Many pumped hydro compressed air energy storage systems suffer from large head variations in the hydraulic machinery. To address this defect, this study proposes a multi-machine compensable pumped hydro compressed air energy storage system and reveals its operational, energy, exergy, and economic performances. First, the energy, exergy, and economic models of the system are established. Second, the operational characteristics of each component are analyzed. Third, the energy, exergy, and economic performances of the system are presented. Finally, the impact of operating pressure on the energy and exergy performance is analyzed. The results indicate that air pressure variations of 0.300 MPa/0.256 MPa in Tank 1 are reduced to head variations of 11.0 m/12.7 m at the hydraulic machinery, respectively. Furthermore, the round-trip efficiency, exergy efficiency, and energy storage density reached were 0.672, 0.694, and 0.038 kW·h/m3, respectively. The most significant work wastage and exergy loss occurred in Tanks 1 and 2, contributing to 48.5 % and 37.5 % of the total, respectively. As the operating pressure increases, the round-trip and exergy efficiencies decrease, and the energy storage density increases. In this study, the head amplitude at the hydraulic machinery under charging and discharging conditions was reduced by nearly 2/3 and 1/2, respectively.