Random Perturbations of a Three-Machine Power System Network

Vishal Chikkerur, Nishanth Lingala, Hoong C. Yeong, N. Sri Namachchivaya, Peter W. Sauer

Research output: Chapter in Book/Report/Conference proceedingChapter


This paper develops an asymptotic method based on averaging and large deviations to study the transient stability of a noisy three-machine power system network. We study the dynamics of these nonlinear oscillators (swing equations) as random perturbations of two-dimensional periodically driven Hamiltonian systems. The phase space for periodically driven nonlinear oscillators consists of many resonance zones. It is well known that, as the strengths of periodic excitation and damping go to zero, the measure of the set of initial conditions which lead to capture in a resonance zone goes to zero. In this paper we study the effect of weak noise on the escape from a resonance zone and obtain the large-deviation rate function for the escape. The primary goal is to show that the behavior of oscillators in the resonance zone can be adequately described by the (slow) evolution of the Hamiltonian, for which simple analytical results can be obtained, and then apply these results to study the transient stability margin of power system with stochastic loads. The classical swing equations of a power system of three interconnected generators with non-zero damping and small noise is considered as a nontrivial example to derive the “exit time” analytically. This work may play an important role in designing and upgrading existing electrical power system networks.

Original languageEnglish (US)
Title of host publicationLecture Notes in Networks and Systems
Number of pages20
StatePublished - 2017

Publication series

NameLecture Notes in Networks and Systems
ISSN (Print)2367-3370
ISSN (Electronic)2367-3389


  • Homoclinic Orbit
  • Large Deviation Principle
  • Periodic Excitation
  • Resonance Zone
  • Transient Stability

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Computer Networks and Communications

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