Grey box modeling of supermarket refrigeration cabinets

Aiming to enable robust large-scale fault diagnostics and optimized control for supermarket refrigeration systems, a data-driven grey box model for an evaporator and its surrounding cooling cabinet (or room) is presented. It is a non-linear model with two states: the cabinet temperature and the refrigerant mass in the evaporator. To demonstrate its applicability, data with one-minute sampling resolution from ten evaporators in a supermarket in Otterup (Denmark) was used. The model parameters were estimated using a Kalman filter and the maximum likelihood method. Since the dynamical properties of the cabinets constantly change as goods are added and removed, the parameters were re-estimated for each night, over a period of approximately 2.5 years. The model is validated through a statistical analysis of the residuals and the importance of the ongoing re-estimation of parameters is highlighted. Furthermore, the physical meaning of the estimated parameters is discussed and potential applications for characterization and classification of cabinets are demonstrated, by showing how they can be differentiated as either open- or closed cabinets or rooms, using only the estimated heat transfer coefficients and heat capacities. For a selected case it is shown that the estimated parameter values are close to physics derived values, and that the accuracy measured by the standard errors of the estimates is approximately ±10% relative to the estimated values. The analysis demonstrates that the model is robust, accurate and reliable in terms of estimating physically meaningful parameters and it is therefore appropriate for large-scale implementation.