On Multiple-Resonator-based Implementation of IEC/IEEE Standard P-Class Compliant PMUs

This article deals with the implementation of the P-Class PMU compliant with IEC/IEEE Standard 60255-118-1:2018 by usage of a multiple-resonator (MR)-based approach for harmonic analysis having been proposed recently. In previously published articles, it has been shown that a trade-off between opposite requirements is possible by shifting a measurement time stamp along the filter window. Positioning the time stamp in a proximity of the time window center assures flat-top frequency responses. In this article, through simulation tests carried out under various conditions, it is shown that requirements of the IEC/IEEE Standard 60255-118-1:2018 can be satisfied by the second and third order MR structure for particular conditions of the time stamp location

Maximally Flat-Frequency-Response Multiple-Resonator-Based Harmonic Analysis

This paper presents an improved approach to the recently proposed multiple-resonator-based method for the harmonic analysis that has been provided in the previous papers. Previously, two inherent particular cases have been considered. In these cases, reference points in which estimation is performed are located either in the middle or at the end of the observation interval. The first case exhibits a good noises and unwanted harmonics attenuation but possesses a large delay time. In the second case, the filters are able to form a zero-flat phase response about the operation frequency and hence able to provide instantaneous estimates, but with large overshoots caused by resonant frequencies at the edges of the passband, and the high level of the sidelobes, that also makes it susceptible to interharmonics and noise interference. The aim of this paper is to propose a compromised solution provided by the tradeoff between those opposite requirements by shifting this point along the observation interval. This way the frequency responses of the estimator are reshaped. A maximally flatness of the frequency response in the operation harmonic frequency is kept in all cases, but only locating the reference point in a fraction around the center of the observation interval provides flat-top frequency responses. The effectiveness of the proposed estimation technique is shown through simulations

Constrained-group-delay-optimized multiple-resonator-based harmonic analysis

Recently, a multiple-resonator structure was proposed as a robust and computationally efficient tool for harmonic analysis. Two trivial cases have been previously observed. The first case exhibits good out-of-band suppression and elimination of unwanted harmonics, but with a high latency. In the second case, a phase frequency response around the passband centre is zero-flat, that provides fast estimates. However, in this case, resonant peaks at the ends of the passband and high interharmonic gains cause large overshoots. In general, the basic algorithm performance requirements: selectivity and speed, are contradictory which makes it impossible to completely fulfil both of them. In this paper, the Constrained Linear Least-Squares (CLLS) optimization method is used to obtain a compromise solution. As a result, the resonant peaks in the passband are avoided and side lobes are mitigated, simultaneously minimizing the group delay in the middle of the passband. Performed simulations confirmed the effectiveness of the proposed algorithm

Frequency-response-controlled multiple-resonator-based harmonic analysis

This Letter proposes a modified method for the dynamic harmonic analysis of signals with non-stationary harmonics, which is based on the previously proposed multiple-resonator observer structure. An optimisation technique is applied to reshape frequency responses of the basic transfer functions. This method, by using a parallel structure with common feedback, is very robust and, in addition, allows a reduction of the computational burden. The proposed method has been investigated for up to 64 harmonics, using LabView software package, under different conditions, and confirmed to be valuable and efficient tool for signal components estimation

IIR Cascaded-Resonator-Based Complex Filter Banks

The use of a filter bank of IIR filters for the spectral decomposition and analysis of signals has been popular for many years. As such, a new filter-bank resonator-based structure, representing an extremely hardware-efficient structure, has received a good deal of attention. Recently, multiple-resonator (MR)-based and general cascaded-resonator (CR)-based filters have been proposed. In comparison to single-resonator-based analyzers, analyzers with a higher multiplicity of resonators in the cascade provide lower side lobes and a higher attenuation in stopbands. In previous works, it was shown that the CR-based filter bank with infinite impulse response (IIR) filters, which is numerically more efficient than one with finite impulse response (FIR) filters, is suitable for dynamic harmonic analysis. This paper uses the same approach to design complex digital filter banks. In the previous case, the optimization task referred to the frequency responses of harmonic filters. In this work, the harmonic filters of the mother filter bank are reshaped so that the frequency response of the sum (or difference, depending on the parity of the number of resonators in the cascade) of two adjacent harmonic filters is optimized. This way, an online adaptive filter base can be obtained. The bandwidth of the filters in the designed filter bank can be simply changed online by adding or omitting the output signals of the corresponding harmonics of the mother filter