Adiabatic compressed air energy storage is an emerging energy storage technology with excellent power and storage capacities. Currently, efficiencies are approximately 70%, in part due to the issue of heat loss during the compression stage. An exergy analysis is presented on a novel adiabatic compressed air energy storage system design utilizing a cascade of PCMs (phase change materials) for waste heat storage and recovery. The melting temperatures and enthalpies of the PCMs were optimized for this system and were shown to be dependent on the number of PCMs, the number of compression stages, and the maximum compression ratio. Efficiencies of storage and recovery using this approach are predicted to be as high as 85%, a 15% increase over current designs which do not incorporate PCMs. (C) 2016 Elsevier Ltd. All rights reserved.