Arabian Journal for Science and Engineering

, Volume 44, Issue 3, pp 2205–2212 | Cite as

Collocation Method for First Passage Time Problem of Power Systems Subject to Stochastic Excitations

  • Junqiang WeiEmail author
  • Gengyin Li
Research Article - Electrical Engineering


Large penetration of renewable energies heavily threats the stable and reliable operation of power systems due to their randomness and intermittence characteristics. The first passage time problem is one of the critical issues in reliability assessment of new energy power systems. In this paper, we present and analyze the first passage time problem of power systems with stochastic excitation by collocation method. The power systems with stochastic excitations are modeled by stochastic differential equations. Then, the backward Kolmogorov equations and the generalized Pontryagin equations governing the conditional reliability function and the conditional moments of first passage time, respectively, are established based on the stochastic averaging method. The corresponding initial and boundary conditions are also provided. A numerical collocation method was proposed to solve the equations, and case studies were executed on a single-machine infinite-bus system under Gaussian excitation. Illustrations of the conditional reliability function and probability density functions for some cases are presented.


SDEs First passage time Stochastic averaging method Backward Kolmogorov equation Generalized Pontryagin equation Collocation method 


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© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  1. 1.School of Mathematical and Physical ScienceNorth China Electric Power UniversityBeijingPeople’s Republic of China
  2. 2.State Key Laboratory of Alternate Electrical Power System with Renewable Energy SourcesNorth China Electric Power UniversityBeijingPeople’s Republic of China

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