The invention relates to a battery system (10), comprising a battery module (11), which comprises a first high-voltage connection (12a), a second high-voltage connection (12b) and a multiplicity of battery cell modules (11a, . . . , 11n) which are connected in series between the first and second high-voltage connections, and a switching matrix (13). The switching matrix comprises a large number of switching rails (14), which are each connected to one of the nodes between in each case two of the battery cell modules which are connected in series, a multiplicity of first switching devices (15a), which are designed to connect in each case one of the switching rails (14) to a first low-voltage connection (13a) of the switching matrix (13), and a multiplicity of second switching devices (15b), which are designed to connect in each case one of the switching rails (14) to a second low-voltage connection (13b) of the switching matrix. In this case, a first total voltage (HV) of all of the battery cell modules (11a, . . . , 11n) which are connected in series is present between the first high-voltage connection (12a) and the second high-voltage connection (12b), and a second total voltage (LV) of some of the battery cell modules (11a, . . . , 11n) which are connected in series is present between the first low-voltage connection (13a) and the second low-voltage connection (13b), depending on the switching state of the first switching devices (15a) and the second switching devices (15b).