Analytical expression for the evaluation of multi-stage adiabatic-compressed air energy storage (A-CAES) systems cycle efficiency

•A new formula for single-stage and multi-stage A-CAES cycle efficiency is provided.•The formula shows good agreement for a large design space.•The impact of pressure ratio and temperature on efficiency is clearly explained.•Contradicting trends that appear in literature are justified. Most renewable energies are intermittent and require electricity storage systems to provide reliable, continuous power. Compressed Air Energy Storage (CAES) is one of the few economically viable potential solutions to store gigawatt-hours of electricity. Adiabatic-CAES (A-CAES) systems store the heat from compression and eliminate the need for injecting fuel before expansion. Literature generally agrees that cycle efficiency, i.e. the ratio of expansion and compression work, increases with compressor pressure ratio or discharge temperature, but a few publications show the opposite trend. This paper explicitly reformulates the cycle efficiency equation, now valid for single and multi-stage A-CAES systems, and clearly explains the impact of pressure ratio and temperature on efficiency. Explanations are given for contradicting trends that appear in literature, and the analytical expression is compared with a numerical model and external studies to evaluate its performance. A Latin hypercube sampling is performed and shows that the discrepancy between the analytical and numerical results lies between −4.1% and +1.0% over a large design space, showing that the simple analytical expression derived is a robust tool for preliminary sizing of A-CAES multi-stage systems.