Abstract
This paper presents an analysis of the evolution of the probability density function of the dynamic trajectories of a single machine infinite bus power system. The probability density function can be used to determine the impact of random (stochastic) load perturbations on system stability. The evolution of the state probability density function over time leads to several interesting observations regarding stability regions as a function of damping parameter. The Fokker-Planck equation (FPE) is used to describe the evolution of the probability density of the states. The FPE is solved numerically using PDE solvers (such as finite difference method). Based on the results, the qualitative changes of the stationary density produce peak-like, ridge-like and other complicated shapes. Lastly, the numerical FPE solution combined with SMIB equivalent techniques lay the framework extended to the multimachine system. © 1969-2012 IEEE.
Recommended Citation
K. Wang and M. L. Crow, "The Fokker-Planck Equation for Power System Stability Probability Density Function Evolution," IEEE Transactions on Power Systems, vol. 28, no. 3, pp. 2994 - 3001, article no. 6416991, Institute of Electrical and Electronics Engineers, Jan 2013.
The definitive version is available at https://doi.org/10.1109/TPWRS.2012.2232317
Department(s)
Electrical and Computer Engineering
Keywords and Phrases
Finite difference methods; Fokker-Planck equation; power system stability; probability density function; stationary stochastic processes; stochastic differential equations
International Standard Serial Number (ISSN)
0885-8950
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 Institute of Electrical and Electronics Engineers, All rights reserved.
Publication Date
29 Jan 2013
Comments
National Science Foundation, Grant 1068996