A key approach to large renewable power management is based on implementing storage technologies, including batteries, power-to-gas and compressed air energy storage (CAES). This work presents the preliminary design and performance assessment of an innovative type of CAES system based on constant hydrostatic pressure and variable volumes underwater storage (UW-CAES) for installation in the proximity of deep water seas or lakes. The proposed system is adiabatic, not using any fuel to increase the air temperature before expansion since a sufficient TIT is instead obtained through a thermal energy storage system which recovers the compression heat. The paper discusses in detail the sizing and the off-design characterization of an UW-CAES system coupled to a wind farm for peak shaving and dispatchability enhancement and it evaluates the impact of a realistic power input on plant average performance and flexibility. Although the assessment shall be considered preliminary, it is shown that round trip efficiency in the range of 75% - 80% can be obtained depending on the compressor section configuration; making the UW-CAES a promising technology compared to electrochemical and pumped-hydro storage systems. Annual simulations considering part load operation result in global round trip efficiency around 75% with a 10 to 15% reduction in the average unplanned energy injection in the electric grid. The investigated case study provides an example of the potential of this system in providing power output peak shaving when coupled with an intermittent and non-predictable energy source.