Application of the Signal Samples Approximation for Accurate RMS Measurement

Nowadays the root-mean-square (RMS) is one of the most informative parameters of electrical power grid signals. By definition, the RMS measurement technique involves averaging the square of the input signal over time multiple of the input signal period. However, for digital measurement methods, the input signal is represented as a sequence of discrete samples obtained by applying analog-to-digital converter (ADC). The paper discusses ways of approximating of the signal samples by applying polynomial functions of zero, first and second order. Analytical expressions are obtained for the RMS measurement error for the case of applying of different order approximation polynomials. The influence of the input signal amplitude, signal frequency, initial phase, sampling frequency and total measurement time on the RMS measurement error for the case of applying these measurement approaches is considered. The influence of the input signal frequency deviation on the RMS measurement error has been especially thoroughly investigated. The methods of reducing the RMS measurement error for the case of sinusoidal and polyharmonic input signals are proposed. By application of Matlab and Simulink software packages, a simulation mathematical model for all considered approaches is performed.