The invention provides a high-efficiency battery storage device system, and a motor driving body and a moving body using the system. The battery storage device system comprises (1) a main battery storage device A having high energy density relative to an auxiliary battery storage device B, (2) the auxiliary battery storage device B having high output density relative to the main battery storage device A, (3) a warm-up means for warming up the main battery storage device A to a predetermined temperature or more, (4) a warm-up monitoring means for monitoring a need for warm-up with respect to the main battery storage device A, (5) an operation mode switching means for selecting an operation mode from a warm-up operation mode and a normal operation mode and performing the selected operation mode, and (6) an electricity supply system supplying an electric power to an outside of the battery storage device system.