INTRODUCTION Electric vehicle powertrain components are optimized with a focus on minimizing the energy consumption in a driving cycle, which represents the real world vehicle operation. Analytical models, which are simple and accurate in estimating the powertrain efficiency, can reduce the computational time of the early stage design optimization process. In this paper, an analytical modelling approach for an outer rotor surface mounted permanent magnet (SPM) machine designed for an in-wheel motor electric powertrain is explained in detail.In literature, the approaches for computing the airgap field solution of the SPM machine, which can be the basis for calculating the efficiency, are given as follows. Carter introduced the use of an equivalent air-gap that is greater than the physical air-gap to model the slotting effect [ 1,2] in the field solution. This method captures the overall reduction in air-gap flux density, but the local distortion of the flux density which produces cogging torque is not modelled. Zhu et al.[3] proposed a relative permeance based method to model the local radial field distortion. As this method does not include the influence of slotting in the tangential field component, Zarko et al.[ 4] suggested Improved Analytical Model of an Outer Rotor Surface Permanent Magnet Machine for Efficiency Calculation with Thermal Effect Kesavan Ramakrishnan Politecnico di Milano Pietro Romanazzi University of Oxford Damir Zarko University of Zagreb Giampiero Mastinu Politecnico di Milano David A. Howey University of Oxford Alessio Miotto BREMBO S.p.A. ABSTRACT In this paper, an improved analytical model accounting for thermal effects in the electromagnetic field solution as well as efficiency map calculation of an outer rotor surface permanent magnet (SPM) machine is described. The study refers in particular to an in-wheel motor designed for automotive electric powertrain. This high torque and low speed application pushes the electric machine close to its thermal boundary, which necessitates estimates of winding and magnet temperatures to update the winding resistance and magnet remanence in the efficiency calculation. An electromagnetic model based on conformal mapping is used to compute the field solution in the air gap. The slotted air-gap geometry is mapped to a simpler slotless shape, where the field solution can be obtained by solving Laplace's equation for scalar potential. The canonical slottless domain solution is mapped back to the original domain and verified with finite element model (FEM) results. Closed form solutions of core loss and magnet loss are derived from the air -gap field solution. The copper loss is calculated by considering the proximity loss and skin ef fects. In order to estimate the winding and magnet temperatures, a thermal model is built using a lumped parameter thermal network with an improved discretization approach. The model has been validated experimentally using the end-winding and coolant temperatures. The ener gy consumption calculation with the New European Driving Cycle (NEDC) is performed and the benefit of having the thermal model is quantified in terms of percentage dif ference in the calculated energy consumptions. CITATION: Ramakrishnan, K., Romanazzi, P., Zarko, D., Mastinu, G. et al., "Improved Analytical Model of an Outer Rotor Surface Permanent Magnet Machine for Efficiency Calculation with Thermal Effect," SAE Int. J. Alt. Power. 6(1):2017, doi:10.4271/2017-01-0185.Published 03/28/2017 Copyright © 2017 SAE International doi:10.4271/2017-01-0185 saealtpow.saejournals.org 34Downloaded from SAE International by University of British Columbia, Tuesday, July 31, 2018a complex relative permeance method. The radial and tangential components of the field solution and the permeance function are represented as real and imaginary parts of a complex number, which enabled the derivation of closed form solutions for the global parameters. The harmonic model [ 5] and m