Short-Term Photovoltaic Power Forecasting Using a Hybrid RF-ICEEMDAN-SE-RWCE-GRU Model

Abstract

To enhance the accuracy of short-term photovoltaic (PV) power forecasting, this study proposes a novel hybrid model that integrates Random Forest (RF), Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN), Sample Entropy (SE), the Random Walk with Compulsory Evolution (RWCE) algorithm, and the Gated Recurrent Unit (GRU) network. Initially, RF is applied to select relevant meteorological features, minimizing redundancy and improving both training efficiency and predictive robustness under complex operating conditions. ICEEMDAN is then employed to decompose the PV power series into multiple quasi-stationary components, mitigating the adverse effects of non-stationarity on forecasting accuracy. Following this, SE is applied to quantify the complexity of each component and reconstruct the decomposed signals into high-, mid-, and low-frequency bands, simplifying the inputs to the forecasting model. To further improve performance, the RWCE algorithm optimizes GRU network hyperparameters through global exploration, individual evolution, and enforced evolution strategies. The optimized GRU network then predicts each reconstructed component, and the component-wise forecasts are aggregated to yield the final PV power output. Simulation results from several representative months indicate that the proposed approach reduces RMSE by an average of 9.02% compared to comparison model and by 43.41% relative to the baseline model, demonstrating its superior forecasting capability. Additionally, the model demonstrated scalability across varying climate conditions, confirming its applicability in real-world scenarios.

1. Introduction

Clean energy plays a crucial role in sustainable development and carbon reduction. In this context, photovoltaic (PV) power generation has attracted considerable attention because it converts solar energy directly into electricity and offers advantages such as safety, high conversion efficiency, cost-effectiveness, and environmental benefits [1]. However, PV output is inherently volatile and intermittent due to rapidly changing meteorological conditions, which poses challenges to power system stability and operational reliability [2]. Therefore, accurate PV power forecasting is essential for large-scale grid integration of renewable energy and for improving real-time scheduling of energy storage systems [3].

PV power forecasting methods are commonly grouped into three categories: physical models, statistical models, and artificial intelligence (AI) models. Physical approaches describe the conversion process from solar irradiance to electrical power and provide a mechanistic representation of PV systems. Nevertheless, their modeling complexity often leads to limited robustness, weak generalization, and reduced tolerance to disturbances [4,5]. Statistical methods, including Autoregressive Moving Average (ARMA) [6], Autoregressive Integrated Moving Average (ARIMA), and Seasonal ARIMA (SARIMA) [7], have also been widely adopted. Yet, their capability to accommodate strong nonlinearity, regime shifts, and exogenous perturbations is typically inadequate, which degrades forecasting accuracy under variable operating conditions [8]. By contrast, AI-based models learn directly from historical data to capture nonlinear relationships and temporal dependencies, and they have become increasingly prominent in PV forecasting research. Representative techniques include Kernel Extreme Learning Machine (KELM) [9], Long Short-Term Memory (LSTM) network [10], and the Gated Recurrent Unit (GRU) network [11]. The GRU network offers competitive generalization with comparatively compact parameterization, enabling effective modeling of long-range dependencies in time-series data [12,13]. Accordingly, this study adopts the GRU network as the base predictor for short-term PV power forecasting.

Despite the strong performance of the GRU network, forecasting accuracy is sensitive to hyperparameter configuration [14]. Manual tuning is time-consuming given the large search space, whereas a random search may be inefficient and unstable [15]. To address this issue, scholars have explored various optimization algorithms to tackle the challenges of selecting deep learning hyperparameters. Ye et al. [16] utilized the whale optimization algorithm (WOA) to tune hyperparameters for residential load forecasting, demonstrating efficacy across multi-household datasets. Zhou et al. [17] applied Bayesian optimization (BO) to ensure the robustness of photovoltaic power prediction under volatile data conditions, whereas Hua et al. [18] confirmed that the Starfish Optimization Algorithm (SFOA) boosts performance in diverse solar energy scenarios. Similarly, Lv et al. [19] employed Particle Swarm Optimization (PSO) for wind energy forecasting, which comparative analysis showed to effectively enhance accuracy across varying seasonal patterns. However, many conventional optimizers struggle to balance global exploration and local exploitation, which can yield premature convergence and suboptimal parameter settings. Recently, the Random Walk with Compulsory Evolution (RWCE) algorithm proposed by our research group has shown strong global search capability and has been applied to challenging optimization problems, including mixed-integer nonlinear programming (MINLP) for heat exchanger network synthesis [20,21] and distributed energy system optimization [22]. The RWCE algorithm is straightforward to implement and requires only a small number of control parameters. Compared with widely used swarm-intelligence optimizers such as PSO, RWCE has been demonstrated to achieve superior optimization performance and stronger global search capability in our previous studies [23]. In this work, the RWCE algorithm is employed to tune GRU network hyperparameters to further evaluate its effectiveness in PV power forecasting.

In addition to hyperparameter optimization, data preprocessing plays a critical role in improving forecasting accuracy, particularly through denoising and dimensionality reduction. Model performance is strongly dependent on input quality [24]. For PV power series, common decomposition-based denoising methods include Empirical Mode Decomposition (EMD), Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), and Variational Mode Decomposition (VMD). Most existing studies follow a “decomposition-prediction” workflow, utilizing signal decomposition techniques to handle data non-stationarity followed by predictive model construction. For instance, Ref. [25] developed a hybrid model combining VMD and LSTM neural network, Ref. [26] introduced a combined ultra-short-term photovoltaic power prediction model based on CEEMDAN and a RIME-optimized Bi-LSTM network, and Ref. [27] proposed a multistep short-term solar radiation prediction method based on EMD and GRU optimized via an attention mechanism. VMD can decompose complex signals into modes across different frequency bands and thereby improve data quality [28], while EMD and CEEMDAN have also been used to smooth PV power sequences effectively [29,30]. However, these approaches may suffer from mode mixing and sensitivity to parameter settings [31]. Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN), an enhanced variant of CEEMDAN, alleviates these limitations and provides more reliable decomposition [32]. Building on decomposition methods, researchers have further explored a “decomposition- reconstruction-prediction” framework that reduces the number of components through Sample Entropy (SE)-based reconstruction. Reference [33] presented the EMD-SE prediction model, while Reference [34] proposed the VMD-SE prediction model. These studies reduce computational complexity while achieving higher forecasting accuracy. Moreover, feature selection is essential for reducing redundancy among meteorological inputs and for improving computational efficiency. Compared with correlation-based screening methods (e.g., Pearson and Spearman), RF feature selection is more robust and practically accurate for short-term PV power forecasting, as it can handle redundant and noisy meteorological predictors and capture nonlinear dependencies, thereby improving the training stability and generalization of deep models [2,35]. Some studies [35,36] have only used feature selection without decomposition, while others [37] have solely relied on decomposition without feature selection. In contrast, this study integrates both feature selection and decomposition, further refining the data preprocessing step and enhancing the effectiveness of model inputs. In Appendix A (

Table A1. Comparison of forecasting methods and their performance improvements.

Study	Methods	Performance Improvement
1	CEEMDAN-JS-BiLSTM	RMSE reduction of 24.85%
4	VMD-IDBO-KELM	MAPE reduction of 2.66% on sunny days, 1.98% on cloudy days, and 6.46% on rainy days
9	VMD-BWO-KELM	RMSE decreases by 59.52%, MAE reduces by 59.52% compared to LSTM and SVM
12	CapSA-VMD-ResGRU-attention	Enhancement in prediction performance by 33.99%, 30.55%, 9.62%, and 1.44% in terms of four metrics
19	PSO-CNN-LSTM	RMSE reduction of 33.42%, MAE reduction of 27.73%. PSO-CNN-LSTM outperforms CNN-LSTM and CNN-LSTM-ATT with superior accuracy in all seasons
30	CEEMDAN-SE-IDBO-LSTM	CSIL decreases MAE by 13.26%, RMSE by 12.20%, MAPE by 14.99%, and R2 by 8%
Proposed Method	RF-ICEEMDAN-SE-RWCE-GRU	RMSE is reduced by an average of 9.02% compared to the comparison model. RMSE decreases by 43.41% relative to the baseline model, demonstrating superior forecasting capability

), a summary of various PV power forecasting methods and their corresponding performance improvements is presented, highlighting different approaches and their effectiveness in enhancing forecasting accuracy.

Based on the analysis above, although various hybrid models have improved the forecasting accuracy of PV power generation, challenges remain in handling complex data, particularly fluctuating high-frequency components that hinder predictive performance. Moreover, existing studies often neglect the importance of considering seasonal temporal characteristics and conducting evaluations across different locations. To address these issues, this paper proposes a novel hybrid model for short-term PV power forecasting that integrates feature selection, signal decomposition, component reconstruction, hyperparameter optimization, and component-wise forecasting and validates its effectiveness and general applicability using multiple datasets from different sites across various seasons.

The principal contributions of this work are summarized as follows.

(1)

RF is employed to analyze meteorological features, effectively identifying irrelevant variables and selecting the key drivers that most strongly affect forecasting performance, thereby reducing input redundancy. In this study, the input dimensionality is reduced from 15 candidate meteorological variables to 8 key features, resulting in lower prediction errors and better goodness of fit.

(2)

The PV power data is decomposed using ICEEMDAN to extract various frequency components. These components are then reconstructed into high-, medium-, and low-frequency groups based on SE, which subsequently serve as inputs for the GRU network. This process mitigates non-stationarity and noise, thereby enhancing the quality of model inputs and enabling more accurate learning of temporal patterns at the component level. In particular, ICEEMDAN yields 9 IMFs, and SE-based reconstruction merges them into 3 groups, reducing the number of sub-models to be trained from 9 to 3 and decreasing computational overhead while preserving essential multi-scale information for accuracy improvement.

(3)

The RWCE algorithm is first applied to automatically tune GRU network hyperparameters for PV power forecasting, thereby avoiding manual tuning and improving forecasting accuracy, while balancing global exploration and local exploitation with only a limited number of control parameters. This automatic tuning strategy yields a prediction error reduction of 9.02% in RMSE compared to the model.

(4)

Extensive experiments, including comparative experiments and ablation studies, are conducted to evaluate the contribution of each module and to demonstrate that the proposed approach consistently outperforms representative baseline models and the comparison model in forecasting performance.

(5)

This study evaluates the proposed model’s scalability and adaptability from spatiotemporal perspectives. By conducting rigorous experiments across diverse geographical locations and varying seasonal conditions, we verify the model’s robustness and generalization capability, confirming its suitability for real-world applications under complex climatic scenarios.

The remainder of this paper is organized as follows. Section 2 (Research Methods) describes the research methodology adopted in this study. Section 3 (Photovoltaic Power Forecasting Model) presents the proposed forecasting model and its overall model. Section 4 (Data Preprocessing and Feature Selection) elaborates on the data preprocessing steps and the feature selection method employed in this study. Section 5 (Model Validation) reports the experimental setup and results and compares the forecasting performance of the proposed method with baseline model and comparison model. Finally, Section 6 (Conclusions) summarizes the paper and discusses this work.

2. Research Methods

2.1. Random Forest

The RF algorithm is widely employed for feature selection, as it can quantify the contribution of each input variable through feature importance scores. By retaining features with higher importance scores and discarding less informative variables, RF reduces input dimensionality, alleviates redundancy, and enhances both computational efficiency and predictive performance.

A key component in RF is out-of-bag (OOB) evaluation. For each decision tree, bootstrap sampling leaves a subset of observations unused during training; these excluded samples constitute the OOB set for the tree and can serve as an internal validation set. Permutation-based OOB importance for feature $x_j$ is computed as follows:

(1)

For the t-th decision tree, evaluate prediction performance on its OOB samples and compute the corresponding OOB error, denoted as $er{r}_{OOB}^{\left(t\right)}$.

(2)

Randomly permute the values of feature $x_j$ in the OOB samples while keeping all other features unchanged. Reevaluate the OOB error for the same tree using the permuted samples and denote it as $er{r}_{OOB,\pi \left(j\right)}^{\left(t\right)}$, where ${\pi }_{\left(j\right)}$ denotes a random permutation of features within the OOB samples.

(3)

After repeating the above steps for all $T$ trees, the OOB importance of feature $x_j$ is defined as the mean increase in OOB error caused by permuting $x_j$:

$$I_{OOB}\left(x_j\right)={\displaystyle \frac{1}{T}}{\displaystyle \sum _{t=1}^T\left(er{r}_{OOB,\pi \left(j\right)}^{\left(t\right)}-er{r}_{OOB}^{\left(t\right)}\right)}$$

(1)

A larger $I_{OOB}\left(x_j\right)$ indicates that disrupting $x_j$ leads to a greater deterioration in prediction accuracy, implying that the feature is more influential for PV power forecasting.

2.2. ICEEMDAN

ICEEMDAN is an adaptive signal decomposition method that addresses the limitations of conventional techniques, including mode mixing and sensitivity to user-defined parameters [38]. By suppressing the mode-mixing effects often encountered in EMD-based approaches, ICEEMDAN provides more stable and accurate decompositions. The main steps of ICEEMDAN are summarized as follows:

(1)

Add white noise to the original signal $x$ to generate the sequence:

$$\begin{array}{cc}{x}^{\left(i\right)}=x+{\beta }_1{w}^{\left(i\right)}& i=1,2,3,\dots N_e\end{array}$$

(2)

(2)

The aforementioned process is repeated $N_e$ times to compute the first residual component $r_1$:

$$r_1={\displaystyle \frac{1}{N_e}}{\displaystyle \sum _{i=1}^{N_e}M\left(x^{\left(i\right)}\right)}$$

(3)

Here, $w^{\left(i\right)}$ denotes the i-th added white noise sequence, which is characterized by a zero mean and unit standard deviation. ${\beta }_1$ is the signal-to-noise ratio for the first decomposition stage, and $M\left(\cdot \right)$ denotes the operator for calculating the local mean of the signal.

(3)

The first intrinsic mode function, $d_1$, is derived by subtracting the first residual from the original signal:

$$d_1=x-r_1$$

(4)

(4)

White noise is subsequently added to the previous residual to derive the k-th residual component $r_k$:

$$\begin{array}{cc}{r}_k={\displaystyle \frac{1}{N_e}}{\displaystyle \sum _{i=1}^{N_e}M\left(r_{k-1}+{\beta }_k{E}_k\left(w^{\left(i\right)}\right)\right)}& k\ge 2\end{array}$$

(5)

Here, ${\beta }_k$ denotes the signal-to-noise ratio at the k-th stage, and $E_k\left(\cdot \right)$ denotes the EMD-based operator used to extract the $k$-th mode.

Subsequently, the k-th modal component $d_k$ is obtained:

$$\begin{array}{cc}{d}_k=r_{k-1}-r_k& k\ge 2\end{array}$$

(6)

(5)

Step (4) is repeated recursively until a stopping criterion is satisfied, yielding the final set of modal components.

2.3. Sample Entropy

Direct prediction of all subsequences derived from modal decomposition results in a substantial increase in computational burden while neglecting the correlations among subcomponents [39]. Classifying and reconstructing correlated components not only reduces computational cost but also enhances the salient patterns shared by similar components. Consequently, SE is utilized to analyze the subsequences. SE is widely applied in signal analysis and processing, primarily to quantify the complexity and irregularity of time series, where a higher entropy value signifies greater complexity. The calculation formula is expressed as follows:

$$W_{SE}\left(m,r,L\right)=-\ln \left[{\displaystyle \frac{A^m\left(r\right)}{B^m\left(r\right)}}\right]$$

(7)

In the formula, $L$ denotes the length of the modal vector, $m$ represents the embedding dimension, and $r$ signifies the similarity tolerance. In the context of time-series analysis, $B^m\left(r\right)$ denotes the probability of matching $m$ points between two consecutive subsequences, whereas $A^m\left(r\right)$ represents the probability of matching $m+1$ points.

2.4. GRU Network

The GRU network constitutes a variant of conventional recurrent neural network, originally proposed by Cho et al. in 2014 [40]. The GRU architecture primarily comprises an update gate and a reset gate. The update gate regulates the extent to which information from the preceding state is retained in the current state; specifically, a larger update gate value implies a greater retention of information from the prior state. Conversely, the reset gate governs the amount of information from the previous state that is incorporated into the current candidate state; a smaller reset gate value results in less information being transferred from the previous state. The internal structure of the GRU network is illustrated in Figure 1. The computational formulation of the GRU is expressed as follows:

$$R_t=\sigma \left(X_t{W}_{xr}+H_{t-1}{W}_{hr}+b_r\right)$$

(8)

$$Z_t=\sigma \left(X_t{W}_{xz}+H_{t-1}{W}_{hz}+b_z\right)$$

(9)

$${\tilde{H}}_t=\tanh \left(X_t{W}_{xh}+\left(R_t\odot H_{t-1}\right)W_{hh}+b_h\right)$$

(10)

$$H_t=Z_t\odot H_{t-1}+\left(1-Z_t\right)\odot {\tilde{H}}_t$$

(11)

In these equations, $X_t$ is the input at the current time step, and $H_{t-1}$ is the hidden state at the previous time step. $R_t$ and $Z_t$ denote the reset gate and update gate, respectively. ${\tilde{H}}_t$ represents the candidate hidden state, which is temporarily computed by controlling the information flow through the reset gate $R_t$, whereas $H_t$ represents the updated hidden state, which is computed by combining the previous time step’s hidden state $H_{t-1}$ and the candidate hidden state ${\tilde{H}}_t$ through the update gate $Z_t$. $W_{x\ast }$ and $W_{h\ast }$ are weight matrices and $b_{\ast }$ are bias terms. The operator $\odot$ denotes the Hadamard product and is computed element-wise. $\sigma \left(\cdot \right)$ and $\tanh \left(\cdot \right)$ denote the sigmoid and hyperbolic tangent activation functions, respectively.

2.5. RWCE Algorithm

Hyperparameter selection and tuning are critical, as they impact not only forecasting accuracy but also computational efficiency and the model’s ability to generalize. The RWCE algorithm incorporates fully stochastic evolution, independent individual evolution, and a compulsory evolution strategy, possessing a simple structure that can effectively avoid local optima, thus enhancing global search performance. In this study, the RWCE algorithm is deployed to automatically optimize the hyperparameters in the GRU model, where the Root Mean Square Error (RMSE) is utilized as the loss function for the optimization model. The specific optimization process of RWCE algorithm is illustrated in Figure 2.

(1)

Initialization

The algorithm begins by randomly generating a population $N_P$ consisting of $N$ individuals, where each individual is initialized within the predefined parameter bounds. Each individual $M_n\left(n=1,2,3,\dots N\right)$ encodes a set of GRU hyperparameters, representing a candidate solution defined by S optimization variables, where $m_{n,s}\left(s=1,2,3,\dots S\right)$ represents the variable to be optimized. The fitness of each individual is then calculated based on the predefined objective function.

(2)

Evolution

This phase performs a “random walk” operation on each dimension of the individual $M_n$, randomly increasing or decreasing the numerical value. To ensure sufficient parameter combinations at each operating point, a small value AN is used to determine whether the operating point has evolved during its update. During the wandering process, the evolution of each operating point is independent of the others.

$$m_{n,s,r}^{\ast }=m_{n,s,r}+\left(1-2rand\left(0,1\right)\right)\times rand\left(0,1\right)\times L\times AN$$

(12)

where $m_{n,s,r}$ and $m_{n,s,r}^{\ast }$ represent the values of the s-th variable for the n-th individual before and after the r-th iteration, respectively; $L$ represents the maximum random walk step length. $\left(1-2rand\left(0,1\right)\right)$ dictates the direction of the random walk, while $rand(0,1)$ controls the step magnitude, and $AN$ is defined as the evolution rate.

(3)

Selection

If the structure $m_{n,s,r}^{\ast }$ obtained after the individual walk exhibits a superior objective function value, the corresponding structure is accepted as the initial structure for the next iteration; otherwise, the individual remains not updated, and the structure from the r-th iteration is retained.

$$m_{n,s,r+1}=\{\begin{array}{cc}{m}_{n.s,r}^{\ast }& F\left(m_{n,s,r}^{\ast }\right)\le F\left(m_{n,s,r}\right)\\ m_{n,s,r}& else\end{array}$$

(13)

(4)

Mutation

Should the individual, after the random walk according to Equation (13), fail to achieve an objective function value better than that of the previous generation, the inferior solution is accepted with a small probability $\delta$. This mechanism ensures the global search capability of the algorithm and prevents it from being trapped in local optima, allowing the algorithm to tolerate temporary performance degradation to a certain extent and explore a broader solution space.

$$m_{n,s,r+1}=\left\{\begin{array}{ccc}{m}_{n.s,r}^{\ast }& if& F\left(m_{n,s,r}^{\ast }\right)\le F\left(m_{n,s,r}\right)\\ m_{n.s,r}^{\ast }& elseif& rand\left(0,1\right)<\delta \\ m_{n,s,r}& else& \end{array}\right.$$

(14)

3. Photovoltaic Power Forecasting Model

3.1. Proposed Hybrid Forecasting Model

To further improve the accuracy of photovoltaic power forecasting and tackle the issues of data redundancy, non-stationary components, and hyperparameter selection, this study proposes a hybrid forecasting model, RF-ICEEMDAN-SE-RWCE-GRU, which focuses on data preprocessing and model optimization. The workflow of this prediction model is illustrated in Figure 3, and the specific procedures are detailed as follows:

(1)

The outliers and missing entries in the dataset are first corrected, after which the data are normalized.

(2)

RF is then applied to meteorological variables to rank feature importance, and the most informative predictors are selected as model inputs.

(3)

Next, the ICEEMDAN decomposes the historical PV power series into a set of relatively stationary intrinsic mode functions (IMF1, IMF2, …, IMF_n) and a residual term (RES), which are subsequently reconstructed using SE to reduce signal complexity and improve computational efficiency.

(4)

The RWCE algorithm is then employed to tune the hyperparameters of the GRU network, and the optimal configuration is used for training and prediction.

(5)

Finally, the forecasts of the reconstructed components are summed to produce the overall PV power prediction, and performance is evaluated using multiple metrics.

3.2. Model Prediction Evaluation Metrics

To quantitatively evaluate forecasting performance, RMSE, Mean Absolute Error (MAE), and the coefficient of determination ($R^2$) are adopted as evaluation metrics. Their mathematical definitions are given as follows:

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

(15)

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

(16)

$$R^2=1-{\displaystyle \frac{{\displaystyle \sum _{i=1}^n{\left(y_i-{\widehat{y}}_i\right)}^2}}{{\displaystyle \sum _{i=1}^n{\left(y_i-{\overline{y}}_i\right)}^2}}}$$

(17)

Here, $n$ denotes the total number of samples; $y_i$ represents the actual value of the i-th sample; ${\widehat{y}}_i$ is the corresponding predicted value; and $\overline{y}$ indicates the mean of the actual values.

3.3. Parameter Settings and Experimental Platform Configuration

All experiments were conducted on a high-performance workstation equipped with an Intel^® Xeon^® Gold 6226R CPU @ 2.90 GHz (dual-processor configuration) and 64 GB RAM. To ensure reproducibility, key GRU hyperparameters were optimized via RWCE within the following search ranges: the number of hidden units in [10, 50], the initial learning rate in [0.0005, 0.001], and the L2 regularization coefficient in [1 × 10⁻⁵, 1 × 10⁻³]. The maximum number of RWCE iterations was set to 30 with a population size of 10, and the GRU activation function was set to ReLU.

4. Data Preprocessing and Feature Selection

4.1. Data Analysis

To evaluate the reliability and effectiveness of the proposed approach, experiments are conducted utilizing operational data from a real PV power station. The dataset is derived from measured records collected at a PV plant in Xinjiang, China, throughout the year 2021. The photovoltaic system is based on poly-Si technology, with a Fixed Ground Mount array structure, installed in 2016. The inverter model used is SMA STC 25000TL-30. The PV power output is measured in MW, and data are sampled at 15 min intervals, yielding 96 time steps per day. The dataset includes 15 candidate features, such as Diffuse Horizontal Irradiance (DHI), Direct Normal Irradiance (DNI), Global Horizontal Irradiance (GHI), cloud cover transparency, wind speed, wind direction, and others. The data collection process was carried out using an integrated solar system, with a radiation measurement accuracy class of ±5%, ensuring precise data acquisition. In addition to the photovoltaic power data, meteorological data were sourced from the China National Meteorological Science Data Center.

In practical operation, the site data may contain outliers and missing entries [41]. These abnormal values are corrected by replacing them with the average of the adjacent observations immediately before and after the affected timestamp, thereby improving data consistency. Furthermore, to eliminate scale differences among variables, all features are normalized utilizing Equation (18).

$$x_i^{\ast }={\displaystyle \frac{x_i-x_{\min }}{x_{\max }-x_{\min }}}$$

(18)

To provide a comprehensive performance assessment, four representative months (January, April, July, and October) are selected as case studies, each covering diverse weather conditions. For each month, a sliding-window strategy is adopted for data partitioning; specifically, the final five days are reserved as an independent test set, while the remaining data are utilized for model training.

4.2. Feature Selection Results Based on RF

To ensure the quality of the input data, RF is employed to identify the factors influencing PV power generation, thereby improving the model’s forecasting efficiency. Historical meteorological data is input into the RF algorithm, which calculates the importance of various features. The contribution ranking of these features in four representative months is presented in Figure 4.

The feature importance analysis reveals that variables related to irradiance, including DHI, DNI, and GHI, contribute most significantly to PV power forecasting, whereas meteorological factors such as wind speed, wind direction, and snow depth exhibit relatively limited influence. This finding suggests that solar radiation conditions are the primary driving factors influencing variations in PV power output, which is consistent with the underlying physical mechanism where PV generation mainly depends on incoming solar irradiance. Based on the resulting importance ranking, the eight highest-scoring variables are selected as model inputs. This feature selection strategy retains the most informative predictors while effectively reducing input dimensionality, thereby providing a representative input set for subsequent time-series modeling.

Considering the stochasticity of RF training, we repeated the RF training and importance calculation multiple times with different random seeds for each representative month. The resulting importance scores were summarized as mean ± standard deviation for each feature. The corresponding numerical importance values and variability across runs are reported in Table S2 to facilitate transparent and robust assessment.

4.3. Signal Decomposition and Grouping Using ICEEMDAN and SE

To enhance input data quality and mitigate the adverse impact of noise on forecasting accuracy, ICEEMDAN is applied to decompose PV power sequences for the four representative seasons, thereby enhancing model performance. The decomposition and reconstruction results for January (winter) are presented in Figure 5, where Figure 5a presents the ICEEMDAN decomposition results, Figure 5b shows the SE analysis of the decomposed modes, and Figure 5c illustrates the reconstructed components after SE-based grouping.

The original power series is decomposed into nine intrinsic mode functions (IMFs). A higher IMF order corresponds to a lower frequency. Oscillatory signals at different frequencies exhibit distinct patterns and characteristics: specifically, IMF1-IMF4 oscillate densely around the zero axis, while IMF5-IMF9 demonstrate comparatively sparser fluctuations. Following the ICEEMDAN decomposition, the obtained subsequences exhibit progressively stabilized oscillations. This suggests effective mitigation of the non-stationarity inherent in the PV power series, thereby facilitating subsequent modeling procedures.

However, constructing prediction models for all subsequences would inevitably lead to a more time-consuming forecasting process. Furthermore, high-frequency components generally require more localized data features for accurate prediction, whereas low-frequency components focus more on capturing overall trend variations. Therefore, to further reduce the computational complexity and enhance prediction efficiency, SE is applied to characterize the complexity of the decomposed modes and to group them accordingly.

The SE values of the decomposed subsequences decrease with increasing IMF order, indicating a progressive reduction in signal complexity. Based on the similarity of entropy values after normalization, the subsequences are merged and reconstructed. IMF5-IMF9 exhibit low and relatively stable SE values, suggesting that they mainly capture trend information and are therefore grouped as low-frequency components. IMF3-IMF4 demonstrate intermediate complexity and are reconstructed as medium-frequency components, whereas IMF1-IMF2 display the highest complexity and are combined into high-frequency components. By reorganizing nine IMFs into three representative components (high-, medium-, and low-frequency), the number of forecasting targets is reduced while the essential multiscale characteristics are retained, thereby improving prediction efficiency.

5. Model Validation

5.1. Performance Evaluation of Feature Selection

To evaluate the influence of feature selection on forecasting performance, comparative experiments are performed across four representative months. A comparison of the prediction accuracy before and after feature selection is presented in Figure 6. Specifically, the results derived from the full feature set are represented by even-numbered cases (#2, #4, #6, and #8), whereas the results obtained utilizing the selected features correspond to the odd-numbered cases (#1, #3, #5, and #7).

It is indicated by the comparative results that, following feature selection, the ICEEMDAN–SE–RWCE–GRU model achieves consistent improvements in key metrics, including RMSE, MAE, and $R^2$, thereby reducing prediction errors and enhancing overall forecasting performance. The effectiveness of the proposed feature-selection scheme in improving PV power forecasting accuracy is confirmed by these results. The performance gains can be attributed to the elimination of redundant or noise-dominated meteorological variables, which enables the GRU network to prioritize on the most informative predictors. Moreover, the findings suggest that higher-dimensional inputs do not necessarily yield better accuracy; instead, selecting an appropriate feature subset is crucial for robust and reliable prediction.

5.2. Contribution Analysis of ICEEMDAN-Based Decomposition

To assess the contribution of ICEEMDAN-based decomposition to the proposed forecasting framework, we conduct comparative experiments against (i) an alternative decomposition scheme, namely RF-VMD-RWCE-GRU, and (ii) direct forecasting without decomposition, namely RF-RWCE-GRU. Figure 7 shows the predicted PV power trajectories for four representative months (January, April, July, and October). Overall, the ICEEMDAN-based model shows the closest agreement with the measured output, especially during rapid ramping periods and around peak regions, where local fluctuations and peak variations are captured more accurately than with the VMD-based counterpart.

Figure 8 further provides a quantitative evaluation in terms of RMSE, MAE, and $R^2$ across different strategies. The results indicate that incorporating ICEEMDAN consistently yields lower RMSE and MAE while achieving higher $R^2$ across all four months, thereby indicating improved fitting accuracy and prediction stability under varying seasonal conditions. In addition, compared with direct forecasting on the raw PV power series (without decomposition), ICEEMDAN-based decomposition noticeably reduces forecasting errors, suggesting that it can effectively mitigate noise and nonstationary disturbances in PV power signals. These observations confirm that the raw PV power data can be decomposed by ICEEMDAN into informative components with clearer temporal characteristics, thereby facilitating more accurate PV power forecasting within the proposed hybrid model.

5.3. Comparison of Different Optimization Algorithms

To evaluate the hyperparameter optimization capability of the RWCE algorithm, Particle Swarm Optimization (PSO) and the Dung Beetle Optimizer (DBO) are selected as baseline algorithms for comparison. All optimization methods are implemented under identical experimental conditions to ensure fairness. Specifically, the maximum number of iterations is set to 30, the population size is fixed at 30, and the search space is defined as follows: the learning rate ranging from 0.001 to 0.05, number of hidden neurons from 10 to 50, and regularization parameter from 0.0001 to 0.001. Using the January and July datasets as representative examples, Figure 9 depicts the convergence behaviors of the fitness value obtained by RWCE algorithm and the competing algorithms. The results indicate that the RWCE algorithm converges faster and achieves higher optimization efficiency during the iterative process, suggesting that more suitable hyperparameter configurations can be identified within a limited number of iterations.

To further assess the impact of hyperparameter optimization on forecasting performance, the RF-ICEEMDAN-SE-GRU model without hyperparameter optimization is adopted as the baseline. Predictions are generated on the test set, and the corresponding error metrics are calculated. In addition, PSO and DBO are incorporated into the forecasting model as comparative optimization strategies to tune the model hyperparameters. Figure 10 illustrates the agreement between the measured PV power and the predicted outputs obtained with different optimization methods, while Figure 11 presents a comparative evaluation of the forecasting metrics across these optimization strategies. To improve transparency and facilitate quantitative comparison, we provide the exact numerical results corresponding to Figure 7, Figure 9 and Figure 12 in the Supplementary Material. Specifically, Table S1 reports the RMSE, MAE, and R² values for all compared models across all test cases shown in these figures.

Across the four representative months, the proposed RF-ICEEMDAN-SE-RWCE-GRU model consistently achieves superior performance across all evaluation metrics when compared with the baseline and alternative optimization approaches. Relative to the non-optimized baseline model, the introduction of metaheuristic optimization enables more effective exploration of the hyperparameter space, leading to reduced prediction errors and enhanced forecasting accuracy. Among the optimization methods considered, the RWCE algorithm yields the lowest RMSE values, indicating its advantage in minimizing forecasting deviations. Moreover, simulation results over the four representative months indicate that the proposed approach reduces RMSE by an average of 9.02% compared with the DBO-optimized model (the best-performing competing optimizer among PSO and DBO) and by 43.41% relative to the non-optimized baseline model. Consistent improvements are also observed in MAE, MAPE, and R², further demonstrating the overall enhancement in forecasting accuracy and stability. These results confirm the effectiveness of the RWCE algorithm for hyperparameter tuning of the GRU network in PV power forecasting and demonstrate its robustness under different temporal conditions.

To strengthen the reliability of the performance claims, we conducted a robustness analysis by repeating the training and forecasting procedure under 10 random seeds. Specifically, we selected January and July as representative months and ran the proposed model multiple times with different seeds while keeping the data split and preprocessing fixed. The forecasting metrics are reported as mean ± standard deviation, which quantifies the variability across runs and provides evidence of performance stability. Robustness results under multiple random seeds are summarized in Table S3. In addition, to avoid reliance on a single fixed test window, we supplemented the evaluation with a rolling-origin (walk-forward) strategy. Specifically, the model is trained on an expanding time window and evaluated on subsequent time blocks of a length of 5 days, repeated for seven folds. The rolling-origin results are summarized in Table S4, demonstrating that RWCE-based tuning yields stable performance improvements across different evaluation windows.

5.4. Evaluation of Model Scalability and Applicability

To further evaluate the cross-regional generalization capability and robustness of the proposed model, independent PV power forecasting was conducted using the Australian Desert Knowledge Edge Solar Centre (DKASC) dataset (available at https://dkasolarcentre.com.au/ (accessed on 23 May 2025)). The dataset comprises 6254 records collected at 5 min intervals, corresponding to 169 data points per day. Compared with typical temperate or urban meteorological conditions, the Australian desert environment is often associated with more pronounced short-term variability and harsher atmospheric conditions, which can induce substantial fluctuations in PV output. Therefore, the DKASC dataset provides a meaningful benchmark for assessing model adaptability under extreme operating scenarios. Following feature selection, the key variables retained for modeling included T-air, RH, GHI, DHI, GTI, and DTI.

As illustrated in Figure 12, the proposed model maintains stable and accurate PV power Forecasting performance despite the strong temporal variability and uncertainty present in the DKASC dataset. Specifically, the model achieves an RMSE of 0.2969, an MAE of 0.1621, and $R^2$ of 0.9724. These results indicate that the proposed approach can effectively track rapid PV power fluctuations and preserve high predictive accuracy in challenging desert conditions. Additionally, the proposed model outperforms several comparison models, further validating its superiority and reliability in complex environments Overall, the DKASC evaluation substantiates the stability, robustness, and strong generalization capability of the proposed model for real-world PV power forecasting across complex environmental scenarios.

6. Conclusions

To enhance the accuracy of short-term PV power forecasting, this study proposes a novel hybrid model, termed RF-ICEEMDAN-SE-RWCE-GRU. The proposed method is designed to address key challenges in PV time-series forecasting, including non-stationarity, feature redundancy, and sensitivity to hyperparameter settings. Based on extensive experiments, the main conclusions are as follows:

(1)

RF effectively identifies meteorological variables that are strongly associated with PV power output, thereby reducing the influence of irrelevant and redundant inputs.

(2)

By incorporating ICEEMDAN, the PV power series is decomposed from a complex non-stationary signal into relatively stationary components, which alleviates stochastic fluctuations that impair forecasting. Furthermore, SE-based reconstruction reduces input complexity and improves forecasting performance.

(3)

RWCE algorithm is first employed to automatically tune the GRU network hyperparameters, enabling the model to obtain more suitable configurations. This strategy mitigates performance degradation caused by suboptimal hyperparameter initialization and enhances both prediction accuracy and generalization.

(4)

The proposed RF-ICEEMDAN-SE-RWCE-GRU model demonstrates strong effectiveness for PV power forecasting. Across four representative months, it achieves an average RMSE reduction of 9.02% relative to comparison models and 43.41% relative to the baseline model, indicating improved robustness and precision.

(5)

The model demonstrates adaptability across various climate conditions, validating the proposed model’s applicability to real-world scenarios. This versatility underscores its capacity to perform well in different environmental contexts, thereby enhancing its practical value for PV power forecasting.

The developed hybrid forecasting model demonstrated its outstanding performance through data preprocessing, model hyperparameter optimization, and multi-experimental validation across climatic regions. Improving forecasting accuracy can reduce the uncertainty of renewable energy, minimize over-design, and optimize equipment configuration, thereby lowering costs, enhancing the overall efficiency and economic viability of solar power plants, and also contribute to the optimization of the dispatch and resource allocation in integrated energy systems.