On LS-Based Power Frequency Estimation Algorithms

Abstract

This paper deals with fundamental properties of the least-squares-based estimation algorithms of power frequency, such as immunity and insensitivity to harmonics and noise. This paper is motivated by a recent study that dealt with an optimal case of the distance between equidistantly spaced samples. This paper extends and generalizes that approach by decoupling of task of canceling dc component from the least-squares estimation task. Two different algorithms derived as particular cases of this generalized approach are investigated. In addition, besides the basic least-squares (LS) method, the Prony-based method previously formulated by Lobos and Rezmer has also been investigated. The task of estimation frequency from a pure sine signal without dc component presence is also considered. Finally, the third method is derived and its basic properties are shown.Index Terms-Comb filter, frequency measurement, leastsquares (LS) method, Prony-based method.

Frequency and Phase-Angle Estimation Using Ordinary Least Squares

“…The estimated current phase-angleθ[n] is given by (12) evaluated at time t = N T s and by (18), resulting in…”

“…In [16], the LMS formulation is used to fit the grid voltage into a series of cosine functions, modeling the fundamental component and the harmonics, with the frequency being detected with an autoregressive model. To obtain the grid frequency, the authors of [17], [18], and [19] proposed three techniques based on the least squares approach. The aforementioned least squares approach tries to fit the voltages into a single or a series of sin/cos functions.…”

Non recursive multi-harmonic least squares fitting for grid frequency estimation

“…The choosing of the time window T is crucial to simplify the expression (9). It is possible to choose a time window equal to an integer multiple of the variable x.…”

“…The results obtained in different conditions using the proposed method and two other algorithms proposed in the literature will be shown. The method proposed by Park et al in [7] is one of the most interesting algorithm using the least squares approach [9] without iterations. The interpolated DFT (ip-DFT) is a fast frequency estimation algorithm and, in the grid frequency estimation problem, it produces good results in terms of accuracy [15].…”

“…Moreover, NRLS2 has in most cases better performance compared with the ip-DFT and the Park's method. These two algorithms represent in the literature the best compromise between accuracy and computational demand [6,7,9].…”