Application of Least-Squares for Frequency Measurement Error Reducing for the Zero-Crossing Technique

The task of the improving of the frequency measurement accuracy is one of the highest priorities for the modern power engineering. The accuracy of the signal frequency measurement affects the accuracy of a lot of the power quality indicators measurement. In a number of the power engineering areas there are some challenges which require the methods assuring the higher frequency measurement accuracy in comparison with the methods for the standard cases. Most of such challenges are related to the deviation of the signal form from the sinusoidal one (the appearance of noise, the presence of harmonics, the presence of a flicker of the sinusoidal or rectangular shapes, the presence of interharmonics and subharmonics, supraharmonics), since the standard measurement approaches for such signal lead to the very high inaccuracy values. In the regard of the above this article reviews the modification of the widespread zero-crossing method of the frequency measurement, based on the linear approximation with the least squares method. The frequency measurement accuracy provided by the classical zero-crossing method of the frequency measurement is compared with the frequency measurement accuracy provided by its modification, based on the common linear approximation usage. Within the specified method the following dependences of the frequency measurement accuracy are obtained: on the signal frequency, on the sampling frequency, on the measurement time and on the number of samples used in the least squares method approximation. An analysis was made of the influence of the number of samples used in the least squares approximation on the frequency measurement error depending on the noise level of the input signal and the sampling frequency. A simulation model of the method developed using the Matlab software is proposed.