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Scientific Reports volume 16, Article number: 24495 (2026) Cite this article
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The prediction and fault diagnosis of photovoltaic power generation are crucial for the efficient utilization of clean energy, but traditional methods have limitations such as low efficiency and strong subjectivity. To this end, an innovative hybrid model combining bidirectional long short-term memory network and Transformer is proposed, integrating the improved Golden Jackal optimization algorithm, time convolutional neural network, and grey wolf algorithm optimized variational mode decomposition to achieve signal adaptive purification, bidirectional temporal dependency capture, and global attention focusing. The experimental results show that the research model has achieved high-precision prediction, with an average accuracy of 95.03% in all seasons, an average absolute error of 4.86 kW, a relative root mean square error of 8.46%, and no significant cross seasonal differences, verifying the stability of the model. In terms of fault diagnosis, the waveform difference of the fault signal is up to 35.2 mm, and the accuracy of classifying five types of faults is 96.87%. SHAP analysis shows that instantaneous irradiance and historical power have the highest contribution, and the component string current is negatively correlated, which conforms to the physical laws of photovoltaics. In terms of deployment, the complete model has a parameter count of 8.77 M and an accuracy rate of 97.08%, making it suitable for high-precision offline and cloud scenarios. These results indicate that the proposed model improves both fault recognition efficiency and prediction accuracy. This study provides a valuable reference for building accurate photovoltaic power prediction and fault diagnosis models under complex environments, thus promoting the development of clean energy.
With the intensifying global energy crisis and environmental pollution, solar energy has gained great attention as a clean and widely distributed resource¹. Photovoltaic power generation, as the main form of solar energy utilization, has the characteristics of cleanliness, environmental protection, flexible application, safety and efficiency². At present, photovoltaic energy has become an important support for the stable operation of hydrogen energy storage based renewable systems and active distribution network renewable integrated energy systems^3,4. To meet the rapidly growing electricity demand in the future, enhancing demand response management in power grids is crucial^5,6. Power prediction and fault diagnosis of photovoltaic systems ensure safe and efficient operation of photovoltaic stations. Improving the accuracy of prediction and diagnosis significantly enhances grid stability, reduces economic loss, improves reliability, and promotes the development of clean energy^7,8. However, this field still faces multiple challenges and significant research gaps. Firstly, the new system architecture of off grid multi energy microgrid scheduling and decentralized coordination, which includes mobile hydrogen storage and refueling stations, requires photovoltaic power prediction to maintain low error in response to sudden changes in irradiance at a minute level update frequency. Otherwise, it will directly lead to an imbalance between hydrogen supply and demand^9,10. At the same time, most existing photovoltaic data analysis methods are limited to physical models and traditional statistical techniques, which are difficult to adapt to the needs of complex scenarios such as improving the resilience of distribution networks under extreme weather conditions and coordinating hydrogen and electricity management^11,12,13. Moreover, traditional methods increase the data processing time of a single prediction task by about 60–80%, and the differences between different operators can reach more than 30%, which has limitations such as low efficiency and strong subjectivity¹⁴. Although deep learning has been introduced, most studies still have shortcomings such as simple stacking of model structures, dependence on manual trial and error for hyperparameters, and separation between preprocessing and feature extraction. These defects result in insufficient generalization performance and weak interpretability of the model. A hybrid model combining Bidirectional Long Short-Term Memory Network (BiLSTM) and Transformer is proposed to address the aforementioned gaps. By using Improved Golden Jackal Optimization (IGJO) to achieve hyperparameter self-tuning, enhancing local features with Time Convolutional Network (TCN), and adaptively denoising with Grey Wolf Optimization Variational Mode Decomposition (GWO-VMD), the accuracy and robustness of prediction and diagnosis are systematically improved. The research expects the proposed model to effectively overcome the three key technical bottlenecks that have long existed in this field, namely insufficient prediction accuracy under multi seasonal fluctuations, poor robustness under extreme weather conditions, and severe dependence on artificial feature engineering and empirical tuning. Through innovative multi module collaborative mechanisms, the model will significantly improve the overall performance and generalization ability of photovoltaic prediction and fault diagnosis, providing reliable and interpretable theoretical support and technical solutions for intelligent operation and maintenance of clean energy systems in complex environments.
With rapid advances in computer technology, performance evaluation of photovoltaic power generation based on intelligent algorithms has become a research hotspot. Intelligent algorithms provide advantages such as high efficiency, objectivity, and reduced manual dependence. Among them, the Long Short-Term Memory (LSTM) network is a specialized recurrent neural network designed to address gradient vanishing and exploding issues, primarily used for time series analysis. Transformer is a deep learning architecture based on the self-attention mechanism, which transforms feature data and improves parallel computing¹⁵. For example, Wu et al. team proposed a prediction model combining Convolutional Neural Network (CNN) and LSTM, which constructs leading related indicators as a sequence array, extracts feature vectors from the sequence data through a convolutional framework, and introduces them into LSTM for analysis, thereby achieving accurate prediction of stock prices and trends¹⁶. Li et al. put forward a dynamic prediction model to address the difficulty of landslide displacement prediction. They decomposed cumulative displacement, used a least square quintic polynomial function to fit the trend, and combined the results with LSTM, which effectively predicted landslide displacement¹⁷. Ozcan et al. focused on phishing prevention. They extracted features through character embedding and natural language processing techniques, then fused them and trained a model using LSTM and deep neural networks to build an accurate phishing detection model¹⁸. Pradani et al. raised an automatic scoring model based on Transformer for essay evaluation. They extracted features with information retrieval and text mining weighting techniques, calculated semantic similarity using cosine similarity, and achieved accurate scoring¹⁹. Zhao et al. raised a multimodal image fusion algorithm based on Transformer. They combined Transformer and Convolutional Neural Network encoders to enhance both global and local information fusion, and results showed good performance²⁰.
Accurate evaluation of photovoltaic power generation effectively promotes the development of clean energy. At present, theories and applications of power prediction and fault diagnosis are relatively mature, and many scholars have carried out in-depth research. Nelega et al. constructed a photovoltaic prediction model using LSTM network to solve output power prediction. They used recursive and non-recursive strategies to calculate input and output variables, and results showed good prediction performance²¹. Salman et al. transformed the data into time series and extracted features with a combination of Convolutional Neural Networks and LSTM. They then optimized the model architecture using Transformer and ultimately developed a hybrid deep learning approach for photovoltaic power prediction²². Said and Alanazi raised a prediction model based on LSTM to address low prediction accuracy. They extracted temporal features using LSTM, further extracted spatial features using an autoencoder, and fused them to achieve high prediction accuracy²³. R. Nelega et al. constructed a photovoltaic power generation prediction model using LSTM and Recurrent Neural Network (RNN) to address issues such as output power prediction in photovoltaic power generation. The input and output quantities were calculated using both recursive and non recursive strategies, and the results showed that the research model had good predictive performance²⁴. Shaban et al. improved the performance and reliability of photovoltaic fault diagnosis by combining preprocessing, feature extraction, selection, and classification modules. They enhanced image quality through preprocessing, filtered the most significant features, and achieved accurate classification of fault types²⁵. X. Chen et al. proposed a cost oriented renewable energy and reserve demand forecasting method to address the issue of insufficient economy in power system unit combination optimization. The predictor was trained using a two-layer mixed integer programming model to induce more economical scheduling plans²⁶. H. Hou et al. proposed an interpretable deep learning model that integrates physical laws, combined with Beluga Whale Optimization (BWO), LSTM, and physical memory units to construct a prediction model. The Shapley value was used to explain the influence of features, and the results showed that the proposed model can effectively predict the ice thickness of overhead transmission lines²⁷. M. The Tan team proposed a soft shared multi task deep learning method to address the problem of difficult extraction of spatiotemporal coupling features in multi node load prediction in power systems. By integrating Gated Temporal Convolutional Network (GTCN) and Gated Recurrent Unit (GRU), a multimodal feature module was constructed, and the soft sharing mechanism was used to collaboratively optimize the prediction tasks of each node²⁸. The summary of the above references is shown in Table 1.
According to Table 1, the current research has the following gaps:
Existing research actively adopts hybrid models, but mainly combines CNN and LSTM, or uses Transformer alone. Most literature does not endogenously and deeply integrate the core mechanisms of LSTM and Transformer to construct a specialized model that combines the advantages of both.
The existing research on photovoltaic power generation prediction and fault diagnosis technology based on intelligent algorithms can collect real-time data according to environmental changes and analyze the characteristics of data changes, but the analysis of seasonal changes is not comprehensive. Most literature focuses on fault diagnosis at specific times, which can easily lead to weak generalization ability, high false alarm rate, and certain limitations.
To address the limitation of incomplete feature extraction in existing photovoltaic (PV) data analysis methods, this study designs a novel hybrid architecture that deeply integrates the BiLSTM network with the Transformer model. The specific design framework for the study is shown in Fig. 1.
Research design framework.
The main contributions of the research are as follows:
Propose a temporal feature collaborative extraction architecture based on deep fusion of BiLSTM and Transformer. To address the shortcomings of incomplete feature extraction in existing methods, the bidirectional long-term dependency capture capability of BiLSTM and the multi head global attention mechanism of Transformer are jointly designed at the mathematical level for the first time. This architecture can simultaneously mine local dynamic patterns and global contextual correlations in photovoltaic time series, improving the completeness of feature expression under complex operating conditions.
Introduce the IGJO algorithm to achieve global optimization of BiLSTM hyperparameters. In response to the problem of traditional gradient optimization easily falling into local optima and weak adaptability, the improved Golden Jackal optimization algorithm is integrated into the BiLSTM framework. By intelligently reconstructing the parameter space, the global search efficiency and convergence speed of the model in high noise and non-stationary photovoltaic data have been significantly improved, endowing the model with stronger deep feature mining capabilities.
Design TCNT algorithm to enhance the local temporal modeling capability of Transformer. In response to the lack of sensitivity of standard Transformers to local fluctuation patterns, an innovative fusion of time convolutional networks, extended causal convolutions, and residual connections is proposed to form the TCNT algorithm. This improvement significantly enhances the modeling accuracy and generalization performance of the model under strong fluctuations in photovoltaic data, ensuring the reliability of predictions in complex scenarios such as extreme weather.
Build an intelligent operation and maintenance model that integrates GWO-VMD with multiple modules. Optimizing VMD parameters through GWO to achieve adaptive decomposition of non-stationary signals. A unified photovoltaic power generation prediction and fault diagnosis model was constructed by integrating signal purification, deep feature collaborative extraction, and multi task joint optimization. This model provides a high-precision and robust solution for the intelligent operation and maintenance of photovoltaic power plants, effectively promoting the reliability and economic benefits of clean energy systems.
This paper is organized into four parts. The first part introduces the background and related literature, analyzing the current research status of photovoltaic power generation. The second part describes in detail the operation process of BiLSTM improved by IGJO, the superiority and operation of TCNT improved Transformer, and the fusion of the two. It also explains how GWO-VMD improves the model and its application to photovoltaic power prediction and fault diagnosis. The third part verifies the performance of the improved model through comparative experiments and evaluates its effect in practical applications. The fourth part summarizes the experimental data and results. The fifth part explores future research directions.
With the rapid development of artificial intelligence, computer intelligent algorithms have provided new technological paths for photovoltaic power expansion, power generation prediction, and fault diagnosis^29,30,31. Traditional prediction and diagnosis methods have defects such as insufficient feature extraction ability, low efficiency, and weak adaptability to different scenarios, which limit their application^32,33. BiLSTM adds a backward LSTM layer. Through the bidirectional structure, it captures information from both directions of the sequence, which effectively improves feature extraction ability, computing efficiency, and accuracy^34,35. At the same time, the IGJO algorithm effectively improves the optimization efficiency and global optimization ability of model parameters through an improved search strategy, and is widely used in the fields of parameter optimization and fault diagnosis of complex systems. Therefore, this paper raises a BiLSTM-based method for photovoltaic power prediction and fault diagnosis. On this basis, the IGJO algorithm is introduced to improve the global search ability of the algorithm under complex environments and to achieve deep mining of data. The operation process of BiLSTM is shown in Fig. 2.
BiLSTM operation process.
As shown in Fig. 2, BiLSTM consists of two forward and backward LSTM structures. The forward LSTM layer handles the sequence in chronological order, capturing historical information at each time step. The backward LSTM layer processes the sequence in reverse, extracting features related to future states. Both LSTM layers calculate the current input and the hidden states of the previous and next moments. They update their states through the input gate, forget gate, and output gate. Finally, the forward and backward hidden states at the same time are fused to enhance the overall representation ability of sequence features. The mathematical expression of information transmission in BiLSTM is shown in Eq. (1)³⁶.
In Eq. (1), ({x_t}) represents input data. ({W_1}) and ({W_2}) represent weight parameters, and ({C_t}) represents the current state. After integrating the forward and backward LSTM layers, the mathematical expression of the obtained information is shown in Eq. (2)
In Eq. (2), ({h_n}^{{[p]}}) represents p layer features. ({W_3}) and ({W_4}) represent weight coefficients, and ({h_a}) and ({h_b}) represent forward and backward information transmission. Traditional BiLSTM still has defects such as slow computing speed and weak global search ability^37,38. The GJO algorithm can track and capture missing features and improve data mining ability. Therefore, this paper introduces the GJO algorithm and modifies it with a cosine factor to escape from local optima, forming the IGJO hybrid algorithm. Its process is shown in Fig. 3.
Operation process of IGJO hybrid algorithm (Icon source from: www.iconfont.cn).
As shown in Fig. 3, the IGJO algorithm initializes by randomly generating a group of solutions and building an initial matrix. The cosine factor helps the algorithm escape from local optima. The algorithm then tracks and captures escape energy, records the global optimal solution, and calculates the fitness value. Position information is updated based on the fitness value. After computing the escape energy, the algorithm adopts hunting and attacking modes on the escaping prey, and then updates the latest position. If the stopping condition is not met, the process returns to recompute the escape energy. If the condition is met, the algorithm outputs the optimal fitness value. IGJO realizes global search in complex spaces. Before iteration, it randomly generates an initial population, whose mathematical expression is shown in Eq. (3).
In Eq. (3), ({X_0}) represents the initial position, (rand) represents a random value in [0,1], ({X_{hbox{max} }}) and ({X_{hbox{min} }}) represent the upper and lower bound of the variable. By calculating escape energy, the IGJO algorithm tracks and captures escaping prey. The mathematical expression of escape energy is shown in Eq. (4).
In Eq. (4), ({c_1}) represents a constant, t is the current iteration, ({E_0}) represents the initial energy value. A cosine control factor is introduced to adjust the algorithm and help the population escape from the local optimal solution. The mathematical expression with cosine factor is shown in Eq. (5).
In Eq. (5), ({X_{0′}}) represents the modified initial population, and (cos) represents the cosine factor. By integrating IGJO with BiLSTM, the IBiLSTM hybrid algorithm is obtained. Its process is shown in Fig. 4.
IBiLSTM hybrid algorithm operation process (Icon source from: www.iconfont.cn).
As shown in Fig. 4, the IGJO algorithm initializes a data matrix, introduces a cosine factor to track and capture escape energy, records the global optimal solution, and updates position information based on fitness value. Then the hunting and attacking modes are applied to escaping prey, and the latest position is obtained until the termination condition is met and the optimal fitness value is output. The optimized data from IGJO is then fed into BiLSTM. The forward and backward LSTM layers process the sequence, update their states through calculation, and fuse hidden states from both directions. This process captures global context information and obtains comprehensive feature data.
The implementation steps of the IBiLSTM algorithm are as follows: Firstly, the photovoltaic timing data denoised by GWO-VMD is divided into 24-hour windows, standardized using Z-score, and input into the network. Build a bidirectional LSTM using the PyTorch framework, with the forward layer processing the sequence in chronological order and the backward layer processing it in reverse order. The number of hidden units is 128, with 2 layers and a dropout rate of 0.3. Each LSTM unit updates its state through input gates, forget gates, output gates, and memory units. Concatenate the forward and backward hidden states at the same time into a 256 dimensional bidirectional context vector. Adopting an improved golden jackal optimization algorithm to automatically search for initial learning rate, L2 coefficient, and number of hidden units. The training uses the Adam optimizer, with a loss function of mean square error, batch size of 64, maximum of 500 rounds, and early stop. Finally, the bidirectional features are mapped into feature data through a fully connected layer.
IBiLSTM enhances data utilization and realizes comprehensive feature search. However, it still faces problems such as the serial structure, which limits full computation, and it may affect the accuracy of power prediction and fault diagnosis of PV systems. It also has some limitations in capturing global long-term dependencies. Transformer enhances data vector representation, reduces gradient vanishing or explosion, and establishes weight association efficiently to realize information transfer^39,40. Therefore, this study introduces Transformer and combines it with the multi-head attention mechanism to further enhance performance and generalization. The Transformer architecture is depicted in Fig. 5.
Structure diagram of the Transformer algorithm (Icon source from: www.iconfont.cn).
As shown in Fig. 5, Transformer adopts an encoder-decoder structure. The encoder and decoder are composed of multi-head attention and feedforward neural networks. Each layer introduces residual structures and layer normalization. The multi-head attention captures information from different perspectives. The feedforward neural network connects feature layers and transforms input features, establishing the relationship between input and output. Residual structures concatenate data, propagate gradients, and enhance stability. Layer normalization ensures consistency during training. The self-attention mechanism evaluates weights of different positions and dynamically analyzes key features. Its mathematical expression is shown in Eq. (6)⁴¹.
In Eq. (6), (sqrt {{d_k}}) represents the scaling factor. Self-attention is calculated independently in each subspace, and multi-head attention is obtained. Its expression is shown in Eq. (7).
In Eq. (7), (concat) represents the connection. The data obtained by multi-head attention are input into the feedforward neural network for feature transformation, capturing relationships among data. The calculation is shown in Eq. (8).
In Eq. (8), (sigma) represents a nonlinear function, ({H^l}) is the output of layer l, ({W^l}) is the weight, and ({b^l}) represents the bias. Traditional Transformer has weak ability in capturing temporal sequences and cannot realize feature extraction in spatial dimensions^42,43. Therefore, this study introduces TCN and integrates dilated causal convolution and residual networks, and finally fuses Transformer to obtain TCNT. The process is shown in Fig. 6.
Schematic diagram of the process of TCN fusion Transformer (Icon source from: www.iconfont.cn).
As shown in Fig. 6, TCNT first inputs feature sequences and processes them through three TCN residual blocks. The TCN residual block expands the receptive field through dilated causal convolution and improves parallel computing. Normalization recalculates weights to speed up convergence. Relu and dropout are applied to fit and filter data. Then the flatten layer and fully connected layer extract features and reduce gradient problems. Finally, the processed data are input into Transformer. Multi-head attention and feedforward networks output the final data. The convolution operation is shown in Eq. (9).
In Eq. (9), ({x_i}^{l}) represents the i-th feature of layer l, ({W_i}^{l}) represents the i-th weight matrix of layer l, f represents the activation function, X represents the output, and ({b_i}^{l}) represents the bias. By replacing standard convolution with causal convolution and expanding the receptive field, the dilated causal convolution is expressed as Eq. (10).
In Eq. (10), (omega) represents the convolution kernel, ({*_d}) represents dilated convolution, d represents sampling distance, and ({x_{t – dn}}) represents data sampled at interval d. The residual block is then added to simplify training. The expression is shown in Eq. (11)
In Eq. (11), x represents input data and (F(x)) represents residual value.
The specific implementation steps of the TCNT algorithm are as follows: the photovoltaic temporal feature sequence is sequentially passed through three TCN residual blocks, each residual block containing dilated causal convolution, weight normalization, ReLU activation, and spatial dropout. The expansion rates are set to 1, 2, and 4, the convolution kernel size is 3, and the number of output channels is 64. Extended causal convolution extracts multi-scale temporal features in parallel by exponentially expanding receptive fields. Set the dropout rate to 0.2 to prevent overfitting. Subsequently, the feature maps output by the three residual blocks are transformed into 1536 dimensional vectors through a flattening layer, followed by dimensionality reduction and abstraction of high-level features through a fully connected layer. Afterwards, input into the Transformer encoder, with 8 heads and 128 attention dimensions in the multi head attention layer, and 512 dimensions and 2 layers in the feedforward network. Finally, the power and fault characteristics are obtained through the linear output layer.
IBiLSTM improves global search ability in complex environments. It updates its state with forward and backward LSTM layers and captures global context information for deep feature mining. Meanwhile, TCNT expands the receptive field through dilated causal convolution, improves parallel ability, and builds relationships between vectors to enhance stability. Therefore, to solve the problems of low efficiency, weak adaptability, and insufficient search ability in traditional PV power prediction and fault diagnosis, this study fuses IBiLSTM and TCNT to form IBiLSTM-TCNT. The process is shown in Fig. 7.
IBiLSTM-TCNT hybrid algorithm operation process (Icon source from: www.iconfont.cn).
As shown in Fig. 7, IBiLSTM-TCNT initializes and introduces the cosine factor to track and capture escape energy. It adopts hunting and attacking modes to update position and outputs the optimal fitness. The optimized data are input into BiLSTM. Forward and backward hidden states are calculated and fused to obtain complete features. Then three TCN residual blocks process sequences. Dilated causal convolution and normalization recalculate weights. Relu and dropout handle the data. The flatten layer and fully connected layer extract features. Finally, the output is processed by Transformer through multi-head attention and feedforward networks. The calculation of the forget gate in convolution is expressed as Eq. (12).
In Eq. (12), (sigma) represents the growth curve function, (omega) represents the weight matrix, ({h_{t – 1}}) represents the neuron output, and ({x_t}) represents the input at time t. The input gate controls information flow and filters new input. It regulates the output of neurons and cell states. The calculation of the output gate ({y_t}) is shown in Eq. (13).
In Eq. (13), (tanh) is the hyperbolic tangent function, and ({C_t}) is the cell state. In order to solve the problems of signal acquisition noise interference in research algorithms, VMD is proposed to remove noise. However, traditional VMD requires pre-set based on experience, resulting in unstable decomposition effects. The GWO algorithm can simulate the social hierarchy and hunting behavior of gray wolves for swarm intelligence optimization, efficiently and globally searching for the optimal solution to the problem. Therefore, the study utilized the GWO algorithm to optimize VMD and obtained the GWO-VMD algorithm. This study combines GWO-VMD with IBiLSTM-TCNT and finally builds a PV power prediction and fault diagnosis model (GV-IBiLSTM-TCNT). The process of GWO-VMD is shown in Fig. 8.
Operation process of GWO-VMD algorithm (Icon source from: www.iconfont.cn).
As shown in Fig. 8, GWO-VMD first processes input signals by GWO, calculates the optimal fitness, and finds optimal parameters. VMD decomposes signals and calculates intrinsic mode functions. Then the components are input into the function to calculate power. A threshold is set. Components greater than the threshold are regarded as noise, and noise amplitudes are set to zero. Components greater than the threshold are kept as effective signals. After filtering, the data are reconstructed to obtain enhanced signals. The normalization of the module is shown in Eq. (14)
In Eq. (14), ({P_j}) represents normalized values, (a(j)) represents the envelope signal, and j represents (left{ {1,2,3,…,N} right}). Normalization reduces noise effectively. Envelope entropy evaluates VMD performance. The expression is shown in Eq. (15).
In Eq. (15), ({E_p}) represents envelope entropy. The final PV power prediction and fault diagnosis model is shown in Fig. 9.
Photovoltaic power generation prediction and fault diagnosis model operation process (Icon source from: www.iconfont.cn).
As shown in Fig. 9, the model first calculates the optimal fitness and finds optimal parameters. VMD decomposes signals, calculates power, and sets a threshold. After filtering effective components, the data are reconstructed to obtain enhanced signals. Then the data are initialized, and the cosine factor is introduced to track and capture escape energy. The hunting and attacking modes update position. The optimized data are input into BiLSTM to obtain complete features. Three TCN residual blocks process sequences. Dilated causal convolution and normalization recalculate weights. The flatten layer and fully connected layer extract data. Multi-head attention and feedforward networks produce the final optimized data. Under sunny, cloudy, and rainy conditions, power prediction is performed and accuracy is evaluated. At the same time, PV faults are classified and identified.
The detailed implementation steps of the model are as follows: Firstly, GWO is used to adaptively search for the optimal parameters of VMD, determine the number of modes K = 5 and the penalty factor α = 2150, and decompose the original photovoltaic signal to obtain 5 intrinsic mode components. Calculate the correlation coefficients between each component and the original signal, and set a threshold of 0.3. Then input the signal into IGJO, population 30, iterate 100 times, and output the optimal solution of BiLSTM parameters. Construct a BiLSTM network based on optimized parameters, extract bidirectional temporal features, and concatenate them into a 256 dimensional vector. This vector sequentially outputs temporal features through three TCN residual blocks. Finally, input the Transformer encoder and output the predicted power value or the probability of five types of faults.
To verify the performance of the IBiLSTM-TCNT algorithm, it was compared with Gorilla Troops Optimizer (GTO), Particle Swarm Optimization-Back Propagation (PSO-BP), and Multi-Marker Similarity Assessment (MMSim). The experiments used Windows 11 Ubuntu 18.04 as the operating system, Intel Core i7-5400 as the processor, 16 GB of memory, Python 3.9 as the programming language, and PyTorch as the deep learning framework. The learning rate was set to 0.0001, and the number of iterations was set within 500. The experimental dataset is selected from the Global Energy Forecasting Competition (GEFCom) dataset, which includes photovoltaic power plant data from different climate zones with a time resolution of 1 h. The dataset is randomly divided into training, validation, and testing sets in an 8:1:1 ratio. Statistical analysis was conducted using SPSS 26.1. All data underwent normality tests and homogeneity of variance tests. Independent and matched t-tests were applied to data conforming to a normal distribution. The significance level was set at p < 0.05. Prior to the significance test, the study assumed that there were no significant differences in the performance of all models. The p-value was calculated to determine whether to reject this assumption. In order to analyze the consistency of cross regional performance of data, independent photovoltaic power station data from sites A, B, C, D, and E with different climate types were collected. Each site came from different regions, and the prediction accuracy of the five sites was cross site verified. Based on site A, the consistency analysis results are shown in Table 2.
As shown in Table 2, the accuracy of Site A is 95.38%. The accuracy results of Sites B, C, D and E in different climates show no statistically significant differences compared to the benchmark Site A (p > 0.05). The above results demonstrate that the model has excellent performance consistency in different geographical and climatic environments, and the learned operating rules are universal. The Generalized Rastrigin and Generalized Rosenbrock functions were applied to evaluate the optimal fitness of IBiLSTM-TCNT, GTO, PSO-BP, and MMSim. The results are shown in Fig. 10.
Optimal fitness evaluation results of the algorithm.
As shown in Fig. 10a, in the Generalized Rastrigin function, the IBiLSTM TCNT algorithm achieves a rapid decrease in fitness value within the first 50 iterations, indicating its strong global exploration ability. The subsequent iterations converge smoothly to the optimal value of 1.05, proving its stability. As shown in Fig. 10b, under the validation of the Generaliad Rosenbrock function, the fitness curve of the IBiLSTM TCNT algorithm rapidly decreases in 0–20 iterations, slows down in 20–130 iterations, then stabilizes, and finally converges with a fitness value of 0.51. Compared with GTO, PSO-BP, and MMSim, the fitness curve of IBiLSTM-TCNT was significantly better and converged faster. This was mainly because the TCN residual block expanded the receptive field through dilated causal convolution and improved parallel ability, which accelerated convergence. The results proved that IBiLSTM-TCNT found the optimal fitness value faster and had excellent optimization ability. To further test prediction performance, the accuracy and loss of IBiLSTM-TCNT, GTO, PSO-BP, and MMSim were evaluated. The results are shown in Fig. 11.
Prediction accuracy and loss value test results.
As shown in Fig. 11a, The accuracy of the IBiLSTM TCNT algorithm sharply rises within the range of 0–50 iterations to 96.18%. After reaching 96.18%, the accuracy curve enters a small oscillation upward phase, and the accuracy eventually converges to a high level of 97.38% and remains stable. As shown in Fig. 11b, the research algorithm rapidly decreases after 50 iterations, with a loss value of 0.27. Within the range of 100–500, the loss value stabilizes at 0.04. The accuracy and loss value data performance of the research algorithm are superior to the other three algorithms, because it indicates that the IGJO algorithm, through its global exploration strategy, enables the algorithm parameters to quickly cross the flat area of the loss surface and efficiently locate the global optimal solution. At the same time, the algorithm tracks and captures escape energy through cosine factors, significantly reducing data loss and further improving the prediction accuracy of the algorithm. The results proved that the algorithm had good prediction performance. To further analyze fitting performance, the residual results of IBiLSTM-TCNT, GTO, PSO-BP, and MMSim were compared, as shown in Fig. 12.
Comparison of fitting performance test results.
As shown in Fig. 12a, the proposed algorithm showed a significant normal distribution, with a fitting value of 0.9314. In Fig. 12b–d, the residual curves of GTO, PSO-BP, and MMSim showed different degrees of deviation. The residual curve of MMSim presented obvious asymmetry, with a fitting value of 0.4254. Although GTO and PSO-BP showed normal distribution, the trends were not obvious, with fitting values of 0.3021 and 0.4287. Compared with MMSim, GTO, and PSO-BP, the fitting performance of the proposed algorithm improved significantly. This was mainly because the multi-head attention captured data information from different perspectives, extended the operating width, and enhanced reliability. In conclusion, the results showed that the proposed algorithm had good fitting performance and superior reliability.
After verifying the performance of IBiLSTM-TCNT, the final GV-IBiLSTM-TCNT model was further evaluated for PV power prediction and compared with GTO, PSO-BP, and MMSim. The convolution kernel number was set to 64, the kernel size to 3, the batch size to 32, and the iteration number to 500. The learning rate was set to 0.0002, and the LSTM node numbers were set to 30 and 15. The dataset used was the GEFCom dataset. Statistical analysis was conducted using SPSS 26.1. All data underwent normality tests and homogeneity of variance tests. Independent and matched t-tests were applied to data conforming to a normal distribution. The significance level was set at p < 0.05. Prior to conducting the significance tests, the study hypothesized that there were no significant differences in the performance of all models. The p-value was calculated to determine whether to reject this hypothesis. The GWO algorithm was used to obtain four optimal parameters as input to VMD for decomposition and denoising. The optimization processes of penalty factor α, modal number K, decomposition level, and denoising threshold were evaluated, and the results are shown in Fig. 13.
Experimental results of the optimization process for multiple indicators.
As shown in Fig. 13a, parameter α rose rapidly with evolution, reached the maximum at the 2nd generation, dropped sharply at the 3rd generation, fluctuated slightly between the 5th and 10th generations, and finally converged to the optimal value of 275.5639. As shown in Fig. 13b, parameter K reached the maximum at the 2nd generation, stabilized between the 4th and 10th generations, and finally converged to the optimal value of 4. As shown in Fig. 13c, the decomposition level increased rapidly between the 1st and 2nd generations, then dropped, and finally stabilized between the 4th and 10th generations, with an optimal value of 2. As shown in Fig. 13d, the denoising threshold increased and decreased sharply between the 1st and 3rd generations, then stabilized near 0, and finally converged to 0.02. Combining these four parameters, the signal-to-noise ratio was 19.3414, which indicated that the model had good denoising performance. In order to further validate the predictive performance of the photovoltaic power generation model, the test set was divided into spring, summer, autumn, and winter groups, and the prediction accuracy of each group was calculated separately. One way analysis of variance was used to test whether the differences between groups were significant. The study tested the predicted values of the model in four seasons: spring, summer, autumn, and winter, and the comparative results are shown in Fig. 14.
Comparison of predicted values and actual values in different seasons.
Figure 14a–d show the power prediction results of the model in spring, summer, autumn, and winter. In spring and autumn, the prediction fluctuations were small, and the results were consistent with the actual values. The prediction accuracies were 95.21% and 96.54%. In summer and winter, the fluctuations were larger, which indicated that seasonal changes affected PV power output. The prediction results were consistent with the actual values, but the accuracies were slightly lower than those in spring and autumn, at 94.25% and 94.11%. The average prediction accuracy of the four seasons was 95.03%. These results showed that the model achieved high accuracy in PV power prediction. This was because the model reduced interference through signal denoising and improved prediction accuracy. The GV-IBiLSTM-TCNT, GTO, PSO-BP, and MMSim models were compared using Mean Absolute Error (MAE) and Relative Root Mean Square Error (rRMSE). The results are shown in Table 3.
As shown in Table 3, the GV BiLSTM TCNT model had MAE and rRMSE of 4.58 kW and 8.44% in spring, respectively. The autumn data was similar to spring, but the errors increased in summer and winter. MAE was 5.06 kW and 5.14 kW, and rRMSE was 8.24% and 8.97%, respectively. Seasonal changes have a certain impact on the model, but the difference compared to the average value is not significant (p > 0.05), indicating that the research model has stability in different climates. However, the other three models showed significant fluctuations in error under different climates, especially in summer, with significant differences (p < 0.05) compared to the mean. The average values of the research models MAE and rRMSE are 4.86 kW and 8.46%, respectively, which were better than GTO, PSO-BP, and MMSim. The reason was that the model mined the influence weights of key meteorological factors through multi-head attention and achieved more accurate prediction results through weighted fusion. In conclusion, the experimental results showed that the model had excellent prediction accuracy.
After verifying the power prediction performance of the GV-IBiLSTM-TCNT model, the study further evaluated its fault diagnosis performance for photovoltaic power generation and compared it with GTO, PSO-BP, and MMSim models. The sampling frequency of the vibration signal was 1.2 kHz, with a sampling number of 12,000 and a duration of 1 µs. The experiment set the number of convolution kernels to 64, the kernel size to 3, the batch size to 32, and the number of iterations to 500. The learning rate was set to 0.0002, and the number of LSTM nodes was set to 30 and 15. The dataset was chosen from GEFCom. The study used sensors to evaluate the fault vibration signals of the GV-IBiLSTM-TCNT, GTO, PSO-BP, and MMSim models. The results were shown in Fig. 15.
Comparison of fault vibration signal experimental results.
As shown in Fig. 15a, the difference between the normal and fault signal waveforms of the research model is most significant, with an average difference of 35.2 mm in vibration signals. In contrast, the waveform discrimination of the GTO, PSO-BP, and MMSim comparison models in Fig. 15b–d gradually weakens, with average signal differences of 23.6 mm, 19.8 mm, and 21.0 mm, respectively. The research results intuitively indicate that the research model has a more sensitive detection and discrimination ability for fault states. This is mainly attributed to the GWO-VMD adaptive signal processing module integrated in the front-end of the model. This module accurately removes the interference components coupled with environmental noise and mechanical background vibration from the original signal through optimization algorithms, and outputs high fidelity fault characteristic signals. To further investigate the fault diagnosis accuracy of the model, select five types of faults: short circuit, obstruction, dust accumulation, hot spot, and aging, with 30 samples for each type, the study compared the classification results of the proposed model with those of the GTO, PSO-BP, and MMSim models. The test results were shown in Fig. 16.
Comparison of classification results of different fault signals.
As shown in Fig. 16a, the proposed model accurately classified the faults into five categories: short circuit, shading, dust accumulation, hotspot, and aging, with a classification accuracy of 96.87%. In Fig. 16b–d, although the GTO, PSO-BP, and MMSim models could classify faults, the number of misclassified samples was significantly higher than that of the proposed model. Their classification accuracies were 89.54%, 91.60%, and 90.37%, respectively. The classification accuracy of the proposed model was significantly higher than that of the comparison models. The reason is that the GWO-VMD layer is effectively used for denoising and enhancing the expression of fault feature data. The IBiLSTM layer captures bidirectional temporal patterns, while the multi head attention of the TCNT layer can adaptively focus on the most discriminative key feature segments of various types of faults, thereby improving classification accuracy. In summary, the proposed model accurately classified photovoltaic faults. To verify the importance of evaluation metrics for the predictive performance of the GV-IBiLSTM-TCNT model, the study selected instantaneous irradiance (W1) and module backplane temperature (W2) as indicators in the meteorological feature dimension, short-term historical power sequence (X1) and first-order difference (X2) in the historical time series dimension, month (Y1) and intra-day time period (Y2) in the time period dimension, and module string current (Z1) and DC bus voltage (Z2) as indicators in the photovoltaic state dimension. The specific contributions of each feature were obtained through Shapley Additive exPlanations (SHAP) analysis and testing. Specifically, the DeepSHAP algorithm is used to approximate based on 1000 randomly sampled background samples. The results are shown in Fig. 17.
SHAP results of research model.
As shown in Fig. 17a, the three indicators with the highest contribution rates are instantaneous irradiance and short-term historical power sequence, while component string current, first-order difference, and DC bus voltage are secondary indicators, with the remaining indicators having relatively smaller contributions. As shown in Fig. 17b, the red part of instantaneous irradiance is concentrated in the positive region, indicating that higher instantaneous irradiance enhances the predictive decision-making of fault diagnosis. The red part of the short-term historical power sequence is more distributed in the positive region, indicating that historical power information has a positive reference value for model prediction. The blue distribution of component string current is in the negative region, indicating that smaller component string current increases the output probability of fault categories. In summary, the GV-IBiLSTM-TCNT model can clearly explain the impact of each feature indicator on fault prediction and diagnosis. In order to further explore the effectiveness of the combination of modules in the GV-IBiLSTM-TCNT model, the fault classification accuracy, recall rate, and F1 value of each module were evaluated, as shown in Table 4.
As shown in Table 4, the classification accuracy of the complete GV-IBiLSTM-TCNT model is 97.08%. With the ablation of the module, the accuracy of the model shows a significant decrease, dropping to 85.02% in the BiLSTM model. At the same time, the recall rate decreased from 96.08% to 87.20%, and F1 decreased to 84.12%. In summary, the ablation experiment results fully validated the effectiveness and necessity of each core module in the GV-IBiLSTM-TCNT model. In order to further analyze the computational complexity of the research model, a comparison was made between the model size and single sample inference time of GV-IBiLSTM-TCNT, GTO, PSO-BP, and MMSim models. The specific results are shown in Fig. 18.
Calculation complexity results of each model.
As shown in Fig. 18a, the median model size of the GV-IBiLSTM-TCNT model is 31.87 MB, which is higher than other comparison models, mainly due to the increased computational overhead caused by the multi module fusion architecture of GV-IBiLSTM-TCNT. According to Fig. 18b, the longest single sample inference time of the GV-IBiLSTM-TCNT model is 2.60ms, which is higher than the comparison model, but the difference is relatively small. The GV-IBiLSTM-TCNT model has paid a moderate computational cost to achieve fault diagnosis performance, and both storage requirements and inference latency can meet the real-time and resource constraints of current mainstream edge devices. The research results reveal the trade-off between model performance and computational complexity, providing clear decision-making basis for practical application deployment.
To address challenges such as low recognition efficiency, complex signal processing, and high parameter computation in PV systems, this study developed a model integrating BiLSTM and Transformer algorithms. The proposed model used IGJO to optimize BiLSTM, which improved the global search ability of the algorithm in complex environments. In addition, the Transformer with a multi-head attention mechanism was introduced to further enhance algorithm performance and generalization ability. The optimized BiLSTM and Transformer were integrated to form the IBiLSTM-TCNT algorithm. Based on this, the study combined the GWO-VMD algorithm to address the problem of noise interference and finally built the GV-IBiLSTM-TCNT model for photovoltaic power prediction and fault diagnosis. To address the issue of noise interference, a photovoltaic power prediction and fault diagnosis model based on GV BiLSTM TCNT was ultimately constructed. The experimental results demonstrate that the prediction accuracy of the core algorithm IBiLSTM TCNT reaches 97.38%, which is 7.84, 5.78, and 7.01% points higher than the three comparison algorithms GTO, PSO-BP, and MMSim, respectively. This significant improvement stems from the global optimization ability of IGJO algorithm for Bilstm super parameters. Unlike the traditional gradient descent method, it is easy to fall into local optimization. IGJO dynamically tracks and escapes energy through cosine factor, enabling the model to quickly converge to the global optimal solution when the irradiance suddenly changes, reflecting the progressiveness of meta heuristic optimization in photovoltaic time series prediction. The complete prediction model has an average power prediction accuracy of 95.03% in all four seasons, with an average absolute error of 4.86 kW and a relative root mean square error of 8.71%, significantly better than all comparison models. The fundamental reason is that the deep fusion architecture of BiLSTM and Transformer breaks through the limitation of the traditional single model feature extraction dimension, while the expansion causal convolution of TCN extracts multi-scale features in parallel, greatly improving the modeling accuracy of the fluctuation period. The classification accuracy of five typical faults reaches 96.87%, which is 5.27% points higher than the optimal comparison model. This result indicates that GWO-VMD achieves adaptive optimal decomposition of signals, removes environmental interference from the source, and overcomes the disadvantage of difficulty in setting manual filtering parameters. In addition, SHAP analysis quantitatively revealed that the model decision conforms to the laws of photovoltaic physics, and ablation experiments verified the effectiveness of the collaborative contribution of each module. In summary, the GV-IBiLSTM-TCNT model efficiently captured feature information, accurately predicted photovoltaic power, and provided fine-grained classification of fault types, thereby improving fault recognition accuracy. This study only included fault detection of simple damage and did not involve research on complex fault types.
The research system constructed and validated the GV BiLSTM TCNT hybrid model, which achieved significant results in high-precision prediction of photovoltaic module power and accurate detection and classification of typical faults, fully demonstrating the excellent ability of the proposed model to extract clear and strong discriminative features from complex data. However, the operation and maintenance environment of actual photovoltaic power plants is much more complex than laboratory conditions, and faults often exist in a composite form of multiple types of mutual coupling, and their evolution is a dynamic process. Therefore, further exploration and verification are needed for the generalization of the model in highly coupled fault detection, which indicates the direction for the performance boundary and next evolutionary direction of the proposed model. Future research will focus on building an intelligent diagnostic framework that can decouple concurrent fault features, further enhancing the decision-making depth and practical value of the model in real complex scenarios.
The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.
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School of Control and Computer Engineering, North China Electric Power University, Beijing, 102206, China
Yuchen Wang & Han Su
School of Mathematics and Physics, North China Electric Power University, Beijing, 102206, China
Zhongyan Li
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Y.C.W. processed the numerical attribute linear programming of communication big data, and the mutual information feature quantity of communication big data numerical attribute was extracted by the cloud extended distributed feature fitting method. Z.Y.L. and H.S. Combined with fuzzy C-means clustering and linear regression analysis, the statistical analysis of big data numerical attribute feature information was carried out, and the associated attribute sample set of communication big data numerical attribute cloud grid distribution was constructed. Y.C.W. and Z.Y.L. did the experiments, recorded data, and created manuscripts. All authors read and approved the final manuscript.
Correspondence to Zhongyan Li.
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Wang, Y., Li, Z. & Su, H. Photovoltaic power prediction and fault diagnosis method based on LSTM and transformer. Sci Rep 16, 24495 (2026). https://doi.org/10.1038/s41598-026-54547-4
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DOI: https://doi.org/10.1038/s41598-026-54547-4
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