Modeling, Control, and Stability Analysis of Heterogeneous Thermostatically Controlled Load Populations Using Partial Differential Equations

Thermostatically controlled loads (TCLs) account for more than one-third of the U.S. electricity consumption. Various techniques have been used to model TCL populations. A high-fidelity analytical model of heterogeneous TCL (HrTCL) populations is of special interest for both utility managers and customers (that facilitates the aggregate synthesis of power control in power networks). We present a deterministic hybrid partial differential equation (PDE) model which accounts for HrTCL populations and facilitates analysis of common scenarios like cold load pick up, cycling, and daily and/or seasonal temperature changes to estimate the aggregate performance of the system. The proposed technique is flexible in terms of parameter selection and ease of changing the set-point temperature and deadband width all over the TCL units. We investigate the stability of the proposed model along with presenting guidelines to maintain the numerical stability of the discretized model during computer simulations. Moreover, the proposed model is a close fit to design feedback algorithms for power control purposes. Hence, we present output- and state-feedback control algorithms, designed using the comparison principle and Lyapunov analysis, respectively. We conduct various simulations to verify the effectiveness of the proposed modeling and control techniques.