Analytical expressions for estimating resonant frequencies of machine and transformer windings

An original analytical procedure for obtaining an algorithm for the simple and rapid estimation of resonant frequencies of machine and transformer windings is presented. In deriving the algorithm, the winding is represented by a finite number of sections with distributed parameters. The only difference with respect to the real winding emerges from the assumption that the parameters of these sections are uniformly distributed lengthwise. In this manner one obtains a model of the winding which is analogous to the transmission line composed of a finite number of different sections, but where each section, taken by itself, is homogeneous along its length. Using this model, the expression for the resonant frequencies of the winding is obtained on the basis of knowledge concerning the resonant phenomena on the transmission line.