Cascaded-Resonator-Based Recursive Harmonic Analysis

It is well known that recursive algorithms for harmonic analysis have better characteristics in terms of monitoring the change of the spectrum in comparison to methods based on the processing of blocks of consecutive samples, such as, for example, discrete Fourier transform (DFT). This property is particularly important when applying spectral estimation in real-time systems. One of the recursive algorithms is the resonator-based one. The approach of the parallel cascades of multiple resonators (MR) with the common feedback has been generalized as the cascaded-resonator (CR)-based structure for recursive harmonic analysis. The resulting filters of the CR structure can be finite impulse response (FIR) type or the infinite impulse response (IIR) ones as a computationally more efficient solution, optimizing the frequency responses of all harmonics simultaneously. In the case of the IIR filter, the unit characteristic polynomial present in the FIR filter is replaced with an optimized characteristic polynomial of the transfer function. Such a change does not lead to an increase in computing requirements and changes only the resonator gain values. By using a conveniently linearized iterative algorithm for stability control purpose, based on the Rouche’s theorem, the iterative linear-programming-based or the constrained linear least-squares (CLLS) optimization techniques can be used

Merenje snage po standardu IEEE 1459-2010 upotrebom rezonatorskih filterskih struktura

Liberalizacijom tržišta električne energije merenje električne snage i energije u nesinusoidalnim uslovima dobilo je veliki značaj. Ta tema je još uvek predmet aktivnih rasprava, tako da ne postoji neka generalizovana teorija koja se može uzeti kao osnova za potrebe obračuna, evaluacije kvaliteta energije, detekcije izvora harmonika i kompenzacije u energetskim sistemima. Kao posledica, postojeći standardi se odnose na sinusoidalne slučajeve i ne daju definiciju reaktivne energije (i/ili snage) u nesinusoidalnim uslovima. Slično, oni ne daju specifične zahteve za tačnost i odgovarajuće uslove testiranja u prisustvu harmonijskih izobličenja. Jedini standard koji se odnosi na ovu problematiku je IEEE Std. 1459-2010 koji ne daje definiciju reaktivne snage u nesinusoidalnim uslovima. Koncept ovog IEEE standarda je baziran na razdvajanju snage na fundamentalni i nefundamentalni deo. Ovaj prilaz separacije na fundamentalni i harmonijski deo može se primeniti na najbitnije veličine i može se iskoristiti kao indikator kvaliteta. U radu je prikazana jedna efikasna algoritamska struktura za računanje električnih veličina definisanih standardom IEEE 1459-2010. Struktura se sastoji od dva dekuplovana dela. Za estimaciju spektra napona i struje korišćena je efikasna metoda bazirana na paralelnoj strukturi rezonantnih filtera sa zajedničkom povratnom vezom. U drugom delu strukture se na osnovu poznatog spektra naponskog i strujnog signala računaju komponente snage i indikatori kvaliteta na osnovu definicija datih u standardu IEEE 1459-2010. Predloženi algoritam je pogodan za primene u realnom vremenu. Realizacijom virtualnog instrumenta baziranog na PC računaru i programskom paketu LabVIEW, u cilju procene performansi algoritma, izvršene su računarske simulacije i eksperimentalna merenja i dati njihovi rezultati.This paper proposes an accurate and computationally efficient implementation of the IEEE Std. 1459-2010 for power measurements. An implementation is based on digital resonators embedded in a feedback loop. In the first algorithm stage, the unknown signal harmonic parameters are estimated. By this, the voltage and current signals are processed independently of each other. In the second algorithm stage, the unknown power components are estimated (calculated) based on estimated spectra. To demonstrate the performance of the developed algorithm, computer-simulated data and laboratory testing records are processed. Simple LabView implementation, based on the point-by-point processing feature, demonstrates techniques modest computation requirements and confirms that the proposed algorithm is suitable for real-time applications

Merenje komponenti električne snage po standardu IEEE 1459-2010

Merenje u nesinusoidalnim uslovima je u centru istraživanja i mnogo se napora ulaže da se pojam reaktivne snage star više od sedamdeset godina definiše na nov način. Postoji niz pristupa rešavanju problema definisanja snaga i/ili pokušaja koncipiranja merne instrumentacije za merenje snaga u sistemima naizmenične struje pod nesinusoidalnim uslovima. Jedini standard koji se odnosi na specifične zahteve za tačnost i odgovarajuće uslove testiranja u prisustvu harmonijskih izobličenja je IEEE Std. 1459-2010, koji ne daje definiciju reaktivne snage u nesinusoidalnim uslovima. Koncept ovog IEEE standarda je baziran na raz-dvajanju snage na fundamentalni i nefundamentalni deo. U literaturi su prisutne različite tehnike za imple-mentaciju standarda IEEE Std. 1459-2010. Ovaj standard je implementiran pomoću dva osnovna prilaza: (1) dvostepeni algoritam sa estimacijom harmonijskih spektara naponskog i strujnog signala u prvom koraku i računanjem nepoznatih komponenti snage u drugom koraku i (2) filterska implementacija kombinovana sa Clarke-Park transformacijom u slučaju trofaznog sistema. U radu je prikazana nova metoda za merenje električnih veličina definisanih standardom IEEE 1459-2010 koristeći drugi pristup. Ključni elementi su adaptivni pojasni i niskopropusni FIR filteri koji izdvajaju fundamentalnu i jednosmernu komponentu. U radu su korišćene tehnike oversemplinga i decimacionih filtera, čime se izbegavaju problemi vezani za osetljivost na zaokruživanje koeficijenata FIR kaskadnih filtera velikog reda, smanjuje obim numeričkih računanja i povećava tačnost merenja. Estimacija simetričnih komponenti vrši se pomoću matrice adaptivnih faznih korektora. U cilju procene performansi algoritma izvršene su računarske simulacije i dati njihovi rezultati.In this paper, the design and implementation of a novel recursive method for the power measurement ac-cording to the IEEE Standard 1459-2010 have been described. The most important parts are adaptive band and low-pass FIR filters that extract fundamental and dc components, respectively. In addition, by using oversampling techniques and decimation filters, coefficient sensitivity problems of the large-order FIR comb cascade structure are overridden and the parameter estimation accuracy is improved. The symmetrical components are estimated through a transformation matrix of adaptive phase shifters. The effectiveness of the proposed techniques is demonstrated by simulation results

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

Design of Digital Constrained Linear Least-Squares Multiple-Resonator-Based Harmonic Filtering

Although voiced speech signals are physical signals which are approximately harmonic and electric power signals are true harmonic, the algorithms used for harmonic analysis in electric power systems can be successfully used in speech processing, including in speech enhancement, noise reduction, speaker recognition, and hearing aids. The discrete Fourier transform (DFT), which has been widely used as a phasor estimator due to its simplicity, has led to the development of new DFT-based algorithms because of its poor performance under dynamic conditions. The multiple-resonator (MR) filter structure proposed in previous papers has proven to be a suitable approach to dynamic harmonic analysis. In this article, optimized postprocessing compensation filters are applied to obtain frequency responses of the transfer functions convenient for fast measurements in dynamic conditions. An optimization design method based on the constrained linear least-squares (CLLS) is applied. This way, both the flatness in the passband and the equiripple attenuation in the stopband are satisfied simultaneously, and the latency is reduced

Design of Digital Constrained Linear Least-Squares Multiple-Resonator-Based Harmonic Filtering

Although voiced speech signals are physical signals which are approximately harmonic and electric power signals are true harmonic, the algorithms used for harmonic analysis in electric power systems can be successfully used in speech processing, including in speech enhancement, noise reduction, speaker recognition, and hearing aids. The discrete Fourier transform (DFT), which has been widely used as a phasor estimator due to its simplicity, has led to the development of new DFT-based algorithms because of its poor performance under dynamic conditions. The multiple-resonator (MR) filter structure proposed in previous papers has proven to be a suitable approach to dynamic harmonic analysis. In this article, optimized postprocessing compensation filters are applied to obtain frequency responses of the transfer functions convenient for fast measurements in dynamic conditions. An optimization design method based on the constrained linear least-squares (CLLS) is applied. This way, both the flatness in the passband and the equiripple attenuation in the stopband are satisfied simultaneously, and the latency is reduced

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

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