Optimal energy consumption in refrigeration systems ‐ modelling and non‐convex optimisation

Abstract

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. © 2012 Canadian Society for Chemical Engineering

Modeling supermarket refrigeration systems for supervisory control in smart grid

“…From smart grid point of view, an appropriate model is introduced in [4] for optimizing the energy consumption of refrigeration systems. Although this model can be employed for a single evaporator system, it cannot model a supermarket refrigeration systems including several display cases.…”

Analyzing control challenges for thermal energy storage in foodstuffs

“…The capacity for energy storage in the refrigerated goods is not exploited by the thermostat (hysteresis) control policy used today and a large potential for energy and cost reductions exits. Preliminary investigations have been carried out in [1]- [4]. However, accurate estimation of the temperature behavior and distribution in the refrigerated foodstuffs is needed in order to take such simulation studies closer to the challenges seen in an actual supermarket.…”

Flexible and cost efficient power consumption using economic MPC a supermarket refrigeration benchmark

“…In the sequel, we adopt the approximation used forẆ c in [2], where polynomials are fitted for the enthalpy differences and the isentropic efficiency, η is , is assumed constant within the range of operation. When a frost room is included, an extra compressor system is usually added between the frost evaporator and the suction side of the other compressors.…”

“…Due to the simple hysteresis control policy most commonly used today, a large unexploited potential for energy and cost reductions exists. Preliminary investigations have been carried out in [1], [2], and in this paper we further analyse this in a realistic setting. Furthermore a novel formulation of the cost function enables the supermarket refrigeration system to benefit from the enablement of flexible power consumption.…”