This is a system that stores energy by compressing atmospheric air and confining it in tanks or caverns, combining the thermodynamic cycle followed by the atmospheric air (Brayton cycle) with another thermodynamic cycle followed by an auxiliary fluid, that is confined in the same cavern within a membrane, following two sections of a Rankine cycle, one during the air compression and entry into the cavern process and the other during the air outlet and turbining process, using heat from the exhaust gases from the turbine as a heat source for an additional Rankine cycle, and being able to use the tanks or caverns for making an extra constant volume heating of compressed air and/or of the auxiliary fluid.