Stochastic hybrid state systems for electric load modeling

A class of hybrid-state stochastic models for the modeling of the switching dynamics of electrical devices such as air conditioners or electric space heaters, associated with some form of energy storage, is presented. Using these models, a statistical method is proposed to model the dynamics of the electrical demand of large aggregates of the devices. The implementation of the method requires the development of evolution equations for the probability densities associated with some hybrid-state Markov systems. This is successfully done for a class of hybrid-state Markov systems driven by Gaussian noise. The result is an extension of the Fokker-Planck equation.