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

  • Research Article - Electrical Engineering
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Abstract

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.

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Authors and Affiliations

  1. School of Mathematical and Physical Science, North China Electric Power University, Beijing, 102206, People’s Republic of China

    Junqiang Wei

  2. State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing, 102206, People’s Republic of China

    Gengyin Li

Authors
  1. Junqiang Wei
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  2. Gengyin Li
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Correspondence to Junqiang Wei.

Additional information

This work was supported in part by National Natural Science Foundation of China (Grant No.51207052), the Major Program of the National Natural Science Foundation of China (Grant No. 51190103), and the Fundamental Research Funds for the Central Universities(Grant No. 2014MS62).

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Wei, J., Li, G. Collocation Method for First Passage Time Problem of Power Systems Subject to Stochastic Excitations. Arab J Sci Eng 44, 2205–2212 (2019). https://doi.org/10.1007/s13369-018-3361-5

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  • DOI: https://doi.org/10.1007/s13369-018-3361-5

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