Proportional-Integral Extremum Seeking for Optimizing Power of Vapor Compression Systems

While traditional perturbation-based extremum seeking controllers (ESC) for vapor compression systems have proven effective at optimizing power without requiring a process model, the algorithm’s requirement for multiple distinct timescales has limited the applicability of this method to laboratory tests where boundary conditions can be carefully controlled, or simulation studies with unrealistic convergence times. In this paper, we optimize power consumption through the application of a newly-developed proportional-integral extremum seeking controller (PI-ESC) that converges at the same timescale as the process. This method uses an improved gradient estimation routine previously developed by the authors but also modifies the control law part of the algorithm to include terms proportional to the estimated gradient. PI-ESC is applied to the problem of compressor discharge temperature selection for a vapor compression system so that power consumption is minimized. We test the performance of this method using a custom-developed model of a vapor compression system written in the Modelica object-oriented modeling language. We compare the convergence times of PI-ESC to our previously developed time-varying ESC method and the conventional perturbation-based ESC method. For the conditions tested, PI-ESC is shown to converge to the optimum in about 15 minutes, whereas TV-ESC converges in 45 minutes and perturbation ESC requires more than 7,000 minutes due to its inefficient estimation of the gradient. Because of the improved convergence properties of PI-ESC, self-optimization algorithms for HVAC equipment can be deployed into situations where previous methods have failed. International Refrigeration and Air conditioning Conference at Purdue This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. Copyright c © Mitsubishi Electric Research Laboratories, Inc., 2016 201 Broadway, Cambridge, Massachusetts 02139