st -. A compressed air energy storage method, comprising: providing a tank or cavern; providing a membrane within the tank or cavern, wherein the membrane is flexible and fluid-impermeable; providing an auxiliary fluid inside of the membrane; during periods of energy surplus in the electric power grid, using the excess power in the power grid to drive an electric motor driving a compressor that compresses air; circulating compressed air into the tank or cavern and outside of the membrane, thereby displacing a corresponding volume of the auxiliary fluid out of the tank or cavern; reducing the displaced volume of the auxiliary fluid by circulating it to a condenser where it is liquefied at constant pressure and temperature; circulating the liquefied auxiliary fluid back into the tank or cavern in the interior of the membrane; shutting off a valve and leaving the compressed air stored in the tank or cavern until there is an energy demand in the electric power grid; during periods of energy demand in the electric power grid, increasing the auxiliary fluid volume by extracting liquefied auxiliary fluid from the tank or cavern with a pump and circulating it to a boiler where it is regasified, the regasified auxiliary fluid being at the same pressure and temperature than the auxiliary fluid in the membrane; circulating regasified auxiliary fluid back into the tank or cavern in the interior of the membrane, thereby displacing the air enclosed in the tank or cavern out of the tank or cavern; circulating the compressed air to a boiler and then to a turbine where it is expanded producing exhaust gases, the turbine driving an alternator and therefore producing electricity, this electricity being injected into the electric grid. providing a tank or cavern; providing a membrane within the tank or cavern, wherein the membrane is flexible and fluid-impermeable; providing an auxiliary fluid inside of the membrane; during periods of energy surplus in the electric power grid, using the excess power in the power grid to drive an electric motor driving a compressor that compresses air; circulating compressed air into the tank or cavern and outside of the membrane, thereby displacing a corresponding volume of the auxiliary fluid out of the tank or cavern; reducing the displaced volume of the auxiliary fluid by circulating it to a condenser where it is liquefied at constant pressure and temperature; circulating the liquefied auxiliary fluid back into the tank or cavern in the interior of the membrane; using the excess power in the power grid to drive an electric motor driving a compressor that compresses air; circulating compressed air into the tank or cavern and outside of the membrane, thereby displacing a corresponding volume of the auxiliary fluid out of the tank or cavern; reducing the displaced volume of the auxiliary fluid by circulating it to a condenser where it is liquefied at constant pressure and temperature; circulating the liquefied auxiliary fluid back into the tank or cavern in the interior of the membrane; shutting off a valve and leaving the compressed air stored in the tank or cavern until there is an energy demand in the electric power grid; during periods of energy demand in the electric power grid, increasing the auxiliary fluid volume by extracting liquefied auxiliary fluid from the tank or cavern with a pump and circulating it to a boiler where it is regasified, the regasified auxiliary fluid being at the same pressure and temperature than the auxiliary fluid in the membrane; circulating regasified auxiliary fluid back into the tank or cavern in the interior of the membrane, thereby displacing the air enclosed in the tank or cavern out of the tank or cavern; circulating the compressed air to a boiler and then to a turbine where it is expanded producing exhaust gases, the turbine driving an alternator and therefore producing electricity, this electricity being injected into the electric grid. increasing the auxiliary fluid volume by extracting liquefied auxiliary fluid from the tank or cavern with a pump and circulating it to a boiler where it is regasified, the regasified auxiliary fluid being at the same pressure and temperature than the auxiliary fluid in the membrane; circulating regasified auxiliary fluid back into the tank or cavern in the interior of the membrane, thereby displacing the air enclosed in the tank or cavern out of the tank or cavern; circulating the compressed air to a boiler and then to a turbine where it is expanded producing exhaust gases, the turbine driving an alternator and therefore producing electricity, this electricity being injected into the electric grid.