The quality of the supplied power by electricity utilities is regulated and of concern to the end user. Power quality disturbances include interruptions, sags, swells, transients and harmonic distortion. The instruments used to measure these disturbances have to satisfy minimum requirements set by international standards. In this paper, an analysis of multi-harmonic least-squares fitting algorithms applied to total harmonic distortion (THD) estimation is presented. The results from the different least-squares algorithms are compared with the results from the discrete Fourier transform (DFT) algorithm. The algorithms are assessed in the different testing states required by the standards.

This overview paper presents and compares different methods traditionally used for estimating damped sinusoid parameters. Firstly, direct nonlinear least squares fitting the signal model in the time and frequency domains are described. Next, possible applications of the Hilbert transform for signal demodulation are presented. Then, a wide range of autoregressive modelling methods, valid for damped sinusoids, are discussed, in which frequency and damping are estimated from calculated signal linear self-prediction coefficients. These methods aim at solving, directly or using least squares, a matrix linear equation in which signal or its autocorrelation function samples are used. The Prony, Steiglitz-McBride, Kumaresan-Tufts, Total Least Squares, Matrix Pencil, Yule-Walker and Pisarenko methods are taken into account. Finally, the interpolated discrete Fourier transform is presented with examples of Bertocco, Yoshida, and Agrež algorithms. The Matlab codes of all the discussed methods are given. The second part of the paper presents simulation results, compared with the Cramér-Rao lower bound and commented. All tested methods are compared with respect to their accuracy (systematic errors), noise robustness, required signal length, and computational complexity.