Modified Second-Order Generalized Integrators With Modified Frequency Locked Loop for Fast Harmonics Estimation of Distorted Single-Phase Signals

Abstract

This paper proposes modified Second-Order Generalized Integrators (mSOGIs) for a fast estimation of all harmonic components of arbitrarily distorted single-phase signals such as voltages or currents in power systems. The estimation is based on the internal model principle leading to an overall observer system consisting of parallelized mSOGIs. The observer is tuned by pole placement. For a constant fundamental frequency, the observer is capable of estimating all harmonic components with prescribed settling time by choosing the observer poles appropriately. For time-varying fundamental frequencies, the harmonic estimation is combined with a modified Frequency Locked Loop (mFLL) with gain normalization, sign-correct anti-windup and rate limitation. The estimation performances of the proposed parallelized mSOGIs with and without mFLL are illustrated and validated by measurement results. The results are compared to standard approaches such as parallelized standard SOGIs (sSOGIs) and adaptive notch filters (ANFs). ; for more details see [1]) *** This long version includes (i) more detailed explanations, (ii) more simulation and measurement results and (iii) a thorough theoretical analysis in its Appendix.CONTENTS ‡ C.M. Hackl is with the Munich University of Applied Sciences (MUAS) and head of the "Control

A unified method for signal parameter estimation of arbitrarily distorted single-phase grids with DC-offset

“…To take appropriate countermeasures, firstly these distortions must be identified as fast and precise as possible to protect users from malfunctioning equipment and to prevent destruction of electronic devices. Therefore, in the recent years, much effort has been put into this research question field which resulted in the development of Second-Order Generalized Integrators (SOGI)s [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12].…”

“…All mentioned papers above have in common that they use the so called standard SOGI with only one gain which only allows for a limited tuning and yields a rather slow estimation performance (> 40 − 50 ms). [5] solved this problem by introducing a so called modified SOGI with two gains which allows "(theoretically) for an arbitrarily fast estimation". Nevertheless, DC-offset was not considered.…”

“…OBSERVER (FAO) This section presents the theoretical background for the development and implementation of the FAO. It consists of the parallelization of mSOGIs (as introduced in [5]) and a DCI. The principle idea of the FAO is based on the Internal Model Principle (as introduced by Wonham in the 1980s [30]).…”

“…If all initial values in x(0) = x 0 and the angular frequency ω were known, then (5) could perfectly reduplicate the singlephase signal y as in (1). But, since those values are not known a priori, an observer must be designed which is actually feasible since the dynamics 5 as a straight forward extension of the proof in [31] shows.…”

A Unified Method for Online Detection of Phase Variables and Symmetrical Components of Unbalanced Three-Phase Systems with Harmonic Distortion

“…As already noted above, for an online detection of the symmetrical components, the quadrature signals of the phase quantities are required. These can be estimated by Second-Order Generalized Integrators (SOGIs) [8,9], which are also called Adaptive Notch Filters (ANFs) [6]. Since SOGIs (or ANFs) require an estimate of the signal angular frequency to compute the quadrature signal, any time-varying change of the frequency degrades the estimation performance of the SOGIs.…”