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Volume 15
Issue 10
10.3390/electronics15102191
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Dynamic Security Assessment and Security Region Construction Based on the Maximum Lyapunov Exponent Criterion

by
Qiuquan Deng
1,
Xikai Liu
2,*,
Cuiyun Luo
1,
Yin Wu
1,
Guangming Li
1,
Xiejin Ling
1,
Zhencheng Liang
1,
Junzhi Ren
2,
Yuan Zeng
2 and
Chao Qin
2
1
Guangxi Power Grid Co., Ltd., Nanning 530000, China
2
School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China
*
Author to whom correspondence should be addressed.
Electronics 2026, 15(10), 2191; https://doi.org/10.3390/electronics15102191
Submission received: 27 March 2026 / Revised: 8 May 2026 / Accepted: 11 May 2026 / Published: 19 May 2026
Versions Notes

Abstract

With the advancement of wide-area measurement systems (WAMSs), response-driven methods for transient stability analysis have gained increasing attention in recent years. The maximum Lyapunov exponent (MLE)-based trajectory analysis technique enables online transient stability assessment by capturing the trend characteristics of system trajectories. Motivated by this capability, a rapid construction methodology for the practical dynamic security region (PDSR) is proposed based on the MLE criterion. Initially, through analyzing the dynamic characteristics of generator rotor angle trajectories after disturbances, the dynamic MLE characteristics of the generator’s angular velocity deviation trajectory are extracted to formulate the MLE-based stability criterion. Subsequently, a stability boundary function based on MLE trajectories is developed, and the linear relationship between the injection space parameters and the MLE stability boundary function is derived. Finally, leveraging the sensitivity of the stability boundary function to the variations in injection space parameters, the dynamic security region is constructed around the dominant instability critical point, thereby establishing a mapping function between transient stability and the injection space parameters. The effectiveness of the proposed method is demonstrated through simulations on the IEEE39 power system. Results show that the method exhibits promising performance in terms of speed and adaptability for transient stability analysis and boundary construction.
Keywords: maximum Lyapunov exponent (MLE); practical dynamic security region (PDSR); transient stability maximum Lyapunov exponent (MLE); practical dynamic security region (PDSR); transient stability

Share and Cite

MDPI and ACS Style

Deng, Q.; Liu, X.; Luo, C.; Wu, Y.; Li, G.; Ling, X.; Liang, Z.; Ren, J.; Zeng, Y.; Qin, C. Dynamic Security Assessment and Security Region Construction Based on the Maximum Lyapunov Exponent Criterion. Electronics 2026, 15, 2191. https://doi.org/10.3390/electronics15102191

AMA Style

Deng Q, Liu X, Luo C, Wu Y, Li G, Ling X, Liang Z, Ren J, Zeng Y, Qin C. Dynamic Security Assessment and Security Region Construction Based on the Maximum Lyapunov Exponent Criterion. Electronics. 2026; 15(10):2191. https://doi.org/10.3390/electronics15102191

Chicago/Turabian Style

Deng, Qiuquan, Xikai Liu, Cuiyun Luo, Yin Wu, Guangming Li, Xiejin Ling, Zhencheng Liang, Junzhi Ren, Yuan Zeng, and Chao Qin. 2026. "Dynamic Security Assessment and Security Region Construction Based on the Maximum Lyapunov Exponent Criterion" Electronics 15, no. 10: 2191. https://doi.org/10.3390/electronics15102191

APA Style

Deng, Q., Liu, X., Luo, C., Wu, Y., Li, G., Ling, X., Liang, Z., Ren, J., Zeng, Y., & Qin, C. (2026). Dynamic Security Assessment and Security Region Construction Based on the Maximum Lyapunov Exponent Criterion. Electronics, 15(10), 2191. https://doi.org/10.3390/electronics15102191

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