The Impact of Power Harmonics and Noise on the Measurement Error of the Frequency by Derivative Technique

Currently, there are a large number of methods for the measurement of the power frequency. The most high-speed measurement method is the derivative technique. The peculiarity of this method bases at the definition of the second derivative of the input signal and calculation of the frequency value. As you know, the harmonics of the input signal and noise are subjected to second order differentiation are strengthening. This results to an additional measurement error of frequency. This paper introduces a measuring the frequency by derivative technique. The sources of the measurement error of frequency by this method are analyzed. It is shown that the effect of input noise on measurement error can be reduced by applying low-pass and band-pass filtering, and by averaging the results of measurement frequency. Conditions under which the error of measurement frequency by this method achieves its minimum and maximum values are obtained. The influence of harmonics of the input signal frequency measurement error is considered. It is shown, that an effective way to reduce the influence of harmonics to the measurement error is use the low-pass or band-pass filter. The obtained analytical expression allows for a given limits of measurement error of frequency to determine the maximal coefficients of the harmonics of the input signal. The use of this expression allows to put forward the requirements for filtering harmonics of the input signal: the minimum attenuation of the applied filter at the stopband. The accuracy of the derived expressions is confirmed by results of simulation modeling by software Mathcad, Matlab and Simulink.