Search results for: matrix inverter

Authors: L. Benbaouche, H. E. , F. Krim

Abstract:

In this paper we propose real-time control of grid-connected single phase inverter, which is flexible and efficient. The first step is devoted to the study and design of the controller through simulation, conducted by the LabVIEW software on the computer 'host'. The second step is running the application from PXI 'target'. LabVIEW software, combined with NI-DAQmx, gives the tools to easily build applications using the digital to analog converter to generate the PWM control signals. Experimental results show that the effectiveness of LabVIEW software applied to power electronics.

Keywords: real-time control, labview, inverter, PWM

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Authors: Najiya Omar, Hamed Aly, Timothy Little

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The optimal size of a photovoltaic (PV) array is considered a critical factor in designing an efficient PV system due to the dependence of the PV cell performance on temperature. A high temperature can lead to voltage losses of solar panels, whereas a low temperature can cause voltage overproduction. There are two possible scenarios of the inverter’s operation in which they are associated with the erroneous calculations of the number of PV panels: 1) If the number of the panels is scant and the temperature is high, the minimum voltage required to operate the inverter will not be reached. As a result, the inverter will shut down. 2) Comparably, if the number of panels is excessive and the temperature is low, the produced voltage will be more than the maximum limit of the inverter which can cause the inverter to get disconnected or even damaged. This article aims to assess theoretical and practical methodologies to calculate size and determine the topology of a PV array. The results are validated by applying an experimental evaluation for a 100 kW Grid-connected PV system for a location in Halifax, Nova Scotia and achieving a satisfactory system performance compared to the previous work done.

Keywords: sizing PV panels, theoretical and practical methodologies, topology of PV array, grid-connected PV

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Authors: Ric Joseph R. Murillo, Edna N. Gueco, Dennis I. Merino

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Let F be C or R, where C and R are the set of complex numbers and real numbers, respectively, and n be a natural number. An n-by-n matrix A over the field F is called an α-involutory matrix or an α-involution if there exists an α in the field such that the square of the matrix is equal to αI, where I is the n-by-n identity matrix. If α is a complex number or a nonnegative real number, then an n-by-n matrix A over the field F can be written as a sum of n-by-n α-involutory matrices over the field F if and only if the trace of that matrix is an integral multiple of the square root of α. Meanwhile, if α is a negative real number, then a 2n-by-2n matrix A over R can be written as a sum of 2n-by-2n α-involutory matrices over R if and only the trace of the matrix is zero. Some other properties of α-involutory matrices are also determined

Keywords: α-involutory Matrices, sum of α-involutory Matrices, Trace, Matrix Theory

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Authors: Dhivya Balakrishnan, Dhamodharan Shanmugam

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Multilevel converters offer high power capability, associated with lower output harmonics and lower commutation losses. Their main disadvantage is their complexity requiring a great number of power devices and passive components, and a rather complex control circuitry. This paper proposes a single-phase seven-level inverter for grid connected PV systems, With a novel pulse width-modulated (PWM) control scheme. Three reference signals that are identical to each other with an offset that is equivalent to the amplitude of the triangular carrier signal were used to generate the PWM signals. The inverter is capable of producing seven levels of output-voltage levels from the dc supply voltage. This paper proposes a new multilevel inverter topology using an H-bridge output stage with two bidirectional auxiliary switches. The new topology produces a significant reduction in the number of power devices and capacitors required to implement a multilevel output using the asymmetric cascade configuration.

Keywords: asymmetric cascade configuration, H-Bridge, multilevel inverter, Pulse Width Modulation (PWM)

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Authors: Spyridon Nikolaidis

Abstract:

A modeling approach for CMOS gates is presented based on the use of the equivalent inverter. A new model for the inverter has been developed using a simplified transistor current model which incorporates the nanoscale effects for the planar technology. Parametric expressions for the output voltage are provided as well as the values of the output and supply current to be compatible with the CCS technology. The model is parametric according the input signal slew, output load, transistor widths, supply voltage, temperature and process. The transistor widths of the equivalent inverter are determined by HSPICE simulations and parametric expressions are developed for that using a fitting procedure. Results for the NAND gate shows that the proposed approach offers sufficient accuracy with an average error in propagation delay about 5%.

Keywords: CMOS gate modeling, inverter modeling, transistor current mode, timing model

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Authors: Zerzouri Nora

Abstract:

In this paper, author presented the generalities of a photovoltaic system study and simulation. Author inserted the DC-DC converter to raise the voltage level and improve the operation of the PV panel by continuing the operating point at maximum power by using the Perturb and Observe technique (P&O). The connection to the network is made by inserting a three-phase voltage inverter allowing synchronization with the network the inverter is controlled by a PWM control. The simulation results allow the author to visualize the operation of the different components of the system, as well as the behavior of the system during the variation of meteorological values.

Keywords: photovoltaic generator PV, boost converter, P&O MPPT, PWM inverter, three phase grid

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Authors: P. Bhavya, P. R. Jayasree

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This paper presents a low cost transformer isolated boost half bridge micro-inverter for single phase grid connected PV system. Since the output voltage of a single PV panel is as low as 20~50V, a high voltage gain inverter is required for the PV panel to connect to the single-phase grid. The micro-inverter has two stages, an isolated dc-dc converter stage and an inverter stage with a dc link. To achieve MPPT and to step up the PV voltage to the dc link voltage, a transformer isolated boost half bridge dc-dc converter is used. To output the synchronised sinusoidal current with unity power factor to the grid, a pulse width modulated full bridge inverter with LCL filter is used. Variable step size Maximum Power Point Tracking (MPPT) method is adopted such that fast tracking and high MPPT efficiency are both obtained. AC voltage as per grid requirement is obtained at the output of the inverter. High power factor (>0.99) is obtained at both heavy and light loads. This paper gives the results of computer simulation program of a grid connected solar PV system using MATLAB/Simulink and SIM Power System tool.

Keywords: boost-half-bridge, micro-inverter, maximum power point tracking, grid connection, MATLAB/Simulink

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Authors: L. Hassaine, A. Mraoui, M. R. Bengourina

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In photovoltaic system, connected to the grid, the main goal is to control the power that the inverter injects into the grid from the energy provided by the photovoltaic generator. This paper proposes a control technique for a photovoltaic system connected to the grid based on the digital pulse-width modulation (DSPWM) which can synchronise a sinusoidal current output with a grid voltage and generate power at unity power factor. This control is based on H-Bridge inverter controlled by bipolar PWM Switching. The electrical scheme of the system is presented. Simulations results of output voltage and current validate the impact of this method to determinate the appropriate control of the system. A digital design of a generator PWM using VHDL is proposed and implemented on a Xilinx FPGA.

Keywords: grid connected photovoltaic system, H-Bridge inverter, control, bipolar PWM

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Authors: A. Elnady

Abstract:

This paper presents an improved Direct Power Control (DPC) scheme applied to the multilevel inverter that forms a Distributed Generation Unit (DGU). This paper demonstrates the performance of active and reactive power injected by the DGU to the smart grid. The DPC is traditionally operated by the hysteresis controller with the Space Vector Modulation (SVM) which is applied on the 2-level inverters or 3-level inverters. In this paper, the DPC is operated by the PI controller with the Phase-Disposition Pulse Width Modulation (PD-PWM) applied to the 5-level diode clamped inverter. The new combination of the DPC, PI controller, PD-PWM and multilevel inverter proves that its performance is much better than the conventional hysteresis-SVM based DPC. Simulations results have been presented to validate the performance of the suggested control scheme in the grid-connected mode.

Keywords: direct power control, PI controller, PD-PWM, and power control

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Authors: Mankour Mohamed, Miloudi Mohamed

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A thorough and accurate simulation is necessary for the study of a High Voltage Direct Current (HVDC) link system during various types of disturbances, including internal faults on both converters, either on the rectifier or on the inverter, as well as external faults, such as AC or DC faults on both converter sides inside the DC link party. In this study, we examine how an HVDC inverter responds to three different types of failures, including faults at the inverter valve, system control faults, and single-phase-to-ground AC faults at the sending end of the inverter side. As this phenomenon represents the most frequent problem that may affect inverter valves, particularly those based on thyristor valves (LCC (line-Commutated converter)), it is more precise to explore which circumstance generates and raises the commutation failure on inverter valves. Because of the techniques used to accelerate the simulation, digital real-time simulators are now the most potent tools that provide simulation results. The real-time-lab RT-LAB platform HYPERSIM OP-5600 is used to implement the Simulation in the Loop (SIL) technique, which is used to validate the results. It is demonstrated how to recover from both the internal faults and the AC problem. The simulation findings show how crucial a role the control system plays in fault recovery.

Keywords: hypersim simulator, HVDC systems, mono-polar link, AC faults, misfiring faults

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Authors: Abdelhalim Kessal, Ali Chebabhi

Abstract:

In this paper, a controller based on fuzzy logic control (FLC) associated to Three Dimensional Space Vector Modulation (3DSVM) is applied for shunt active filter in αβo axes domain. The main goals are to improve power quality under disturbed loads, minimize source currents harmonics and reduce neutral current magnitude in the four-wire structure. FLC is used to obtain the reference current and control the DC-bus voltage at the inverter output. The switching signals of the four-leg inverter are generating through a Three Dimensional Space Vector Modulation (3DSVM). Selected simulation results have been shown to validate the proposed system.

Keywords: flc, 3dsvm, sapf, harmonic, inverter

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Authors: Irtaza M. Syed, Kaamran Raahemifar

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In this paper, we present a comparative assessment of Space Vector Pulse Width Modulation (SVPWM) and Model Predictive Control (MPC) for two-level three phase (2L-3P) Voltage Source Inverter (VSI). VSI with associated system is subjected to both control techniques and the results are compared. Matlab/Simulink was used to model, simulate and validate the control schemes. Findings of this study show that MPC is superior to SVPWM in terms of total harmonic distortion (THD) and implementation.

Keywords: voltage source inverter, space vector pulse width modulation, model predictive control, comparison

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Authors: Bendiabdellah Azzeddine, Cherif Bilal Djamal Eddine

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The three-phase power converter voltage structure is widely used in many power applications but its failure can lead to partial or total loss of control of the phase currents and can cause serious system malfunctions or even a complete system shutdown. To ensure continuity of service in all circumstances, effective and rapid techniques of detection and location of inverter fault is to be implemented. The present paper is dedicated to open-circuit fault detection in a three-phase two-level inverter fed induction motor. For detection purpose, the proposed contribution addresses the Park’s current vectors associated to a polar coordinates calculation tool to compute the exact value of the fault angle corresponding directly to the faulty IGBT switch. The merit of the proposed contribution is illustrated by experimental results.

Keywords: diagnosis, detection, Park’s vectors, polar coordinates, open-circuit fault, inverter, IGBT switch

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Authors: M. Hadji, N. Chiker, Y. Hadji, A. Haddad

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In this paper, we report for the first time on the synthesis and characterization of novel MAX phases (Ti3SiC2, Ti2AlC) reinforced Ni-matrix and Ti2AlC reinforced Al-matrix. The stability of MAX phases in Al-matrix and Ni-matrix at a temperature of 985°C has been investigated. All the composites were cold pressed and sintered at a temperature of 985°C for 20min in H2 environment, except (Ni/Ti3SiC2) who was sintered at 1100°C for 1h.Microstructure analysis by scanning electron microscopy and phase analysis by X-Ray diffraction confirmed that there was minimal interfacial reaction between MAX particles and Ni, thus Al/MAX samples shown that MAX phases was totally decomposed at 985°C.The Addition of MAX enhanced the Al-matrix and Ni-matrix.

Keywords: MAX phase, microstructures, composites, hardness, SEM

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Authors: Renata Masarova, Bohuslava Juhasova, Martin Juhas, Zuzana Sutova

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In dynamic system theory a mathematical model is often used to describe their properties. In order to find a transfer matrix of a dynamic system we need to calculate an inverse matrix. The paper contains the fusion of the classical theory and the procedures used in the theory of automated control for calculating the inverse matrix. The final part of the paper models the given problem by the Matlab.

Keywords: dynamic system, transfer matrix, inverse matrix, modeling

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Authors: Abhimanyu Kumar, Chirag Gupta

Abstract:

This work presents a comprehensive study on the employment of Model Predictive Control (MPC) for a three-phase voltage-source inverter to regulate the output voltage efficiently. The inverter is modeled via the Clarke Transformation, considering a scenario where the load is unknown. An LC filter model is developed, demonstrating its efficacy in Total Harmonic Distortion (THD) reduction. The system, when implemented with fault-tolerant multilevel inverter topologies, ensures reliable operation even under fault conditions, a requirement that is paramount with the increasing dependence on renewable energy sources. The research also integrates a Fuzzy Logic based fault tolerance system which identifies and manages faults, ensuring consistent inverter performance. The efficacy of the proposed methodology is substantiated through rigorous simulations and comparative results, shedding light on the voltage prediction efficiency and the robustness of the model even under fault conditions.

Keywords: total harmonic distortion, fuzzy logic, renewable energy sources, MLI

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Authors: M. Helaimi, R. Taleb, D. Benyoucef, B. Belmadani

Abstract:

This paper presents the design of a polynomial controller with coefficient diagram method (CDM). This controller is used to control the output power of high frequency resonant inverter with LLC tank. One of the most important problems associated with the proposed inverter is achieving ZVS operating during the induction heating process. To overcome this problem, asymmetrical voltage cancellation (AVC) control technique is proposed. The phased look loop (PLL) is used to track the natural frequency of the system. The small signal model of the system with the proposed control is obtained using extending describing function method (EDM). The validity of the proposed control is verified by simulation results.

Keywords: induction heating, AVC control, CDM, PLL, resonant inverter

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Authors: Shefeen Maliyakkal, Pranav Satheesh, Steve Simon, Sharath Kuruppath

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This paper researches the impact of battery voltage sag on the performance and efficiency of E-motor in electric cars. Terminal voltage of battery reduces with the S.o.C. This results in the downward shift of torque-speed curve of E-motor and increased copper losses in E-motor. By introducing a buck-boost inverter between the battery and E-motor, an additional degree of freedom was achieved. By boosting the AC voltage, the dependency of voltage sag on the performance of E-motor was eliminated. A strategy was also proposed for the operation of the buck-boost inverter to minimize copper and iron losses in E-motor to maximize efficiency. MATLAB-SIMULINK model of E-drive was used to obtain simulation results. The temperature rise in the E-motor was reduced by 14% for a 10% increase in AC voltage. From the results, it was observed that a 20% increase in AC voltage can result in improvement of running torque and maximum torque of E-motor by 44%. Hence it was concluded that using a buck-boost inverter for E-drive significantly improves both performance and efficiency of E-motor.

Keywords: buck-boost, E-motor, battery, voltage sag

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Authors: M. Suresh Kumar, K. Ramani

Abstract:

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: P.Kiruthika, K. Ramani

Abstract:

This paper presented the design and advancement of a single-phase 27-level Hybrid Multilevel DC-AC Converter interfacing with Photo Voltaic. In this context, the Multicarrier Pulse Width Modulation method can be implemented in 27-level Hybrid Multilevel Inverter for generating a switching pulse. Perturb & Observer algorithm can be used in the Maximum Power Point Tracking method for the Photo Voltaic system. By implementing Maximum Power Point Tracking with three separate solar panels as an input source to the 27-level Hybrid Multilevel Inverter. This proposed method can be simulated by using MATLAB/simulink. The result shown that the proposed method can achieve silky output wave forms, more flexibility in voltage range, and to reduce Total Harmonic Distortion in medium-voltage drives.

Keywords: Multi Carrier Pulse Width Modulation Technique (MCPWM), Multi Level Inverter (MLI), Maximum Power Point Tracking (MPPT), Perturb and Observer (P&O)

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Authors: Evren Isen

Abstract:

In grid-connected renewable energy systems, input power is controlled by AC/DC converter or/and DC/DC converter depending on output voltage of input source. The power is injected to DC-link, and DC-link voltage is regulated by inverter controlling the grid current. Inverter performance is considerable in grid-connected renewable energy systems to meet the utility standards. In this paper, modelling and simulation of hysteresis current controlled single-phase grid-connected inverter that is utilized in renewable energy systems, such as wind and solar systems, are presented. 2 kW single-phase grid-connected inverter is simulated in Simulink and modeled in Matlab-m-file. The grid current synchronization is obtained by phase locked loop (PLL) technique in dq synchronous rotating frame. Although dq-PLL can be easily implemented in three-phase systems, there is difficulty to generate β component of grid voltage in single-phase system because single-phase grid voltage exists. Inverse-Park PLL with low-pass filter is used to generate β component for grid angle determination. As grid current is controlled by constant bandwidth hysteresis current control (HCC) technique, average switching frequency and variation of switching frequency in a fundamental period are considered. 3.56% total harmonic distortion value of grid current is achieved with 0.5 A bandwidth. Average value of switching frequency and total harmonic distortion curves for different hysteresis bandwidth are obtained from model in m-file. Average switching frequency is 25.6 kHz while switching frequency varies between 14 kHz-38 kHz in a fundamental period. The average and maximum frequency difference should be considered for selection of solid state switching device, and designing driver circuit. Steady-state and dynamic response performances of the inverter depending on the input power are presented with waveforms. The control algorithm regulates the DC-link voltage by adjusting the output power.

Keywords: grid-connected inverter, hysteresis current control, inverter modelling, single-phase inverter

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Authors: Syed Masood Hussain

Abstract:

An effective control method, including system-level control and pulse width modulation for quasi-Z-source cascade multilevel inverter (qZS-CMI) based grid-tie photovoltaic (PV) power system is proposed. The system-level control achieves the grid-tie current injection, independent maximum power point tracking (MPPT) for separate PV panels, and dc-link voltage balance for all quasi-Z-source H-bridge inverter (qZS-HBI) modules. A recent upsurge in the study of photovoltaic (PV) power generation emerges, since they directly convert the solar radiation into electric power without hampering the environment. However, the stochastic fluctuation of solar power is inconsistent with the desired stable power injected to the grid, owing to variations of solar irradiation and temperature. To fully exploit the solar energy, extracting the PV panels’ maximum power and feeding them into grids at unity power factor become the most important. The contributions have been made by the cascade multilevel inverter (CMI). Nevertheless, the H-bridge inverter (HBI) module lacks boost function so that the inverter KVA rating requirement has to be increased twice with a PV voltage range of 1:2; and the different PV panel output voltages result in imbalanced dc-link voltages. However, each HBI module is a two-stage inverter, and many extra dc–dc converters not only increase the complexity of the power circuit and control and the system cost, but also decrease the efficiency. Recently, the Z-source/quasi-Z-source cascade multilevel inverter (ZS/qZS-CMI)-based PV systems were proposed. They possess the advantages of both traditional CMI and Z-source topologies. In order to properly operate the ZS/qZS-CMI, the power injection, independent control of dc-link voltages, and the pulse width modulation (PWM) are necessary. The main contributions of this paper include: 1) a novel multilevel space vector modulation (SVM) technique for the single phase qZS-CMI is proposed, which is implemented without additional resources; 2) a grid-connected control for the qZS-CMI based PV system is proposed, where the all PV panel voltage references from their independent MPPTs are used to control the grid-tie current; the dual-loop dc-link peak voltage control.

Keywords: Quzi-Z source inverter, Photo voltaic power system, space vector modulation, cascade multilevel inverter

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Authors: Nur Aisyah Jalalludin, Arwindra Rizqiawan, Goro Fujita

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In this study, we aim to demonstrate a microgrid system experimental simulation for an easy understanding of a large-scale microgrid system. This model is required for industrial training and learning environments. However, in order to create an exact representation of a microgrid system, the laboratory-scale system must fulfill the requirements of a grid-connected inverter, in which power values are assigned to the system to cope with the intermittent output from renewable energy sources. Aside from that, during changes in load capacity, the grid-connected system must be able to supply power from the utility grid side and microgrid side in a balanced manner. Therefore, droop control is installed in the inverter’s control board to maintain equal power sharing in both sides. This power control in a stand-alone condition and droop control in a grid-connected condition must be implemented in order to maintain a stabilized system. Based on the experimental results, power control and droop control can both be applied in the system by comparing the experimental and reference values.

Keywords: droop control, droop characteristic, grid-connected inverter, microgrid, power control

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Authors: Boris Melnikov, Dmitrii Chaikovskii, Elena Melnikova

Abstract:

The traveling salesman problem (TSP) is a well-known optimization problem that seeks to find the shortest possible route that visits a set of points and returns to the starting point. In this paper, we apply some heuristics of the TSP for the task of restoring the DNA matrix. This restoration problem is often considered in biocybernetics. For it, we must recover the matrix of distances between DNA sequences if not all the elements of the matrix under consideration are known at the input. We consider the possibility of using this method in the testing of distance calculation algorithms between a pair of DNAs to restore the partially filled matrix.

Keywords: optimization problems, DNA matrix, partially filled matrix, traveling salesman problem, heuristic algorithms

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Authors: Ahmed Shariful Alam, Abu Hena M. Mustafa Kamal, M. Abdul Rahman, M. Nasmus Sakib Khan Shabbir, Atiqul Islam

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According to the rules of quantum mechanics there is a non-vanishing probability of for an electron to tunnel through a thin insulating barrier or a thin capacitor which is not possible according to the laws of classical physics. Tunneling of electron through a thin insulating barrier or tunnel junction is a random event and the magnitude of current flowing due to the tunneling of electron is very low. As the current flowing through a Single Electron Transistor (SET) is the result of electron tunneling through tunnel junctions of its source and drain the supply voltage requirement is also very low. As a result, the power consumption across a Single Electron Transistor is ultra-low in comparison to that of a MOSFET. In this paper simulations have been done with PSPICE for an inverter built with both SETs and MOSFETs. 35mV supply voltage was used for a SET built inverter circuit and the supply voltage used for a CMOS inverter was 3.5V.

Keywords: ITRS, enhancement type MOSFET, island, DC analysis, transient analysis, power consumption, background charge co-tunneling

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Authors: A. Djahbar, E. Bounadja, A. Zegaoui, H. Allouache

Abstract:

In this paper, vector control of a series-connected two-machine drive system fed by a single inverter (CSI/VSI) is presented. The two stator windings of both machines are connected in series while the rotors may be connected to different loads, are called series-connected two-machine drive. Appropriate phase transposition is introduced while connecting the series stator winding to obtain decoupled control the two-machines. The dynamic decoupling of each machine from the group is obtained using the vector control algorithm. The independent control is demonstrated by analyzing the characteristics of torque and speed of each machine obtained via simulation under vector control scheme. The viability of the control techniques is proved using analytically and simulation approach.

Keywords: drives, inverter, multi-phase induction machine, vector control

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Authors: Mohd Tariq

Abstract:

The three phase system drives produce the problem of more torque pulsations and harmonics. This issue prevents the smooth operation of the drives and it also induces the amount of heat generated thus resulting in an increase in power loss. Higher phase system offers smooth operation of the machines with greater power capacity. Five phase variable-speed induction motor drives are commonly used in various industrial and commercial applications like tractions, electrical vehicles, ship propulsions and conveyor belt drive system. In this work, a comparative analysis of the different modulation schemes applied on the five-level five-phase Packed U Cell (PUC) inverter fed induction motor drives is presented. The performance of the inverter is greatly affected with the modulation schemes applied. The system is modeled, designed, and implemented in MATLAB^®/Simulink environment. Experimental validation is done for the prototype of single phase, whereas five phase experimental validation is proposed in the future works.

Keywords: Packed U-Cell (PUC) inverter, five-phase system, pulse width modulation (PWM), induction motor (IM)

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Authors: S.Pandeeswari, Raju Padma

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In this paper a new solution to implement and control single-stage electronic ballast based on the integration of a buck-boost power factor correction stage and a half bridge resonant inverter is presented. The control signals are obtained using the inverter resonant current by means of a saturable transformer. Core saturation is used to control the required dead time between the control pulses on both switches. The turn-on time of one of the inverter switches is controlled to provide proper cathode preheating during the lamp ignition process. No special integrated circuits are required to control the ballast and the total number of components is minimized. Analysis and basic design of phase cut dimmer.

Keywords: MOSFET dimmer, PIC 16F877A, voltage regulator, bridge rectifier

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Authors: Malika Yaici, Kamel Hariche

Abstract:

In control engineering, systems described by matrix fractions are studied through properties of block roots, also called solvents. These solvents are usually dealt with in a block Vandermonde matrix form. Inverses and determinants of Vandermonde matrices and block Vandermonde matrices are used in solving problems of numerical analysis in many domains but require costly computations. Even though Vandermonde matrices are well known and method to compute inverse and determinants are many and, generally, based on interpolation techniques, methods to compute the inverse and determinant of a block Vandermonde matrix have not been well studied. In this paper, some properties of these matrices and iterative algorithms to compute the determinant and the inverse of a block Vandermonde matrix are given. These methods are deducted from the partitioned matrix inversion and determinant computing methods. Due to their great size, parallelization may be a solution to reduce the computations cost, so a parallelization of these algorithms is proposed and validated by a comparison using algorithmic complexity.

Keywords: block vandermonde matrix, solvents, matrix polynomial, matrix inverse, matrix determinant, parallelization

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Authors: Dalia Salem, Detlef Schulz

Abstract:

As Germany pursues its ambitious plan towards a power system based on renewable energy sources, the necessity to establish steady, robust microgrids becomes more evident. Inside the microgrid, there is at least one grid-forming inverter responsible for generating the coupling voltage and stabilizing the system frequency within the standardized accepted limits when the microgrid is forced to operate as a stand-alone power system. Grid-forming control for distributed inverters is required to enable steady control of a low-inertia power system. In this paper, a designed droop control technique is tested at the controller of an inverter as a component of a hardware test bed to understand the microgrid behavior in two modes of operation: i) grid-connected and ii) operating in islanding mode. This droop technique includes many current and voltage inner control loops, where the Q-V and P-f droop provide the required terminal output voltage and frequency. The technique is tested first in a simulation model of the inverter in MATLAB/SIMULINK, and the results are compared to the results of the hardware laboratory test. The results of this experiment illuminate the pivotal role of the grid-forming inverter in facilitating microgrid resilience during grid disconnection events and how microgrids could provide the functionality formerly provided by synchronous machinery, such as the black start process.

Keywords: microgrid, grid-forming inverters, droop-control, islanding-operation

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