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A New Symmetric Multilevel Inverter Topology Using Single and Double Source Sub-Multilevel Inverters
A New Symmetric Multilevel Inverter Topology Using Single and Double Source Sub-Multilevel Inverters
Journal of Power Electronics. 2015. Jan, 15(1): 96-105
Copyright © 2015, The Korean Institute Of Power Electronics
  • Received : June 15, 2005
  • Accepted : August 13, 2014
  • Published : January 20, 2015
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About the Authors
Kannan Ramani
Dept. of Electrical and Electronics Engg., K. S. Rangasamy College of Technology, Tiruchengode, India
Mohd. Ali Jagabar Sathik
Dept. of Electrical and Electronics Engg., J. J. College of Engineering and Technology, Tiruchirappalli, India
jagabarsathik@gmail.com
Selvam Sivakumar
Dept. of Electrical and Electronics Engg., J. J. College of Engineering and Technology, Tiruchirappalli, India

Abstract
In recent years, the multilevel converters have been given more attention due to their modularity, reliability, failure management and multi stepped output waveform with less total harmonic distortion. This paper presents a novel symmetric multilevel inverter topology with reduced switching components to generate a high quality stepped sinusoidal voltage waveform. The series and parallel combinations of switches in the proposed topology reduce the total number of conducting switches in each level of output voltages. In addition, a comparison between the proposed topology with another topology from the literature is presented. To verify the proposed topology, the computer based simulation model is developed using MATLAB/Simulink and experimentally with a prototype model results are then compared.
Keywords
I. INTRODUCTION
The demand for Energy keeps on increasing and the supply of non-renewable energy sources continues decreasing day-to-day. The best way to face these problems is by the use of renewable energy sources with the help of power electronics devices. Power electronic devices help to build power converters. This grabbed the attention of researchers to focus on power electronics converters to develop more topologies, especially in DC/AC power modulators with higher efficiency and a high quality output. This paved way for multilevel converters to predominant usage in medium and high power applications [1] . To improve the performance of multilevel converters, the experts are developing new converter topologies, novel modulation techniques and improved control techniques for various applications. Multilevel inverters can provide higher power handling capability while considering a high power conversion process [2] . For multilevel inverters, fault tolerance can be achieved by bypassing the faulty devices and/or modules while the switching patterns of the rest of the modules can be reconfigured to a new normal condition [3] . The conventional multilevel inverters are: (i) Diode Clamped; its required single dc source with multiple capacitors are connected parallel to equally share the dc voltage. The diode clamp is very suitable for higher voltage applications since the single dc source is divided into several dc sources via a capacitor. The main challenge of these topologies is the larger number of clamped diodes for which the capacitor balancing requires an additional circuit. (ii) Flying Capacitor (FC); a clamping capacitor is used, a larger number of storage capacitors is required, and maintaining the voltage of each capacitor is difficult. (iii) Cascaded H-Bridge (CHB); this is a series of cascaded connections of H-bridge or full bridge inverters. It does not require any clamping capacitor or diode and it has great modularity and fault tolerance. The main drawback of CHB is the requirement of isolated dc sources. However, these conventional multilevel inverter topologies are used by employing a larger number of power switches for a higher number of output voltage levels [4] . To rectify this problem, many topologies are presented [5] - [15] . A new asymmetric topology was proposed in [5] . In this topology, a power switch with an anti-parallel diode will create an inter-looping current circulation. To avoid this, the combination of MOSFET and IGBT is proposed. A new attempt was made [6] with reduced number of switches for both symmetric and asymmetric topologies. In this topology, the symmetric method uses different ratings of the switches which leads to different voltage capabilities and increases the maximum voltage capability of the circuit. A new converter topology presented in [7] . In this topology, the power circuit complexity is reduced with the help of auxiliary switches. In addition, this topology may require bidirectional switches. In [8] , a cascaded connection of power cells proposed with a minimum number of switches when compared to conventional CHB. Even then, it requires a larger number of power switches. Some other topologies are presented in the literature which is mainly focused on reducing the power switches [9] - [11] . Even though these topologies suffer from a higher number of power diodes and capacitors. A combination of two or more conventional or new topologies can be referred to as a hybrid. Hybrid topologies have some significance advantages to reduce the switching losses and improve the converter efficiency. Hybrid modulations for cascaded converters have been proposed. This allows for the use of a lower switching frequency in higher voltage cells, and a higher switching frequency in lower voltage cells. By using hybrid modulation techniques, the medium and high power applications are strengthened. Both high and low switching frequencies are used to generate a higher number of voltage levels and to strengthen medium and high power applications. The hybrid method’s drawback is the requirement of different voltage ratings of the power switches [12] . A recent topology has been introduced with an even number of dc sources in [13] . It consists of both double voltage ratings and bidirectional switches which may further increase the power electronic devices. In this paper, a new approach to reduce the number of power switches and gate driver circuits by using the double voltage ratings of power switches to obtain a synthesized stepped waveform is discussed.
II. PROPOSED TOPOLOGY
In this section, detailed explanations of two different basic structures of proposed topology are introduced and mathematical expressions for a number of voltages level ( Nlevel ), number of switches ( Nswitch ) and number of dc source voltages ( n ) are presented.
- A. Suggested Topology
A basic single dc source with series/parallel unit is explained in Fig.1 (a). The dc source E1 is connected in series with switch S1 and in parallel with switch P1 . This basic unit is called a Single Source Sub Multilevel Inverter ( SSSMLI ). Fig.1 (b) shows the series/parallel connection of power switches along with two dc sources. The E1 & E2 dc sources are connected in series with S1 and in parallel with P1 . This is often referred to as a Double Source Sub Multilevel Inverter ( DSSMLI ). In both the cases, the switches should not be turned on simultaneously to avoid a short circuit of the dc source. The proposed topology is separated into two units: (i) a combined single and double source sub multilevel inverter which is called a level generator unit and (ii) a series connection of the level generator with an H-Bridge inverter which is called a polarity changer. The series connection of dc sources with switches is called a voltage adder, and the parallel connection of switches is called a voltage subtractor. The combination of both a single source unit and a double source unit is connected in series to form a level generator as shown in Fig. 1 (c) and Fig 1 (d). In this proposed topology, both the even source and odd source have separate generalized structures as shown in Fig. 1 .
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Proposed Symmetric Topology. (a) Basic single source sub multilevel inverter (SSSMLI). (b) Basic double source sub multilevel inverter (DSSMLI). (c) Generalized structure for odd number of sources. (d) Generalized structure for even number of sources.
This topology requires multiple dc sources, which may be available through renewable energy sources such as photovoltaic panels or Fuel cells or through energy storage devices such as capacitors. “ n ” is the number of dc source voltages, which are separated with series connected unidirectional controlled power switches ( S1 , S2 , S3 …. Sj ). In addition, each unit has parallel switches ( P1 , P2 , P3 …. Pi ). The nth E is represented as En . In the proposed method, En is not connected with any parallel switches. Table I illustrates the switching pattern for n dc sources. The 1’s and 0’s represents the turn on and turn off switches. The corresponding switches will be fired to synthesize a positive stepped waveform in the level generator. The adder/subtractor unit is connected in sequence with the H-bridge, which is used to create a current flow in both directions at the load terminals. Fig. 1 (c) and Fig. 1 (d) show the generalized structure of the new symmetrical topology proposed for Nlevel with equal magnitudes of the dc source voltages ( E ). The proposed symmetric topology is used in order to provide a larger number of output voltage steps with a minimum number of switches. Generally, the difference is presented in [14] , the proposed topology in each dc source is constructed with a pair of series/parallel switches. However, in this case, any two dc source voltages can be connected with one parallel switch, which may increase the voltage ratings of the switches. Here worth mentioning that the number of switches is getting reduced. According to Fig. 1 , the IGBTs of ( S1 , P1 ), ( S2 , P2 ) · · · · · ( Sj , Pi ) turn on simultaneously and E1 , E2 ….. En-1 will be short circuited with the same dc source. Either one of the corresponding adder/subtractor switches will turn on or turn off as per Table I . The maximum output voltage ( Eo, max ) is the sum of all the dc source voltages, and it is given as below:
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GENERALIZED SWITCHING PATTERN FOR PROPOSED TOPOLOGY
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GENERALIZED SWITCHING PATTERN FOR PROPOSED TOPOLOGY
Equations (1) and (2) illustrate the output level of the adder/subtraction circuit. Both the positive and negative levels are synthesized by the H-bridge circuit. At load ( Vo,Load ), the synthesized stepped output voltage level will be obtained as mentioned below:
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In proposed topology, the number of output voltage levels ( N Level ), the number of IGBTs ( NIGBT ) and the number of dc sources (n) are calculated as follows:
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The proposed topology structure varies with odd and even numbers of dc sources. Therefore, it is necessary to express the required number of IGBTs for given output levels and for a given number of dc sources. This is calculated in equation (6) and (7).
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The determination of the required number of single and double source sub multilevel inverters is calculated based on a given n of dc sources as follows:
For even number of n :
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For Odd number of n :
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The operating modes for the 9-level inverter, explained diagrammatically for both the positive and negative cycles, is depicted in Fig.2 . The switches P1 and P2 are turned on to produce the first level output from either ( HS1 , HS4 ) or ( HS2 , HS3 ). This is done to generate the corresponding polarity output. A similar sequence will continue to obtain the remaining levels as per the switching pattern in Table I .
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Different operating mode of proposed symmetric topology for 9-level inverter.
- B. Peak Inverse Voltage (PIV) Calculation
To choose an appropriate IGBT, the individual switch peak inverse voltages should be taken into account. Voltage stress, also known as the standing voltage of the switches, can be calculated by using the following expression:
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- C. Blocking Voltage Capability (EBLOCK)
One of the most important parameters of a multilevel inverter is to determine the maximum blocking voltage capability of the power switches. A SSSMLI switch requires the maximum blocking voltage of the single dc source magnitude ( E ). In a DSSMLI , a maximum of two dc source magnitude switches is required 2E . As shown in Fig. 1 (c), the blocking voltages of S1 , S2 Sj , and P1 , P2 Pi are calculated as follows. In the symmetric method, all of the dc source voltages are considered to be equal values so that E = E1 = E2 = E3 ……= En . The different voltage ratings of the level generator switches are as follows:
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The level generator and polarity changer blocking voltage capability are as follows:
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HS1 = HS2 = HS3 = HS4 = 4 * n
EBH = HS1 + HS2 + HS3 + HS4
The total blocking voltage can be calculated as follows:
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Where, EB1 , EB2 , EBH and EBLOCK are the maximum blocking voltages of the E and 2E switches, the H-bridge maximum blocking voltage and the total blocking voltage of the inverter, respectively. The determination of the total blocking voltage for the proposed multilevel inverter is expressed in equation (14).
III. STATE SPACE MODELING
A state space representation is a mathematical model of a system comprising a set of input, output and state variables. The state space representation provides a convenient and flexible way to model and analyze systems with z number of inputs and outputs. Consider S1 , S2 , S3 , and S4 be the signals for each level of output to the 9-level inverter for which the series/parallel combinations of switches are influenced. A simplified model for the state space switched modelling for each level of output is shown in Fig.3 b. This circuit is applicable for both odd and even numbers of equal dc sources.
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(a) Topology of single Phase SDSSMLI. (b) Simplified Circuit for State space Model.
Let,
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The variable H is the realization of the H-Bridge in the proposed topology. Therefore, the net output EL from the m - level inverter is given by:
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where, Edc is the magnitude sum of each dc source, and G1 to G4 is the comparator output signals (Binary output). By applying KVL to the circuit:
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where, RL = R + Rind , and R , Rind , RSW , and L are the total load resistance in ohms, the load resistance in ohms, the internal resistance of a load inductor in ohms, the ON state resistance of the total conducting IGBT’s in each level, and the load inductance in mH, respectively. In this topology, in each level, the number of conducting components is the same. Rewriting equation (17) and substituting the value of EL from equation (16) gives:
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Let the state variable be the current through the inductor x = iL(t) and input variable u = EL :
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where,
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Similarly, the voltage across the load is given by the expression:
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where y = Eout ;
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and D = 0
In general, the state space switched model of the proposed topology is given by:
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Where the dimension of [A]=1 x (Nlevel -1)/2 , k varies from 1 to (Nlevel -1)/2 , Edc is the magnitude of each dc source, and iL(t) is the current through the inductor. The generalized state space switched model is explained in equations (21) and (22) and it is applicable for proposed asymmetric topology with any number of levels. The state space switched model for the proposed topology is sculpted using MATLAB for a RL load of R=5Ω and L=100mH, and the results are as shown in Fig.4 and Fig. 5 .
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Simulated State Space Model Voltage waveform.
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Simulated State Space Model current waveform.
IV. COMPARISON WITH OTHER TOPOLOGIES
In order to verify the performance of the proposed topology, it should be compared with other topologies discussed in the literature.
- A. Comparison of the Required Number of IGBTs for Symmetric Topologies
The topologies in [6] , [8] , [13] and [14] , generate 2n+1 levels for n number of dc sources with an equal magnitude. However, the required number of IGBTs varies for each topology as shown in the comparison chart in Fig.6 . In [7] the delta modulation technique is used to generate a stepped waveform with a combination of unidirectional and bidirectional switches. The bidirectional switch may require a power diode or one additional switch leading to an increase in the power electronics component and a reduction in the system modularity. The topologies in [9] - [13] generate a stepped waveform by using n dc sources or a single dc source with a multi dc-link capacitor.
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Comparison with other topologies (a) NS vs N Switches.
These topologies suffer from either an increased number of capacitors or an increased number of power diodes. (i) More attention paid to protect the power diode from failure. The power diode is dissipating a lot of power when conducting current. Due to the stray inductance, large voltage spikes will occur when diode is turned off and reverse recovery is most crucial in a diode with a large reverse blocking voltage rating [16] . (ii) The capacitor accounts for the largest portion of failures in most power converters. However, the useful life of a capacitor is strongly affected by the different operating conditions [17] .
It is obvious that the proposed inverter requires a lower number of IGBTs with a freewheeling diode and no additional diodes are required. The maximum voltage blocking capability decides the reliable operation and the overall cost of the inverter. In Fig. 7 , a comparison of the maximum voltage blocking capability of the proposed topology with the other mentioned topologies is illustrated by assuming each of the dc sources is 100V . The maximum voltage blocking capability of the proposed topology is always lower since the number of the dc source magnitude is increased when compared with the other topologies.
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Comparison of Total Blocking Voltage Capability for various Topologies.
In medium voltage applications, a higher voltage class of H-Bridge switches ( HS1 , HS2 , HS3 and HS4 ) is required, which may significantly increase the blocking voltage of the proposed topology when compared with the CHB. Here it is worth mentioning that the number of power switches is reduced. Fig. 8 illustrates a comparison of the different topologies in terms of the required number power diodes for n number of dc sources.
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Comparison of Number of Sources Vs Number of Power Diode.
- B. Cost Comparison
The cost of the proposed topology is less when compared with the other topologies presented in the literature and more than the conventional topologies. The different voltage rating of the switch cost is shown in Table III .
The general cost calculation formula is given as:
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Where, NIGBT , Ndriver , Ndc , Nvariety , and OC are the cost of the number of IGBTs used in the circuit, the cost of the driver circuits for each IGBT, the cost of ‘ n ’ dc sources, the cost of using different varieties of dc sources as in case of the asymmetric MLI and other miscellaneous costs, respectively. The cost of the proposed MLI is less than that presented in [6] , [11] and [14] but higher than the CHB. This is due to the fact that the cost of the polarity generator part is significantly increased in the proposed topology. These are the biggest advantage of the CHB. It is evident from Table II that when the voltage rating is doubled with the same current, the cost of the switch is less than normal voltage rating devices. However, the current ratings become high when the double voltage rating switch cost increases. As a result, the proposed topology is very well suitable for medium voltage applications. Although the proposed topology can be cascaded to significantly reduce the cost of the inverter and to increase the high number of voltage levels with a lower number of power switches, this is most suitable for high power applications.
COST OF IGBT FOR DIFFERENT VOLTAGE AND CURRENT RATINGS
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*as on 07/05/2014 (http://www.galco.com )
- C. Fault Tolerances & Efficiency
The CHB topology has good modularity, which can easily bypass faulty switches [15] . In addition, the CHB topology presents many redundant states for effective fault-tolerant operation. The proposed topology has a very limited number of redundant states for a lower number of dc source voltages, and more redundant states for a higher number of levels. It is important to show the efficiency of the proposed topology because it is the prime factor when a load is considered. The efficiency of any converter is determined by η=(Pout/Pin)*100 . The proposed topology is highly efficient even when inductive types of loads are employed. The efficiency of the proposed structure is tabulated in Table III .
PERFORMANCE OF PROPOSED 9-LEVEL INVERTER ON VARIOUS LOADS
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PERFORMANCE OF PROPOSED 9-LEVEL INVERTER ON VARIOUS LOADS
V. SIMULATION AND EXPERIMENTAL RESULTS
To examine the proposed topologies and to generate the desired output voltage level waveforms, 9-Level proposed symmetric multilevel inverter is simulated using the computer simulation tool MATLAB / Simulink. The simulated output voltage and current is shown in Fig. 9 and Fig. 10 . They are very much similar to the simulated output voltage and current of the state space model.
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Simulation output voltage waveform with harmonic spectrum.
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Simulation output current waveform with harmonic spectrum.
In the simulation, each dc source magnitude is 60V with load value R = and L = 100mH . The nearest voltage level modulation techniques is implied as a modulation method which is preferable for a higher number of voltage steps [18] , [19] . A schematic representation of the switching signal generation logic from the given sine reference and comparison constants ( C1 , C2 Cn ) is shown in Fig. 11 .
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Switching Signal Generation.
The power quality of the proposed topology is measured by various parameters as listed in Table III . It is clear from Table III that the efficiency of the proposed topology is higher than the other topologies. Fig. 12 and Fig.13 show the voltage across the level generator switches and the current through the level generator switches. As shown in Fig. 12 , the blocking voltage on the S1 , P1 and S2 , P2 switches are 60V and 120V, respectively.
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Voltage across level generator switches.
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Current through level generator switches.
In the experimental setup, each dc source has a magnitude of 15V and the load values are R = 100 and L = 100mH . Based on the load value, the output voltage, current waveform and measured THD is shown in Fig. 14 and Fig. 15 . The nearest voltage control technique is embedded into a FPGA Spartan XE3S250E controller. The gate driver circuit switches in the proposed topologies are shown in Fig. 16 , which consists of an Opto-coupler, a Schmitt trigger and a buffer. To examine the simulated output voltage and current, the prototype model is developed, as shown in Fig. 17 .
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Experimental output Voltage and Current waveform of 9-level Inverter.
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Experimental Harmonic content of 9-level Proposed Inverter.
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Gate driver circuit for unidirectional Switch.
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Experimental Prototype Model.
VI. CONCLUSIONS
A new symmetric multilevel inverter has been proposed in this paper. It is a combination of a multi-stepped dc-dc converter (level generator) and an H- bridge inverter (polarity changer). The dc-dc conversion section consists of both single and double source sub multilevel inverters. It has been shown that the proposed inverter provides 2n+1 levels on the output voltage, using only n number of dc sources. It enables a simple structure with a reduced number of switches. It also provides a high quality output and a reduced THD. A comparison of the proposed topology with other topologies has been presented in this paper. In order to the performance of the proposed topology, the results of MATLAB simulations of the state space switched model, proposed circuit, and experimental outputs have been presented along with this paper. The improvements in the efficiency, power factor, and THD of the proposed topology are major breakthroughs. This proposed topology is best suited for medium power applications. Future work on this proposed topology should consider: (i). High voltage applications by cascading the proposed topology. (ii). Performance for various modulation techniques. (iii) Use in practical applications such as, induction motor drives and FACTS controllers. (iv). Protection requirements for various applications.
Acknowledgements
The authors want to thank AICTE New Delhi for the support given to this work through the research work and awarded the “Career Award for Young Teachers.”Dr. K. Ramani(F.No.11.8/AICTE/RIFD/CAYT/POL-I/2013-14)
BIO
Kannan Ramani was born in Vedaranyam, India, in 1982. He is graduated from Bharathiar University, Coimbatore, India, in 2004, and post graduated in Anna University, Chennai, India, in 2006, and his Ph.D. degree in Electrical Engineering from Anna University, in 2012. He is currently working as an Associate Professor in the department of Electrical and Electronics Engineering at the K.S. Rangasamy College of Technology, Tiruchengode, India, since January 2006. He has published 56 papers in international/national conferences and journals. His research interest involves in power electronics, inverters, the modeling of induction motors, and optimization techniques. He is guiding undergraduate, graduate and Ph.D scholars at Anna University. He is an ISTE, IETE and IEEE Member. He is a awardees CAYT from AICTE, New Delhi. He is an acting member of many editorial boards and editor in chief of international journals and IEEE conferences.
Mohd. Ali Jagabar Sathik was born in Tamil Nadu, India, in 1979. He received the Under graduate degree in Electronics and Communication Engineering from Madurai Kamaraj University, Madurai, India, in 2002, and his Master degree in Power Electronics and Drives from Anna University, Chennai, India, in 2004. He is presently working toward his Ph.D. degree in the Department of Electrical Engineering, Anna University. In 2011, he joined the Department of Electrical and Electronics Engineering, J.J. College of Engineering and Technology, Tiruchirappalli, India. His current research interests include the analysis and control of power electronic converters and renewable energy systems.
Selvam Sivakumar was born in Tamil Nadu, India, in 1991. He received his B.E. degree in Electrical and Electronics Engineering from the Saranathan College of Engineering, Tamil Nadu, India, in 2013. He presently working toward his Master Degree in Power Electronics and Drives from the J.J. College of Engineering and Technology, Tiruchirappalli, India. His current research interests include DC/AC converters, induction motor drives, and the design of digital control circuits for power converters and renewable energy sources.
References
Blaabjerg F. “Power electronics-key technology for renewable energy systems.” in Proc. 2nd IEEE Power Electron. Drive Systems and Technologies Conf. (PEDSTC) 2011 445 - 466
Kouro S. , Malinowski M. , Gopakumar K. , Pou J. , Franquelo L. G. , Wu B. , Rodriguez J. , Perez M. A. , Leon J. I. 2010 “Recent advances and industrial applications of multilevel converters.” IEEE Trans. Ind. Electron. 57 (8) 2553 - 2580    DOI : 10.1109/TIE.2010.2049719
Mirafzal B. 2014 “Survey of Fault-Tolerance Techniques for Three-Phase Voltage Source Inverters,” IEEE Trans. Ind. Electron 61 (10) 5192 - 5202    DOI : 10.1109/TIE.2014.2301712
Rodriguez J. , Lai J. S. , Peng F. Z. 2002 “Multilevel inverters: a survey of topologies, controls, and applications,” IEEE Trans. Ind. Electron 49 (4) 724 - 738    DOI : 10.1109/TIE.2002.801052
Ramkumar S. , Kamarajb V. , Thamizharasana S. , Jeevananthanc S. 2012 “A new series parallel switched multilevel c-link inverter topology,” International Journal of Electrical Power & Energy Systems 36 (1) 93 - 99    DOI : 10.1016/j.ijepes.2011.10.028
Kangarlu M. F. , Babaei E. 2013 “A generalized cascaded multilevel inverter using series connection of submultilevel nverters,” IEEE Trans. Power Electron 28 (2) 625 - 636    DOI : 10.1109/TPEL.2012.2203339
Ceglia G. , Guzman V. , Sanchez C. , Ibanez F. , Walter J. , Gimenez M. I. 2006 “A new simplified multilevel inverter topology for DC&AC conversion,” IEEE Trans. Power Electron 21 (5) 1311 - 1319    DOI : 10.1109/TPEL.2006.880303
Waltrich G. , Barbi I. 2010 “Three-phase cascaded multilevel inverter using power cells with two inverter legs in series,” IEEE Trans. Ind. Electron 57 (8) 2605 - 2612    DOI : 10.1109/TIE.2010.2043040
Alishah R. S. , Nazarpour D. , Hosseini S. H. , Sabahi M. 2014 “Novel topologies for symmetric, asymmetric, and cascade switched-diode multilevel converter with minimum number of power electronic components,” IEEE Trans. Ind. Electron. 61 (10) 5300 - 5310    DOI : 10.1109/TIE.2013.2297300
Ye Y. , Cheng K. W. E. , Liu J. , Ding K. 2014 “A step-up switched-capacitor multilevel inverter with self voltage balancing,” IEEE Trans. Ind. Electron 61 (12) 6672 - 6680    DOI : 10.1109/TIE.2014.2314052
Hinago Y. , Koizumi H. 2012 “A switched-capacitor inverter using series/parallel conversion with inductive load,” IEEE Trans. Ind. Electron 59 (2) 878 - 887    DOI : 10.1109/TIE.2011.2158768
Nami A. , Zare F. , Ghosh A. , Blaabjerg F. 2011 “A hybrid cascade converter topology with series-connected symmetrical and asymmetrical diode clamped H-bridge cells,” IEEE Trans. Power Electron. 26 (1) 51 - 65    DOI : 10.1109/TPEL.2009.2031115
Mokhberdoran A. , Ajami A. 2014 “Symmetric and asymmetric design and implementation of new cascaded multilevel inverter topology,” IEEE Trans. Power Electron. 29 (12) 6712 - 6724    DOI : 10.1109/TPEL.2014.2302873
Nagarajan R. , Saravanan M. 2014 “Performance analysis of a novel reduced switch cascaded multilevel inverter,” Journal of Power Electronics 14 (1) 48 - 60    DOI : 10.6113/JPE.2014.14.1.48
Lezana P. , Ortiz G. 2009 “Extended operation of cascade multicell converters under fault condition,” IEEE Trans. Ind. Electron 56 (7) 2697 - 2703    DOI : 10.1109/TIE.2009.2019771
Mohan N. , Undeland T. M. , Robbins W. P. 1995 Power Electronics: Converters, Applications and Design 2nd Ed. John Wiley & Sons New York 524 - 543
Pang H. M. , Bryan P. M. H. “A life prediction scheme for electrolytic capacitors in power converters without current sensor,” in Proc.25th IEEE Applied Power Electronics Conference and Exposition (APEC) 2010 973 - 979
Perez M. , Rodriguez J. , Pontt J. , Kouro S. “Power distribution in hybrid multi-cell converter with nearest level modulation,” in Proc. ISIE IEEE International Symposium on Ind. Elelctron 2007 736 - 741
Hu P. , Jiang D. “A level-increased nearest level modulation method for modular multilevel converters,” IEEE Trans. Power Electron. to be published.