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

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.

Keywords

Security region / Distributionally robust optimization / Deep learning / Transformer model / Data-driven

References

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

[2] Avila OF , Passos Filho JA , Peres W , 2021. Steady-state security assessment in distribu-tion 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 electricitygas 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 bench-mark 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:con-cepts, 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 denois-ing 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 renew-able accommodations.

[16] Lin W , Jiang H , Jian HJ , et al., High-dimension tie-line security regions for renew-able 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 sce-narios 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 co-herent 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 steadystate 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 optimiza-tion-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 assess-ment. IEEE Trans Power Syst, 3(1): 1- 9.

[28] Wu XW , Zhang B , Nielsen MP , et al., 2023. Neural network based feasible region approxi-mation 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 stor-age 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 distri-butionally robust chance-constrained dispatch with Wasserstein distance. IEEE Trans Power Syst, 35(5): 3366- 3377.

RIGHTS & PERMISSIONS

The Authors. Published by Zhejiang University Press Co., Ltd.