Optimal Energy Consumption in Refrigeration Systems - Modelling and Non-Convex Optimisation

Supermarket refrigeration consumes substantial amounts of energy. However, due to the thermal capacity of the refrigerated goods, parts of the cooling capacity delivered can be shifted in time without deteriorating the food quality. In this study, we develop a realistic model for the energy consumption in super market refrigeration systems. This model is used in a Nonlinear Model Predictive Controller (NMPC) to minimise the energy used by operation of a supermarket refrigeration system. The model is non-convex and we develop a computational efficient algorithm tailored to this problem that is somewhat more efficient than general purpose optimisation algorithms for NMPC and still near to optimal. Since the non-convex cost function has multiple extrema, standard methods for optimisation cannot be directly applied. A qualitative analysis of the system's constraints is presented and a unique minimum within the feasible region is identified. Following that finding we propose a tailored minimisation procedure that utilises the nature of the feasible region such that the minimisation can be separated into two linear programs; one for each of the control variables. These subproblems are simple to solve but some iterations might have to be performed in order to comply with the maximum capacity constraint. Finally, a nonlinear solver is used for a small example without separating the optimisation problem, and the results are compared to the outcome of our proposed minimisation procedure for the same conceptual example. The tailored approach is somewhat faster than the general optimisation method and the solutions obtained are almost identical.