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Improving the small-signal stability of a stochastic power system — Algorithms and mathematical analysis

Author

Listed:
  • Wang, Zhen
  • Xi, Kaihua
  • Cheng, Aijie
  • Lin, Hai Xiang
  • van Schuppen, Jan H.

Abstract

Tools and analysis for improving the small-signal stability of a stochastic power system by optimal power dispatch in each short time horizon, such as five-minute intervals, are provided in this paper. An objective function which characterizes the maximal exit probability from the static stability region (−π/2,π/2) across the phase-angle differences of all power lines is formulated. This objective function is proven to be Lipschitz continuous, nondifferentiable, and nonconvex, with a finite minimum defined over the region of power supply vectors. The formulas of the generalized subgradient and directional derivative of the objective function are provided, and based on these formulas, a two-step algorithm is designed to approximate a minimizer accompanied by the convergence proof: (1) using a projected generalized subgradient method to compute an effective initial vector, and (2) applying the steepest descent method to approximate a local minimizer. The algorithms have been verified using a synthesized power network, demonstrating computational validity and effectiveness in minimizing the maximal exit probability of all power lines.

Suggested Citation

  • Wang, Zhen & Xi, Kaihua & Cheng, Aijie & Lin, Hai Xiang & van Schuppen, Jan H., 2025. "Improving the small-signal stability of a stochastic power system — Algorithms and mathematical analysis," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
    • Handle: RePEc:eee:chsofr:v:199:y:2025:i:p1:s0960077925006290
    DOI: 10.1016/j.chaos.2025.116616
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    References listed on IDEAS

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    1. Marina Danilova & Pavel Dvurechensky & Alexander Gasnikov & Eduard Gorbunov & Sergey Guminov & Dmitry Kamzolov & Innokentiy Shibaev, 2022. "Recent Theoretical Advances in Non-Convex Optimization," Springer Optimization and Its Applications, in: Ashkan Nikeghbali & Panos M. Pardalos & Andrei M. Raigorodskii & Michael Th. Rassias (ed.), High-Dimensional Optimization and Probability, pages 79-163, Springer.
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