Stochastic model for power grid dynamics

Marian Anghel, Kenneth A. Werley, Adilson E. Motter

Research output: Chapter in Book/Report/Conference proceedingConference contribution

122 Scopus citations


We introduce a stochastic model that describes the quasistatic dynamics of an electric transmission network under perturbations introduced by random load fluctuations, random removing of system components from service, random repair times for the failed components, and random response times to implement optimal system corrections for removing line overloads in a damaged or stressed transmission network. We use a linear approximation to the network flow equations and apply linear programming techniques that optimize the dispatching of generators and loads in order to eliminate the network overloads associated with a damaged system. We also provide a simple model for the operator’s response to various contingency events that is not always optimal due to either failure of the state estimation system or due to the incorrect subjective assessment of the severity associated with these events. This further allows us to use a game theoretic framework for casting the optimization of the operator’s response into the choice of the optimal strategy which minimizes the operating cost. We use a simple strategy space which is the degree of tolerance to line overloads and which is an automatic control (optimization) parameter that can be adjusted to trade off automatic load shed without propagating cascades versus reduced load shed and an increased risk of propagating cascades. The tolerance parameter is chosen to describes a smooth transition from a risk averse to a risk taken strategy. We present numerical results comparing the responses of two power grid systems to optimization approaches with different factors of risk and select the best blackout controlling parameter.

Original languageEnglish (US)
Title of host publicationProceedings of the Annual Hawaii International Conference on System Sciences
EditorsRalph Sprague, Jr.
PublisherIEEE Computer Society
Number of pages10
ISBN (Print)0769527558, 9780769527550
StatePublished - 2007
Event40th Annual Hawaii International Conference on System Sciences 2007, HICSS'07 - Big Island, HI, United States
Duration: Jan 3 2007Jan 6 2007

Publication series

NameProceedings of the Annual Hawaii International Conference on System Sciences
ISSN (Print)1530-1605


Other40th Annual Hawaii International Conference on System Sciences 2007, HICSS'07
Country/TerritoryUnited States
CityBig Island, HI

ASJC Scopus subject areas

  • General Engineering


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