Determination of frequency in three-phase electric circuits with autocorrelated noise

Аннотация

Ascertaining the frequencies in three-phase systems is an important element in the automation of power systems. In three-phase systems, none of the individual phases can precisely describe the entire system and its properties. Thus, for a reliable frequency assessment, information on all three phases should be considered. This paper considers a real signal that is obtained via the Clarke transform and that contains information on all of three phases. The objective of this study was to develop methods for adaptive determination of the frequency of three-phase electric circuits on the basis of identification of the parameters of the second-order autoregression. The least-squares (LS) method has become most widespread in technical applications. However, estimations of the autoregression parameters that were obtained with this method from the noise observations are biased. Using such frequency estimations reduces the reliability of power-system automation. Therefore, the application of methods for frequency assessment that allow unbiased estimations to be obtained is an urgent task. In this study, an algorithm for the frequency assessment based on the method of instrumental variables (IV) was used for the first time. It makes it possible to obtain unbiased frequency estimations for both white-noise and autocorrelated-noise interference. Different variations of the algorithms on the basis of the total least-squares (TLS) method for various classes of noise are considered. Recurrent modifications of the LS method, the method of instrumental variables, and the total leastsquares (TLS) method are analyzed, which allow one to determine the frequency in real time. A computer experiment showed that the IV and TLS methods make it possible to obtain more accurate estimations for the cases of correlated and uncorrelated noise than does the LS method. The obtained results can be used to improve the efficiency of the diagnostics and analysis of electric systems.