The increasing penetration of stochastic renewable energy has raised interest in energy storage to supply electricity on demand. Batteries are currently the preferred solution but concerns about their environmental impact remain. An alternative solution can be Compressed Air Energy Storage (CAES), which is intrinsically more flexible since, contrary to batteries, the energy capacity and power rating are decoupled. In this study, we present a detailed thermodynamic model of a multistage quasi-isothermal CAES, which is optimized to increase photovoltaic (PV) self-consumption in a micro-grid located in Switzerland. A Genetic Algorithm (GA) opti-mization is applied to determine the best operation schedule as well as capacity and power sizing and a parametric study is performed for various ratios of PV generation to load. Our results show that for a multi-family house that already invested in a PV system, adding CAES is not economically viable for a power level below 50 kW. However, CAES could become cost-effective for microgrids with a large PV generation share, since the cost of the energy-related part is rather low compared to the power-related part, making it more suitable for longer-term storage solutions (in comparison to batteries).