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Durga Bhavani. Peeta et al Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 5, Issue 1( Part 2), January 2015, pp122-126
www.ijera.com 122 | P a g e
Design & Simulation Of 3-Phase, 15-Level Inverter with Reverse
Voltage Topology
Durga Bhavani. Peeta, Sathish Kumar.K
M. Tech (P.E) scholar Dept of EEE, Ramachandra College of Engineering and Technology, JNTUK, A.P
Assisant Professor, Dept of EEE, Ramachandra College of Engineering and Technology, JNTUK, A.P
Abstract:
Multilevel inverters have been widely accepted for high-power high-voltage applications. Their performance is
highly superior to that of conventional Seven-level inverters due to reduced harmonic distortion, lower
electromagnetic interference, and higher dc link voltages. In this paper, a new topology with a reversing-voltage
component is proposed to improve the multilevel performance. This topology requires fewer components
compared to existing inverters (particularly in higher levels) and requires fewer carrier signals and gate drives.
Therefore, thecomplexity is greatly reduced particularly for higher output voltage levels. The Proposed 15-level
inverter is modelled and simulated in Matlab 2012a using Simulink and Sim Power Systems set tool boxes
Keywords: Multilevel inverter, power electronics, SPWM, topology.
I. INTRODUCTION
Advancement in the research of Power electronic
invertersis still increasing with the rapid demands in
electrical systems. The emergence of multilevel
inverters has been in increase since the last decade.
These new types of converters are suitable for high
voltage and high power application due to their
ability to synthesize waveforms with better harmonic
spectrum[10].
Multilevel converters are mainly utilized to
synthesis a desired single- or three-phase voltage
waveform. Thedesired multi-staircase output voltage
is obtained by combining several dc voltage sources.
Solar cells, fuel cells,batteries and ultra-capacitors
are the most common independent sources used [1].
One important application ofmultilevel converters is
focused on medium and high-power conversion.
Nowadays, there exist three commercialtopologies of
multilevel voltage-source inverters: neutral point
clamped (NPC), cascaded H-bridge (CHB), and
flyingcapacitors (FCs)[2]. Among these inverter
topologies, cascaded multilevel inverter reaches the
higher output voltage and power levels (13.8 kV,30
MVA) and the higher reliability due to its modular
topology[3].
Diode-clamped multilevel converters are used in
conventional high-power ac motor drive applications
likeconveyors, pumps, fans, and mills. They are also
utilized in oil, gas, metals, power, mining, water,
marine, andchemical industries. They have also been
reported to be used in a back-to-back configuration
for regenerativeapplications[4]. Flying capacitor
multilevel converters have been used in high-
bandwidth high-switching frequencyapplications
such as medium-voltage traction drives. Finally,
cascaded H-bridge multilevel converters have
beenapplied where high power and power quality are
essential, for example, static synchronous
compensators active filterand reactive power
compensation applications, photovoltaic power
conversion, uninterruptible power supplies,
andmagnetic resonance imaging. Furthermore, one of
the growing applications for multilevel motor drives
is electric andhybrid power trains.
For increasing voltage levels the number of
switches also will increase in number. Hence the
voltage stresses andswitching losses will increase and
the circuit will become complex. By using the
proposed topology number ofswitches will reduce
significantly and hence the efficiency will improve.
A multi-stage inverter using three-state
converters is being analyzed for multipurpose
applications, such asactive power filters, static var
compensators and machine drives for sinusoidal and
trapezoidal currentapplications. The great advantage
of this kind of converter is the minimum harmonic
distortion obtained.
The circuit of Fig.1 shows the basic topology of
oneconverter used for the implementation of multi-
stageconverters.It is based on the simple, four
switches converter,used for single phase inverters or
for dual converters. Theseconverters are able to
produce three levels of voltage in theload: +Vdc, -
Vdc, and Zero[7].
RESEARCH ARTICLE OPEN ACCESS
Durga Bhavani. Peeta et al Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 5, Issue 1( Part 2), January 2015, pp122-126
www.ijera.com 123 | P a g e
Fig.1. Basic idea diagram of three-level module for
building multi stage inverter
This paper mainly focuses on the general
multilevel inverter schematic. A general method of
multilevel modulation phase disposition (PD) SPWM
is utilized to drive the inverter and can be extended to
any number of voltage levels. Here , in this paper the
proposed multilevel scheme extended up to 15-
levels.. In this work, the asymmetric 15 level inverter
is presented. This inverter is designed to avoid the
regeneration problem - power flow from the load to
the inverter - in some of the power cells. This is
achieved by obtaining the firing angles associated
with the power cells considering a minimum load
voltage THD. The simulation and experimental
results of the proposed 15-level inverter topology are
also presented. Finally, a power flow analysis is
accomplished and simulated results show the
feasibility of this approach
II. PROPOSED 15-LEVEL INVERTER
Multilevel inverters are the alternative for
medium voltage applications. Within the inverters
types there are symmetric and asymmetric topologies.
The asymmetric inverters have different DC voltage
values. The most common topology is when the
different cells are implemented in cascade
arrangement, where the DC voltage are in multiples
of 3, obtaining an AC voltage with 3n
= 27 levels (n =
3 cascaded inverters). This topology provides a load
voltage with low harmonic content, THD <; 3%.
However, this high quality voltage has a non-
negligible drawback, which is the presence of
regeneration in some of the inverters, independent of
load type[1]. This phenomenon is due to the
modulation technique (Nearest Level Modulation)
used by this inverter. In this work, the asymmetric 15
level inverter is presented. This inverter is designed
to avoid the regeneration problem - power flow from
the load to the inverter - in some of the power cells.
This is achieved by obtaining the firing angles
associated with the power cells considering a
minimum load voltage THD. Finally, a power flow
analysis is accomplished and simulated results show
the feasibility of this approach.
Fig.2 shows the proposed inverter fed to 3-phase
a.c load and Fig.3 shows the simplified diagram with
three inverters per phase.
Fig.2. Basic idea diagram of three-phase inverter
Fig.3. Schematic of seven level inverter in single
phase
The most commonly used multilevel topologyis
the diode clamped inverter, in which the diode isused
as the clamping device to clamp the dc busvoltage so
as to achieve steps in the output voltage.
A three-level diode clamped inverter consistsof
two pairs of switches and two diodes. Each
switchpairs works in complimentary mode and the
diodesused to provide access to mid-point voltage. In
athree-level inverter each of the three phases of
theinverter shares a common dc bus, which has
beensubdivided by two capacitors into three levels.
TheDC bus voltage is split into three voltage levels
byusing two series connections of DC capacitors,C1
andC2. The voltage stress across each switching
device islimited to Vdc through the clamping diodes
Dc1 andDc2. It is assumed that the total dc link
voltage is Vdcand mid point is regulated at half of the
dc linkvoltage, the voltage across each capacitor is
Vdc/2(Vc1=Vc2=Vdc/2).[1]
A. Switching Sequences:
In order to avoid unwanted voltage levels during
switchingcycles, the switching modes should be
selected so that theswitching transitions become
minimal during each mode transfer.This will also
help to decrease switching power dissipation.
Durga Bhavani. Peeta et al Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 5, Issue 1( Part 2), January 2015, pp122-126
www.ijera.com 124 | P a g e
In order to produce 15- levels by Sinusoidal Pulse
Width Modulation (SPWM), three saw-
toothwaveforms for carrier and a sinusoidal reference
signal formodulator are required as shown in Fig. 4.
Fig. 4.SPWM carrier and modulator for proposed 15-
level inverter
III. MATLAB BASED SIMULATION&
RESULTS
A. MATLAB based simulation :
Fig.4. shows the complete MATLAB based
simulation masked diagram of the proposed 15-level,
3-phase inverter.
Fig.4.MATLAB based simulation masked diagram of
the proposed 15-level, 3-phase inverter
Fig.5. shows the input DC voltage source to the
proposed 15-level, 3-phase inverter
Fig.5. Input DC voltage source to the proposed 15-
level, 3-phase inverter
Fig.6. shows power electronic based bridge circuit of
the proposed 15-level, 3-phase inverter
Fig.6. Simulation diagram of power electronic based
bridge circuit of the proposed 15-level, 3-phase
inverter
Fig.7. shows the gate controlled pulse to the proposed
15-level, 3-phase inverter
Fig.8.shows the inversion of DC to 3-phase
MATLAB based simulation diagram.
Durga Bhavani. Peeta et al Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 5, Issue 1( Part 2), January 2015, pp122-126
www.ijera.com 125 | P a g e
Fig.7. Gate controlled pulse to the proposed 15-level,
3-phase inverter
Fig.8. DC to AC 3-phase inversion MATLAB based
simulation diagram.
Simulation parameters for the proposed 15-level,
3-phase inverter is given by in the Table.1
B. Simulation Results:
Fig.9. shows the 3-phase, 15-level output voltage
waveform from the proposed inverter.
Fig.10. shows the THD calculation of proposed 3-
phase, 15-level inverter using powergui FFT Analysis
tool.
Fig.9. 3-Phase, 15-level output voltage waveform
from the proposed inverter
Fig.10. THD calculation of proposed 3-phase, 15-
level inverter using powergui FFT Analysis tool
Fig.11. shows the 3-phase voltage and 3-phase
current waveform from the proposed inverter.
Fig.11. 3-phase voltage (upper) and 3-phase current
(lower) waveform from the proposed inverter
respectively
Table .2. Shows the r.m.s values from phase voltages
and currents
Durga Bhavani. Peeta et al Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 5, Issue 1( Part 2), January 2015, pp122-126
www.ijera.com 126 | P a g e
TABLE1.SIMULATION SPECIFICATIONS
Parameter Rating
Input DC supply (V) 50V
IGBT/Diode Internal
Resistance Ron
1 m Ω
Snubber Resistance ,
Rs (Ω)
1µΩ
Nominal frequency
(Hz)
50 Hz
Active Power (W) 10KW
Reactive Power (Var) 8Kvar
Damping factor of
filter
0.8
TABLE.2. RMS VALUES OF OUTPUT
RESPONSES OF PROPOSED INVERTER
Output Response RMS Value
Phase A voltage (V) 363.4
Phase B voltage (V) 363.3
Phase C voltage (V) 363.3
Phase A Current (A) 43.89
Phase B Current (A) 43.85
Phase C Current (A) 43.85
IV. CONCLUSION
An efficient 3-phase, 15-level inverter is
presented in the paper. The resultant simulation
graphs show the accuracy of the proposed
inverter.High performance switchesare adopted to
reduce the conductionlosses and improve the
efficiency.Experimental results that confirm the
feasibilityof the proposed 3-phase, 15-level
inverter.Finally, MATLAB based simulink results
showns the THD value at reasonable level.
REFERENCES
[1] K. Gopakumar, Haitham Abu-Rub, P. P.
Rajeevan and K.Sivakumar, “A Nine-Level
Inverter Topology for Medium-Voltage
Induction Motor Drive With Open-End
Stator Winding” IEEE Transactions , 2013
on industrial electronics,vol.60, no.9.
[2] M. N. Abdul Kadir and S. Mekhilef “Novel
vector controlmethod for three-stage hybrid
cascaded multilevel inverter” IEEE 2011,
Trans. Ind.Electron., vol. 58,
[3] L. A. Córdova, L. Empringham, P. Lezana
and C. A. Silva“Implementation and control
of a hybrid multilevel converter withfloating
dc links for current waveform improvement”
IEEE Trans. Ind.Electron., 2011 vol. 58,no.
6.
[4] Ehsan Najafi and Abdul Halim Mohamed
Yatim, “Design and Implementation of a
New MultilevelInverter Topology”,
IEEETrans. Ind. Electron. November 2012,
Vol. 59,no. 7, pp.no . 4148-4154
[5] L. G. Franquelo, K. Gopakumar, S. Kouro,
J. I. Leon, M.Malinowski, M. A. Pérez, J.
Pou and B.Wu, J. Rodríguez,“Recent
advances and industrial applications of
multilevel converters”IEEE Trans. Ind.
Electron,2010,vol. 57, no. 8.
[6] G. Franquelo, S. Kouro, J. I. Leon, R.
Portillo, M. A. M.Prats andJ. Rodriguez.
(2008) “The age of multilevel converters
arrives” IEEE 2008, Vol.2, no.2.
[7] E.Vellaneava, P.Correa, M.Pacas, “ Control
of Single-Phase Cascaded H-Bridge
Multilevel Inverter for Grid-Connected
photovoltaic Systems”, IEEE trans.
Industrial Eleectronics , 2009 ,
Vol.56,pp.4399-4406 .
[8] Malinowski Mariusz, Gopakumar K,
Rodriguez Jose, Pérez Marcelo A, “A survey
on cascaded multilevel inverters”, IEEE
Trans Ind Electron 2010;57(7).
[9] Malinowski Mariusz, GopakumarK,
Rodriguez Jose, Pérez Marcelo A., “A
survey on cascaded multilevel inverters.”,
IEEE Trans Ind Electron 2010;57(7).
Convers Manage 2011; 52:1114–28.
[10] K. Jang-Hwan, S.-K. Sul, and P. N. Enjeti,
“A carrier-based PWM method with optimal
switching sequence for a multilevel four-leg
voltage source inverters”,IEEE Trans. Ind.
Appl., vol. 44, no. 4, pp. 1239–1248 ,
Jul./Aug. 2008.

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15-Level Inverter Design & Simulation

  • 1. Durga Bhavani. Peeta et al Int. Journal of Engineering Research and Applications www.ijera.com ISSN : 2248-9622, Vol. 5, Issue 1( Part 2), January 2015, pp122-126 www.ijera.com 122 | P a g e Design & Simulation Of 3-Phase, 15-Level Inverter with Reverse Voltage Topology Durga Bhavani. Peeta, Sathish Kumar.K M. Tech (P.E) scholar Dept of EEE, Ramachandra College of Engineering and Technology, JNTUK, A.P Assisant Professor, Dept of EEE, Ramachandra College of Engineering and Technology, JNTUK, A.P Abstract: Multilevel inverters have been widely accepted for high-power high-voltage applications. Their performance is highly superior to that of conventional Seven-level inverters due to reduced harmonic distortion, lower electromagnetic interference, and higher dc link voltages. In this paper, a new topology with a reversing-voltage component is proposed to improve the multilevel performance. This topology requires fewer components compared to existing inverters (particularly in higher levels) and requires fewer carrier signals and gate drives. Therefore, thecomplexity is greatly reduced particularly for higher output voltage levels. The Proposed 15-level inverter is modelled and simulated in Matlab 2012a using Simulink and Sim Power Systems set tool boxes Keywords: Multilevel inverter, power electronics, SPWM, topology. I. INTRODUCTION Advancement in the research of Power electronic invertersis still increasing with the rapid demands in electrical systems. The emergence of multilevel inverters has been in increase since the last decade. These new types of converters are suitable for high voltage and high power application due to their ability to synthesize waveforms with better harmonic spectrum[10]. Multilevel converters are mainly utilized to synthesis a desired single- or three-phase voltage waveform. Thedesired multi-staircase output voltage is obtained by combining several dc voltage sources. Solar cells, fuel cells,batteries and ultra-capacitors are the most common independent sources used [1]. One important application ofmultilevel converters is focused on medium and high-power conversion. Nowadays, there exist three commercialtopologies of multilevel voltage-source inverters: neutral point clamped (NPC), cascaded H-bridge (CHB), and flyingcapacitors (FCs)[2]. Among these inverter topologies, cascaded multilevel inverter reaches the higher output voltage and power levels (13.8 kV,30 MVA) and the higher reliability due to its modular topology[3]. Diode-clamped multilevel converters are used in conventional high-power ac motor drive applications likeconveyors, pumps, fans, and mills. They are also utilized in oil, gas, metals, power, mining, water, marine, andchemical industries. They have also been reported to be used in a back-to-back configuration for regenerativeapplications[4]. Flying capacitor multilevel converters have been used in high- bandwidth high-switching frequencyapplications such as medium-voltage traction drives. Finally, cascaded H-bridge multilevel converters have beenapplied where high power and power quality are essential, for example, static synchronous compensators active filterand reactive power compensation applications, photovoltaic power conversion, uninterruptible power supplies, andmagnetic resonance imaging. Furthermore, one of the growing applications for multilevel motor drives is electric andhybrid power trains. For increasing voltage levels the number of switches also will increase in number. Hence the voltage stresses andswitching losses will increase and the circuit will become complex. By using the proposed topology number ofswitches will reduce significantly and hence the efficiency will improve. A multi-stage inverter using three-state converters is being analyzed for multipurpose applications, such asactive power filters, static var compensators and machine drives for sinusoidal and trapezoidal currentapplications. The great advantage of this kind of converter is the minimum harmonic distortion obtained. The circuit of Fig.1 shows the basic topology of oneconverter used for the implementation of multi- stageconverters.It is based on the simple, four switches converter,used for single phase inverters or for dual converters. Theseconverters are able to produce three levels of voltage in theload: +Vdc, - Vdc, and Zero[7]. RESEARCH ARTICLE OPEN ACCESS
  • 2. Durga Bhavani. Peeta et al Int. Journal of Engineering Research and Applications www.ijera.com ISSN : 2248-9622, Vol. 5, Issue 1( Part 2), January 2015, pp122-126 www.ijera.com 123 | P a g e Fig.1. Basic idea diagram of three-level module for building multi stage inverter This paper mainly focuses on the general multilevel inverter schematic. A general method of multilevel modulation phase disposition (PD) SPWM is utilized to drive the inverter and can be extended to any number of voltage levels. Here , in this paper the proposed multilevel scheme extended up to 15- levels.. In this work, the asymmetric 15 level inverter is presented. This inverter is designed to avoid the regeneration problem - power flow from the load to the inverter - in some of the power cells. This is achieved by obtaining the firing angles associated with the power cells considering a minimum load voltage THD. The simulation and experimental results of the proposed 15-level inverter topology are also presented. Finally, a power flow analysis is accomplished and simulated results show the feasibility of this approach II. PROPOSED 15-LEVEL INVERTER Multilevel inverters are the alternative for medium voltage applications. Within the inverters types there are symmetric and asymmetric topologies. The asymmetric inverters have different DC voltage values. The most common topology is when the different cells are implemented in cascade arrangement, where the DC voltage are in multiples of 3, obtaining an AC voltage with 3n = 27 levels (n = 3 cascaded inverters). This topology provides a load voltage with low harmonic content, THD <; 3%. However, this high quality voltage has a non- negligible drawback, which is the presence of regeneration in some of the inverters, independent of load type[1]. This phenomenon is due to the modulation technique (Nearest Level Modulation) used by this inverter. In this work, the asymmetric 15 level inverter is presented. This inverter is designed to avoid the regeneration problem - power flow from the load to the inverter - in some of the power cells. This is achieved by obtaining the firing angles associated with the power cells considering a minimum load voltage THD. Finally, a power flow analysis is accomplished and simulated results show the feasibility of this approach. Fig.2 shows the proposed inverter fed to 3-phase a.c load and Fig.3 shows the simplified diagram with three inverters per phase. Fig.2. Basic idea diagram of three-phase inverter Fig.3. Schematic of seven level inverter in single phase The most commonly used multilevel topologyis the diode clamped inverter, in which the diode isused as the clamping device to clamp the dc busvoltage so as to achieve steps in the output voltage. A three-level diode clamped inverter consistsof two pairs of switches and two diodes. Each switchpairs works in complimentary mode and the diodesused to provide access to mid-point voltage. In athree-level inverter each of the three phases of theinverter shares a common dc bus, which has beensubdivided by two capacitors into three levels. TheDC bus voltage is split into three voltage levels byusing two series connections of DC capacitors,C1 andC2. The voltage stress across each switching device islimited to Vdc through the clamping diodes Dc1 andDc2. It is assumed that the total dc link voltage is Vdcand mid point is regulated at half of the dc linkvoltage, the voltage across each capacitor is Vdc/2(Vc1=Vc2=Vdc/2).[1] A. Switching Sequences: In order to avoid unwanted voltage levels during switchingcycles, the switching modes should be selected so that theswitching transitions become minimal during each mode transfer.This will also help to decrease switching power dissipation.
  • 3. Durga Bhavani. Peeta et al Int. Journal of Engineering Research and Applications www.ijera.com ISSN : 2248-9622, Vol. 5, Issue 1( Part 2), January 2015, pp122-126 www.ijera.com 124 | P a g e In order to produce 15- levels by Sinusoidal Pulse Width Modulation (SPWM), three saw- toothwaveforms for carrier and a sinusoidal reference signal formodulator are required as shown in Fig. 4. Fig. 4.SPWM carrier and modulator for proposed 15- level inverter III. MATLAB BASED SIMULATION& RESULTS A. MATLAB based simulation : Fig.4. shows the complete MATLAB based simulation masked diagram of the proposed 15-level, 3-phase inverter. Fig.4.MATLAB based simulation masked diagram of the proposed 15-level, 3-phase inverter Fig.5. shows the input DC voltage source to the proposed 15-level, 3-phase inverter Fig.5. Input DC voltage source to the proposed 15- level, 3-phase inverter Fig.6. shows power electronic based bridge circuit of the proposed 15-level, 3-phase inverter Fig.6. Simulation diagram of power electronic based bridge circuit of the proposed 15-level, 3-phase inverter Fig.7. shows the gate controlled pulse to the proposed 15-level, 3-phase inverter Fig.8.shows the inversion of DC to 3-phase MATLAB based simulation diagram.
  • 4. Durga Bhavani. Peeta et al Int. Journal of Engineering Research and Applications www.ijera.com ISSN : 2248-9622, Vol. 5, Issue 1( Part 2), January 2015, pp122-126 www.ijera.com 125 | P a g e Fig.7. Gate controlled pulse to the proposed 15-level, 3-phase inverter Fig.8. DC to AC 3-phase inversion MATLAB based simulation diagram. Simulation parameters for the proposed 15-level, 3-phase inverter is given by in the Table.1 B. Simulation Results: Fig.9. shows the 3-phase, 15-level output voltage waveform from the proposed inverter. Fig.10. shows the THD calculation of proposed 3- phase, 15-level inverter using powergui FFT Analysis tool. Fig.9. 3-Phase, 15-level output voltage waveform from the proposed inverter Fig.10. THD calculation of proposed 3-phase, 15- level inverter using powergui FFT Analysis tool Fig.11. shows the 3-phase voltage and 3-phase current waveform from the proposed inverter. Fig.11. 3-phase voltage (upper) and 3-phase current (lower) waveform from the proposed inverter respectively Table .2. Shows the r.m.s values from phase voltages and currents
  • 5. Durga Bhavani. Peeta et al Int. Journal of Engineering Research and Applications www.ijera.com ISSN : 2248-9622, Vol. 5, Issue 1( Part 2), January 2015, pp122-126 www.ijera.com 126 | P a g e TABLE1.SIMULATION SPECIFICATIONS Parameter Rating Input DC supply (V) 50V IGBT/Diode Internal Resistance Ron 1 m Ω Snubber Resistance , Rs (Ω) 1µΩ Nominal frequency (Hz) 50 Hz Active Power (W) 10KW Reactive Power (Var) 8Kvar Damping factor of filter 0.8 TABLE.2. RMS VALUES OF OUTPUT RESPONSES OF PROPOSED INVERTER Output Response RMS Value Phase A voltage (V) 363.4 Phase B voltage (V) 363.3 Phase C voltage (V) 363.3 Phase A Current (A) 43.89 Phase B Current (A) 43.85 Phase C Current (A) 43.85 IV. CONCLUSION An efficient 3-phase, 15-level inverter is presented in the paper. The resultant simulation graphs show the accuracy of the proposed inverter.High performance switchesare adopted to reduce the conductionlosses and improve the efficiency.Experimental results that confirm the feasibilityof the proposed 3-phase, 15-level inverter.Finally, MATLAB based simulink results showns the THD value at reasonable level. REFERENCES [1] K. Gopakumar, Haitham Abu-Rub, P. P. Rajeevan and K.Sivakumar, “A Nine-Level Inverter Topology for Medium-Voltage Induction Motor Drive With Open-End Stator Winding” IEEE Transactions , 2013 on industrial electronics,vol.60, no.9. [2] M. N. Abdul Kadir and S. Mekhilef “Novel vector controlmethod for three-stage hybrid cascaded multilevel inverter” IEEE 2011, Trans. Ind.Electron., vol. 58, [3] L. A. Córdova, L. Empringham, P. Lezana and C. A. Silva“Implementation and control of a hybrid multilevel converter withfloating dc links for current waveform improvement” IEEE Trans. Ind.Electron., 2011 vol. 58,no. 6. [4] Ehsan Najafi and Abdul Halim Mohamed Yatim, “Design and Implementation of a New MultilevelInverter Topology”, IEEETrans. Ind. Electron. November 2012, Vol. 59,no. 7, pp.no . 4148-4154 [5] L. G. Franquelo, K. Gopakumar, S. Kouro, J. I. Leon, M.Malinowski, M. A. Pérez, J. Pou and B.Wu, J. Rodríguez,“Recent advances and industrial applications of multilevel converters”IEEE Trans. Ind. Electron,2010,vol. 57, no. 8. [6] G. Franquelo, S. Kouro, J. I. Leon, R. Portillo, M. A. M.Prats andJ. Rodriguez. (2008) “The age of multilevel converters arrives” IEEE 2008, Vol.2, no.2. [7] E.Vellaneava, P.Correa, M.Pacas, “ Control of Single-Phase Cascaded H-Bridge Multilevel Inverter for Grid-Connected photovoltaic Systems”, IEEE trans. Industrial Eleectronics , 2009 , Vol.56,pp.4399-4406 . [8] Malinowski Mariusz, Gopakumar K, Rodriguez Jose, Pérez Marcelo A, “A survey on cascaded multilevel inverters”, IEEE Trans Ind Electron 2010;57(7). [9] Malinowski Mariusz, GopakumarK, Rodriguez Jose, Pérez Marcelo A., “A survey on cascaded multilevel inverters.”, IEEE Trans Ind Electron 2010;57(7). Convers Manage 2011; 52:1114–28. [10] K. Jang-Hwan, S.-K. Sul, and P. N. Enjeti, “A carrier-based PWM method with optimal switching sequence for a multilevel four-leg voltage source inverters”,IEEE Trans. Ind. Appl., vol. 44, no. 4, pp. 1239–1248 , Jul./Aug. 2008.