Frequency-constrained Economic Dispatch via Physics-informed Piecewise Linearization Under <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mi>N</mi><mo>–</mo><mn mathvariant="normal">1</mn></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/E4A8C82C-6C0A-4de9-9753-47796F6312EE-M001.jpg"><?fx-imagestate width="14.39333248" height="6.01133299"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/E4A8C82C-6C0A-4de9-9753-47796F6312EE-M001c.jpg"><?fx-imagestate width="14.39333248" height="6.01133299"?></graphic></alternatives></inline-formula> Contingencies

Danyang Xu; Yongzhe Li; Zhigang Wu; Lin Guan

doi:10.35833/MPCE.2025.000344

欢迎来到能源电力期刊网！

English Version 期刊登录

您当前的位置：

首页 >

文章列表页 >

Frequency-constrained Economic Dispatch via Physics-informed Piecewise Linearization Under

N - 1

Contingencies

Original Paper | 更新时间：2026-09-28

- Frequency-constrained Economic Dispatch via Physics-informed Piecewise Linearization Under $N - 1$ Contingencies
- Frequency-constrained Economic Dispatch via Physics-informed Piecewise Linearization Under $N - 1$ Contingencies
- MPCE 2026年14卷第5期页码：1597-1608
- 作者机构：
  
  1.State Key Laboratory of Smart Power Distribution Equipment and System, Tianjin University, Tianjin 300072, China
  2.School of Electric Power Engineering, South China University of Technology, Guangzhou 510641, China
- 作者简介：
  
  Danyang Xu received the B.S. degree in electrical engineering from Hunan University, Changsha, China, in 2022, and the M.S. degree in electrical engineering from South China University of Technology, Guangzhou, China, in 2025. He is currently pursuing the Ph.D. degree in electrical engineering at Tianjin University, Tianjin, China. His research interests include aggregated feasible region characterization in power systems and optimal operation of low-inertia power systems. Email: scutxdy@gmail.com
  Yongzhe Li received the B.S. degree in electrical engineering from the South China University of Technology, Guangzhou, China, in 2022, where he is currently pursuing the Ph.D. degree. His research interests include deep learning and large language model technique for power system analysis. Email:1070671983@qq.com
  Zhigang Wu received the B.S. degree in electrical engineering from Tianjin University, Tianjin, China, in 1996, where he also received the M.S. and Ph.D. degrees in 1998 and 2002, respectively. He is currently an Associate Professor with the School of Electric Power Engineering, South China University of Technology, Guangzhou, China. His current research interests include numerical simulation of power system and complex network theory. Email:epzgwu@scut.edu.cn
  Lin Guan received the B.S. and Ph.D. degrees in electric power engineering from Huazhong University of Science and Technology, Wuhan, China, in 1990 and 1995, respectively. She is currently a Professor in Electric Power College, South China University of Technology, Guangzhou, China. Her research interests include application of artificial intelligence technology in electrical engineering, power system security and control, and power system planning and reliability. Email:lguan@scut.edu.cn
- 基金信息：
  
  Smart Grid National Science and Technology Major Project (2030)(2025ZD0807200);National Natural Science Foundation of China(U22B6007)
- DOI：10.35833/MPCE.2025.000344
  中图分类号：
- 收稿：2025-08-13，
  
  修回：2025-11-18，
  
  录用：2026-01-05，
  
  网络首发：2026-02-02，
  
  纸质出版：2026-09-15
- 稿件说明：
移动端阅览
Danyang Xu, Yongzhe Li, Zhigang Wu, 等. Frequency-constrained Economic Dispatch via Physics-informed Piecewise Linearization Under $N - 1$ Contingencies[J]. MPCE, 2026,14(5):1597-1608. DOI: 10.35833/MPCE.2025.000344.

Xu Danyang,Li Yongzhe,Wu Zhigang,et al.Frequency-constrained Economic Dispatch via Physics-informed Piecewise Linearization Under N–1 Contingencies[J].Journal of Modern Power Systems and Clean Energy,2026,14(05):1597-1608.
Danyang Xu, Yongzhe Li, Zhigang Wu, 等. Frequency-constrained Economic Dispatch via Physics-informed Piecewise Linearization Under $N - 1$ Contingencies[J]. MPCE, 2026,14(5):1597-1608. DOI: 10.35833/MPCE.2025.000344. DOI：

Xu Danyang,Li Yongzhe,Wu Zhigang,et al.Frequency-constrained Economic Dispatch via Physics-informed Piecewise Linearization Under N–1 Contingencies[J].Journal of Modern Power Systems and Clean Energy,2026,14(05):1597-1608. DOI： 10.35833/MPCE.2025.000344.

Frequency-constrained Economic Dispatch via Physics-informed Piecewise Linearization Under

N - 1

Contingencies

摘要

Abstract

This paper presents a frequency constrained economic dispatch (FCED) method designed to prevent frequency violations under

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=119194208&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=119194207&type=

5.58799982

2.28600001

contingencies

encompassing both generator outages and high-voltage direct current (HVDC) infeed losses. Firstly

the coordinated frequency dynamics of synchronous generators

wind turbines

and HVDC lines are modeled

and the resulting frequency constraints are derived. To address the challenging frequency nadir (FN) constraint

a physics-informed piecewise linearization (PI-PWL) model is introduced to learn the FN security boundary. The formulation of the proposed FCED method is then presented

incorporating frequency constraints under

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=119194208&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=119194207&type=

5.58799982

2.28600001

contingencies. Additionally

an error-aware constraint cut (EACC) is proposed to eliminate errors introduced by data-driven methods and accelerate solution convergence. Case studies on the modified IEEE 39-bus and IEEE 118-bus test systems validate the effectiveness of the proposed FCED method. Results indicate that the proposed PI-PWL model more accurately captures the FN security boundary than the traditional PWL (T-PWL) model

particularly in scenarios with limited unstable samples. Moreover

the proposed FCED method ensures frequency security under

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=119194208&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=119194207&type=

5.58799982

2.28600001

contingencies

while the EACC effectively eliminates approximation errors and accelerates convergence compared with fixed-step constraint cuts.

关键词

Keywords

references

J. Wang, H. Jia, X. Jin et al. , “A decentralized peer-to-peer framework for integrated electricity-heat-carbon sharing among multiple microgrids,” Journal of Modern Power Systems and Clean Energy , vol. 13 , no. 5 , pp. 1787 - 1799 , Sept. 2025.

J. Liu, X. Xu, L. Liu et al. , “Optimal scheduling of wind power generators for isolated offshore field microgrids considering unified frequency response and spinning reserve,” Journal of Modern Power Systems and Clean Energy , vol. 13 , no. 6 , pp. 1980 - 1989 , Nov. 2025 .

Y. Zhang, C. He, X. Liu et al. , “Coordinated restoration of integrated gas-electricity distribution system with dynamic islanding: a multi-stage stochastic model with nonanticipativity,” IEEE Transactions on Power Systems , vol. 40 , no. 3 , pp. 2165 - 2178 , May 2025.

D. Xu, Z. Wu, L. Zhu et al. , “A novel frequency constrained unit commitment considering VSC-HVDC frequency support in asynchronous interconnected system under renewable energy source uncertainty,” Electric Power Systems Research , vol. 238 , p. 111098 , Jan. 2025 .

D. Xu and Z. Wu, “Enhanced frequency-aware microgrid scheduling towards seamless islanding under frequency support of heterogeneous resources: a distributionally robust chance-constrained approach,” International Journal of Electrical Power & Energy Systems , vol. 162 , p. 110310 , Nov. 2024 .

B. She, F. Li, H. Cui et al. , “Virtual inertia scheduling (VIS) for real-time economic dispatch of IBR-penetrated power systems,” IEEE Transactions on Sustainable Energy , vol. 15 , no. 2 , pp. 938 - 951 , Apr. 2024 .

B. She, F. Li, J. Wang et al. , “Virtual inertia scheduling (VIS) for microgrids with static and dynamic security constraints,” IEEE Transactions on Sustainable Energy , vol. 16 , no. 2 , pp. 785 - 796 , Apr. 2025 .

J. Fu, C. He, T. Liu et al. , “Resilience-oriented optimal allocation of splitting devices for intentional controlled islanding considering frequency stability constraints and demand response,” IEEE Transactions on Power Systems , vol. 40 , no. 4 , pp. 3074 - 3089 , Jul. 2025 .

F. Teng, V. Trovato, and G. Strbac, “Stochastic schedu ling with inertia-dependent fast frequency response requirements,” IEEE Transactions on Power Systems , vol. 31 , no. 2 , pp. 1557 - 1566 , Mar. 2016 .

L. Yang, Z. Li, Y. Xu et al. , “Frequency constrained scheduling under multiple uncertainties via data-driven distributionally robust chance-constrained approach,” IEEE Transactions on Sustainable Energy , vol. 14 , no. 2 , pp. 763 - 776 , Apr. 2023 .

L. Badesa, F. Teng, and G. Strbac, “Optimal portfolio of distinct frequency response services in low-inertia systems,” IEEE Transactions on Power Systems , vol. 35 , no. 6 , pp. 4459 - 4469 , Nov. 2020 .

Y. Shen, W. Wu, B. Wang et al. , “Data-driven convexification for frequency nadir constraint of unit commitment,” Journal of Modern Power Systems and Clean Energy , vol. 11 , no. 5 , pp. 1711 - 1717 , Sept. 2023.

D. Xu, Z. Wu, Y. Liu et al. , “Enhancing frequency security for renewable-dominated power systems via distributionally robust frequency constrained unit commitment,” Electric Power Systems Research , vol. 239 , p. 111078 , Feb. 2025 .

J. Zhang, H. Jia, and N. Zhang, “Alternate support vector machine decision trees for power systems rule extractions,” IEEE Transactions on Power Systems , vol. 38 , no. 1 , pp. 980 - 983 , Jan. 2023 .

B. Jiang, C. Guo, and Z. Chen, “Frequency constrained dispatch with energy reserve and virtual inertia from wind turbines,” IEEE Transactions on Sustainable Energy , vol. 16 , no. 2 , pp. 1340 - 1355 , Apr. 2025 .

H. Ahmadi and H. Ghasemi, “Security-constrained unit commitment with linearized system frequency limit constraints,” IEEE Transactions on Power Systems , vol. 29 , no. 4 , pp. 1536 - 1545 , Jul. 2014 .

Z. Zhang, E. Du, F. Teng et al. , “Modeling frequency dynamics in unit commitment with a high share of renewable energy,” IEEE Transactions on Power Systems , vol. 35 , no. 6 , pp. 4383 - 4395 , Nov. 2020 .

J. Li, Y. Qiao, Z. Lu et al. , “Integrated frequency-constrained scheduling considering coordination of frequency regulation capabilities from multi-source converters,” Journal of Modern Power Systems and Clean Energy , vol. 12 , no. 1 , pp. 261 - 274 , Jan. 2024 .

Y. Yuan, Y. Zhang, J. Wang et al. , “Enhanced frequency-constrained unit commitment considering variable-droop frequency control from converter-based generator,” IEEE Transactions on Power Systems , vol. 38 , no. 2 , pp. 1094 - 1110 , Mar. 2023 .

B. Huang and J. Wang, “Applications of physics-informed neural networks in power systems – a review,” IEEE Transactions on Power Systems , vol. 38 , no. 1 , pp. 572 - 588 , Jan. 2023 .

L. Badesa, F. Teng, and G. Strbac, “Simultaneous scheduling of multiple frequency services in stochastic unit commitment,” IEEE Transactions on Power Systems , vol. 34 , no. 5 , pp. 3858 - 3868 , Sept. 2019.

C. O’Malley, L. Badesa, F. Teng et al. , “Probabilistic scheduling of UFLS to secure credible contingencies in low inertia systems,” IEEE Transactions on Power Systems , vol. 37 , no. 4 , pp. 2693 - 2703 , Jul. 2022 .

L. Wang, Y. Yang, H. Gu et al. , “Bottleneck generator identification and the corresponding N –1 frequency security constrained intraday generator dispatch,” IEEE Transactions on Power Systems , vol. 38 , no. 1 , pp. 739 - 752 , Jan. 2023 .

F. Teng, Y. Mu, J. Wu et al. , “Challenges on primary frequency control and potential solution from EVs in the future GB electricity system,” Applied Energy , vol. 194 , pp. 353 - 362 , Jun. 2017 .

D. Xu. (2024, Aug.). Supplement materials of FCED. [Online]. Available: https://github.com/SCUT-DanyangXu/Supplement-Materials-of-FCED.git

J. Zhang, Z. Chen, N. Zhang et al. , “Frequency-constrained unit commitments with linear rules extracted from simulation results considering regulations from battery storage,” Journal of Modern Power Systems and Clean Energy , vol. 11 , no. 4 , pp. 1041 - 1052 , Jul. 2023 .

J. Zhu, Z. Shen, L. Yu et al. , “Bilateral inertia and damping emulation control scheme of VSC-HVDC transmission systems for asynchronous grid interconnections,” IEEE Transactions on Power Systems , vol. 38 , no. 5 , pp. 4281 - 4292 , Sept. 2023.

Y. Shen, W. Wu, B. Wang et al. , “Optimal allocation of virtual inertia and droop control for renewable energy in stochastic look-ahead power dispatch,” IEEE Transactions on Sustainable Energy , vol. 14 , no. 3 , pp. 1881 - 1894 , Jul. 2023 .

M. Huang, X. Cui, N. Zhang et al. , “Optimal planning of standalone net-zero energy systems with small modular reactors,” IEEE Transactions on Smart Grid , vol. 15 , no. 4 , pp. 3751 - 3767 , Jul. 2024 .

Q. Hou, N. Zhang, D. S. Kirschen et al. , “Sparse oblique decision tree for power system security rules extraction and embedding,” IEEE Transactions on Power Systems , vol. 36 , no. 2 , pp. 1605 - 1615 , Mar. 2021 .

浏览量

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

A Data-driven and Deep Learning-based Method for Power System Operating Mode Identification

Multiscale Energy Coordination of Integrated Thermal Power-Energy Storage System for Enhanced Primary Frequency Regulation

A Data-driven Multi-agent Framework for Electricity Market Simulation Using Practical and Heterogeneous Bidding Strategy Spaces

Modeling and Integrating Frequency Security Constraints in Generation Portfolio Optimization for Low-inertia Grids

Optimal Scheduling of Wind Power Generators for Isolated Offshore Field Microgrids Considering Unified Frequency Response and Spinning Reserve

Frequency-constrained Economic Dispatch via Physics-informed Piecewise Linearization Under N–1 Contingencies

Frequency-constrained Economic Dispatch via Physics-informed Piecewise Linearization Under N–1 Contingencies

DOI：10.35833/MPCE.2025.000344

摘要

Abstract

关键词

Keywords

references

Frequency-constrained Economic Dispatch via Physics-informed Piecewise Linearization Under $N - 1$ Contingencies

Frequency-constrained Economic Dispatch via Physics-informed Piecewise Linearization Under $N - 1$ Contingencies