The invention relates to a battery (1) having at least two battery cells (2), which are connected to one another by means of at least one electrical connecting element (3), and a higher-level control unit (6), wherein each of the battery cells (2) has at least one galvanic element, a battery cell housing to accommodate the galvanic element, at least one sensor device (7, 8, 9) for detecting a physical and/or chemical characteristic of the battery cell (2) and a communication device (10, 11) for communicating with the higher-level control unit (6), wherein the higher-level control unit (6) is designed to control an energy flow into at least one of the battery cells (2) and/or from at least one of the battery cells (2) as a function of the physical and/or chemical characteristics of the battery cells (2). The invention further relates to a motor vehicle having such a battery (1).