Analysis of 3-Leg Transformer Cores and a New Instrument for Measurement of Exciting-Current Waveforms

This analysis may be considered as an extension of the core-loss relationships, given in reference 1, to the general case which gives exciting-current waveform relationships as well. For such purposes as special testing of 3-phase 3-leg transformer cores or developing the design of these cores, it would be desirable to have a method for determining an "a-c loop" for each leg of the core. In this paper the a-c loop is taken either as a curve of flux plotted against drop in mmf (magnetomotive force) or of flux density versus mmf per unit length. An a-c loop for each leg of a core may be determined by a combination of single-phase tests, but the results are not completely representative of the conditions within the core in 3-phase operation. In this paper a method is given whereby data from 3-phase tests may be utilized. First, the waveforms of the exciting currents are quantitatively described by measuring the amplitudes and phase angles of both the fundamental and harmonic terms. These measurements are taken directly using a new instrument called a "harmonic phase comparator." Then, formulas are developed to convert the measured data directly into a description of the a-c loop for each of the legs. A numerical example from actual test data is given, and a convenient technique to plot the data is demonstrated.