Computing end-turn leakage inductance of concentric coil windings by asymptotical series approximation of Neumann integrals

In the design of electric machinery concentric coil windings are often used where each end-turn consists of straight conductors connected by circular arcs. This paper proposes an analytical approach to the evaluation of end-turn leakage inductance for this winding geometry. The technique employs an asymptotical series expansion of Neumann integrals and, unlike existing methods, does not require to approximate the end-turn shape by a succession of elementary straight filaments. The computation formulas obtained have the advantage of a fast convergence speed and are easy to implement for practical use. Their correctness is assessed against direct numerical integration results.