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The Evolution of Probability Density Function for Power System Excited by Fractional Gaussian Noise

Author

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  • Hufei Li

    (School of Mathematics and Information Science & Ningxia Key Laboratory of Intelligent Information and Big Data Processing, North Minzu University, Yinchuan 750021, China)

  • Shaojuan Ma

    (School of Mathematics and Information Science & Ningxia Key Laboratory of Intelligent Information and Big Data Processing, North Minzu University, Yinchuan 750021, China)

Abstract

This article is devoted to investigating the evolution of the probability density function for power system excited by fractional stochastic noise. First, the single-machine-infinite-bus (SMIB) power system model excited by fractional Gaussian noise (FGN) is established. Second, we derive the Fokker–Planck–Kolmogorov (FPK) equation for the proposed model and solve the FPK equation using the finite difference method. Finally, the numerical results verify that the addition of FGN would influence dynamical stability of the SMIB power system under certain conditions.

Suggested Citation

  • Hufei Li & Shaojuan Ma, 2023. "The Evolution of Probability Density Function for Power System Excited by Fractional Gaussian Noise," Mathematics, MDPI, vol. 11(13), pages 1-16, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2854-:d:1179305
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    References listed on IDEAS

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    1. Baudoin, Fabrice & Coutin, Laure, 2007. "Operators associated with a stochastic differential equation driven by fractional Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 117(5), pages 550-574, May.
    2. Xue Lin & Lixia Sun & Ping Ju & Hongyu Li, 2019. "Stochastic Control for Intra-Region Probability Maximization of Multi-Machine Power Systems Based on the Quasi-Generalized Hamiltonian Theory," Energies, MDPI, vol. 13(1), pages 1-16, December.
    3. Backus, David K & Zin, Stanley E, 1993. "Long-Memory Inflation Uncertainty: Evidence from the Term Structure of Interest Rates," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 25(3), pages 681-700, August.
    4. Stefan Rostek, 2009. "Option Pricing in Fractional Brownian Markets," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-00331-8, July.
    5. Stefan Rostek, 2009. "Risk Preference Based Option Pricing in a Continuous Time Fractional Brownian Market," Lecture Notes in Economics and Mathematical Systems, in: Option Pricing in Fractional Brownian Markets, chapter 5, pages 79-110, Springer.
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