Method for operating a storage system for storing electrical energy by conversion into thermal energy, in which - in a charging process via a charging side, by means of a charging arrangement, a high-temperature storage device is charged by storing energy, in particular fed-in electrical energy, in the form of thermal energy, wherein the charging process takes place via a heat pump process within the charging assembly, which is designed as a first Joule arrangement comprising a low-pressure side and a high-pressure side, with an interposed compressor assembly and turbine assembly, and - in a discharging process, by means of a Rankine process, the high-temperature storage device is discharged via a discharging side with the thermal energy being released from the high-temperature storage device and converted into electrical energy, wherein an energy conversion arrangement provided in the storage system, in addition to the charging arrangement, in the form of a second Joule arrangement, comprising a low-pressure side and a high-pressure side and compressor/turbine assemblies (406, 414) arranged therebetween, is operated during the charging process and/or during the discharging process of the storage system in a heat pump process and/or in a thermal power process, wherein in particular during the second discharging process and/or the second charging process of the second Joule arrangement and the charging process via the charging side, thermal energy is transferred between the second Joule arrangement and the charging side, characterized in that, during the second discharging process and/or the second charging process of the second Joule arrangement and the discharging process via the discharging side, thermal energy is transferred between the second Joule arrangement and the discharging side. - in a charging process via a charging side, by means of a charging arrangement, a high-temperature storage device is charged by storing energy, in particular fed-in electrical energy, in the form of thermal energy, wherein the charging process takes place via a heat pump process within the charging assembly, which is designed as a first Joule arrangement comprising a low-pressure side and a high-pressure side, with an interposed compressor assembly and turbine assembly, and - in a discharging process, by means of a Rankine process, the high-temperature storage device is discharged via a discharging side with the thermal energy being released from the high-temperature storage device and converted into electrical energy, wherein an energy conversion arrangement provided in the storage system, in addition to the charging arrangement, in the form of a second Joule arrangement, comprising a low-pressure side and a high-pressure side and compressor/turbine assemblies (406, 414) arranged therebetween, is operated during the charging process and/or during the discharging process of the storage system in a heat pump process and/or in a thermal power process, wherein in particular during the second discharging process and/or the second charging process of the second Joule arrangement and the charging process via the charging side, thermal energy is transferred between the second Joule arrangement and the charging side, characterized in that, during the second discharging process and/or the second charging process of the second Joule arrangement and the discharging process via the discharging side, thermal energy is transferred between the second Joule arrangement and the discharging side.