Modeling and control of aggregate air conditioning loads for robust renewable power management

This paper examines the problem of demand-side energy management in smart power grids through the setpoint control of aggregate thermostatic loads. This paper models these loads using a novel partial differential equation framework that builds on existing diffusion- and transport-based load modeling ideas in the literature. Both this partial differential equation (PDE) model and its finite-difference approximations are bilinear in the state and control variables. This key insight creates a unique opportunity for designing nonlinear load control algorithms with theoretically guaranteed Lyapunov stability properties. This paper's main contribution to the literature is the development of the bilinear PDE model and a sliding mode controller for the real-time management of thermostatic air conditioning loads. The proposed control scheme shows promising performance in adapting aggregate air conditioning loads to intermittent wind power.