Control-oriented modeling of TCLs

Ensembles of thermostatically controlled loads (TCLs) have the potential to be a valuable resource for the power grid. Examples of TCLs include air conditioners and water heaters. To perform design of a distributed coordination/control algorithm, a coordinator requires a control oriented model that describes the relevant dynamics of an ensemble. In this work, we develop such a model. We leverage techniques from computational fluid dynamics (CFD) to discretize a pair of Fokker-Planck equations derived in earlier work by Malhame et. al [1]. The discretized equations are shown to admit a certain factorization that separates the effects of control command and disturbance from weather. This enables control oriented modeling of a population of TCLs for a central coordinator.