Performance evaluation for frequency estimation of transients using the ESPRIT: Measured noise versus white noise

A number of papers have proposed to use the ESPRIT method for estimating some power system transients. The mathematical model for using the ESPRIT requires that the additive noise be white. Fail to satisfy this could lead to degraded performance of frequency estimation. However, in practical situations the noise is often non-white. In this paper we study the performance of the ESPRIT frequency estimation method when the additive noise is measured from power systems. It is shown that tests using synthetic white noise are not sufficient for realistic power-system scenarios, as the noise is often non-white and not i.i.d. distributed. First, a set of measured voltage waveforms is superimposed to synthetic transients with known frequencies. This yields a set of semi-measured transients. The ESPRIT method is then applied to estimate the frequencies. The performance of the ESPRIT is then evaluated in term of the mean value and standard deviation. Our experiments show that, for a transient contains one sinusoid, the ESPRIT of sinusoidal model order K=2 results in an acceptable accuracy if the amplitude of the transient is well above the noise level and the transient frequency is not too close to the power-system frequency. This is sufficient for most practical applications. A better performance for higher noise levels is obtained by significantly increasing the sinusoidal model order in the ESPRIT.