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Research Papers

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

[+] Author and Article Information
Andrew T. Rice, Caleb J. Sanckens

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

Perry Y. Li

Professor
Department of Mechanical Engineering,
University of Minnesota,
Minneapolis, MN 55455
e-mail: perry-li@umn.edu

1Present address: Stratasys, Ltd., Eden Prairie, MN 55344.

2Corresponding author.

3Present address: Interpretive Simulations, Charlottesville, VA 22901.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received August 30, 2016; final manuscript received August 10, 2017; published online October 9, 2017. Assoc. Editor: Kevin Fite.

J. Dyn. Sys., Meas., Control 140(2), 021011 (Oct 09, 2017) (10 pages) Paper No: DS-16-1423; 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 (C/E) is critical for the success of a compressed air energy storage (CAES) system. There is a tradeoff 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 tradeoff 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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## References

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## Figures

Fig. 1

Schematic of the open accumulator compressed air energy storage system architecture as described in Refs. [1] and [20]

Fig. 2

P-V diagram showing compression (ζc) and expansion (ζe) trajectories. The shaded area under the curves represents the work input (vertical lines) and work output (with added horizontal lines). Isothermal compression and expansion follows the dashed black trajectory. The total energy stored is the area under the isothermal curve. Reducing the area between ζc and the isothermal curve increases compression efficiency. Reducing the area between the isothermal curve and ζe increases expansion efficiency.

Fig. 3

Fig. 4

A compression trajectory is broken up into N adjacent volume intervals, each with a constant hA. Over each interval, the optimal form of the compression trajectory is adiabatic–isothermal–adiabatic.

Fig. 5

Replacing the pI-A-pI trajectory A-B-C-D by the pI-A trajectory A-E-D reduces work input (shaded area) and eliminates time to execute E-B and C-D

Fig. 6

Optimal compression for a continuously varying hA product consists of three stages: adiabatic compression, hA-dependent compression, and adiabatic compression. The slow hA-dependent curve is determined by the parameter λ.

Fig. 7

Schematic of the compressor with liquid piston and porous mesh for the case study

Fig. 8

Compression efficiency versus storage power for optimal ApIA, suboptimal AIA, sinusoidal, and linear trajectories

Fig. 9

Compression volume profiles normalized by process times, with optimal ApIA, suboptimal AIA, sinusoidal, linear trajectories at 60% and 90% efficiencies

Fig. 10

Expansion efficiency versus power for sinusoidal, linear, AIA, and optimal (ApIA) trajectories

Fig. 11

AIA efficiency-power relation for various compression rate limitation p

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