The invention discloses a charging and discharging control method, apparatus and device of an energy storage battery, and a medium. The method is applied to a charging and discharging control system of a target energy storage battery based on cascade PID control, an amplitude limiting controller, a forward PI regulator and a reverse PI regulator are arranged in an outer loop control structure, andthe method comprises the following steps of: detecting a target current of a target energy storage battery at the current moment; determining whether the target current is within a preset range or not; if not, switching on the reverse PI regulator, acting the output current of the outer loop control structure on the reverse PI regulator, and feeding back the output signal of the reverse PI regulator to the forward PI regulator, so that the direct-current side output current of the target energy storage battery is regulated until the output current of the target energy storage battery is within a preset range, and switching off the reverse PI regulator. Therefore, the jump phenomenon of the output current of the direct current side of the target energy storage battery can be avoided, and the quality of the output current of the direct current side of the target energy storage battery is improved.