Journal
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS
Volume 60, Issue 12, Pages 3341-3353Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCSI.2013.2265972
Keywords
Continuous time Markov chains (CTMCs); power system dynamics; stochastic hybrid systems
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Funding
- National Science Foundation (NSF) [ECCS-CAR-0954420]
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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.
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