Realtime setpoint optimization with time-varying extremum seeking for vapor compression systems

In many formulations of controller architectures for variable-speed vapor compression machines, evaporator superheat temperature is commonly selected as a regulated variable due to its correlation with cycle efficiency. Further, the superheat temperature setpoint is conveniently taken as a constant value over the wide range of operating conditions. However, direct measurement of superheat is not always available, and estimates of superheat have limited robustness. Therefore identifying alternate signals in the control of vapor compression machines that correlate to efficiency is desired. In this paper, we consider a model-free extremum seeking algorithm that adjusts compressor discharge temperature setpoints in order to optimize energy efficiency. While perturbation-based extremum seeking methods have been known for some time, they suffer from slow convergence rates-a problem emphasized in application by the long time constants associated with thermal systems. Our method uses a new algorithm (time-varying extremum seeking), which has dramatically faster and more reliable convergence properties. In particular, we regulate the compressor discharge temperature using setpoints selected from a model-free time-varying extremum seeking algorithm. We show that the relationship between compressor discharge temperature and power consumption is convex (a requirement for this class of realtime optimization), and use time-varying extremum seeking to drive these setpoints to values that minimize power. The results are compared to the traditional perturbation-based extremum seeking approach. Experiments are performed demonstrating discharge temperature optimization from 72°C to 62°C for a particular set of experimental conditions where the power consumption is decreased from 525 W to 450 W, resulting in an increase in observed coefficient of performance (COP) of 14%.