A battery system 11 for storing electrical energy comprises at least one battery (1a-c, fig 1) having at least one battery cell 2a, 2b and comprising a cooling system for cooling at least two battery cells of the battery system 11. The battery system 11 comprises at least a first and a second battery cell 2a, 2b, and the cooling system comprises conducts for conducting cooling fluid, wherein a first section 5a of the conducts is attached to the first battery cell 2a and a second section 5b of the conducts is attached to the second battery cell 2b. The first section 5a and the second section 5b are located downstream and upstream with respect to each other, so that cooling fluid continuously flows through the first section 5a and afterwards through the second section 5b, or, depending on the flow direction, vice versa. The cooling system also comprises a pumping arrangement 16 for pumping the cooling fluid through the conducts and a control 17 for controlling operation of the pumping arrangement 16, wherein th
