Characteristics of equivalent circuits of synchronous machines

Frequency response tests have now become accepted as a sound alternative to sudden short-circuit tests for the determination of parameters for synchronous machines for transient studies. The standard approach to the extraction of machine parameters from the results of frequency response tests generally concentrate on curve-fitting techniques to match the measured magnitude and phase with a set of time constants. These processes are fraught with difficulty in respect of needing to: first, define the order of the model before the analysis can commence; and secondly, initiate the curve fitting with initial estimates of the parameters. Unfortunately, there is not a unique set of time constants which produce a frequency response which fits the measured data, and a better method than a ‘blind’ numerical method is therefore needed. The author presents the application of standard linear systems theory to predict the positions of the poles and zeros in the frequency response and to determine the order of the equivalent circuit required to model the machine accurately. The process breaks quite naturally into two parts; the extraction of the time constants from the frequency response, and the determination of the parameters of the equivalent circuit from those time constants. The basis for the measurement technique is reviewed and the effects of different levels of complexity of the equivalent circuit are considered with respect to the increased difficulty normally experienced in extracting the parameters. The ease with which this method copes with the higher-order models and the sequential nature of the process, working from the lowest frequency to the highest frequency in the frequency response, justify accepting the procedure. Results obtained from tests on production machines are used to illustrate the procedures for both time constant extraction and equivalent circuit parameter determination to confirm the capabilities of the methods.