Various configurations of compressed air energy storage technology have received attention over the last years due to the advantages that this technology offers relative to other power storage technologies. This work proposes a new configuration of this technology aiming at cogeneration of electricity, heat and cooling. The new system may be very advantageous for locations with high penetration of renewable energy in the electricity grid as well as high heating and cooling demands. The latter would typically be locations with district heating and cooling networks. A thorough design, sizing and thermodynamic analysis of the system for a typical wind farm with 300 MW capacity in Denmark is presented. The results show a great potential of the system to support the local district heating and cooling networks and reserve services in electricity market. The values of power-to-power, power-to-cooling and power-to-heat efficiencies of this system are 30.6%, 32.3% and 92.4%, respectively. The exergy efficiency values are 30.6%, 2.5% and 14.4% for power, cooling and heat productions. A techno-economic comparison of this system with two of the most efficient previous designs of compressed air energy storage system proves the firm superiority of the new concept.