An Implementation of 9-Level MLI using IPD-Topology for Harmonic Reduction

Similar documents
THD Minimization in Single Phase Symmetrical Cascaded Multilevel Inverter Using Programmed PWM Technique

Comparison of GA and PSO Algorithms in Cascaded Multilevel Inverter Using Selective Harmonic Elimination PWM Technique

CARRIER BASED PWM TECHNIQUE FOR HARMONIC REDUCTION IN CASCADED MULTILEVEL INVERTERS

DWINDLING OF HARMONICS IN CML INVERTER USING GENETIC ALGORITHM OPTIMIZATION

COMPARATIVE STUDY OF DIFFERENT TOPOLOGIES OF FIVE LEVEL INVERTER FOR HARMONICS REDUCTION

Literature Survey: Multilevel Voltage Source Inverter With Optimized Convention Of Bidirectional Switches

Analysis of Asymmetrical Cascaded 7 Level and 9 Level Multilevel Inverter Design for Asynchronous Motor

A Novel Cascaded Multilevel Inverter Using A Single DC Source

Switching of Three Phase Cascade Multilevel Inverter Fed Induction Motor Drive

Analysis of IM Fed by Multi-Carrier SPWM and Low Switching Frequency Mixed CMLI

Simulation of Cascade H-Bridge Multilevel Inverter With Equal DC Voltage Source

Keywords: Multilevel inverter, Cascaded H- Bridge multilevel inverter, Multicarrier pulse width modulation, Total harmonic distortion.

Harmonic Minimization for Cascade Multilevel Inverter based on Genetic Algorithm

Size Selection Of Energy Storing Elements For A Cascade Multilevel Inverter STATCOM

Performance of Indirectly Controlled STATCOM with IEEE 30-bus System

Low Order Harmonic Reduction of Three Phase Multilevel Inverter

A New Transistor Clamped 5-Level H-Bridge Multilevel Inverter with voltage Boosting Capacity

SPECIFIC HARMONIC ELIMINATION SCHEME FOR NINELEVEL CASCADED H- BRIDGE INVERTER FED THREE PHASE INDUCTION MOTOR DRIVE

ADVANCED PWM SCHEMES FOR 3-PHASE CASCADED H-BRIDGE 5- LEVEL INVERTERS

THD Minimization of 3-Phase Voltage in Five Level Cascaded H- Bridge Inverter

Simulation and Experimental Results of 7-Level Inverter System

II. WORKING PRINCIPLE The block diagram depicting the working principle of the proposed topology is as given below in Fig.2.

NEW VARIABLE AMPLITUDE CARRIER OVERLAPPING PWM METHODS FOR THREE PHASE FIVE LEVEL CASCADED INVERTER

MULTICARRIER TRAPEZOIDAL PWM STRATEGIES FOR A SINGLE PHASE FIVE LEVEL CASCADED INVERTER

Non-Carrier based Digital Switching Angle Method for 81-level Trinary Cascaded Hybrid Multi-level Inverter using VHDL Coding

Study of Unsymmetrical Cascade H-bridge Multilevel Inverter Design for Induction Motor

Speed Control of Induction Motor using Multilevel Inverter

The Selective Harmonic Elimination Technique for Harmonic Reduction of Multilevel Inverter Using PSO Algorithm

International Journal of Advance Engineering and Research Development

Harmonic Evaluation of Multicarrier Pwm Techniques for Cascaded Multilevel Inverter

Selective Harmonic Elimination (SHE) for 3-Phase Voltage Source Inverter (VSI)

Implementation of Multicarrier Based Control Schemes for Cascaded 9-Levels Multilevel Inverter

International Journal of Advance Engineering and Research Development

Harmonic Analysis & Filter Design for a Novel Multilevel Inverter

Performance of Sinusoidal Pulse Width Modulation based Three Phase Inverter

COMPARATIVE STUDY OF PWM TECHNIQUES FOR DIODE- CLAMPED MULTILEVEL-INVERTER

Total Harmonic Distortion Minimization of Multilevel Converters Using Genetic Algorithms

Design and Development of Multi Level Inverter

International Journal Of Engineering And Computer Science ISSN: Volume 2 Issue 12 December, 2013 Page No Abstract

IMPLEMENTATION OF MODIFIED REDUCED SWITCH MULTILEVEL INVERTER USING MCPWM AND MSPWM TECHNIQUES

Australian Journal of Basic and Applied Sciences. Simulation and Analysis of Closed loop Control of Multilevel Inverter fed AC Drives

Modified Multilevel Inverter Topology for Driving a Single Phase Induction Motor

Multilevel Inverter with Coupled Inductors with Sine PWM Techniques

Design of Multi-Level Inverter and Its Application As Statcom to Compensate Voltage Sags Due to Faults

SIMULATION, DESIGN AND CONTROL OF A MODIFIED H-BRIDGE SINGLE PHASE SEVEN LEVEL INVERTER 1 Atulkumar Verma, 2 Prof. Mrs.

Simulation and Analysis of ASCAD Multilevel Inverter with SPWM for Photovoltaic System

A Comparative Study of Different Topologies of Multilevel Inverters

Level Shifted Pulse Width Modulation in Three Phase Multilevel Inverter for Power Quality Improvement

Harmonic elimination control of a five-level DC- AC cascaded H-bridge hybrid inverter

Performance Evaluation of a Cascaded Multilevel Inverter with a Single DC Source using ISCPWM

Implementation of Novel Low Cost Multilevel DC-Link Inverter with Harmonic Profile Improvement

Reduction of THD in Thirteen-Level Hybrid PV Inverter with Less Number of Switches

Harmonic Reduction in Induction Motor: Multilevel Inverter

A NOVEL APPROACH TO ENHANCE THE POWER QUALITY USING CMLI BASED CUSTOM POWER DEVICES

Simulation of Five-Level Inverter with Sinusoidal PWM Carrier Technique Using MATLAB/Simulink

Comparison of Multi Carrier PWM Techniques applied to Five Level CHB Inverter

Neural Network Based Optimal Switching Pattern Generation for Multiple Pulse Width Modulated Inverter

Reduced PWM Harmonic Distortion for a New Topology of Multilevel Inverters

Simulation & Implementation Of Three Phase Induction Motor On Single Phase By Using PWM Techniques

Performance Evaluation of Single Phase H-Bridge Type Diode Clamped Five Level Inverter

Performance Evaluation of Multi Carrier Based PWM Techniques for Single Phase Five Level H-Bridge Type FCMLI

Series Parallel Switched Multilevel DC Link Inverter Fed Induction Motor

Symmetrical Multilevel Inverter with Reduced Number of switches With Level Doubling Network

Timing Diagram to Generate Triggering Pulses for Cascade Multilevel Inverters

Analysis of Cascaded Multilevel Inverters with Series Connection of H- Bridge in PV Grid

Comparison of 3-Phase Cascaded & Multi Level DC Link Inverter with PWM Control Methods

Keywords Asymmetric MLI, Fixed frequency phase shift PWM (FFPSPWM), variable frequency phase shift PWM (VFPSPWM), Total Harmonic Distortion (THD).

Enhanced Performance of Multilevel Inverter Fed Induction Motor Drive

A STUDY OF CARRIER BASED PULSE WIDTH MODULATION (CBPWM) BASED THREE PHASE INVERTER

Keywords Cascaded Multilevel Inverter, Insulated Gate Bipolar Transistor, Pulse Width Modulation, Total Harmonic Distortion.

Performance Improvement of Multilevel Inverter through Trapezoidal Triangular Carrier based PWM

ISSN: International Journal of Science, Engineering and Technology Research (IJSETR) Volume 1, Issue 5, November 2012

Study of five level inverter for harmonic elimination

A Fifteen Level Cascade H-Bridge Multilevel Inverter Fed Induction Motor Drive with Open End Stator Winding

MATLAB Implementation of a Various Topologies of Multilevel Inverter with Improved THD

Three Phase 15 Level Cascaded H-Bridges Multilevel Inverter for Motor Drives

Modified Transistor Clamped H-bridge-based Cascaded Multilevel inverter with high reliability.

COMPENSATION OF VOLTAGE SAG USING LEVEL SHIFTED CARRIER PULSE WIDTH MODULATED ASYMMETRIC CASCADED MLI BASED DVR SYSTEM G.Boobalan 1 and N.

ANALYSIS AND SIMULATION OF CASCADED FIVE AND SEVEN LEVEL INVERTER FED INDUCTION MOTOR

ISSN Vol.05,Issue.05, May-2017, Pages:

Cascaded Connection of Single-Phase & Three-Phase Multilevel Bridge Type Inverter

Diode Clamped Multilevel Inverter for Induction Motor Drive

Hybrid Cascaded H-bridges Multilevel Motor Drive Control for Electric Vehicles

Multilevel Inverter Based Statcom For Power System Load Balancing System

AN INVERTED SINE PWM SCHEME FOR NEW ELEVEN LEVEL INVERTER TOPOLOGY

Comparison between Conventional and Modified Cascaded H-Bridge Multilevel Inverter-Fed Drive

Performance Analysis of Three Phase Cascaded H-Bridge Multi Level Inverter for Voltage Sag and Voltage Swell Conditions

Performance Metric of Z Source CHB Multilevel Inverter FED IM for Selective Harmonic Elimination and THD Reduction

Three Phase 11-Level Single Switch Cascaded Multilevel Inverter

Analysis and Simulation of Multilevel DC-link Inverter Topology using Series-Parallel Switches

Hardware Implementation of SPWM Based Diode Clamped Multilevel Invertr

A Comparative Analysis of Modified Cascaded Multilevel Inverter Having Reduced Number of Switches and DC Sources

Comparison of carrier based PWM methods for Cascaded H-Bridge Multilevel Inverter

New Multi Level Inverter with LSPWM Technique G. Sai Baba 1 G. Durga Prasad 2. P. Ram Prasad 3

MODIFIED CASCADED MULTILEVEL INVERTER WITH GA TO REDUCE LINE TO LINE VOLTAGE THD

THREE PHASE SEVENTEEN LEVEL SINGLE SWITCH CASCADED MULTILEVEL INVERTER FED INDUCTION MOTOR

A comparative study of Total Harmonic Distortion in Multi level inverter topologies

A SOLUTION TO BALANCE THE VOLTAGE OF DC-LINK CAPACITOR USING BOOST CONVERTER IN DIODE CLAMPED MULTILEVEL INVERTER

Reduction in Total Harmonic Distortion Using Multilevel Inverters

International Journal of Emerging Researches in Engineering Science and Technology, Volume 1, Issue 2, December 14

Transcription:

Volume-6, Issue-4, July-August 2016 International Journal of Engineering and Management Research Page Number: 456-460 An Implementation of 9-Level MLI using IPD-Topology for Harmonic Reduction Harish Tata 1, Prof. Meha Shrivastava 2 1 Department of Electrical and Electronics, Truba Institute of Science & Technology (TCST), Bhopal, INDIA 2 HOD, Department of Electrical and Electronics, Truba College of Science & Technology (TCST), Bhopal, INDIA ABSTRACT Multi Level Inverters (MLI) are today used in medium and large power applications. There are three major topologies of multilevel inverters; they are capacitor clamped, diode camped and cascaded. During this paper implement the nine-level asymmetric cascaded multilevel inverter with IM for various kinds of level-shifted PWM techniques in Matlab Simulink. As the number of levels will increase, the synthesized output waveform has more steps that produces a staircase wave that approaches the required waveform. Also, as more steps are added to the waveform, the harmonic distortion of the output wave decreases, approaching zero as the number of levels will increase. As the number of levels will increase, the voltage that can be spanned by connecting devices serial also increases. output voltage levels using only standard low voltage components [4]. Typically, it is necessary to connect three to ten inverters in series to reach the required output voltage. These converters also feature a high modularity degree because each inverter can be seen as a module with similar circuit topology, control structure, and modulation. Therefore, in the case of a fault in one of these modules, it is possible to replace it quickly and easily. Moreover, with an appropriated control strategy, it is possible to bypass the faulty module without stopping the load, bringing an almost continuous overall availability. Keywords Inverter, Multilevel Inverter, Power Electronics, PWM, AC, DC I. INTRODUCTION In recent years, multilevel inverters have received more attention in industrial applications, such as motor drives, Static VAR Compensators (STATCOMs), Flexible AC Transmission System (FACTS), high voltage direct current lines, electrical drives and renewable energy systems [2]. Compared to the traditional two level voltage source inverters, the stepwise output voltage is the major advantage of multilevel inverters. This advantage results in higher power and needlessness of a transformer at distribution voltage level, thereby reducing the costs. Multilevel inverters are generally divided into three configurations: diode-clamped, flying-capacitor, and cascaded H-bridge multilevel inverters [3]. Among these inverter topologies, cascaded multilevel inverter reaches the higher output voltage and power levels and the higher reliability due to its modular structure. Cascaded multilevel inverters are based on a series connection of several single phase full bridge inverters. This structure is capable of reaching medium Figure 1: General staircase waveform of multilevel inverters A typical multilevel inverter utilizes voltage levels from multiple dc sources. These dc sources can be isolated as in cascade multilevel structures or interconnected as in diode-clamped structures. In most published multilevel inverter circuit topologies, the dc sources in the circuits need to be maintained to supply identical voltage levels. Based on these identical voltage levels and proper control of the switching angles of the switches, a staircase waveform can be synthesized, such as a six-level staircase waveform with five switching angles shown in Figure 1. II. LITERATURE SURVEY [1] M. Mythili, N. Kayalvizhi, Harmonic Minimization in Multilevel Inverters Using Selective Harmonic Elimination PWM Technique 2013 456 Copyright 2016. Vandana Publications. All Rights Reserved.

Summary- In general, the inverter output voltage must be sinusoidal. However, the waveforms of the inverters practical non-sinusoidal and contain certain harmonics. For low and medium power applications, square wave or quasi-square wave may be acceptable, but for high power applications, low distorted sinusoidal waveforms are required. By number of levels in the UPS by increasing the output voltage has several steps generating a form of stairs, which reduces harmonic distortion. Emerges need a multilevel inverter. In this cascade research work multilevel inverter with selective removal of Pulse Width Modulation harmonics (SHE-PWM) technique is implemented. The SHE-PWM problem is to solve the non-linear transcendental equations that are used to determine the switching angles. Here the evolutionary algorithm based on natural selection is proposed to solve the equations that reduce the computational load resulting from the faster convergence. The main benefits are reduced total harmonic distortion and low switching frequency. To validate the results of calculation for the switching angles, a simulation is performed in the MATLAB / Simulink software tool for a level 7 cascade H-bridge inverter. [1] [2] Jin Wang, Damoun Ahmadi, A Precise and Practical Harmonic Elimination Method for Multilevel Inverters 2010 Summary- Multilevel inverters have been widely used in applications in medium and high voltage. Selective Harmonic Elimination for voltage waveform generated by the staircase multilevel inverter has been widely studied in the last decade. Most methods published on this subject were based on solving multivariate groups of high order polynomial equation from the Fourier series expansion. This research presents a different approach, which is based on criteria of equal and harmonic injection area. With the proposed method, regardless of the number of voltage levels are involved, only four simple equations are needed. The results of a case study, with a maximum of five switching angles show that the proposed method can be used to achieve excellent removal performance of the harmonics of the modulation index range of at least 0, 2 to 0.9. To demonstrate the adaptability of the proposed method for waveforms with a high number of switching angles, experimental results on a 1-MVA 6000 V-17 level cascaded multilevel inverter are also presented to the end of this research. [2] [3] Jagdish Kumar, Biswarup Das, Pramod Agarwal, Harmonic reduction technique for a cascade multilevel inverter, 2009 Summary- In this research, an optimization technique is proposed to calculate the switching angles to the fundamental frequency of switch system by solving nonlinear transcendental equations (known as selective harmonic elimination equations), thus eliminating certain harmonics predominating lower order, and at the same time, control over the magnitude of the output voltage of a multilevel inverter is reached. Since these equations are nonlinear transcendental in nature, there may be a simple, multiple or even for a particular value of a modulation index. The proposed scheme is implemented so that all possible solutions are obtained without knowing the proper initial estimate solutions. Moreover, this technique is suitable for the high level of multilevel inverters where other existing methods fail to calculate switching angles due to more computational load. For values of modulation indices for which there are many solutions, the solutions that produce less THD in the output voltage is selected. A significant decrease DHT is obtained by considering several sets of solutions instead of taking a single set of solution. Calculation results are displayed graphically for better understanding and proving the effectiveness of the method. An experimental 11-level multi-level cascade inverter is used to validate the results of calculation. [6] III. PROPOSED METHODOLOGY During this chapter implement the nine-level asymmetric cascaded multilevel inverter with IM for various kinds of level-shifted PWM techniques in Matlab Simulink. As the number of levels will increase, the synthesized output waveform has more steps that produces a staircase wave that approaches the required waveform. Also, as more steps are added to the waveform, the harmonic distortion of the output wave decreases, approaching zero as the number of levels will increase. As the number of levels will increase, the voltage that can be spanned by connecting devices serial also increases. The output voltage of the MLI has several levels synthesized from many dc voltage sources, the quality of the output voltage is improved as the no of voltage levels increase, therefore total harmonic distortions and therefore the quantity of output filter can be reduces. IV. PROPOSED SYSETEM 4.1 Block Diagram of Proposed Work In case of 9 level Asymmetric Cascaded MLI three DC sources are used having 2 same and third different and 12 power switches are used. The Asymmetric Multilevel Inverter increases the number of levels in the output and reduces the number of input DC sources required. IGBT is used as semiconductor switch for designing the inverter circuit. It has the high power rating, less conduction loss and less switching loss. These topology uses level-shifted multi carrier based new PWM method, used to produce a 9- level output voltage. Figure 2: Proposed block diagram of 9-levels Hybrid Cascaded Multilevel Inverter 457 Copyright 2016. Vandana Publications. All Rights Reserved.

4.2 SCHEMATIC DESCRIPTION OF THE SYSTEM 4.2.1 Simulation Diagram The Simulink model of 9-level multilevel inverter implemented in Matlab-Simulink is shown in Figure 3. It is basically a Cascaded H-bridge type of Multilevel Inverter. Here the used DC source is Asymmetrical type, Asymmetrical source defines that it has different value of DC sources used in an Inverter. For 9-level inverter the DC sources are 100V, 200V, and 100V respectively. The Simulink model for 9-level multilevel inverter shown in figure 3. Since S1, S4, S5, S6, S10 & S12 are ON and gives 200V level. D. For 300V voltage level Since S1, S2, S5, S6, S10 & S12 are ON and gives 300V level. E. For 400V voltage level Since S1, S2, S5, S6, S9 & S10 are ON and gives 400V level. F. For 0V voltage level Since S1and S3 are ON or all power switches are OFF, the current will cancelled out in the bridge and hence it gives 0 V voltage level. G. For- 100V voltage level Since S3, S4, S6, S8, S10, and S12 are ON and gives -100V level. H. For -200V voltage level Since S2, S4, S7, S8 S10, and S12are ON and gives -200V level. I. For- 300V voltage level Since S3, S4, S7, S8, S10, & S12 are ON and gives -300V level. I. For- 300V voltage level. J. For -400V voltage level Since S3, S4, S7, S8, S11, & S12 are ON and gives -400V level. For detail operation of new topology can also be understand by analyzing table 1 which is given below. Here 0 means switches are OFF and 1 means switches are ON. Table 4.1: Switching pattern for asymmetrical cascaded nine level inverter Figure 3: Simulink model of 9 level with IM 4.2.2. Working and Analysis Working of this inverter is nothing but how we make power switches (IGBTs) ON and OFF as per voltage level desired. We have generated switching pulses to obtain staircase output voltage which resembles nearly equal to sine wave. For different switching angles the power circuit behaves differently producing different waveforms. In this topology, we have generated 9 voltage levels as 0, 100V, 200V, 300V and 400V. The circuit working for each level is described below: A. For 0 voltage level Since S1and S3 are ON or all power switches are OFF, the current will cancelled out in the bridge and hence it gives 0 V voltage level. B. For 100V voltage level Since S1, S10, S12, S6, S8 and S2 are ON and gives 100V level. C. For 200V voltage level Table 4.2: System parameters for 9-level Inverter System Parameters Value Reference frequency 50 Hz Carrier frequency 1.2K Hz Load resistance 1Ω Load inductance 1 mh DC Sources 100V, 200V, 300V 458 Copyright 2016. Vandana Publications. All Rights Reserved.

Figure 5: Output phase voltage waveform for asymmetric (9-level) MLI using IPD-CLSPWM Figure 6: FFT analysis of voltage waveform of asymmetric (9-level) cascaded MLI using IPD-CLSPWM VI. RESULT COMPRESSION Figure 4: Different stages of output voltage level V. SIMULATION AND RESULT This section shows the comparative study of output voltage of 9-level asymmetrical cascaded multilevel inverters cascaded is compared for the PD, POD, APOD techniques, and it also shows the THD profile and performance of the circuit with IM for three PWM techniques, and also the compare all result with 7-level MLI. Cascaded multi-level inverter shows the lowest THD profile without any type of filter and also any type of dependency of inductor and capacitor used for smooth the current wave form and due to less number of switching devices gate firing circuit also reduced that s why total cost and performance has been increased. 5.1 SIMULATION RESULT OF (9-LEVEL) ACMLI WITH IM USING IPD-CLSPWM In this of the compare the result of proposed method 9-level with 7 level MLI. In the below figure 7 shows the output of 7 level multi level inverter. In the genetic cascaded multilevel inverter with Selective Harmonic Elimination Pulse Width Modulation (SHE- PWM) technique is implemented. The problem of SHE- PWM is to solve the nonlinear transcendental equations which are used to determine switching angles. Figure 7: FFT analysis of voltage waveform of (7-level) cascaded MLI using Genetic Algorithm 459 Copyright 2016. Vandana Publications. All Rights Reserved.

The total harmonic distortion of the 7 level genetic algorithm is near about 11.33%. In the proposed 9- level asymmetric (9-level) MLI using IPD-CLSPWM THD is shown in below figure 8. Fig 8. Show the THD of Proposed 9 Level Inverter VII. CONCLUSION In this work, the multicarrier pulse width modulation (PWM) techniques for 9-level have been presented. Performance factor like total harmonic distortion (THD) of the output voltage of asymmetric cascade multilevel inverter (CMLI) have been evaluated, presented and analyzed. The total harmonic distortion (THD) of the output voltage of unbalanced cascade multi-level inverter (CMLI) is studied under different techniques such as IPD, POD & APOD, compare for seven and nine level multi-level inverter (MLI) and less total harmonic distortion (THD) is observed for APOD techniques for 7-level and IPD techniques best for 9-level multi-level inverter (MLI). Therefore, it concluded that the 9-level cascade multi-level inverter (CMLI) provide a lower percentage total harmonic distortion (THD) as compared to 7-level multi-level inverter (MLI). The harmonic distortions present in the output voltage waveforms were experiential and calculate from side to side Fast Fourier Transform (FFT) analysis tool in Matlab and Simulink. The proposed inverter has been operated by only three control schemes, namely IPD, POD and APOD PWM schemes. Applying the improved switching techniques can still improve the output quality. So potential of proposed version could be explored by adopting different switching techniques. The proposed version of CMI is only adopted for harmonic reduction applications. In fact the merits of CMI can be used to build for photovoltaic/grid connected systems. So it can extend to multiple applications like STATCOM, SSSC and UPQC etc. REFERENCES [1] M.Mythili, N.Kayalvizhi, Harmonic Minimization in Multilevel Inverters Using Selective Harmonic Elimination PWM Technique, 2013 International Conference on Renewable Energy and Sustainable Energy [ICRESE 13], IEEE 2013. [2] Jin Wang and Damoun Ahmadi, A precise and practical harmonic elimination method for multilevel inverters IEEE Transactions on Industry Applications, vol. 46, no. 2, pp. 857-865, March/April 2010. [3] Jose Rodriguez, Jih-Sheng Lai, and Fang Zheng Peng, Multilevel inverters: A survey of topologies, controls, and applications IEEE Transactions on Industrial Electronics, vol. 49, no. 4, pp.724-738, Aug.2002. [4] Mariusz Malinowski, K. Gopakumar, Jose Rodriguez, and Marcelo A. Perez, A survey on cascaded multilevel inverters IEEE Transactions on Industrial Electronics, vol. 57, no. 7, pp.2197-2206, July 2010. [5] Jason R. Wells, Brett M. Nee, Patrick L. Chapman, and Philip T. Krein, Selective harmonic control: a general problem formulation and selected solutions IEEE Transactions on Power Electronics, vol. 20, no.6, pp.1337-1345, Nov. 2005. [6] Jagdish Kumar, Biswarup Das, and Pramod Agarwal, Harmonic reduction technique for a cascade multilevel inverter International Journal of Recent Trends in Engineering, vol.1, no. 3, May 2009. [7] Mohamed S. A. Dahidah and Vassilios G. Agelidis Selective harmonic elimination PWM control for cascaded multilevel voltage source converters: a generalized formula IEEE Transactions on Power Electronics, vol. 23, no. 4, pp.1620-1630, July 2008. [8] Nima Yousefpoor, Seyyed Hamid Fathi, Naeem Farokhnia, and Hossein Askarian Abyaneh, THD minimization applied directly on the line-to-line voltage of multilevel inverters IEEE Transactions on Industrial Electronics, vol. 59, no. 1, pp.373-380, Jan. 2012. [9] Zhong Du, Leon M. Tolbert, and John N. Chiasson, Active harmonic elimination for multilevel converters IEEE Transactions on Power Electronics, vol. 21, no. 2, pp.459-469, March 2006. [10] Li Li, Dariusz Czarkowski, Yaguang Liu, and Pragasen Pillay, Multilevel selective harmonic elimination PWM technique in series connected voltage inverters IEEE Transactions on Industry Applications, vol. 36, no. 1, pp. 160-170, Jan./Feb.2000. [11] Wanmin Fei, Xinbo Ruan, and Bin Wu, A generalized formulation of quarter-wave symmetry SHE- PWM problems for multilevel inverters IEEE Transactions on Power Electronics, vol. 24, no. 7, pp.1758-1766, July 2009. 460 Copyright 2016. Vandana Publications. All Rights Reserved.