Numerical Calculation of End-Coil'S Leakage Inductance for Concentrated and Hairpin Windings

The identification of end-coil's leakage inductance during the design stage of an electrical machine is even nowadays a challenging and error-prone task. Due to the lack of accurate and fast calculation methods empirical values are widely-used. Empirical values are strongly dependent on the developer's experience. In case of new machine designs underestimating end-coil's leakage inductance can lead to serious failures that degrade the predicted operating behavior. This paper uses an approach to calculate end-coil's leakage inductance by combining the Neumann-Integral and the Method of Images. The method has been applied to concentrated windings and hairpin windings which are commonly used in traction applications. The results can be used to improve existing calculation methods which are usually based on analytical approaches and 2D-Finite-Element-Analysis (FEA). The results are compared to 3D-FEA and measurements.