Application of Harmonic Functions to Estimate the Active Power Measurement Error Caused by ADC Nonlinearity and Quantization Error

Active power is one of the most important parameters of electrical power grids. To measure active power the digital measurement methods are currently applied, which are characterizes high accuracy and suitable for the measurement of sinusoidal and polyharmonic signals. When applying digital measurement methods, analog to digital converters are used to obtain voltage and current samples, the conversion function of which is nonlinear. This introduces a measurement error that cannot be eliminated by zero-adjustment and calibration technique. The nonlinearity shape depends on the analog to digital converter (ADC) architecture. Sigma-delta ADCs are characterized by a relatively smooth nonlinearity shape, while successive-approximation register (SAR) ADCs characterizes a nonlinearity close to a stochastic function. In this paper, to approximate nonlinearity and estimate the measurement error of active power, the application of harmonic function is considered. By changing the number of nonlinear oscillations, this approach can be applied to approximate the nonlinearity of sigma-delta, SAR and pipeline ADC architectures. Analytical expressions are obtained that make it possible to estimate the active power measurement error by nonlinearity parameters, input signal parameters and ADC architecture. The analysis of the influence of integral nonlinearity, the number of oscillations and the input signals amplitude value on the active power error is carried out. The influence of the sampling frequency on the active power measurement error is analyzed in detail. An algorithm is proposed for choosing the number of nonlinearity oscillations which is based on analysis of the typical shape of ADC nonlinearity. The reliability of analytical expressions is confirmed by the results of simulation modeling performed by Matlab.