PERFORMANCE ANALYSIS OF SEVEN LEVEL INVERTER WITH SOFT SWITCHING CONVERTER FOR PHOTOVOLTAIC SYSTEM

Similar documents
Solar Power Generation with Capacitor Based Seven Level Inverter System

THE extensive use of fossil fuels has resulted in the global

PERFORMANCE ANALYSIS OF PV BASED BOOST - SEPIC CASCADED INVERTER FED INDUCTION MOTOR SYSTEM USING PI & FLC 1 Jasmine David, 2 Gopinath Mani,

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

CAPACITOR VOLTAGE BALANCING IN SINGLE PHASE SEVEN-LEVEL PWM INVERTER

Hybrid Five-Level Inverter using Switched Capacitor Unit

Levels of Inverter by Using Solar Array Generation System

A New Method In Grid Interconnecting Solar Generation System Using Multilevel Inverter

Multilevel Inverter for Single Phase System with Reduced Number of Switches

Design of Power Inverter for Photovoltaic System

A Seven Level Inverter using a Solar Power Generation System

Simulation of Three Phase Cascaded H Bridge Inverter for Power Conditioning Using Solar Photovoltaic System

Implementation of New Three Phase Modular Multilevel Inverter for Renewable Energy Applications

A Novel Cascaded Multilevel Inverter Using A Single DC Source

A Single Phase Multistring Seven Level Inverter for Grid Connected PV System

SINGLE PHASE THIRTY ONE LEVEL INVERTER USING EIGHT SWITCHES TOWARDS THD REDUCTION

An Interleaved High Step-Up Boost Converter With Voltage Multiplier Module for Renewable Energy System

ADVANCES in NATURAL and APPLIED SCIENCES

A New 5 Level Inverter for Grid Connected Application

A Three Phase Seven Level Inverter for Grid Connected Photovoltaic System by Employing PID Controller

Modular Grid Connected Photovoltaic System with New Multilevel Inverter

Multilevel Inverter for Grid-Connected PV SystemEmploying MPPT and PI Controller

PERFORMANCE ANALYSIS OF SOLAR POWER GENERATION SYSTEM WITH A SEVEN-LEVEL INVERTER SUDHEER KUMAR Y, PG STUDENT CHANDRA KIRAN S, ASSISTANT PROFESSOR

11 LEVEL SWITCHED-CAPACITOR INVERTER TOPOLOGY USING SERIES/PARALLEL CONVERSION

Online Dynamic Topology Type PV Grid - Connected Inverter for Efficiency Expansion

Modified Multilevel Inverter Topology for Driving a Single Phase Induction Motor

A DC-DC Boost Converter with Voltage Multiplier Module and Fuzzy Logic Based Inverter for Photovoltaic System

Harmonic mitigation in secondary distribution by using cascaded based nine-level inverters in solar generation stations

A Solar Powered Water Pumping System with Efficient Storage and Energy Management

ADVANCES in NATURAL and APPLIED SCIENCES

International Journal of Advance Engineering and Research Development

Implementation of a Voltage Multiplier based on High Step-up Converter using FLC

SINGLE PHASE MULTI STRING FIVE LEVEL INVERTER FOR DISTRIBUTED ENERGY SOURCES

Modified Multilevel Inverter Topology for Grid Connected Pv Systems

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

A Single Dc Source Based Cascaded H-Bridge 5- Level Inverter P. Iraianbu 1, M. Sivakumar 2,

A Five-Level Single-Phase Grid-Connected Converter for Renewable Distributed Systems

Multilevel Current Source Inverter Based on Inductor Cell Topology

Matlab/Simulink Modeling of Novel Hybrid H-Bridge Multilevel Inverter for PV Application

A Five Level Inverter for Grid Connected PV System Employing Fuzzy Controller

High Voltage Gain Interleaved Boost Converter

Enhanced Performance of Multilevel Inverter Fed Induction Motor Drive

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

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

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

A New Multilevel Inverter Topology of Reduced Components

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

Multilevel Inverter with Coupled Inductors with Sine PWM Techniques

Analysis And Comparison Of Flying Capacitor And Modular Multilevel Converters Using SPWM

Design and Development of Multi Level Inverter

MULTILEVEL INVERTER WITH LEVEL SHIFTING SPWM TECHNIQUE USING FEWER NUMBER OF SWITCHES FOR SOLAR APPLICATIONS

IMPLEMENTATION OF MULTILEVEL INVERTER WITH MINIMUM NUMBER OF SWITCHES FOR DIFFERENT PWM TECHNIQUES

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

SINGLE PHASE GRID CONNECTED PV SYSTEM EMPLOYED BY A NOVEL MODIFIED H BRIDGE INVERTER

Comparative Analysis of Flying Capacitor and Cascaded Multilevel Inverter Topologies using SPWM

Simulation and Experimental Results of 7-Level Inverter System

Single Phase Multi- Level Inverter using Single DC Source and Reduced Switches

An Investigation Study of Total Harmonic Distortion in a Flying Capacitor Multilevel Inverter With / Without Closed Loop Feedback Schemes

A New Single-Phase Multilevel Inverter with Reduced Number of Switches for Solar Applications

Modeling and Simulation of a Novel Three-phase Multilevel Inverter with Induction Motor Drive

CARRIER BASED PWM TECHNIQUE FOR HARMONIC REDUCTION IN CASCADED MULTILEVEL INVERTERS

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

Modelling of Five-Level Inverter for Renewable Power Source

ANALYSIS OF PWM STRATEGIES FOR Z-SOURCE CASCADED MULTILEVEL INVERTER FOR PHOTOVOLTAIC APPLICATIONS

Switching of Three Phase Cascade Multilevel Inverter Fed Induction Motor Drive

International Research Journal of Engineering and Technology (IRJET) e-issn: Volume: 03 Issue: 11 Nov p-issn:

A Novel 2 - Stage Power Conditioning System for PV Power Generation Using FPGA

A Comparative Analysis of Multi Carrier SPWM Control Strategies using Fifteen Level Cascaded H bridge Multilevel Inverter

Comparison Of DC-DC Boost Converters Using SIMULINK

Multilevel inverter with cuk converter for grid connected solar PV system

ISSN Vol.07,Issue.06, July-2015, Pages:

This paper deals with a new family of high boostvoltage inverters, called switched-inductor quasi-z-source inverters.

Performance Analysis of Switched Capacitor Three Phase Symmetrical Inverter Topology with Induction Drive

Implementation of an Interleaved High-Step-Up Dc-Dc Converter with A Common Active Clamp

Hybrid Modulation Switching Strategy for Grid Connected Photovoltaic Systems

Design and Simulation of Simplified Five-Level and Seven-Level Inverters Using Modified PWM For PV Applications

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

High Current Gain Multilevel Inverter Using Linear Transformer

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

Electromagnetic Compatibility and Better Harmonic Performance with Seven Level CHB Converter Based PV-Battery Hybrid System

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

Implementation of Single Stage Three Level Power Factor Correction AC-DC Converter with Phase Shift Modulation

Analysis and Design of a Bidirectional Isolated buck-boost DC-DC Converter with duel coupled inductors

Reduction of Power Electronic Devices with a New Basic Unit for a Cascaded Multilevel Inverter fed Induction Motor

Modelling and Simulation of High Step up Dc-Dc Converter for Micro Grid Application

IJSRD - International Journal for Scientific Research & Development Vol. 4, Issue 04, 2016 ISSN (online):

A Pv Fed Buck Boost Converter Combining Ky And Buck Converter With Feedback

A Modified Single-Phase Quasi z source converter

Simulation Study of Hysteresis Current Controlled Single Phase Inverters for PhotoVoltaic Systems with Reduced Harmonics level

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

Low Order Harmonic Reduction of Three Phase Multilevel Inverter

Nine-Level Cascaded H-Bridge Multilevel Inverter Divya Subramanian, Rebiya Rasheed

Modeling and Analysis of Novel Multilevel Inverter Topology with Minimum Number of Switching Components

Hybrid Modulation Technique for Cascaded Multilevel Inverter for High Power and High Quality Applications in Renewable Energy Systems

Implementation of Microcontroller Based PWM Scheme for PV Multilevel Inverter

Diode Clamped Multilevel Inverter for Induction Motor Drive

Minimization Of Total Harmonic Distortion Using Pulse Width Modulation Technique

International Journal of Advance Engineering and Research Development

Analysis, Simulation of 3-Stage Cockcroft- Walton Voltage Multiplier for High Step-Up Dc-Dc Converter

Renewable Energy Integrated High Step-Up Interleaved Boost Converter for DC Microgrid Applications

Transcription:

50 PERFORMANCE ANALYSIS OF SEVEN LEVEL INVERTER WITH SOFT SWITCHING CONVERTER FOR PHOTOVOLTAIC SYSTEM M.Vidhya 1, Dr.P.Radika 2, Dr.J.Baskaran 3 1 PG Scholar, Dept.of EEE, Adhiparasakthi Engineering College, Melmaruvathur, Tamilnadu, India 2 Professor, Dept.of EEE, Adhiparasakthi Engineering College, Melmaruvathur, Tamilnadu, India 3 HOD, Dept. of EEE, Adhiparasakthi Engineering College, Melmaruvathur, Tamilnadu, India ABSTRACT This paper analyse the performance of Seven Level Inverter which is configured by means of capacitor selection circuit and an H- bridge inverter. Multicarrier Sinusoidal Phase Disposition Pulse Width Modulation (MCSPDPWM) and Variable Frequency Inverted Sinusoidal PWM technique (VFISPWM) are employed for analysing the Total Harmonic Distortion (THD) of the Seven Level output. The capacitor selection circuit converts the output of the Soft Switching Interleaved Boost Converter and solar source into three level direct current (DC) voltage and an H- bridge inverter further converts three level dc voltage to seven level alternating current (AC) voltage. The performance parameters like output voltage and efficiency of two different Soft Switching Interleaved Boost Converters are compared and analysed with the conventional Interleaved Boost Converter. Keywords- Soft Switching Interleaved BoostConverter,Efficiency,Multilevel Inverter, Pulse Width Modulation technique, Total Harmonic Distortion (THD) I. INTRODUCTION Electric power is the most commonly used type of energy. The use of fossil fuels results in the global problem of greenhouse emissions. Moreover the cost of fossil fuel keeps increasing as the supplies of fossil fuels are depleted in the future. Thus solar energy is becoming more important since it produces less pollution. The power conversion interface is important because it converts the dc power generated by the solar cell array into ac power and feeds the utility. An inverter is necessary in the power conversion interface to convert the direct current (DC) into alternating current (AC).Since the output voltage from the solar cell array is not sufficient enough to be given as input to the inverter circuit, a soft switching interleaved boost converter is used. The converter boost the solar cell output so that it can match with the dc bus voltage. Here soft switching interleaving boost converter has been discussed with two different topologies and compared with conventional interleaved boost converter to obtain high voltage gain and efficiency. Multicarrier Sinusoidal PWM technique and Variable Frequency Inverted Sinusoidal PWM technique are employed to analyse the Total Harmonic Distortion of seven level output waveform.seven level inverter with only six power electronic switches was proposed [4]. Hence switching losses are reduced. Two dc dc converters are used to step the output voltage of solar array which leads to complexity of the circuit. Transformer based converter are used which reduces the power efficiency.one H- bridge inverter and two diodeembedded bidirectional switches was proposed [8] to produce seven level. The number of diodes are increased which leads to complex circuit.however three capacitors are used to produce the voltage levels.hence balancing the voltages across three capacitors is more complex. A five level diode clamped multilevel inverter was proposed [3]. A separate dc voltage balancing circuit was equipped to maintain and balance the capacitor voltage. Coupled inductor is also used in the balancing circuit and the amplitude of flux will be reduced by means of the voltage balancing circuit. An interleaved boost converter with a capacitor for battery charger applications was proposed [13]. The capacitor is used for soft switching purpose to reduce the voltage stress of the converter switches and also to improve the efficiency. An interleaved boost converter with zero - voltage transition was proposed [14]. The inductor is used for the soft switching phenomenon to reduce the voltage stress and also to improve the conversion efficiency. Seven level inverter topology with ten power electronic switches and three capacitors was proposed [6].Balancing of capacitor voltage becomes complex and also switching loss increases due to more number of switches. II. PROPOSED METHODOLOGY This paper proposes a seven level inverter which is fed by a solar input source. The input from the solar is stepped up by means of soft switching interleaved boost converter. This paper compares operation of conventional interleaved boost converter with two different topologies. Topology 1 demonstrates theoperation of interleaved boost converter with soft

51 switching inductor and topology 2 deals with the operation of interleaved boost converter with soft switching capacitor. Multicarrier Sinusoidal Phase Disposition PWM and Variable Frequency Inverted Sinusoidal PWM techniques are used for the generation of gate pulses for the inverter switches and the THD of the seven level output voltage are analysed. The circuit diagram of conventional interleaved boost converter is shown in Fig.1 converter. The seven level inverter consists of a capacitor selection circuit and full bridge inverter connected in cascade. The solar input is given to the capacitor C 1 and output from the converter is given to the capacitor C 2. The capacitor selection circuit converts the input dc voltage into three level dc voltage and inverter further converts the three level dc voltage into seven level ac output voltage. The circuit diagram of proposed seven level inverter is shown in Fig. 4 Fig. 1 Circuit Diagram of Conventional Interleaved Boost Converter Topology 1: (Soft switched inductor) The circuit diagram of topology 1 shows the two shunted boost conversion units and a soft switching inductor is used to improve the efficiency and also to increase the output voltage. Fig. 2 shows the circuit diagram of topology 1 Fig. 2 Circuit Diagram of Topology 1 Topology 2: (Soft switched capacitor) The circuit diagram of topology 2 shows the two shunted boost converter units and a soft switching capacitor to improve the efficiency and also to increase the output voltage. The circuit diagram of topology 2 is shown in Fig. 3 Fig.4 Circuit Diagram of Seven Level Inverter with Topology 2 The output voltage of the seven level inverter has the following voltage levels: V dc, V dc /3, 2Vdc/3, 0,- V dc /3,-2V dc /3,-V dc.the different modes of operation for obtaining the seven level output voltage was discussed below. The operation of seven level inverter in positive half cycle is divided into four different modes. Mode 1: In mode 1 operation both the switches S S1 and S S2 of the capacitor selection circuit are turned OFF.S 1 and S 4 switches of the full bridge power converter are turned ON and C 1 is discharged through diode D 1 to obtain a voltage level of V dc/3.the operation of mode 1 is shown in Fig.5 Mode 2: In mode 2 operation, S S2 of the capacitor selection circuit and S 1 and S 4 of the full bridge power converter is ON and C 2 is discharged through the diode D 2 toobtain a voltage level of 2V dc/3.the equivalent circuit of mode 2 is shown in Fig.5 Mode 3: In mode 3 operation, in the capacitor selection circuit S S1 is ON.S 1 and S 4 of the full bridge power converter is turned ON to obtain V dc output voltage level. The mode 3 operation is shown in Fig. 5(c) Mode 4: In mode 4 operation, all the switches are turned OFF to get a zero output voltage level and its operation is shown in Fig. 5(d) Fig. 3 Circuit Diagram of Topology 2 Proposed Seven Level Inverter with Topology 2 (Capacitor) The proposed seven level is fed by means of solar input through a soft switching interleaving boost

52 with different topologies and seven level inverter with topology 2 has been simulated in MATLAB Simulink model. Fig.7shows the Simulink model of conventional interleaved boost converter. (c) (d) Fig. 5 Operation of different modes in positive half cycle Mode 1 mode 2 (c) mode 3 (d) mode 4 Mode 5: In mode 5 operation, the switches S2 and S3 of the full bridge power converter are turned ON and capacitor C1 is discharged through the diode D1to obtain a voltage level of Vdc/3.The equivalent circuit of mode 5 operation is shown in Fig. 6 Mode 6: In mode 6 operation, switches S S2, S 2 and S 3 are turned ON.C 2 is discharged through the diode D 2 to obtain a voltage level of -2V dc /3.The operation of mode 6 is shown in Fig. 6 Mode 7: In mode 7 operation, switch S S1 of the capacitor selection circuit is turned ON and S 3 and S 2 of the full bridge power converter is turned ON to obtain the voltage level of V dc. The equivalent circuit of mode 7 is shown in Fig. 6(c) Mode 8: In mode 8 operation, all the switches of inverter circuit are turned OFF to get the zero output. The operation of mode 8 is shown in Fig. 6(d) Fig.7 Simulation circuit of Conventional Interleaved Boost Converter Simulink model of soft switching interleavedboost converter with topology 1 and topology 2 is shown in Fig.8 and Fig.8 Simulation circuit of topology 1 and topology 2 Fig.9 shows input voltage of 48V for the interleaved boost converters and Fig. 9 shows the gate pulses for the switches S 1 and S 2.Fig. 10 and shows the output voltage and output power of conventional interleaved boost converter. (c) (d) Fig. 6 Operation of different modes in negative half cycle Mode 5 mode 6 (c) mode 7 (d) mode 8 III. SIMULATION RESULTS Simulation of the proposed seven level inverter was done in MATLAB/ Simulink. The generalized PV model, conventional interleaved boost converter, proposed soft switching interleaved boost converter

53 Fig. 9 Input voltage and gate trigger pulses for the switches Fig.11 Output voltage and Output power of topology 1 The output voltage of 94V is obtained for an input voltage of 48V and it is shown in Fig.12 Fig.12 shows the output power waveform of topology 2 Fig. 10 Output voltage and Output power of conventional Interleaved boost converter The output voltage of 114V is obtained for topology 1 with input voltage of 48V and it is shown in Fig.11. Fig.11 shows the output power waveform of topology 1. Fig.12 Output voltage and Output power of topology 2 COMPARISON RESULTS Table 1 shows the output voltage comparison results of different interleaved boost converter topologies. From the obtained results it is concluded that topology 1 has high voltage gain when compared to topology 2

54 TABLE 1: Output voltage comparison of two interleaved boost converters Table 2 shows the efficiency comparison results of different interleaved boost converters. The obtained results shows that topology 2 has better efficiency when compared to topology 1 and the efficiency increases in the order of 0.65 to 0.75% Fig.14 Solar input Output voltage of topology 2 Fig.15 shows the carrier and reference signal of phase disposition PWM technique. Fig.15 shows the variable frequency inverted sinusoidal PWM technique. TABLE 2: Efficiency comparison results of two interleaved boost converters Fig.13 shows the Simulink model of seven level inverter. Fig.14 and shows the solar input and interleaved boost converter output voltage. Fig.13 Proposed Seven Level Inverter with Topology 2 Fig.15 Phase disposition PWM and Variable Frequency Inverted Sinusoidal PWM techniques Fig.16 and shows the seven level output voltage and FFT analysis for Phase Disposition PWM technique with THD of 23.03%

55 that topology 1 gives high voltage gain and topology 2 results in better efficiency which increases in the order 0.65 to 0.75% when compared to topology 1. Fig.16 Seven Level output FFT analysis (Phase Disposition PWM technique) Fig.17 and shows the seven level output voltage and FFT analysis for variable frequency inverted sinusoidal PWM technique with THD of 25.54% Fig.17 Seven Level output FFT analysis (Variable frequency inverted sinusoidal PWM technique) IV. CONCLUSION The circuit model involves a seven level inverter which is fed by solar source through soft switching interleaved boost converter. The performance of seven level inverter was analysed my means of Multicarrier Sinusoidal Phase Disposition Pulse Width Modulation (MCSPDPWM) and Variable Frequency Inverted Sinusoidal Pulse Width Modulation (VFISPWM) technique. The obtained Total Harmonic Distortion (THD) results are 23.03% for MCSPDPWM and 25.54% for VFISPWM techniques respectively. The different topology operation of soft switching interleaved boost converters are simulated and compared with conventional interleaved boost converter. From the obtained results it is concluded REFERENCES [1] J. Chavarria, D. Biel, F. Guinjoan, C. Meza, and J. J. Negroni, Energy balance control of PV cascaded multilevel grid-connected inverters under level-shifted and phase-shifted PWMs, IEEE Trans.Ind.Electron.,Vol. 60,no.1,pp. 98 111,Jan. 2013. [2] S. Choi and M. Saeedifard, Capacitor voltage balancing of flying capacitor multilevel converters by space vector PWM, IEEE Trans. Power Delivery, Vol. 27, no. 3, pp. 1154 1161, Jul. 2012. [3] K. Hasegawa and H. Akagi, Low modulation index operation of a five level diode clamped PWM inverter with a dc- voltage balancing circuit for a motor drive, IEEE Trans. Power Electron.,Vol.27,no.8,pp.3495-3505,Aug.2012 [4] Jinn Chang Wu, Chia-Wei Chou, A Solar power generation system with a seven - level inverter IEEE Trans. Power Electronics,Vol.29,No.7,July 2014. [5] J.Mei,B.Xiao, K.Shen, L.M.Jian Yong Zheng, Modular multilevel inverter with new modulation method and its application to photovoltaic grid - connected generator IEEE Trans. Power Electron., Vol.28, no.11, pp.5063-5073, Nov.2013. [6] Y.Ounejjar, K. Al Hadded and L.A. Dessaint A novel six band hysteresis control for packed U-cells seven level converter: Experimental validation. IEEE Trans. Ind. Electron., Vol.5, no.10, pp.3808-3816, Oct.2012 [7] J.Pereda and J. Dixon, High- frequency link: A solution for using only one DC source in asymmetric cascaded multilevel inverters IEEE Trans. Ind. Electron., Vol.58, no.9, pp. 3884-3892, Sep.2011. [8] N.A.Rahim, K.Chaniago and Selvaraj, Single phase seven level grid-connected inverter for photovoltaic system, IEEE Trans. Ind.Electr., vol.58 no.6, pp. 2435 2443, Jun.2011 [9] A.K Sadigh, S.H.Hosseini, M. Sabahi, and G.B. Gharehpetian, Double flying capacitor multicell converter based on modified phase shifted pulse width modulation IEEE Trans. Power Electron., Vol. 25,no.6,pp.1517-1526, Jun.2010 [10] J. Selvaraj and N. A. Rahim, Multilevel inverter for grid-connected PV system employing digital PI controller, IEEE Trans. Ind. Electron., Vol. 56, no. 1, pp. 149-158, Jan. 2009. [11] X.She, A. Q. Huang, T. Zhao, and G. Wang, Coupling effect reduction of a voltage-balancing controller in single-phase cascaded multilevel converters, IEEE Trans. Power Electron., Vol. 27, no. 8, pp. 3530 3543, Aug.2012.

56 [12] J.M Shen, H. L. Jou, and J. C. Wu, Novel transformer-less grid connected power converter with negative grounding for photovoltaic generation system, IEEE Trans. Power Electron., Vol. 27, no. 4, pp. 1818 1829, Apr. 2012 [13] Sheng Yu Tseng, Cheng Tao Tsai, Photovoltaic Power System with an Interleaving Boost Converter for battery charger applications International Journal of Photoenergy, Vol. 2012, Sep. 2012. [14] CH. Shravan, D.Narasimharao, An Interleaved Boost Converter with Zero Voltage Transition for grid connected PV system International Journal of Emerging trends in Engineering and Development, Vol.2, March 2012. [15] Thielemans, A. Ruderman, B. Reznikov, Improved natural balancing with modified phaseshifted PWM for single-leg five level flying-capacitor converters, IEEE Trans. Power Electron., Vol. 27,no. 4, pp. 1658 1667, Apr. 2012. [16] S. Vazquez, J. I. Leon, L. G. Franquelo, J. J. Padilla, and J. M. Carrasco, DC-voltage-ratio control strategy for multilevel cascaded converters fed with a single DC source, IEEE Trans. Ind. Electron., Vol. 56, no. 7,pp. 2513 2521