Numerous researches about hybrid electrical vehicles (HEVs) deal with topologies, technologies, sizing and control. These aspects allow reducing transportation costs and environmental impacts. This study focuses on the sizing of the electrical machine (EM) of the HEV, taking into account its surroundings: the hybrid system, the driving cycle and an optimal energy management. In this study, the parallel HEV is the study case. In a classical HEV design process, a scaling factor is usually applied on an efficiency map model to fix the standard power of the EM. The efficiency and the maximum torque power are scaled using a linear dependency on the rated maximum power. However, this method has some disadvantages. This study proposes two formulations of a scaling model based on a magnetic circuit model (MCM) with one or ten parameters. Then, the MCM is involved in a multi-objective optimisation process of the HEV. This process is a global sizing process using dynamic programming as an optimal energy management. Optimal sizings of the hybrid vehicle are then proposed for various driving conditions

Hybrid electrical vehicles involve two sources of energy, usually gasoline and electricity. The energy management determines the power sharing between the internal combustion engine and the electrical machine (EM). It is highly dependent on the driving cycle (i.e. the use of the vehicle). In this context, the optimal sizing of the EM is determined by: the driving cycle, the power-train characteristics (i.e. ratios and physical limitations e.g. maximum torque available) and the energy management. The key idea of this work is to involve the driving cycle and the environment of the electrical machine in a global multi-objective optimization process taking into account an optimal energy management and an accurate model of the EM based on magnetic circuit equivalent model