Analysis of power system dynamics subject to stochastic power injections

Sairaj V. Dhople, Yu Christine Chen, Lee Deville, Alejandro D. Dominguez-Garcia

Research output: Contribution to journalArticlepeer-review


We propose a framework to study the impact of stochastic active/reactive power injections on power system dynamics with a focus on time scales involving electromechanical phenomena. In this framework, the active/reactive power injections evolve according to a continuous-time Markov chain (CTMC), while the power system dynamics are described by the standard differential algebraic equation (DAE) model. The DAE model is linearized around a nominal set of active/reactive power injections, and the combination of the linearized DAE model and the CTMC forms a stochastic process known as a stochastic hybrid system (SHS). The extended generator of the SHS yields a system of ordinary differential equations that governs the evolution of the power system dynamic and algebraic state moments. We illustrate the application of the framework to the computation of long-term power system state statistics, and to short-term probabilistic dynamic performance/reliability assessment.

Original languageEnglish (US)
Article number6557091
Pages (from-to)3341-3353
Number of pages13
JournalIEEE Transactions on Circuits and Systems I: Regular Papers
Issue number12
StatePublished - Dec 2013


  • Continuous time Markov chains (CTMCs)
  • power system dynamics
  • stochastic hybrid systems

ASJC Scopus subject areas

  • Hardware and Architecture
  • Electrical and Electronic Engineering


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