Parameter Identifiability and Estimation of Thermostatically Controlled Loads

Thermostatically controlled loads (TCLs) are ubiquitous and have the potential to assist grid operation through aggregate control. In order to adequately represent TCL dynamic behavior, a second-order model that takes into account both air and mass temperature must be considered. However, the parameters of such models cannot always be estimated from readily available measurements. In this paper, we adopt a hybrid systems perspective to describe device behavior, and utilize trajectory sensitivities to explore model identifiability. A novel nonlinear least-squares problem is formulated and solved to estimate the underlying thermal parameters. By exploring the eigenvalues of the sensitivity matrix formed from the trajectory sensitivities, we show that not all parameters can be estimated. A subset selection algorithm is used to establish a set of identifiable parameters. The resulting estimates are validated using synthetic data. We show that attempting to estimate non-identifiable parameter sets often results in estimates that are biased by the values used to initialize the iterative estimation algorithm. This emphasizes the importance of identifiability analysis in parameter estimation schemes.