Effect of m.m.f. and permeance harmonics in electrical machines, with special reference to a synchronous machine

Real electrical machines differ from the conventional models of generalised theory primarily in three ways: they are magnetically nonlinear, windings produce m.m.f. harmonics in addition to the fundamental, and air-gap permeance harmonics higher than the second are significant. The practical effects of the latter two complications on terminal characteristics are discussed with particular reference to waveforms in a small but otherwise conventional synchronous machine. Axis transform methods are of little or no value in such situations, and two numerical techniques for direct solution of the machine equations are discussed. A Runge-Kutta computation establishes that high accuracy is obtained by consideration of a modest number of harmonics, so that a highly efficient procedure based on Newton-Raphson reduction is possible. In the case of the popular 3-wire star connection, the equations reduce to essentially the conventional d, qaxis equations plus an additional one giving the neutral potential. On the other hand, the 4-wire star and the mesh connections yield equations not in accord with the d, q equations, and significant time harmonics can result.