Photovoltaic power generation exhibits distinct diurnal periodicity and weather dependence, requiring the capture of characteristic patterns over extended time spans. The Temporal Convolutional Network (TCN) addresses this need through stacked dilated causal convolutional layers that expand the receptive field to effectively capture multi-timescale temporal patterns [22]. TCN can process longer input sequences, which helps simplify the model architecture while preventing gradient explosion, and enables the construction of larger receptive fields without requiring excessive network depth.

By employing TCN, the convolutional operations can extract correlation patterns between different features at concurrent timesteps from the input time-series data. Fig. 1 illustrates the TCN convolutional architecture, where adjusting network parameters such as the dilation coefficient in the Dilated Causal Convolution (DCC) network can effectively expand the input receptive field. The conclusions from the DCC operation are as follows: (1)DCC(T)=∑t=0K−1f(i)xT−diwhere, DCC(T) is the output computation of DCC at time step T. f(i) is learnable convolutional kernel weight parameters. xT−di represents the PV power from time T to the previous time shifted by d_i. K denotes the kernel size of the filter, d is the dilation coefficient.

The residual block is computed as follows: (2)Lh=δ(G(Lh−1)+Cov1(Lh−1))where, L represents the input data before residual connection. G denotes the operations of DCC and normalization. Conv1(·) indicates the convolution operation. δ stands for the activation function.

To effectively capture both short-term fluctuations and long-term trends in photovoltaic power forecasting, a time-series model capable of learning bidirectional temporal dependencies is required. The Bidirectional Long Short-Term Memory network (Bi-LSTM) incorporates gated units comprising three control mechanisms: input gate, output gate, and forget gate, which collectively determine the hidden state transmission between timesteps. By implementing a bidirectional architecture that adds reverse-direction hidden layer propagation [23], Bi-LSTM performs both forward and backward state transmissions during hidden state updates. This unique operational mechanism enhances the model’s nonlinear fitting capability and improves prediction accuracy for photovoltaic power generation cycles, with its detailed structure illustrated in Fig. 2.

Let xt∈Rn×1 denote the relationship between meteorological factors and photovoltaic power generation fed into the bidirectional long short-term memory network at timestep t, where n represents the sample size. In Fig. 2, h→t∈Rh×1 indicates the forward-propagating hidden state, h←t∈Rh×1 represents the backward-propagating hidden state, and h denotes the number of hidden units in both directions. The final hidden state output h→t∈Rh×1 of the bidirectional long short-term memory network is as follows: (3)h→t=σ→t⊙tanh(c→t) (4)h←t=σ←t⊙tanh(c←t) (5)ht=concat(h→t,h←t)where, ⊙ represents element-wise multiplication; σ→t and σ←t represent the computation results of the forward and backward LSTM output gates at time step t, respectively; c→t and c←t represent the output values of the forward and backward LSTM memory cells at time step t, where tanh is the hyperbolic tangent activation function applied to the memory cells. (6)ft=σ(W(f)⋅[xt,ht-1]T+bf) (7)it=σ(W(i)⋅[xt,ht-1]T+bi) (8)ot=σ(W(o)⋅[xt,ht-1]T+bo) (9)c~t=tanh(W(c~)⋅[xt,ht−1]T+bc~) (10)ct=ft⊙ct−1+it⊙c~twhere, ft denotes the output of the forget gate, it denotes the output of the forget gate, σ denotes Sigmoid activation function, [xt,ht-1]T represents the concatenated input vector, which is the input of the gating computations. c~t denotes the candidate memory cell output, whose value can be calculated through Eq. (10). The weight matrix W(f) contains Wxf∈Rh×1 (input feature weights) and Whf∈Rh×h (hidden state weights); and correspond to the bf (forget gate), bi (input gate), bo (output gate), and bc~ (candidate memory cell), respectively, where represents the activation function.

TCN and BiLSTM each have advantages in perceiving local features and long-term temporal dependencies. Traditional model architectures employ serial concatenation structures to capture both local and global temporal patterns, but overly complex models require more computational memory and time, significantly increasing training costs. This adversely affects the timeliness of ultra-short-term predictions, leading to increased computational costs and substantially reduced efficiency during training.

The parallel dual-stream prediction model utilizes a tensor pooling concatenation module to merge the output matrices of both models along the feature dimension, achieving feature information fusion, and generates target values through output neurons. By adopting a parallel structure, all individual models within the hybrid model can be trained independently side by side, learning feature information from the original time series before the tensor concatenation module. Thus, the depth of the hybrid model is not increased by stacking network layers. Furthermore, the tensor concatenation module combines the feature information learned by each individual model, fully preserving their respective perceptual capabilities. Consequently, this parallel dual-stream structure maintains feature learning and perceptual ability while significantly improving learning efficiency and drastically reducing training time costs due to reduced model depth. A schematic diagram of the parallel structure is shown in Fig. 3.

Photovoltaic power generation is simultaneously influenced by local meteorological factors and temporal periodicity, exhibiting continuous fluctuation characteristics. However, conventional TCN and Bi-LSTM prediction models equally process all temporal and spatial features in photovoltaic power forecasting, failing to adapt to scenarios like abrupt weather changes. By integrating a Temporal-Spatial Attention (TSA) mechanism with the parallel TCN-BiLSTM architecture, dynamic adjustment of spatial features from TCN outputs and temporal features from Bi-LSTM outputs can be achieved. The multi-head mechanism enables parallel learning of spatiotemporal relationships across different subspaces, followed by lightweight feature fusion through tensor pooling concatenation. This approach significantly enhances the performance of photovoltaic power prediction models under complex weather conditions.

The calculation formula of Temporal-Spatial Attention is as follows: (11)Qs,t=Xs,tWqs,t (12)Ks,t=Xs,tWks,t (13)Vs,t=Xs,tWvs,t (14)As,t=softmax(Qs,tKs,tT dk) (15)X~s,t=As,tVs,twhere, s and t represent spatial and temporal features, respectively, Q is the query vector, K is the key vector, V is the value vector, X∈RB×T×D is the output spatial/temporal feature, Wqs,t,Wks,t,Wvs,t∈RDs,t×dk are learnable weight matrices, As,t is the attention matrix, softmax(⋅) converts the similarity score into a probability distribution, indicating the dependency of the position (s,t) on the position (s′,t′). dk is the scaling factor, and X~s,t denotes the spatiotemporally enhanced feature.

The multi-head attention extension calculation formula is as follows, where h = 4 represents minute fluctuations, hourly trends, spatial coupling, and anomaly detection, respectively. (16)headi=Attention(XWqi,XWki,XWvi) (17)MultiHead(Q,K,V)=Concat(head1,…,headh)Wowhere, headi represents the output of the i−th attention head, h represents the number of heads, Attention(⋅) represents core computational logic of attention mechanism, X represents the input data for the attention heads usually comes from the output of the previous layer, MultiHead(Q,K,V) represents the final output of the multi-head attention mechanism, Concat(⋅) represents concatenation operation and Wo∈Rh⋅dv×D denotes the output projection matrix.

Feature fusion decision enables complementary information enhancement of spatiotemporal features while reducing output dimensionality. The fusion incorporates RELU activation functions to model the irradiance-power exponential relationship and introduce nonlinear transformation capabilities. The calculation formula is as follows: (18)Ps=1T∑t=1TX~s(t) (19)Pt=1T∑t=1TX~t(t) (20)Ffused=[Ps∥Pt] (21)y^=W2⋅RELU(W1⋅Ffused+b1)+b2where, Ps represents spatial pooling, T denotes the length of time series data, X~s(t) denotes Spatial features at time t, Pt denotes temporal pooling, X~t(t) denotes Temporal features at time t. Ffused signifies spatial concatenation, ∥ signifies concatenation operation, y^ corresponds to fully-connected prediction, W1, W2 represent the weights of the first fully-connected layer and the second fully-connected layer, respectively, b1, b2 represent the bias of the first fully-connected layer and the second fully-connected layer, respectively, and RELU is activation function.

The actual power generation output of photovoltaic systems, known as active power output, is influenced by various factors. The active power output formula is as follows: (22)Pout=G⋅A⋅ηmodule⋅ηsystem⋅ηotherwhere, G represents solar irradiance, A denotes the effective area of the PV module, ηmodule represents module conversion efficiency, ηsystem stands for system efficiency, and ηother represents other correction factors.

In the actual process of photovoltaic power generation, the effect of solar irradiance is influenced by factors such as solar incidence angle, cloud cover, and dust shading. The module conversion efficiency η_module of the system is primarily affected by temperature. Accurate photovoltaic power prediction requires considering these correlated factors, but each factor impacts PV output to varying degrees. Insufficient consideration of these factors will significantly reduce prediction accuracy, while incorporating all factors will drastically increase the system’s input dimensions, affecting the model’s computation and learning efficiency and negatively impacting the timeliness of short-term forecasting. Therefore, we process the input variables by combining Pearson correlation analysis. As shown in the Fig. 5.

As evident from the heatmap, irradiance exhibits the highest correlation 0.96, making it the most critical influencing factor. The hourly sine value (hour_sin) also shows a correlation of 0.96, indirectly reflecting the temporal distribution of irradiance throughout the day, thus serving as another key predictive feature for power output. Temperature demonstrates a correlation of 0.81, indicating its significance as both excessive heat and cold can reduce solar cell conversion efficiency. In contrast, humidity and air pressure display lower correlations, suggesting their minimal impact on PV output. Consequently, the primary input variables for PV power forecasting can be identified as irradiance, temperature, and time-periodic factors.

Based on the Pearson analysis results, it can be concluded that temporal periodicity is one of the important influencing factors affecting photovoltaic output. Therefore, autocorrelation analysis [24] must be performed on the photovoltaic power generation sequence to determine historical windows based on statistical patterns, analyze the temporal dependencies within the time series, identify historically significant time-point data that substantially influence current predictions, and reveal temporal correlations between power generation outputs at different time steps. The autocorrelation function is calculated as follows: (23)ACF(n)=∑t=1T−n(xt−x¯)(xt+n−x¯)∑t=1T(xt−x¯)2where, xt is the photovoltaic power output at time t, x¯ is the average value of photovoltaic power output, n is the lag order of photovoltaic power output, and T is the length of the photovoltaic power output sequence.

The resolution of the photovoltaic power generation dataset is 15 min, and its autocorrelation analysis results are shown in Fig. 6.

Fig. 6 shows that the photovoltaic power output exhibits an autocorrelation coefficient greater than 0.4 at a 3-h lag, indicating significant correlation between current power generation and that from three hours prior. Moreover, the autocorrelation coefficient exceeds 0.6 for corresponding periods within a two-day lag, demonstrating distinct daily periodicity in PV power generation. Therefore, historical load data from the preceding 3 h and corresponding time periods from the previous two days were selected as input features for the model, validating the scientific rationale behind the chosen historical data time window and confirming pronounced intraday periodicity and 72-h persistence in PV power output.

The Shapley additive explanation technique [25] is employed to analyze the contribution of input features to the model, enhancing the interpretability of prediction results by quantifying how different features influence the output, thereby facilitating better understanding of model decisions. The expression is as follows: (24)v=vbase+f(xi1)+f(xi2)+⋯+f(xin)where, vbase is the mean prediction of selected samples, f(xi1) represents the contribution of the first feature in the i sample, and v denotes the model’s predicted value.

SHAP values are used for visual analysis and model interpretation, with 128 samples randomly selected from the training set to calculate the feature contributions within a specific time frame. SHAP conducts numerical analysis for prediction days in summer and winter, determining the specific contributions of each input feature, as shown in Fig. 7.

The SHAP analysis results indicate that the contribution of irradiance reaches up to 62.3% in winter and 58.7% in summer, validating its role as a core variable in photovoltaic power prediction. It also confirms the conclusion from Pearson analysis that irradiance intensity exhibits a strong positive correlation with the output power of photovoltaic modules. Additionally, the analysis suggests that high summer temperatures may lead to a decrease in component efficiency, reflected by negative SHAP values, while low winter temperatures combined with high irradiance result in positive SHAP values, potentially linked to enhanced snow reflection. The autocorrelation analysis of model inputs and Pearson analysis form a closed-loop feedback optimization, identifying strongly correlated factors for input.

The probabilistic forecasting model for photovoltaic power requires selecting an appropriate loss function to guide the training process, which should effectively reflect the proximity between the predicted probability distribution and the true distribution. Root mean square error (RMSE), mean absolute percentage error (MAPE), mean absolute error (MAE), and continuous ranked probability score (CRPS) are chosen as evaluation metrics for the forecasting model. RMSE, MAPE, and MAE can respectively reflect large errors, average errors, and relative errors of the forecasting model, all of which belong to point forecasting methods. A comprehensive evaluation of the model’s prediction accuracy also requires combining continuous ranked probability score (CRPS), for interval probabilistic forecasting.

CRPS is one of the most widely used comprehensive evaluation metrics in probabilistic forecasting, capable of assessing the global performance of predictive distributions across the entire domain. Therefore, it is selected in this paper as the loss function for combined probabilistic forecasting of photovoltaic power. Its definition formula is: (25)S(FY,y)=∫−∞+∞[FY(z)−Iy<z]2dzwhere, FY(z) is the cumulative distribution function (CDF) of the forecast variable Y; The observation value of the forecast variable is y; Iy<z indicators function that takes the value 1 when the condition y<z is satisfied and 0 otherwise.

Following data preprocessing and correlation analysis, parameter configuration for the parallel TCN-BiLSTM-TSA model architecture was performed, with detailed model parameters specified in Table 1.

Through Pearson correlation analysis and SHAP additive explanations applied to the input data, we completed data cleaning and selected highly representative samples. Based on the temporal periodicity results from autocorrelation analysis, the experiment employed four consecutive days as the test set to validate the model’s superior performance, with prediction outcomes illustrated in Fig. 8.

The Fig. 8 demonstrates the predictive performance of different models, while Table 2 and Fig. 9 visually illustrate the accuracy of the proposed TCN-BiLSTM-TSA model across evaluation metrics including MAE, RMSE, MAPE, and CRPS.

Fig. 10 compares the training times of four models: parallel TCN-BiLSTM-TSA, series TCN-BiLSTM-TSA, DTCN-BiLSTM-TSA, and SHAP-TCN-BiLSTM, using error metric as the evaluation criterion. The analysis demonstrates that while the parallel and series TCN-BiLSTM-TSA models achieve comparable prediction accuracy, and the DTCN-BiLSTM-TSA and SHAP-TCN-BiLSTM models show slightly inferior performance, Fig. 10 reveals that when the training times of series TCN-BiLSTM-TSA, DTCN-BiLSTM-TSA, and SHAP-TCN-BiLSTM models exceed 1600 s, their error metric reaches approximately 0.06. In contrast, the parallel TCN-BiLSTM-TSA model achieves the same 0.06 error metric with merely 200 s of training time. This clearly indicates that under comparable prediction errors, the parallel TCN-BiLSTM-TSA model requires significantly less training time.

To more comprehensively evaluate the prediction performance of the TCN-BiLSTM-TSA model and verify its superiority, simulations were conducted under consistent conditions using the TCN-BiLSTM-TSA, SHAP-TCN-BiLSTM, and DTCN-BiLSTM-TSA models to predict PV power output under “rainy” and “overcast” weather conditions. The prediction results and evaluation metrics for each model are shown in Fig. 11 and Table 3.

From Fig. 11 and Table 3, it can be observed that under “rainy” and “overcast” conditions, the TCN-BiLSTM-TSA model exhibits smaller prediction errors compared to other models, enabling effective PV power prediction under these weather scenarios.

In summary, across five distinct weather conditions—clear skies with high temperatures, cloudy, overcast, rainy, and snowy/low-temperature conditions—the TCN-BiLSTM-TSA model successfully captures the variation trends of PV power sequences. It achieves accurate power predictions under diverse meteorological scenarios, demonstrating robust forecasting performance and strong generalization capabilities.

Test results demonstrate that the proposed parallel dual-stream architecture with spatiotemporal attention mechanism reduces training time by 5.4% compared to serial architecture. This spatiotemporal attention mechanism improves RMSE by 17.6% for predictions under overcast, rainy and snowy conditions, verifying the effectiveness of parallel architecture in feature decoupling. Furthermore, the proposed prediction model exhibits superior performance during both extreme weather and stable PV generation periods, while significantly enhancing computational efficiency and substantially reducing training time. Performance comparison shows Parallel TCN-BiLSTM-TSA and Series TCN-BiLSTM-TSA curves nearly overlapping actual values with minimal errors, MAE ≤ 15 kW, MAPE ≤ 3%. DTCN-TCN-BiLSTM-TSA exhibits moderate dispersion but captures fluctuations with intermediate errors, MAE ≤ 19 kW, MAPE ≤ 3.6%. SHAP-TCN-BiLSTM significantly deviates from actual values with maximum errors, MAE ≥ 21 kW, MAPE ≥ 4.3%. Weather impacts reveal slightly higher errors in high-variability scenarios like snowfall and sunny-to-cloudy transitions, though Parallel TCN-BiLSTM-TSA maintains superior accuracy, while its advantage becomes more pronounced in stable conditions like overcast and cloudy weather with lower errors. The model achieves 5.00% MAPE on Northeast China field data, outperforming comparison models by 1.27%, proving parallel TCN-BiLSTM-TSA delivers optimal prediction performance for specific winter/summer dates with significantly improved accuracy over single models. Under constraints of Pearson feature selection, autocorrelation analysis and SHAP interpretability feedback fusion, peak power prediction errors remain below 8% even during extreme winter weather, validating multi-module collaboration robustness. SHAP analysis reveals irradiance contribution reaches 62.3%, providing quantitative basis for PV array cleaning maintenance.