  Commercial refrigeration systems consume 7% of the total commercial energy
consumption in the United States. Improving their energy efficiency contributes
to the sustainability of global energy systems and the supermarket business
sector. This paper proposes a new control method that can save the energy
consumption of multi-case supermarket refrigerators by explicitly taking into
account their interconnected and switched system dynamics. Its novelty is a
bilevel combinatorial optimization formulation to generate ON/OFF control
actions for expansion valves and compressors. The inner optimization module
keeps display case temperatures in a desirable range and the outer optimization
module minimizes energy consumption. In addition to its energy-saving
capability, the proposed controller significantly reduces the frequency of
compressor switchings by employing a conservative compressor control strategy.
However, solving this bilevel optimization problem associated with
interconnected and switched systems is a computationally challenging task. To
solve the problem in near real time, we propose two approximation algorithms
that can solve both the inner and outer optimization problems at once. The
first algorithm uses a linear approximation, and the second is based on the
submodular structure of the optimization problem. Both are (polynomial-time)
scalable algorithms and generate near-optimal solutions with performance
guarantees. Our work complements existing optimization-based control methods
(e.g., MPC) for supermarket refrigerators, as our algorithms can be adopted as
a tool for solving combinatorial optimization problems arising in these
methods.
