Delay-dependent stability analysis of power system: A Monotone-Interval-Partition method for time-varying delays

Shihao Wang; Jin Yang; Yuejiang Wang; Qishui Zhong; Kaibo Shi; Shihao Wang; Jin Yang; Yuejiang Wang; Qishui Zhong; Kaibo Shi

doi:10.3934/math.2025752

AIMS Mathematics

2025, Volume 10, Issue 7: 16746-16761. doi: 10.3934/math.2025752

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Delay-dependent stability analysis of power system: A Monotone-Interval-Partition method for time-varying delays

1.
School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu 611731, China
2.
School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
3.
School of Government, University of Birmingham, Birmingham, B15 2TT, United Kingdom
4.
School of Electronic Information and Electrical Engineering, Chengdu University, Chengdu 610106, China

Received: 19 June 2025 Revised: 10 July 2025 Accepted: 16 July 2025 Published: 25 July 2025
MSC : 93B52, 93C05

This paper investigates the problem of a delay-dependent stability analysis in power systems, where the communication delay is modeled as a continuous, differentiable, aperiodic, and bounded function with constrained derivatives. First, a unified load frequency control system model is formulated that explicitly incorporates time-varying delays. Then, to more accurately address the delay characteristics, a monotonic interval partitioning strategy is introduced, which divides the delay trajectory into multiple segments based on its increasing or decreasing behavior. Each segment is associated with corresponding local extremal points of the delay function. Furthermore, to more effectively exploit the delay information, a new Lyapunov-Krasovskii functional (LKF) is developed, which integrates system states related to the local extremal values of the delay in each subinterval. By leveraging this LKF together with a convex combination method, less conservative stability conditions are derived. Finally, numerical case studies are presented to demonstrate the proposed approach's capability of enlarging the admissible delay bounds and validating its improved performance.
- power system,
- stability analysis,
- time-varying delays,
- monotone-interval-partition method
Citation: Shihao Wang, Jin Yang, Yuejiang Wang, Qishui Zhong, Kaibo Shi. Delay-dependent stability analysis of power system: A Monotone-Interval-Partition method for time-varying delays[J]. AIMS Mathematics, 2025, 10(7): 16746-16761. doi: 10.3934/math.2025752

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Abstract

This paper investigates the problem of a delay-dependent stability analysis in power systems, where the communication delay is modeled as a continuous, differentiable, aperiodic, and bounded function with constrained derivatives. First, a unified load frequency control system model is formulated that explicitly incorporates time-varying delays. Then, to more accurately address the delay characteristics, a monotonic interval partitioning strategy is introduced, which divides the delay trajectory into multiple segments based on its increasing or decreasing behavior. Each segment is associated with corresponding local extremal points of the delay function. Furthermore, to more effectively exploit the delay information, a new Lyapunov-Krasovskii functional (LKF) is developed, which integrates system states related to the local extremal values of the delay in each subinterval. By leveraging this LKF together with a convex combination method, less conservative stability conditions are derived. Finally, numerical case studies are presented to demonstrate the proposed approach's capability of enlarging the admissible delay bounds and validating its improved performance.

References

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