The off-design performance of compressed air energy storage (CAES) system is crucial when integrated with intermittent renewable energy generation due to increasing requirements for demand response and a wide range of part load operation. In this study, a computationally efficient bi-directional nozzle control strategy was developed to optimize nozzle openings of multistage radial-inflow turbines during the discharge process, which is shown to minimize the energy loss of CAES and meet the requirements for demand response control. In addition, a quasi-steady-state method was employed to simulate the part-load operation using a mean-line model for radial-inflow turbines, and thermodynamic models for the rest of CAES components. According to our analysis, the optimized bi-directional nozzle control strategy is able to improve the discharge efficiency of a multistage radial-inflow turbine by 2-7% under part-load operation (<= 50% of rated load), compared with only adjusting the nozzle opening of the first stage. We also compared nozzle control with valve throttling that is commonly used for CAES. Although there was a decrease in turbine efficiency, the proposed nozzle control strategy significantly increased discharge efficiency by 10-18% under part-load operation due to the absence of throttling losses. Our study demonstrated that the bi-directional nozzle control is an effective solution for part-load operation of CAES systems.