This document summarizes a research paper that proposes using artificial neural networks to generate optimal switching functions for voltage and harmonic control of three-phase inverters. Specifically:
1) A new training algorithm is developed for an artificial neural network to determine switching angles without using pre-computed desired angles. Instead, it uses the desired solution of harmonic elimination equations.
2) Theoretical analysis of the proposed solving algorithm with neural networks is provided. Simulation results show the high performance and advantages of the developed modulator.
3) An artificial neural network is trained using a backpropagation algorithm. Training data comes from optimal switching angles determined through selective harmonic elimination equations for different modulation indices.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Harmonic elimination at the fundamental frequency is very much appropriate for high and medium range of power generation and applications. This paper considers a new technique for selective harmonic elimination (SHE), in which the total harmonic distortion (THD) is minimized when compared with that of the conventional one. With this technique, the harmonics at lower order are eliminated, which are more predominant than the higher ones.Cascaded H-Bridge inverter fed by a single DC is considered which is simulated with the switching angles generated by both the conventional method of SHE and the new method of SHE. The simulated results of the load voltage and the waveforms of the harmonic analysis are shown. The THD values are compared for the two techniques. The experimental results are also shown for the new technique. The switching angles are generated with the help of field programmable gated array (FPGA) in the hardware. The value of experimental THD of voltage is compared with that of simulated THD and the comparison prove that the results are satisfactory.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Harmonic elimination at the fundamental frequency is very much appropriate for high and medium range of power generation and applications. This paper considers a new technique for selective harmonic elimination (SHE), in which the total harmonic distortion (THD) is minimized when compared with that of the conventional one. With this technique, the harmonics at lower order are eliminated, which are more predominant than the higher ones.Cascaded H-Bridge inverter fed by a single DC is considered which is simulated with the switching angles generated by both the conventional method of SHE and the new method of SHE. The simulated results of the load voltage and the waveforms of the harmonic analysis are shown. The THD values are compared for the two techniques. The experimental results are also shown for the new technique. The switching angles are generated with the help of field programmable gated array (FPGA) in the hardware. The value of experimental THD of voltage is compared with that of simulated THD and the comparison prove that the results are satisfactory.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Genetic Algorithm Application in Asymmetrical 9-Level InverterIJPEDS-IAES
Selective harmonic elimination (SHE) has been a widely researched
alternative to traditional PWM techniques. This paper presents the selective
harmonic elimination of a uniform step asymmetrical multilevel inverter
(USAMI) using genetic algorithm (GA) which eliminates specified higher
order harmonics while maintaining the required fundamental voltage. This
technique can be applied to USAMI with any number of levels. As an
example, in this paper a 9-level USAMI is considered and the optimum
switching angles are calculated to eliminate the 5th, 7th and 11th harmonics.
Mitigation of Lower Order Harmonics with Filtered Svpwm In Multiphase Voltage...IJERA Editor
Multi-phase machines and drives is a topic of growing relevance in recent years, and it presents many challenging issues that still need further research. This is the case of multi-phase space vector pulse width modulation (SVPWM), which shows not only more space vectors than the standard three-phase case, but also new subspaces where the space vectors are mapped. In the digital implementation, multiphase reference voltages are sampled and fed into the digital modulator to produce gating signals at a constant clock rate f. This means a finite pulse-width resolution because the gating state transition can only occur at some specific time instants depending on frequency. This results in a deviation of produced phase voltages from the desired phase voltages, i.e., increasing harmonic distortion especially for a small modulation index signal. In the present paper a filtered space-vector pulse-width modulation (SVPWM) considering finite pulse-width resolution is proposed to produce a switching sequence with reduced baseband harmonics for multiphase voltage source inverters (VSI). This is achieved by incorporating a pseudo feedback loop regarding weighted voltage difference between desired and produced phase voltages.
Analysis Approach for Five Phase Two-Level Voltage Source Inverter with PWM T...ijsrd.com
this paper gives idea of comparison of five phase two-level voltage inverter (FPTLVSI) without filter circuit and control scheme and FPTLVSI with filter circuit and PWM control scheme for induction motor drive. The paper demonstrates using mat lab simulations about comparison in term of harmonics analysis for different firing angles and find best angle suitable for output with minimum harmonics for FPTLVSI without filter circuit and control scheme and harmonics analysis of FPTLVSI with filter and PWM control scheme. This paper suggests simulation of comparison of harmonics point of view five phase two-level voltage inverter (FPTLVSI) without filter circuit and control scheme and with filter circuit and PWM control scheme for induction motor drive.
Implementation of SVPWM control on FPGA for three phase MATRIX CONVERTERIDES Editor
This paper presents a simple approach for
implementation of a Space Vector Pulse Width
Modulation (SVPWM) Technique for control of three
phase Matrix Converter (MC) using MATLAB/Simulink
& FPGA Software. The Matrix converter is a direct
AC/AC Power conversion without an intermediate DC
link. This converter is inherently capable of bi-directional
power flow and also offers virtually sinusoidal input
currents. The SVPWM technique improves good voltage
transfer ratio with less harmonic distortion. This paper
presents FPGA test bench waveforms & MATLAB
simulations of SVPWM pulses and output waveforms for
three phase matrix converter.
Two leg three-phase inverters (FSTPIs) have been proposed to be used in low-power; low-cost applications because of the reduced number of semiconductor devices, and space vector pulse width modulation (SVPWM) techniques have also been introduced to control FSTPIs. However, high-performance controllers are needed to implement complicated SVPWM algorithms, which limit their low-cost applications. To simplify algorithms and reduce the cost of implementation, an equivalent scalar method for SVPWM of FSTPIs is proposed. SVPWM for FSTPIs is actually a sine PWM by modulating two sine waves of 600 phase difference with a triangle wave, but in this method third harmonics doesn’t eliminated. So as to eliminate the third harmonics we have to compose a high frequency sine wave to on existing sine waves. So such a special sine PWM can be used to control FSTPIs. The Mathematical and simulation results demonstrate the validity of the proposed method.
http://www.mathworks.com/matlabcentral/fileexchange/authors/126814
A Refined Space Vector PWM Signal Generation for Multilevel InvertersIDES Editor
A refined space vector modulation scheme for
multilevel inverters, using only the instantaneous sampled
reference signals is presented in this paper. The proposed
space vector pulse width modulation technique does not require
the sector information and look-up tables to select the
appropriate switching vectors. The inverter leg switching times
are directly obtained from the instantaneous sampled
reference signal amplitudes and centers the switching times
for the middle space vectors in a sampling time interval, as in
the case of conventional space vector pulse width modulation.
The simulation results are presented to a five-level inverter
system for dual-fed induction motor drive. The dual-fed
structure is realized by opening the neutral-point of the
conventional squirrel cage induction motor. The five-level
inversion is obtained by feeding the dual-fed induction motor
with four-level inverter from one end and two-level inverter
from the other end.
Memristor-Capacitor Based Startup Circuit for Voltage Reference Generatorsmangal das
This paper presents the design of Memristorcapacitor based startup circuit. Memristor is a novel device and has many advantages over conventional CMOS devices such as no leakage current and is easy to manufacture. In this work the switching characteristics of memristor is utilized. First the
theoretical equations describing the switching behavior of memristor are derived. To prove the switching capabilities of Memristor, a startup circuit based on series combination of Memristor-capacitor is proposed. This circuit is compared with the reference circuit (which utilizes resistor in place of memristor) and the previously reported MOSFET based startup circuits. Comparison of different circuits was done to validate the results. Simulation results shows that memristor based circuit attains on (I = 2.25 mA) to off state (I = 10 μA) in 2.8 ns while the MOSFET based startup circuits takes (I = 1 mA) to off state (I = 10 μA) in 55.56 ns. However no significant difference in switching time was observed when compared with resistance based startup circuit. The benefit comes in terms of area because much larger die area is required for manufacturing of resistance in comparison to fabrication of memristor.
Fast svm based 3 phase cascaded five level invertereSAT Journals
Abstract Introduction of nearest three vector algorithm is a major achievement in the area of space vector technology. Complexity and severe computations are still the drawbacks of SVM methods mainly for multilevel inverter applications. A fast SVM technique is introduced in this project which allows the calculation of switch time duration and the efficient determination of switching times based on the two level inverter scheme. SVM modulating waves are generated based on the two level system and then this modulating waves are compared with required number of carrier signals in order to generate the switching pulses for the inverter. Four triangular carrier signals are needed for a five level system in order to generate the switching pulses. Coordinates of the nearest three voltage vectors is not needed, so the complexity of the SVM technique can be reduced and it is the major advantage of the proposed technique compared with conventional SVM techniques used for multilevel inverters. A three phase five level cascaded H bridge topology is used here to verify the effectiveness of the proposed technique. MATLAB simulation and hardware implementation of the proposed system is done. From the analysis of both simulation and hardware it is clear that proposed SVM technique have more fundamental output and less THD than sinusoidal PWM technique. Key Words: Cascaded H bridge, Multilevel, Modulating wave, Space vector
Genetic Algorithm Application in Asymmetrical 9-Level InverterIJPEDS-IAES
Selective harmonic elimination (SHE) has been a widely researched
alternative to traditional PWM techniques. This paper presents the selective
harmonic elimination of a uniform step asymmetrical multilevel inverter
(USAMI) using genetic algorithm (GA) which eliminates specified higher
order harmonics while maintaining the required fundamental voltage. This
technique can be applied to USAMI with any number of levels. As an
example, in this paper a 9-level USAMI is considered and the optimum
switching angles are calculated to eliminate the 5th, 7th and 11th harmonics.
Mitigation of Lower Order Harmonics with Filtered Svpwm In Multiphase Voltage...IJERA Editor
Multi-phase machines and drives is a topic of growing relevance in recent years, and it presents many challenging issues that still need further research. This is the case of multi-phase space vector pulse width modulation (SVPWM), which shows not only more space vectors than the standard three-phase case, but also new subspaces where the space vectors are mapped. In the digital implementation, multiphase reference voltages are sampled and fed into the digital modulator to produce gating signals at a constant clock rate f. This means a finite pulse-width resolution because the gating state transition can only occur at some specific time instants depending on frequency. This results in a deviation of produced phase voltages from the desired phase voltages, i.e., increasing harmonic distortion especially for a small modulation index signal. In the present paper a filtered space-vector pulse-width modulation (SVPWM) considering finite pulse-width resolution is proposed to produce a switching sequence with reduced baseband harmonics for multiphase voltage source inverters (VSI). This is achieved by incorporating a pseudo feedback loop regarding weighted voltage difference between desired and produced phase voltages.
Analysis Approach for Five Phase Two-Level Voltage Source Inverter with PWM T...ijsrd.com
this paper gives idea of comparison of five phase two-level voltage inverter (FPTLVSI) without filter circuit and control scheme and FPTLVSI with filter circuit and PWM control scheme for induction motor drive. The paper demonstrates using mat lab simulations about comparison in term of harmonics analysis for different firing angles and find best angle suitable for output with minimum harmonics for FPTLVSI without filter circuit and control scheme and harmonics analysis of FPTLVSI with filter and PWM control scheme. This paper suggests simulation of comparison of harmonics point of view five phase two-level voltage inverter (FPTLVSI) without filter circuit and control scheme and with filter circuit and PWM control scheme for induction motor drive.
Implementation of SVPWM control on FPGA for three phase MATRIX CONVERTERIDES Editor
This paper presents a simple approach for
implementation of a Space Vector Pulse Width
Modulation (SVPWM) Technique for control of three
phase Matrix Converter (MC) using MATLAB/Simulink
& FPGA Software. The Matrix converter is a direct
AC/AC Power conversion without an intermediate DC
link. This converter is inherently capable of bi-directional
power flow and also offers virtually sinusoidal input
currents. The SVPWM technique improves good voltage
transfer ratio with less harmonic distortion. This paper
presents FPGA test bench waveforms & MATLAB
simulations of SVPWM pulses and output waveforms for
three phase matrix converter.
Two leg three-phase inverters (FSTPIs) have been proposed to be used in low-power; low-cost applications because of the reduced number of semiconductor devices, and space vector pulse width modulation (SVPWM) techniques have also been introduced to control FSTPIs. However, high-performance controllers are needed to implement complicated SVPWM algorithms, which limit their low-cost applications. To simplify algorithms and reduce the cost of implementation, an equivalent scalar method for SVPWM of FSTPIs is proposed. SVPWM for FSTPIs is actually a sine PWM by modulating two sine waves of 600 phase difference with a triangle wave, but in this method third harmonics doesn’t eliminated. So as to eliminate the third harmonics we have to compose a high frequency sine wave to on existing sine waves. So such a special sine PWM can be used to control FSTPIs. The Mathematical and simulation results demonstrate the validity of the proposed method.
http://www.mathworks.com/matlabcentral/fileexchange/authors/126814
A Refined Space Vector PWM Signal Generation for Multilevel InvertersIDES Editor
A refined space vector modulation scheme for
multilevel inverters, using only the instantaneous sampled
reference signals is presented in this paper. The proposed
space vector pulse width modulation technique does not require
the sector information and look-up tables to select the
appropriate switching vectors. The inverter leg switching times
are directly obtained from the instantaneous sampled
reference signal amplitudes and centers the switching times
for the middle space vectors in a sampling time interval, as in
the case of conventional space vector pulse width modulation.
The simulation results are presented to a five-level inverter
system for dual-fed induction motor drive. The dual-fed
structure is realized by opening the neutral-point of the
conventional squirrel cage induction motor. The five-level
inversion is obtained by feeding the dual-fed induction motor
with four-level inverter from one end and two-level inverter
from the other end.
Memristor-Capacitor Based Startup Circuit for Voltage Reference Generatorsmangal das
This paper presents the design of Memristorcapacitor based startup circuit. Memristor is a novel device and has many advantages over conventional CMOS devices such as no leakage current and is easy to manufacture. In this work the switching characteristics of memristor is utilized. First the
theoretical equations describing the switching behavior of memristor are derived. To prove the switching capabilities of Memristor, a startup circuit based on series combination of Memristor-capacitor is proposed. This circuit is compared with the reference circuit (which utilizes resistor in place of memristor) and the previously reported MOSFET based startup circuits. Comparison of different circuits was done to validate the results. Simulation results shows that memristor based circuit attains on (I = 2.25 mA) to off state (I = 10 μA) in 2.8 ns while the MOSFET based startup circuits takes (I = 1 mA) to off state (I = 10 μA) in 55.56 ns. However no significant difference in switching time was observed when compared with resistance based startup circuit. The benefit comes in terms of area because much larger die area is required for manufacturing of resistance in comparison to fabrication of memristor.
Fast svm based 3 phase cascaded five level invertereSAT Journals
Abstract Introduction of nearest three vector algorithm is a major achievement in the area of space vector technology. Complexity and severe computations are still the drawbacks of SVM methods mainly for multilevel inverter applications. A fast SVM technique is introduced in this project which allows the calculation of switch time duration and the efficient determination of switching times based on the two level inverter scheme. SVM modulating waves are generated based on the two level system and then this modulating waves are compared with required number of carrier signals in order to generate the switching pulses for the inverter. Four triangular carrier signals are needed for a five level system in order to generate the switching pulses. Coordinates of the nearest three voltage vectors is not needed, so the complexity of the SVM technique can be reduced and it is the major advantage of the proposed technique compared with conventional SVM techniques used for multilevel inverters. A three phase five level cascaded H bridge topology is used here to verify the effectiveness of the proposed technique. MATLAB simulation and hardware implementation of the proposed system is done. From the analysis of both simulation and hardware it is clear that proposed SVM technique have more fundamental output and less THD than sinusoidal PWM technique. Key Words: Cascaded H bridge, Multilevel, Modulating wave, Space vector
Fuzzy Logic Controlled Harmonic Suppressor in Cascaded Multilevel InverterIJPEDS-IAES
This paper presents an investigation of seven level cascaded H-bridge (CHB)
inverter in power system for compensation of harmonics. For power quality
control a Fuzzy Logic Control (FLC) giving comparatively better harmonic
reduction than the conventional controllers. Harmonic distortion is the most
important power quality problem stirring in multilevel inverter; the
harmonics can be eliminated by an optimal selection of switching angles. A
hybrid evaluation technique evaluates the obtained optimal switching angles
that are attained from the fuzzy inference system as well as neural network.
The proposed method will be implemented in MATLAB working platform
and the harmonic elimination performance will be evaluated.
Harmonic Minimization In Multilevel Inverters By Using PSOIDES Editor
Harmonic Elimination in a multilevel inverters is
an optimization problem which is solved by applying particle
swarm optimization (PSO) technique. The derived equation
for the computation of total harmonic distortion (THD) of the
output voltage of the multilevel inverter is used as the objective
function in PSO algorithm. The objective function used is to
reduce the THD of the multilevel inverter and obtain the
corresponding switching angles with the elimination of
possible lower order harmonics. In this paper a pseudo code
based algorithm is proposed to deal with inequality constraints
which will helps in accelerating the optimization process. The
proposed method is applied for seven level cascade inverter to
eliminate the 5th and 7th order harmonics to reduce the total
harmonic distortion .This proposed PSO algorithm is effective
in reducing the total harmonic distortion corresponding the
range of modulation index. The simulation results shows that
the proposed PSO method is indeed capable of obtaining
higher quality of solutions to eliminate 5th and 7th order
harmonics and to reduce the total harmonic distortion of 7-
level cascade inverter
Total Harmonic Distortion of Dodecagonal Space Vector ModulationIJPEDS-IAES
Space vector modulation technique is one of the best PWM techniques which have been implemented to the Multilevel inverter circuit to get the purely sinusoidal cuurent. This is a important algorithm which is implemented in open wind induction motor. This type of I.M has great impact on Electric Drive system. SVM is nothing but the technique of switching algorithm. The Hexagonal space vector modulation has been implemented before, but elimination of higher order harmonics is not possible. Torque pulsation arises. Speed control of Induction motor was not smooth. So Dodecagonal (12) structure developed. A 12 side polygonal space vector structure is meant for eliminating (6n±1) harmonics in the phase current waveform throughout the modulating range. A high resolution of PWM technique is proposed involving multiple 12 sided polygonal (Dodecagonal) structure that can generate highly sinusoidal voltage at a reduced switching frequency. In this paper different values of frequencies have been taken for harmonic analysis. SVM method features a higher level of dc-bus voltage utilization compared to the conventional PWM.
Development of Improved Diode Clamped Multilevel Inverter Using Optimized Sel...eeiej_journal
In this paper the role of Selective Harmonic Elimination (SHE) is presented for diode clamped twelve-level multilevel inverter (DCMLI) based on dog leg optimization algorithm. Non-linear equations has been solved to eliminate specific low order harmonics, using the developed DOP algorithm, while at the same time the fundamental component is retained efficiently. The non-linear nature of transcendental equation provide multiple or even no solution for a particular modulation index. The proposed optimization method solving the nonlinear transcendental equations providing all possible solutions. The paper also showing the comparison between different modulation techniques including the proposed method. The entire system has been simulated using MATLAB/Simulink. Simulation results confirm the effectiveness with negligible
THD.
Improved hybrid algorithm based on GA and local search method for asymmetric...nooriasukmaningtyas
Selective harmonic elimination has emerged as an in-depth research method to replace traditional PWM technology. This study demonstrates the selective harmonic elimination by using a hybrid Genetic algorithm GA and local search (GA-LS) method of a uniform asymmetric multilevel inverter called USAMI That removes the higher-order harmonics defined while maintaining the fundamental voltage needed. This new technology can be implemented at any USAMI level. For example, in this article, we plan to use USAMI at 9 levels and find the optimal switching angle to remove the 5th, 7th, and 11th harmonics.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
This paper provides a new approach to reducing high-order harmonics in 400 Hz inverter using a three-level neutral-point clamped (NPC) converter. A voltage control loop using the harmonic compensation combined with NPC clamping diode control technology. The capacitor voltage imbalance also causes harmonics in the output voltage. For 400 Hz inverter, maintain a balanced voltage between the two input (direct current) (DC) capacitors is difficult because the pulse width modulation (PWM) modulation frequency ratio is low compared to the frequency of the output voltage. A method of determining the current flowing into the capacitor to control the voltage on the two balanced capacitors to ensure fast response reversal is also given in this paper. The combination of a high-harmonic resonator controller and a neutral-point voltage controller working together on the 400 Hz NPC inverter structure is given in this paper.
A Review of Matrix Converter and Novel Control Method of DC-AC Matrix Converteridescitation
For the past three decades, research work in matrix
converter has increased much. This paper presents a new
topology of DC-AC matrix converter, starting with a brief
historical review of different modulation and control strategies
which was developed recently. The purpose of the Paper is to
generate a multilevel output voltage equal to multilevel
inverter with reduced switches. An important part of the paper
is to design a dedicated DC-AC matrix converter and some
new arrays of bidirectional switches in a single module are
also presented. To find the performance of the module the
entire module is designed with MATLAB simulation and tested
with three phase induction motor.
Geomagnetically-Induced Currents (GIC) are very low-frequency currents due to the electromagnetic field induced in the earth caused by solar Geomagnetic Disturbances (GMD) such as coronal mass ejections.
For analysis purposes, the frequencies are so low that the currents may be represented as direct currents (dc) on the bulk power system. The induced currents flow through the transmission system and complete the circuit through the neutral paths in grounded-wye transformers. This quasi-dc current causes part-cycle saturation of the magnetic circuit of the transformer, yielding highly-distorted exciting currents containing both even and odd harmonics. This results in high harmonic currents in transformers, generators, and capacitor banks in the bulk power system that can damage these power delivery elements.
The capability to estimate the GIC has been incorporated into common power flow tools used in transmission system planning. However, this has not been combined with frequency-domain harmonics analysis tools. The main alternative has been to use electromagnetic transients program with lengthy run times and complicated model setups that are unfamiliar to many planning engineers.
A New Multilevel Inverter Structure For High-Power Applications using Multi-c...IJPEDS-IAES
In recent, several numbers of multilevel inverter structures have been
introduced that the numbers of circuit devices have been reduced. This paper
introduces a new structure for multilevel inverter which can be used in highpower
applications. The proposed topology is based on cascaded connection
of basic units. This topology consists of minimum number of circuit
components such as IGBT, gate driver circuit and antiparallel diode. For
proposed topology, two methods are presented for determination of dc
voltage sources values. Multi-carrier PWM method for 25-level proposed
topology is used. Verification of the analytical results is done using
MATLAB simulation.
Modified T-type topology of three-phase multi-level inverter for photovoltaic...IJECEIAES
In this article, a three-phase multilevel neutral-point-clamped inverter with a modified t-type structure of switches is proposed. A pulse width modulation (PWM) scheme of the proposed inverter is also developed. The proposed topology of the multilevel inverter has the advantage of being simple, on the one hand since it does contain only semiconductors in reduced number (corresponding to the number of required voltage levels), and no other components such as switching or flying capacitors, and on the other hand, the control scheme is much simpler and more suitable for variable frequency and voltage control. The performances of this inverter are analyzed through simulations carried out in the MATLAB/Simulink environment on a threephase inverter with 9 levels. In all simulations, the proposed topology is connected with R-load or RL-load without any output filter.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
2. Bouhali et al: Solving Harmonics Elimination Problem in Three-Phase Voltage-controlled Inverter..
equation to define the harmonic-elimination switching angles [6] and by using piecewise constant
orthogonal functions [16].
In this paper, a new training algorithm is developed without using the pre-computed switching
angles. But, we use the application of the output of the ANN in the nonlinear elimination harmonic
equation. The desired output of this equation is known (the first equation equal the modulation
index and the lasts equal to zero to eliminate this harmonics). The complete set of solutions to the
non linear equations is found using the back propagation of the errors between the desired
harmonic elimination and the non linear equation systems using the switching angle given by the
ANN. Illustrative examples are given to demonstrate the feasibility of the proposed method.
2. HARMONICS IN ELECTRICAL SYSTEMS
One of the biggest problems in power quality aspects is the harmonic contents in the electrical
system. Generally, harmonics may be divided into two types: 1) voltage harmonics, and 2) current
harmonics. Current harmonic are usually generated by harmonics contained in voltage supply and
depends on the type of the load such as resistive load, capacitive load, and inductive load. Both
harmonics can be generated by either the source or the load side. Harmonics generated by load are
caused by nonlinear operation of device, including power converters, arc-furnaces, gas discharge
lighting devices, etc. Load harmonics can cause the overheating of the magnetic cores of
transformer and motors. On the other hand, source harmonics are mainly generated by power
supply with non-sinusoidal voltage and /or non-sinusoidal current waveforms. Voltage and current
source harmonics imply power losses, Electro-Magnetic Interference (EMI) and pulsating torque
in AC motor drives [13-15]. Any periodic wave form can be shown to be the superposition of a
fundamental and a set of harmonic components. By applying Fourier transformation, these
components can be extracted. The frequency of each harmonic component is a multiple of its
fundamental [4]. There are several methods to indicate the quantity of harmonics contents. The
most widely used measure is the total harmonics distortion (THD), which is defined in terms of the
magnitudes of the harmonics, H n at pulsation nω , where ω is the pulsation of the fundamental
component whose magnitude is H 1 and n is an integer [7][16]. The THD is mathematically
given by
∞
∑H
n =2
2
n
THD = (1)
H1
S1 S2
va
vdc
n S3 S4
Fig. 1: Single phase three-level inverter structure.
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3. J. Electrical Systems 1-1 (2005): 39-51
3. SELECTIVE HARMONIC ELIMINATION (SHE) STRATEGY
Various objective functions can be used in the optimal control of an inverter. For the described
study, the classic harmonic elimination strategy was selected. It consists in determining s optimal
switching angles. The primary angles are limited to the first quarter cycle of the inverter output
line voltage (phase a ) Fig.1. Switching angles in the remaining three quarters are referred to as
secondary angles. The full-cycle switching pattern must have the half-wave and quarter-wave
symmetry in order to eliminate even harmonics. Hence, the secondary angles are linearly
dependent on their primary counterparts Fig. 2. The resultant optimal switching pattern yields a
fundamental voltage corresponds to a given value of the modulation index, whereas (s − 1) low-
order, odd, and triple harmonics are absent in the output voltage [8][11-12].
V(ω ⋅ t )
vdc
π 2π
3π/2
θ1 θ2 θs-1 θs ω ⋅t
-vdc
Fig. 2: Output Voltage Waveform of a three-level inverter angle SHE-PWM.
Note that, each of the waveforms have a Fourier series expansion of the form [8]
∞
4 dc
V 1 s
sin(nwt ) × ∑ ∑ ( −1) cos(nθi )
i +1
V (wt ) = (2)
π n =1,3,5, n i =1
Where 0 ≤ θ1 ≤ θ2 ≤ ≤ θs ≤ π 2 , the Fourier series is summed over only the odd harmonics.
Again, the aim here is to use these switching schemes to achieve the fundamental voltage. And to
eliminate the fifth, seventh and 11th harmonics, etc, for those values of the modulation index
m (m = H1 ( 4vdc π ) ) .
The harmonic elimination technique is very suitable for inverters control. By employing this
technique, the low THD output waveform without any filter circuit is possible. Switching devices,
in addition, turn on and off only one time per cycle. Fig. 2 shows a general quarter symmetric
inverter waveform.
The expression of the amplitude of the fundamental and all harmonics content are given as:
4vdc
with hn = ∑ ( −1) cos (nθi )
h for odd n s
i +1
Hn (θ) = nπ n (3)
for even n i =1
0
41
4. Bouhali et al: Solving Harmonics Elimination Problem in Three-Phase Voltage-controlled Inverter..
where:
vdc is the DC voltage supply, s is the number of switching angles and θ i is the optimized
harmonic switching angles.
In the three-phase inverter, the aim is to use this switching scheme to achieve the fundamental
voltage and eliminate the fifth, seventh and 11th harmonics, etc ( n = 1, 5, 7, 11, 13, 17, 19, ).
For those values of the modulation index m , the switching angles θ1 , θ2 , , θs are chosen to
satisfy
h = cos(θ ) − cos(θ ) + + ( −1)
s +1
cos(θs ) = m
1 1 2
+ ( −1)
s +1
h2 = cos(5θ1 ) − cos(5θ2 ) + cos(5θs ) = 0
(4)
h = cos(nθ ) − cos(nθ )
+ ( −1) cos(nθs ) = 0
s +1
2 +
n 1
These equations are nonlinears, contain trigonometric terms and are transcendental in nature.
Consequently, multiple solutions are possible. A Newton Raphson method has to be first applied
to obtain a linearized set of equations [8]. The solution of these equations is achieved by means of
the Gauss-Jordan iterative method. In order to obtain convergence with this method, the starting
values of switching angles should be close to the exact solution. A great deal of effort has been
spent in this technique. However after a great computational time and efforts, no optimal solution
is usually reached and convergence problems are highly arising especially when the number of
equations is increased [4][16].
The application of the ANN to obtain the switching angles can be introduced to overcome the
aforementioned difficulties.
4. ARTIFICIAL NEURAL NETWORKS
A typical multilayer ANN is shown in Fig. 3. It consists of one input layer, a middle layer and an
output layer, where each layer has a specific function. The input accepts an input data and
distributes it to all neurons in the middle layer. The input layer is usually passive and does not alter
the input data. The neurons in the middle layer act as feature detectors. They encode in their
weights a representation of the features present in the input patterns. The output layer accepts a
stimulus pattern from the middle layer and passes a result to a transfer function block which
usually applies a nonlinear function and constructs the output response pattern of the network. The
number of hidden layers and the number of neurons in each hidden layer depend on the network
design consideration and there is no general rule for an optimum number of hidden layers or nodes
[17-18]. The ANN to be used for the generation of the optimal switching angles has a single input
neuron fed by the modulation index, one hidden layer and s outputs where each output represents
a switching angle [8][10-11].
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5. J. Electrical Systems 1-1 (2005): 39-51
x1 w11 1 v11 y1
1 v12 1
w12
2 v1p y2
x2
2 2
w1h
vh1
xn yp
n vh2 p
h vhp
Fig 3: A typical multilayer ANN.
The model of an artificial neuron can be represented by the op-amp summer-like configuration
shown in Fig. 4. It can be described by the following equation:
k
y = σ(w0 + ∑ wi xi ) (5)
i =1
where,
y : the output of the neuron,
xi : the ith input to the neuron,
wi : the ith connection weight,
w0 : the bias weight,
σ (⋅) : the transfer function of the neuron,
k : the number of connections with the neurons in the preceding layer.
1
w0
x1 w1
y
σ(.)
wk
xk
Fig. 4: Structure of a single neuron
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6. Bouhali et al: Solving Harmonics Elimination Problem in Three-Phase Voltage-controlled Inverter..
The input signals x1 , x 2 , , xk are normally continuous variables. Each of the input signals flows
through a gain or weight. The weights can be positive or negative corresponding to acceleration or
inhibition of the flow of signals. The summing node accumulates all the input weighted signals
and then passes to the output through the transfer function which is usually nonlinear, such as
sigmoid, inverse-tan, hyperbolic or Gaussian type. The sigmoid transfer function used in output
layer has the form given by:
1
σ1 (x ) = (6)
1 + e −α x
Where α is the coefficient or gain which adjusts the slope of the function that change between the
two asymptotic values (0 and +1). The sigmoid function is nonlinear, monotonic, and
differentiable and has the largest incremental gain at zero signals.
In the hidden layer, the Gaussian transfer function has been used
2
x −w
−
σ
σ 2 (x , w ) = e v
(7)
5. DIRECT SUPERVISED TRAINING OF ANN FOR SHE
Back Propagation training Algorithm (BPA) is most commonly used in feed forward ANNs. When
a set of input values are presented to the ANN, step by step calculations are made in the forward
direction to drive the output pattern. A cost functional given by the squared difference between the
net output and the desired net output for the set of input patterns is generated and this is minimized
by gradient descent method altering the weights one at a time starting from the output layer [10-
12][18] (Fig.5).
θ1 Sa
Switching Van
m θ2 Sb two-level
ANN signal Vbn
θs Inverter
generator Sc Vcn
BPA
θ
Selective θ d1
d2
Harmonic
Elimination
θ ds
Fig. 5 Direct Supervised Training of ANN for SHE.
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7. J. Electrical Systems 1-1 (2005): 39-51
1 v11 θ1
v12 1
w1
w2 2 v1s θ2
m 2
1
wl vl1
θs
vl2 s
l vls
Fig. 6 ANN set for the Selective Harmonic Elimination
In this section, an ANN with a single input neuron fed by the modulation index, l hidden neurons
and s outputs each representing a switching angle are used. The network was training using the
Back Propagation Algorithm (BPA). The training data extracted from the optimal switching
angles, designated by θ1 to θs as functions of the modulation index m . This set of angles is
required to eliminate the 5th, 7th and 11th harmonics, etc, given by equation (4).
The outputs of the ANN shown in Fig. 6 are given by
l
θi = σ1 ∑ vij σ 2 (m,w j ) , i = 1, ,s (8)
j =1
The BPA is given by:
Step 1: Define the nodes W of the Gaussian functions. Random initialization of the weights V .
Step 2: present at the input of the network a value of the modulation index m ,
Step 3: calculate the output of the neurons of the hidden layer and the output layer;
_ Hidden layer: σ 2 (m,W ) with W = [w1 w2 wl ] , l : number of the neurons in
T
the hidden layer.
_ Output layer: θ = σ1 (V ⋅ σ 2 (m,W ) ) , with size (V ) = (s , l ) .
Step 4: Normalize the outputs of the neuron network between 0 and π / 2, one should multiply the
output vector by π / 2, i.e. θnor = θ× π 2 .
Step 5: Calculate the total error E = θd − θnor , and E 2 = ( θd − θnor ) ( θd − θnor ) ,
T
θd is given by
the Newton Raphson Algorithm.
Step 6: Back propagate this error on the network using gradient descent algorithm
1 ∂E 2
V new =V old − ηv (9)
2 ∂V
∂θ
V new =V old + ηv E (10)
∂V
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8. Bouhali et al: Solving Harmonics Elimination Problem in Three-Phase Voltage-controlled Inverter..
Step 7: Adapt the weights recursively by
Vi new =Vi old + ηv ⋅ δ1 ⋅ σ 2 (m,Wj ) ,
,j ,j i
with (11)
l
i = 1,..., s
δ1 = E (i ) σ1 ' ∑Vi ,k ⋅ σ 2 (m,Wk ) , and
j = 1,...,l
i
k =1
Step 8: Repeat steps 3 to 7 until obtaining the desired precision.
6. INDIRECT SUPERVISED TRAINING OF ANN FOR SHE
In this case, the neural network is trained to generate the switching angles in a way to eliminate the
first harmonics without the knowledge of the desired switching angles given by the Newton
Raphson method. The problem which arises in this indirect learning paradigm is that the desired
outputs of the ANN, i.e. optimal angles, are unknown. However, the application of the desired
outputs on the nonlinear equation system (equation (4)) is known, i. e., to place the first harmonics
at zero by approximating the output voltage by the fundamental one.
To avoid this problem, we will insert in series with the ANN the equivalent nonlinear system
equations (equation (4)). Therefore, instead of the minimization of the error between the switching
angles given by the ANN and the wished switching angles often unknown, we will minimize the
error at the output of the nonlinear system equation of the harmonics to be eliminated.
Fig. 7 shows the diagram of the indirect training strategy of artificial neuron networks used for
harmonics elimination. When the desired precision is obtained the output of the ANN is used to
generate the control sequence of the inverter.
θ1 Sa
Switching Van
m θ2 Two-level
ANN signal Sb Vbn
θs Inverter
generator Sc Vcn
π/4 BPA
hd1 h1
hd2=0 H(θ)
hds=0
hs
Fig. 7 Indirect Training of ANN for Selective Elimination Harmonic.
The ANN is trained by the back-propagation algorithm of the error between the desired solutions
of the nonlinear system equations to eliminate the first harmonics and the output of this equation
using the switching angle given by the ANN.
The training algorithm (BPA) is summarized as follow:
Step 1: Define the nodes W of the Gaussian functions. Random initialization of the weights V .
Step 2: present at the input of a network the value of the modulation index m ,
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9. J. Electrical Systems 1-1 (2005): 39-51
Step 3: calculate the output of the neurons of the hidden layer and the output layer;
- Hidden layer: σ 2 (m,W ) with W = [w1 w2 wl ] , l : number of the neurons in the
T
hidden layer.
- Output layer: θ = σ1 (V ⋅ σ 2 (m,W ) ) , with size (V ) = (s , l ) .
Step 4: Standardize the outputs of the network of neuron between 0 and π / 2, one multiplies the
output vector by π / 2, i.e., θnor = θ× π 2 .
Step 5: Apply the ANN outputs to the nonlinear system equation H ( θ ) (equation (4)).
Step 6: Calculate the total error E = Hd ( θ ) − H ( θ ) , and E 2 = ( Hd ( θ ) − H ( θ ) ) (Hd ( θ) − H ( θ) ) .
T
Step 7: Back propagate this error on the network using gradient descent algorithm
1 ∂E 2
V new =V old − ηv (12)
2 ∂V
∂H ∂θ
V new =V old + ηv E (13)
∂θ ∂V
with,
sin(θ1 ) − sin(θ2 ) ( − ) sin(θs )
s +1
( − ) sin(5θs )
s +1
∂H sin(5θ1 ) − sin(5θ2 )
=− (14)
∂θ
sin(nθ ) − sin(nθ )
( − ) sin(nθs )
s +1
1 2
Step 8:Adapt the weights recursively by
Vi new =Vi old + ηv ⋅ δ1 ⋅ σ 2 (m,Wj ) ,
,j ,j i
with (15)
0 s
δi = ∑ ( −1) ⋅ E (i ) ⋅ n(k ) ⋅ sin (n(k ) ⋅ θ (i ) )
i +1
k =1 i = 1,..., s
, and
δ1 = δ0 σ ' V ⋅ σ (m,W ) j = 1,...,l
l
i 1 ∑ i ,k k
i
k =1
2
Step 9: Repeat steps 3 to 8 until obtaining the desired precision.
After the termination of the training phase, the obtained ANN can be used to generate the control
sequence of the inverter as shown in Fig. 8.
θ1 Sa
m Switching Van
θ2 Two-level
ANN signal Sb Vbn
θs Inverter
generator Sc Vcn
Fig. 8: Generating switching angles by using an ANN
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10. Bouhali et al: Solving Harmonics Elimination Problem in Three-Phase Voltage-controlled Inverter..
7. SIMULATION RESULTS
The indirect training strategy of ANN (with l = 201 , σv = 1 500 , ηv = 0.2 and ∆w = 0.005 ) for
SHE (with s = 5 ) was evaluated for the range of the modulation index, with excellent results in all
cases. Fig. 9 shows the obtained switching angles for various values of modulation index
( m ∈ [ 0,1] with ∆m = 0.01 ) without BPA (Fig. 8).
It is clear that the 5th, 7th, 11th and 13th harmonics are strongly suppressed and their magnitudes are
negligible relatively to the fundamental component (Fig. 10-11). The higher harmonics are also
low which contributes to a high quality of the output voltage.
1.6
1.4
1.2
1
angle
0.8
θ1
0.6 θ2
θ3
0.4 θ4
θ5
0.2
0 0.2 0.4 0.6 0.8 1 m
Fig. 9: Switching angles after training phase.
0.8
0.7
0.6
0.5
0.4
0.3
0.2 h1
hd1
0.1
0
0 0.2 0.4 0.6 0.8 1 m
Fig. 10: Fundamental load voltage ( h1 ) versus modulation index ( m ) in a two-level three phase inverter with
the proposed modulation scheme.
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Fig. 10 represents the relationship between the amplitude of the fundamental load voltage h1 and
the modulation index, which must be linear for a good modulation method. It can be observed that
the proposed method, after training phase, has a good relationship between h1 and m . Another
important aspect, to be considered in the evaluation of this modulation method, is the total
harmonic distortion (THD ) of the load voltage (Fig. 12).
-3
x 10
5
h5
4 h7
h11
3
h13
2
1
0
-1
-2
-3
0 0.2 0.4 0.6 0.8 1 m
Fig. 11: Harmonic contents for various values of modulation index
0.14
0.12
0.1
0.08
THD
0.06
0.04
0.02
0
0 0.2 0.4 0.6 0.8 1 m
Fig. 12: Load voltage THD for different modulation indexes.
8. CONCLUSION
In this paper, we proposed the use of the ANN to solve the selective harmonics elimination
problem in PWM inverters. This technique allows successful voltage control of the fundamental as
well as suppression of a selective set of harmonics. Some problems occurring at lower modulation
index values can be eliminated. Among the main advantages of the proposed method is that it
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12. Bouhali et al: Solving Harmonics Elimination Problem in Three-Phase Voltage-controlled Inverter..
requires neither high computing power nor specialized ANN hardware. The main drawback of this
technique lies in the training phase, since; this phase is quite complex and time consuming.
Fortunately, the training is executed off-line. After training phase, the connection weights can be
stored on a memory for further use.
In the indirect supervised scheme, the ANN is trained without using the desired switching angles
what makes it possible to solve the problems of the traditional methods. By adding in series the
harmonic elimination equations and using the fact that the desired output of these equations are
nulls. Only the first are corresponding to the fundamental is equal to the modulation index m .The
given simulation results proving the feasibility of the proposed technique.
9. REFERENCE
[1] M. Kojima, K. Hirabayashi, Y. Kawabata, E. C. Ejiogu and T. Kawabata, “Novel Vector Control
System Using Deadbeat Controlled PWM Inverter With Output LC Filter”, IEEE Transactions on
Industrial Applications, Vol. 40, No. 1, January/February 2004, pp. 132-169.
[2] P. Z. Grabowski, M. P. Kazmierkowski, B. K. Bose and F. Blaabjerg, “A Simple Direct-Torque Neuro-
Fuzzy Control of PWM-Inverter-Fed Induction Motor Drive”, IEEE Transactions on Industrial
Electronics, Vol. 47, No. 4, August 2000, pp. 863-870.
[3] J. O. P. Pinto, B. K. Bose, L. E. B. da Silva and M. P. Kazmierkowski, “A Neural-Network-Based
Space-Vector PWM Controller for Voltage-Fed Inverter Induction Motor Drive”, IEEE Transactions
on Industrial Applications, Vol. 36, No. 6, November/December 2000, pp. 1628-1636.
[4] S. sirisukprasert, J. S. Lai and T. H. Liu, “Optimum Harmonic Reduction With a Wide Range of
Modulation Indexes for Multilevel Converters”, IEEE Transactions on Industrial Electronics, Vol. 49,
No. 4, August 2002, pp. 875-881.
[5] S. Jian, S. Beineke and H. Grotstollen, “Optimal PWM based on real-time solution of harmonic
elimination equations”, IEEE Transactions on Power Electronics, Volume: 11, Issue: 4, July 1996
Pages:612 - 621
[6] S. R. Bowes and P. R. Clark, “Simple Microprocessor Implementation of New Regular-Sampled
Harmonic Elimination PWM Techniques”, IEEE Transactions on Industrial Applications, Vol. 28, No.
1, January/February 1992, pp. 89-92.
[7] J. N. Chaisson, L. M. Tolbert, K. J. Mckenzie and Z. Du, “A Unified Approach to Solving the
Harmonic Elimination Equations in Multilevel Converters”, IEEE Transactions on Power Electronics,
Vol. 19, No. 2, March 2004, pp. 478-490.
[8] T. H. Abdelhamid, “Application of Artificial Neural Networks to the Voltage Inverters Controlled by
Programmed PWM Control Techniques”, Proceedings of the IEEA’97, International Conference 7-9
Dec.1997, Batna University, Algeria. pp. 165-168.
[9] Y. J. Wang and R. M. O’Connell, “Experimental Evaluation of a Novel Switch Control Scheme for an
Active Power Line Conditioner”, IEEE Transactions on Industrial Electronics, Vol. 50, No. 1,
February 2003, pp. 243-246.
[10] D. Daniolos, M. K. Darwish and P. Mehta, “Optimised PWM inverter Control using Artificial Neural
Networks”, IEE 1995 Electronics Letters Online No : 19951186, 14 August1995, pp. 1739-1740.
[11] A. M. Trzynadlowski, and S. Legowski, “Application of Neural Networks to the Optimal Control of
Three-Phase Voltage-Controlled Inverters”, IEEE Transactions on Power Electronics, Vol. 9, No. 4,
July 1994, pp. 397-402.
[12] M. Mohaddes, A. M. Gole and P. G. McLaren, “A neural network controlled optimal pulse-width
modulated STATCOM”, IEEE Transactions on Power Delivery, Volume: 14 Issue: 2 , April 1999
Pages:481 – 488.
50
13. J. Electrical Systems 1-1 (2005): 39-51
[13] O. Bouhali, E.M. Berkouk, C. Saudemont and B. François, “A Five level Diode Clamped Inverter with
self-stabilization of the DC-Link Voltage for Grid Connection of Distributed Generators”, IEEE
International Symposium on Industrial Electronics : ISIE 2004, May 3-7, 2004, Ajaccio, France.
[14] O. Bouhali, E.M. Berkouk, C Saudemont and B. François, “Direct Modulation of Electrical Conversion
for a Multilevel Inverter including stabilization of the unbalance DC-Link Voltage”, IEEE Power
Electronics Specialist Conference : PESC 2004, June 24-25, 2004, Aachen, Allemagne.
[15] Q. Song, W. H. Liu, MC Wong, Y.D. Han, “A Novel Universal Space Vector Modulator for Multilevel
Voltage-Source Inverters”, 29th Annual Conference of the IEEE Industrial Electronics Society,
Roanoke, Virginia, USA, November 2nd – 6th 2003.
[16] J. Nazarzadeh, M. Razzaghi, and K. Y. Nikravesh, “Harmonic Elimination in Pulse-Width Modulated
Inverters using Piecewise Constant Orthogonal Functions”, Electric Power Systems Research, Vol. 40,
1997, pp. 45-49.
[17] B. Francois, “Orthogonal Considerations in the Design of Neural Networks for Function
Approximation”, Mathematics and Computers in Simulation, Vol.41, 1996, pp. 95-108.
[18] L. A. Cabrera, M. E. Elbuluk, and D. S. Zinger, “Learning Techniqus to Train Neural Networks as a
State Selector for Inverter-Fed Induction Machines using Direct Torque Control”, IEEE Transactions
on Power Electronics, Vol. 12, No. 5, September 1997, pp. 788-799.
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