Calculating the short-circuit impedances of a multiwinding transformer from its geometry

By considering the set of short-circuit tests which can be performed on a multiwinding transformer, analytical expressions are derived for the leakage inductances between all pairs of transformer windings, expressions which depend only on the winding geometry and the frequency of excitation. For each short-circuit test, a simplified field analysis gives the complete solution for the frequency-independent magnetic field intensity between winding layers, and the frequency-dependent distribution of magnetic field intensity within each layer. Then, for any frequency of interest, the magnetic energy stored in each winding layer and interlayer space is calculated, and the results are summed to give the total energy stored in the entire winding space of the transformer. Finally, the leakage inductance between excited and short-circuited windings is derived from the total stored energy. Experimental data are provided that illustrate the accuracy and the limitations of such leakage-inductance calculations as well as the accuracy of AC-winding-resistance calculations carried out using a similar, previously published method