The invention relates to a modular battery storage system comprising a group of n energy storage modules. A switch is associated with each of the n energy storage modules, by means of which the respective energy storage module can be activated and deactivated. The n energy storage modules can be interconnected by means of the switch in such a way that the individual voltages U individual of activated energy storage modules add up to form a total voltage U total . According to a method for operating the battery storage system, at least one power value is determined for each of the n energy storage modules, which characterises the power of the respective module. A temporally variable total voltage U tot (t) is produced by activating at least two energy storage modules from the group such that they temporally overlap but over activation time intervals of different durations. According to the determined at least one power value, each of the at least two energy storage modules is associated with one of the activation time intervals of different durations. In order to carry out the method, the battery storage system comprises a battery management system specifically designed for this purpose.