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Leakage Inductance Calculation of the Transformers With Disordered Windings

In switching power supplies, the transformer leakage inductance (TLI) is of considerable practical significance. Ordered winding is the certain assumption in previously reported works for the calculation of the TLI value. However, disordered windings are usually unavoidable in practice and their effect on the value of the TLI is considerable. The problem becomes more complex when the number of winding turns increases. In this paper, the effect of winding disorder on the TLI value is investigated. In disordered wrapping, the winding turns arrangement (WTA) of each produced transformer is different from the others. Thus, each produced transformer has an exclusive TLI value in a disordered wrapping. Moreover, the number of possible WTAs is high, especially in transformers with a large number of winding turns. The proposed method utilizes an analytical tool for estimating the distribution of the TLI values for all of the possible WTAs. This estimation is carried out based on the limited number of the WTAs. The required number of WTAs is calculated and the validity of the proposed method is checked with Kolmogorov–Smirnov theorem. The TLI value is calculated by means of the stored magnetic energy in different parts of the transformer using the magnetomotive force variation method. Finite element simulation and experimental results are presented to show the effects of disorder on the TLI value and the validity of the proposed analytical method.