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International Journal on Recent and Innovation Trends in Computing and Communication ISSN: 2321-8169
Volume: 5 Issue: 7 201 – 205
_______________________________________________________________________________________________
201
IJRITCC | July 2017, Available @ http://www.ijritcc.org
_______________________________________________________________________________________
Hardware Implementation of SPWM Based Diode Clamped Multilevel Invertr
Darshni M. Shukla
Electrical Engineering Department
Government Engineering College Valsad, India
darshnishukla@yahoo.com
Abstract: This paper present three phase three level diode clamped multi level inverter. The control technique used here is sine pulse width
modulation. The inverter can reduce the harmonic components compared with that of traditional full-bridge inverter under the condition of
identical supply DC voltage and switching frequency. Here this paper presents a operational principles and switching functions are analyzed.
The proposed inverter improves the dynamic performances Inverter is simulated using MATLAB/SIMULINK FFT analysis has been done.
Proto type hardware is developed in laboratory and simulation results are compared with experimental results. Voltage to frequency control in
open loop for three phase induction motor has also been done.
Keywords: Diode-clamped multilevel inverter, sine pulse width modulation(SPWM), Total harmonic distortion.g(THD)
__________________________________________________*****_________________________________________________
I. INTRODUCTION
The concept of multilevel converters has been introduced
since 1975. The cascade multilevel inverter was first
proposed in 1975 [1]. Subsequently, several multilevel
converter topologies have been developed [2]. In 1981,
diode-clamped multilevel inverter also called the Neutral-
Point Clamped (NPC) inverter schemes were proposed .The
output voltage waveform of a multilevel inverter is
composed of the number of levels of voltages, typically
obtained from capacitor voltage sources. The multilevel
starts from three levels. As the number of levels reach
infinity, the output THD (Total Harmonic Distortion)
approaches zero. The number of the achievable voltage
levels, however, is limited by voltage unbalance problems,
voltage clamping requirement, circuit layout, and packaging
constraints. Multilevel inverters synthesizing a large number
of levels have a lot of merits such as improved output
waveform, a smaller filter size, a lower EMI (Electro
Magnetic Interference), and other advantages. The principle
advantage of using multilevel inverters is the low harmonic
distortion obtained due to the multiple voltage levels at the
output and reduced stresses on the switching devices used
Improvements in fast switching power devices have led to
an increased interest in voltage source inverters (VSI) with
pulse width modulation control (PWM) used
Improvements in fast switching power devices have led to
an increased interest in voltage source inverters (VSI) with
pulse width modulation control (PWM) there are many
techniques[3] [4], which are applied to multilevel inverter
topologies. PWM inverters can control their output voltage
and frequency simultaneously. And also they can reduce the
harmonic components in load currents [5]. These features
have made them favorable in many industrial applications
such as variable speed drives, uninterruptible power
supplies, and other power conversion systems. However, the
reduction of harmonic components in output currents is still
the main focus to reduce the influences of electromagnetic
interferences or noise and vibrations. , a three-phase three-
level PWM (Pulse Width Modulation) is presented in the
paper. The main objective of paper is to design a three-phase
three-level PWM (Pulse Width Modulation) inverter to
reduce the harmonic components of the output voltage and
the load current. The proposed inverter can reduce the
harmonic components compared with that of traditional full-
bridge PWM inverter In general, neutral point clamped
PWM three-phase inverter which uses four switching
elements in each arm has the five- level voltage waveforms
that results in considerable suppression of the harmonic
currents comparing with the conventional full-bridge type
three-level PWM inverters.
II. DIODE CLAMPED MULTI LEVEL
INVERTER
The most commonly used multilevel topology is the diode
clamped inverter, in which the diode is used as the clamping
device to clamp the dc bus voltage so as to achieve steps in
the output voltage. The neutral point converter proposed by
Nabae, Takahashi, and Akagi in 1981 was essentially a
three-level diode-clamped inverter [1]. A three-level diode
clamped inverter consists of two pairs of switches and two
diodes. Each switch pairs works in complimentary mode and
the diodes used to provide access to mid-point voltage. In a
three-level inverter each of the three phases of the inverter
shares a common dc bus, which has been subdivided by two
International Journal on Recent and Innovation Trends in Computing and Communication ISSN: 2321-8169
Volume: 5 Issue: 7 201 – 205
_______________________________________________________________________________________________
202
IJRITCC | July 2017, Available @ http://www.ijritcc.org
_______________________________________________________________________________________
capacitors into three levels. The DC bus voltage is split into
three voltage levels by using two series connections of DC
capacitors, C1 and C2. The voltage stress across each
switching device is limited to Vdc through the clamping
diodes Dc1 and Dc2. It is assumed that the total dc link
voltage is Vdc and mid point is regulated at half of the dc
link voltage, the voltage across each capacitor is Vdc/2
(Vc1=Vc2=Vdc/2). In a three level diode clamped inverter,
there are three different possible switching states which
apply the stair case voltage on output voltage relating to DC
link capacitor voltage rate. For a three-level inverter, a set of
two switches is on at any given time and in a five-level
inverter, a set of four switches is on at any given time and so
on. Figure 1 shows the circuit for a diode clamped inverter
for a three-level. Switching states of the three level inverter
are summarized in table I.
SWITCHING STATE TABLE-I
Switch status State Output
voltage
Sa1=on,Sa2=on
Sa3=off,Sa4=off
Mode1 Vao=+Vdc/2
Sa2=on,Sa3=on
Sa1=off,Sa4=off
Mode2 Vao=0
Sa3=on,S4=on
Sa1=off,Sa2=off
Mode
3
Vao=-Vdc/2
Figure 1 Topology of the diode-clamped three-level inverter
Fig 2 shows the phase voltage and line voltage of the three-
level inverter in the balanced condition. The line voltage
Vab consists of a phase-leg a voltage and a phase-leg b
voltage. The resulting line voltage is a 5-level staircase
waveform for three-level inverter and 9-level staircase
waveform for a five-level inverter. This means that an N-
level diode-clamped inverter has an N-level output phase
voltage and a (2N-1)-level output line voltage. In general the
voltage across each capacitor for an N level diode clamped
inverter at steady state is Vdc/ (N-1). Although each active
switching device is required to block only a voltage level of
Vdc, the clamping diodes require different ratings for
reverse voltage blocking.
Figure 2: Output voltage in three-level diode- clamped
inverter (a) Phase voltage (b) Line voltage
In general for an N level diode clamped inverter, for each
leg 2(N-1) switching devices, (N-1) * (N-2) clamping diodes
and (N-1) dc link capacitors are required. By increasing the
number of voltage levels the quality of the output voltage is
improved and the voltage waveform becomes closer to
sinusoidal waveform. However, capacitor voltage balancing
will be the critical issue in high level inverters. When N is
sufficiently high, the number of diodes and the number of
switching devices will increase and make the system
impracticable to implement. If the inverter runs under pulse
width modulation (PWM), the diode reverse recovery of
these clamping diodes becomes the major design challenge.
III. SIMULATION OF PROPOSED INVERTER
A three-phase full bridge inverter and the SPWM[7] [8].
modulator that has been designed to generate switching
signals for three-phase full bridge inverter. In the designed
three-level inverter, modulated SPWM [6] Signals have
been used to control switches of the inverter, and THD
analysis of output voltage and current have been performed
as seen in figure 3,4,5.
Figure 3: Line voltage wave form.
International Journal on Recent and Innovation Trends in Computing and Communication ISSN: 2321-8169
Volume: 5 Issue: 7 201 – 205
_______________________________________________________________________________________________
203
IJRITCC | July 2017, Available @ http://www.ijritcc.org
_______________________________________________________________________________________
Figure 4: Phase voltage waveform.
Figure 5: FFT analysis of SPWM based three phase three
level inverter
IV. HARDWARE IMPLPMENTATION
In the laboratory a three-level diode clamed inverter
prototype is being built. The primary purpose of the
prototype is to verify the analytical and control algorithms
that are developed here. The prototype built is flexible and
robust enough to conduct the experiments.
Specifications of inverter
1. Voltage rating 200Vdc input.
2. Current rating 5 A.
3. Switching frequency 2KHz.
4. All the devices in the inverter are isolated and have
separate driving circuits.
Inverter design which include building gate drive, building
of power circuit. Microcontroller coding which include
coding for sine pulse width modulation using STM-32
microcontroller. Hardware with complete lab setup shown
below in Figure-6, 7, 8
Figure 6: Image of gate drive and isolation circuit.
Figure 7: power circuit of three level inverter
Figure 8: complete setup.
When inverter is supplied with 100 V d.c. power source and
three phase resistive load applied across it the phase and line
voltage waveform are shown in figure 11&12 here. Two
triangular waveform generated by microcontroller for
comparison is shown in figure 9 and gate pulses for any one
phase switches is shown in figure 10.
Figure 9: Triangular wave form generated by
microcontroller for comparison
International Journal on Recent and Innovation Trends in Computing and Communication ISSN: 2321-8169
Volume: 5 Issue: 7 201 – 205
_______________________________________________________________________________________________
204
IJRITCC | July 2017, Available @ http://www.ijritcc.org
_______________________________________________________________________________________
Figure 10: Gate pulses four switches of phase A
Figure 11: Phase voltage waveform
Figure 12: Line voltage wave form.
V. FFT AND THD ANALYSIS
Table -2 gives the THD values of inverter voltage for
different modulation indices with switching frequency of 2
KHz.
TABLE-II
MODULATION
INDEX
RMS
OUTPUT
VOLTAGE
RMS F
FUNDAMENTAL
VOLTAGE
%THD
0.9 74.8 67.66 47.6
0.8 71.09 58.8 67.9
0.7 66.89 53.7 74.26
0.6 61.6 42.6 104.4
Figure 13 to 16 shows the FFT analysis of the inverter
output voltage for different modulation indices. The graph
shows all the components from 0 Hz to 32.29 KHz.
Figure13. FFT window for line to line voltage and 0.9
modulation index
Figure14. FFT window for line to line voltage and 0.8
modulation index
Figure15. FFT window for line to line voltage and 0.7
modulation index
International Journal on Recent and Innovation Trends in Computing and Communication ISSN: 2321-8169
Volume: 5 Issue: 7 201 – 205
_______________________________________________________________________________________________
205
IJRITCC | July 2017, Available @ http://www.ijritcc.org
_______________________________________________________________________________________
Figure16 FFT window for line to line voltage and 0.6
modulation index
VI. RESULTS AND DISCUSSION
The simulation results for three-level diode clamped inverter
is presented in this paper THD analyses for different
modulation index and switching frequencies have been
carried out. To verify the simulation results, three phase
three level prototype hardware has been made in laboratory.
Both simulation and experimental results are in close
agreement It is seen in both simulation that by using that
largest lower order harmonics shifted to switching
frequency also value of fundamental voltage is significant.
VII. CONCLUSION
It is concluded from this analysis; SPWM and Three Level
with Neutral Point Clamped Inverter are helpful techniques
for harmonic reduction and to improve voltage or current.
Profile without additional filters requirements. This
multilevel inverter improves output voltage, reduces output
total harmonic distortion and voltage stress on
semiconductors switches, acoustic noise and Electro
Magnetic Interference (EMI)also decreases and hence the
schemes are confirmed by simulation and experimental.
The principle of the scheme for the three-level diode
clamped converter could be extended in generalizing the
technique to N level converter. The carrier-based PWM
scheme proposed in the present work, developing a
generalized logic, which can remove the shorting of the
devices for any level of the inverter.
REFERENCES
[1] A. Nabae, I. Takahashi, H. Agaki, “A New Neutral-Point-
Clamped PWM, Inverter,”IEEE Transactions on Industry
Applicaitions. Vol.IA-17, No.5, Sep./Oct., 1981,pp.518-523
[2] F. Z. Peng, J-S Lai, “Multilevel Converters – A New Breed of
Power Converters,” IEEE Transactions on Industry
Applications, Vol.32, No.3, May/June, 1996, pp.509-517.
[3] Mohan N, Undeland TM, Robbins WP. Power electronics-
converters, application and design. New York: John Wiley &
Sons Inc.Third edition.
[4] Rashid M.H. Power electronics handbook. Florida, USA:
Academic Press; 2001
[5] S. R. Bowes, “New Sinusoidal Pulse width-Modulated
Inverter,” Proc.IEE, Vol.122, No.11, Nov, 1975..
[6] J. Rodriguez, J. S. Lai and F. Z. Peng, “Multilevel Inverters:
Survey of Topologies, Controls, and Applications,” IEEE
Transactions on Industry Applications, vol.49, no. 4, Aug.
2002,pp. 724-738..
[7] G. Carrara, S Gardella, M Marchesoni, R. Salutari, G. Sciutto,
“A New Multilevel PWM Method: A Theoretical Analysis,”
in Proc. IEEE Power Electron. Specialist Conf. (PESC), June,
1990, pp.363-371
[8] L. M. Tolbert, and T. G. Habetler, “Novel Multilevel Inverter
Carrier-Based PWM Method,” IEEE Transactions on Industry
Applications, vol. 25, no. 5,Sep/Oct , 1999, pp. 1098-1107.
[9] N. S. Choi, J. G. Cho, and G. H. Cho, “A general circuit
topology of multilevel inverter,” in Proc. IEEE PESC’91,
1991, pp. 96–103
[10] W. A. Hill and C. D. Harbourt, "Performance of medium
voltage multi-level inverters," Conf. Rec. IEEE-IAS Annu.
Meeting, 1999, pp. 1186-92.

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Hardware Implementation of SPWM Based Diode Clamped Multilevel Invertr

  • 1. International Journal on Recent and Innovation Trends in Computing and Communication ISSN: 2321-8169 Volume: 5 Issue: 7 201 – 205 _______________________________________________________________________________________________ 201 IJRITCC | July 2017, Available @ http://www.ijritcc.org _______________________________________________________________________________________ Hardware Implementation of SPWM Based Diode Clamped Multilevel Invertr Darshni M. Shukla Electrical Engineering Department Government Engineering College Valsad, India darshnishukla@yahoo.com Abstract: This paper present three phase three level diode clamped multi level inverter. The control technique used here is sine pulse width modulation. The inverter can reduce the harmonic components compared with that of traditional full-bridge inverter under the condition of identical supply DC voltage and switching frequency. Here this paper presents a operational principles and switching functions are analyzed. The proposed inverter improves the dynamic performances Inverter is simulated using MATLAB/SIMULINK FFT analysis has been done. Proto type hardware is developed in laboratory and simulation results are compared with experimental results. Voltage to frequency control in open loop for three phase induction motor has also been done. Keywords: Diode-clamped multilevel inverter, sine pulse width modulation(SPWM), Total harmonic distortion.g(THD) __________________________________________________*****_________________________________________________ I. INTRODUCTION The concept of multilevel converters has been introduced since 1975. The cascade multilevel inverter was first proposed in 1975 [1]. Subsequently, several multilevel converter topologies have been developed [2]. In 1981, diode-clamped multilevel inverter also called the Neutral- Point Clamped (NPC) inverter schemes were proposed .The output voltage waveform of a multilevel inverter is composed of the number of levels of voltages, typically obtained from capacitor voltage sources. The multilevel starts from three levels. As the number of levels reach infinity, the output THD (Total Harmonic Distortion) approaches zero. The number of the achievable voltage levels, however, is limited by voltage unbalance problems, voltage clamping requirement, circuit layout, and packaging constraints. Multilevel inverters synthesizing a large number of levels have a lot of merits such as improved output waveform, a smaller filter size, a lower EMI (Electro Magnetic Interference), and other advantages. The principle advantage of using multilevel inverters is the low harmonic distortion obtained due to the multiple voltage levels at the output and reduced stresses on the switching devices used Improvements in fast switching power devices have led to an increased interest in voltage source inverters (VSI) with pulse width modulation control (PWM) used Improvements in fast switching power devices have led to an increased interest in voltage source inverters (VSI) with pulse width modulation control (PWM) there are many techniques[3] [4], which are applied to multilevel inverter topologies. PWM inverters can control their output voltage and frequency simultaneously. And also they can reduce the harmonic components in load currents [5]. These features have made them favorable in many industrial applications such as variable speed drives, uninterruptible power supplies, and other power conversion systems. However, the reduction of harmonic components in output currents is still the main focus to reduce the influences of electromagnetic interferences or noise and vibrations. , a three-phase three- level PWM (Pulse Width Modulation) is presented in the paper. The main objective of paper is to design a three-phase three-level PWM (Pulse Width Modulation) inverter to reduce the harmonic components of the output voltage and the load current. The proposed inverter can reduce the harmonic components compared with that of traditional full- bridge PWM inverter In general, neutral point clamped PWM three-phase inverter which uses four switching elements in each arm has the five- level voltage waveforms that results in considerable suppression of the harmonic currents comparing with the conventional full-bridge type three-level PWM inverters. II. DIODE CLAMPED MULTI LEVEL INVERTER The most commonly used multilevel topology is the diode clamped inverter, in which the diode is used as the clamping device to clamp the dc bus voltage so as to achieve steps in the output voltage. The neutral point converter proposed by Nabae, Takahashi, and Akagi in 1981 was essentially a three-level diode-clamped inverter [1]. A three-level diode clamped inverter consists of two pairs of switches and two diodes. Each switch pairs works in complimentary mode and the diodes used to provide access to mid-point voltage. In a three-level inverter each of the three phases of the inverter shares a common dc bus, which has been subdivided by two
  • 2. International Journal on Recent and Innovation Trends in Computing and Communication ISSN: 2321-8169 Volume: 5 Issue: 7 201 – 205 _______________________________________________________________________________________________ 202 IJRITCC | July 2017, Available @ http://www.ijritcc.org _______________________________________________________________________________________ capacitors into three levels. The DC bus voltage is split into three voltage levels by using two series connections of DC capacitors, C1 and C2. The voltage stress across each switching device is limited to Vdc through the clamping diodes Dc1 and Dc2. It is assumed that the total dc link voltage is Vdc and mid point is regulated at half of the dc link voltage, the voltage across each capacitor is Vdc/2 (Vc1=Vc2=Vdc/2). In a three level diode clamped inverter, there are three different possible switching states which apply the stair case voltage on output voltage relating to DC link capacitor voltage rate. For a three-level inverter, a set of two switches is on at any given time and in a five-level inverter, a set of four switches is on at any given time and so on. Figure 1 shows the circuit for a diode clamped inverter for a three-level. Switching states of the three level inverter are summarized in table I. SWITCHING STATE TABLE-I Switch status State Output voltage Sa1=on,Sa2=on Sa3=off,Sa4=off Mode1 Vao=+Vdc/2 Sa2=on,Sa3=on Sa1=off,Sa4=off Mode2 Vao=0 Sa3=on,S4=on Sa1=off,Sa2=off Mode 3 Vao=-Vdc/2 Figure 1 Topology of the diode-clamped three-level inverter Fig 2 shows the phase voltage and line voltage of the three- level inverter in the balanced condition. The line voltage Vab consists of a phase-leg a voltage and a phase-leg b voltage. The resulting line voltage is a 5-level staircase waveform for three-level inverter and 9-level staircase waveform for a five-level inverter. This means that an N- level diode-clamped inverter has an N-level output phase voltage and a (2N-1)-level output line voltage. In general the voltage across each capacitor for an N level diode clamped inverter at steady state is Vdc/ (N-1). Although each active switching device is required to block only a voltage level of Vdc, the clamping diodes require different ratings for reverse voltage blocking. Figure 2: Output voltage in three-level diode- clamped inverter (a) Phase voltage (b) Line voltage In general for an N level diode clamped inverter, for each leg 2(N-1) switching devices, (N-1) * (N-2) clamping diodes and (N-1) dc link capacitors are required. By increasing the number of voltage levels the quality of the output voltage is improved and the voltage waveform becomes closer to sinusoidal waveform. However, capacitor voltage balancing will be the critical issue in high level inverters. When N is sufficiently high, the number of diodes and the number of switching devices will increase and make the system impracticable to implement. If the inverter runs under pulse width modulation (PWM), the diode reverse recovery of these clamping diodes becomes the major design challenge. III. SIMULATION OF PROPOSED INVERTER A three-phase full bridge inverter and the SPWM[7] [8]. modulator that has been designed to generate switching signals for three-phase full bridge inverter. In the designed three-level inverter, modulated SPWM [6] Signals have been used to control switches of the inverter, and THD analysis of output voltage and current have been performed as seen in figure 3,4,5. Figure 3: Line voltage wave form.
  • 3. International Journal on Recent and Innovation Trends in Computing and Communication ISSN: 2321-8169 Volume: 5 Issue: 7 201 – 205 _______________________________________________________________________________________________ 203 IJRITCC | July 2017, Available @ http://www.ijritcc.org _______________________________________________________________________________________ Figure 4: Phase voltage waveform. Figure 5: FFT analysis of SPWM based three phase three level inverter IV. HARDWARE IMPLPMENTATION In the laboratory a three-level diode clamed inverter prototype is being built. The primary purpose of the prototype is to verify the analytical and control algorithms that are developed here. The prototype built is flexible and robust enough to conduct the experiments. Specifications of inverter 1. Voltage rating 200Vdc input. 2. Current rating 5 A. 3. Switching frequency 2KHz. 4. All the devices in the inverter are isolated and have separate driving circuits. Inverter design which include building gate drive, building of power circuit. Microcontroller coding which include coding for sine pulse width modulation using STM-32 microcontroller. Hardware with complete lab setup shown below in Figure-6, 7, 8 Figure 6: Image of gate drive and isolation circuit. Figure 7: power circuit of three level inverter Figure 8: complete setup. When inverter is supplied with 100 V d.c. power source and three phase resistive load applied across it the phase and line voltage waveform are shown in figure 11&12 here. Two triangular waveform generated by microcontroller for comparison is shown in figure 9 and gate pulses for any one phase switches is shown in figure 10. Figure 9: Triangular wave form generated by microcontroller for comparison
  • 4. International Journal on Recent and Innovation Trends in Computing and Communication ISSN: 2321-8169 Volume: 5 Issue: 7 201 – 205 _______________________________________________________________________________________________ 204 IJRITCC | July 2017, Available @ http://www.ijritcc.org _______________________________________________________________________________________ Figure 10: Gate pulses four switches of phase A Figure 11: Phase voltage waveform Figure 12: Line voltage wave form. V. FFT AND THD ANALYSIS Table -2 gives the THD values of inverter voltage for different modulation indices with switching frequency of 2 KHz. TABLE-II MODULATION INDEX RMS OUTPUT VOLTAGE RMS F FUNDAMENTAL VOLTAGE %THD 0.9 74.8 67.66 47.6 0.8 71.09 58.8 67.9 0.7 66.89 53.7 74.26 0.6 61.6 42.6 104.4 Figure 13 to 16 shows the FFT analysis of the inverter output voltage for different modulation indices. The graph shows all the components from 0 Hz to 32.29 KHz. Figure13. FFT window for line to line voltage and 0.9 modulation index Figure14. FFT window for line to line voltage and 0.8 modulation index Figure15. FFT window for line to line voltage and 0.7 modulation index
  • 5. International Journal on Recent and Innovation Trends in Computing and Communication ISSN: 2321-8169 Volume: 5 Issue: 7 201 – 205 _______________________________________________________________________________________________ 205 IJRITCC | July 2017, Available @ http://www.ijritcc.org _______________________________________________________________________________________ Figure16 FFT window for line to line voltage and 0.6 modulation index VI. RESULTS AND DISCUSSION The simulation results for three-level diode clamped inverter is presented in this paper THD analyses for different modulation index and switching frequencies have been carried out. To verify the simulation results, three phase three level prototype hardware has been made in laboratory. Both simulation and experimental results are in close agreement It is seen in both simulation that by using that largest lower order harmonics shifted to switching frequency also value of fundamental voltage is significant. VII. CONCLUSION It is concluded from this analysis; SPWM and Three Level with Neutral Point Clamped Inverter are helpful techniques for harmonic reduction and to improve voltage or current. Profile without additional filters requirements. This multilevel inverter improves output voltage, reduces output total harmonic distortion and voltage stress on semiconductors switches, acoustic noise and Electro Magnetic Interference (EMI)also decreases and hence the schemes are confirmed by simulation and experimental. The principle of the scheme for the three-level diode clamped converter could be extended in generalizing the technique to N level converter. The carrier-based PWM scheme proposed in the present work, developing a generalized logic, which can remove the shorting of the devices for any level of the inverter. REFERENCES [1] A. Nabae, I. Takahashi, H. Agaki, “A New Neutral-Point- Clamped PWM, Inverter,”IEEE Transactions on Industry Applicaitions. Vol.IA-17, No.5, Sep./Oct., 1981,pp.518-523 [2] F. Z. Peng, J-S Lai, “Multilevel Converters – A New Breed of Power Converters,” IEEE Transactions on Industry Applications, Vol.32, No.3, May/June, 1996, pp.509-517. [3] Mohan N, Undeland TM, Robbins WP. Power electronics- converters, application and design. New York: John Wiley & Sons Inc.Third edition. [4] Rashid M.H. Power electronics handbook. Florida, USA: Academic Press; 2001 [5] S. R. Bowes, “New Sinusoidal Pulse width-Modulated Inverter,” Proc.IEE, Vol.122, No.11, Nov, 1975.. [6] J. Rodriguez, J. S. Lai and F. Z. Peng, “Multilevel Inverters: Survey of Topologies, Controls, and Applications,” IEEE Transactions on Industry Applications, vol.49, no. 4, Aug. 2002,pp. 724-738.. [7] G. Carrara, S Gardella, M Marchesoni, R. Salutari, G. Sciutto, “A New Multilevel PWM Method: A Theoretical Analysis,” in Proc. IEEE Power Electron. Specialist Conf. (PESC), June, 1990, pp.363-371 [8] L. M. Tolbert, and T. G. Habetler, “Novel Multilevel Inverter Carrier-Based PWM Method,” IEEE Transactions on Industry Applications, vol. 25, no. 5,Sep/Oct , 1999, pp. 1098-1107. [9] N. S. Choi, J. G. Cho, and G. H. Cho, “A general circuit topology of multilevel inverter,” in Proc. IEEE PESC’91, 1991, pp. 96–103 [10] W. A. Hill and C. D. Harbourt, "Performance of medium voltage multi-level inverters," Conf. Rec. IEEE-IAS Annu. Meeting, 1999, pp. 1186-92.