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research-article

# Optimal Efficiency-Power Tradeoff for an Air Compressor/Expander

[+] Author and Article Information
Andrew T. Rice

Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minnesota 55455
Andrew.Rice@stratasys.com

Perry Y. Li

Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minnesota 55455
lixxx099@umn.edu

Caleb J. Sancken

Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minnesota 55455

1Corresponding author.

ASME doi:10.1115/1.4037652 History: Received August 30, 2016; Revised August 10, 2017

## Abstract

An efficient and power dense high pressure air compressor/expander is critical for the success of a compressed air energy storage (CAES) system. There is a trade-off between efficiency and power density that is mediated by heat transfer within the compression/expansion chamber. This paper considers the optimal control for the compression and expansion processes that provides the optimal trade-off between efficiency and power. Analytical Pareto optimal solutions are developed for the cases in which hA, the product of the heat transfer coefficient and heat transfer surface area, is either a constant or is a function of the air volume. It is found that the optimal trajectories take the form fast-slow-fast'' where the fast stages are adiabatic and the slow stage is either isothermal for the constant-hA assumption, or a pseudo-isothermal (where the temperature depends on the instantaneous hA) for the volume-varying-hA assumption. A case study shows that at 90\% compression efficiency, power gains are in the range of 500-1500% over ad-hoc linear and sinusoidal profiles.

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