Effect of harmonics on hunting of synchronous machines

Existing analyses of small oscillations in synchronous machines are based on the 2-axis theory, which assumes an `ideal¿ machine defined by Park and Kron. Real machines, however, have been shown to depart considerably from the Park-Kron definition in that windings produce m.m.f. harmonics in addition to the fundamental, and air-gap permeance harmonics higher than the second are significant. The effects of such a departure on the hunting behaviour of a synchronous machine are studied in the paper. The electromechanical performance equations of free hunting are derived in the holonomic frame, with the significant harmonics taken into account. The frequency of oscillation, and hence the decrement, are obtained by solving the equations numerically on a digital computer. They are also calculated by the 2-axis theory, and the two sets of results are compared with experimental observations on a small synchronous motor. It is found that, for 3-wire star connection of the armature, the 2-axis theory gives correct results; but, in 4-wire star and delta connections, it can lead to appreciable error if the harmonic effects are pronounced. In the latter cases, the analysis presented can be used to predict the hunting behaviour more accurately.