Higher Harmonic Components Research Articles

Применение асинхронизированных генераторов в электрических сетях с пониженным качеством электроэнергии

For decentralized power generation, small-capacity asynchronized generators (AGs) can be used, which are able to yield a number of positive effects in comparison with conventional synchronous machines: higher stability limits, wider reactive power adjustment ranges, simpler synchronization with the grid due to the ability to control the EMF phase, and the possibility to maintain synchronous operation in case of failure in one of the field windings. The article describes the model of a grid equipped with asynchronized generators with automatic excitation and rotor speed control systems, which is developed in the MATLAB software package environment. Normal and emergency operation modes of a 35 kV grid with distributed generation plants based on asynchronized machines under the conditions of degraded electric power quality due to the presence of electric traction loads are simulated. The influence of AGs on emergency and post-emergency modes are determined, and the harmonic distortion levels are estimated. For comparison, the grid operation modes are simulated for the case of using synchronous machines as generation sources. The influence of higher harmonic components on the performance of the proposed automatic control system is analyzed. The obtained study results have shown that with using asynchronized generators, better control processes and better quality of electric power are obtained in comparison with those in a grid equipped with synchronous machines; in addition, the stability limits are increased, and the synchronization processes are simplified.

Учёт несинусоидального/несимметричного режима работы электрической сети коммунально-бытового назначения при расчете уровня тока нулевого проводника

During the operation of 0.4 kV electric networks, asymmetry of currents and voltages is unavoidable. As is known, unbalanced operation of 0.4 kV networks is stemming from nonuniform distribution of loads between the phases. This results in that a fundamental frequency zero-sequence current will flow through the neutral conductor in a four-wire three-phase electric network. On the other hand, during balanced operation of a four-wire electric network containing loads with a nonlinear volt-ampere characteristic, higher harmonic currents multiple to three are summed in the neutral conductor. Therefore, it is of relevance to analyze unbalanced operating conditions of a four-wire electric network containing loads with a nonlinear volt-ampere characteristic. The article presents the characteristics of a municipal load for analyzing unbalanced/nonsinusoidal conditions of its operation. For carrying out full-valued assessment of unbalanced operating conditions of a four-wire electric network, a simulation model of a 0.4 kV network section containing a nonsinusoidal load is developed. It is shown that during unbalanced operation of an electric network containing electric loads with a nonlinear volt-ampere characteristic it is recommended to take into account zero-sequence current higher harmonic components that are not multiple to three. An algorithm for calculating the neutral conductor current harmonic component for determining the cable temperature rating is developed.

Influence of indicators of quality of electric power on reliability of work of power transformer equipment of power plants and distribution networks

The lifespan of power transformers is largely determined by the state of their internal insulation, which is prone to aging during operation, now this problem is especially relevant for the operation of power transformers that have worked out a nominal life.Direct control of internal insulation during the work is difficult due to the inaccessibility of windings for direct survey, and it is advisable to predict the residual resource for planning timely repairs. A refined model of the dependence of the speed of relative wear of the coil insulation not only on the load of the transformer, but also on the presence of asymmetry and higher harmonic components of the current is proposed

Numerical and experimental investigation of a spur gear pair with unloaded static transmission error

PurposeThe purpose of this paper is to investigate the dynamic responses of a spur gear pair with unloaded static transmission error (STE) excitation numerically and experimentally and the influences of the system factors including mesh stiffness, error excitation and torque on the dynamic transmission error (DTE).Design/methodology/approachA simple lumped parameters dynamic model of a gear pair considering time-varying mesh stiffness, backlash and unloaded STE excitation is developed. The STE is calculated from the measured tooth profile deviation under the unloaded condition. A four-square gear test rig is designed to measure and analyze the DTE and vibration responses of the gear pair. The dynamic responses of the gear transmission are studied numerically and experimentally.FindingsThe predicted numerical DTE matches well with the experimental results. When the real unloaded STE excitation without any approximation is used, the dynamic response is dominated by the mesh frequency and its high order harmonic components, which may not be result caused by the assembling error. The sub-harmonic and super-harmonic resonant behaviors are excited because of the high order harmonic components of STE. It will not certainly prevent the separations of mesh teeth when the gear pair is under the condition of high speed and heavy load.Originality/valueThis study helps to improve the modeling method of the dynamic analysis of spur gear transmission and provide some reference for the understanding of the influence of mesh stiffness, STE excitation and system torque on the vibration behaviors.

Harmonic current suppression method with adaptive filter for permanent magnet synchronous motor

ABSTRACT Due to the distortion of air gap magnetic field and the inherent non-linear characteristics of the inverter, the stator current of permanent magnet synchronous motor (PMSM) contains a large number of high order harmonic components, which distorts the current waveform and generates torque ripple, limiting the application of the PMSM in high speed and precision situations. To solve this problem, a harmonic current suppression method is proposed based on synchronous rotating coordinate transformation theory and adaptive filtering algorithm. The PMSM harmonic mathematical model is established and the coordinate transformation method is used to extract the 5th and 7th harmonic currents. On the basis of the original double closed-loop control system, the harmonic current loop is added, and the harmonic components are suppressed by injecting harmonic voltages. In order to improve the filtering effect and reduce the harmonic content, an adaptive filter is designed to replace the conventional low pass filter in the process of harmonic current extraction. According to the results of coordinate transformation, the adaptive filter continuously adjusts the parameters online through the least mean square (LMS) algorithm to extract the harmonic current. The simulation and experimental results proved the correctness and effectiveness of the proposed method.

EXPERIMENTAL STUDY OF THE POSSIBILITY TO SINGLE OUT THE MODE OF SINGLE-PHASE CLOSURE TO THE GROUND IN THE CIRCUIT 6– 10 kV BY THE INTELLIGENCE SYSTEM OF ELECTRICITY METERING

The problem of increasing the reliability of electricity supply is relevant at the current stage of electric power systems development both in the territory of the Russian Federation and in foreign electric power systems. One of the ways to improve the reliability of electricity supply is to prevent the development of emergency situations on overhead power transmission lines as the most important components of electric power systems, which is confirmed by a substantial number of annual domestic and foreign publications. Preventing the development of emergency situations is largely facilitated by early detecting the signs of emergency modes onset in the functioning of all voltage classes’ electric networks. At the same time, the development of intelligence systems for technical and commercial electricity metering opens up new opportunities for monitoring numerous parameters of different operational modes of electrical networks, including those of 6-10-35 kV voltage with isolated neutral operation mode. Numerous works of author’s teams are devoted to the theoretical analysis of the possibility to early detect the diagnostic signs of emergency signals. However, existing publications do not always present the results of field experimental studies in existing electrical networks on the subject under consideration, which demonstrates some discrepancy between theoretical provisions and the possibility of their practical implementation. The present article attempts to assess the possibility of practical implementing the part of theoretical provisions on early detection of diagnostic signs for emergency regimes and, as a result, increase reliability of electricity supply. At the same time, the article presents the results of the field study the basis of which were used to open up current possibilities of early detecting the diagnostic signs of emergency regimes on the example of individual singling out higher harmonic components of currents and voltages, including when using already existing intelligence electricity metering systems installed in the existing electrical distribution systems with the voltage of 10 kV. At the same time, the article demonstrates implementability and further development of online monitoring of emergency modes in electric networks functioning on the example of identifying a single-phase ground fault, which makes it possible to significantly reduce the costs of temporary and material resources when localizing the single-phase closure zone.

Experimental investigation of the turbulent cascade development by injection of single large-scale Fourier modes

The current work presents an experimental investigation of the dynamic interactions between flow scales caused by repeated actions of the nonlinear term of the Navier-Stokes equation. Injecting a narrow band oscillation, representing a single Fourier mode, into a round jet flow allows the measurement of the downstream generation and development of higher harmonic spectral components and to measure when these components are eventually absorbed into fully developed turbulence. Furthermore, the dynamic evolution of the measured power spectra observed corresponds well to the measured cascaded delays reported by others. Closely matching spectral development and cascade delays have also been derived directly from a one-dimensional solution of the Navier-Stokes equation described in a companion paper. The results in the current work provide vital information about how initial conditions influence development of the shape of the spectrum and about the extent of the time scales in the triad interaction process, which should be of significance to turbulence modelers.

Two-dimensional numerical study of gap resonance coupling with motions of floating body moored close to a bottom-mounted wall

The piston mode fluid resonance in the narrow gap between a moored floating body and a bottom-mounted vertical wall is numerically investigated based on a two-dimensional potential flow model and viscous numerical simulations. This study focuses on understanding the effect of mooring stiffness on the coupling dynamics of the gap resonance and the sway or heave motion of the floating body in regular waves. Numerical studies show that the resonant wave amplitude in the gap is reduced by the sway and heave motions. The reduction is highly dependent on the mooring stiffness. Two resonant frequencies are confirmed, and both increase with the mooring stiffness. Different modes of motions are identified in terms of the phase difference between the oscillatory motions of the gap flow and the floating body. Higher harmonic components of responses are found for the specific mooring stiffness. The performance of potential flow models in predicting resonant responses is revisited based on the understanding that the overall damping effect consists of two parts: (1) radiation damping and (2) viscous dissipation. It is confirmed that a potential model is also able to produce reasonable predictions as radiation damping plays a dominant role, for example, at the second resonant frequencies of coupling the gap resonance with the sway motion. Otherwise, as viscous dissipation dominates radiation damping, noticeable over-predictions by a potential model occur as recognized before, for example, the present results at the second peak response of gap resonance with the heave motion. The relative viscous dissipation is quantified with the reflection coefficient of viscous numerical results, while the radiation damping is quantified based on a specially designed radiation potential model with inputs of viscous numerical solutions.

Robust model predictive current control without dead‐zone compensation

To solve the problems of large steady-state errors, high harmonic components and poor robustness of traditional current model prediction, a novel three-vector model predictive current control for permanent magnet synchronous motor is presented in this study. The vectors operating time is calculated with the combination of current increment and the unconventional modulation method is adopted to generate duty cycle containing dead zone. Adopting the current command correction link, the current deviation caused by inaccuracy parameter is reduced. Proved by experiment, novel control system not only the current steady-state error and current harmonic component are reduced, but also the parameter robustness is enhanced.

Method of dynamic mode decomposition and reconstruction with application to a three-stage multiphase pump

Helico-axial multiphase pumps are significant equipment in the exploitation of petroleum resources in offshore platforms, and in-depth understanding of gas-liquid flow fields is beneficial for the design and optimization. The method of dynamic mode decomposition and reconstruction is introduced and applied to study gas-liquid flow characteristics in a three-stage multiphase pump. Firstly, the theoretical relation between decomposed results and DMD parameters is investigated. Then, the dominant frequency and corresponding coherent structures inside the multiphase pump are revealed, which are induced by rotor-stator interaction and gas-liquid flow patterns. The reconstruction residual versus mode number represents a stepped curve, and the minimum residuals are below 10−5 governed by linear combination approximation. Comparison among reduced-order reconstruction, full-order reconstruction, and raw data shows that reduced-order reconstruction fields are effective in reflecting main flow characteristics, but fail to capture high order harmonic components, which is related to complex flow in diffuser passages and following vaneless areas.

Review and results of studies of the harmonic composition of the current consumed by low-power frequency converters, as well as methods and devices to reduce their negative impact on power supply systems

The ACS150 frequency Converter was chosen as the object for experimental research. On the basis of the measurements it is concluded that in the spectral composition of current drawn by the frequency Converter, in addition to currents the main harmonic component is dominated by currents 5, 7, 11, 13, and 17th harmonics, i.e. harmonic components of odd non-multiple of three. Currents 3, 9 and 15 th harmonic components are also present in the spectral composition, but their value is much smaller. Also, based on the data obtained, it can be argued that with a decrease in the frequency of motor speed control and the load value of the frequency Converter, the number of pulsations on the current waveform increases, as a result, there is an increase in the values of the higher harmonic components and an increase in the value of the total harmonic components of the current. The main contribution to the increase in the index of the total harmonic components of the amperage with a decrease in the load of the frequency Converter and the output frequency of the motor speed control is made by odd harmonic components of the amperage multiple of three, at the same time harmonic components of the amperage non-multiple of three, namely the 5th and 7th order, are not subject to change. A brief review of technical solutions aimed at improving the electromagnetic compatibility of asynchronous frequency-controlled drive is given. In particular, such solutions as increasing the number of semiconductor switches used in inverters, improving control modes, the use of special separation transformers, passive (resonant) and active filters are noted.

Design of Experiments Predictive Models as a Tool for Lifespan Prediction and Comparison for Enameled Wires Used in Low-Voltage Inverter-Fed Motors

Since the development of power electronic components, which allowed the manufacturing of reliable and efficient inverters, variable speed drives using inductive motors have become more and more popular. The pulsewidth modulation (PWM) technique has proven to be a very effective method of rotational speed control. However, the fast-changing voltage pulses, with very steep slopes (in the order of a few kilovolt/microsecond), have brought new hazards for the electrical insulation system of such motors. Very high frequency harmonic components of PWM voltage will result in significant overvoltage due to an impedance mismatch between the cable and the motor. As an effect, the voltage seen by some parts of the insulation system may exceed the partial discharge inception voltage stating the localized partial discharges activity. The aim of this article is to investigate and analyze the aging process of the enameled wire exposed to different factors and to propose a method allowing them to predict their lifespans in given conditions. This study introduces a prediction based on the design of experiments method and the statistical Weibull distribution. Thanks to the model obtained with short multistress aging tests, it is possible to predict the results of significantly longer ones. Moreover, the adopted methodology is proposed that allows us to predict the scatter of the long tests based on the short-time results dispersion. The same approach is used to compare different products between each other and rank them. All model predictions are compared with the experimental data in order to prove the model accuracy.

Rating of amplitudes of high harmonics in determining feeder with single-phase ground fault

The aim of the paper is theoretical and experimental research of processes during the single-phase ground faults in electrical distribution grids of 10/06/35 kV with isolated neutral mode. The mathematical method of rationing is used for the analysis of the spectral composition of currents and voltages increasing the information content of the allocated higher harmonics of current and voltage. The paper show a comparison of the results of spectral analysis with and without taking into account the mathematical rationing obtained on the simulation model. Field experiments have demonstrated the effectiveness of using of the method of mathematical rationing of the higher harmonic components of current and voltage for various types of single-phase ground faults. The results of field experiments provided an opportunity of improving the methodology of yearling detection of single-phase ground faults in electric grids of 6-10-35 kV with an isolated mode of neutral. The conclusion of the research is the possibility of a significantly more accurate selection of the resonant frequencies of the spectrum of currents and voltages obtained by using of the method of mathematical rationing. The possibility of earlier and more precise localization of the feeder with ground fault is shown on the base more precise selection of the resonant frequency currents and voltages.

Backside delamination detection in composites through local defect resonance induced nonlinear source behavior

Shallow damages can be detected by searching for local defect resonance behavior in the fundamental vibrational response. However, this is not possible for defects which are deeper than half the thickness of the coupon due to the limited bending stiffness difference between the defect and the sound material.In this study, it is shown that delaminations under harmonic excitation at the local defect resonance frequency behave as sources of higher harmonic vibration components. These higher harmonic components are detectable when examining the delaminated component from the side where the delamination is close to the surface, but more importantly, also from the other side where the delamination is at the backside. As such, monitoring of these harmonics allows for the detection of backside delaminations which cannot be found using linear LDR techniques. First, a finite element simulation with nonlinear contact conditions is performed as a proof of concept. Experimental validation is performed for a delaminated CFRP coupon using low-power piezoelectric actuation and scanning laser Doppler vibrometer response measurements.

Comparison of the Wideband Power Sources Used to Supply Step-Up Current Transformers for Generation of Distorted Currents

In this paper a comparison of the wideband power sources of a pulse width modulation (PWM) inverter and a power supply composed of an audio power amplifier and a two-channel arbitrary generator is discussed. Their application is to supply a step-up current transformer for generation of the distorted current required to test the transformation accuracy of the distorted currents of the inductive current transformers. The proposed equations allow to calculate the maximum rms values of higher harmonic of distorted currents for its required main harmonic component. Moreover, they also enable the calculation of the maximum rms values of the main harmonic of the distorted current for which the required higher harmonic component may be obtained. This defines the usable bandwidth of the tested power source for their specific load. During work on high inductive impedance, the maximum voltage is the limitation that determines the higher harmonic value. While for resistive loads, the maximum current and the transistor’s slew rate are the limiting factors. The usage of the compensation system for the inductive reactance of the step-up current transformer under supply significantly increased its maximum output current. Its rms value with a 10% higher harmonic component up to 5 kHz was almost 400 A instead 100 A for the PWM-based power source and about 800 A instead 200 A for the power supply system with the audio amplifier.

Loss and temperature rise of the skin effect electric heat tracing system

In actual operation, the skin effect electric heat tracing system is powered by the inverter circuit, and the higher harmonic components are inevitably introduced. There is not much research on the influence of harmonic current on the electric heat tracing load loss. In this paper, the harmonic distribution under PWM driving mode is analyzed, and the load loss of the electric heat tracing body under harmonic current is derived. The co-simulation method of PWM inverter circuit and skin electric heat tracing body coupling is proposed. The simulation results of current and loss of co-simulation method and sine wave driving method are compared. The results show that the parameters of PWM driving mode increase to different degrees, which proves the correctness of the joint simulation method. At the same time, the influence of the output characteristics and modulation parameters of the PWM inverter circuit on the load loss of the electric heat tracing body is analyzed, which provides a theoretical basis for the determination of the parameters of the inverter circuit. In addition, combined with multi-physics coupling analysis, this paper obtains more accurate temperature distribution results of the electric heat tracing system without scaling the size of the electric heat tracing ontology. Not only can we intuitively understand the material selection and hot spot configuration of the electric heat tracing components, but also further understand the influence of current harmonics on the load loss in actual operation, so as to better realize the efficient heat tracing of the skin electric heat tracing system.

Optimization approach to reduce the negative impact of high harmonic components of currents and voltages in high-voltage mine networks

The article presents an analysis of the work of the high-voltage mine network, which confirms the presence of higher harmonic components of currents and voltages of significant magnitude and their negative impact on the elements of the power supply system. The most pronounced higher harmonics of currents and voltages in the high-voltage mine network, as well as the most probable ranges of load currents and distortion currents are revealed. It is proved that the load change in the mine network as a function of time refers to random processes. The mathematical apparatus of the theory of random processes was used to study and predict load currents and distortion currents. The obtained quantitative values of trends of load currents and distortion currents were used in the estimation of power losses and in the calculation of parameters of filter compensating devices. An optimization approach is proposed to reduce the negative influence of higher harmonic components of currents and voltages, based on minimizing the target function of additional active power losses from the action of higher harmonics. To reduce the negative impact of higher harmonic components of currents and voltages in the high-voltage mine network, it is proposed to use two resonant passive filters tuned to the 11-th and 13-th harmonics, and a second-order broadband filter tuned to compensate harmonics, starting from the 23-rd and above.

A Numerical Investigation of Gap and Shape Effects on a 2D Plunger-Type Wave Maker

The installation of plunger-type wave makers in experimental tanks will generally include a gap between the back of the wedge and the wall of the tank. In this study, we analyze the influence of this gap on the wave making performance of the plunger using two-dimensional (2D) CFD calculations for a range of nearly linear wave conditions and compare the results with both experimental measurements and linear potential flow theory. Three wedge-shaped profiles, all with the same submerged volume, are considered. Moreover, the generated waves are compared with the predictions of linear potential flow theory. The calculations are made using the commercial ANSYS FLUENT finite-volume code with dynamic meshes to solve the Navier–Stokes equations and the volume of fluid scheme to capture the air–water interface. Furthermore, the linear potential flow solution of Wu (J Hydraul Res 26:481–493, 1988) is extended to consider an arbitrary profile and serve as a reference solution. The amplitude ratios of the generated waves predicted by the CFD calculations compare well with the predictions of linear potential flow theory for a simple wedge, indicating that viscous effects do not influence this ratio for small-amplitude motions in 2D. By contrast, significant higher harmonic components are produced by larger amplitude motions. Also, the simple wedge is found to produce the smallest spurious higher harmonic content in the far-field wave.

Обеспечение когерентности цифровой обработки сигналов токов и напряжений электроэнергетических систем при снижении частоты дискретизации

The development of Russia’s electric power industry includes, as one of important objectives, step by step intellectualization of the electric power system under the conditions of decentralized generating capacities and wide use of facilities on the basis of renewable energy sources. The Smart Energy System of Russia national project implies construction of digital substations equipped with state of the art relayprotection and automatic control devices, which exchange instantaneous values of currents and voltages. In implementing such exchange, a need may arise to decrease or increase the signal sampling frequency for optimally suiting to the process tasks. The results from analyzing the effects of digital processing involving loss of coherence of power frequency voltage and current signals, which arise in decreasing the sampling frequency, are presented. It is shown that, if the coherence requirements are not complied with in decimation, this will result in significant errors in estimating the signal parameters. It is also shown that for determining the current and voltage signals sine wave distortion degree due to loss of coherence in processing, it is advisable to use a normalized mutual correlation ratio. It has been demonstrated based on simulation results that for signals containing high frequency harmonic components, incoherent samplingaggravates the distorting effect; it is also pointed out that in analyzing distortion effects on power frequency signals, it is important to take into account the initial phases of high frequency harmonic components.

Loss Counter in Power Double Winding Transformers Implementing the Method of Conditionally Constant Coefficients in Online Mode Using the Information Platform

The article describes the developed loss counter in power double-winding transformers of distribution net-works. The principle of operation of the proposed measuring unit of the loss counter is considered on the exam-ple of one channel for measuring current and voltage in accordance with the above functional scheme. The ap-pearance and main characteristics of the loss counter are given. The main characteristics of the developed loss counter are confirmed by the adjustment Protocol based on the results of measurements in the FBU «Rostov CSM» and are at the level of existing characteristics of electric energy quality analyzers. The data measured and calculated by the microcontroller of the loss counter, necessary for the implementation of the method of conditionally constant coefficients, are transmitted over the USB bus to a single-Board computer. Using the de-veloped software written in the high-level General-purpose programming language Python, the formation and sending of data to the information platform Yandex.Cloud. The approbation of the operation of the loss coun-ter on the developed physical model «power transformer-asymmetric and non-sinusoidal load» and operating substations is shown. Thus, the developed loss counter can be used to calculate losses from higher harmonic components in power transformers by the method of conditionally constant coefficients in the online mode us-ing the resources of the information platform Yandex.Cloud.