metrics are utilized to compare the performance of different datasets or models, exploring the effects of different variables, data processing methods, and environments on photovoltaic power prediction.\u003c/p\u003e\n \u003cdiv id=\"Sec20\" class=\"Section3\"\u003e\n \u003ch2\u003e4.6.1 Day and night comparison\u003c/h2\u003e\n \u003cp\u003eThe dataset is divided into daytime and full-day datasets based on sunlight hours. The full-day dataset includes data for all 24 hours of the day, including nighttime data when photovoltaic power is zero. The daytime dataset, on the other hand, is derived from the full-day dataset by removing all data points where photovoltaic power is zero. Both datasets undergo the same data preprocessing steps and are used for combined model predictions to investigate the impact of nighttime values on prediction.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e illustrates the comparison between the prediction results of the daytime dataset and the full-day dataset. The horizontal axis represents a time span of one week (7 days), with the black solid line indicating the trend of real values. Subplot (a) presents the comparison between the prediction results and real values of the daytime dataset, with 320 samples. The predicted values are depicted by the green solid line. Subplot (b) illustrates the comparison for the full-day dataset, containing 680 samples, with the predicted values shown by the red solid line. In subplot (a), the 3rd day is rainy, and the 7th day is cloudy, while the remaining 5 days are sunny. During sunny and cloudy days, the predicted values exhibit a significant deviation below the real values in the morning hours, but align closely with the real values in the afternoon, indicating good prediction accuracy. However, on rainy days, due to rapid power fluctuations caused by cloud cover, the prediction accuracy is slightly lower. In subplot (b), the 1st day is cloudy, and the remaining 6 days are sunny. The prediction for the cloudy day fails to capture the extreme peak in real values, while on sunny days, there is a lag between the predicted and real values, resulting in misalignment of the two curves. Additionally, the predicted values fail to simulate the peak in photovoltaic power generation during the strongest sunlight hours around noon, and they also lag behind in reaching zero at sunset compared to the real values.\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003ctable id=\"Tab4\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eErrors for the daytime dataset and the all-day dataset\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eDataset\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMAE\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMSE\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eRMSE\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R^2}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDaytime dataset\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.1123\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.0207\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.1438\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.8835\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAll-day dataset\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1436\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0325\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1804\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.8386\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003eTable \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e presents the errors for both the daytime and full-day datasets. From the table, it can be observed that the MAE, MSE, RMSE and\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R^2}\\)\u003c/span\u003e\u003c/span\u003eof the daytime dataset are all better than those of the full-day dataset. This indicates that the prediction accuracy, stability, capability, and fitting degree are higher when using the daytime dataset, further suggesting that removing nighttime values can reduce data redundancy and make the dataset more refined and effective.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec21\" class=\"Section3\"\u003e\n \u003ch2\u003e4.6.2 Seasonal comparisons\u003c/h2\u003e\n \u003cp\u003eThe dataset is divided into spring, summer, autumn, and winter datasets based on seasonal variations, covering the periods from March to May, June to August, September to November, and December to February for the years 2019 and 2020, respectively. These four datasets undergo the same data preprocessing and combined model prediction to investigate the impact of seasonal changes on predictions.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e11\u003c/span\u003e depicts the comparative forecast results of the seasonal dataset, comprising four subplots, each representing the prediction results for one week in the corresponding seasonal dataset. Subplot (a) shows that the trend of the predicted values is close to the actual values, but the predicted values fail to simulate peak changes when abrupt changes occur in the actual values. Subplot (b) illustrates that the variation in predicted values is synchronized with the actual values, with the two curves overlapping closely most of the time; however, the predicted values can only roughly simulate the numerical range when abrupt changes occur in the actual values, failing to accurately capture every short-term extreme change. In subplot (c), there are several peaks in the actual values on overcast days, while the predicted values can roughly simulate one peak. Subplot (d) shows that the predicted values almost coincide with the actual values, with slight discrepancies in numerical simulation when there are short-term abrupt changes in the actual values, indicating the best prediction performance.\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003ctable id=\"Tab5\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eSeasonal dataset errors\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSeason\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMAE\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMSE\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eRMSE\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R^2}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSpring\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.2656\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1153\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3396\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.8375\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSummer\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.2864\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1310\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3619\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.8468\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAutumn\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.2673\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1147\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3386\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.8486\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWinter\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.2477\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.1038\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.3222\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.8334\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003eTable \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e presents the numerical values of four evaluation metrics corresponding to the four seasons. The MAE, MSE, and RMSE of the winter dataset are the lowest, at 0.2477, 0.1038, and 0.3222, respectively, while the\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R^2}\\)\u003c/span\u003e\u003c/span\u003eof the autumn dataset is the highest, at 0.8486. The numerical values of MAE, MSE, and RMSE indicate that the overall prediction accuracy from highest to lowest is in the order of winter, autumn, spring, and summer. Winter experiences fewer cloudy days, relatively stable weather patterns, and abundant and stable sunlight. Conversely, summer exhibits significant weather fluctuations, more rainy days, and difficulties in accurately predicting cloud cover changes, which may lead to decreased output power of photovoltaic panels due to extremely high temperatures.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec22\" class=\"Section3\"\u003e\n \u003ch2\u003e4.6.3 Comparison of step lengths\u003c/h2\u003e\n \u003cp\u003eBy categorizing according to time step lengths, the four datasets can be divided into predicting the next time point value every 4, 8, 12, or 16 time steps. Since the data are collected every 15 minutes in the dataset, these four datasets use data from the previous 1, 2, 3, or 4 hours to predict the next time point data.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e12\u003c/span\u003e presents a comparison of the prediction results for datasets with different time steps. Subplot (a) exhibits the highest overlap between actual values and predicted values, while subplots (b), (c), and (d) show varying degrees of deviation around the midday peak values.\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003ctable id=\"Tab6\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eErrors in the step size dataset\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eStep size\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMAE\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMSE\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eRMSE\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R^2}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.1962\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.0616\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.2483\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.9297\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.2441\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0976\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3125\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.8598\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.2801\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1212\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3481\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9097\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.2455\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0942\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3069\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9272\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003eTable \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e displays the error indicator data corresponding to different step lengths. Overall, when using data from the previous 4 time steps to predict the next time step, the MAE, MSE, RMSE, and\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R^2}\\)\u003c/span\u003e\u003c/span\u003eare optimal, followed by using data from the previous 8 time steps, then 16 time steps, and finally 12 time steps. This is because in photovoltaic power generation forecasting, the operation of photovoltaic systems and weather conditions change minimally over short periods of time, and shorter time steps can more accurately capture the temporal correlation of the data. Longer time step models need to deal with more variables and uncertainties, which may lead to a decrease in prediction accuracy. As the prediction time step increases, errors may gradually accumulate, potentially significantly affecting the final prediction accuracy.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec23\" class=\"Section3\"\u003e\n \u003ch2\u003e4.6.4 Comparison of models\u003c/h2\u003e\n \u003cp\u003eIn this subsection, various prediction models, including the proposed VMD-Attention-BiLSTM composite model, and baseline models such as the LSTM model, CNN model, and RNN model, for forecasting the daytime dataset. The time step is uniformly set to 8, while the remaining model hyperparameters are set to their respective optimal configurations.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e13\u003c/span\u003e illustrates the comparison of all models used in this section for predicting photovoltaic power generation on the dataset, which spans three consecutive days. Due to significant performance variations of the models at different time intervals, certain weather factors affect prediction accuracy. From the Fig., it can be observed that on the first day (samples 0\u0026ndash;50), the CNN and RNN models predict values close to the ground truth in the morning, with none of the models predicting the peak value that appears at noon. In the afternoon, the prediction of each model is relatively close to the ground truth. On the second day (samples 51\u0026ndash;110), overcast conditions in the midday result in insufficient sunlight and a decrease in power generation. The trend predicted by the proposed model in this paper is similar to the ground truth, while the other models still show clear weather predictions based on the morning trends of the second day. On the third day (samples 111\u0026ndash;170), the predicted trends of all models are consistent, with slight numerical deviations.\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003ctable id=\"Tab7\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eErrors of the models\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eModel\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMAE\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMSE\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eRMSE\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R^2}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eProposed\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.1123\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.0207\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.1438\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.8835\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eLSTM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.2867\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1274\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3569\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.7910\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCNN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.1579\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0520\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.2280\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.9258\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRNN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.2142\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0787\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.2805\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.8956\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003eTable \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e displays the performance metrics of prediction errors for each model. The proposed model exhibits the lowest MAE, MSE, and RMSE, with values of 0.1123, 0.0207, and 0.1438, respectively, while the CNN model shows the highest values, with an\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R^2}\\)\u003c/span\u003e\u003c/span\u003eof 0.9258. From the perspective of MAE, MSE, and RMSE, the prediction accuracy decreases from our proposed model to the CNN model, RNN model, and LSTM model sequentially. The proposed model, which incorporates subsequence decomposition and weight allocation, effectively reduces prediction errors. In terms of fitting ability, the models rank from highest to lowest as CNN model, RNN model, our proposed model, and LSTM model. This indicates that the CNN model and RNN model exhibit higher short-term prediction fitting but lower long-term trend prediction ability compared to our proposed model.\u003c/p\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eIn order to enhance the accuracy of ultra-short-term photovoltaic power prediction, this study proposes a VMD-Attention-BiLSTM combined model and evaluates its performance. The main conclusions are as follows: Firstly, VMD decomposes the original time series data of photovoltaic power generation into multiple modal components with different frequency characteristics. This decomposition process helps refine the information in the original data, reduce data non-stationarity, and improve modeling accuracy. Secondly, the Attention mechanism plays a crucial role in the model by dynamically focusing on important parts of different modal components, further improving prediction accuracy. Lastly, BiLSTM, as the core part of the model, captures long-term dependencies in time series data. In summary, the VMD-Attention-BiLSTM combined model integrates the respective characteristics of VMD, Attention, and BiLSTM, enabling a more accurate description of the variation patterns of photovoltaic power generation and improving prediction accuracy. Additionally, this study conducts multiple control experiments, including ablation analysis of the modules in the combined model, day-night comparison experiments demonstrating the simplification of data by removing nighttime data, seasonal comparison experiments showing the influence of different seasonal features on power generation, stride comparison experiments indicating that appropriate time steps can improve prediction accuracy and avoid error accumulation, and model comparison experiments demonstrating the superiority of the proposed model in prediction accuracy and stability, as well as its adaptability in different prediction environments.\u003c/p\u003e \u003cp\u003eAlthough the VMD-Attention-BiLSTM combined model exhibits high accuracy in single-step photovoltaic power prediction, there is room for improvement. Due to the large amount of data, the next step involves adding a data preprocessing step to simplify the data, facilitating the extraction of features as soon as possible. The hierarchical structure of the model results in long execution times, necessitating improvements to reduce runtime while maintaining result accuracy and stability.\u003c/p\u003e \u003cp\u003eIn summary, the VMD-Attention-BiLSTM combined model possesses many advantages in predicting photovoltaic power generation. By integrating the characteristics of VMD, Attention, and BiLSTM, it can more accurately describe the variation patterns of photovoltaic power generation and improve prediction accuracy. These advantages make the model widely applicable in the field of photovoltaic power generation prediction.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe datasets analyzed during the current study are available from the corresponding author on reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgments\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was supported by Social Science Planning Project of Shandong Province (22CSDJ13).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eHaisheng Yu: Funding acquisition, Resources, Supervision, Writing \u0026ndash; review and editing. Shenhui Song: Conceptualization, Data curation, Methodology, Software, Validation, Visualization, Writing \u0026ndash; original draft.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eYu, C. et al. A new temporal frequency ensemble transformer for day-ahead photovoltaic power prediction. \u003cem\u003eJ. Clean. Prod.\u003c/em\u003e \u003cb\u003e448\u003c/b\u003e, 141690. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.jclepro.2024.141690\u003c/span\u003e\u003cspan address=\"10.1016/j.jclepro.2024.141690\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eliu, Q., li, Y., jiang, H., chen, Y. \u0026amp; zhang, J. Short-term photovoltaic power forecasting based on multiple mode decomposition and parallel bidirectional long short term combined with convolutional neural networks. \u003cem\u003eEnergy\u003c/em\u003e. \u003cb\u003e286\u003c/b\u003e, 129580. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.energy.2023.129580\u003c/span\u003e\u003cspan address=\"10.1016/j.energy.2023.129580\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiu, W. \u0026amp; Mao, Z. Short-term photovoltaic power forecasting with feature extraction and attention mechanisms. \u003cem\u003eRenew. Energy\u003c/em\u003e. \u003cb\u003e226\u003c/b\u003e, 120437. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.renene.2024.120437\u003c/span\u003e\u003cspan address=\"10.1016/j.renene.2024.120437\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSabadus, A. et al. A cross-sectional survey of deterministic PV power forecasting: Progress and limitations in current approaches. \u003cem\u003eRenew. Energy\u003c/em\u003e. \u003cb\u003e226\u003c/b\u003e, 120385. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.renene.2024.120385\u003c/span\u003e\u003cspan address=\"10.1016/j.renene.2024.120385\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZang, H. et al. Improving ultra-short-term photovoltaic power forecasting using a novel sky-image-based framework considering spatial-temporal feature interaction. \u003cem\u003eEnergy\u003c/em\u003e. \u003cb\u003e293\u003c/b\u003e, 130538. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.energy.2024.130538\u003c/span\u003e\u003cspan address=\"10.1016/j.energy.2024.130538\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKhalil, I. U. \u0026amp; Haq ul Islam, N. A novel procedure for photovoltaic fault forecasting. \u003cem\u003eElectr. Power Syst. Res.\u003c/em\u003e \u003cb\u003e226\u003c/b\u003e, 109881. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.epsr.2023.109881\u003c/span\u003e\u003cspan address=\"10.1016/j.epsr.2023.109881\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhou, S., Lu, W., Li, W. \u0026amp; Wang, S. Forecasting the temperature of a building-integrated photovoltaic panel equipped with phase change material using artificial neural network. \u003cem\u003eCase Stud. Therm. Eng.\u003c/em\u003e \u003cb\u003e57\u003c/b\u003e, 104355. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.csite.2024.104355\u003c/span\u003e\u003cspan address=\"10.1016/j.csite.2024.104355\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLi, G. et al. Research on a novel photovoltaic power forecasting model based on parallel long and short-term time series network. \u003cem\u003eEnergy\u003c/em\u003e. \u003cb\u003e293\u003c/b\u003e, 130621. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.energy.2024.130621\u003c/span\u003e\u003cspan address=\"10.1016/j.energy.2024.130621\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eXu, S., Zhang, R., Ma, H., Ekanayake, C. \u0026amp; Cui, Y. On vision transformer for ultra-short-term forecasting of photovoltaic generation using sky images. \u003cem\u003eSol. Energy\u003c/em\u003e. \u003cb\u003e267\u003c/b\u003e, 112203. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.solener.2023.112203\u003c/span\u003e\u003cspan address=\"10.1016/j.solener.2023.112203\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHu, Z., Gao, Y., Ji, S., Mae, M. \u0026amp; Imaizumi, T. Improved multistep ahead photovoltaic power prediction model based on LSTM and self-attention with weather forecast data. \u003cem\u003eAppl. Energy\u003c/em\u003e. \u003cb\u003e359\u003c/b\u003e, 122709. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.apenergy.2024.122709\u003c/span\u003e\u003cspan address=\"10.1016/j.apenergy.2024.122709\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLee, D. S., Lai, C. W. \u0026amp; Fu, S. K. A short- and medium-term forecasting model for roof PV systems with data pre-processing. \u003cem\u003eHeliyon\u003c/em\u003e. \u003cb\u003e10\u003c/b\u003e (6), e27752. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.heliyon.2024.e27752\u003c/span\u003e\u003cspan address=\"10.1016/j.heliyon.2024.e27752\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSakib, S. et al. Attention-Based Models for Multivariate Time Series Forecasting: Multi-step Solar Irradiation Prediction. \u003cem\u003eHeliyon\u003c/em\u003e. 10, (6), e27795. (2024). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.heliyon.2024.e27795\u003c/span\u003e\u003cspan address=\"10.1016/j.heliyon.2024.e27795\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAit Mansour, A., Tilioua, A., Touzani, M. \u0026amp; Bi-LSTM GRU and 1D-CNN models for short-term photovoltaic panel efficiency forecasting case amorphous silicon grid-connected PV system. \u003cem\u003eResults Eng.\u003c/em\u003e \u003cb\u003e21\u003c/b\u003e, 101886. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.rineng.2024.101886\u003c/span\u003e\u003cspan address=\"10.1016/j.rineng.2024.101886\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiu, J. \u0026amp; Li, T. Multi-step power forecasting for regional photovoltaic plants based on ITDE-GAT model. \u003cem\u003eEnergy\u003c/em\u003e. \u003cb\u003e130468\u003c/b\u003e \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.energy.2024.130468\u003c/span\u003e\u003cspan address=\"10.1016/j.energy.2024.130468\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eShi, J., Wang, S., Qu, P. \u0026amp; Shao, J. Time series prediction model using LSTM-Transformer neural network for mine water inflow. \u003cem\u003eSci. Rep.\u003c/em\u003e \u003cb\u003e14\u003c/b\u003e (1). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41598-024-69418-z\u003c/span\u003e\u003cspan address=\"10.1038/s41598-024-69418-z\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHerrera Casanova, R. \u0026amp; Conde, A. Enhancement of LSTM models based on data pre-processing and optimization of Bayesian hyperparameters for day-ahead photovoltaic generation prediction. \u003cem\u003eComput. Electr. Eng.\u003c/em\u003e \u003cb\u003e116\u003c/b\u003e, 109162. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.compeleceng.2024.109162\u003c/span\u003e\u003cspan address=\"10.1016/j.compeleceng.2024.109162\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHong, Y. Y. \u0026amp; Martinez, J. J. F. Forecasting solar irradiation using convolutional long short-term memory and feature selection of data from neighboring locations. \u003cem\u003eSustainable Energy Grids Networks\u003c/em\u003e. \u003cb\u003e38\u003c/b\u003e, 101271. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.segan.2023.101271\u003c/span\u003e\u003cspan address=\"10.1016/j.segan.2023.101271\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBai, M. et al. Spatial-temporal characteristics analysis of solar irradiance forecast errors in Europe and North America. \u003cem\u003eEnergy\u003c/em\u003e. \u003cb\u003e297\u003c/b\u003e, 131187. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.energy.2024.131187\u003c/span\u003e\u003cspan address=\"10.1016/j.energy.2024.131187\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBai, M. et al. Deep graph gated recurrent unit network-based spatial\u0026ndash;temporal multi-task learning for intelligent information fusion of multiple sites with application in short-term spatial\u0026ndash;temporal probabilistic forecast of photovoltaic power. \u003cem\u003eExpert Syst. Appl.\u003c/em\u003e \u003cb\u003e240\u003c/b\u003e, 122072. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.eswa.2023.122072\u003c/span\u003e\u003cspan address=\"10.1016/j.eswa.2023.122072\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNguyen-Duc, T., Nguyen-Trong, T., Nguyen-Hoang-Minh, G., Fujita, G. \u0026amp; Tran-Thanh, S. Spectral-temporal convolutional approach for PV systems output power forecasting: Case studies in single-site and multi-site. \u003cem\u003eSustainable Energy Grids Networks\u003c/em\u003e. \u003cb\u003e38\u003c/b\u003e, 101357. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.segan.2024.101357\u003c/span\u003e\u003cspan address=\"10.1016/j.segan.2024.101357\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZang, H. et al. Multi-site solar irradiance forecasting based on adaptive spatiotemporal graph convolutional network. \u003cem\u003eExpert Syst. Appl.\u003c/em\u003e \u003cb\u003e236\u003c/b\u003e, 121313. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.eswa.2023.121313\u003c/span\u003e\u003cspan address=\"10.1016/j.eswa.2023.121313\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLong, H. et al. Defect monitoring method for Al-CFRTP UFSW based on BWO\u0026ndash;VMD\u0026ndash;HHT and ResNet. \u003cem\u003eScientific Reports\u003c/em\u003e. 14, (1). (2024). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41598-024-69596-w\u003c/span\u003e\u003cspan address=\"10.1038/s41598-024-69596-w\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAbouzeid, A. F. et al. Experimental validation of a low-cost maximum power point tracking technique based on artificial neural network for photovoltaic systems. \u003cem\u003eScientific Reports\u003c/em\u003e. 14, (1). (2024). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41598-024-67306-0\u003c/span\u003e\u003cspan address=\"10.1038/s41598-024-67306-0\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang, H., Mao, L., Zhang, H. \u0026amp; Wu, Q. Multi-prediction of electric load and photovoltaic solar power in grid-connected photovoltaic system using state transition method. \u003cem\u003eAppl. Energy\u003c/em\u003e. \u003cb\u003e353\u003c/b\u003e, 122138. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.apenergy.2023.122138\u003c/span\u003e\u003cspan address=\"10.1016/j.apenergy.2023.122138\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMeng, X., Shi, X., Wang, W., Zhang, Y. \u0026amp; Gao, F. An upscaling minute-level regional photovoltaic power forecasting scheme. \u003cem\u003eInt. J. Electr. Power Energy Syst.\u003c/em\u003e \u003cb\u003e155\u003c/b\u003e, 109609. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.ijepes.2023.109609\u003c/span\u003e\u003cspan address=\"10.1016/j.ijepes.2023.109609\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eReal, A. C., Luz, G. P., Sousa, J. M. C., Brito, M. C. \u0026amp; Vieira, S. M. Optimization of a photovoltaic-battery system using deep reinforcement learning and load forecasting. \u003cem\u003eEnergy AI\u003c/em\u003e. \u003cb\u003e16\u003c/b\u003e, 100347. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.egyai.2024.100347\u003c/span\u003e\u003cspan address=\"10.1016/j.egyai.2024.100347\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eD\u0026iacute;az-Bello, D., Vargas-Salgado, C., Alc\u0026aacute;zar-Ortega, M. \u0026amp; G\u0026oacute;mez-Navarro, T. Demand response of prosumers integrating storage system for optimizing grid-connected photovoltaics through time-pricing. \u003cem\u003eJ. Energy Storage\u003c/em\u003e. \u003cb\u003e88\u003c/b\u003e, 111536. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.est.2024.111536\u003c/span\u003e\u003cspan address=\"10.1016/j.est.2024.111536\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLi, M., Wang, W., He, Y. \u0026amp; Wang, Q. Deep learning model for short-term photovoltaic power forecasting based on variational mode decomposition and similar day clustering. \u003cem\u003eComput. Electr. Eng.\u003c/em\u003e \u003cb\u003e115\u003c/b\u003e, 109116. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.compeleceng.2024.109116\u003c/span\u003e\u003cspan address=\"10.1016/j.compeleceng.2024.109116\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSareen, K., Panigrahi, B. K., Shikhola, T. \u0026amp; Nagdeve, R. Deep learning solar forecasting for green hydrogen production in India: A case study. \u003cem\u003eInt. J. Hydrog. Energy\u003c/em\u003e. \u003cb\u003e50\u003c/b\u003e, 334. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.ijhydene.2023.08.323\u003c/span\u003e\u003cspan address=\"10.1016/j.ijhydene.2023.08.323\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTang, Y., Yang, K., Zhang, S. \u0026amp; Zhang, Z. Photovoltaic power forecasting: A dual-attention gated recurrent unit framework incorporating weather clustering and transfer learning strategy. \u003cem\u003eEng. Appl. Artif. Intell.\u003c/em\u003e \u003cb\u003e130\u003c/b\u003e, 107691. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.engappai.2023.107691\u003c/span\u003e\u003cspan address=\"10.1016/j.engappai.2023.107691\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang, X. \u0026amp; Ma, W. A hybrid deep learning model with an optimal strategy based on improved VMD and transformer for short-term photovoltaic power forecasting. \u003cem\u003eEnergy\u003c/em\u003e. \u003cb\u003e295\u003c/b\u003e, 131071. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.energy.2024.131071\u003c/span\u003e\u003cspan address=\"10.1016/j.energy.2024.131071\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMa, C. et al. Scenario-based ultra-short-term rolling optimal operation of a photovoltaic-energy storage system under forecast uncertainty. \u003cem\u003eAppl. Energy\u003c/em\u003e. \u003cb\u003e356\u003c/b\u003e, 122425. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.apenergy.2023.122425\u003c/span\u003e\u003cspan address=\"10.1016/j.apenergy.2023.122425\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMassidda, L., Bettio, F. \u0026amp; Marrocu, M. Probabilistic day-ahead prediction of PV generation. A comparative analysis of forecasting methodologies and of the factors influencing accuracy. \u003cem\u003eSol. Energy\u003c/em\u003e. \u003cb\u003e271\u003c/b\u003e, 112422. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.solener.2024.112422\u003c/span\u003e\u003cspan address=\"10.1016/j.solener.2024.112422\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMatera, N., Longo, M. \u0026amp; Leva, S. Time-dependent photovoltaic performance assessment on a global scale using artificial neural networks. \u003cem\u003eSustainable Energy Grids Networks\u003c/em\u003e. \u003cb\u003e38\u003c/b\u003e, 101337. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.segan.2024.101337\u003c/span\u003e\u003cspan address=\"10.1016/j.segan.2024.101337\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYadav, A. K., Khargotra, R., Lee, D., Kumar, R. \u0026amp; Singh, T. Novel applications of various neural network models for prediction of photovoltaic system power under outdoor condition of mountainous region. \u003cem\u003eSustainable Energy Grids Networks\u003c/em\u003e. \u003cb\u003e38\u003c/b\u003e, 101318. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.segan.2024.101318\u003c/span\u003e\u003cspan address=\"10.1016/j.segan.2024.101318\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDing, Z. et al. Long-term operation rules of a hydro\u0026ndash;wind\u0026ndash;photovoltaic hybrid system considering forecast information. \u003cem\u003eEnergy\u003c/em\u003e. \u003cb\u003e288\u003c/b\u003e, 129634. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.energy.2023.129634\u003c/span\u003e\u003cspan address=\"10.1016/j.energy.2023.129634\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNiu, Y. et al. Attend Next: A Mid-Term PV forecasting system with attention mechanism and encoder\u0026ndash;decoder structure. \u003cem\u003eApplied Energy\u003c/em\u003e. 353, 122169. (2024). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.apenergy.2023.122169\u003c/span\u003e\u003cspan address=\"10.1016/j.apenergy.2023.122169\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eVarga, G., Gresina, F., Szeber\u0026eacute;nyi, J., Gelencs\u0026eacute;r, A. \u0026amp; Rost\u0026aacute;si, \u0026Aacute;. Effect of Saharan dust episodes on the accuracy of photovoltaic energy production forecast in Hungary (Central Europe). \u003cem\u003eRenew. Sustain. Energy Rev.\u003c/em\u003e \u003cb\u003e193\u003c/b\u003e, 114289. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.rser.2024.114289\u003c/span\u003e\u003cspan address=\"10.1016/j.rser.2024.114289\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang, J., Yu, Y., Zeng, B. \u0026amp; Lu, H. Hybrid ultra-short-term PV power forecasting system for deterministic forecasting and uncertainty analysis. \u003cem\u003eEnergy\u003c/em\u003e. \u003cb\u003e288\u003c/b\u003e, 129898. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.energy.2023.129898\u003c/span\u003e\u003cspan address=\"10.1016/j.energy.2023.129898\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePerera, M., De Hoog, J., Bandara, K., Senanayake, D. \u0026amp; Halgamuge, S. Day-ahead regional solar power forecasting with hierarchical temporal convolutional neural networks using historical power generation and weather data. \u003cem\u003eAppl. Energy\u003c/em\u003e. \u003cb\u003e361\u003c/b\u003e, 122971. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.apenergy.2024.122971\u003c/span\u003e\u003cspan address=\"10.1016/j.apenergy.2024.122971\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTziolis, G. et al. Direct short-term net load forecasting in renewable integrated microgrids using machine learning: A comparative assessment. \u003cem\u003eSustainable Energy Grids Networks\u003c/em\u003e. \u003cb\u003e37\u003c/b\u003e, 101256. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.segan.2023.101256\u003c/span\u003e\u003cspan address=\"10.1016/j.segan.2023.101256\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eQamili, A. \u0026amp; Kapia, S. Evaluation and integration of photovoltaic (PV) systems in Albanian energy landscape. \u003cem\u003eSolar Compass\u003c/em\u003e. \u003cb\u003e10\u003c/b\u003e, 100070. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.solcom.2024.100070\u003c/span\u003e\u003cspan address=\"10.1016/j.solcom.2024.100070\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChen, Y. \u0026amp; Xu, J. Solar and wind power data from the Chinese State Grid Renewable Energy Generation Forecasting Competition. \u003cem\u003eSci. Data\u003c/em\u003e. \u003cb\u003e9\u003c/b\u003e (1). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41597-022-01696-6\u003c/span\u003e\u003cspan address=\"10.1038/s41597-022-01696-6\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2022).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Photovoltaic Power Prediction, Variational Mode Decomposition (VMD), Attention Mechanism, Bidirectional Long Short-Term Memory model (BiLSTM)","lastPublishedDoi":"10.21203/rs.3.rs-4909901/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4909901/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eResearch on photovoltaic systems (PV) power prediction contributes to optimizing configurations, responding promptly to emergencies, reducing costs, and maintaining long-term system stability. This study proposes a VMD-Attention-BiLSTM model for predicting ultra-short-term photovoltaic power to further enhance prediction performance. Firstly, VMD decomposes historical photovoltaic power data into multiple sub-sequences with different frequencies, treating each sub-sequence as a separate input variable for data expansion. Secondly, the Attention mechanism calculates the correlation coefficients between variables and assigns corresponding weights based on the magnitude of the correlation coefficients between each input variable and the output variable. Finally, the BiLSTM model adopts a dual-layer LSTM structure to more accurately extract features. Experimental results show that compared to various advanced deep learning methods, the MAE of the VMD-Attention-BiLSTM combined model improves by at least 29%.\u003c/p\u003e","manuscriptTitle":"Ultra-short-term Single-step Photovoltaic Power Prediction based on VMD-Attention-BiLSTM Combined Model","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-09-20 09:42:26","doi":"10.21203/rs.3.rs-4909901/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"65365721-bd76-4287-b03b-81bc14fd7e3d","owner":[],"postedDate":"September 20th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":37720498,"name":"Physical sciences/Energy science and technology/Renewable energy/Solar energy"},{"id":37720499,"name":"Physical sciences/Mathematics and computing/Statistics"}],"tags":[],"updatedAt":"2024-10-28T08:24:10+00:00","versionOfRecord":[],"versionCreatedAt":"2024-09-20 09:42:26","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4909901","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4909901","identity":"rs-4909901","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}