Application of the Vernier Method to Reduce the Effect of Amplitude Spectrum Leakage

The spectrum of an electric power signal is its most important parameter, since it allows indirectly determining most of the other parameters required for measurements in the electric power industry. It is known that the “spectrum leakage” effect leads to the occurrence of a methodical measurement error of both the amplitude and phase spectrum of a signal. For the case of implementing a discrete Fourier transform (DFT) by direct implementation, through a digital IIR filter or by using a Goertzel transducer, the most effective approach to reducing the “spectrum leakage” effect is to adjust the number of samples. The accuracy limitation for this approach is due to the discrete nature of the number of processed samples, as a result of which it is not possible to accurately adjust the measurement time to the period of the input signal. To improve the accuracy of this approach, this publication proposes a “vernier” method. The so-called “vernier” method is proposed when performing approximation by zero- and first-order polynomials. A comparative analysis of both approaches is carried out and a modification is proposed that combines the compensation method and the “vernier” method. For the case of a sinusoidal input signal, the maximum achievable error was estimated for the case of application of this method. Simulation modeling was performed by using Simulink and Matlab packages, which allowed to obtain the error dependencies on the influencing quantities: the initial phase of the signal, the sampling frequency, and the relative frequency deviation from the nominal value. The obtained models also allowed to evaluate the correctness of the obtained analytical expressions and the efficiency of the proposed “vernier” methods: based on stepwise and piecewise linear approximations.