Using a first-principles approach, the constituent components of a series hybrid electric car are modelled and integrated to form an overall coupled dynamic model. Controllers for the individual components are constructed, and are combined with a load follower supervisory controller and driver model to enable simulation of the vehicle under general operating conditions. The powertrain includes AC/DC, DC/AC and DC/DC converters which are described by standard average models with realistic power efficiencies. The powertrain also includes permanent magnet synchronous machines that are modelled using conventional d-q frame equations. There is novelty in the use of a general purpose friction moment, acting on each of the electrical machines, that is included to capture the equivalent energy loss due to friction, eddie currents and hysteresis, thus providing a good match between the predicted steady-state behaviour of the machines and experimental data. A longitudinal vehicle dynamics model with realistic descriptions for the tyres, aerodynamic resistance, suspension and continuously variable transmission (CVT) is also included. A scheme for improving the motor efficiency under general operating conditions, by controlling the CVT, is devised. The overall vehicle model is used to track the New European Drive Cycle (NEDC), for two design scenarios, one with fixed and one with variable final drive ratio. The simulation results demonstrate the applicability of the model for control system design, realistic prediction of vehicle behaviour and energy losses in the various components, and design optimisation.