Approximation of ADC Nonlinearity by a Random Function in the Case of Measurement of Electric Power Parameters

Abstract

Currently, the most informative parameters of electric power are active, reactive and apparent power in the considered frequency band. To measure the parameters of active and reactive power, the application of the method based on averaging of instantaneous power is the most widespread. One of the reasons of the measurement error of these parameters is related to the nonlinearity of the ADC conversion function. To reduce this error in practice, it is required to apply such expensive procedures as individual calibration, which is difficult in the case of mass-produced devices. As a rule, in the electric power measurement instruments, an ADC of successive approximation is used. The shape of the ADC nonlinearity is close to random, which makes it difficult to use polynomial functions for approximation of nonlinearity. This article proposes a method of approximation the ADC nonlinearity by using a random function. Analytical expressions are obtained for the estimation of the measurement error of power parameters caused by the nonlinearity of ADC conversion function. By Matlab software package the simulation modeling is performed. The simulation results are confirmed the validity of the obtained analytical relations. It is shown that the proposed error analysis technique can significantly reduce the final estimation of measurement error of the electric power parameters in comparison with the existing estimation methods.