Power management strategies have impacts on fuel economy, greenhouse gasses (GHG) emission, as well as effects on the durability of power-train components. This is why different off-line and real-time optimal control approaches are being developed. However, real-time control seems to be more attractive than off-line control because it can be directly implemented for managing power and energy flows inside an actual vehicle. One interesting illustration of these power management strategies is the model predictive control (MPC) based algorithm. Inside a MPC, a cost function is optimized while system constraints are validated in real time. The MPC algorithm relies on dynamic models of the vehicle and the battery. The complexity and accuracy of the battery model are usually neglected to benefit the development of new cost functions or better MPC algorithms. The contribution of this manuscript consists of developing and evaluating a high-fidelity battery model of a plug-in hybrid electric vehicle (PHEV) that has been used for MPC. Via empirical work and simulation, the impact of a high-fidelity battery model has been evaluated and compared to a simpler model in the context of MPC. It is proven that the new battery model reduces the absolute voltage, state of charge (SoC), and battery power loss error by a factor of 3.2, 1.9 and 2.1 on average respectively, compared to the simpler battery model.