A detailed mathematical model was developed for the complete Hybrid Compressed Air Energy Storage (HCAES) configuration with underground storage site and liquid thermal energy storage, operating with a sequence of processes (charging, holding and discharging with respective duration) in arbitrary order. A sensitivity analysis was carried out in order to calculate several performance indicators of the complete H-CAES configuration, in relation to the simultaneous change of several process parameters. The methodology "Design of Experiments" was applied to the results of the sensitivity analysis in order to calculate the main effects of each process parameter on each performance indicator. The influence of the storage site volume on each performance indicator is negligible. The reduction of the compressor group outlet pressure and of the turbine group power allows a more effective thermodynamic utilization both of the energy stored by the compressors and of the overall energy supplied to the plant. Furthermore, the former utilization is more effective by an increase of the gas temperature in the combustion chambers, whereas the latter utilization is worsened. Moreover, as case study, the existing diabatic CAES plant of Huntorf was modified by introducing a diathermic oil thermal storage. This plant is suitable to operate according to a partial hybrid configuration by the deactivation of the heat exchanger located upstream of the low pressure turbine. The thermodynamic utilization of the overall energy supplied to the plant in the partial hybrid configuiation increases in percentage by 9.1% with respect to the diabatic configuration.