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

Abstract

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
PublisherSpringer
Pages13-32
Number of pages20
DOIs
StatePublished - 2017

Publication series

NameLecture Notes in Networks and Systems
Volume6
ISSN (Print)2367-3370
ISSN (Electronic)2367-3389

Keywords

  • 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

Cite this