Solving dynamic electric circuit with nonlinear hysteretic inductor using harmonics interpolation method

Abstract

SummaryThe aim of this paper is to present a methodology for solving а dynamic electric circuit with nonlinear hysteretic inductor without the use of hysteresis model or equivalent circuits. A consideration of nonlinear and hysteretic behaviour of the magnetic core under quasistatic conditions is based on applying harmonics interpolation method (HIM) to the measured magnetising field strength waveforms. A dynamic behaviour of the magnetic core is considered through the application of the statistical theory of losses (STL). A considered electric circuit consists of AC voltage source connected in series with shunt resistor, additional linear resistor and inductor, as well as a nonlinear hysteretic inductor. The solution for electric current of the circuit is obtained by solving equation derived from Kirchhoff's laws through a series of successive iterations. Coupling of electric and magnetic part of the circuit is obtained from fundamental laws of electromagnetism. Methodology is validated for four cases of the considered electric circuit — without additional elements, with one additional or both additional elements, for sinusoidal voltage source amplitudes of 2, 4, 6, 8 and 9 V and frequency of 50 Hz. Validation is repeated for frequencies of 100, 200 and 300 Hz while keeping the ratio of the amplitude to frequency constant. Detailed theoretical approach and methodology, comparisons between measured and calculated results, as well as adequate discussion are presented.