Optimal Efficiency-Power Tradeoff for an Air Motor/Compressor With Volume Varying Heat Transfer Capability

Abstract

This paper presents the pressure-volume trajectories that yield the optimal trade-off between efficiency and power during the compression and expansion of air. These results could benefit applications such as compressed air energy storage where both high efficiency and power density are required. Earlier work established solutions for the simple case in which hA, the product of the heat transfer coefficient and heat transfer surface area, is constant. This paper extends that analysis by allowing hA to vary with air volume. Solutions to the constrained, nonlinear optimization problem are developed utilizing the method of Lagrange multipliers and Karush-Kuhn-Tucker (KKT) conditions. It is found that the optimal trajectory takes the form "fastslow-fast" where the fast stages are adiabatic and the temperature change during the slow stage is proportional to the inverse root of the hA product. A case study predicts a 60% improvement in power over the constant-hA solution when both trajectories are run at 90% efficiency and hA = hA (V ). Compared to linearand sinusoidal-shaped trajectories, also at 90% effiency, power gains are expected to be around 500-1500%.

Modeling and control of a novel compressed air energy storage system for offshore wind turbine

“…Here we develop a continuous average model for the compressor/expander. The trajectory of the liquid piston in each cycle affects significantly the efficiency and power of the compressor/expander [4,5,8]. An optimized compression/expansion profile can increase the power by up to 500%, at the same efficiency over ad-hoc profiles, such as linear or sinusoidal profiles.…”

Iterative optimal and adaptive control of a near isothermal liquid piston air compressor in a compressed air energy storage system

“…In both cases, the optimal trajectories consist of fast adiabatic portions at the beginning and at the end. For the constant hA case [3], the middle portion is isothermal resulting in an Adiabatic-Isothermal-Adiabatic (AIA) trajectory, whereas for the volume-dependent hA(V ) case [4], the temperature difference from the ambient is inversely proportional to hA(V ) leading to an AdiabaticPseudo-Isothermal-Adiabatic (APIA) trajectory.…”

“…For high compression/expansions ratios 200:1-350:1, such Pareto optimal trajectories have been shown, theoretically, to increase the power of the C/E by 200-500% at the same efficiency, over ad-hoc trajectories such as linear and sinusoidal trajectories [3], [4], [5]. In [3], [4], the optimal trajectories were derived analytically based on simple heat transfer models and by considering thermodynamic losses alone.…”

“…For high compression/expansions ratios 200:1-350:1, such Pareto optimal trajectories have been shown, theoretically, to increase the power of the C/E by 200-500% at the same efficiency, over ad-hoc trajectories such as linear and sinusoidal trajectories [3], [4], [5]. In [3], [4], the optimal trajectories were derived analytically based on simple heat transfer models and by considering thermodynamic losses alone. For example in [3], the product of the heat transfer coefficient and heat transfer surface area hA is assumed to be constant; and in [4], hA is allowed to vary with air volume to take into account the decrease in surface area as the porous material is submerged in the liquid piston.…”

“…In [3], [4], the optimal trajectories were derived analytically based on simple heat transfer models and by considering thermodynamic losses alone. For example in [3], the product of the heat transfer coefficient and heat transfer surface area hA is assumed to be constant; and in [4], hA is allowed to vary with air volume to take into account the decrease in surface area as the porous material is submerged in the liquid piston. In both cases, the optimal trajectories consist of fast adiabatic portions at the beginning and at the end.…”