  This paper describes the application of stochastic grey-box modeling to
identify electrical power consumption-to-temperature models of a domestic
freezer using experimental measurements. The models are formulated using
stochastic differential equations (SDEs), estimated by maximum likelihood
estimation (MLE), validated through the model residuals analysis and
cross-validated to detect model over-fitting. A nonlinear model based on the
reversed Carnot cycle is also presented and included in the modeling
performance analysis. As an application of the models, we apply model
predictive control (MPC) to shift the electricity consumption of a freezer in
demand response experiments, thereby addressing the model selection problem
also from the application point of view and showing in an experimental context
the ability of MPC to exploit the freezer as a demand side resource (DSR).
