Search results for: harmonics

Authors: Saeed Asiri, Yousuf Z. AL-Zahrani

Abstract:

A new class of support structures, called periodic structures, is introduced in this paper as a viable means for isolating the vibration transmitted from the sea waves to offshore platform structures through its legs. A passive approach to reduce transmitted vibration generated by waves is presented. The approach utilizes the property of periodic structural components that creates stop and pass bands. The stop band regions can be tailored to correspond to regions of the frequency spectra that contain harmonics of the wave frequency, attenuating the response in those regions. A periodic structural component is comprised of a repeating array of cells, which are themselves an assembly of elements. The elements may have differing material properties as well as geometric variations. For the purpose of this research, only geometric and material variations are considered and each cell is assumed to be identical. A periodic leg is designed in order to reduce transmitted vibration of sea waves. The effectiveness of the periodicity on the vibration levels of platform will be demonstrated theoretically. The theory governing the operation of this class of periodic structures is introduced using the transfer matrix method. The unique filtering characteristics of periodic structures are demonstrated as functions of their design parameters for structures with geometrical and material discontinuities; and determine the propagation factor by using the spectral finite element analysis and the effectiveness of design on the leg structure by changing the ratio of step length and area interface between the materials is demonstrated in order to find the propagation factor and frequency response.

Keywords: vibrations, periodic structures, offshore, platforms, transfer matrix method

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Authors: Reza Soleimanpour, Ching Tai Ng

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Fibre-composites are widely used in various structures due to their attractive properties such as higher stiffness to mass ratio and better corrosion resistance compared to metallic materials. However, one serious weakness of this composite material is delamination, which is a subsurface separation of laminae. A low level of this barely visible damage can cause a significant reduction in residual compressive strength. In the last decade, the application of guided waves for damage detection has been a topic of significant interest for many researches. Among all guided wave techniques, nonlinear guided wave has shown outstanding sensitivity and capability for detecting different types of damages, e.g. cracks and delaminations. So far, most of researches on applications of nonlinear guided wave have been dedicated to isotropic material, such as aluminium and steel, while only a few works have been done on applications of nonlinear characteristics of guided waves in anisotropic materials. This study investigates the nonlinear interactions of the fundamental antisymmetric lamb wave (A0) with delamination in composite laminates using three-dimensional (3D) explicit finite element (FE) simulations. The nonlinearity considered in this study arises from interactions of two interfaces of sub-laminates at the delamination region, which generates contact acoustic nonlinearity (CAN). The aim of this research is to investigate the phenomena of CAN in composite laminated beams by a series of numerical case studies. In this study interaction of fundamental antisymmetric lamb wave with delamination of different sizes are studied in detail. The results show that the A0 lamb wave interacts with the delaminations generating CAN in the form of higher harmonics, which is a good indicator for determining the existence of delaminations in composite laminates.

Keywords: contact acoustic nonlinearity, delamination, fibre reinforced composite beam, finite element, nonlinear guided waves

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Authors: M. Almutairi, S. Hadjiloucas

Abstract:

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: Daniel O. Johnson, Abiodun A. Ogunseye, Aaron Aransiola, Majors Samuel

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Power Inverter is a very important device in renewable energy use particularly for solar photovoltaic power application because it is the effective interface between the DC power generator and the load or the grid. Transformerless inverter is getting more and more preferred to the power converter with galvanic isolation transformer and may eventually supplant it. Transformerless inverter offers advantages of improved DC to AC conversion and power delivery efficiency; and reduced system cost, weight and complexity. This work presents thorough analysis of the design and prototyping of 3KVA grid-tie transformerless inverter. The inverter employs electronic switching method with minimised heat generation in the system and operates based on the principle of pulse-width modulation (PWM). The design is such that it can take two inputs, one from PV arrays and the other from Battery Energy Storage BES and addresses the safety challenge of leakage current. The inverter system was designed around microcontroller system, modeled with Proteus® software for simulation and testing of the viability of the designed inverter circuit. The firmware governing the operation of the grid-tied inverter is written in C language and was developed using MicroC software by Mikroelectronica® for writing sine wave signal code for synchronization to the grid. The simulation results show that the designed inverter circuit performs excellently with very high efficiency, good quality sinusoidal output waveform, negligible harmonics and gives very stable performance under voltage variation from 36VDC to 60VDC input. The prototype confirmed the simulated results and was successfully synchronized with the utility supply. The comprehensive analyses of the circuit design, the prototype and explanation on overall performance will be presented.

Keywords: grid-tied inverter, leakage current, photovoltaic system, power electronic, transformerless inverter

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Authors: Adinarayana S., Sudhakar I.

Abstract:

Energy conversion is one of the inevitable parts of any industries. It involves either conversion of mechanical energy in to electrical or vice versa. The later conversion of energy i.e. electrical to mechanical emphasizes the need of motor. Statistics reveals, about 8 % of industries’ annual turnover met on maintenance. Thus substantial numbers of efforts are required to minimize in incurring expenditure met towards break down maintenance. Condition monitoring is one of such techniques based on vibration widely used to recognize premature failures and paves a way to minimize cumbersome involved during breakdown of machinery. The present investigation involves a case study of squirrel cage induction motor (frequently in the electro machines) has been chosen for the conditional monitoring to predict its soundness on the basis of results of FFT analyser. Accelerometer which measures the acceleration converts in to impulses by FFT analyser generates vibration spectrum and time spectrum has been located at various positions on motor under different conditions. Results obtained from the FFT analyser are compared to that of ISO standard vibration severity charts are taken to predict the preventative condition of considered machinery. Initial inspection of motor revealed that stator faults, broken end rings in rotor, eccentricity faults and misalignment between bearings are trouble shootings areas for present investigation. From the results of the shaft frequencies, it can be perceived that there is a misalignment between the bearings at both the ends. The higher order harmonics of FTF shows the presence of cracks on the race of the bearings at both the ends which are in the incipient stage. Replacement of the bearings at both the drive end (6306) and non drive end (6206) and the alignment check between the bearings in the shaft are suggested as the constructive measures towards preventive maintenance of considered squirrel cage induction motor.

Keywords: FFT analyser, condition monitoring, vibration spectrum, time wave form

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Authors: Adi Narayana S Sudhakar. I

Abstract:

Energy conversion is one of the inevitable parts of any industries. It involves either conversion of mechanical energy in to electrical or vice versa. The later conversion of energy i.e. electrical to mechanical emphasizes the need of motor .Statistics reveals, about 8 % of industries’ annual turnover met on maintenance. Thus substantial numbers of efforts are required to minimize in incurring expenditure met towards break down maintenance. Condition monitoring is one of such techniques based on vibration widely used to recognize premature failures and paves a way to minimize cumbersome involved during breakdown of machinery. The present investigation involves a case study of squirrel cage induction motor (frequently in the electro machines) has been chosen for the conditional monitoring to predict its soundness on the basis of results of FFT analyser. Accelerometer which measures the acceleration converts in to impulses by FFT analyser generates vibration spectrum and time spectrum has been located at various positions on motor under different conditions. Results obtained from the FFT analyzer are compared to that of ISO standard vibration severity charts are taken to predict the preventative condition of considered machinery. Initial inspection of motor revealed that stator faults, broken end rings in rotor, eccentricity faults and misalignment between bearings are trouble shootings areas for present investigation. From the results of the shaft frequencies, it can be perceived that there is a misalignment between the bearings at both the ends. The higher order harmonics of FTF shows the presence of cracks on the race of the bearings at both the ends which are in the incipient stage. Replacement of the bearings at both the drive end (6306) and non-drive end (6206) and the alignment check between the bearings in the shaft are suggested as the constructive measures towards preventive maintenance of considered squirrel cage induction motor.

Keywords: FFT analyser, condition monitoring, vibration spectrum, time spectrum accelerometer

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Authors: P. Serrão, E. Costa, A. Ribeiro, V. Infante

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The characteristic sonority of the Portuguese guitar is in great part what makes Fado so distinguishable from other traditional song styles. The Portuguese guitar is a pear-shaped plucked chordophone with six courses of double strings. This study compares the two types of plain strings available for Portuguese guitar and used by the musicians. One is stainless steel spring wire, the other is high carbon spring steel (music wire). Some musicians mention noticeable differences in sound quality between these two string materials, such as a little more brightness and sustain in the steel strings. Experimental tests were performed to characterize string tension at pitch; mechanical strength and tuning stability using the universal testing machine; dimensional control and chemical composition analysis using the scanning electron microscope. The string dynamical behaviour characterization experiments, including frequency response, inharmonicity, transient response, damping phenomena and were made in a monochord test set-up designed and built in-house. Damping factor was determined for the fundamental frequency. As musicians are able to detect very small damping differences, an accurate a characterization of the damping phenomena for all harmonics was necessary. With that purpose, another improved monochord was set and a new system identification methodology applied. Due to the complexity of this task several adjustments were necessary until obtaining good experimental data. In a few cases, dynamical tests were repeated to detect any evolution in damping parameters after break-in period when according to players experience a new string sounds gradually less dull until reaching the typically brilliant timbre. Finally, each set of strings was played on one guitar by a distinguished player and recorded. The recordings which include individual notes, scales, chords and a study piece, will be analysed to potentially characterize timbre variations.

Keywords: damping factor, music wire, portuguese guitar, string dynamics

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Authors: Mario J. Meco-Gutierrez, Francisco Perez-Hidalgo, Juan R. Heredia-Larrubia, Antonio Ruiz-Gonzalez, Francisco Vargas-Merino

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More and more applications power inverters connected to transformers, for example, the connection facilities to the power grid renewable generation. It is well known that the quality of signal power inverters it is not a pure sine. The harmonic content produced negative effects, one of which is the heating of electrical machines and therefore, affects the life of the machines. The decrease of life of transformers can be calculated by Arrhenius or Montsinger equation. Analyzing this expression any (long-term) decrease of a transformer temperature for 6º C - 7º C means doubles its life-expectancy. Methodologies: This work presents the technique of pulse width modulation (PWM) with an injection of harmonic and triangular frequency carrier modulated in frequency. This technique is used to improve the quality of the output voltage signal of the power inverters controlled PWM. The proposed technique increases in the fundamental term and a significant reduction in low order harmonics with the same commutations per time that control sine PWM. To achieve this, the modulating wave is compared to a triangular carrier with variable frequency over the period of the modulator. Therefore, it is, advantageous for the modulating signal to have a large amount of sinusoidal “information” in the areas of greater sampling. A triangular signal with a frequency that varies over the modulator’s period is used as a carrier, for obtaining more samples in the area with the greatest slope. A power inverter controlled by PWM proposed technique is connected to a transformer. Results: In order to verify the derived thermal parameters under different operation conditions, another ambient and loading scenario is involved for a further verification, which was sampled from the same power transformer. Temperatures of different parts of the transformer will be exposed for each PWM control technique analyzed. An assessment of the temperature be done with different techniques PWM control and hence the life of the transformer is calculated for each technique. Conclusion: This paper analyzes such as transformer heating produced by this technique and compared with other forms of PWM control. In it can be seen as a reduction the harmonic content produces less heat transformer and therefore, an increase in the life of the transformer.

Keywords: heating, power-inverter, PWM, transformer

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Authors: Krystof Kryniski, Asa Kassman Rudolphi, Su Zhao, Per Lindholm

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ABB offers range of turbochargers from 500 kW to 80+ MW diesel and gas engines. Those operate on ships, power stations, generator-sets, diesel locomotives and large, off-highway vehicles. The units need to sustain harsh operating conditions, exposure to high speeds, temperatures and varying loads. They are expected to work at over-critical speeds damping effectively any transients and encountered resonances. Components are often connected via friction joints. Designs of those interfaces need to account for surface roughness, texture, pre-stress, etc. to sustain against fretting fatigue. The experience from field contributed with valuable input on components performance in hash sea environment and their exposure to high temperature, speed and load conditions. Study of tribological interactions of oxide formations provided an insight into dynamic activities occurring between the surfaces. Oxidation was recognized as the dominant factor of a wear. Microscopic inspections of fatigue cracks on turbine indicated insufficient damping and unrestrained structural stress leading to catastrophic failure, if not prevented in time. The contact interface exhibits strongly non-linear mechanism and to describe it the piecewise approach was used. Set of samples representing the combinations of materials, texture, surface and heat treatment were tested on a friction rig under range of loads, frequencies and excitation amplitudes. Developed numerical technique extracted the friction coefficient, tangential contact stiffness and damping. Vast amount of experimental data was processed with the multi-harmonics balance (MHB) method to categorize the components subjected to the periodic excitations. At the pre-defined excitation level both force and displacement formed semi-elliptical hysteresis curves having the same area and secant as the actual ones. By cross-correlating the terms remaining in the phase and out of the phase, respectively it was possible to separate an elastic energy from dissipation and derive the stiffness and damping characteristics.

Keywords: contact interface, fatigue, rotor-dynamics, torsional resonances

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Authors: Marilou Cadatal-Raduban, Minh Hong Pham, Duong Van Pham, Tu Nguyen Xuan, Mui Viet Luong, Kohei Yamanoi, Toshihiko Shimizu, Nobuhiko Sarukura, Hung Dai Nguyen

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There is a great deal of interest in developing all-solid-state tunable ultrashort pulsed lasers emitting in the ultraviolet (UV) region for applications such as micromachining, investigation of charge carrier relaxation in conductors, and probing of ultrafast chemical processes. However, direct short-pulse generation is not as straight forward in solid-state gain media as it is for near-IR tunable solid-state lasers such as Ti:sapphire due to the difficulty of obtaining continuous wave laser operation, which is required for Kerr lens mode-locking schemes utilizing spatial or temporal Kerr type nonlinearity. In this work, the transient cavity method, which was reported to generate ultrashort laser pulses in dye lasers, is extended to a solid-state gain medium. Ce:LiCAF was chosen among the rare-earth-doped fluoride laser crystals emitting in the UV region because of its broad tunability (from 280 to 325 nm) and enough bandwidth to generate 3-fs pulses, sufficiently large effective gain cross section (6.0 x10⁻¹⁸ cm²) favorable for oscillators, and a high saturation fluence (115 mJ/cm²). Numerical simulations are performed to investigate the spectro-temporal evolution of the broadband UV laser emission from Ce:LiCAF, represented as a system of two homogeneous broadened singlet states, by solving the rate equations extended to multiple wavelengths. The goal is to find the appropriate cavity length and Q-factor to achieve the optimal photon cavity decay time and pumping energy for resonator transients that will lead to ps UV laser emission from a Ce:LiCAF crystal pumped by the fourth harmonics (266nm) of a Nd:YAG laser. Results show that a single ps pulse can be generated from a 1-mm, 1 mol% Ce³⁺-doped LiCAF crystal using an output coupler with 10% reflectivity (low-Q) and an oscillator cavity that is 2-mm long (short cavity). This technique can be extended to other fluoride-based solid-state laser gain media.

Keywords: rare-earth-doped fluoride gain medium, transient cavity, ultrashort laser, ultraviolet laser

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Authors: Nawras Kurzom, Avi Mendelsohn

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The effects of background music on learning and memory are inconsistent, partly due to the intrinsic complexity and variety of music and partly to individual differences in music perception and preference. A prominent musical feature that is known to elicit strong emotional responses is musical tension. Musical tension can be brought about by building anticipation of rhythm, harmony, melody, and dynamics. Delaying the resolution of dominant-to-tonic chord progressions, as well as using dissonant harmonics, can elicit feelings of tension, which can, in turn, affect memory formation of concomitant information. The aim of the presented studies was to explore how forming declarative memory is influenced by musical tension, brought about within continuous music as well as in the form of isolated chords with varying degrees of dissonance/consonance. The effects of musical tension on long-term memory of declarative information were studied in two ways: 1) by evoking tension within continuous music pieces by delaying the release of harmonic progressions from dominant to tonic chords, and 2) by using isolated single complex chords with various degrees of dissonance/roughness. Musical tension was validated through subjective reports of tension, as well as physiological measurements of skin conductance response (SCR) and pupil dilation responses to the chords. In addition, music information retrieval (MIR) was used to quantify musical properties associated with tension and its release. Each experiment included an encoding phase, wherein individuals studied stimuli (words or images) with different musical conditions. Memory for the studied stimuli was tested 24 hours later via recognition tasks. In three separate experiments, we found positive relationships between tension perception and physiological measurements of SCR and pupil dilation. As for memory performance, we found that background music, in general, led to superior memory performance as compared to silence. We detected a trade-off effect between tension perception and memory, such that individuals who perceived musical tension as such displayed reduced memory performance for images encoded during musical tension, whereas tense music benefited memory for those who were less sensitive to the perception of musical tension. Musical tension exerts complex interactions with perception, emotional responses, and cognitive performance on individuals with and without musical training. Delineating the conditions and mechanisms that underlie the interactions between musical tension and memory can benefit our understanding of musical perception at large and the diverse effects that music has on ongoing processing of declarative information.

Keywords: musical tension, declarative memory, learning and memory, musical perception

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Authors: Markus Rütten, Olaf Wünsch

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Non-Newtonian fluid properties can change the flow behaviour significantly, its prediction is more difficult when thermal effects come into play. Hence, the focal point of this work is the wake flow behind a heated circular cylinder in the laminar vortex shedding regime for thermo-viscous shear thinning fluids. In the case of isothermal flows of Newtonian fluids the vortex shedding regime is characterised by a distinct Reynolds number and an associated Strouhal number. In the case of thermo-viscous shear thinning fluids the flow regime can significantly change in dependence of the temperature of the viscous wall of the cylinder. The Reynolds number alters locally and, consequentially, the Strouhal number globally. In the present CFD study the temperature dependence of the Reynolds and Strouhal number is investigated for the flow of a Carreau fluid around a heated cylinder. The temperature dependence of the fluid viscosity has been modelled by applying the standard Williams-Landel-Ferry (WLF) equation. In the present simulation campaign thermal boundary conditions have been varied over a wide range in order to derive a relation between dimensionless heat transfer, Reynolds and Strouhal number. Together with the shear thinning due to the high shear rates close to the cylinder wall this leads to a significant decrease of viscosity of three orders of magnitude in the nearfield of the cylinder and a reduction of two orders of magnitude in the wake field. Yet the shear thinning effect is able to change the flow topology: a complex K´arm´an vortex street occurs, also revealing distinct characteristic frequencies associated with the dominant and sub-dominant vortices. Heating up the cylinder wall leads to a delayed flow separation and narrower wake flow, giving lesser space for the sequence of counter-rotating vortices. This spatial limitation does not only reduce the amplitude of the oscillating wake flow it also shifts the dominant frequency to higher frequencies, furthermore it damps higher harmonics. Eventually the locally heated wake flow smears out. Eventually, the CFD simulation results of the systematically varied thermal flow parameter study have been used to describe a relation for the main characteristic order parameters.

Keywords: heat transfer, thermo-viscous fluids, shear thinning, vortex shedding

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Authors: Aleksandr I. Korobov, Natalia V. Shirgina, Aleksey I. Kokshaiskiy, Vyacheslav M. Prokhorov

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The paper presents the results of an experimental study of the effect of reverse mechanical load-unloading on the mechanical, linear, and nonlinear elastic properties of n-AMg6/C60 nanocomposite. Samples for experimental studies of n-AMg6/C60 nanocomposite were obtained by grinding AMg6 polycrystalline alloy in a planetary mill with 0.3 wt % of C60 fullerite in an argon atmosphere. The resulting product consisted of 200-500-micron agglomerates of nanoparticles. X-ray coherent scattering (CSL) method has shown that the average nanoparticle size is 40-60 nm. The resulting preform was extruded at high temperature. Modifications of C60 fullerite interferes the process of recrystallization at grain boundaries. In the samples of n-AMg6/C60 nanocomposite, the load curve is measured: the dependence of the mechanical stress σ on the strain of the sample ε under its multi-cycle load-unloading process till its destruction. The hysteresis dependence σ = σ(ε) was observed, and insignificant residual strain ε < 0.005 were recorded. At σ≈500 MPa and ε≈0.025, the sample was destroyed. The destruction of the sample was fragile. Microhardness was measured before and after destruction of the sample. It was found that the loading-unloading process led to an increase in its microhardness. The effect of the reversible mechanical stress on the linear and nonlinear elastic properties of the n-AMg6/C60 nanocomposite was studied experimentally by ultrasonic method on the automated complex Ritec RAM-5000 SNAP SYSTEM. In the n-AMg6/C60 nanocomposite, the velocities of the longitudinal and shear bulk waves were measured with the pulse method, and all the second-order elasticity coefficients and their dependence on the magnitude of the reversible mechanical stress applied to the sample were calculated. Studies of nonlinear elastic properties of the n-AMg6/C60 nanocomposite at reversible load-unloading of the sample were carried out with the spectral method. At arbitrary values of the strain of the sample (up to its breakage), the dependence of the amplitude of the second longitudinal acoustic harmonic at a frequency of 2f = 10MHz on the amplitude of the first harmonic at a frequency f = 5MHz of the acoustic wave is measured. Based on the results of these measurements, the values of the nonlinear acoustic parameter in the n-AMg6/C60 nanocomposite sample at different mechanical stress were determined. The obtained results can be used in solid-state physics, materials science, for development of new techniques for nondestructive testing of structural materials using methods of nonlinear acoustic diagnostics. This study was supported by the Russian Science Foundation (project №14-22-00042).

Keywords: nanocomposite, generation of acoustic harmonics, nonlinear acoustic parameter, hysteresis

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Authors: Jyh Sheen, Yang-Hung Cheng

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This paper presents a design of a microstrip bandpass filter with a compact size and wide stopband by using 0.15-μm GaAs pHEMT process. The wide stop band is achieved by suppressing the first and second harmonic resonance frequencies. The slow-wave coupling stepped impedance resonator with cross coupled structure is adopted to design the bandpass filter. A two-resonator filter was fabricated with 13.5GHz center frequency and 11% bandwidth was achieved. The devices are simulated using the ADS design software. This device has shown a compact size and very low insertion loss of 2.6 dB. Microstrip planar bandpass filters have been widely adopted in various communication applications due to the attractive features of compact size and ease of fabricating. Various planar resonator structures have been suggested. In order to reach a wide stopband to reduce the interference outside the passing band, various designs of planar resonators have also been submitted to suppress the higher order harmonic frequencies of the designed center frequency. Various modifications to the traditional hairpin structure have been introduced to reduce large design area of hairpin designs. The stepped-impedance, slow-wave open-loop, and cross-coupled resonator structures have been studied to miniaturize the hairpin resonators. In this study, to suppress the spurious harmonic bands and further reduce the filter size, a modified hairpin-line bandpass filter with cross coupled structure is suggested by introducing the stepped impedance resonator design as well as the slow-wave open-loop resonator structure. In this way, very compact circuit size as well as very wide upper stopband can be achieved and realized in a Roger 4003C substrate. On the other hand, filters constructed with integrated circuit technology become more attractive for enabling the integration of the microwave system on a single chip (SOC). To examine the performance of this design structure at the integrated circuit, the filter is fabricated by the 0.15 μm pHEMT GaAs integrated circuit process. This pHEMT process can also provide a much better circuit performance for high frequency designs than those made on a PCB board. The design example was implemented in GaAs with center frequency at 13.5 GHz to examine the performance in higher frequency in detail. The occupied area is only about 1.09×0.97 mm2. The ADS software is used to design those modified filters to suppress the first and second harmonics.

Keywords: microstrip resonator, bandpass filter, harmonic suppression, GaAs

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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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