Short-Term Solar Photovoltaic Power Prediction Utilizing the VMD-BKA-BP Neural Network
Abstract
:1. Introduction
2. Related Works
2.1. SHAP Analysis
2.2. K-Means++ Clustering
- A sample is randomly chosen as the initial center of mass in the total radiated power raw data.
- is the data sample, and for each sample , its Euclidean distance from the existing clustering centroid of mass is , while the likelihood of a sample point being chosen as the subsequent clustering centroid of mass is . When selecting a new centroid of mass, a weighted probability selection is conducted based on the distance between the sample and the chosen centroid of mass, and this process is repeated until M centroids of mass have been selected.
- Calculate the distance of each sample in the dataset from the M cluster centroids of mass and assign it to the cluster corresponding to the cluster centroid of mass with the closest distance and update the centroid of mass of each cluster.
- Repeat steps 2 and 3 until the position of the clustered center of mass stabilizes or the maximum number of iterations is attained.
2.3. VMD
- Initialize and .
- Initiate the loop, .
- For everyone
- Update and repeat steps 3–4 to refresh all the parameters pertaining to the components of :
- Update :
- Repeat steps 2–5 until the accuracy criterion is met:
2.4. BKA
2.4.1. Population Initialization Phase
2.4.2. Attack Phase
2.4.3. Migration Phase
2.5. BP Neural Network
2.6. Assessment Metrics
3. Methods
- We sanitize and replenish the raw data of PV power generation, then partition the data into training, validation and test sets. Next, employ SHAP analysis to identify the most significant correlating factor with PV output power among the climatic variables, using it as the input criterion for K-means++ clustering.
- Similar-day clustering using K-means++ divides days into categories of sunny, cloudy, and rainy.
- Pearson feature selection is employed to identify the five weather features exhibiting the strongest link with PV power across various weather circumstances.
- BKA is employed to optimize the core parameters of VMD [K,α], and the VMD decomposition of historical PV output power is conducted for three weather conditions, sunny, cloudy, and rainy, utilizing the optimum parameter combinations.
- We input each sub-sequence into the BKA-BP neural network model, train it using the sample training set and overlay the prediction results of each sub-sequence upon the completion of the training.
- We compare the mean absolute error NMAE, root mean square error NRMSE and coefficient of determination R2 as evaluation metrics to assess the prediction efficacy of various models.
3.1. Shap Analysis
3.2. Clustering Based on Day Similarity
- The time series of total daily daylight radiation from 6:30 to 21:00 for June, July and August were compiled into a 92 × 59 matrix, with each row denoting a 1-day PV power series.
- For each M value, we executed the following procedures: we applied the K-means++ algorithm to partition the data into M clusters; we computed the profile coefficient for each clustering outcome and documented the average profile coefficient associated with that M value, subsequently identifying the M at which the profile coefficient reached its maximum.
- We employed conclusive K-means++ clustering of the radiometric data utilizing the established optimal M value.
3.3. Pearson Feature Selection
3.4. VMD Decomposition
3.5. VMD-BKA-BP Neural Network Prediction
4. Results
5. Conclusions
- The additional categorization of weather types by K-means++ clustering allows the model to refine the pertinent parameters for sunny, cloudy and rainy days, resulting in enhanced training efficiency and increased predictive accuracy.
- The optimization of the decomposition count K and the maximum iteration limit α in the VMD are achieved using the BKA optimization technique. This methodology enables the forecasting model to more effectively comprehend the elements of the time series, hence enhancing the precision and clarity of the predictions.
- To address the issue of diminished prediction accuracy resulting from challenges in identifying important parameters in BP neural networks, the optimization of these parameters by BKA can enhance both the prediction accuracy and stability of the model. Comparative analysis with alternative prediction models demonstrates that the model suggested in this research exhibits enhanced predictive accuracy and robustness.
6. Discussion
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
Bi-LSTM | Bidirectional Long- and Short-term Memory Network |
BKA | black-winged kite optimization Algorithm |
BP | Back Propagation |
CEEMDAN | Complete ensemble empirical mode decomposition with adaptive noise |
EMD | Empirical mode decomposition |
HDN | Hybrid Deep Neural Networks |
IMF | Intrinsic Mode Function |
MVMD | Multivariate Variational Mode Decomposition |
PV | Photovoltaic |
SHAP | Shapley Additive exPlanations |
SSA | Sparrow Search Algorithm |
VMD | Variational mode decomposition |
References
- Yufei, W.; Lu, S.; Hua, X. Photovoltaic output power chaotic characteristic and trend prediction based on the actual measurement data. In Proceedings of the IEEE 11th Conference on Industrial Electronics and Applications (ICIEA), Hefei, China, 5–7 June 2016. [Google Scholar]
- Xuan, J.; Hu, L.; Niu, G.; Fu, X.; Zheng, Q.; Jin, C.; Wu, M. Rooftop Photovoltaic Power Prediction Method Considering the Characteristics of Photovoltaic Blocks. In Proceedings of the 2024 6th International Conference on Energy Systems and Electrical Power (ICESEP), Wuhan, China, 21–23 June 2024. [Google Scholar]
- Scott, C.; Ahsan, M.; Albarbar, A. Machine learning for forecasting a photovoltaic (PV) generation system. Energy 2023, 278, 127807. [Google Scholar] [CrossRef]
- Wang, C.; Yang, B.; Ying, X.; Song, X.; Gao, M. A short-term power prediction method for photovoltaic power generation under non-clear sky conditions. Sol. Energy J. 2022, 43, 188–196. [Google Scholar]
- Gupta, M.; Arya, A.; Varshney, U.; Mittal, J.; Tomar, A. A review of PV power forecasting using machine learning techniques. Prog. Eng. Sci. 2025, 2, 100058. [Google Scholar] [CrossRef]
- Hategan, S.-M.; Stefu, N.; Petreus, D.; Szilagyi, E.; Patarau, T.; Paulescu, M. Short-term forecasting of PV power based on aggregated machine learning and sky imagery approaches. Energy 2025, 316, 134595. [Google Scholar] [CrossRef]
- Dai, H.; Zhen, Z.; Wang, F.; Lin, Y.; Xu, F.; Duić, N. A short-term PV power forecasting method based on weather type credibility prediction and multi-model dynamic combination. Energy Convers. Manag. 2025, 326, 119501. [Google Scholar] [CrossRef]
- Di Leo, P.; Ciocia, A.; Malgaroli, G.; Spertino, F. Advancements and Challenges in Photovoltaic Power Forecasting: A Comprehensive Review. Energies 2025, 18, 2108. [Google Scholar] [CrossRef]
- Santos Ld, O.; AlSkaif, T.; Barroso, G.C.; Carvalho, P.C.M.d. Photovoltaic power estimation and forecast models integrating physics and machine learning: A review on hybrid techniques. Sol. Energy 2024, 284, 113044. [Google Scholar] [CrossRef]
- Fan, S.; Geng, H.; Zhang, H.; Yang, J.; Hiroichi, K. Photovoltaic power forecasting model employing epoch-dependent adaptive loss weighting and data assimilation. Sol. Energy 2025, 290, 113351. [Google Scholar] [CrossRef]
- Deng, R.; Wang, Y.; Xu, P.; Luo, F.; Chen, Q.; Zhang, H.; Chen, Y.; Zhang, D. A high-precision photovoltaic power forecasting model leveraging low-fidelity data through decoupled informer with multi-moment guidance. Renew. Energy 2025, 250, 123391. [Google Scholar] [CrossRef]
- Khouili, O.; Hanine, M.; Louzazni, M.; Flores, M.A.L.; Villena, E.G.; Ashraf, I. Evaluating the impact of deep learning approaches on solar and photovoltaic power forecasting: A systematic review. Energy Strategy Rev. 2025, 59, 101735. [Google Scholar] [CrossRef]
- Liu, H.; Cai, C.; Li, P.; Tang, C.; Zhao, M.; Zheng, X.; Li, Y.; Zhao, Y.; Liu, C. Hybrid prediction method for solar photovoltaic power generation using normal cloud parrot optimization algorithm integrated with extreme learning machine. Sci. Rep. 2025, 15, 6491. [Google Scholar] [CrossRef] [PubMed]
- Kumar, A.; Kashyap, Y.; Rai, A. An integrated frequency domain decomposition and deep neural network approach for short-term PV power forecast. Electr. Eng. 2024, 24, 282–303. [Google Scholar] [CrossRef]
- Guo, W.; Sun, S.; Tao, P.; Xu, J.; Bai, X. Short-term photovoltaic power prediction based on multi-variational mode decomposition and hybrid deep neural network. Sol. Energy J. 2024, 45, 489–499. [Google Scholar]
- Qu, Z.; Qin, S.; Xiong, G.; Zhu, X.; Ling, F.; Wang, Y.; Kong, J. Short-Term Power Prediction of a Photovoltaic Power Station Based on the SSA-CEEMDAN-FCN Model. Comput. Intell. Neurosci. 2022, 2022, 6486876. [Google Scholar] [CrossRef]
- Kang, Y.; Lanqing, L.; Yifeng, L.; Dongkuo, S.; Bolun, W.; Jin, C.; Xia, Z.; Yu, S. A novel distributed photovoltaic power output interval prediction method. Power Gener. Technol. 2024, 45, 684–695. [Google Scholar]
- Liu, L.; Zhang, J.; Xue, S. Photovoltaic power forecasting: Using wavelet threshold denoising combined with VMD. Renew. Energy 2025, 249, 123152. [Google Scholar] [CrossRef]
- Wang, Z.; Ying, Y.; Kou, L.; Ke, W.; Wan, J.; Yu, Z.; Liu, H.; Zhang, F. Ultra-Short-Term Offshore Wind Power Prediction Based on PCA-SSA-VMD and BiLSTM. Sensors 2024, 24, 444. [Google Scholar] [CrossRef]
- Ait Mansour, A.; Tilioua, A.; Touzani, M. Bi-LSTM, GRU and 1D-CNN models for short-term photovoltaic panel efficiency forecasting case amorphous silicon grid-connected PV system. Results Eng. 2024, 21, 101886. [Google Scholar] [CrossRef]
- Yang, R. Short-Term Photovoltaic Power Forecasting Based on Cluster Ensemble Analysis and Deep Learning Algorithms. Master’s Thesis, Xi’an University of Technology, Xi’an, China, 30 June 2023. [Google Scholar]
- Chen, Y.; Chen, X. Short-term photovoltaic power generation prediction based on adaptive K-means and LSTM. Electr. Meas. Instrum. 2023, 60, 94–99. [Google Scholar]
- Shen, M.; An, Z.; Zhao, L. Research on a Short term Power Prediction Method for Photovoltaic Power Generation. In Proceedings of the 2024 4th Power System and Green Energy Conference (PSGEC), Shanghai, China, 22–24 August 2024. [Google Scholar]
- Liu, J.; Wang, H.; Hao, T. Short-Term Photovoltaic Power Prediction Based on Bayesian Regularized BP Neural Networks. In Proceedings of the 2023 6th International Conference on Electrical Engineering and Green Energy (CEEGE), Grimstad, Norway, 6–9 June 2023. [Google Scholar]
- Huang, Y.; Chen, S.; Tan, X.; Hu, M.; Zhang, C. Power Prediction Method of Distributed Photovoltaic Digital Twin System Based on GA-BP. In Proceedings of the 2022 4th International Conference on Electrical Engineering and Control Technologies (CEECT), Shanghai, China, 16–18 December 2022. [Google Scholar]
- Wang, Z.; Liu, H.; Wu, S.; Liu, N.; Liu, X.; Hu, Y.; Fu, Y. Explainable time-varying directional representations for photovoltaic power generation forecasting. J. Clean. Prod. 2024, 468, 143056. [Google Scholar] [CrossRef]
- Fu, J.; Sun, Y.; Li, Y.; Wang, W.; Wei, W.; Ren, J.; Han, S.; Di, H. An investigation of photovoltaic power forecasting in buildings considering shadow effects: Modeling approach and SHAP analysis. Renew. Energy 2025, 245, 122821. [Google Scholar] [CrossRef]
- Zhai, C.; He, X.; Cao, Z.; Abdou-Tankari, M.; Wang, Y.; Zhang, M. Photovoltaic power forecasting based on VMD-SSA-Transformer: Multidimensional analysis of dataset length, weather mutation and forecast accuracy. Energy 2025, 324, 135971. [Google Scholar] [CrossRef]
- Wang, K.; Tian, J.; Zheng, C.; Yang, H.; Ren, J.; Liu, Y.; Han, Q.; Zhang, Y. Interpretable prediction of 3-year all-cause mortality in patients with heart failure caused by coronary heart disease based on machine learning and SHAP. Comput. Biol. Med. 2021, 137, 104813. [Google Scholar] [CrossRef] [PubMed]
- Liu, H.; Chen, J.; Dy, J.; Fu, Y. Transforming Complex Problems Into K-Means Solutions. IEEE Trans. Pattern Anal. Mach. Intell. 2023, 45, 9149–9168. [Google Scholar] [CrossRef] [PubMed]
- Qin, H.; Huang, L.; Li, K.; Cheng, G. Short-Term Offshore Wind Power Prediction based on VMD-SE-BP Neural Network Model. In Proceedings of the 2024 IEEE 2nd International Conference on Power Science and Technology (ICPST), Yunnan, China, 9–11 May 2024. [Google Scholar]
- Zhang, X.; Wang, X.; Li, H.; Sun, S.; Liu, F. Monthly runoff prediction based on a coupled VMD-SSA-BiLSTM model. Sci. Rep. 2023, 13, 13149. [Google Scholar] [CrossRef]
- Li, Y.; Shi, B.; Qiao, W.; Du, Z. A black-winged kite optimization algorithm enhanced by osprey optimization and vertical and horizontal crossover improvement. Sci. Rep. 2025, 15, 6737. [Google Scholar] [CrossRef]
- Wang, Z.; Wu, J.; Wang, H.; Wang, H.; Hao, Y. Optimal Underwater Acoustic Warfare Strategy Based on a Three-Layer GA-BP Neural Network. Sensors 2022, 22, 9701. [Google Scholar] [CrossRef]
- Zhang, Y.; Kong, L. Photovoltaic power prediction based on hybrid modeling of neural network and stochastic differential equation. ISA Trans. 2022, 128 Pt B, 181–206. [Google Scholar] [CrossRef]
- Tahir, M.F.; Tzes, A.; Yousaf, M.Z. Enhancing PV power forecasting with deep learning and optimizing solar PV project performance with economic viability: A multi-case analysis of 10 MW Masdar project in UAE. Energy Convers. Manag. 2024, 311, 118549. [Google Scholar] [CrossRef]
Modeling | Unclustered Weather | Clear Sky | ||||
---|---|---|---|---|---|---|
NMAE | NRMSE | R2 | NMAE | NRMSE | R2 | |
BP | 1.9208 | 3.7441 | 0.9422 | 1.8159 | 3.6192 | 0.9457 |
VMD-BP | 1.0852 | 2.3142 | 0.9779 | 0.9346 | 1.7375 | 0.9875 |
LSTM | 2.1587 | 3.5596 | 0.9478 | 2.1958 | 3.5829 | 0.9468 |
VMD-LSTM | 1.9499 | 3.1475 | 0.9591 | 1.7274 | 2.5292 | 0.9735 |
VMD-BKA-LSTM | 1.1422 | 1.7189 | 0.9878 | 1.1797 | 1.7114 | 0.9879 |
EMD-BKA-BP | 1.6663 | 2.7268 | 0.9693 | 1.3934 | 2.3341 | 0.9774 |
VMD-PSO-BP | 1.1266 | 2.1844 | 0.9803 | 0.9600 | 1.8186 | 0.9863 |
VMD-BKA-BP | 0.5090 | 0.9483 | 0.9963 | 0.4851 | 0.8153 | 0.9973 |
Modeling | Cloudy (Meteorology) | Rainy Day | ||||
---|---|---|---|---|---|---|
NMAE | NRMSE | R2 | NMAE | NRMSE | R2 | |
BP | 1.1749 | 3.1026 | 0.9587 | 1.2677 | 2.1132 | 0.9008 |
VMD-BP | 0.7239 | 1.4531 | 0.9910 | 0.7733 | 1.3283 | 0.9608 |
LSTM | 1.6966 | 3.0426 | 0.9603 | 1.5397 | 2.4496 | 0.8668 |
VMD-LSTM | 1.3597 | 2.1372 | 0.9804 | 0.98424 | 1.4790 | 0.9514 |
VMD-BKA-LSTM | 0.7382 | 1.1385 | 0.9944 | 0.6996 | 0.9688 | 0.9792 |
EMD-BKA-BP | 1.2355 | 2.3112 | 0.9771 | 1.2050 | 1.7365 | 0.9330 |
VMD-PSO-BP | 0.5521 | 1.3540 | 0.9921 | 0.7564 | 1.2091 | 0.9675 |
VMD-BKA-BP | 0.3347 | 0.7625 | 0.9975 | 0.3286 | 0.5248 | 0.9939 |
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Sun, Y.; Wang, Z.; Wang, J.; Li, Q. Short-Term Solar Photovoltaic Power Prediction Utilizing the VMD-BKA-BP Neural Network. Symmetry 2025, 17, 784. https://doi.org/10.3390/sym17050784
Sun Y, Wang Z, Wang J, Li Q. Short-Term Solar Photovoltaic Power Prediction Utilizing the VMD-BKA-BP Neural Network. Symmetry. 2025; 17(5):784. https://doi.org/10.3390/sym17050784
Chicago/Turabian StyleSun, Yuanquan, Zhongli Wang, Jiahui Wang, and Qiuhua Li. 2025. "Short-Term Solar Photovoltaic Power Prediction Utilizing the VMD-BKA-BP Neural Network" Symmetry 17, no. 5: 784. https://doi.org/10.3390/sym17050784
APA StyleSun, Y., Wang, Z., Wang, J., & Li, Q. (2025). Short-Term Solar Photovoltaic Power Prediction Utilizing the VMD-BKA-BP Neural Network. Symmetry, 17(5), 784. https://doi.org/10.3390/sym17050784