Presence Of Harmonic Distortion Research Articles

ТЕСТУВАННЯ ЕЛЕКТРООБЛАДНАННЯ НА НЕСПРИЙНЯТЛИВІСТЬ ДО ПРОВАЛІВ НАПРУГИ, КОРОТКОЧАСНИХ ПЕРЕРИВАНЬ ТА ЗМІН НАПРУГИ

The article examines the testing of electrical equipment for immunity to voltage dips, short-term interruptions, and voltage changes. Special attention is paid to the influence of the starting point of the dip on the sensitivity of electrical equipment, as well as to the study of the resistance of the electromagnetic relay to voltage dips, phase angle jumps, and the starting and ending points of dips. The reaction mechanism of the electromagnetic relay to a voltage drop, its sensitivity to a change in frequency, the presence of harmonic distortions and changes in the nominal value of the voltage are analyzed. The symmetry of a quarter cycle with respect to a point on the wave is considered separately. Ref. 6, fig. 6.

Model Predictive Control of a Modular Multilevel Converter with Reduced Computational Burden

Recent advances in high-power applications employing voltage source converters have been primarily fuelled by the emergence of the modular multilevel converter (MMC) and its derivatives. Model predictive control (MPC) has emerged as an effective way of controlling these converters because of its high response. However, the practical implementation of MPC encounters hurdles, particularly in MMCs featuring many sub-modules per arm. This research introduces an approach termed folding model predictive control (FMPC), coupled with a pre-processing sorting algorithm, tailored for modular multilevel converters. The objective is to alleviate a significant part of the computational burden associated with the control of these converters. The FMPC framework combines multiple control objectives, encompassing AC current, DC current, circulating current, arm energy, and leg energy, within a unified cost function. Both simulation studies and real-time hardware-in-the-loop (HIL) testing are conducted to verify the efficacy of the proposed FMPC. The findings underscore the FMPC’s ability to deliver fast response and robust performance under both steady-state and dynamic operating conditions. Moreover, the FMPC adeptly mitigates circulating currents, reduces total harmonic distortion (THD%), and upholds capacitor voltage stability within acceptable thresholds, even in the presence of harmonic distortions in the AC grid. The practical applicability of MMCs, notwithstanding the presence of a large number of sub-modules (SMs) per arm, is facilitated by the significant reduction in switching states and computational overhead achieved through the FMPC approach.

Demodulation of Three-Phase AC Power Transients in the Presence of Harmonic Distortion

Load switches in power systems may cause oscillations in active and reactive power flow. Such oscillations can be damped by synthetic inertia provided by smart inverters providing power from DC sources such as photovoltaic or battery storage. However, AC current provided by inverters is inherently non-sinusoidal, making measurements of active and reactive power subject to harmonic distortion. As a result, transient effects due to load switching can be obscured by harmonic distortion. An RLC circuit serves as a reference load. The oscillation caused by switching in the load presents as a dual-sideband suppressed-carrier signal. The carrier frequency is available via voltage data but the phase is not. Given a group of candidate signals formed from phase voltages, an algorithm based on Costas Loop that can quickly quantify the phase difference between each candidate and carrier (thus identifying the best signal for demodulation) is presented. Algorithm functionality is demonstrated in the presence of inverter-induced distortion.

Selective Harmonic Current Rejection for Virtual Oscillator Controlled Grid-Forming Voltage Source Converters

Virtual oscillator control (VOC) is a nonlinear grid-forming controller that simultaneously achieves the functionality of output voltage control and primary control layers in a power electronics interfaced distributed generation (DG) unit. Unlike conventional phasor-based primary control methods such as the droop control and virtual synchronous machine control, VOC is a time-domain controller that can guarantee almost global asymptotic synchronization. However, the high-frequency dynamics has largely been ignored in the analysis of VOC in prior art; as a result, VOC-based DGs fail to suppress harmonic current in the presence of harmonic distortion in the network-side voltage. In this work, we demonstrate that frequency-domain method can be used for oscillator-based converters in the high-frequency range, specifically, for harmonic mitigation in the converter output current. We propose a virtual impedance-based selective harmonic current suppression method, and demonstrate that it is better to use the network-side current feedback rather than that of the converter-side current for VOC implementation with virtual impedance control. Established harmonic rejection strategies for grid-following and conventional grid-forming converters are compared with the proposed method for VOC. Through impedance-based analysis, we demonstrate that the proposed method augments the passivity range of the converter terminal response with a much simpler implementation. The proposed harmonic suppression strategy is validated through hardware experiments using a single-phase inverter prototype.

A Novel Approach for the Error Correction of CT in the Presence of Harmonic Distortion

Current transformers (CTs) are extensively used for the measurement of electrical energy, and hence they play a crucial role in the revenue generation for power distribution utilities. The novelty of this paper is that it presents artificial neural network (ANN) application for the ratio and phase angle error corrections of CTs in the presence of harmonic distortions. In this paper, the behaviors of silicon iron alloy and nanocrystalline alloy CTs are examined by the means of a number of experimental tests under the sinusoidal and distorted waveform conditions. The relation between the nature of CTs secondary current waveforms (CTSwf) with their metrological properties, connected burdens, and nature of load currents (linear or nonlinear) is established. The training data are obtained by the nature of CTSwf in terms of amplitude errors, time shifts, and deviations caused by different harmonic contents between input and output quantities. The ANN is trained for various operating conditions. The implementation of the error correction system and data acquisition is done using dSPACE 1104 software. The experimental results illustrate that the proposed technique can be used for error compensation in case of sinusoidal and the distorted waveform composed of fundamental and many harmonics.

Waveform-Based Method for Fast and Accurate Identification of Subsynchronous Resonance Events

An increasing number of unstable subsynchronous resonance (SSR) has occurred for wind farms recently. These events can lead to significant loss of generation, threatening the safe operation of the system, and even damaging the generators. Accurate knowledge of SSR characteristics (SSR frequency, current magnitude, and damping) at an early stage of the event is critical for its effective mitigation. This paper proposes a method for fast and accurate identification of an SSR event and its characteristics. It takes advantage of time-stamped waveform measurements that are typically available on the terminals of series compensated transmission lines. It uses the known model of the line as a “filter” to extract the SSR components. Case studies demonstrate that the proposed algorithm can accurately compute the SSR frequency, SSR current magnitude, and damping in around one SSR cycle or less. In addition to line parameters uncertainties, the method has also proven to remain robust in the presence of harmonic distortions and reduced waveform sampling rates.

Efficiency in Distribution Networks with Harmonic Distortion

Smart grids are reliable and easy to operate though it increases the challenges of harmonic distortion due to many electronic devices. Traditionally, harmonic distortion is neglected when efficiency in distribution networks is determined. They are usually calculated using fundamental frequency only. The efficiency of equipment and the overall efficiency of the network is negatively affected by the harmonic distortion. Thus, this paper seeks to develop a methodology and new formulae for determining individual and overall efficiencies when harmonic distortion is present in a distribution network. The methodology and new formulae are developed using the directional active power flow. A radial distribution network with two harmonic sources (non-linear load and Solar Photovoltaic(PV)) and a capacitor bank is used for analysis. The method and case-specific formulae are applied in this case study and results are generated. A harmonic filter is designed and implemented. It is indicated that the overall efficiency of the distribution network as well as the individual efficiency of the network is affected by the presence of harmonic distortion. Once the harmonic filter is implemented the overall efficiency of the network is improved significantly. The methodology and formulae have shown to be effective since it gives a better understanding of efficiency when distortion exists and its application is recommended for industrial use.

Оцінювання впливу нелінійних несиметричних навантажень на низьковольтні електричні мережі

The possibility of detection and evaluation of the influence of distortion sources (asymmetry and higher harmonics) on the quality of electricity of three-phase networks using instantaneous conditional capacities of the reverse and zero sequences is analyzed. Such sources are nonlinear consumers, whose share in total load increases year by year. Nonlinear consumers consume active power at the main frequency and at the same time generate power to the higher harmonics in the network. Significantly in low voltage networks, there is also a share of consumers with asymmetric load of phases. On the basis of the theory of instantaneous power, instantaneous values are allocated on the basis of which informative values can be formed that allow characterizing the influence of nonlinear and asymmetric consumers on deterioration of the quality of electricity, as well as assessing the inefficiency of the distribution network of the electricity supplying organization. To evaluate the impact of nonlinear and asymmetric consumers, it is expedient to use instantaneous conditional capacities  and , which are essentially the product of instantaneous direct current voltage on the current of the reverse and zero sequence, and to assess the fault of the electricity supply organization, which consists in the ineffective construction of the distribution network — instant conditional capacities  and , which is essentially a product of instantaneous current of direct sequence on the back and zero sequence voltage. The formation of these values is carried out using the system of α, β, 0-coordinates, which greatly simplifies the construction of measuring devices. In the presence of harmonic distortions, the RMS values of conditional capacities  and  grow and make up from one to ten percent relatively to the main power generated by the voltage and current of the main frequency of the direct sequence. In the case of load asymmetry, the average values of these quantities increase. At the same time an increase  and testifies to the lack of power of power transformers and the inappropriate use of transformers with the scheme of winding connection "star / star with zero sequence" for powering nonlinear consumers.

Dynamic Phasor-Based Analysis of Unbalanced Three-Phase Systems in Presence of Harmonic Distortion

In this paper, a frequency-based analytical approach for dynamic analyzing of unbalanced three-phase systems in the presence of harmonic distortion using sequence domain is put forward. As will be shown, classical symmetrical components proposed by Fortescue is not applicable under nonsinusoidal periodic condition. In such cases, generalized symmetrical components proposed by Tenti et al. can be used to calculate sequences from phase domain values. However, it introduces a new sequence component called residual component, which has a different value for each phase and cannot be directly obtained based on sequence networks. To such aim, using dynamic harmonic domain, an approach that makes it possible to use features of classical symmetrical components and modify the outputs to compute sequences based on the concept of generalized symmetrical components is proposed. Moreover, it is shown that using equivalent circuit for triplen harmonics is essential to find a relation between residual components since if sequences are connected in parallel, it is not possible to modify results of classical symmetrical components and this equivalent circuit should be directly analyzed. Time domain software is used to perform conventional lumped circuit simulation and validate the time domain responses resulted from DHD.

Optimal capacitor placement in distorted distribution systems considering resonance constraint using multi‐swarm particle swarm optimisation algorithm

Optimal capacitor placement in distribution systems has been studied for many reasons such as the improvement of voltage profile, mitigation of total harmonic distortion, and reduction of power losses. In this study, a new approach is presented for capacitor placement in the presence of harmonic distortion along with a proposed resonance index (RI). In this approach, a sensitivity analysis is first applied to find candidate buses. After that, the size and location of capacitors are optimised by a proposed fitness function. The fitness function includes a fuzzy membership function of annual net benefit, maximum THD of voltage, maximum voltage deviation, and a resonance constraint. This procedure supports different load levels employing fixed and switched capacitors. Also, a new RI is presented to prevent resonance conditions. Finally, the approach is tested on an IEEE 18-bus and an IEEE 69-bus system using the multi-swarm particle swarm optimisation algorithm. The simulation results show the efficiency of the method in comparison with the other methods.

Compensation of the reactive power in the presence of higher voltage harmonics at coke plants

The capacitive compensation of reactive power in the presence of harmonic distortion in the supply voltage is considered. Such distortion may be introduced both by factors in the external grid and by factors within the enterprise. That must be taken into account in selecting systems for reducing the effect of higher harmonics on compensating capacitor banks and improving the power quality at coke plants.

Characterization and Error Compensation of a Rogowski Coil in the Presence of Harmonics

This paper reports the results of an experimental study dealing with a commercial Rogowski coil current transducer (RCCT) in the presence of harmonic distortion. The RCCT was observed under two conditions: 1) sinusoidal excitation with frequencies from 50 to 750 Hz and 2) nonsinusoidal excitation using fundamental frequency and one harmonic, with adjustable amplitude and phase shift. The experimental results show only a weak dependence of the harmonic current ratio error and phase displacement on the amplitude and phase shift of the excitation harmonic. The phase displacement is also independent of the conductor position within the Rogowski coil window. An error compensation method, based on the frequency response, was implemented and tested with a distorted waveform. The compensation method allows one to obtain an improvement of the RCCT accuracy class from 1% and 1 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$^{\circ}$</tex></formula> , in the case of a sinusoidal signal at mains frequency, to 0.05% and 0.05 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$^{\circ}$</tex></formula> , both for the fundamental and the distorted signal harmonics.

Improvement of Hall Effect Current Transducer Metrological Performances in the Presence of Harmonic Distortion

The performance of Hall effect current transducers (HECTs), under distorted waveform conditions, is usually characterized by means of a frequency response test. In this paper, it was investigated if frequency response is able to correctly evaluate the ratio and the phase errors under distorted conditions. Two HECTs, with the accuracy class level of 1% and 0.5%, respectively, were experimentally characterized under two conditions: 1) sinusoidal excitation with frequencies ranging from 50 to 750 Hz, which is the well-known frequency response test, and 2) nonsinusoidal excitation using fundamental frequency and one harmonic with adjusted amplitude and phase shift. It was found that ratio and phase errors are weakly affected by the harmonic amplitude and phase shift, with respect to the fundamental in the accuracy level of 0.1% and 0.05°. They have, instead, a strong dependence from conductor location in the HECT window. These results suggest that the frequency response approach for the evaluation of HECT performance, under distorted waveform conditions, can be used for an error compensation method only if the position of the primary conductor is known. An error compensation method, based on the frequency response, was implemented and tested with a distorted waveform composed of fundamental and many harmonics. For each of the harmonic components, the errors were reduced to one tenth of the measured ones.

Static Meters for the Reactive Energy in the Presence of Harmonics: An Experimental Metrological Characterization

Electricity metering plays a crucial role for all the commercial transactions on the energy market. Thus, an accurate evaluation of the performance of the electricity metering equipment is required not only in the reference operating conditions but also in the presence of disturbances affecting the power systems. As regards this matter, this paper analyzes the main aspects related to the metrological characterization of the static meters for the reactive energy in the presence of harmonic distortion. Attention is focused not only to the meters covered by the current standards but also to the meters of better accuracy and to the reference standard meters. The analysis is supported by several experimental tests.

A Novel Approach to Current Transformer Characterization in the Presence of Harmonic Distortion

The current transformer (CT) performance under distorted waveform conditions is usually characterized by means of the frequency-response test. In this paper, a new way to characterize CTs, closer to real operation conditions, is proposed. The harmonic phase-angle and ratio errors are measured using a nonsinusoidal current composed of fundamental and one harmonic with adjustable phase shift. The new method was tested by determining the performance of two metering class CTs commonly used by the Italian power company. The errors measured using the proposed approach are larger than the ones obtained with the frequency response. This result suggests that the frequency-response approach for the evaluation of CT performance under distorted waveform conditions is not a reliable method.

The Measurement of Reactive Energy in Polluted Distribution Power Systems: An Analysis of the Performance of Commercial Static Meters

This paper presents a comparative analysis of the performances of both a traditional induction meter and various types of commercial static meters for reactive energy in the presence of harmonic distortion. This is a topical issue, since there are several types of static meters on the market, based on different principles of construction. In accordance with current standards, these meters are designed to operate in sinusoidal conditions and their performance is not tested in the presence of harmonic distortion. However, with the increase of pollution levels in power systems, the meters may be used even in the presence of distorted voltages and/or currents; in such cases, their accuracy may be very different from the nominal conditions, and the various meters may lead to different measurements of energy for the same load conditions. In this paper, the analysis is supported by several experimental tests, performed by means of a power calibrator.

A Repetitive-Based Controller for a Power Factor Precompensator

In this paper, a repetitive-based controller for a boost-based power factor precompensator is presented. The controller guarantees voltage regulation with a power factor close to unity, despite of the presence of harmonic distortion in the source voltage and uncertainties in the system parameters. It is shown that the repetitive scheme considered here is, in fact, equivalent to a bank of resonant filters, which has shown to be a useful technique in harmonic compensation. Out of this equivalence, a negative feedback structure is obtained for the repetitive scheme which is aimed for the compensation of odd harmonics only. This is in contrast to usual positive feedback repetitive schemes aimed to compensate for all harmonic components. The repetitive scheme consists on a simple feedback array involving a time delay plus a feedforward path, which is simple to implement. The closed-loop stability analysis of such and infinite-dimensional system is performed appealing to the well-known small gain theorem. Experimental results in a 400-W boost-based power factor compensator (PFC), with a fixed-point digital signal processor (DSP)-based implementation of the proposed controller, are provided to assess the performance of the controlled system.

Detrimental Effects of Capacitors in Distribution Networks in the Presence of Harmonic Pollution

The main goal of this paper is to analyze the behavior of an electric power network in the presence of harmonic distortion, when capacitors are installed. The work starts from a case study, where failure and malfunctioning of an industrial plant are described with the help of experimental measurements. The theoretical and mathematical details of the phenomena involved are analyzed by suitable computer simulations. The study is performed by considering some important electrical quantities, evaluated according to the definitions proposed by the standard IEEE 1459. The results put in evidence that using some typical quantities, such as the power factor, could lead to ambiguous conclusions in evaluating the actual "quality" of the loads, and this can assume special importance in virtue of the economic relevance of such quantities

A novel three‐phase time domain load modelling technique using instantaneous symmetrical components

AbstractThis paper presents a new time domain load modelling technique based on the method of Instantaneous Symmetrical Components (ISC) for three‐phase unbalanced and distorted power system loads. ISC is used here to obtain instantaneous symmetrical voltage and current components and these components are used in the calculation of the symmetrical component model parameters, resistance (R(0,1,2)), inductance (L(0,1,2)), capacitance (C(0,1,2)) and a harmonic instantaneous current source (j (t)), which are all connected in parallel. The results cover four cases of the system operation and the load parameters are found for each case, even in the presence of harmonic distortion. Consequently, it is shown that the developed method is a very powerful modelling technique to model time varying, unbalanced and distorted three‐phase loads, such as general loads: i.e. residential and commercial buildings. Copyright © 2004 John Wiley &amp; Sons, Ltd.

Evaluating power system unbalance in the presence of harmonic distortion

This paper presents a new method to evaluate power system unbalance in the presence of harmonic distortion. The balanced, the first unbalanced, and the second unbalanced components are obtained from the original three-phase current and voltage phasors of each harmonic component. The equivalent root-mean-square (RMS) value of three-phase voltage and current is then decomposed into the balanced fundamental, the unbalanced fundamental, the balanced harmonic, and the unbalanced harmonic components. The same decomposition is applied to the apparent power, and the system unbalance can then be evaluated through the proposed system total unbalance distortion factor. The unbalanced fundamental, the balanced harmonic, and the unbalanced harmonic distortion factors are defined. These distortion factors clarify the interleaving between the unbalance and harmonic distortion, and are suitable for unbalance evaluation in the presence of harmonics. Numerical examples are also presented to illustrate the application of the proposed method on the study and characterization of unbalance in power systems.