Pumped hydro compressed air energy storage systems are a new type of energy storage technology that can promote development of wind and solar energy. In this study, the effects of single- and multi-parameter combination scenarios on the operational performance of a pumped compressed air energy storage system are investigated. The impacts of 11 design parameters on the evaluation indices are explored, and the local sensitivity of each parameter is determined. Five key design parameters are selected and the global sensitivity under two-, three-, four-, and five-parameter combination scenarios are revealed. Finally, the energy and exergy flow processes in the original and seven preferred scenarios are compared and analyzed. The results show that the larger the pump efficiency, turbine efficiency, and cylinder 1 upper side cross-sectional area, and the lower the initial pressure, the higher is the eta RTE and eta X. For ED, the sensitivity of the termination air pressure is the highest, reaching 0.747. In scenarios where all three indices are increased, the maximum values of 0.586, 0.691, and 0.313 kW h/m3 are achieved for eta RTE, eta X, and ED, respectively.