ENGINEERING Information Technology & Electronic Engineering  2026 Vol.27 No.5 P.1-13

http://doi.org/10.1631/ENG.ITEE.2026.0024


An approach to characterizing the power system security region by integrating distributionally robust optimization and Transformer-based deep learning


Author(s):  Yuekai CHEN, Zhejing BAO, Miao YU

Affiliation(s):  1. College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   zjbao@zju.edu.cn

Key Words:  Security region, Distributionally robust optimization, Deep learning, Transformer model, Data-driven


Yuekai CHEN, Zhejing BAO, Miao YU. An approach to characterizing the power system security region by integrating distributionally robust optimization and Transformer-based deep learning[J]. Journal of Zhejiang University Science C, 2026, 27(5): 1-13.

@article{title="An approach to characterizing the power system security region by integrating distributionally robust optimization and Transformer-based deep learning",
author="Yuekai CHEN, Zhejing BAO, Miao YU",
journal="Journal of Zhejiang University Science C",
volume="27",
number="5",
pages="1-13",
year="2026",
publisher="Zhejiang University Press & Springer",
doi="10.1631/ENG.ITEE.2026.0024"
}

%0 Journal Article
%T An approach to characterizing the power system security region by integrating distributionally robust optimization and Transformer-based deep learning
%A Yuekai CHEN
%A Zhejing BAO
%A Miao YU
%J Frontiers of Information Technology & Electronic Engineering
%V 27
%N 5
%P 1-13
%@ 1869-1951
%D 2026
%I Zhejiang University Press & Springer
%DOI 10.1631/ENG.ITEE.2026.0024

TY - JOUR
T1 - An approach to characterizing the power system security region by integrating distributionally robust optimization and Transformer-based deep learning
A1 - Yuekai CHEN
A1 - Zhejing BAO
A1 - Miao YU
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 27
IS - 5
SP - 1
EP - 13
%@ 1869-1951
Y1 - 2026
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/ENG.ITEE.2026.0024


Abstract: 
Renewable generation and load uncertainty pose significant challenges to power system security, necessitating efficient approaches to characterizing high-dimensional security regions. To overcome the curse of dimensionality, uncertainty neglect, and undue conservatism in existing methods, this paper proposes an approach integrating distributionally robust optimization (DRO) and deep learning for security region characterization. First, to properly account for uncertainty while avoiding excessive conservatism, a DRO-based active search strategy is developed to identify critical boundary points, where diffusion-generated renewable scenarios and load-deviation samples constructed around typical demand profiles are jointly used to build a robust probabilistic ambiguity set. Subsequently, a Transformer-based model learns from these boundary points to reconstruct the full high-dimensional security region. The model’s self-attention mechanism captures the global nonlinear dependencies among dimensions, enabling a precise and efficient boundary fit. Simulations on IEEE test systems confirm that the approach accurately characterizes high-dimensional security regions at a low computational cost, yielding a security region with strong robustness to renewable-load uncertainty. This work offers a new paradigm for security assessment and decision support in power systems under high uncertainty.

融合分布鲁棒优化与Transformer深度学习的电力系统安全域表征方法

陈悦锴,包哲静,于淼
浙江大学电气工程学院,中国杭州市,310027
摘要:可再生能源与负荷的不确定性给电力系统安全运行带来严峻挑战,亟需表征高维安全域的高效方法。为克服现有方法中存在的维数灾难、对不确定性考虑不足或者过度保守等问题,提出一种融合分布鲁棒优化与深度学习的安全域表征方法。首先,为在合理考虑不确定性的同时避免过强保守性,构建了一种基于分布鲁棒优化的主动搜索策略,用于识别关键边界点;其中,联合了基于扩散模型生成的可再生能源场景以及围绕典型负荷曲线构造的负荷偏差样本,共同建立鲁棒概率模糊集。随后,设计了基于Transformer的模型,利用这些边界点学习并重构完整的高维安全域。该模型的自注意力机制能够捕捉各维度之间的全局非线性依赖关系,从而实现对安全域边界的高精度、高效率拟合。在IEEE测试系统上的仿真结果表明,所提方法能够以较低计算成本准确表征高维安全域,并获得对源–荷不确定性具有较强鲁棒性的安全域。本文为高不确定性背景下的电力系统安全评估与决策支持提供了一种新的研究范式。

关键词:安全域;分布鲁棒优化;深度学习;Transformer模型;数据驱动

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1]Aryani DR, Song H, 2024. A review on power system security issues in the high renewable energy penetration environment. J Electr Eng Technol, 19:4649-4665.

[2]Avila OF, Passos Filho JA, Peres W, 2021. Steady-state security assessment in distribution systems with high penetration of distributed energy resources. Electr Power Syst Res, 201:107500.

[3]Bharati AK, Ajjarapu V, Du W, et al., 2023. Role of distributed inverter-based-resources in bulk grid primary frequency response through HELICS based SMTD co-simulation. IEEE Syst J, 17(1):1071-1082.

[4]Chen S, Wei Z, Sun G, et al., 2019. Convex hull based robust security region for electricity-gas integrated energy systems. IEEE Trans Power Syst, 34(3):1740-1748.

[5]Dai W, Yang Z, Yu J, et al., 2019. Security region of renewable energy integration: characterization and flexibility. Energy, 187:115975.

[6]Dolatabadi SH, Ghorbanian M, Siano P, et al., 2021. An enhanced IEEE 33 bus benchmark test system for distribution system studies. IEEE Trans Power Syst, 36(3):2565-2572.

[7]Feng J, Ren ZY, Jiang YP, et al., 2024. Committed carbon emissions operation regions of power system: concept and method. Proc CSEE, 44(22):8846-8859(in Chinese).

[8]Gao Y, Ren Z, Jiang Y, et al., 2023. Analysis method of committed carbon emission operational region for electricity-hydrogen coupling system. Electr Power Autom Equip, 43(12):29-36(in Chinese).

[9]Jiang T, Zhang R, Li X, et al., 2021. Integrated energy system security region: concepts, methods, and implementations. Appl Energy, 283:116124.

[10]Jiang YP, Ren ZY, Lu CH, et al., 2024. A region-based low-carbon operation analysis method for integrated electricity-hydrogen-gas systems. Appl Energy, 355:122230.

[11]Jin Y, Acquah MA, Seo M, et al., 2023. Optimal EV scheduling and voltage security via an online bi-layer steady-state assessment method considering uncertainties. Appl Energy, 347:121356.

[12]Li S, Xiong H, Chen Y, 2024. DiffCharge: generating EV charging scenarios via a denoising diffusion model. IEEE Trans Smart Grid, 15(4):3936-3949.

[13]Li X, Zhang LW, Jiang T, et al., 2021. General algorithm for exploring security region boundary in power systems using Lagrange multiplier. Proc CSEE, 41(15):5139-5152(in Chinese).

[14]Lin W, Yang Z, Yu J, et al., 2021. Tie-line security region considering time coupling. IEEE Trans Power Syst, 36(2):1274-1284.

[15]Lin W, Jiang H, Yang Z, 2022. Tie-line security regions in high dimension for renewable accommodations.

[16]Lin W, Jiang H, Jian HJ, et al., 2023. High-dimension tie-line security regions for renewable accommodations. Energy, 270:126887.

[17]Liu L, Wang D, Hou K, et al., 2020. Region model and application of regional integrated energy system security analysis. Appl Energy, 260:114268.

[18]Liu W, Wang CG, Cao Y, et al., 2025. A method for generating wind power output scenarios based on improved conditional generative diffusion model. Electr Power Syst Res, 247:111779.

[19]Monteiro MR, Alvarenga GF, Rodrigues YR, et al., 2020. Network partitioning in coherent areas of static voltage stability applied to security region enhancement. Int J Electr Power Energy Syst, 117:105623.

[20]Nguyen HD, Dvijotham K, Turitsyn K, 2019. Constructing convex inner approximations of steady-state security regions. IEEE Trans Power Syst, 34(1):257-267.

[21]Rahimian H, Mehrotra S, 2019. Distributionally robust optimization: a review.

[22]Su J, Chiang HD, Zeng Y, et al., 2021. Toward complete characterization of the steady-state security region for the electricity-gas integrated energy system. IEEE Trans Smart Grid, 12(4):3004-3015.

[23]Sun D, Yu Y, 2023. Accurate identification of critical boundary hyperplanes of practical steady-state security region in distribution grids. IEEE Trans Smart Grid, 14(6):4312-4321.

[24]Teng F, Zhang YX, Yang TK, et al., 2024. Distributed optimal energy management for We-Energy considering operation security. IEEE Trans Netw Sci Eng, 11(1):225-235.

[25]Tinoco RAG, Passos Filho JA, Peres W, et al., 2021. A new particle swarm optimization-based methodology for determining online static security regions. Int Trans Electr Energy Syst, 31(3):e12790.

[26]Wu F, Kumagai S, 1982. Steady-state security regions of power systems. IEEE Trans Circ Syst, 29(11):703-711.

[27]Wu FF, Tsai YK, Yu YX, 1988. Probabilistic steady-state and dynamic security assessment. IEEE Trans Power Syst, 3(1):1-9.

[28]Wu XW, Zhang B, Nielsen MP, et al., 2023. Neural network based feasible region approximation model for optimal operation of integrated electricity and heating system. CSEE J Power Energy Syst, 9(5):1808-1819.

[29]Xiao J, Li C, She B, et al., 2024. Distribution system security region with energy storage systems. Energy, 313:133841.

[30]Xie W, 2021. On distributionally robust chance constrained programs with Wasserstein distance. Math Program, 186(1-2):115-155.

[31]Yorino N, Abdillah M, Sasaki Y, et al., 2018. Robust power system security assessment under uncertainties using bi-level optimization. IEEE Trans Power Syst, 33(1):352-362.

[32]Zhang S, Gu W, Zhang XP, et al., 2024. Steady-state security region of integrated energy system considering thermal dynamics. IEEE Trans Power Syst, 39(2):4138-4153.

[33]Zhang ZY, Yang ZB, Yau DKY, et al., 2023. Data security of machine learning applied in low-carbon smart grid: a formal model for the physics-constrained robustness. Appl Energy, 347:121405.

[34]Zhang ZY, Liu MX, Sun MY, et al., 2024. Vulnerability of machine learning approaches applied in IoT-based smart grid: a review. IEEE Int Things J, 11(11):18951-18975.

[35]Zhou A, Yang M, Wang M, et al., 2020. A linear programming approximation of distributionally robust chance-constrained dispatch with Wasserstein distance. IEEE Trans Power Syst, 35(5):3366-3377.

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Full Text:   <316>

Summary:  <369>

CLC number: TM71

On-line Access: 2026-05-27

Received: 2026-01-21

Revision Accepted: 2026-04-16

Crosschecked: 2026-05-27

Cited: 0

Clicked: 384

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Yuekai CHEN

0009-0009-9946-9688

Zhejing BAO

0000-0002-8678-3805

Miao YU

0000-0002-7638-5264

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2026 Journal of Zhejiang University-SCIENCE