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

Abstract

This paper presents a method for online detection of symmetrical components of arbitrarily distorted and biased three-phase input signals. This method is based on Second-Order Generalized Integrators (SOGIs), for which a new tuning based on a gradient search is presented to achieve the fastest possible estimation. Frequency estimation is achieved by a Frequency Locked Loop (FLL) with Gain Normalization (GN) for which an Output Saturation (OS) is applied; this OS guarantees stability of the overall system. Offset detection is implemented by a combination of High-Pass Filter (HPF) and HPF-Amplitude Phase Correction (APC); the HPF filters out any offset, where the APC reconstructs the original offset-free signal. An identical method (APC) can be used for the implemented Low-Pass Filter (LPF) used for noise filtering. The resulting estimates are then used for Harmonic Sequence Detection (HSD) of each harmonic. For the overall system, stability is proven. The estimation performances of the proposed overall system are verified by simulation results. The improvements in tuning and offset detection are compared to standard approaches.

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

“…In future contributions, the following three main goals shall be achieved: (i) Estimation of arbitrary harmonic content without knowing the harmonic orders, (ii) improvement of the frequency adaption to achieve significantly faster estimation speeds and (iii) application of the proposed FAO to three-phase systems to extract symmetrical components of all harmonic components (i.e. to extend the results in [20]).…”

“…The frequency adaption usually denotes the bottleneck of the estimation since it significantly decelerates the settling time of the overall estimation process (e.g. [12]: 1,5 s; [20]: 120 ms; [22]: 60 ms). Moreover, the presented FLLs can get locked at zero frequency or even become unstable.…”

Coordinate Transformation-Free Observer-Based Adaptive Estimation of Distorted Single-Phase Grid Voltage Signal

“…As a result, bounded input bounded output (BIBO) stability of the proposed multiple adaptive observer can be established using Theorem 2 given in [38]. Moreover, the boundedness and exponential decay of the signal estimation error can be established using Theorem A.3 given in [38]. It is to be noted here that this result is mathematically weaker than the global exponential stability results presented in [21], [22].…”

“…For properly tuned observer gain matrix L i , individual observers are stable. As a result, bounded input bounded output (BIBO) stability of the proposed multiple adaptive observer can be established using Theorem 2 given in [38]. Moreover, the boundedness and exponential decay of the signal estimation error can be established using Theorem A.3 given in [38].…”

A Unified Method for Generic Signal Parameter Estimation of Arbitrarily Distorted Single-Phase Grids With DC-Offset

“…Only few papers [7], [12], [14], [15], [22], [23], [24], [25], [26] explicitly deal with multiple harmonics. In [14], an input signal with six harmonics and varying fundamental frequency was considered; the overall estimation time took about 1.5 s. Additionally, the authors proved the stability of the parallelized SOGI system (without considering the FLL) but did not give a reasonable tuning rule for their observer.…”