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Mean first passage time in the stochastic security analysis of renewable energy power system
Author(s) -
Wei Junqiang,
Li Gengyin
Publication year - 2018
Publication title -
international journal of energy research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.808
H-Index - 95
eISSN - 1099-114X
pISSN - 0363-907X
DOI - 10.1002/er.4003
Subject(s) - renewable energy , stochastic differential equation , monte carlo method , electric power system , nonlinear system , gaussian , mathematics , control theory (sociology) , power (physics) , mathematical optimization , computer science , physics , engineering , statistics , electrical engineering , control (management) , quantum mechanics , artificial intelligence
Summary The variability of renewable energy offers significant challenges to the power system security with a large penetration of renewables. The paper models the wind farm penetration as a Gaussian excitation in which the stochastic differential equations (SDEs) are considered to characterize wind energy uncertainties in nonlinear power systems. The SDE‐based power system model is first reduced to the averaged Itô SDEs by the stochastic averaging method. Then, a backward Kolmogorov equation for the conditional reliability function and the generalized Pontryagin equations governing the conditional moments of first passage time are established. Finally, numerical results are provided given the designated boundary and initial conditions. The first passage time of both single‐machine infinite‐bus power system and 3‐machine 9‐bus system under Gaussian excitation are studied. The analytical results are verified by using a Monte Carlo simulation.