Presence Of Interharmonics Research Articles

Ground and phase fault classification for half-wavelength transmission lines relaying purposes

In this work, a new fault classification and phase selection methodology for half-wavelength (HWL) transmission lines is developed. Initially, the basic principles of phase currents transformations are presented. Then, an innovative faulted phase selection methodology based on the variation of those currents is developed. The behavior of the electrical quantities related to short circuits in such long lines is very different when compared to conventional lines. The faulted phase selection method employed in this work is built on the fact that those decoupled currents are expected to not vary or vary less than the others, depending on how many phases are in short circuit. The robustness of the method was analyzed considering different load conditions and fault resistances. Furthermore, different sampling rates were considered for the phase currents. Extensive simulation studies showed that the developed method can accurately identify the fault types and the faulted phase with a relatively low sample rate. Moreover, the simulation results showed that the proposed method is not affected by the presence of inter-harmonics and responds precisely with high-resistance faults. The proposed algorithm presented errors smaller than 0.04%.

A New Analytical Model of Single-Phase Diode Bridge Rectifiers in the Presence of Interharmonics in Supply Voltage

In this paper, a new accurate and comprehensive analytical model of harmonic and interharmonic distortion produced by a single-phase AC/DC diode bridge rectifier (DBR) is presented. Its main and new characteristic is the ability to consider the presence of interharmonics in addition to harmonics in the voltage at the terminals of DBR due to the background distortion. Analytical expressions able to predict DC voltage and AC current either in time or frequency domains are obtained. Several numerical and experimental tests have been performed showing very accurate results. The proposed model presents all the advantages of analytical models (e.g., fastness); therefore, it can be easily integrated with iterative harmonic and interharmonic analysis procedures. Subsequent applications are the possibility to perform parametric analyses and probabilistic studies, to derive harmonically and interharmonically coupled admittance matrices, to help in introducing standard limits for interharmonics.

The Influence of Power Network Disturbances on Short Delayed Estimation of Fundamental Frequency Based on IpDFT Method with GMSD Windows

This paper presents an application of the IpDFT spectrum interpolation method to estimate the fundamental frequency of a power waveform. Zero-crossing method (ZC) with signal prefiltering was used as a reference method. Test models of disturbances were applied, based on real disturbances recorded in power networks, including voltage harmonics and interharmonics, transient overvoltages, frequency spikes, dips and noise. It was determined that the IpDFT method is characterized by much better dynamic parameters with better estimation precision. In an example, in the presence of interharmonics, the frequency estimation error was three times larger for the reference method than that for the IpDFT method. Furthermore, during the occurrence of fast transient overvoltages, the IpDFT method reached its original accuracy about three times faster than the ZC method. Finally, using IpDFT, it was possible to identify the type of disturbances: impulsive, step changes of frequency or voltage dips.

PMU-Assisted Zone-3 Protection Scheme for PV Integrated Power Systems Immune to Interharmonics

In this article, the impact of interharmonics generated in photovoltaic (PV) integrated systems on phasor measurement unit (PMU)-assisted zone-3 protection scheme (Z3PS) is investigated. Generally, PMUs integrated with conventional discrete Fourier transform (DFT) algorithm are employed to compute time-synchronized voltage and current phasors. However, the presence of interharmonics in PV integrated systems may force to cease the proper performance of Z3PS since DFT algorithm integrated with PMUs fails to identify and eliminate closely spaced interharmonics resulting in incorrect computation of phasors. This phenomena further leads to improper estimation of apparent impedances by relays. To overcome this issue, a phasor signal processing model (PSPM) is proposed where a preprocessing filtering step involving signal processing by an estimation of signal parameters via rotational invariance techniques (ESPRIT) or matrix pencil (MP) algorithm is added before PMUs. Proposed PSPM helps in eliminating noise and closely spaced interharmonics present in the signals and consequently, enhances the performance of PMU-assisted Z3PS. Integration of PV to IEEE 39-bus system is done in PSCAD/EMTDC software whereas ESPRIT and MP algorithms are implemented in MATLAB. Comparative analysis with exiting methods are carried out for systems operating under different conditions to examine the performance of the proposed Z3PS.

Power measurement accuracy analysis in the presence of interharmonics

Interharmonics present in voltage/current signals affect the measurement accuracy of power quantities defined in standard IEEE 1459. In this paper, the measurement errors caused by the measurement time intervals not satisfying integral multiple periods of interharmonics are discussed. First, the mathematical models of power quantities between arbitrary frequency components are constructed. Next, four parameters that affect the power measurement accuracy are summarized, which are interharmonic frequency, measurement start time, voltage/current initial phase angle, and the length of measurement time intervals. The simulation results and corresponding analysis show the effects of each parameter on measurement accuracy. In conclusion, the maximum errors are always caused by interharmonics within particular frequency range which relates to the length of measurement time interval. Moreover, the relative errors of power quantities can be restricted within 1%, by using a time interval of 3 s, even if under the condition of selecting the worst measurement start time.

Distance relaying algorithm for phasor measurement unit assisted zone‐3 relays of series compensated wind integrated system

The signals of wind integrated system are contaminated with inter-harmonic components which may result in erroneous calculations of apparent impedance seen by the distance relays. Therefore, it is indispensable to filter these signals before being used by relays. Presently, the measurements obtained from phasor measurement units (PMUs) are effectively used by distance relays for zone-3 protection. However, PMUs use discrete Fourier transform (DFT) algorithm to compute phasors which may produce incorrect results in presence of inter-harmonics. To overcome this issue, a matrix pencil method is proposed as a pre-processing filtering technique for PMU assisted distance relays. The analog input signals to PMUs are filtered by the matrix pencil algorithm to eliminate inter-harmonics present in the signals and the phasors are computed using DFT algorithm. These phasors are utilized by zone-3 distance relays to estimate the impedance trajectories. To test the effectiveness of proposed distance relaying algorithm, IEEE 14-bus system with a series compensated line is integrated with wind energy and is simulated under diverse test cases of different operating conditions. The impacts of fault resistances, type of faults and fault inception angles on the performance of proposed technique are examined and the results are compared with different signal processing techniques.

Statistic, probabilistic, correlation and spectral analyses of regenerative braking current of dc electric rolling stock

Purpose. Defining and analysis of the probabilistic and spectral characteristics of random current in regenerative braking mode of DC electric rolling stock are observed in this paper. Methodology. The elements and methods of the probability theory (particularly the theory of stationary and non-stationary processes) and methods of the sampling theory are used for processing of the regenerated current data arrays by PC. Findings. The regenerated current records are obtained from the locomotives and trains in Ukraine railways and trams in Poland. It was established that the current has uninterrupted and the jumping variations in time (especially in trams). For the random current in the regenerative braking mode the functions of mathematical expectation, dispersion and standard deviation are calculated. Histograms, probabilistic characteristics and correlation functions are calculated and plotted down for this current too. It was established that the current of the regenerative braking mode can be considered like the stationary and non-ergodic process. The spectral analysis of these records and “tail part” of the correlation function found weak periodical (or low-frequency) components which are known like an interharmonic. Originality. Firstly, the theory of non-stationary random processes was adapted for the analysis of the recuperated current which has uninterrupted and the jumping variations in time. Secondly, the presence of interharmonics in the stochastic process of regenerated current was defined for the first time. And finally, the patterns of temporal changes of the correlation current function are defined too. This allows to reasonably apply the correlation functions method in the identification of the electric traction system devices. Practical value. The results of probabilistic and statistic analysis of the recuperated current allow to estimate the quality of recovered energy and energy quality indices of electric rolling stock in the regenerative braking mode. But the correlation and spectral analysis is required to determine the electromagnetic compatibility of the electric rolling stock in the regenerative braking mode with the subsystems and the electric traction devices.

Low-Order Dominant Harmonic Estimation Using Adaptive Wavelet Neural Network

In recent years, harmonic pollution has worried the power engineers considerably due to the increased penetration of power-electronics-based devices in the utility grid. Monitoring of certain low-order harmonics in the power supply is more important than monitoring of the entire spectrum because, usually, these are the most significant ones. In this paper, a technique based on an adaptive wavelet neural network that is the most suitable for dominant low-order harmonic estimation is presented. The proposed method works with only half-cycle data point inputs, compared to the requirement of at least one-complete-cycle data for other estimation techniques. A simple, fast converging, and reliable learning algorithm based on back propagation is used for training of the network parameters. The proposed method is examined with a number of simulated and experimental signals. The test results confirm that the proposed method accurately estimates the dominant low-order harmonics in pragmatic situations of fundamental frequency deviation, presence of interharmonics, low signal-to-noise ratio, etc.

Sources, Effects, and Modelling of Interharmonics

Recently, the increasing use of power electronic systems and time-variant nonlinear loads has brought number of power harmonics/interharmonics, and the power supply quality is therefore seriously threatened. The presence of interharmonics strongly poses more difficulties in modelling and measuring the distorted waveforms. Therefore, this paper reviews the sources, effects, and modelling of interharmonics. It provides a variety of crucial phenomena caused by interharmonics. More importantly, it also gives a possible solution for engineers/researchers to use appropriate tools to measure interharmonics. Some methods with implementation results are introduced and discussed for details.

Weighting Method to Identify Interharmonics based on Calculating the Bandwidth in Group-Harmonics

Power converters produce a vast range of harmonics, subharmonics and interharmonics. Harmonics analyzing tools based on the Fast Fourier Transform (FFT) assume that only harmonics are present and the periodicity intervals are fixed, while these periodicity intervals are variable and long in the presence of interharmonics. Using FFT may lead to invalid and undesired results due to the above mentioned issues. They can also lead to problems such as frequency blending, spectral leakage and the picket-fence effect. In this paper, the group-harmonic weighting (GHW) approach has been presented to identify the interharmonics in a power system. Afterwards, a modified GHW has been introduced to calculate the proper bandwidth for analyzing the various values of interharmonics. Modifying this method leads to more precise results in the FFT of a waveform containing inter harmonics especially in power systems with a fundamental frequency drift or frequency interference. Numerical simulations have been performed to prove the efficiency of the presented algorithm in interharmonics detection and to increase the accuracy of the FFT and the GWH methods.

High-precision time domain reactive power measurement in the presence of interharmonics

When interharmonics exist in power system signals, large errors emerge in traditional time domain reactive power measurement. In this paper, we present a novel time domain integral method with good effect of restraining interharmonics, synchronization error, and white noise, as well as the principle of the selection of the sampling periods when employing this approach. The current signal and phase-shifted voltage signal are reconstructed after the harmonic components of signals are extracted, so that the interharmonics are filtered. The influence of the synchronization error on the measurement is reduced through removing the weight coefficients of the reactive components. In the simulation, we apply several cosine windows to the proposed method and analyze signals containing both harmonics and interharmonics. The results show that, in the presence of interharmonics, synchronization error, and white noise (with a fundamental signal-to-noise ratio of 40 dB) all together, the relative errors are within the magnitude of 10−4, which perfectly satisfies the practical requirement.

Determination of the Truncation Errors in Case of Asynchronous Processing of the AC Signals in the Presence of Interharmonics and Subharmonics

The paper deals with the problem of estimating the influence of truncation error in case of asynchronous sampling of the ac signal in the presence of subharmonics and interharmonics. The analysis makes use of the most general model of the voltage and current signal, i.e. the most complex spectral content that can be expected to appear in practice. In this paper, different processing methods are compared end equations derived for worst-case errors. A simulations and experimental check of the suggested procedure have been done as well. On the base of the derived relation it is possible to select, the best processing method and select the necessary number of samples in case of such a complex signal. The paper investigates the errors related to the proposed processing method, and provides estimation of truncation affect.

Time-frequency single-phase power components measurements for harmonics and inter-harmonics distortion based on wavelet packet transform; Part II: case studies and results

This is the second part of a two-part study concerning power components measurement in the time-frequency domain using Wavelet Packet Transform (WPT). Four case studies are presented comparing the recommended power components that are contained in the IEEE Standard 1459-2010 [1] based on Fourier Transform approach, versus power components suggested by the newly developed time-frequency 'in-phase quadrature' approach using Wavelet Packet Transform; the latter derived in the first part of this two-part study. The first two cases are simulated cases in the Matlab environment to include both harmonic and interharmonic distortion, while the other two cases are real data cases acquired from computer loads and Adjustable Speed Drives. The values of the recommended power components using both approaches are compared and the results indicate that the time-frequency 'in-phase quadrature' approach using WPT is more accurate, especially in the presence of interharmonics. Both time and frequency information is preserved, allowing representation of the power components in a time-frequency spectrum. This provides a complete performance picture compatible with present practical load configurations.

Detection of Flicker Caused by Interharmonics

International standard bodies have specified an instrument capable of detecting and assessing the severity of lighting flicker, which is called a flickermeter. However, a deficiency with regard to flicker caused by high-frequency interharmonics has been reported in the recent literature. In this paper, another deficiency of the International Electrotechnical Commission (IEC) flickermeter with regard to low-frequency interharmonics, whose frequencies are below the difference between the fundamental frequency and the cutoff frequency of a bandpass filter of the IEC standard flickermeter, will be discussed and illustrated based on analysis and numerical experiments. A new approach based on down-up sampling in the discrete-time sample domain is also proposed to address the flicker-detection problem associated with interharmonics. We demonstrate the efficacy of the proposed method by a comparison with the current flickermeter standard in the presence of interharmonics.

Operation and Control of a DVR in the Presence of Interharmonics

The paper discusses the operating principles and control characteristics of a dynamic voltage restorer (DVR). It is assumed that the source voltages contain interharmonic components in addition to fundamental components. The main aim of the DVR is to produce a set of clean balanced sinusoidal voltages across the load terminals irrespective of unbalance, distortion and voltage sag/swell in the supply voltage. An algorithm has been discussed for extracting fundamental phasor sequence components from the samples of three-phase voltages or current waveforms having integer harmonics and interharmonics. The DVR operation based on extracted components is demonstrated. The switching signal is generated using a deadbeat controller. It has been shown that the DVR is able to compensate these interharmonic components such that the load voltages are perfectly regulated. The DVR operation under deep voltage sag is also discussed. The proposed DVR operation is verified through the computer simulation studies using the MATLAB software package.

Digital Processing of Synchronously Sampled AC Signals in the Presence of Interharmonics and Subharmonics

This paper deals with the problem of estimating the value of the active power of the ac signal in the presence of subharmonics and interharmonics. The method can also be analogously applied to determine the root-mean-square (rms) value of the basic electric values. The analysis makes use of the most general model of the voltage and current signal, i.e., the most complex spectral content that can be expected to appear in practice. A simulation of the suggested procedure has been done as well, as a final confirmation of the possibility of having accurate processing by using the synchronized sampling technique, even in the presence of subharmonics and interharmonics.

High-Resolution Spectrum-Estimation Methods for Signal Analysis in Power Systems

The spectrum-estimation methods based on the Fourier transform suffer from the major problem of resolution. The methods were developed and are mostly applied for periodic signals under the assumption that only harmonics are present and the periodicity intervals are fixed, while periodicity intervals in the presence of interharmonics are variable and very long. A novel approach to harmonic and interharmonic analysis based on the subspace methods is proposed. Min-norm and music harmonic retrieval methods are examples of high-resolution eigenstructure-based methods. Their resolution is theoretically independent of the signal-to-noise ratio (SNR). The Prony method as applied for parameter estimation of signal components was also tested in the paper. Both the high-resolution methods do not show the disadvantages of the traditional tools and allow exact estimation of the interharmonic frequencies. To investigate the methods, several experiments were carried out using simulated signals, current waveforms at the output of an industrial frequency converter, and current waveforms during out-of-step operation of a synchronous generator. For comparison, similar experiments were repeated using the fast Fourier transform (FFT). The comparison proved the superiority of the new methods.

Measuring active power of synchronously sampled AC signals in presence of interharmonics and subharmonics

The problem of estimating the value of the active power of the AC signal in the presence of subharmonics and interharmonics is considered. Recently suggested methods are analysed, especially those that are based on the application of the undersampling method; their limitations and the errors that occur with their application have also been included in the analysis. The analysis makes use of the most general model of the voltage and current signal, i.e. the most complex spectral content that can be expected to appear in practice. A simulation of the suggested procedure has been carried out, as a final confirmation of the possibility of having accurate processing by using the synchronised sampling technique, even in the presence of subharmonics and interharmonics.

Modelling of Power Components in Non-sinusoidal Power Systems Using Hilbert Transform

AbstractThis article presents a Hilbert transform-based approach of power components definition in non-sinusoidal power systems. Instantaneous phasors of current and voltage, apparent power, and power factor are also defined. The proposed Hilbert transform-based method is applicable to sinusoidal or non-sinusoidal, single-phase systems as well as balanced and unbalanced three-phase systems. The method is also applicable in the presence of interharmonics. The properties and physical meanings of defined power-related quantities are discussed in detail. The presented method leads to the formulas used in the conventional RMS concept method. Study cases of power systems at different loads are examined to test the validity and practicability of the proposed approach.

Modelling of Power Components in Non-Sinusoidal Power Systems Using Hilbert Transform

This article presents a Hilbert transform-based approach of power components definition in non-sinusoidal power systems. Instantaneous phasors of current and voltage, apparent power, and power factor are also defined. The proposed Hilbert transform-based method is applicable to sinusoidal or non-sinusoidal, single-phase systems as well as balanced and unbalanced three-phase systems. The method is also applicable in the presence of interharmonics. The properties and physical meanings of defined power-related quantities are discussed in detail. The presented method leads to the formulas used in the conventional RMS concept method. Study cases of power systems at different loads are examined to test the validity and practicability of the proposed approach.