Electric load model synthesis by diffusion approximation of a high-order hybrid-state stochastic system

A statistical approach is used to model the dynamics of the electric demand of large aggregates of electric space heaters or air conditioners. The importance of such loads is twofold. First, they account for a significant portion of power system dynamics following a power outage. Second, because they are associated with energy storage, they are often selected for load shedding within a load management program. The derivation of the aggregate electrical dynamics is considered first for a homogeneous group of devices. Subsequently, a perturbation analysis yields the dynamics for a nonhomogeneous group. The homogeneons group aggregrate load model is a system of coupled ordinary, and partial differential equations (Fokker-Planck equations). It is obtained by writing evolution equations for the probability density of a hybrid-state Markov system used to model the switching dynamics of individual devices. This result is new and could give a clue to the analysis of a broad class of hybrid-state stochastic systems. In turn, this could provide a new impetus not only in the area of electric load modeling but other areas such as power system reliability and the design of relay control systems, where stochastic hybrid-state models occur frequently. Simulation results which illustrate the dynamical properties of the model are presented.