Calculation of end-winding leakage inductance for hairpin winding high power density traction machines using the PEEC method

The computation of end-winding leakage inductance is often an expensive task during the design process of electrical machines, but still important for an accurate estimation of the expected short circuit current of the evaluated design. Since commonly used 3D finite element analysis (FEA) based approaches require complex modelling and consist of time consuming solving, they are less suitable for a fast evaluation. Alternatively, methods based on the Neumann-Integral can decrease the calculation time and reduce the model complexity, but suffer from the requirement of numerical integration. This paper presents an enhanced approach, based on the partial element equivalent circuit (PEEC) method, to estimate the end-winding leakage inductance by applying closed form analytical solutions for fundamental PEEC cell geometries to arbitrary hairpin winding configurations. To emphasize the benefit and the merits of the proposed approach, a study case traction motor is analyzed and the results are compared to complex 3D FEA and measurements by evaluating the short circuit current. Finally, the approach is used to estimate the influence of short pitchening on the end-winding leakage inductance.