This paper presents the modeling, control, and performance analysis of a hybrid energy system integrating a photovoltaic (PV) solar system with a Compressed Air Energy Storage (CAES) system. This integrated system aims to address the intermittency of solar energy by utilizing excess PV energy to compress and store air, which is later expanded to drive a turbine connected to an induction generator during periods of low solar irradiance. The generator output also supplies to the compressor motor for making a recycled CAES system and maintain it for a long duration. A comprehensive mathematical model is developed for the PV and CAES subsystem, incorporating maximum power point tracking (MPPT), DC-DC boost conversion, and power electronics interfacing. PID controllers are used for optimal pressure regulation and control of the CAES system cycle. The entire systems is simulated using MATLAB/Simulink. Results validate enhanced power reliability, improved load support during PV system intermittency, and overall system efficiency in a renewable energy system microgrid context.