A unified Stochastic Hybrid System approach to aggregated load modeling for demand response

Nondisruptive demand response programs often result in complex and fast aggregated load dynamics, which may lead to severe impact on the distribution and transition systems. Accurate modeling of aggregated load dynamics is of fundamental importance for systematic analysis and design of various demand response strategies. Existing methods mostly focus on simple first-order linear Thermostatically Controlled Loads (TCLs). This paper develops a novel stochastic hybrid system (SHS) framework to model individual responsive loads. The proposed SHS has general nonlinear diffusion dynamics in each discrete mode and has both random and deterministic state-dependent mode transitions. The corresponding Fokker-Planck equation is derived to characterize the aggregated load dynamics with a special emphasis on establishing the boundary conditions due to the deterministic switchings. The proposed modeling approach includes many existing methods as special cases and provides a unified representation of a variety of responsive loads. Realistic demand response examples are also provided to illustrate the effectiveness of the proposed SHS framework.