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

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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
- Journal of Modern Power Systems and Clean Energy Vol. 14, Issue 5, Pages: 1597-1608(2026)
- 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：
- DOI：10.35833/MPCE.2025.000344
  CLC：
- Received：13 August 2025，
  
  Revised：2025-11-18，
  
  Accepted：05 January 2026，
  
  Online First：02 February 2026，
  
  Published：15 September 2026
- 稿件说明：
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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：

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

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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