Analytic Algorithm for Strand Slot Leakage Reactance of the Transposition Bar in an AC Machine

Calculation of circulating current in transposition bars is the key problem in the design of stator windings, which will determine the transposition type of stator windings. The circuit equation method, in which the calculation of strand slot leakage reactance in transposition bars is the premise, is widely used in engineering to calculate circulating current. This paper describes an analytical algorithm for the calculation of strand slot leakage reactance in transposition bars called discrete integral method. The presented method is based on Ampere's circuit law. The slot leakage reactance of strands in transposition bars is calculated by the integral of the transposition path discretized into many key points under the proper coordinate system. Contrary to the existing calculation formula, the discrete integral method is a general method for the calculation of slot leakage reactance, which can simulate the transposition path of different transposition types. In order to validate the discrete integral method, the circulating current generated by slot leakage magnetic field of two typical transposition bars is calculated by circuit equation method and finite-element method.