An Introduction to Goodness of Fit for PMU Parameter Estimation

It is posited that the process of measuring the various parameters that characterize a signal is equivalent to a fitting problem in mathematics. The equation being fit is a model based on the “physics” of the signal. The Fourier transform or rms calculations in a phasor measurement unit (PMU) furnish the values of the coefficients. Regardless of exactly how the measurement is made, a metric we define and call the goodness of fit allows the measuring system to comment on the match between the signal it is observing and the model. The metric is based on the residuals, the differences between the signal itself and the value calculated from the result of measurement. Results from real-word PMUs and real-world signals illustrate that the equation of the PMU is well solved during steady conditions. We examine the effect of a fault in the transmission system on the goodness-of-fit metric for a PMU. We also apply the metric to results from a microPMU in the distribution system.