Search results for: harmonic spread factor (HSF)

Authors: N. Janjamraj, A. Oonsivilai

Abstract:

This paper present the harmonic elimination of hybrid multilevel inverters (HMI) which could be increase the number of output voltage level. Total Harmonic Distortion (THD) is one of the most important requirements concerning performance indices. Because of many numbers output levels of HMI, it had numerous unknown variables of eliminate undesired individual harmonic and THD nonlinear equations set. Optimized harmonic stepped waveform (OHSW) is solving switching angles conventional method, but most complicated for solving as added level. The artificial intelligent techniques are deliberation to solve this problem. This paper presents the Particle Swarm Optimization (PSO) technique for solving switching angles to get minimum THD and eliminate undesired individual harmonics of 15-levels hybrid multilevel inverters. Consequently it had many variables and could eliminate numerous harmonics. Both advantages including high level of inverter and Particle Swarm Optimization (PSO) are used as powerful tools for harmonics elimination.

Keywords: Multilevel Inverters, Particle Swarms Optimization, Harmonic Elimination.

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Authors: Wilfred Fritz

Abstract:

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: Azali Saudi, Jumat Sulaiman

Abstract:

Harmonic functions are solutions to Laplace’s equation that are known to have an advantage as a global approach in providing the potential values for autonomous vehicle navigation. However, the computation for obtaining harmonic functions is often too slow particularly when it involves very large environment. This paper presents a two-stage iterative method namely Modified Arithmetic Mean (MAM) method for solving 2D Laplace’s equation. Once the harmonic functions are obtained, the standard Gradient Descent Search (GDS) is performed for path finding of an autonomous vehicle from arbitrary initial position to the specified goal position. Details of the MAM method are discussed. Several simulations of vehicle navigation with path planning in a static known indoor environment were conducted to verify the efficiency of the MAM method. The generated paths obtained from the simulations are presented. The performance of the MAM method in computing harmonic functions in 2D environment to solve path planning problem for an autonomous vehicle navigation is also provided.

Keywords: Modified Arithmetic Mean method, Harmonic functions, Laplace’s equation, path planning.

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Authors: Daniel Zammit, Cyril Spiteri Staines, Maurice Apap

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This paper presents a study on Proportional Resonant (PR) current control with additional PR harmonic compensators for Grid Connected Photovoltaic (PV) Inverters. Both simulation and experimental results will be presented. Testing was carried out on a 3kW Grid-Connected PV Inverter which was designed and constructed for this research.

Keywords: Inverters, Proportional-Resonant Controllers, Harmonic Compensation, Photovoltaic.

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Authors: Thomas I. Kounitis

Abstract:

The purpose of this paper is to investigate the influence of a number of variables on the conditional mean and conditional variance of credit spread changes. The empirical analysis in this paper is conducted within the context of bivariate GARCH-in- Mean models, using the so-called BEKK parameterization. We show that credit spread changes are determined by interest-rate and equityreturn variables, which is in line with theory as provided by the structural models of default. We also identify the credit spread change volatility as an important determinant of credit spread changes, and provide evidence on the transmission of volatility between the variables under study.

Keywords: Credit spread changes, GARCH-in-Mean models, structural framework, volatility transmission.

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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: T. Patrice Nna Nna, S. Ndjakomo Essiane, S. Pérabi Ngoffé, F. Amigue Fissou

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This paper deals with the harmonic decontamination of current in an electrical grid by an active shunt filter in order to improve power quality. The contribution of this paper is mainly based on the proposal of a control strategy for an active filter based on Duty Cycle Modulation (DCM). First, three-monophase method is applied for the identification of disturbing currents. A Simulink model of this method is given for one phase of the grid. Secondly, two orders were designed: the first one is the Hysteresis Control and the second one is the DCM Control. Finally, a comparative study of the two controls was performed. The results obtained show a significant improvement in the rate of harmonic distortion for both controls. The harmonic distortion for the Hysteresis control is limited by the non-controllability of the switching frequencies of the inverter's switches and reduces the harmonic distortion rate (THD) to 3.12% as opposed to the DCM control which limits the THD to 2.82% which makes it better.

Keywords: Harmonic pollution, shunt active filter, hysteresis, Duty Cycle Modulation.

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Authors: Mihaela Popescu, Alexandru Bitoleanu, Mircea Dobriceanu, Vlad Suru

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The aim of this paper is to identify an optimum control strategy of three-phase shunt active filters to minimize the total harmonic distortion factor of the supply current. A classical PIPI cascade control solution of the output current of the active filterand the voltage across the DC capacitor based on Modulus–Optimum criterion is taken into consideration. The control system operation has been simulated using Matlab-Simulink environment and the results agree with the theoretical expectation. It is shown that there is an optimum value of the DC-bus voltage which minimizes the supply current harmonic distortion factor. It corresponds to the equality of the apparent power at the output of the active filter and the apparent power across the capacitor. Finally, predicted results are verified experimentally on a MaxSine active power filter.

Keywords: Active filtering, Controller tuning, Modulus Optimum criterion, Optimum control.

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

Abstract:

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: Elena Kotevska

Abstract:

This paper presents a generalization kernel for gravitational potential determination by harmonic splines. It was shown in [10] that the gravitational potential can be approximated using a kernel represented as a Newton integral over the real Earth body. On the other side, the theory of geopotential approximation by harmonic splines uses spherically oriented kernels. The purpose of this paper is to show that in the spherical case both kernels have the same type of representation, which leads us to conclusion that it is possible to consider the kernel represented as a Newton integral over the real Earth body as a kind of generalization of spherically harmonic kernels to real geometries.

Keywords: Geopotential, Reproducing Kernel, Approximation, Regular Surface

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Authors: Basant Kumar, Animesh Anand, S.P. Singh, Anand Mohan

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This paper presents a new spread-spectrum watermarking algorithm for digital images in discrete wavelet transform (DWT) domain. The algorithm is applied for embedding watermarks like patient identification /source identification or doctors signature in binary image format into host digital radiological image for potential telemedicine applications. Performance of the algorithm is analysed by varying the gain factor, subband decomposition levels, and size of watermark. Simulation results show that the proposed method achieves higher watermarking capacity.

Keywords: Watermarking, spread-spectrum, discrete wavelettransform, telemedicine

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Authors: T. Tanitteerapan, E.Thanpo

Abstract:

This paper, a simple continuous conduction mode (CCM) pulse-width-modulated (PWM) controller for high power factor boost converters is introduced. The duty ratios were obtained by the comparison of a sensed signal from inductor current or switch current and a negative slope ramp carrier waveform in each switching period. Due to the proposed control requires only the inductor current or switch current sensor and the output voltage sensor, its circuit implementation was very simple. To verify the proposed control, the circuit experimentation of a 350 W boost converter with the proposed control was applied. From the results, the input current waveform was shaped to be closely sinusoidal, implying high power factor and low harmonics.

Keywords: High power factor converters, boost converters, low harmonic rectifiers, power factor correction, and current control.

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Authors: Atul Krishna Banik

Abstract:

Nonlinear response behaviour of a cracked RC beam under harmonic excitation is analysed to investigate various instability phenomena like, bifurcation, jump phenomena etc. The nonlinearity of the system arises due to opening and closing of the cracks in the RC beam and is modelled as a cubic polynomial. In order to trace different branches at the bifurcation point on the response curve (amplitude versus frequency of excitation plot), an arc length continuation technique along with the incremental harmonic balance (IHBC) method is employed. The stability of the solution is investigated by the Floquet theory using Hsu-s scheme. The periodic solutions obtained by the IHBC method are compared with these obtained by the numerical integration of the equation of motion. Characteristics of solutions fold bifurcation, jump phenomena and from stable to unstable zones are identified.

Keywords: Incremental harmonic balance, arc-length continuation, bifurcation, jump phenomena.

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Authors: Abdelhalim Kessal

Abstract:

This paper treats a design of combined control of a single phase power factor correction (PFC). The strategy of the proposed control is based on two parts, the first, for the outer loop (DC output regulated voltage), and the second govern the input current of the converter in order to achieve a sinusoidal form in phase with the grid voltage. Two kinds of regulators are used, Fuzzy controller for the outer loop and predictive controller for the inner loop. The controllers are verified and discussed through simulation under MATLAB/Simulink platform. Also an experimental confirmation is applied. Results present a high dynamic performance under various parameters changes.

Keywords: Boost converter, harmonic distortion, Fuzzy, prediction, unity power factor.

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Authors: A. K. Al-Othman, Nabil A. Ahmed, A. M. Al-Kandari, H. K. Ebraheem

Abstract:

Selective harmonic elimination-pulse width modulation techniques offer a tight control of the harmonic spectrum of a given voltage waveform generated by a power electronic converter along with a low number of switching transitions. Traditional optimization methods suffer from various drawbacks, such as prolonged and tedious computational steps and convergence to local optima; thus, the more the number of harmonics to be eliminated, the larger the computational complexity and time. This paper presents a novel method for output voltage harmonic elimination and voltage control of PWM AC/AC voltage converters using the principle of hybrid Real-Coded Genetic Algorithm-Pattern Search (RGA-PS) method. RGA is the primary optimizer exploiting its global search capabilities, PS is then employed to fine tune the best solution provided by RGA in each evolution. The proposed method enables linear control of the fundamental component of the output voltage and complete elimination of its harmonic contents up to a specified order. Theoretical studies have been carried out to show the effectiveness and robustness of the proposed method of selective harmonic elimination. Theoretical results are validated through simulation studies using PSIM software package.

Keywords: PWM, AC/AC voltage converters, selectiveharmonic elimination, direct search method, pattern search method, Real-coded Genetic algorithms, evolutionary algorithms andoptimization.

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Authors: D. R. Patil, U. Gudaru

Abstract:

Most electrical distribution systems are incurring large losses as the loads are wide spread, inadequate reactive power compensation facilities and their improper control. A typical static VAR compensator consists of capacitor bank in binary sequential steps operated in conjunction with a thyristor controlled reactor of the smallest step size. This SVC facilitates stepless control of reactive power closely matching with load requirements so as to maintain power factor nearer to unity. This type of SVC-s requiring a appropriately controlled TCR. This paper deals with an air cored reactor suitable for distribution transformer of 3phase, 50Hz, Dy11, 11KV/433V, 125 KVA capacity. Air cored reactors are designed, built, tested and operated in conjunction with capacitor bank in five binary sequential steps. It is established how the delta connected TCR minimizes the harmonic components and the operating range for various electrical quantities as a function of firing angle is investigated. In particular firing angle v/s line & phase currents, D.C. components, THD-s, active and reactive powers, odd and even triplen harmonics, dominant characteristic harmonics are all investigated and range of firing angle is fixed for satisfactory operation. The harmonic spectra for phase and line quantities at specified firing angles are given. In case the TCR is operated within the bound specified in this paper established through simulation studies are yielding the best possible operating condition particularly free from all dominant harmonics.

Keywords: Binary Sequential switched capacitor bank, TCR, Nontriplen harmonics, step less Q control, Active and Reactivepower, Simulink

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Authors: Yiming Jin, Yuanhao Gao

Abstract:

In this paper, using the method of multiple scales, the second sub-harmonic resonance in vortex-induced vibrations (VIV) of a marine pipeline close to the seabed is investigated based on a developed wake oscillator model. The amplitude-frequency equations are also derived. It is found that the oscillation will increase all the time when both discriminants of the amplitude-frequency equations are positive while the oscillation will decay when the discriminants are negative.

Keywords: Vortex-induced vibrations, marine pipeline, seabed, sub-harmonic resonance.

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Authors: M. Najafi, S. Bab, F. Rahimi Dehgolan

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The motion of an axially moving beam with rotating prismatic joint with a tip mass on the end is analyzed to investigate the nonlinear vibration and dynamic stability of the beam. The beam is moving with a harmonic axially and rotating velocity about a constant mean velocity. A time-dependent partial differential equation and boundary conditions with the aid of the Hamilton principle are derived to describe the beam lateral deflection. After the partial differential equation is discretized by the Galerkin method, the method of multiple scales is applied to obtain analytical solutions. Frequency response curves are plotted for the super harmonic resonances of the first and the second modes. The effects of non-linear term and mean velocity are investigated on the steady state response of the axially moving beam. The results are validated with numerical simulations.

Keywords: Axially moving beam, Galerkin method, non-linear vibration, super harmonic resonances.

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Authors: Nerguè Kassahan Kone, Souleymane Oumtanaga

Abstract:

The third generation (3G) of cellular system adopted the spread spectrum as solution for the transmission of the data in the physical layer. Contrary to systems IS-95 or CDMAOne (systems with spread spectrum of the preceding generation), the new standard, called Universal Mobil Telecommunications System (UMTS), uses long codes in the down link. The system is conceived for the vocal communication and the transmission of the data. In particular, the down link is very important, because of the asymmetrical request of the data, i.e., more remote loading towards the mobiles than towards the basic station. Moreover, the UMTS uses for the down link an orthogonal spreading out with a variable factor of spreading out (OVSF for Orthogonal Variable Spreading Factor). This characteristic makes it possible to increase the flow of data of one or more users by reducing their factor of spreading out without changing the factor of spreading out of other users. In the current standard of the UMTS, two techniques to increase the performances of the down link were proposed, the diversity of sending antenna and the codes space-time. These two techniques fight only fainding. The receiver proposed for the mobil station is the RAKE, but one can imagine a receiver more sophisticated, able to reduce the interference between users and the impact of the coloured noise and interferences to narrow band. In this context, where the users have long codes synchronized with variable factor of spreading out and ignorance by the mobile of the other active codes/users, the use of the sequences of code pseudo-noises different lengths is presented in the form of one of the most appropriate solutions.

Keywords: DS-CDMA, multiple access interference, ratio Signal / interference + Noise.

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Authors: D. Im, S. Choi, H. Kwon, S. H. Park, J. H. Kwon

Abstract:

This paper is an extension of a previous work where a diagonally implicit harmonic balance method was developed and applied to simulate oscillatory motions of pitching airfoil and wing. A more detailed study on the accuracy, convergence, and the efficiency of the method is carried out in the current paperby varying the number of harmonics in the solution approximation. As the main advantage of the method is itsusage for the design optimization of the unsteady problems, its application to more practical case of rotor flow analysis during forward flight is carried out and compared with flight test data and time-accurate computation results.

Keywords: Design optimization, Implicit harmonic balancemethod, number of harmonics, rotor flows

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

Abstract:

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 emissions, finite element analysis.

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Authors: M. Nirmala

Abstract:

Power quality in terms of power factor, THD and precisely regulated output voltage are the major key factors for efficient operation of power electronic converters. This paper presents an easy and effective active wave shaping control scheme for the pulsed input current drawn by the uncontrolled diode bridge rectifier thereby achieving power factor nearer to unity and also satisfying the THD specifications. It also regulates the output DC-bus voltage. CCM boost power factor correction with constant frequency operation features smaller inductor current ripple resulting in low RMS currents on inductor and switch thus leading to low electromagnetic interference. The objective of this work is to develop an active PFC control circuit using CCM boost converter implementing variable duty cycle control. The proposed scheme eliminates inductor current sensing requirements yet offering good performance and satisfactory results for maintaining the power quality. Simulation results have been presented which covers load changes also.

Keywords: CCM Boost converter, Power factor Correction, Total harmonic distortion, Variable Duty Cycle.

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Authors: T. Messikh, S. Mekhilef, N. A. Rahim

Abstract:

This paper presents an effective technique for harmonic current mitigation using an adaptive notch filter (ANF) to estimate current harmonics. The proposed filter consists of multiple units of ANF connected in parallel structure; each unit is governed by two ordinary differential equations. The frequency estimation is carried out based on the output of these units. The simulation and experimental results show the ability of the proposed tracking scheme to accurately estimate harmonics. The proposed filter was implemented digitally in TMS320F2808 and used in the control of hybrid active power filter (HAPF). The theoretical expectations are verified and demonstrated experimentally.

Keywords: Adaptive notch filter, Active power filter, harmonic filtering, Time varying frequency.

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Authors: R. Ziaie Moayed, A. Mahigir

Abstract:

Stone column technique has been successfully employed to improve the load-settlement characteristics of foundations. A series of finite element numerical analyses of harmonic dynamic loading have been conducted on strengthened raft footing to study the effects of single and group stone columns on settlement of circular footings. The settlement of circular raft footing that improved by single and group of stone columns are studied under harmonic dynamic loading. This loading is caused by heavy machinery foundations. A detailed numerical investigation on behavior of single column and group of stone columns is carried out by varying parameters like weight of machinery, loading frequency and period. The result implies that presence of single and group of stone columns enhanced dynamic behavior of the footing so that the maximum and residual settlement of footing significantly decreased. 

Keywords: Finite element analysis, harmonic loading, settlement, stone column.

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Authors: A. K. Al-Othman, H. A. Al-Mekhaizim

Abstract:

Multilevel inverters supplied from equal and constant dc sources almost don-t exist in practical applications. The variation of the dc sources affects the values of the switching angles required for each specific harmonic profile, as well as increases the difficulty of the harmonic elimination-s equations. This paper presents an extremely fast optimal solution of harmonic elimination of multilevel inverters with non-equal dc sources using Tanaka's fuzzy linear regression formulation. A set of mathematical equations describing the general output waveform of the multilevel inverter with nonequal dc sources is formulated. Fuzzy linear regression is then employed to compute the optimal solution set of switching angles.

Keywords: Multilevel converters, harmonics, pulse widthmodulation (PWM), optimal control.

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Authors: Isao Tomita

Abstract:

We develop a periodically-poled LiNbO3 (PPLN) device for highly-efficient third-harmonic generation (THG), where the THG efficiency is enhanced with a cavity. THG can usually be produced via χ(3)-nonlinear materials by optical pumping with very high pump-power. Instead, we here propose THG by moderate-power pumping through a specially-designed PPLN device containing only χ(2)-nonlinearity, where sum-frequency generation in the χ(2) process is employed for the mixing of a pump beam and a second-harmonic-generation (SHG) beam produced from the pump beam. The cavity is designed to increase the SHG power with dichroic mirrors attached to both ends of the device that perfectly reflect the SHG beam back to the device and yet let the pump and THG beams pass through the mirrors. This brings about a THG-power enhancement because of THG power proportional to the enhanced SHG power. We examine the THG-efficiency dependence on the mirror reflectance and show that very high THG-efficiency is obtained at moderate pump-power when compared with that of a cavity-free PPLN device.

Keywords: Cavity, periodically-poled LiNbO3, sum-frequency generation, third-harmonic generation.

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Authors: A. Morsli, A.Tlemçani, N. Ould Cherchali, M. S. Boucherit

Abstract:

This article presents two methods for the compensation of harmonics generated by a nonlinear load. The first is the classic method P-Q. The second is the controller by modern method of artificial intelligence specifically fuzzy logic. Both methods are applied to a shunt Active Power Filter (sAPF) based on a three-phase voltage converter at five levels NPC topology. In calculating the harmonic currents of reference, we use the algorithm P-Q and pulse generation, we use the intersective PWM. For flexibility and dynamics, we use fuzzy logic. The results give us clear that the rate of Harmonic Distortion issued by fuzzy logic is better than P-Q.

Keywords: Fuzzy logic controller, P-Q method, Pulse Width Modulation (PWM), shunt Active Power Filter (sAPF), Total Harmonic Distortion (THD).

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Authors: Sikder Mohammad Faruk, Mir Mofajjal Hossain, Muhibul Haque Bhuyan

Abstract:

In this investigative research paper, we have presented the simulation results of a three-phase rectifier circuit to improve the input side current using the passive filters, such as capacitors and inductors at the output and input terminals of the rectifier circuit respectively. All simulation works were performed in a personal computer using the PSPICE simulator software, which is a virtual circuit design and simulation software package. The output voltages and currents were measured across a resistive load of 1 k. We observed that the output voltage levels, input current wave shapes, harmonic contents through the harmonic spectrum, and total harmonic distortion improved due to the use of such filters.

Keywords: input current wave, three-phase rectifier, passive filter, PSPICE Simulation

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Authors: S. Janpong, K-L. Areerak, K-N. Areerak

Abstract:

This paper aims to present the reviews of the application of neural network in shunt active power filter (SAPF). From the review, three out of four components of SAPF structure, which are harmonic detection component, compensating current control, and DC bus voltage control, have been adopted some of neural network architecture as part of its component or even substitution. The objectives of most papers in using neural network in SAPF are to increase the efficiency, stability, accuracy, robustness, tracking ability of the systems of each component. Moreover, minimizing unneeded signal due to the distortion is the ultimate goal in applying neural network to the SAPF. The most famous architecture of neural network in SAPF applications are ADALINE and Backpropagation (BP).

Keywords: Active power filter, neural network, harmonic distortion, harmonic detection and compensation, non-linear load.

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Authors: K. N. Dinesh Babu, P. K. Gargava

Abstract:

Energization of a transformer results in sudden flow of current which is an effect of core magnetization. This current will be dominated by the presence of second harmonic, which in turn is used to segregate fault and inrush current, thus guaranteeing proper operation of the relay. This additional security in the relay sometimes obstructs or delays differential protection in a specific scenario, when the 2^nd harmonic content was present during a genuine fault. This kind of scenario can result in isolation of the transformer by Buchholz and pressure release valve (PRV) protection, which is acted when fault creates more damage in transformer. Such delays involve a huge impact on the insulation failure, and chances of repairing or rectifying fault of problem at site become very dismal. Sometimes this delay can cause fire in the transformer, and this situation becomes havoc for a sub-station. Such occurrences have been observed in field also when differential relay operation was delayed by 10-15 ms by second harmonic blocking in some specific conditions. These incidences have led to the need for an alternative solution to eradicate such unwarranted delay in operation in future. Modern numerical relay, called as intelligent electronic device (IED), is embedded with advanced protection features which permit higher flexibility and better provisions for tuning of protection logic and settings. Such flexibility in transformer protection IEDs, enables incorporation of alternative methods such as dynamic switching of second harmonic feature for blocking the differential protection with additional security. The analysis and precautionary measures carried out in this case, have been simulated and discussed in this paper to ensure that similar solutions can be adopted to inhibit analogous issues in future.

Keywords: Differential protection, intelligent electronic device (IED), 2nd harmonic, inrush inhibit.

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