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Article

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

by
Hufei Li
and
Shaojuan Ma
*
School of Mathematics and Information Science & Ningxia Key Laboratory of Intelligent Information and Big Data Processing, North Minzu University, Yinchuan 750021, China
*
Author to whom correspondence should be addressed.
Mathematics 2023, 11(13), 2854; https://doi.org/10.3390/math11132854
Submission received: 11 May 2023 / Revised: 14 June 2023 / Accepted: 24 June 2023 / Published: 26 June 2023
(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering, 2nd Edition)
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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.
Keywords: Fokker–Planck–Kolmogorov equation; fractional Gaussian noise; probability density function; power system; stability Fokker–Planck–Kolmogorov equation; fractional Gaussian noise; probability density function; power system; stability

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MDPI and ACS Style

Li, H.; Ma, S. The Evolution of Probability Density Function for Power System Excited by Fractional Gaussian Noise. Mathematics 2023, 11, 2854. https://doi.org/10.3390/math11132854

AMA Style

Li H, Ma S. The Evolution of Probability Density Function for Power System Excited by Fractional Gaussian Noise. Mathematics. 2023; 11(13):2854. https://doi.org/10.3390/math11132854

Chicago/Turabian Style

Li, Hufei, and Shaojuan Ma. 2023. "The Evolution of Probability Density Function for Power System Excited by Fractional Gaussian Noise" Mathematics 11, no. 13: 2854. https://doi.org/10.3390/math11132854

APA Style

Li, H., & Ma, S. (2023). The Evolution of Probability Density Function for Power System Excited by Fractional Gaussian Noise. Mathematics, 11(13), 2854. https://doi.org/10.3390/math11132854

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