This paper deals with the modeling and the control of a new high power 12V Integrated Starter Alternator (ISA). This system is used to bring micro-hybrid functions to standard Internal Combustion Engine (ICE) vehicles. The drive is composed of a seven-phase synchronous claw-pole machine with separate excitation, supplied with a seven-leg Voltage Source Inverter (VSI) designed for low voltage and high current. The system is modeled in a generalized Concordia frame and a graphical description is used to highlight energetic properties of such a complex system. A control scheme is then deduced from this graphical description. Two controls are achieved in generator mode and compared: one is using the VSI in a square-wave mode, the other in a Pulse Width Modulation (PWM) mode. Experimental results are provided.