Application of the Least Squares Technique to Reduce the Frequency Measurement Error by Phase Increment Analysis

Abstract

Frequency is the most important parameter of electrical power grids. For its successful measurement, a method based on determining the phase increment can be applied. This method allows measuring the frequency of polyharmonic signals, however, the presence of harmonics, noise and flicker results in an increase of error. The paper is devoted to the application of the least squares technique to approximate the phase change over time to reduce the influence of noise, harmonics and flicker on the frequency measurement error. The application of direct implementation of discrete Fourier transform (DFT) and the Goertzel transducer to obtain the phase values of the measured signal is considered. The influence of the number of approximating samples on the final measurement error for a first-order approximation polynomial is considered. An analytical dependence of the frequency measurement error on the number of approximating points is obtained. The influence of the applied approach on the measurement error caused by the ADC nonlinearity and the quantization error is considered. It is shown that with an increase in the number of approximating samples, the error tends to decrease. The reliability of the obtained expressions was evaluated by using simulation modeling performed in Matlab.