A Markovian jump process-driven stochastic hybrid-state model, and its application for the prediction of the behavior of controlled electric water heating loads in power systems

Load management is a rapidly emerging concept in the electric power systems area. Not with standing the particular kind of load management used by an electric utility, analytical models of the load behavior are essential if one wishes to address the issues of optimal load management, using the tools of control theory. A statistical aggregation based load synthesis methodology has been developed elsewhere [4] and successfully applied for the modeling of heating and cooling loads [3, 4]. We demonstrate here that the methodology can be used to generate a model of the statistical behavior of electric water heating loads within a load management program. The resulting model is a system of coupled ordinary and partial differential equations describing the evolution of the probability density functions associated with a markovian, jump process-driven, stochastic hybrid state process, used as a representation of individual electric water heating demands.