Application of the “Worst Case” Method to Estimate the Spectrum and Power Measurement Error Caused by ADC Imperfection

The complex spectrum is used as a basic parameter for calculating spectrum and power parameters of the signals of real electrical power grids. For measuring the complex spectrum, the most popular is the discrete Fourier transform technique. Analog-to-digital converters are used to convert voltage and current samples to the digital form. The conversion function of analog-to-digital converters is not ideal. The largest contribution to the spectrum measurement error is due to the influence of quantization error and nonlinearity, since these components almost impossible to reduce by offset-adjustment and calibration. The “worst case” method can be applied to estimate the measurement error of the spectrum, electric power and other parameters. This method makes it possible to estimate “from above” the measurement error of considerate parameters, which makes it in demand in applications where the error estimate must necessarily exceed its real value. The analytical relationships are obtained for calculation of the error estimation of spectrum and power parameters caused by quantization error and nonlinearity. The influence of parameters of input signals and analog-to-digital converter on the error of the measured parameters is investigated. The influence of the nonlinearity form on the measurement error of considered parameters is estimated by simulation modeling in Matlab environment. It is shown that for all the considered nonlinearity forms, the error estimation result does not exceed the “worst case” method estimation.