A damping circuit for an energy storage device. The damping circuit comprises a current detection device designed to detect an output current of energy supply strings or the energy storage device and to generate an output current signal dependent on the output current. The damping circuit also includes a closed-loop control circuit coupled to the current detection device. The closed-loop control circuit designed to adjust the output current signal to a setpoint current signal and to output a corresponding current control signal. A first winding of a transformer is coupled to an output connection of the energy storage device. A second winding is galvanically isolated from the first winding. A compensation current generation device is coupled to the closed-loop control circuit, and is designed to feed a compensation current into the second winding of the transformer depending on the current control signal.