Application of Chebyshev Polynomials to Assess the Active Power Error Caused by ADC Nonlinearity

Active power in a given frequency band is one of the most important parameters of electrical power grids. To measure active power, the most popular methods are based on averaging of instantaneous power or low-pass filtration of instantaneous power. Regardless of the measurement method, ADC nonlinearity is one of the most important causes of measurement error. In paper the Chebyshev polynomials are applied to evaluate the ADC nonlinearity and its influence on the active power measurement error. A research of influence of the signal parameters (voltage and current amplitudes, frequency, phase shift between voltage and current) and nonlinearity parameters on the active power measurement error is performed. The effect of the Chebyshev polynomial order on the active power measurement error is considered in detail. Analytical relations are obtained to assess this effects. A simplified approach of determining of the approximation polynomial parameters by a typical nonlinearity dependence is proposed. By the application of Matlab, a simulation model was perform that allows to estimate the reliability of obtained analytical expressions. Based on the research results, an estimation of the active power measurement error, caused by ADC nonlinearity with Chebyshev polynomials approximation is proposed.