Suboptimal hierarchical control strategy to improve energy efficiency of vapour-compression refrigeration systems

This paper deals with optimal control of vapour-compression refrigeration systems, where only the compressor speed and the expansion valve opening are considered as manipulable inputs. Any given cycle is completely defined by a three-variable set, thus it is an underactuated control problem. The controllability analysis presented by the authors in a previous work applying linear theory is extended to a pointwise nonlinear analysis based on the phase portrait method. It is concluded that there is no full controllability and only a two-dimensional subspace of the three-dimensional solution space can be explored. A suboptimal hierarchical control strategy is proposed, where an online optimizer explores the two-dimensional controllable subspace to generate the reference on the degree of superheating, which, along with the cooling demand set point and the uncontrolled state, defines the cycle in steady state. The uncontrolled state is, by definition, not manipulable and defines the maximum achievable efficiency. Some simulation results comparing the proposed control architecture with other strategies studied in the literature are included, regarding the energy efficiency achieved in steady state and the dynamic behaviour of the controlled variables, where the controllability issues are highlighted.