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Scientific Reports volume 15, Article number: 44556 (2025) Cite this article
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The unpredictability of photovoltaic (PV) power output poses challenges to real-time demand matching, making accurate forecasting is crucial for better utilization of solar energy. To address the inherent uncertainty and intermittency, a dual-domain seasonal hybrid forecasting strategy for PV power is proposed. First, photovoltaic power data is classified by season and then the distinction between high dynamic features and low dynamic features is made through autocorrelation analysis. Moreover, an extended receptive field convolutional neural network (ERCNN) is developed for features extraction. In detail, a hierarchical architecture is established: integrating multi-head attention mechanism and modified input-output gates (MIOGBiLSTM-attention), a bidirectional long short-term memory (BiLSTM) is adopted for non-frequent fluctuation data, and a BiLSTM network model integrating multi-head attention mechanism and modified output gate (MOGBiLSTM-attention) is used for frequent fluctuation data. Furthermore, a temporal convolutional network (TCN) is introduced for residual error correction. A real PV dataset validates the model effectiveness, outperforming comparison models in forecasting accuracy and robustness.
Driven by the advancement of renewable sources, photovoltaic power has emerged as a key pillar in the worldwide shift to sustainable energy owing to its advantages of cleanliness, sustainability, and low cost¹. In recent years, driven by supportive policies and technological advancements, the global installations of PV power have grown steadily². However, the output power of PV systems is highly rely on weather conditions, for instance cloud cover, temperature and solar irradiance, resulting in significant intermittency and volatility³. These uncertainties pose substantial challenges to secure operation of power systems, energy dispatching and the reliability of the power grid⁴. Therefore, accurate forecasting is essential to enhance the controllability of PV generation and optimize dispatching strategies⁵.
In fact, the existing PV forecasting approaches are categorized into physics-based models and data-driven statistical models⁶. Physics-based models rely on numerical weather prediction (NWP) systems and require a large amount of meteorological and geographical data. Although it provides acceptable accuracy over a longer time horizon, the low update frequency and high computational cost make them less suitable for high-resolution short-term forecasting⁷. In contrast, data-driven models aim to capture the relationship between historical PV output and meteorological variables without the requirement for detailed topographic inputs⁸. Conventional statistical models, that is support vector regression (SVR) and autoregressive integrated moving average (ARIMA), have been widely applied in PV forecasting⁹. However, the models are typically based on linear assumptions, which limits the effectiveness in modeling the nonlinear and time complexity nature of PV data¹⁰. At present, deep learning models have attracted increasing attention, owing to the strong nonlinear modeling capabilities and adaptability to complex time series data, particularly in the domain of PV forecasting¹¹.
In recent years, deep learning techniques have been increasingly applied to PV power forecasting due to the powerful capabilities in feature extraction and nonlinear modeling¹². Unlike traditional methods, deep learning models do not require explicit physical formulations or manual feature engineering. Instead, deep learning models are capable of automatically capturing latent patterns through end-to-end learning¹³. It makes them especially effective in handling multi-scale, highly nonlinear, and non-stationary characteristics commonly observed in PV power time series data.
Common deep learning architectures widely adopted in PV power forecasting include long short-term memory networks (LSTM), recurrent neural networks (RNN), convolutional neural networks (CNN), gated recurrent units (GRU), and Transformer-based models¹⁴. Each architecture offers distinct advantages in capturing spatial and temporal dependencies, and researchers have progressively explored the applications with increasing architectural sophistication. Wang et al. applied an LSTM model and demonstrated its superior performance over traditional statistical methods for short-term PV power forecasting¹⁵. Moreover, Tovar et al. present a hybrid CNN-LSTM model, where CNN is used to extract spatial patterns from meteorological inputs and LSTM captures temporal dependencies, resulting in improved forecasting accuracy in real-world scenarios¹⁶. Furthermore, attention mechanism is introduced to dynamically adjust the importance of input features. Li et al. present a CFOA-CNN-BiLSTM-attention model, integrating convolutional and bidirectional recurrent layers with attention modules to enhance forecasting performance under complex weather conditions¹⁷.
Recent studies have further emphasized the significance of environmental and seasonal variability in PV power forecasting. Liu et al. proposed a forecasting framework that integrates bias-corrected numerical weather prediction with domain generalization to mitigate the distribution differences between seasons and locations, effectively enhancing the robustness of the model in unexperienced weather conditions¹⁸. In addition, Wang et al. developed a dual-layer decomposition and multi-model combination strategy that captures multi-scale seasonal dynamics and provides calibrated uncertainty intervals for PV power forecasting¹⁹.
The performance of models is largely determined by the quality of the data, in addition to the design of the forecasting algorithm. In practice, PV datasets are often affected by noise and missing values, and abrupt fluctuations caused by sensor malfunctions or external environmental disturbances, which may severely compromise the accuracy and reliability of the forecasting results²⁰. As a result, effective data preprocessing becomes a fundamental prerequisite for robust forecasting. Common preprocessing techniques include normalization and standardization to ensure uniform feature scaling, outlier detection and removal to mitigate anomalous interference, and missing value imputation to maintain data continuity²¹. Moreover, appropriate data classification and signal decomposition methods are crucial for further enhancing model performance. The strategies not only improve data consistency but also allow deep learning models to concentrate on informative patterns²². Recent research highlights that effective data preprocessing is crucial to boosting the robustness and accuracy of models. Dai et al. introduced a weather-type classification strategy that groups input data based on meteorological conditions prior to model training, thereby improving forecasting stability under variable weather scenarios²³. In another study, Choudhury and Dash applied structured preprocessing techniques to clean and organize time series data, reducing noise and irregularities that could hinder model convergence and predictive performance²⁴. Furthermore, Fan et al. utilized variational mode decomposition (VMD) to decompose PV output signals into intrinsic mode components, effectively reducing data complexity and enhancing the ability of the model to learn relevant temporal features²⁵. The studies show that preprocessing methods like classification, denoising, and signal decomposition significantly improve data quality and provide more meaningful inputs for deep learning models, leading to better forecasting results.
PV power forecasting has gradually evolved from isolated architectural models to comprehensive strategies that integrates data preprocessing, representation, and model design. A typical process involves partitioning the data by weather type or season to mitigate distribution differences, decomposing signals or extracting features to capture multi-scale dynamics, and employing deep learning-based models for forecasting. Empirical studies have demonstrated consistent improvements in temporal and spatial modeling using LSTM and CNN-LSTM architectures^15,16, and further enhanced under complex weather conditions through the introduction of attention mechanisms¹⁷. Besides, season-aware and cross-domain approaches, such as bias-corrected numerical weather prediction and domain generalization, explicitly address the variations across different locations and seasons^18,19. Complementary preprocessing procedures, including weather-type classification and variational mode decomposition (VMD), improve data consistency and reduce effective complexity, thereby enabling more robust and accurate predictions^23,25. Overall, these developments mark a shift from single-model predictors to hybrid and domain-general strategies, providing guidance for the dual-domain seasonal hybrid perspective of this study. Table 1 provides a concise comparison of a series of representative deep learning-based PV power forecasting studies, summarizing the model designs, overall strategies, and reported advantages.
In summary, recent studies have demonstrated the remarkable effectiveness of deep learning models in PV power forecasting, particularly those that integrate attention mechanisms, hybrid architectures, and advanced preprocessing techniques such as weather classification and signal decomposition²⁶. The approaches enhance the model ability to capture temporal dependencies while effectively suppressing noise and fluctuations in the raw data, thereby significantly improving forecasting accuracy.
The literature review has brought inspiration and encouragement to the research of this paper. However, in view of the uncertainty and complexity of photovoltaic power generation, there are still several limitations for the PV power forecasting. Actually, photovoltaic power generation has inherent variability and is influenced by different seasonal and dynamic conditions. If a single forecasting model is trained on the annual PV power generation data, it may lead to a degradation in forecasting performance due to inconsistent distribution. Moreover, the PV power shows different characteristics under various weather conditions. On sunny days, it does not fluctuate frequently, demonstrating a low dynamic feature, while on cloudy and rainy days, it fluctuates frequently, showing a high dynamic feature. Thus, determining the forecasting model structure based on the inherent characteristics of different PV data types cannot guarantee the validity of the forecasting.
To address the challenges, this paper introduces a dual-domain seasonal hybrid forecasting method for PV power considering dynamic uncertain fluctuations. The PV power data is classified by season and further separated into high dynamic features and low dynamic features. Then, an extended receptive field convolutional neural network is designed for extracting rich temporal features. For each dynamic category, a customized hierarchical forecasting model is designed: a forecasting model based on MIOGBiLSTM-attention is adopted for low dynamic data and a forecasting model combining MOGBiLSTM-attention is used for high dynamic data, where the BiLSTM network is structurally modified according to the data properties. Furthermore, the TCN is introduced for residual error correction, enhancing the overall forecasting precision and ensure the validity of model. The main contributions are outlined below:
A hierarchical data classification strategy is proposed, and the PV power data is firstly divided into four seasons. Then, it is categorized into high dynamic feature and low dynamic feature using autocorrelation analysis to reduce data distribution discrepancies and improve forecasting adaptability.
An extended receptive field convolutional neural network (ERCNN) is employed to extract deep temporal features from the input PV power data. By combining large and small convolutional kernels, both local and long-range dependencies of the model are captured, enhancing feature representation quality.
Two-layer customized forecasting models are developed based on dynamic characteristics: the MIOGBiLSTM-attention model for low dynamic data and the MOGBiLSTM-attention model for high dynamic data. Targeted modifications are incorporated by these models to the BiLSTM network, adjusting the input and output gates according to the temporal behavior of the data, enabling more precise sequence modeling.
The temporal convolutional network (TCN) is introduced as a residual error correction module. By leveraging dilated convolutions and residual connections, temporal dependencies are learned effectively through TCN in residual patterns, thereby further refining forecasting accuracy and enhancing robustness.
The remains are included as: “The dual-domain seasonal hybrid forecasting framework” presents the overall framework of the proposed forecasting model. In “Methods”, variable seasonal data classification, multi-scale feature extraction, hybrid forecasting modeling, and TCN-based error correction are introduced in detail. A case study for comparison and analysis is provided in “Case study”. Finally, “Conclusion” concludes key findings and future research directions.
Taking into account the research difficulties, PV power generation exhibits significant intermittency and instability, with its output highly influenced by weather conditions including humidity, solar radiation, cloud cover and temperature, leading to considerable power fluctuations²³. To address this issue, the development of PV power forecasting is considered essential for the stable operation of power grids. Accurate forecasting of PV output not only optimizes grid dispatching and improves the utilization of PV energy, but also enhances the reliability and stability of the power system⁶. In response to the demand, a dual-domain seasonal forecasting PV power forecasting model is proposed, aiming to improve forecasting accuracy and effectively address the uncertainties. The overall framework of the dual-domain seasonal hybrid forecasting model for short-term PV power is illustrated in Fig. 1.
The framework of the proposed forecasting model.
In fact, PV power generation is significantly influenced by weather conditions, which exhibit distinct seasonal characteristics. Meteorological parameters such as solar radiation, temperature, precipitation, and cloud cover vary considerably across different seasons, leading to pronounced periodic fluctuations in the temporal characteristics of PV power output²³. If a model is trained directly on year-round data, seasonal discrepancies in data distribution may reduce forecasting accuracy. Thus, the data is divided into four seasons to alleviate the distribution bias and enhance the model forecasting accuracy. Except seasonal factors, PV power data also exhibit significant differences in dynamic characteristics, primarily due to the instability of weather conditions²⁷. For example, on sunny days, solar irradiance remains stable and power output changes smoothly, corresponding to low dynamic data. In contrast, under complex weather conditions like rainy or days, solar irradiance fluctuates frequently, resulting in strong dynamic responses in power output, which is characterized as high dynamic data. Since the significant differences in temporal structures and statistical characteristics between these two types of data, modeling jointly may reduce the forecasting accuracy. For improved adaptability of the model, the data needs to be further divided into high dynamic and low dynamic characteristics. Then, model training and model forecasting are conducted separately for each group to enable the model to capture and learn diverse data patterns effectively.
Therefore, to address the differences in dynamic characteristics of PV power data, a dual-domain seasonal forecasting strategy is developed to achieve targeted modeling and refined forecasting. Firstly, the extended receptive field convolutional neural network (ERCNN) is introduced to extract features efficiently from the original input. It can capture local temporal dependencies while also enhancing the perception of long-term sequence, thus providing more discriminative feature representations for the subsequent forecasting models. Hence, a dual-domain seasonal forecasting model architecture is constructed to better align with the temporal dynamics of diverse data categories. For low dynamic data, which exhibit relatively smooth variations and significant trend features, a forecasting model based on MIOGBiLSTM-attention is adopted. The model enhances the focus on key time steps and effectively captures fine-grained information in the sequence. In contrast, for high dynamic data, which show intense temporal variations with strong uncertainty and short-term mutations, a forecasting model combining MOGBiLSTM-attention is employed. This design improves the responsiveness of the model in highly dynamic scenarios and enhances the ability to capture sudden changes. Furthermore, considering that there might still be residual errors in practical forecasting, the TCN is introduced for error correction. TCN, integrating dilated convolutions and residual connections, effectively captures temporal dependencies within residual patterns. Additionally, its parallel computing capability ensures higher computational efficiency, thereby further enhancing the overall forecasting performance.
Based on the above analysis and model design, the proposed forecasting framework integrates dynamic seasonal characteristic classification, advanced feature extraction, targeted forecasting, and error correction strategies, forming a comprehensive and highly adaptive forecasting system. Overall, the framework provides a flexible and effective solution to address the complexity and variability of PV power generation.
Building upon the overall forecasting framework, an in-depth exploration of the core components of the proposed methodology is conducted, including variable seasonal data classification, multi-scale feature extraction, hybrid forecasting modeling, and TCN-based error correction. It provides an in-depth discussion on the underlying principles, implementation details, and functional contributions, demonstrating how to achieve greater accuracy, adaptability, and robustness in the forecasting system.
Effective data classification is essential to enhance the model generalization capability and accuracy²⁸. In this study, the variable seasonal data classification stage consists of three main steps. Firstly, the dataset is categorized by season into spring, summer, autumn, and winter, to account for seasonal variations in weather patterns and PV power. Secondly, an autocorrelation function (ACF) is applied to analyze the dynamic characteristics of the data, thereby classifying it into high dynamic characteristics and low dynamic characteristics. Finally, the self-recursive sliding average (SSA) method is employed to denoise the data and mitigate the impact of random fluctuations and noise, thus enhancing the quality of the input features for the forecasting model.
PV power generation is highly sensitive to seasonal variations due to fluctuations in solar radiation, temperature, precipitation, and cloud cover throughout the year. The seasonal factors lead to significant differences in the temporal distribution and statistical characteristics of PV power output²⁹. Training a forecasting model directly on year-round data may introduce distribution bias and reduce forecasting accuracy, especially when the model fails to capture the seasonal patterns effectively. To address the issue, the dataset is segmented into spring (March–May), summer (June–August), autumn (September–November), and winter (December–February). The segmentation enables the forecasting model to learn seasonal patterns more accurately and mitigates the negative impact of distributional inconsistencies caused by seasonal transitions.
The ACF is a fundamental statistical approach utilized to measure the association between current and lagged values within a time series at different time intervals. It reveals the extent to which observations are correlated across time lags, and is widely applied in analyzing the temporal structure and patterns of time series data³⁰. In this study, PV power data is classified into two types on the basis of the ACF: low dynamic data and high dynamic data, which is made by the differences in the temporal variation patterns. Low dynamic data is typically associated with clear and stable weather conditions, exhibiting strong autocorrelation and smooth variation trends. In contrast, high dynamic data often occur in cloudy, rainy, or highly variable weather conditions, characterized by weak autocorrelation and more frequent fluctuations in power output.
To analyze the dynamic characteristics of daily PV power data, the ACF is calculated from the power series for each day³¹. The mathematical expression of ACF is defined as follows:
where (overline {X}) is the mean of the time series; ({X_t}) is the value at time step t; k is the lag order; and T is the length of the time series.
To facilitate classification, the last ACF of each day is standardized using Z-score normalization, which converts the ACF into a normalized metric. The Z-score is calculated as:
where ({rho _i}) is the last ACF of the ith day; (mu) and (sigma) represent the mean and standard deviation of all ACF, respectively.
Based on the Z-score distribution, a threshold of zero is applied for classification:
When Z-score(geqslant)0, the sequence is classified as low dynamic data, indicating stronger autocorrelation and smoother variations.
When Z-score ≥ 0, the sequence is classified as high dynamic data, reflecting weaker autocorrelation and higher variability.
The classification results are visualized in Fig. 2, which illustrates the Z-scores of daily ACF and the division of high dynamic characteristics and low dynamic characteristics.
Z-score of ACF for daily PV power.
Due to fluctuations in solar radiation, atmospheric conditions, and sensor measurement errors, PV power data inherently contains a certain degree of noise. The data noise obscures underlying patterns, increases forecasting uncertainty, and negatively impacts the performance of forecasting model³². Hence, SSA is employed to denoise the PV power data before model training, aiming to extract more representative temporal structures.
SSA is a powerful non-parametric time series decomposition method that effectively separates the deterministic and stochastic components of time series³³. It transforms the one-dimensional time series into a trajectory matrix, followed by singular value decomposition (SVD) to identify the dominant patterns and isolate the noise components³⁴. The data denoising process through SSA as the following steps:
Firstly, the time series X(t) is transformed into an embedding matrix X, which is generated by selecting embeddedness dimension L and hysteresis m. The embedding matrix is present as:
where T is the sequence length; L is the embedding dimension.
Then, the embedding matrix X is decomposed by singular value:
where (sum) is a diagonal matrix containing singular values; V and U are orthogonal matrices.
Finally, by retaining the component with the largest singular value and removing the component with the smaller singular value and reconstructing, a smooth power sequence is obtained:
where ({{mathbf{U}}_k}), ({Sigma _k}) and ({mathbf{V}}_{k}^{{}}) are the principal components of corresponding retention.
The application of SSA effectively suppresses noise and irregular fluctuations in photovoltaic power data, while maintaining the basic trend. The denoised data set serves as a more reliable input for the forecasting model, significantly improving the training stability and enhancing the overall forecasting accuracy and robustness.
Based on the denoised sequence with seasonal and dynamic characteristics obtained in “Variable seasonal data classification with multi-dynamic characteristics”, multi-scale feature extraction is carried out using ERCNN. Feature extraction plays an important role in time series forecasting model³⁵. To enhance the ability to learn the temporal features, the ERCNN is employed to extract deep representations from the input sequence. By adjusting the kernel size of different convolution layers, the model captures both local and long-distance temporal information, constructing a more discriminative multi-scale feature representation. The network structure of the ERCNN for feature extraction is showed in Fig. 3.
The diagram of ERCNN structure.
The core idea of ERCNN lies in expanding the receptive field in the early stages of the network. Specifically, the first convolutional layer utilizes a larger kernel size, enabling the network to capture broad temporal contexts and global trends from the input sequence. Thus, the initial wide perspective helps the model identify overarching patterns such as seasonal variations or general fluctuation trends across multiple time steps. Besides, smaller kernels are used in subsequent convolutional layers, focusing on fine-grained local features and short-term variations. The hierarchical structure combining both wide and narrow receptive fields enables the network to effectively balance global perception and local sensitivity.
Mathematically, the output for a convolutional layer is expressed as:
where (h_{t}^{{(l)}}) is the output at time t in layer l; k is the kernel size; ({w_i}^{{(l)}}) is the convolution kernel weights; ({x_{t – i}}) is the input at position t–i; (fleft( cdot right)) is a nonlinear activation function; ({b^{(l)}}) is the bias term.
Obviously, global context awareness from large kernels and local detail sensitivity from smaller kernels are combined through ERCNN to enhance the feature extraction capability. Thus, the extracted features are richer and more discriminative, providing a strong foundation for downstream forecasting model.
Following the ERCNN-based multi-scale feature extraction in “Multi-scale feature extraction based on ERCNN”, a hybrid forecasting model leveraging the dual-domain dynamic fluctuation information is formulated to better capture the diverse temporal characteristics of PV power data. Given the significant differences in sequence smoothness, autocorrelation, and fluctuation patterns between low dynamic and high dynamic data, a single forecasting model may not be able to effectively accommodate both types of data. Therefore, differentiated forecasting models are developed for the temporal characteristics of each data category.
The low dynamic data in PV power sequences are generally associated with smooth variations and clear temporal trends. To effectively capture such stable patterns, a MIOGBiLSTM network with the multi-head attention mechanism is developed for PV power forecasting, forming a hybrid structure tailored for low-dynamic scenarios.
The overall architecture of the forecasting model for low dynamic data is illustrated in Fig. 4. The proposed model comprises two key modules: the MIOGBiLSTM layer and the multi-head attention mechanism layer. The MIOGBiLSTM layer is responsible for modeling temporal dependencies within the sequence and enhancing the ability of the model to learn trend information. Meanwhile, the multi-head attention mechanism layer further refines the temporal feature representation by emphasizing critical time steps. It equips the model with the ability to capture both global trends and local correlations in the sequence, enhancing forecasting stability and accuracy.
Overall architecture of the forecasting model for low dynamic data.
MIOGBiLSTM is an enhanced structure of the standard BiLSTM network. It improves the capability of capturing trend-related information in low dynamic data by refining the gating mechanism within the LSTM memory unit.
In a standard BiLSTM network, the input sequence is processed by two LSTM layers in opposite directions, and their outputs are concatenated. Each LSTM unit consists of a memory cell controlled by three gates: the input gate, forget gate, and output gate³⁶. The internal operations of a standard LSTM cell are defined as follows:
where ({o_t}), ({f_t}), and ({i_t}) are the output, forget, and input gates, respectively; ({c_t}) is the updated cell state; ({tilde {c}_t}) is the candidate cell state; ({h_t}) is the hidden state output; (odot) is element-wise multiplication; (sigma left( cdot right)) is the sigmoid function.
While BiLSTM is well-suited for capturing complex temporal dependencies, it may introduce unnecessary complexity and overfitting risks when applied to relatively smooth and low-variability sequences (such as low dynamic PV power). Thus, the modified LSTM cell structure, namely MIOGBiLSTM, is shown in Fig. 5.
In detail, firstly, the activation function of the input gate is replaced with a ReLU function, which allows the gate to pass stronger signals for linearly growing features. Compared with the Sigmoid function, ReLU introduces non-saturation behavior and avoids gradient vanishing issues, thus improving the ability of the network to capture subtle trend variations in smooth sequences. Secondly, the activation function of the output gate is removed. For standard LSTM, the output gate often regulates the final hidden state based on the cell state. However, in low dynamic sequences where output fluctuations are mild and the internal state already represents the underlying trend, the output gate may introduce unnecessary constraints. By removing the output gate, the computational complexity is reduced and more direct propagation of useful trend information is allowed.
The structure of MIOGBiLSTM for low dynamic data.
The revised operations in the MIOGBiLSTM memory unit are expressed as:
where ({underset{raise0.3emhbox{$smash{scriptscriptstylefrown}$}}{x} _t}) is low dynamic data; ({underset{raise0.3emhbox{$smash{scriptscriptstylefrown}$}}{h} _t}_{{ – 1}}) is hidden state input for low dynamic data; ({underset{raise0.3emhbox{$smash{scriptscriptstylefrown}$}}{h} _t}) is hidden state output for low dynamic data; (operatorname{Re} {text{LU}}left( cdot right)) is activation function for rectified linear unit.
Besides, the structural adjustments allow the MIOGBiLSTM to more effectively learn the continuity of trends and long-term dependencies without excessive gating interference. Additionally, the use of a bidirectional structure ensures that both past and future contextual information are utilized, which enhances the representation ability of the model, especially in sequences with smooth transitions. Overall, MIOGBiLSTM offers a more efficient and accurate solution for forecasting low dynamic PV power output by balancing model complexity and trend sensitivity.
Furthermore, for the proposed forecasting model, the multi-head attention mechanism plays a vital role, aimed at improving the representation of temporal features after the MIOGBiLSTM layer. Unlike traditional attention mechanisms that only focus on a single representation space, multi-head attention enables the model to attend to information from multiple subspaces simultaneously, capturing broader temporal dependencies and improving expressiveness of model. The core operation of the attention mechanism is the scaled dot-product attention, which computes the similarity between the query and the key, and applies the corresponding weights to the value vectors³⁷, as follows:
where ({d_k}) is the dimension of the key vectors; V, K, and Q are the value, key, and query matrices, respectively.
The multi-head attention mechanism performs multiple parallel attention operations and concatenates the results to obtain richer feature representations, as follows:
where each attention head is computed independently, and ({W^O}) is a learnable projection matrix applied to the concatenated outputs.
For the developed strategy, the multi-head attention mechanism is applied directly after the MIOGBiLSTM layer. The MIOGBiLSTM is capable of capturing bidirectional temporal dependencies and learning smooth trend features, and the attention mechanism contributes to improved model output by assigning higher weights to key time steps and suppressing less informative ones. Thus, the integration enables the model to better capture key temporal patterns relevant to future power forecasting, thereby improving forecasting accuracy and robustness. By integrating sequential trend learning with dynamic temporal importance modeling, the MIOGBiLSTM-attention model becomes better suited to the inherent temporal features of low-dynamic PV power data. In Table 2, the detailed implementation process is present.
The high dynamic data in PV power generation often exhibits strong fluctuations, abrupt transitions, and weak temporal smoothness, which is typically caused by rapidly changing weather conditions such as clouds, rain, or storms. To address the high variability and uncertainty in such sequences, a forecasting model is proposed, which integrates the MOGBiLSTM network with a multi-head attention mechanism, as shown in Fig. 6. The aim is to enhance the responsiveness of the model and adaptability in dynamic scenarios. The model consists of two main parts: the MOGBiLSTM layer, which is used to capture bidirectional temporal dependencies and model dynamic patterns, and the multi-head attention mechanism, which refines temporal features by emphasizing critical time steps. The structure enables the model to capture both long-range dependencies and short-term variations, enhancing forecasting accuracy in highly dynamic conditions.
The forecasting model for high dynamic data.
In high dynamic sequences, by removing the activation function of the output gate, MOGBiLSTM enables the unit state to be directly converted into the output, allowing for a faster response to instantaneous fluctuations and enhancing the flexibility. The modified LSTM cell structure is shown in Fig. 7. The other gate structures (input gate, forget gate, candidate cell state) remain unchanged compared to the standard form, ensuring the temporal continuity of memory and enhancing the dynamic responsiveness. The improved operations in the MIOGBiLSTM memory unit are expressed as:
where, ({overset{lower0.5emhbox{$smash{scriptscriptstylesmile}$}}{x} _t}) is high dynamic data input; ({overset{lower0.5emhbox{$smash{scriptscriptstylesmile}$}}{h} _t}_{{ – 1}}) is high dynamic data hidden state input; ({overset{lower0.5emhbox{$smash{scriptscriptstylesmile}$}}{h} _t}) is high dynamic data hidden state output.
The improved LSTM cell structure for high dynamic data.
In fact, the MOGBiLSTM is integrated with the multi-head attention mechanism to construct a hybrid forecasting model suitable for high dynamic PV power data. By assigning different weights to different time steps in the complex sequence, the key information is focused on. The model structure significantly improves the adaptability and robustness of the forecasting system, enabling it to cope with drastic changes and being applicable to practical scenarios with variable climatic conditions. The detailed implementation process of the model is presented in Table 3.
After the hybrid forecasting stage, TCN is introduced for error correction to address potential residual errors in the practical forecasting results. TCN is a powerful sequence modeling structure that integrates dilated convolutions and residual connections, enabling it to effectively capture the temporal dependence in residual patterns³⁸. The TCN-based error correction module is illustrated in Fig. 8. Unlike recurrent networks, TCN allows parallel computation and supports longer effective memory through dilation mechanisms, making it more scalable and efficient and in time series tasks.
The TCN-based error correction module.
The core operation of the dilated convolution is defined as:
where (y(t)) is the output; (x(t)) is the input residual sequence; d is the dilation factor; k is the kernel size; (w(i)) is the convolution kernel weight.
For TCN, the residual error sequence ({e_t}={y_t} – {hat {y}_t}) is taken as input and the temporal error pattern is learned. The corrected output is obtained by combining the original forecasting with the output from the TCN,
The error correction strategy enhances the forecasting accuracy and improves the robustness of the model under various external disturbances, thereby exerting a significant positive effect on overall system performance.
To assess the practical effectiveness of the forecasting strategy described in “Methods”, a case study is present to comprise dataset specification, parameter settings, and comprehensive evaluation protocols. “Data determination and parameter setting” details the Xinjiang PV station data and feature configuration, and “Experimental results and analysis” reports ablation and comparative experiments on low-dynamic and high-dynamic subsets, examining accuracy gains attributable to each component and comparing it with the mainstream benchmarks.
In this study, a PV power station located in Xinjiang, China, is selected as the research object. The dataset is selected from January 1, 2019 to December 31, 2019, and includes continuous 24-h PV power data. To comprehensively capture the influence of environmental conditions on PV output, multiple meteorological variables are incorporated into the dataset, including global radiation (W/m²), direct radiation (W/m²), diffuse radiation (W/m²), humidity (%), ambient temperature (°C), atmospheric pressure (hPa), and module temperature (°C). These features provide rich background information and are crucial for building accurate and robust forecasting models.
For consistency and completeness, data from 00:00 to 23:45 each day are selected, with a sampling interval of 15 min, producing a total of 96-time steps per day. The high-resolution dataset equips the model with enhanced capability to extract fine-grained temporal patterns and dynamic fluctuations in PV power output. The collected dataset serves as a solid foundation for training, testing, and evaluation of the model. The system environment and the visualization of sample data are presented in Fig. 9, while Table 4 summarizes the statistical characteristics of the dataset, which provides further insights into the distribution and variability of the selected features. The specific training sample size and corresponding proportion of each category are shown in Table 5. The specific test sample size and corresponding proportion of each category are shown in Table 6. In addition, the proposed model undergoes a comprehensive performance evaluation using coefficient of determination (R²), mean absolute error (MAE), root mean square error (RMSE), and mean squared error (MSE). In Tables 7 and 8, the parameter setting and performance metrics are detailed.
The experimental data and specific information for solar energy system.
where (hat {y}(i)) is forecasted value at time step i; (y(i)) is actual value at time step i; M is number of samples; (bar {y}) is mean of actual values.
To verify the effectiveness and superiority of the proposed forecasting framework, ablation experiments and comparative experiments are conducted to comprehensively evaluate the model performance. The ablation experiments are conducted to evaluate the role of each essential component within the model by systematically removing or replacing individual modules, and to analyze the corresponding impact on forecasting accuracy. The comparative experiments are designed to benchmark the proposed model against several mainstream forecasting models to further validate the advantages. In this section, experiments are conducted separately for the differentiated models of low dynamic data and high dynamic data, and the evaluation results under various experimental settings are analyzed in detail to highlight the forecasting performance improvement brought by each component.
To comprehensively evaluate the contribution of each core component, ablation experiments are conducted for low dynamic data and high dynamic data. By integrating the key modules of the model, including the ERCNN-based feature extractor, multi-head attention mechanism, and TCN-based residual correction, several benchmark models are constructed. For the low dynamic data, the ablation experiments include the comparison models: BiLSTM, CNN, CNN-BiLSTM, ERCNN-BiLSTM, ERCNN-BiLSTM-TCN, and ERCNN-BiLSTM-attention-TCN. For the high dynamic data, the ablation comparison models remain the same. The experiments enable a comprehensive analysis of the contribution of each module under different dynamic conditions.
The forecasting performance is quantitatively evaluated using MSE, RMSE, R², and MAE. All comparison models are labeled as model 1, model 2, model 3, etc., and the structural definitions are summarized in Table 9. The detailed evaluation results for low dynamic data are presented in Table 10, with visual comparisons shown in Fig. 10. In Fig. 11, visualizations are illustrated. Corresponding results for high dynamic data are listed in Table 11. For better readability, the visual and quantitative comparisons clearly reflect the contribution of each model component to forecasting accuracy and further validate the effectiveness of the proposed model design.
Comparison of different models for low dynamic data in ablation experiments.
Comparison of different models for high dynamic data in ablation experiments.
Besides, a detailed analysis of Tables 10 and 11; Figs. 10, and 11, as follows:
By comparing the performance metrics between BiLSTM and CNN-BiLSTM, it can be observed that for low dynamic data in spring, the MAE, RMSE, and MSE of CNN-BiLSTM are reduced by 1.548, 1.379, and 13.8843, respectively, while the R² increases by 5.12%. For high dynamic data in spring, the MAE, RMSE, and MSE decrease by 0.8149, 0.3069, and 3.2947, respectively, with an R² improvement of 2.22%. Similarly, in the other three seasons, the MSE shows a notable decrease, which demonstrates the effectiveness of using CNN for feature extraction.
Compared with CNN-BiLSTM, the ERCNN-BiLSTM model achieves better results. For low dynamic data in summer, the MSE, RMSE, and MAE are further reduced by 1.4034, 0.159, and 0.39, respectively, and R² increases by 0.61%. For high dynamic data in summer, MSE, RMSE, and MAE are reduced by 7.7719, 0.6816, and 0.2985, respectively, while R² increases by 5.09%. Similar improvements are also observed in other seasons, indicating that the proposed ERCNN can further improve the forecasting performance.
Taking the autumn results as an example, the ERCNN-BiLSTM-attention-TCN model shows significant improvements over ERCNN-BiLSTM. For low dynamic data, MSE, RMSE, and MAE are reduced by 1.0231, 0.1902, and 0.0329, respectively, and R² increases by 0.37%. For high dynamic data, MSE, RMSE, and MAE are reduced by 11.0756, 1.2337, and 0.52, respectively, with R² increasing by 6.61%. Similar enhancements are observed in other seasons. It confirms that incorporating the multi-head attention mechanism and TCN-based error correction can significantly improve the forecasting capability of the model.
Moreover, comparing ERCNN-MIOGBiLSTM-attention-TCN and ERCNN-BiLSTM-attention-TCN for low dynamic data, it is evident that the MIOGBiLSTM achieves better performance in all four-evaluation metrics. Similarly, for high dynamic data, ERCNN-MOGBiLSTM-attention-TCN outperforms ERCNN-BiLSTM-attention-TCN, confirming that the improved BiLSTM structure tailored to different data characteristics is more suitable for PV power forecasting.
Compared with all baselines in Tables 10 and 11; Figs. 10 and 11, the proposed ERCNN-MIOGBiLSTM-attention-TCN for low dynamic data and ERCNN-MOGBiLSTM-attention-TCN for high dynamic data achieve the lowest MSE, RMSE, and MAE as well as the highest R² across all seasons. The outstanding performance is attributed to the extended receptive-field feature extraction (ERCNN), enhanced BiLSTM gates tailored to the dynamics data (MIOG/MOG), attention-based adaptive reweighting, and the TCN residual correction. In contrast, the BiLSTM model is lightweight and stable but lacks spatial perception and multi-scale learning capability. The CNN model performs well in denoising and extracting local patterns but fails to capture long-term temporal dependencies. The CNN-BiLSTM model combines spatial and temporal learning effectively for low-dynamic conditions, but may degrade under frequent fluctuations. The ERCNN-BiLSTM model enhances contextual perception and reduces variance but still leaves residual bias around abrupt transitions. The ERCNN-BiLSTM-TCN model suppresses noise and bias more effectively, though excessive smoothing may lead to the loss of detailed variation. The ERCNN-BiLSTM-attention-TCN model adaptively emphasizes important features and improves robustness but requires careful regularization under limited samples. Overall, the proposed dual models demonstrate the most reliable and accurate forecasting capabilities under both seasonal and dynamic conditions.
Furthermore, to visually demonstrate the forecasting performance under different dynamic characteristics, the comparisons between actual PV power data and forecasting results for low dynamic data models and high dynamic data models are present in Figs. 12 and 13, respectively. The figures illustrate PV power data for a single day from 00:00 to 23:45, with a 15-min sampling interval, comprising 96-time steps in total. The visual comparisons comprehensively illustrate the performance of the models in different time periods and are helpful for further evaluating the sequence fitting capability and dynamic responsiveness of each model.
Comparison of forecasting and actual PV power of different models for low dynamic data.
Comparison of forecasting and actual PV power of different models for high dynamic data.
As shown in Figs. 12 and 13, the proposed model exhibits significant advantages in forecasting accuracy under different dynamic data conditions. In Fig. 12, for low dynamic data, the proposed model (ERCNN-MIOGBiLSTM-attention-TCN) demonstrates excellent sequence fitting across all seasons, with forecasting curves closely aligned with actual PV power data. The model shows superior performance in capturing trend features and maintaining high consistency during smooth and stable power variation periods.
In contrast, for high dynamic data (Fig. 13), where power output fluctuates more dramatically due to complex weather conditions, traditional models exhibit noticeable forecasting errors and poor adaptability. However, the proposed model (ERCNN-MOGBiLSTM-attention-TCN) effectively tracks sudden changes and short-term volatility, demonstrating better robustness and dynamic responsiveness. The forecasting curves align more closely with the actual data, resulting in lower forecasting errors.
Overall, the differentiated modeling strategy based on dynamic characteristic classification significantly enhances forecasting accuracy and generalization capability under diverse climate conditions, validating the effectiveness and practicality of the proposed forecasting framework.
In addition, comparative benchmarking is undertaken to further assess the effectiveness of the model. Three time series forecasting models: GRU, Transformer and RNN, are selected for comparative experiments. All models are trained and tested under the same dataset and experimental conditions to ensure fair and consistent evaluation. The comparison is conducted separately for low dynamic data and high dynamic data, providing a comprehensive assessment under different dynamic environments.
The forecasting performance is quantitatively evaluated using MSE, RMSE, R², and MAE. The detailed evaluation outcomes for low dynamic data are reported in Table 12, and the evaluation outcomes for high dynamic data are summarized in Table 13. The corresponding visual comparisons of the performance metrics are illustrated in Fig. 14 (low dynamic data) and Fig. 15 (high dynamic data). For better readability, each model is labeled as model A, model B, model C, etc., and the structural definitions summarized in Table 14.
Comparison of performance indicators of different models (low dynamic data).
Comparison of performance indicators of different models (high dynamic data).
As shown in Figs. 14 and 15, the proposed ERCNN-MIOGBiLSTM-attention-TCN model (for low dynamic data) and ERCNN-MOGBiLSTM-attention-TCN model (for high dynamic data) consistently outperform comparison models such as RNN, GRU, and Transformer across all evaluation metrics. The proposed model achieves lower MSE and RMSE, indicating significantly improved forecasting accuracy. Higher R² demonstrates better sequence fitting capabilities, while lower MAE reflects more stable and consistent forecasting performance. For low dynamic data, the proposed model performs consistently well across four seasons, showcasing its strong adaptability to smooth and stable temporal patterns. For high dynamic data, the proposed model effectively handles abrupt changes and fluctuations, maintaining robustness and accuracy under complex conditions.
To further illustrate the performance differences among various models, this study provides comparisons between forecasting and actual PV power. The forecasting results for low and high dynamic data are presented in Figs. 16 and 17, respectively. The comparisons clearly illustrate the extent to which the forecasting results correspond to the actual PV power output, facilitating an intuitive assessment of fitting quality and forecasting precision. It can be seen from Figs. 16 and 17 that the comparison forecasting model cannot follow the real data trend well, while the proposed model for data with different characteristics forecasts well, which is consistent with the real data trend.
In addition, Figs. 16 and 17 show that the comparison forecasting models, such as RNN, GRU, and Transformer, have obvious limitations when dealing with data with different dynamic characteristics. For the data with low dynamic characteristics, the comparison forecasting models provide certain forecasting accuracy in the time period when the power change is relatively stable, but at the moment of strong light, the forecasting results often deviate from the real data, and cannot accurately capture the trend change. However, for data with high dynamic characteristics, the forecasting curve of the comparison forecasting model shows large deviations, especially in complex scenes such as sudden weather changes or cloud cover, and its forecasting ability is significantly reduced, resulting in power fluctuations that cannot reflect the actual situation correctly. In contrast, the differentiated forecasting models proposed (ERCNN-MIOGBiLSTM-attention-TCN and ERCNN-MOGBiLSTM-attention-TCN) show strong adaptability under different dynamic characteristics of data. In summary, the proposed forecasting model for different data dynamic characteristics can significantly enhance the accuracy of photovoltaic power forecasting, and has stronger generalization ability and robustness in different seasons.
Comparison of forecasting and actual PV power data for different models (low dynamic data).
Comparison of forecasting and actual PV power data for different models (high dynamic data).
In this paper, a dual-domain seasonal hybrid forecasting framework for short-term PV power is developed to effectively address the variability and complexity of PV generation under diverse weather and temporal conditions. Firstly, a hierarchical data classification strategy is introduced, and the PV data is divided according to season and dynamic characteristics (high and low), which reduces data heterogeneity and enhances the adaptability in varying scenarios. Moreover, the ERCNN is employed for deep temporal feature extraction, enabling the model to effectively capture both short- and long-term dependencies in the data. Besides, the MIOGBiLSTM-attention model for low dynamic data and the MOGBiLSTM-attention model for high dynamic data are established based on customized modifications from BiLSTM units, significantly improving the prediction performance. Meanwhile, the TCN is integrated as an error correction module to further refine forecasting accuracy, especially by modeling residual patterns. Finally, a large number of experiments are performed using real PV datasets, and both ablation and comparative results demonstrate the effectiveness and advantages of the proposed framework. The developed model demonstrates excellent performance in capturing the temporal trends of PV power and significantly outperforms several comparison models in multiple metrics.
Future research will aim to incorporate real-time meteorological data, expand the applicability of the model in larger-scale PV systems, and explore techniques for quantifying the uncertainty of interval forecasting.
The data are available from the corresponding author on reasonable request.
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The authors gratefully acknowledge the financial support and the study participants for their time and contribution.
This work is supported by the National Natural Science Foundation of China (62373260), Research Projects of Department of Education of Guangdong Province (2024ZDZX1053), and Shenzhen Science and Technology Program (20231127173014002), Digital Factory Management and Control Technology R&D Center (6025310013PQ).
Institute of Electrical and Control Engineering, Liaoning Technical University, Huludao, 125100, China
Zhaowei Yuan, Yaosong Xu & Zijian Zhang
Institute of Intelligence Science and Engineering, Shenzhen Polytechnic University, Shenzhen, 518055, China
Zhaowei Yuan, Sen Xie & Zijian Zhang
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Z.Y.: Data curation, methodology, software, validation, writing-original draft. Y.X.: Conceptualization, methodology, writing-review and editing. S.X.: Conceptualization, methodology, funding acquisition, writing-review and editing. Z.Z.: Software, validation.
Correspondence to Sen Xie.
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Yuan, Z., Xu, Y., Xie, S. et al. A dual-domain seasonal hybrid forecasting strategy for PV power considering dynamic uncertain fluctuations. Sci Rep 15, 44556 (2025). https://doi.org/10.1038/s41598-025-28389-5
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Received: 17 September 2025
Accepted: 10 November 2025
Published: 22 November 2025
Version of record: 24 December 2025
DOI: https://doi.org/10.1038/s41598-025-28389-5
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