International audienceThis paper describes a 3-D numerical hybrid method (NHM) of the permanent-magnet (PM) eddy-current losses in axial-flux PM synchronous machines (PMSMs). The PM magnetic flux density is determined using the multi-static 3-D finite-element method (FEM) at resistance-limited (i.e., without eddy-current reaction field). Based on the predicted flux density distribution, the eddy-currents induced in the PMs and the 3-D PM eddy-current losses are calculated by 3-D finite-difference method (FDM) considering a large mesh. Therefore, this 3-D NHM is based on a coupling between the multi-static 3-D FEM and the 3-D FDM. Two 24-slots/16-poles (i.e., fractional-slot number) axial-flux PMSMs having a non-overlapping winding (all teeth wound type) with stator double-sided structure are studied: 1) surface-PM (SPM) and 2) interior-PM (IPM) To evaluate the reliability of the proposed technique, the 3-D PM eddy-current losses are determined and compared with transient 3-D FEM (i.e., magneto-dynamical 3-D FEM). The same nonlinear properties of the laminations have been applied for multi-static/transient 3-D FEM. The computation time can be divided by 25 with a difference less than 12%

In this paper, a global optimization methodology is described to pre-design an electric vehicle powertrain in order to find the best compromises between components. The modeled system includes a transmission, an electric machine, an inverter and a battery pack. The challenge is to find the dedicated formulations, with the vehicle performance requirements, electric range, and cost calculation that include the whole system without exploding computational time. Bi-objective, range/costs, optimizations with performance constraints are performed to find the potential gain with the system model. Keywords-Electric vehicle powertrain, optimization methodology, electric system design, methodology Notations:Sp: Vehicle Speed (km/h) t: driving cycle time (s) Sl: Road slope dp: number of operating points that represent a portion of a driving cycle pp: number of operation points that represent a performance requirements ng: number of gears of the transmission Tw: required torque at the wheel (Nm) Ωw: wheel speed (rpm) Tm: required machine torque (Nm) Ωm: machine speed (rpm) Tm max : maximum machine achievable torque (Nm) Tm req : required machine torque for performance (Nm) f: stator frequency (Hz) Um: machine voltage (V) Im: machine current (A) cos(φ): machine power factor J: stator current density (A/mm²) Ib: battery current (A) Ub: battery voltage (V) x i : design variable ns: number of cells in series for the battery pack np: number of cells in parallel for the battery pack SOC: battery state of charge