Estimation of the Power Parameters Measurement Error Resulted by ADC Nonlinearity and Quantization Noise in Case of DFT Application

Abstract

The measurement method of electric power parameters (apparent, reactive and active power) which is based on the application of discrete Fourier transform (DFT) characterizes a lot of advantages. Its application makes possible to measure the complex spectrum (which results to amplitude spectrum and phase spectrum measurement) as well as the electrical power parameters (active, reactive and apparent). The analog-to-digital converters (ADC) are used to get signal samples results of additional error components (instrumental-type error). Samples errors result to the measurement errors of all power parameters. The multiplicative-type and additive-type components of sampling error can be easily compensated in contrast to nonlinearity and quantization noise. This paper discusses an approach of estimating the power parameters measurement error based on the ADC nonlinearity representation and quantization error in the stochastic function form. The nonlinearity of successive approximation ADCs is similar to a stochastic process, so this approach is especially effective for this ADC type. This approach to the error estimation is considered for the measurement method which uses a voltage and current spectral analysis. Analytical expressions of the power parameters estimate have been obtained. The dependences of error on signal parameters and ADC parameters (sampling time, resolution, integral nonlinearity) are researched. Additionally, an assessment of the “spectrum leakage” effect influence on the power parameters error has been proposed.