journal article·2026-07-27

VSTCformer for Wind Power Interval Forecasting via Adaptive Variational Mode Decomposition and Spatio-Temporal Cross-Attention

Zeyuan Wu, Yuan Shi, Tengyue Guo, Min Xia

Applied Sciences· Volume 16· Issue 15
Publisher page

Abstract

Reliable interval forecasting is essential for risk-aware wind power scheduling, yet the strong nonstationarity and complex spatio-temporal coupling of wind power sequences make probabilistic prediction difficult. This study proposes VSTCformer (Variational-mode-decomposition-enhanced Spatio-Temporal Cross-attention transformer), a wind power interval forecasting framework that integrates adaptive variational mode decomposition (VMD) with spatio-temporal cross-attention and multi-quantile regression. The adaptive VMD module automatically determines the number of modes from the uniformity of center-frequency spacing and decomposes the raw power signal into frequency-aligned intrinsic components, while the undecomposed multivariate sequence is preserved to provide global temporal context. Spatial-guided and temporal-modulated attention realize implicit spatio-temporal coupling during encoding, and explicit fusion is achieved through inter-component interaction before the features are passed to the prediction head. Nine quantiles are jointly estimated to produce the median forecast and prediction intervals at multiple confidence levels. Two public benchmarks with markedly different temporal resolution and volatility are used for evaluation. The results show that VSTCformer preserves competitive point-forecast accuracy while substantially improving interval quality: it produces the narrowest prediction intervals at all evaluated horizons and achieves the best coverage-width trade-off in most settings. The central contribution of the framework is therefore an enhanced and well-calibrated uncertainty quantification capability, confirming that decomposition-enhanced spatio-temporal modeling is an effective route for wind power interval forecasting.
Source: crossref · Quality: baseline

Affiliations

Jiangsu Provincial University Key Laboratory of Big Data Analysis and Intelligent Systems, Nanjing University of Information Science and Technology, Nanjing 210044, China

Collaborative Innovation Center on Atmospheric Environment and Equipment Technology, Nanjing University of Information Science and Technology, Nanjing 210044, China

Department of Computer Science, University of Reading, Whiteknights, Reading RG6 6DH, UK

Funding

SGCC

References (65)

Show source-provided references
1. A hybrid data-driven robust optimization approach for unit commitment considering volatile wind power10.1016/j.epsr.2021.107758 ↗
2. Data-driven robust day-ahead unit commitment model for hydro/thermal/wind/photovoltaic/nuclear power systems10.1016/j.ijepes.2020.106427 ↗
3. Current methods and advances in forecasting of wind power generation10.1016/j.renene.2011.05.033 ↗
4. Hanifi, S., Liu, X., Lin, Z., and Lotfian, S. (2020). A critical review of wind power forecasting methods—Past, present and future. Energies, 13.10.3390/en13153764 ↗
5. Ansari, A.F., Stella, L., Turkmen, C., Zhang, X., Mercado, P., Shen, H., Shchur, O., Rangapuram, S.S., Pineda Arango, S., and Kapoor, S. (2024). Chronos: Learning the Language of Time Series. arXiv.
6. Woo, G., Liu, C., Kumar, A., Xiong, C., Savarese, S., and Sahoo, D. (2024, January 21–27). Unified Training of Universal Time Series Forecasting Transformers. Proceedings of the International Conference on Machine Learning (ICML), Vienna, Austria.
7. Receding horizon D-optimal input design for identification of wireless power transfer systems10.1109/JESTPE.2023.3257960 ↗
8. Short-term prediction of wind vector at multi-heights via deep learning techniques based on marine measurements from Light-Detection-and-Ranging device10.1063/5.0297152 ↗
9. An Active-Soft-Switching DC Transformer with Auxiliary Converter for DC Offshore Wind Turbine10.1109/TIE.2026.3675144 ↗
10. Hierarchical bidding strategy for heterogeneous P2H loads and wind power: State-driven aggregation and switching time scheduling10.1016/j.energy.2025.137766 ↗
11. Typhoon-induced risk evolution in wind farms: From disaster-inducing factors identification to domino effect assessment10.1016/j.ress.2026.112638 ↗
12. Li, J., Zhu, C., Dong, Y., and Xia, M. (2026). Fault Prediction Method of Boost Converter Based on Multi-Modal Components and Temporal Convolutional Networks. Energies, 19.10.3390/en19081974 ↗
14. Probabilistic energy forecasting: Global energy forecasting competition 2014 and beyond10.1016/j.ijforecast.2016.02.001 ↗
15. Regression quantiles10.2307/1913643 ↗
16. Review on probabilistic forecasting of wind power generation10.1016/j.rser.2014.01.033 ↗
17. Conditional prediction intervals of wind power generation10.1109/TPWRS.2010.2045774 ↗
18. Probabilistic forecasting of wind power generation using extreme learning machine10.1109/TPWRS.2013.2287871 ↗
19. Jin, M., Wang, S., Ma, L., Chu, Z., Zhang, J.Y., Shi, X., Chen, P.-Y., Liang, Y., Li, Y.-F., and Pan, S. (2024, January 7–11). Time-LLM: Time Series Forecasting by Reprogramming Large Language Models. Proceedings of the International Conference on Learning Representations (ICLR), Vienna, Austria.
20. Rapid and less conservative interval power flow analysis based on a scenario reflection method for renewable penetrated power systems10.1109/TSTE.2025.3603573 ↗
21. Fully simulated data-driven domain generalized method for multiphase converters fault diagnosis10.1109/TPEL.2024.3461159 ↗
22. An advanced energy-coordinated control for half-bridge submodule-based centralized DC chopper in offshore wind MMC-HVDC Systems
23. Turbulence correlation between moving trains and anemometer towers: Theoretical analysis, field measurements and simulation10.1016/j.jweia.2024.105949 ↗
24. Multi-target detection for safety monitoring in complex substation environments using YOLO-DySE10.1007/s11760-025-04425-9 ↗
25. An efficient distributionally robust framework for multi-period energy storage planning in renewable-dominated power systems under normal and hurricane conditions10.1016/j.apenergy.2026.127748 ↗
26. Digital disaster prevention for ocean engineering: Current progress and future directions10.1016/j.oceaneng.2026.125101 ↗
27. Comprehensive review of neural network-based prediction intervals and new advances10.1109/TNN.2011.2162110 ↗
28. Lu, A., Wang, J., Guo, T., Wang, Z., and Xia, M. (2026). LECloud: Efficient Cloud and Cloud-Shadow Segmentation Based on Windowed State Space Model and Lightweight Attention Mechanism. Remote Sens., 18.10.3390/rs18091341 ↗
29. Multiple-constraints exploration and prototype-guided noise identification for semi-supervised medical image segmentation10.1016/j.bspc.2026.110004 ↗
30. Variational mode decomposition10.1109/TSP.2013.2288675 ↗
31. Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lió, P., and Bengio, Y. (May, January 30). Graph attention networks. Proceedings of the International Conference on Learning Representations, Vancouver, BC, Canada.
32. A Low noise readout circuit with input-common-mode-feedback charge sensitive amplifier using differential pseudo resistors for MEMS gyroscopes10.1109/TCSI.2025.3583902 ↗
33. Kipf, T.N., and Welling, M. (2017, January 24–26). Semi-supervised classification with graph convolutional networks. Proceedings of the International Conference on Learning Representations (ICLR), Toulon, France.
34. Enhanced YOLO-IASE for robust safety inspection in complex substation environments10.1007/s11760-025-04281-7 ↗
35. Han, L., Ye, H.-J., and Zhan, D.-C. (2024, January 10–15). SOFTS: Efficient Multivariate Time Series Forecasting with Series-Core Fusion. Proceedings of the Advances in Neural Information Processing Systems (NeurIPS), Vancouver, BC, Canada.10.52202/079017-2046 ↗
36. Causes identification and sources localization method for multistage voltage sag under the influence of high penetration of renewable energy sources10.1016/j.apenergy.2025.126891 ↗
37. Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A.N., Kaiser, Ł., and Polosukhin, I. (2017, January 4–9). Attention is all you need. Proceedings of the Advances in Neural Information Processing Systems (NeurIPS), Long Beach, CA, USA.
38. Distributed optimization and statistical learning via the alternating direction method of multipliers10.1561/2200000016 ↗
39. Detecting novel associations in large data sets10.1126/science.1205438 ↗
40. Dauphin, Y.N., Fan, A., Auli, M., and Grangier, D. (2017, January 6–11). Language modeling with gated convolutional networks. Proceedings of the International Conference on Machine Learning, Sydney, Australia.
41. Luo, D., and Wang, X. (2024, January 7–11). ModernTCN: A Modern Pure Convolution Structure for General Time Series Analysis. Proceedings of the International Conference on Learning Representations (ICLR), Vienna, Austria.
42. Ni, Y., Liu, S., Guo, T., and Xia, M. (2026). Tibt-net: A high-resolution remote sensing image change detection network integrating bi-temporal space enhancement and token interaction. Remote Sens., 18.10.3390/rs18050805 ↗
43. GLMamba: A Global–Local Mamba Network for Efficient Remote Sensing Change Detection10.1109/JSTARS.2026.3675679 ↗
44. The early warning method for offshore wind turbine gearbox oil temperature based on FSTAE-ATT
45. Perez, E., Strub, F., de Vries, H., Dumoulin, V., and Courville, A. (2018, January 2–7). FiLM: Visual reasoning with a general conditioning layer. Proceedings of the AAAI Conference on Artificial Intelligence, New Orleans, LA, USA.10.1609/aaai.v32i1.11671 ↗
46. Quantile and probability curves without crossing10.3982/ECTA7880 ↗
47. Zhou, J., Lu, X., Xiao, Y., Lin, B., Zhao, Y., Wang, J., Zhang, Q., Liu, J., and Luo, W. (2022). SDWPF: A dataset for spatial dynamic wind power forecasting challenge at KDD Cup 2022. arXiv.
48. Global Energy Forecasting Competition 201210.1016/j.ijforecast.2013.07.001 ↗
49. Loshchilov, I., and Hutter, F. (2017, January 24–26). SGDR: Stochastic gradient descent with warm restarts. Proceedings of the International Conference on Learning Representations, Toulon, France.
50. Long short-term memory10.1162/neco.1997.9.8.1735 ↗
51. Cho, K., van Merriënboer, B., Gulcehre, C., Bahdanau, D., Bougares, F., Schwenk, H., and Bengio, Y. (2014, January 25–29). Learning phrase representations using RNN encoder–decoder for statistical machine translation. Proceedings of the Conference on Empirical Methods in Natural Language Processing (EMNLP), Doha, Qatar.10.3115/v1/D14-1179 ↗
52. Bai, S., Kolter, J.Z., and Koltun, V. (2018). An empirical evaluation of generic convolutional and recurrent networks for sequence modeling. arXiv.
53. Are transformers effective for time series forecasting?
54. Informer: Beyond efficient transformer for long sequence time-series forecasting
55. Nie, Y., Nguyen, N.H., Sinthong, P., and Kalagnanam, J. (2023, January 1–5). A time series is worth 64 words: Long-term forecasting with transformers. Proceedings of the International Conference on Learning Representations (ICLR), Kigali, Rwanda.
56. Liu, Y., Hu, T., Zhang, H., Wu, H., Wang, S., Ma, L., and Long, M. (2024, January 7–11). iTransformer: Inverted transformers are effective for time series forecasting. Proceedings of the International Conference on Learning Representations (ICLR), Vienna, Austria.
57. Wang, Y., Wu, H., Dong, J., Liu, Y., Qiu, Y., Zhang, H., Wang, J., and Long, M. (2024, January 10–15). TimeXer: Empowering transformers for time series forecasting with exogenous variables. Proceedings of the Advances in Neural Information Processing Systems (NeurIPS), Vancouver, BC, Canada.10.52202/079017-0015 ↗
58. Yu, B., Yin, H., and Zhu, Z. (2018, January 13–19). Spatio-temporal graph convolutional networks: A deep learning framework for traffic flow forecasting. Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI), Stockholm, Sweden.10.24963/ijcai.2018/505 ↗
59. Li, Y., Yu, R., Shahabi, C., and Liu, Y. (May, January 30). Diffusion convolutional recurrent neural network: Data-driven traffic forecasting. Proceedings of the International Conference on Learning Representations (ICLR), Vancouver, BC, Canada.
60. Yuan, S., Mao, Y., Tian, C., Yu, F., Guo, T., and Xia, M. (2026). GSTAformer: Graph-Guided Spatio-Temporal Autoformer for Mid-Term Wind Power Forecasting. Energies, 19.10.3390/en19010254 ↗
61. Gal, Y., and Ghahramani, Z. (2016, January 19–24). Dropout as a Bayesian approximation: Representing model uncertainty in deep learning. Proceedings of the International Conference on Machine Learning (ICML), New York, NY, USA.
62. Lakshminarayanan, B., Pritzel, A., and Blundell, C. (2017, January 4–9). Simple and scalable predictive uncertainty estimation using deep ensembles. Proceedings of the Advances in Neural Information Processing Systems (NeurIPS), Long Beach, CA, USA.
63. Blundell, C., Cornebise, J., Kavukcuoglu, K., and Wierstra, D. (2015, January 6–11). Weight uncertainty in neural networks. Proceedings of the International Conference on Machine Learning (ICML), Lille, France.
64. Liu, Y., Zhang, H., Li, C., Huang, X., Wang, J., and Long, M. (2024, January 21–27). Timer: Generative Pre-trained Transformers Are Large Time Series Models. Proceedings of the International Conference on Machine Learning (ICML), Vienna, Austria.
65. Wang, S., Wu, H., Shi, X., Hu, T., Luo, H., Ma, L., Zhang, J.Y., and Zhou, J. (2024, January 7–11). TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting. Proceedings of the International Conference on Learning Representations (ICLR), Vienna, Austria.