Search results for: low order harmonic voltages

Authors: K. A. Chinmaya, M. Udaya Bhaskar

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Multiphase motor drives are now a day considered for numerous applications due to the advantages that they offer when compared to their three-phase counterparts. Proper modeling of inverters and motors are important in devising an appropriate control algorithm. This paper develops a complete modeling of a five-phase inverter and five-phase space vector modulation schemes which can be used for five-phase motor drives. A novel modified algorithm is introduced which enables the sinusoidal output voltages up to certain voltage value. The waveforms of phase to neutral voltage are compared with the different modulation techniques and also different modulation indexes in terms of Low-order Harmonic (LH) voltage of 3rd and 7th present. A detailed performance evolution of existing and newly modified schemes is done in terms of Total Harmonic Distortion (THD).

Keywords: multi-phase drives, space vector modulation, voltage source inverter, low order harmonic voltages, total harmonic distortion

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Authors: Nur Sarma, Paul M. Tuohy, Siniša Djurović

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This paper presents an in-depth investigation of the effects of several grid supply harmonic voltages on the stator currents of an example wound rotor induction machine. The observed effects of higher order grid supply harmonics are identified using a finite element time stepping transient model, as well as a time-stepping electromagnetic model. In addition, a number of analytical equations to calculate the spectral content of the stator currents are presented in the paper. The presented equations are validated through comparison with the obtained spectra predicted using the finite element and electromagnetic models. The presented study provides a better understanding of the origin of supply harmonic effects identified in the stator currents of the example wound rotor induction machine. Furthermore, the study helps to understand the effects of higher order supply harmonics on the harmonic emissions of the wound rotor induction machine.  

Keywords: wound rotor induction machine, supply harmonics, current spectrum, power spectrum, power quality, harmonic emmisions, finite element analysis

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Authors: Ying-Pin Chang

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This paper presents a method for combining a particle swarm optimization with nonlinear time-varying evolution and orthogonal arrays (PSO-NTVEOA) in the planning of harmonic filters for the high speed railway traction system with specially connected transformers in unbalanced three-phase power systems. The objective is to minimize the cost of the filter, the filters loss, the total harmonic distortion of currents and voltages at each bus simultaneously. An orthogonal array is first conducted to obtain the initial solution set. The set is then treated as the initial training sample. Next, the PSO-NTVEOA method parameters are determined by using matrix experiments with an orthogonal array, in which a minimal number of experiments would have an effect that approximates the full factorial experiments. This PSO-NTVEOA method is then applied to design optimal harmonic filters in Taiwan High Speed Rail (THSR) traction system, where both rectifiers and inverters with IGBT are used. From the results of the illustrative examples, the feasibility of the PSO-NTVEOA to design an optimal passive harmonic filter of THSR system is verified and the design approach can greatly reduce the harmonic distortion. Three design schemes are compared that V-V connection suppressing the 3rd order harmonic, and Scott and Le Blanc connection for the harmonic improvement is better than the V-V connection.

Keywords: harmonic filters, particle swarm optimization, nonlinear time-varying evolution, orthogonal arrays, specially connected transformers

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Authors: Melike Aydoğan, Dürdane Öztürk

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Let H(D) be the linear space of all analytic functions defined on the open unit disc. A log-harmonic mappings is a solution of the nonlinear elliptic partial differential equation where w(z) ∈ H(D) is second dilatation such that |w(z)| < 1 for all z ∈ D. The aim of this paper is to define some inequalities of starlike logharmonic functions of order α(0 ≤ α ≤ 1).

Keywords: starlike log-harmonic functions, univalent functions, distortion theorem

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Authors: Ahmad Zahran, Ahmed Herzallah, Ahmad Ahmad, Mahran Quraan

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Generation of high DC voltages is necessary for testing the insulation material of high voltage AC transmission lines with long lengths. The harmonic and ripple contents of the output DC voltage supplied by high voltage DC circuits require the use of costly capacitors to smooth the output voltage after rectification. This paper proposes a new modular multiplier high voltage DC generator with embedded Cockcroft-Walton circuits that achieve a negligible harmonic and ripple contents of the output DC voltage without the need for costly filters to produce a nearly constant output voltage. In this new topology, Cockcroft-Walton modules are connected in series to produce a high DC output voltage. The modules are supplied by low input AC voltage sources that have the same magnitude and frequency and shifted from each other by a certain angle to eliminate the harmonics from the output voltage. The small ripple factor is provided by the smoothing column capacitors and the phase shifted input voltages of the cascaded modules. The constituent harmonics within each module are determined using Fourier analysis. The viability of the proposed DC generator for testing purposes and the effectiveness of the cascaded connection are confirmed by numerical simulations using MATLAB/Simulink.

Keywords: Cockcroft-Walton circuit, harmonics, ripple factor, HVDC generator

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Authors: Jugal K. Prajapat, Manivannan M.

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In this article we have studied a class of sense preserving harmonic mappings in the unit disk D. Let B⁰H (α, β) denote the class of sense-preserving harmonic mappings f=h+g ̅ in the open unit disk D and satisfying the condition |z h״(z)+α (h׳(z)-1) | ≤ β - |z g″(z)+α g′(z)| (α > -1, β > 0). We have proved that B⁰H (α, β) is close-to-convex in D. We also prove that the functions in B⁰H (α, β) are stable harmonic univalent, stable harmonic starlike and stable harmonic convex in D for different values of its parameters. Further, the coefficient estimates, growth results, area theorem, boundary behavior, convolution and convex combination properties of the class B⁰H (α, β) of harmonic mapping are obtained.

Keywords: analytic, univalent, starlike, convex and close-to-convex

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Authors: Mohamed Elhosieny Aly Ismail

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The paper illustrates the total voltage and current harmonic distortion impact caused by fast-charging an electric bus and maintaining standard limit compliance. Measuring the current harmonic level in the range of 2 kHz-9 kHz. Also, the impact of the total demand distortions current caused by fast charger electric bus on the utility by measuring at the point of common coupling and comparing the measurement with IEEE519 -2014 standard. The results show that the total harmonic current distortion for the charger is within the limits of IEC 61000-3-12 and the fifth harmonic current was the most dominant frequency then the seventh harmonic current. The harmonic current in the range of 2 kHz- 9 kHz shows the frequency 5.1kHz is the most dominant frequency.

Keywords: electric vehicle, total harmonic distortion, IEEE519-2014, IEC 61000-3-12, super harmonic distortion

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Authors: M. Suresh Kumar, K. Ramani

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This paper proposed the harmonic elimination of Cascaded H-Bridge Multi-Level Inverter by using Selective Harmonic Elimination-Pulse Width Modulation method programmed with Particle Swarm Optimization algorithm. PSO method determine proficiently the required switching angles to eliminate low order harmonics up to the 11th order from the inverter output voltage waveform while keeping the magnitude of the fundamental harmonics at the desired value. Results demonstrate that the proposed method does efficiently eliminate a great number of specific harmonics and the output voltage is resulted in minimum Total Harmonic Distortion. The results shown that the PSO algorithm attain successfully to the global solution faster than other algorithms.

Keywords: multi-level inverter, Selective Harmonic Elimination Pulse Width Modulation (SHEPWM), Particle Swarm Optimization (PSO), Total Harmonic Distortion (THD)

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Authors: Hussein Al-bayaty

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This paper presents a novel idea to show the ability to benefit of the harmonic currents which are produced on the load side of the power grid. The proposed circuit contributes in reduction of the total harmonic distortion (THD) percentage through adding a high pass filter to draw harmonic currents with 150 Hz and multiple frequencies a and convert them to DC current and then reconvert it to AC current with 50 Hz frequency in order to feed different loads. The circuit has been designed, investigated and simulated in the MATLAB, Simulink program; the results will be assessed and compared the two cases: firstly, the system without adding the new circuit. Secondly, with adding the high pas filter circuit to the power system.

Keywords: harmonics elimination, passive filters, Total Harmonic Distortion (THD), filter circuit

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Authors: Stanislav Babaev, Vladimir Cuk, Sjef Cobben, Jan Desmet

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The procedures for performing harmonic studies for medium-voltage distribution feeders have become relatively mature topics since the early 1980s. The efforts of various electric power engineers and researchers were mainly focused on handling large harmonic non-linear loads connected scarcely at several buses of medium-voltage feeders. In order to assess the impact of these loads on the voltage quality of the distribution system, specific modeling and simulation strategies were proposed. These methodologies could deliver a reasonable estimation accuracy given the requirements of least computational efforts and reduced complexity. To uphold these requirements, certain analysis assumptions have been made, which became de facto standards for establishing guidelines for harmonic analysis. Among others, typical assumptions include balanced conditions of the study and the negligible impact of impedance frequency characteristics of various power system components. In latter, skin and proximity effects are usually omitted, and resistance and reactance values are modeled based on the theoretical equations. Further, the simplifications of the modelling routine have led to the commonly accepted practice of neglecting phase angle diversity effects. This is mainly associated with developed load models, which only in a handful of cases are representing the complete harmonic behavior of a certain device as well as accounting on the harmonic interaction between grid harmonic voltages and harmonic currents. While these modelling practices were proven to be reasonably effective for medium-voltage levels, similar approaches have been adopted for low-voltage distribution systems. Given modern conditions and massive increase in usage of residential electronic devices, recent and ongoing boom of electric vehicles, and large-scale installing of distributed solar power, the harmonics in current low-voltage grids are characterized by high degree of variability and demonstrate sufficient diversity leading to a certain level of cancellation effects. It is obvious, that new modelling algorithms overcoming previously made assumptions have to be accepted. In this work, a simulation approach aimed to deal with some of the typical assumptions is proposed. A practical low-voltage feeder is modeled in PowerFactory. In order to demonstrate the importance of diversity effect and harmonic interaction, previously developed measurement-based models of photovoltaic inverter and battery charger are used as loads. The Python-based script aiming to supply varying voltage background distortion profile and the associated current harmonic response of loads is used as the core of unbalanced simulation. Furthermore, the impact of uncertainty of feeder frequency-impedance characteristics on total harmonic distortion levels is shown along with scenarios involving linear resistive loads, which further alter the impedance of the system. The comparative analysis demonstrates sufficient differences with cases when all the assumptions are in place, and results indicate that new modelling and simulation procedures need to be adopted for low-voltage distribution systems with high penetration of non-linear loads and renewable generation.

Keywords: electric power system, harmonic distortion, power quality, public low-voltage network, harmonic modelling

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Authors: Mahmoud Enayati, Sirous Mohammadi

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In this paper, a novel procedure to find the firing angles of the multilevel inverters of supply voltage and, consequently, to decline the total harmonic distortion (THD), has been presented. In order to eliminate more harmonics in the multilevel inverters, its number of levels can be lessened or pulse width modulation waveform, in which more than one switching occur in each level, be used. Both cases complicate the non-algebraic equations and their solution cannot be performed by the conventional methods for the numerical solution of nonlinear equations such as Newton-Raphson method. In this paper, Cuckoo algorithm is used to compute the optimal firing angle of the pulse width modulation voltage waveform in the multilevel inverter. These angles should be calculated in such a way that the voltage amplitude of the fundamental frequency be generated while the total harmonic distortion of the output voltage be small. The simulation and theoretical results for the 9-levels inverter offer the high applicability of the proposed algorithm to identify the suitable firing angles for declining the low order harmonics and generate a waveform whose total harmonic distortion is very small and it is almost a sinusoidal waveform.

Keywords: evolutionary algorithms, multilevel inverters, total harmonic content, Cuckoo Algorithm

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Authors: K. Khlifi, A. Haddouk, M. Hlaili, H. Mechergui

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The present paper provides a detailed analysis of prior methods and approaches for non-linear load identification in residential buildings. The main goal of this analysis is to decipher the distorted signals and to estimate the harmonics influence on power systems. We have performed an analytical study of non-linear loads behavior in the residential environment. Simulations have been performed in order to evaluate the distorted rate of the current and follow his behavior. To complete this work, an instrumental platform has been realized to carry out practical tests on single-phase non-linear loads which illustrate the current consumption of some domestic appliances supplied with single-phase sinusoidal voltage. These non-linear loads have been processed and tracked in order to limit their influence on the power grid and to reduce the Joule effect losses. As a result, the study has allowed to identify responsible circuits of harmonic pollution.

Keywords: distortion rate, harmonic analysis, harmonic pollution, non-linear load, power factor

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Authors: M. Almutairi, S. Hadjiloucas

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The harmonic distortion of voltage is important in relation to power quality due to the interaction between the large diffusion of non-linear and time-varying single-phase and three-phase loads with power supply systems. However, harmonic distortion levels can be reduced by improving the design of polluting loads or by applying arrangements and adding filters. The application of passive filters is an effective solution that can be used to achieve harmonic mitigation mainly because filters offer high efficiency, simplicity, and are economical. Additionally, possible different frequency response characteristics can work to achieve certain required harmonic filtering targets. With these ideas in mind, the objective of this paper is to determine what size single tuned passive filters work in distribution networks best, in order to economically limit violations caused at a given point of common coupling (PCC). This article suggests that a single tuned passive filter could be employed in typical industrial power systems. Furthermore, constrained optimization can be used to find the optimal sizing of the passive filter in order to reduce both harmonic voltage and harmonic currents in the power system to an acceptable level, and, thus, improve the load power factor. The optimization technique works to minimize voltage total harmonic distortions (VTHD) and current total harmonic distortions (ITHD), where maintaining a given power factor at a specified range is desired. According to the IEEE Standard 519, both indices are viewed as constraints for the optimal passive filter design problem. The performance of this technique will be discussed using numerical examples taken from previous publications.

Keywords: harmonics, passive filter, power factor, power quality

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Authors: Alireza Zabihi, Saeed Peyghami, Hossein Mokhtari

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With the increasing deployment of renewable power plants, such as solar and wind, it is crucial to measure the harmonic situation of the grid. This paper proposes a global voltage harmonic index to measure the harmonic situation of the power grid with a focus on power transformers. The power electronics systems used to connect these plants to the network can introduce harmonics, leading to increased losses, reduced efficiency, false operation of protective relays, and equipment damage due to harmonic intensifications. The proposed index considers the losses caused by harmonics in power transformers which are of great importance and value to the network, providing a comprehensive measure of the harmonic situation of the grid. The effectiveness of the proposed index is evaluated on a real-world distribution network, and the results demonstrate its ability to identify the harmonic situation of the network, particularly in relation to power transformers. The proposed index provides a comprehensive measure of the harmonic situation of the grid, taking into account the losses caused by harmonics in power transformers. The proposed index has the potential to support power companies in optimizing their power systems and to guide researchers in developing effective mitigation strategies for harmonics in the power grid.

Keywords: global voltage harmonic index, harmonics, power grid, power quality, power transformers, renewable energy

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Authors: Jyoti Wadhwa, Arvinder Singh

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This work presents the theoretical investigation of an enhanced second-harmonic generation of higher-order Gaussian laser beam in plasma having a density ramp. The mechanism responsible for the self-focusing of a laser beam in plasma is considered to be the relativistic mass variation of plasma electrons under the effect of a highly intense laser beam. Using the moment theory approach and considering the Wentzel-Kramers-Brillouin approximation for the non-linear Schrodinger wave equation, the differential equation is derived, which governs the spot size of the higher-order Gaussian laser beam in plasma. The nonlinearity induced by the laser beam creates the density gradient in the background plasma electrons, which is responsible for the excitation of the electron plasma wave. The large amplitude electron plasma wave interacts with the fundamental beam, which further produces the coherent radiations with double the frequency of the incident beam. The analysis shows the important role of the different modes of higher-order Gaussian laser beam and density ramp on the efficiency of generated harmonics.

Keywords: density rippled plasma, higher order Gaussian laser beam, moment theory approach, second harmonic generation.

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Authors: Setareh Gorji Ghalamestani, Lieven Vandevelde, Jan Melkebeek

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In this work, an experimental technique is applied for the measurements of the vibrations and deformation of a test transformer core. Since the grid voltage contains some higher harmonics, in addition to a purely sinusoidal magnetisation of the core the presence of third harmonic is also studied. The vibrations of the transformer core for points as well as the surface scan of the leg show more deformation in the corners of the leg than the middle of the leg. The influence of the higher harmonic of the magnetisation on the core deformation is also more significant in the corners of the leg. The core deformation shape under a sinusoidal magnetisation with a higher harmonic is more wavy and fluctuating than that under a purely sinusoidal magnetisation.

Keywords: vibrations and noise, transformer, vibration measurements, laser vibrometer, higher harmonic

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Authors: R. Ondarza-Rovira, T. J. M. Boyd

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Intense femtosecond laser light incident on over-critical density plasmas has shown to emit a prolific number of high-order harmonics of the driver frequency, with spectra characterized by power-law decays Pm ~ m-p, where m denotes the harmonic order and p the spectral decay index. When the laser pulse is p-polarized, plasma effects do modify the harmonic spectrum, weakening the so-called universal decay with p=8/3 to p=5/3, or below. In this work, appeal is made to a single particle radiation model in support of the predictions from particle-in-cell (PIC) simulations. Using this numerical technique we further show that the emission radiated by electrons -that are relativistically accelerated by the laser field inside the plasma, after being expelled into vacuum, the so-called Brunel electrons is characterized not only by the plasma line but also by ultraviolet harmonic orders described by the 5/3 decay index. Results obtained from these simulations suggest that for ultra-relativistic light intensities, the spectral decay index is further reduced, with p now in the range 2/3 ≤ p ≤ 4/3. This reduction is indicative of a transition from the regime where Brunel-induced plasma radiation influences the spectrum to one dominated by bremsstrahlung emission from the Brunel electrons.

Keywords: ultra-relativistic, laser-plasma interactions, high-order harmonic emission, radiation, spectrum

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Authors: Yiming Jin, Ping Dong

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The third super-harmonic resonance of a pipeline close to the seabed is investigated in this paper. To analyse the vortex-induced vibration (VIV) of the pipeline close to the seabed, the classic Van der Pol equation is extended with a nonlinear item. Then, on the base of the multi-scale method, the frequency-response curves of the pipeline with regard to the third super-harmonic resonance are studied with a series of parameters, such as the mass ratio, frequency, damp ratio and gap ratio. On the whole, the numerical results show that the characters of third super-harmonic resonance are quite from that of primary resonance, though with the same trend that the larger is the mass ratio, the smaller impact the gap ratio has on the frequency-response curves of the third super-harmonic resonance.

Keywords: the third super-harmonic resonance, gap ratio, vortex-induced vibration, multi-scale method

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Authors: Hedi Dghim, Ahmed El-Naggar, Istvan Erlich

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Power electronic converters are being introduced in low voltage (LV) grids at an increasingly rapid rate due to the growing adoption of power electronic-based home appliances in residential grid. Photovoltaic (PV) systems are considered one of the potential installed renewable energy sources in distribution power systems. This trend has led to high distortion in the supply voltage which consequently produces harmonic currents in the network and causes an inherent voltage unbalance. In order to investigate the effect of harmonic distortions, a case study of a typical LV grid configuration with high penetration of 3-phase and 1-phase rooftop mounted PV from southern Germany was first considered. Electromagnetic transient (EMT) simulations were then carried out under the MATLAB/Simulink environment which contain detailed models for power electronic-based loads, ohmic-based loads as well as 1- and 3-phase PV. Note that, the switching patterns of the power electronic circuits were considered in this study. Measurements were eventually performed to analyze the distortion levels when PV operating under different solar irradiance. The characteristics of the load-side harmonic impedances were analyzed, and their harmonic contributions were evaluated for different distortion levels. The effect of the high penetration of PV on the harmonic distortion of both positive and negative sequences was also investigated. The simulation results are presented based on case studies. The current distortion levels are in agreement with relevant standards, otherwise the Total Harmonic Distortion (THD) increases under low PV power generation due to its inverse relation with the fundamental current.

Keywords: harmonic distortion analysis, power quality, PV systems, residential distribution system

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Authors: Rumana Ali

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The presence of nonlinear and power electronic switching devices produce distorted output and harmonics into the system. This paper presents a technique to analyze harmonics using digital series oscilloscope (DSO). In power distribution system further measurements are done by DSO, and the waveforms are analyzed using FFT program. The results of this proposed work are helpful for the investigator to install an appropriate compensating device to mitigate the harmonics, in turn, improve the power quality. This case study is carried out at AIT Chikmagalur. It is done as a starting step towards the improvement of energy efficiency at AIT Chikmagalur, and with an overall aim of reducing the electricity bill with a complete energy audit of the institution. Strategies were put forth to reach the above objective: The following strategies were proposed to be implemented to analyze the power quality in EEE department of the institution. Strategy 1: The power factor has to be measured using the energy meter. Power factor improvement may reduce the voltage drop in lines. This brings the voltages at the socket in the labs closer to the nominal voltage of 230V, and thus power quality improves. Strategy 2: The harmonics at the power inlet has to be measured by means of a DSO. The DSO waveform is analyzed using FFT to know the percentage harmonic up to the 13th harmonics of 50Hz. Reduction in the harmonics in the inlet of the EEE department may reduce line losses and therefore reduces energy bill to the institution.

Keywords: harmonic analysis, energy bill, power quality, electronic switching devices

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Authors: Markus Meyer, Bastian Maucher, Rolf Witzmann

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The ever increasing amount of distributed generation in low voltage distribution grids (mainly PV and micro-CHP) can lead to reverse load flows from low to medium/high voltage levels at times of high feed-in. Reverse load flow leads to rising voltages that may even exceed the limits specified in the grid codes. Furthermore, the share of electrical loads connected to low voltage distribution grids via switched power supplies continuously increases. In combination with inverter-based feed-in, this results in high harmonic levels reducing overall power quality. Especially high levels of third-order harmonic currents can lead to neutral conductor overload, which is even more critical if lines with reduced neutral conductor section areas are used. This paper illustrates a possible concept for smart grids in order to increase the feed-in capacity, improve power quality and to ensure safe operation of low voltage distribution grids at all times. The key feature of the concept is a hierarchically structured control strategy that is run on a superordinated controller, which is connected to several distributed grid analyzers and inverters via broad band powerline (BPL). The strategy is devised to ensure both quick response time as well as the technically and economically reasonable use of the available inverters in the grid (PV-inverters, batteries, stepless line voltage regulators). These inverters are provided with standard features for voltage control, e.g. voltage dependent reactive power control. In addition they can receive reactive power set points transmitted by the superordinated controller. To further improve power quality, the inverters are capable of active harmonic filtering, as well as voltage balancing, whereas the latter is primarily done by the stepless line voltage regulators. By additionally connecting the superordinated controller to the control center of the grid operator, supervisory control and data acquisition capabilities for the low voltage distribution grid are enabled, which allows easy monitoring and manual input. Such a low voltage distribution grid can also be used as a virtual power plant.

Keywords: distributed generation, distribution grid, power quality, smart grid, virtual power plant, voltage control

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Authors: Zakir Husain, Deepak Kumar

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The harmonics are very harmful within an electrical system and can have serious consequences such as reducing the life of apparatus, stress on cable and equipment etc. This paper cites extensive analytical study of harmonic characteristics of multiphase (six-phase) and three-phase system equipped with two and three level inverters for non-linear loads. Multilevel inverter has elevated voltage capability with voltage limited devices, low harmonic distortion, abridged switching losses. Multiphase technology also pays a promising role in harmonic reduction. Matlab simulation is carried out to compare the advantage of multi-phase over three phase systems equipped with two or three level inverters for non-linear load harmonic reduction. The extensive simulation results are presented based on case studies.

Keywords: fast Fourier transform (FFT), harmonics, inverter, ripples, total harmonic distortion (THD)

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Authors: M. Sarikanat, E. Akar, I. Şen, Y. Seki, O. C. Yılmaz, B. O. Gürses, L. Cetin, O. Özdemir, K. Sever

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Chitosan is a natural, nontoxic, polyelectrolyte, cheap polymer. In this study, chitosan based electroactive polymer (CBEAP) was fabricated. Electroactive properties of this polymer were investigated at different voltages. It exhibited excellent tip displacement at low voltages (1, 3, 5, 7 V). Tip displacement was increased as the applied voltage increased. Best tip displacement was investigated as 28 mm at 5V. Characterization of CBEAP was investigated by scanning electron microscope, X-ray diffraction and tensile testing. CBEAP exhibited desired electroactive properties at low voltages. It is suitable for using in artificial muscle and various robotic applications.

Keywords: chitosan, electroactive polymer, electroactive properties

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Authors: Wilfred Fritz

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Grid connected solar PV inverters need to be compliant to standard regulations regarding unwanted harmonic generation. This paper gives an introduction to harmonics, solar PV inverter voltage regulation and balancing through compensation and investigates the behaviour of harmonic generation at different power levels. Practical measurements of harmonics and power levels with a power quality data logger were made, on a test network at a university in Germany. The test setup and test results are discussed. The major finding was that between the morning and afternoon load peak windows when the PV inverters operate under low solar insolation and low power levels, more unwanted harmonics are generated. This has a huge impact on the power quality of the grid as well as capital and maintenance costs. The design of a single-tuned harmonic filter towards harmonic mitigation is presented.

Keywords: harmonics, power quality, pulse width modulation, total harmonic distortion

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Authors: R. S. Al Abri, M. H. Albadi, M. H. Al Abri, U. K. Al Rasbi, M. H. Al Hasni, S. M. Al Shidi

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This paper presents an analysis study on the impacts of the changes of the capacitor banks, the loss of a transformer, and the installation of distributed generation on the voltage total harmonic distortion and harmonic resonance. The study is applied in a real system in Oman, Sohar Industrial Port–C Substation Network. Frequency scan method and Fourier series analysis method are used with the help of EDSA software. Moreover, the results are compared with limits specified by national Oman distribution code.

Keywords: power quality, capacitor bank, voltage total harmonics distortion, harmonic resonance, frequency scan

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Authors: Emad K. Jaradat, Ala’a Al-Faqih

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Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.

Keywords: non-linear Schrodinger equation, Elzaki decomposition method, harmonic oscillator, one and two-dimensional Schrodinger equation

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Authors: Leonid Borisov, Yuri Orlov

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We obtain explicit formulas of finitely multiple approximations of the equilibrium density matrix for the case of the harmonic oscillator using Chernoff's theorem and the notion of semigroup which is Chernoff equivalent to average semigroup. Also we found explicit formulas for the corresponding approximate Wigner functions and average values of the observable. We consider a superposition of τ -quantizations representing a wide class of linear quantizations. We show that the convergence of the approximations of the average values of the observable is not uniform with respect to the Gibbs parameter. This does not allow to represent approximate expression as the sum of the exact limits and small deviations evenly throughout the temperature range with a given order of approximation.

Keywords: Chernoff theorem, Feynman formulas, finitely multiple approximation, harmonic oscillator, Wigner function

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Authors: A. Prajapati, K. L. Koo, F. Ghassemi, M. Mulimakwenda

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In the UK, as the volume of non-linear loads connected to transmission grid continues to rise steeply, the harmonic distortion levels on transmission network are becoming a serious concern for the network owners and system operators. This paper outlines the findings of the study conducted to verify the proposal that the harmonic mitigation could be optimized and can be managed economically and effectively at the transmission network level by the Transmission Owner (TO) instead of the individual polluter connected to the grid. Harmonic mitigation studies were conducted on selected regions of the transmission network in England for recently connected offshore wind power plants to strategize and optimize selected harmonic filter options. The results – filter volume and capacity – were then compared against the mitigation measures adopted by the individual connections. Estimation ratios were developed based on the actual installed and optimal proposed filters. These estimation ratios were then used to derive harmonic filter requirements for future contracted connections. The study has concluded that a saving of 37% in the filter volume/capacity could be achieved if the TO is to centrally manage the harmonic mitigation instead of individual polluter installing their own mitigation solution.

Keywords: C-type filter, harmonics, optimization, offshore wind farms, interconnectors, HVDC, renewable energy, transmission owner

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Authors: Mohammed Ali Hjaji, A.K. El-Senussi, Said H. Eshtewi

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The flexural dynamic response of symmetric laminated composite beams subjected to general transverse harmonic forces is investigated. The dynamic equations of motion and associated boundary conditions based on the first order shear deformation are derived through the use of Hamilton’s principle. The influences of shear deformation, rotary inertia, Poisson’s ratio and fibre orientation are incorporated in the present formulation. The resulting governing flexural equations for symmetric composite Timoshenko beams are exactly solved and the closed form solutions for steady state flexural response are then obtained for cantilever and simply supported boundary conditions. The applicability of the analytical closed-form solution is demonstrated via several examples with various transverse harmonic loads and symmetric cross-ply and angle-ply laminates. Results based on the present solution are assessed and validated against other well established finite element solutions and exact solutions available in the literature.

Keywords: analytical solution, flexural response, harmonic forces, symmetric laminated beams, steady state response

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Authors: Ali Asheibi

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The rapid increase in the size of databases required to store power quality monitoring data has demanded new techniques for analysing and understanding the data. One suggested technique to assist in analysis is data mining. Preparing raw data to be ready for data mining exploration take up most of the effort and time spent in the whole data mining process. Clustering is an important technique in data mining and machine learning in which underlying and meaningful groups of data are discovered. Large amounts of harmonic data have been collected from an actual harmonic monitoring system in a distribution system in Australia for three years. This amount of acquired data makes it difficult to identify operational events that significantly impact the harmonics generated on the system. In this paper, harmonic data preparation processes to better understanding of the data have been presented. Underlying classes in this data has then been identified using clustering technique based on the Minimum Message Length (MML) method. The underlying operational information contained within the clusters can be rapidly visualised by the engineers. The C5.0 algorithm was used for classification and interpretation of the generated clusters.

Keywords: data mining, harmonic data, clustering, classification

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