A Technique for Measuring the Frequency of Electrical Power Network Based on Spectral Analysis with Application of Henning Window

Signal frequency is one of the most important parameters of electrical networks. To measure the frequency of an electrical network, methods based on magnitude spectrum analysis are very popular. The main factor reducing the accuracy of these methods is the effect of spectrum leakage. The article discusses two main approaches for measuring frequency in the frequency domain while reducing the influence of spectrum leakage, based on the application of window functions and arithmetic spectrum transformation (the case of calculating samples of the modified spectrum from the three closest samples of the original spectrum is considered). The accuracy of existing techniques is compared for the case of a sinusoidal input signal, a polyharmonic input signal (the case of two harmonics is considered) and a sinusoidal input signal distorted by random noise (the ratio of signal power to noise power equal to 20 dB is considered). The parameters of the simulated input influences are selected in accordance with the current regulatory documents. For the case of reducing the effect of spectrum leakage by using window functions, a rectangular window and a Henning window are considered for the case of performing two-point and three-point approximation of amplitude spectrum samples. The paper discusses a new approach based on the application of the Henning window and approximation by two points and subsequent arithmetic transformation of the spectrum. By means of simulation modeling, an analytical relation was obtained that allows to determine the frequency value from the largest two spectrum samples after performing an arithmetic transformation. The accuracy characteristics of the proposed and existing approaches are compared for the case of a sinusoidal input signal, a polyharmonic input signal, and a sinusoidal input signal distorted by random noise. It has been proven that the proposed approach is significantly more efficient for the case of both sinusoidal and polyharmonic signals under conditions of spectrum leakage. Simulation mathematical modeling was carried out in the Matlab environment.