Modeling heterogeneous populations of thermostatically controlled loads using diffusion-advection PDEs

This paper focuses on developing a partial differential equation (PDE)-based model and parameter identification scheme for heterogeneous populations of thermostatically controlled loads (TCLs). First, a coupled two-state hyperbolic PDE model for homogenous TCL populations is derived. This model is extended to heterogeneous populations by including a diffusive term, which provides an elegant PDE control-oriented model. Second, a novel parameter identification scheme is derived for the PDE model structure, which utilizes only boundary measurements and aggregated power measurements. Simulation results against a Monte Carlo model of a large TCL population demonstrate the usefulness of the approach. The proposed model and parameter identification scheme provide system critical information for advanced demand side management control systems.