Design and Simulation of Single-Phase Three-Level, Four-Level and Five-Level Inverter Fed Asynchronous Motor Drive with Diode Clamped Topology

Transcription

1 International Journal of nineerin Trends and Technoloy (IJTT) Volume 12 Number 1 - Jun 214 Desin and Simulation of Sinle-Phase Three-Level, Four-Level and Five-Level Inverter Fed Asynchronous Motor Drive with Diode lamped Topoloy Gerald Diyike 1, Aniekan ffion 2, Daniel Nnadi 3 1 Department of Mechanical nineerin, Michael Okpara University of Ariculture, Umudike, P.M.B 7267, Abia State, Nieria 2 Department of Mechanical nineerin, University of Uyo, Uyo, P.M.B. 117, Akwa Ibom State, Nieria 3 Departments of Mechanical nineerin, Michael Okpara University of Ariculture, Umudike, P.M.B 7267, Abia State, Nieria ABSTRAT - This paper deals with study of sinle-phase three-level, four-level and five-level inverter fed asynchronous motor drive. Both three-level, four-level and five-level inverters are realized by diode clamped inverter topoloy. The poor quality of voltae and current of a convectional inverter fed asynchronous motor is due to presence of harmonic contents and hence there is sinificant level of enery losses. The multilevel inverter is used to reduce the harmonic contents. The inverter with a lare number of steps can enerate a hih quality voltae waveform. The hiher inverter levels can be modulated by comparin a sinusoidal reference sinal and multiple trianular carrier sinals by the means of pulse width modulation I. INTRODUTION Adjustable speed drives are the vital and endless demand of the industries and researchers. Asynchronous motors are widely used in the factories and industries to control the speed of conveyor systems, blower speeds, machine tool speeds and applications that require adjustable speed controls. Thus, sinlephase asynchronous motors are extensively used for smaller loads, such as household appliances like fans, water pumps. In many industrial applications, traditionally, D motors, provide excellent speed control for acceleration and deceleration with effective and simple torque control. The supply of a D motor connects directly to the field of the motor allows for precise voltae control, which is necessary with speed and torque control applications. D motors perform better than A motors on the some traction equipment. They are also used for mobile equipment like olf cart, quarry and minin equipment. D motors are conveniently portable and well suited to special applications, such as industrial tools and machinery that is not easily run from remote sources. But, they have inherent demerit of commutator and mechanical brushes, which undero wear and tear with the passae of time. In most cases, A motors are preferred to D motors, in particular, an asynchronous motor due to its simple desin, low cost, reliable operation, easily found replacements or low maintenance, variety of mountin styles, many environmental enclosures, lower weiht, hiher efficiency, improved ruedness. All these and more features technique. The simulation of sinle-phase three-level, four-level and five-level inverter fed asynchronous motor model is done usin (The math Works, Natick, Massachusetts, USA). The Fast Fourier Transform (FFT) spectrums of the outputs are analyzed to study the reduction in the harmonic contents. Keywords - Asynchronous Motor, Multi-level inverters, pulse width modulation, Total harmonic distortion. make the use of induction motor compulsory in many areas of industrial applications. The main demerit of A motor, when compared with D motor, is that its speed is more difficult to control. A motors can be equipped with variable frequency/pwm drives, which provide smooth turnin moment, or torque, at low speeds and complete control over the speed of the motor up to its rated value. Variable frequency drives improves speed control, but do create losses with reduced power quality [1]. The advancement in Power lectronics and semiconductor technoloy has triered the development of hih power and hih speed semiconductor devices in order to achieve a smooth, continuous and step less variation in motor speed. Applications of solid state converters/inverters for adjustable speed induction motor drive are wide spread in electromechanical systems for a lare spectrum of industrial systems,[2],[3],[4]. As far as convectional two-level inverter is concerned, it exhibits many problems when used in hih power application [5], [6]. Poor quality of output current and voltae of an asynchronous motor fed by a classical/ convectional two-level inverter confiuration is due to the presence of harmonic content. The presence of sinificant amount of harmonic makes the motor to suffer from severe torque pulsations, especially at low speed, which manifest themselves in coin of the shaft. It will also causes undesired motor heatin and lectromanetic interference [7]. Minimization in harmonics calls for lare sized filter, resultin increased size and the cost of the system. The advancements in ISSN: Pae 27

2 International Journal of nineerin Trends and Technoloy (IJTT) Volume 12 Number 1 - Jun 214 the field of power electronics and microelectronics made it possible to reduce the manitude of harmonics with multilevel inverters, in which the number of levels of the inverters are increased rather than increasin the size of the filters [8]. Nowadays, multilevel inverters have been ained more attention for hih power application in recent years which operate at hih switchin frequencies while producin lower order harmonic components. Multilevel inverter not only achieves hih power ratins, but also enables the use of renewable enery sources [9]. In this paper Sinle-phase three-level, four-level, and fivelevel inverter fed asynchronous motor drive are desined and simulated. Both the different levels are realized by usin diode clamped multilevel inverter topoloy. The simulations are done usin Matlab/Simulink/SimPowerSystems software with PWM control. The FFT spectrum for the output voltaes and currents are analyzed to study the reduction in the harmonic contents. II. MULTILVL INVRTR Multilevel inverters have drawn tremendous interest in the power industry applications. They present a new set of features that are well suited for use in reactive power compensation. Multilevel inverters will most importantly reduce the manitude of harmonics and increases the output voltae and power without the use of step-up transformer. Numerous multilevel inverters topoloies have been proposed durin the last decades. Modern research, have involved novel inverter topoloies and unique modulation techniques [1]. Basically, three different major multilevel inverter topoloies have been reported in the literature, which includes: diode clamped (neutral clamped) inverter, flyin capacitors inverter, and cascaded H-bride. Multilevel inverter presented in this paper consists of diode clamped inverter topoloy connected to sinle phase asynchronous motor. The eneral function of this multilevel inverter is to synthesize a desired voltae from several D sources. A. SINGL-PHAS THR-LVL, FOUR-LVL AND FIV-LVL INVRTR IRUIT ONFIGURATIONS USING DIOD LAMPD TOPOLOGY The neutral point inverter proposed by Nabae, and Akai in 1981 was essentially a three-level, diode-clamped inverter [1]. The diode-clamped inverter provides multiple voltae levels throuh connection of the phases to a series bank of capacitors [11]. The main concept of this type of multilevel inverter topoloy is to use diodes to limit the power devices voltae stress. The voltae over each capacitor and each switch is. A sinle-phase full bride -level inverter needs ( voltae source, switchin devices and 8( diodes. This topoloy can be extended to any number of levels by increasin the number of capacitor banks. Diode clamped multilevel inverter topoloy can be discussed under a sinlephase structures. Fi. 1 show sinle-phase three-level structure of Diode lamped Inverter. D V dc 1 2 V dc 2 V dc 2 a1 T a1 Da1 a2 T a2 va _ a1 T a1 a2 _ T a2 Da2 io Da1 Da2 Dbc1 b1 T b1 b2 Tb2 vb _ b1 Tb1 Dbc2 b2 _ Tb2 Db1 Db2 Fi. 1 Power circuit for Sinle-phase, three-level diode clamped inverter As shown in the fi. 1 above, a sinle-phase full bride threelevel diode clamped inverter consists of two bulk capacitor ( and ), four clampin diodes (,, and ), eiht antiparallel diodes (,,,,,,, and ) and eiht power switches (,,,,,,, and ). For a iven D link voltae, the two capacitors and are connected in series across the D link input. They split the D link voltae across the capacitors with a constant value equals to. The clampin diodes,, and are used to maintain the potential across the switches. Thus, the voltae stress of each switch is limited to one capacitor voltae. For a sinle-phase three-level full bride diode clamped inverter, the voltae across the output of the two les can be equal to, and. Fi. 2 shows a Sinle-phase four-level structure of Diode lamped Inverter. A Db1 Db2 ISSN: Pae 28

3 International Journal of nineerin Trends and Technoloy (IJTT) Volume 12 Number 1 - Jun 214 a1 b1 a1 b1 Ta1 Da1 Tb1 Db1 Ta1 Da1 Tb1 Db1 1 V D 3 1 V D 4 a2 Ta2 Da2 b2 Tb2 Db2 a2 Ta2 Da2 Dbc1 b2 Tb2 Db2 Ta3 Da3 Dbc1 Tb3 Db3 a3 b3 2 V D 4 a4 Ta4 Da4 a4 Ta4 Db4 a3 b3 D V D A io va vb D V D 2 V D 3 a1 Ta3 va _ Ta1 Da3 io Da1 A b1 Tb3 vb _ Tb1 Db3 Db1 3 4 V D 4 V D 4 a1 a2 a3 _ Ta1 _ Ta2 _ Ta3 Da1 Da2 Da3 Dbc2 b1 b2 b3 _ Tb1 _ Tb2 _ Tb3 Db1 Db2 Db3 Dbc2 a4 _ b4 _ 3 V D 3 a2 a3 _ Ta2 _ Ta3 Da2 Da3 b2 b3 _ Tb2 _ Tb3 Db2 Db3 Ta4 Fi. 3 Power circuit for Sinle-phase, five-level diode clamped inverter Finally, sinle-phase structure of diode clamped five-level inverter is illustrated in Fi. 3. D voltae source is connected to the inverter circuit throuh four dividin capacitors which are connected in series. They split the D link voltae across the capacitors with a constant value equals to. Thus, the voltae Da4 Tb4 Db4 Fi. 2 Power circuit for Sinle-phase, four-level diode clamped inverter The sinle-phase Structure of diode clamped four-level inverter is illustrated in Fi. 2. D voltae source is connected to the inverter circuit throuh three capacitors connected are connected in series. They split the D link voltae across the capacitors with a constant value equals to. Thus, the voltae stress of each switch is limited to one capacitor voltae. For a sinle-phase four-level full bride diode clamped inverter, the voltae across the output of the two les can be equal to,, and. Fi. 3 shows a Sinle-phase five-level structure of Diode lamped Inverter. stress of each switch is limited to one capacitor voltae. For a sinle-phase five-level full bride diode clamped inverter, the voltae across the output of the two les can be equal to,,, and. B. ASYNHRONOUS MOTOR DRIV Synchronous speed of Asynchronous Motor varies directly proportional to the supply frequency. Hence, by chanin the frequency, the synchronous speed and the motor speed can be controlled below and above the normal full load speed. The voltae induced in the stator, is directly proportional to the product of slip frequency and air ap flux. The Asynchronous Motor terminal voltae can be considered proportional to the product of the frequency and flux, if the stator voltae is nelected. Any reduction in the supply frequency without a chane in the terminal voltae causes an increase in the air ap flux. Asynchronous motors are desined to operate at the knee ISSN: Pae 29

4 International Journal of nineerin Trends and Technoloy (IJTT) Volume 12 Number 1 - Jun 214 point of the manetization characteristic to make full use of the manetic material. Therefore the increase in flux will saturate the motor. This will increase the manetizin current, distort the line current and voltae, increase the core loss and the stator copper loss, and produce a hih pitch acoustic noise. While any increase in flux beyond rated value is undesirable from the consideration of saturation effects, a decrease in flux is also avoided to retain the torque capability of the motor. Therefore, the pulse width modulation (PWM) control below the rated frequency is enerally carried out by reducin the machine phase voltae, V, alon with the frequency in such a manner that the flux is maintained constant. Above the rated frequency, the motor is operated at a constant voltae because of the limitation imposed by stator insulation or by supply voltae limitations [1]. In this paper split-phase sinle-phase Asynchronous Motor is used as inverter load throuhout the simulation process. Fi. 4 shows Split-phase Sinle-phase Asynchronous Motor. of Diode lamped Multilevel inverter usin three-level diode clamped confiuration is shown in Fi. 5. Discrete, Ts = 5e-5 s powerui Firin Pulses Va Vb Load Torque 4Nm Tm + - Inverter Output Voltae Measurement v split phase m Sinle Phase Asynchronous Machine Ratin.25 Hp, 22 V, 5 Hz, 15 rpm <Main windin current Ia (A or pu)> -K- <Rotor speed (rad/s or pu)> Gain <lectromanetic torque Te (N*m or pu)> Scope Firin Sinal Generator Multilevel Inverter System Fi. 5 Matlab/Simulink model of multilevel asynchronous motor drive. Fi. 4 Split-phase sinle-phase asynchronous motor A three-phase symmetrical induction motor upon losin one of its stator phase supplies while runnin may continue to operate as essentially a sinle-phase motor with the remainin line-to-line voltae across the other two connected phases. When the main windin coil is connected in parallel with ac voltae, as in the split-phase sinle-phase asynchronous motor of fi. 4, the current of the auxiliary windin,, leads of the main windin. For even a larer sinle-phase induction motor, that lead can be further increased by connectin a capacitor in series with the auxiliary windin, this arranement brins about a apacitor-start sinle-phase asynchronous motor. III. SIMULATION MODL AND RSULTS Multilevel inverter fed asynchronous motor drive inverter is implemented in MATLAB SIMULINK which is shown in Fi. 5. The MATLAB SIMULINK model of Sinle-phase full bride The sinle-phase three-level diode clamped inverter output voltae after feedin to asynchronous motor is shown in Fi. 6. The stator main windin output current with respect to sinlephase is shown in Fi. 7. The Variation in speed is shown in Fi. 8. The machine starts at no load and then at t=2. sec, once the machine has reached its steady state, the load torque is increased to its nominal value (4 N.m) in 1. sec. The speed increases and settles at 15 rpm without torque load and drops to 145 rpm when loaded with torque load. The lectromanetic torque is shown in Fi. 1. The Fast Fourier Transform (FFT) analysis is done for the output voltae and stator main windin current and the correspondin spectrum is shown in Fi. 11 and Fi. 12 respectively. It can be seen that the manitude of fundamental voltae for three-level inverter fed asynchronous motor drive is 27.6 Volts. The total harmonic distortion is 3.4 percent and the manitude of fundamental current is 28.6 Amperes. The total harmonic distortion is 1.43 percent. ISSN: Pae 3

5 Ma (% of Fundamental) Output Stator Main windin urrent (A) Output Voltae International Journal of nineerin Trends and Technoloy (IJTT) Volume 12 Number 1 - Jun 214 [Vo] Discrete, Ts = 5e-5 s powerui [a 1] From 2 Ta 2 [b 1] From 7 Tb 2 From 8 [Io ] Scope D Voltae [a 2] From 1 Pulse Generator Tm [b 2] From 5 From 9 [a 2] D Ta 3 split phase m D4 Tb 3 Vref SIN T1 a [Nota 2] [a 1] Nota 1] From3 Sinle Phase Asynchronous Machine [Notb 1] From 6 Vtri2 b [Nota 1] D1 Ta 22 Tb 22 Vtri1 Vtri3 Vtri4 T2 fcn T4 T5 d e [Notb 2] [b 2] [Notb 1] [b 1] D Voltae 1 Nota 2] From Ta 33 D5 [Notb 2] From 4 Tb 33 mbedded MATLAB Function Fi. 6 Matlab/Simulink model of Sinle-phase Three-level Diode lamped Inverter Fi. 7 Sinle-phase three-level inverter output Voltae Fi. 8 Sinle-phase three-level inverter output Stator Main windin current Fundamental (5Hz) = 28.6, THD= 1.43% ISSN: Pae

6 Ma (% of Fundamental) Output Stator Main windin urrent (A) Ma (% of Fundamental) lectromanetic torque (Nm) Rotor Speed (rpm) International Journal of nineerin Trends and Technoloy (IJTT) Volume 12 Number 1 - Jun Fiure 9: Variation in speed Fi. 1 Variation in electromanetic torque Fundamental (5Hz) = 27.6, THD= 3.4% Frequency (Hz) Fi. 11 FFT analysis of voltae 1 Fundamental (5Hz) = 28.6, THD= 1.43% Frequency (Hz) Fi. 12 FFT analysis of current The MATLAB SIMULINK model of Sinle-phase of four-level Diode lamped Inverter confiuration is shown in Fi. 13 ISSN: Pae 32

7 Ma (% of Fundamental) Output Voltae (V) International Journal of nineerin Trends and Technoloy (IJTT) Volume 12 Number 1 - Jun 214 Discrete, Ts = 5e-5 s powerui [a 3] [a 1] From Ta 1 [b 1] From 6 Tb 1 Vref Vtri 3 Vtri2 Vtri1 Tb 2 Tb 3 Vtri4 Vtri5 Vtri6 b 1] From 9 Tb 11 SIN T1 T2 T3 fcn T4 a b c d [a 3 [a 2] [a 2 [a 1] [a 1] [b 3 D Voltae 3 D2 D [a 2] From 1 [a 3] From 2 Ta 2 Ta 3 Pulse Generator Tm split phase m Sinle Phase Asynchronous Machine [b 2] From 7 [b 3] From 8 D4 D6 T5 e [b 2 [b3] D Voltae 2 T6 mbedded MATLAB Function f [b 2] [b 1 [b 1] D3 a 1] From 3 Ta 11 D7 [Vo] From 12 [Io ] D Voltae 1 D1 a 2] From 4 Ta 22 b 2] From 1 Tb 22 D5 From 13 a 3] From 5 b 3] From 11 Ta 33 Tb 33 Fi. 13 Matlab/Simulink model of sinle-phase four-level diode clamped inverter The sinle-phase four-level diode clamped inverter output voltae after feedin to asynchronous motor is shown in Fi. 14. The output stator main windin current with respect to sinle-phase is shown in Fi. 15. The Variation in speed is shown in Fi. 16. The speed increases and settles at 15 rpm without torque load and drops to 145 rpm when loaded with torque load of 4 Nm. The lectromanetic torque is shown in Fi. 17. The Fast Fourier Transform (FFT) analysis is done for the voltae and output stator main windin current and the correspondin spectrum is shown in Fi. 18 and Fi. 19 respectively. It can be seen that the manitude of fundamental voltae for four-level inverter fed asynchronous motor drive is 29.5 Volts. The total harmonic distortion is 2.32 percent and the manitude of fundamental current is Amperes. The total harmonic distortion is.99 percent Fi. 14 Sinle-phase four-level inverter output voltae Fundamental (5Hz) = 29.5, THD= 2.32% ISSN: Pae 33 2

8 Ma (% of Fundamental) Ma (% of Fundamental) Output Stator Main windin urrent (A) lectromanetic Torque (Nm) Rotor Speed (rpm) Output Stator Main windin urrent (A) International Journal of nineerin Trends and Technoloy (IJTT) Volume 12 Number 1 - Jun Fi. 15 Sinle-phase four-level inverter output stator main windin current Fi. 16 Variation in speed Fi. 17 Variation in electromanetic torque Fundamental (5Hz) = 29.5, THD= 2.32% Frequency (Hz) Fi. 18 FFT analysis of voltae Fundamental (5Hz) = 28.74, THD=.99% Frequency (Hz) Fi.19 FFT analysis of current ISSN: Pae 34

9 % of Fundamental) Output Voltae (V) International Journal of nineerin Trends and Technoloy (IJTT) Volume 12 Number 1 - Jun 214 The MATLAB SIMULINK model of Sinle-phase of five-level Diode lamped Inverter confiuration is shown in Fi. 2 Discrete, Ts = 5e-5 s powerui [a 1] From Ta 1 [b 1] From 15 Tb 1 Ta 2 From 14 Tb 2 Vcontrol Vtri 4 Vtri 3 [a 4] [a 3] [a 3 [a 2] [a 2 Ta 3 Tb 3 Vtri 2 Vtri5 Vtri6 [a 4] From 3 Ta 4 [b 4] From 12 Tb 4 Vtri7 [b 2] SIN a [a 4] [a 2] From 1 T1 T2 b c D Voltae 3 D2 [a 3] From 2 D1 Pulse Generator Tm split phase m [b 3] From 13 [b 3 [b 4 [b 4] [b 3] Sinle Phase Asynchronous Machine [a 1] [b 2 a 1] D8 D6 T3 T4 fcn d D D4 e D Voltae 2 T5 Vtri1 Vtri8 T6 T7 T8 mbedded MATLAB Function f h [b 1 [b 2] [b 1] [a 1] D3 D Voltae D11 a 2] From 5 a 3] From 4 NTa 1 NTa 2 b 1] NTb 1 From 11 b 2] From 1 NTb 2 D9 D7 D Voltae 1 D1 From 6 b 3] From 9 NTa 3 NTb 3 D5 a 4] From 7 NTa 4 b 4] From 8 NTb 4 Fi. 2 Matlab/Simulink model of sinle-phase five-level diode clamped inverter The sinle-phase five-level diode clamped inverter output voltae after feedin to asynchronous motor is shown in Fi. 21. The output stator main windin current with respect to sinle-phase is shown in Fi. 22. The Variation in speed is shown in Fi. 23. The speed increases and settles at 15 rpm without torque load and drops to 145 rpm when loaded with torque load of 4 Nm. The lectromanetic torque is shown in Fi. 24. The Fast Fourier Transform (FFT) analysis is done for the voltae and output stator main windin current and the correspondin spectrum is shown in Fi. 25 and Fi. 26 respectively. It can be seen that the manitude of fundamental voltae for five-level inverter fed asynchronous motor drive is 28.2 Volts. The total harmonic distortion is 1.7 percent and the manitude of fundamental current is Amperes. The total harmonic distortion is.84 percent Fundamental (5Hz) = 23.8, THD=.89% 1 ISSN: Pae

10 Ma (% of Fundamental) lectromanetic Torque (Nm) Rotor Speed (rpm) Output Stator Main windin urrent (A) International Journal of nineerin Trends and Technoloy (IJTT) Volume 12 Number 1 - Jun 214 Fi. 21 Sinle-phase five-level inverter output voltae Fi. 22 Sinle-phase five-level inverter output stator main windin current Fi. 23 Variation in speed Fi. 24 Variation in electromanetic torque Fundamental (5Hz) = 28.2, THD= 1.7% Frequency (Hz) Fi. 25 FFT analysis of voltae ISSN: Pae 36

11 Ma (% of Fundamental) International Journal of nineerin Trends and Technoloy (IJTT) Volume 12 Number 1 - Jun 214 The results are tabulated in Table I below: TABL I TH ANALYSIS OF THR-LVL, FOUR-LVL and FIV- LVL DIOD Parameters Voltae Level (V) THD for Voltae (%) urrent Level (A) THD for urrent (%) Diode lamped Multilevel Inverter Three-level Inverter Four-level Inverter Five-level Inverter Fundamental (5Hz) = 28.58, THD=.84% Frequency (Hz) Fi. 26 FFT analysis of urrent IV. ONLUSIONS Three-level, Four-level and Five-level Diode lamped inverter fed asynchronous motor drive are simulated usin the blocks of Matlab/Simulink/SimPowerSystems. The results of three-level, four-level and five-level systems are compared. It is observed that the total harmonic distortion produced by the fivelevel inverter system is less than those of three-level and fourlevel inverter fed drive system. Therefore the heatin due to five-level inverter system is less than those of three-level and four-level inverter fed drive system. The switchin losses due to five-level inverter system is hiher than those of three-level and four-level inverter fed system because of hih number of power switches involved in the desin. The simulation results of voltae, current, electromanetic torque, speed and spectrum are presented. This drive system can be used in industries where adjustable speed drives are required to produce output with reduced harmonic content. The scope of this work is the modelin and simulation of three-level, four-level and five-level inverter fed asynchronous motor drive systems. An Improved Multilevel topoloy will be used to drive the asynchronous motor in future work. Five-level or hiher level inverter system is a viable alternative since it has better performance. RFRNS [1] Manasa, S., Balajiramakrishna, S., Madhura, S. and Mohan, H. M., Desin and Simulation of Three Phase Five Level and Seven Level inverter fed Induction Motor Drive with Two ascaded H-Bride onfiuration, International Journal of lectrical and lectronics nineerin (IJ),, vol. 1, pp [2] Tolbert, L. M., Pen, F. Z. and Habetler, T. G., Multilevel onverters for Lare lectric Drives, I Transactions on Industry Applications, vol. 35, no. 1, pp , [3] Pandian, G. and Rama, R. S., Implementation of Multilevel Inverter-Fed Induction Motor Drive, Journal of Industrial Technoloy, vol. 24, pp , 28. [4] Neelashetty, Kashappa and Ramesh, Reddy, Performance Of Voltae Source Multilevel Inverter Fed Induction Motor Drive Usin Simulink, ARPN Journal of nineerin and Applied Sciences, vol. 6, no. 6, pp , 211. ISSN: Pae 37

12 International Journal of nineerin Trends and Technoloy (IJTT) Volume 12 Number 1 - Jun 214 [5] Rodríuez, J., Lai, J. S. and Pen, F. Z., Multilevel inverters: A Survey of Topoloies, ontrols, and Applications, I Transactions on Industrial lectronics, vol. 49, no. 4, pp , 22. [6] Lai, J. S. and Pen, F. Z., Multilevel onverters-a New Breed of Power onverters, I Transactions on Industry Applications, vol. 32, no. 3, pp , [7] Shivakumar,.G., Gopukumar, K.., Sinha S. K. and Rananathan, V.T., Space Vector PWM ontrol of Dual Inverter Feed-open-end Windin induction Motor Drive, I AP onf., vol. 1, pp , 21 [8] Dixon, J. and Moran, L., Hih-level Multi-Step Inverter Optimization usin a Minimum number of Power Transistors, I Tran. Power lectron, vol. 21, no.23, pp , 26. [9] Muruesan, M., Sakthivel, R., Muthukumaran, and Sivakumar, R. Sinusoidal PWM Based Modified ascaded Multilevel Inverter, International Journal of omputational nineerin Research, vol. 2, no. 2, pp , 212. [1] Surin, Khomfoi and Tolbert, L. M., Multilevel Power onverters, University of Tennessee, client/wed.eecs.utk.edu/~tolbert/publications/multilevel_book_chapter. pdf, 212. [11] Kith orzine, Operation and desin of Multilevel Inverters, Developed for the office of Naval research, 23. ISSN: Pae 38