Three-transfer-function approach for building phenomenological models of synchronous machines

The established practice of using only two transfer functions when modelling the d-axis of a synchronous machine at rest is physically questionable since it leads, from the network theory point of view, to ambiguous equivalent circuit realisations. The paper provides analytical and experimental evidence for the claim that a triple transfer function (3TF) parameterisation is the only one general enough to cope with both stator and rotor voltage perturbations, thus broadening the range of physical phenomena the model can account for. It is proposed that the third transfer function can be conveniently chosen from three closely related impedance operators, only two of which are classical. Using standstill frequency response test data from the Ontario Hydro´s Lambton generator, it is shown that, for a given number of damper windings (3, 5, or 6), at least one equivalent circuit exists capable of accurately modelling the stator input inductance L_d(s) and the short-circuit stator to rotor transfer function sG(s), but failing dramatically to fit the third transfer function, i.e. the stator to field transfer inductance with field open L_afo(s). Only the 3TF approach consistently leads to equivalent circuits with definite phenomenological significance, thus enhancing the understanding of machine behaviour as affected by damper-cage design and excitation system