Final Report (3) (1) PDF

Multilevel Inverter Major Project Interim Report 2015

Department of EEE 1 TIST,Arakkunnam

CHAPTER 1

INTRODUCTION

1.1 INTRODUCTION

Inverters are the power electronic circuit, which converts the DC

voltage into AC voltage. The DC source is normally a battery or output of the controlled

rectifier. The output voltage waveform of the inverter can be square wave, quasi-square

wave or low distorted sine wave. The output voltage can be controlled with the help of

drives of the switches. The pulse width modulation techniques are most commonly used

to control the output voltage of inverters. Such inverters are called as PWM inverters.

The output voltage of the inverter contain harmonics whenever it is not sinusoidal. These

harmonics can be reduced by using proper control schemes.

Inverters can be broadly classified into two types. They are-

Voltage Source Inverter (VSI)

Current Source Inverter (CSI)

When the DC voltage remains constant, then it is called voltage inverter

(VSI) or voltage fed inverter (VFI). When input current is maintained constant, then it is

called current source inverter (CSI) or current fed inverter (CFI). Sometimes, the DC

input voltage to the inverter is controlled to adjust the output. Such inverters are called

variable DC link inverters. The inverters can have single phase or three-phase output.

1.1.1 MULTILEVEL INVERTER

Multilevel power conversion was first introducedmore than two decades

ago. The general concept involvesutilizing a higher number of active semiconductor

switches to perform the power conversion in small voltagesteps. There



are several advantages to this approach whencompared with the conventional power

conversion approach.

The smaller voltage steps lead to the production of higher powerquality

waveforms and also reduce voltage (dv/dt) stress onthe load and the electromagnetic

compatibility concerns.Another important feature of multilevel converters is that

thesemiconductors are wired in a series-type connection, whichallows operation at higher

voltages. However, the series connectionis typically made with clamping diodes, which

eliminatesovervoltage concerns. Furthermore, since the switches are nottruly series

connected, their switching can be staggered, whichreduces the switching frequency and

thus the switching losses.

One clear disadvantage of multilevel power conversion is the higher

number of semiconductor switches required. It should be pointed out that lower voltage

rated switches can be used in the multilevel converter and, therefore, the active

semiconductorcost is not appreciably increased when compared with the twolevelcases.

However, each active semiconductor added requiresassociated gate drive circuits and

adds further complexity to theconverter mechanical layout.

Another disadvantage of multilevel power converters is that the small

voltage steps are typicallyproduced by isolated voltage sources or a bank of

seriescapacitors. Isolated voltage sources may not always be readilyavailable, and series

capacitors require voltage balancing .To some extent, the voltage balancing can be

addressed by usingredundant switching states, which exist due to the high numberof

semiconductor devices. However, for a complete solutionto the voltage-balancing

problem, another multilevel converter may be required .

1.2 NECESSITY

In recent years, industry has begun to demand higher power conversion

equipment,which now reaches the megawatt level. Controlled ac drives in the megawatt

range are usually connected to the medium-voltage network. Today, it is hard to connect

a single power semiconductor switch directly to medium voltage grids (2.3, 3.3, 4.16, or



6.9 kV). For these reasons, a new family of multilevel inverters has emerged as the

solution for working with higher voltage levels

In excising system multiple bridges are used which in turn increases

the no of switches, and assymetrical supply sources. The supply sources used in each

bridge is doubled for each bridge.The inverter design is difficult to construct and robust

in operation. In single-phase multilevel inverters, the most common topologies are the

cascaded, diode-clamped, and capacitor clamped this types are conventional multilevel

inverter .In practice, bulky transformers either of low or medium frequency are usually

necessary. Difference in the ratings of the switches used is also a major drawback of the

existing topologies.

So a new multilevel inverter topology named reversing voltage

topology is used in this project to reduce the number of componentscompared to

conventional topologies. It is also moreefficient since the inverter has a component

whichoperates the switching power devices at line frequency.Therefore, there is no need

for all switches to workin high frequency which leads to simpler and morereliable control

of the inverter. In this topology 7 leveloutput voltage is produced.

1.3 OBJECTIVES

The main objective of the project is to design and implement a new multilevel

inverter with reverse voltage topology.

To reduce the number of switching devices.

To reduce the total harmonic distortion of the output waveform.

To obtain a 7 level output waveform with approximates a sine wave.



CHAPTER 2

LITERATURE SURVEY

2.1 LITERATURE SURVEY

Several topologies of multi-level inverter system have

beenintroduced in the recent past [2]. The main topologies arediode clamped inverter

system [3], flying capacitor invertersystem and Cascaded H-bridge inverter system ,

[8]in order to generate a high voltage waveform using lowvoltage devices. Each of these

topologies has a differentmechanism for providing the required voltage levels. But

thenumber of main switches of each topology is equal.Comparing with respect to the

other components, for instance,DC-link capacitors having the same capacity per unit,

diodeclamped inverter has the least number of capacitors among thevarious multi-level

inverter system topologies but requiresadditional clamping diodes. Flying capacitor

inverters havethe largest number of capacitors required but need noclamping diode. H

bridge inverters require isolated voltagesources but need no clamping diodes.

Recent research has involved the introduction of novel converter

topologies andunique modulation strategies. However, the most recently usedinverter

topologies, which are mainly addressed as applicablemultilevel inverters, are cascade

converter, neutral-pointclamped(NPC) inverter, and flying capacitor inverter. There are

also some combinations of the mentioned topologies asseries combination of a two-level

converter with a three-levelNPC converter which is named cascade 3/2 multilevel

inverter. There is also a series combination of a three-level cascadeconverter with a five-

level NPC converter which is namedcascade 5/3 multilevel inverter .

Some new approaches have been recently suggested such as the

topology utilizing low-switching-frequency high-powerdevices . Although the topology

has some modification toreduce output voltage distortion, the general disadvantage of

this method is that it has significant low-order current harmonics.



It is also unable to exactly manipulate the magnitudeof output voltage due to an adopted

pulsewidth modulation.

There is also another topology which requires more switchesthan the

proposed topology for the same number of levels .Some of the proposed topologies suffer

from complexities ofcapacitor balancing . In, the capacitor values usedin the topology are

proportional to the load current, and as theload current increases, a larger capacitor

should be selected.In, the capacitor voltage will affect the output voltage

whenmodulation index reaches near its extreme values, i.e., zeroor one. [3]

The proposed topology in this project is an overview of a new multilevel

invertertopology named reversing voltage (RV). This topology requiresless number of

components compared to conventional topologies.It is also more efficient since the

inverter has a componentwhich operates the switching power devices at line

frequency.Therefore, there is no need for all switches to work in highfrequency which

leads to simpler and more reliable control ofthe inverter. [1]



CHAPTER 3

CIRCUIT DESCRIPTION

3.1 INTRODUCTION

In conventional multilevel inverters, the power semiconductor

switches are combined to produce a high-frequency waveformin positive and negative

polarities. However, there is noneed to utilize all the switches for generating bipolar

levels.This idea has been put into practice by the new topology.This topology is a hybrid

multilevel topology which separatesthe output voltage into two parts. One part is

namedlevel generation part and is responsible for level generating inpositive polarity.

This part requires high-frequency switches togenerate the required levels. The switches in

this part shouldhave high-switching-frequency capability.The other part is called polarity

generation part and isresponsible for generating the polarity of the output voltage,which

is the low-frequency part operating at line frequency.The topology combines the two

parts (high frequency andlow frequency) to generate the multilevel voltage output.

Inorder to generate a complete multilevel output, the positivelevels are generated by the

high-frequency part (level generation),and then, this part is fed to a full-bridge inverter

(polaritygeneration), which will generate the required polarity for theoutput. This will

eliminate many of the semiconductor switcheswhich were responsible to generate the

output voltage levels inpositive and negative polarities.



3.2 BLOCK DIAGRAM

Fig 3.2 Block diagram

3.2.1 DESCRIPTION OF VARIOUS BLOCKS

3.2.1.1 AC SUPPLY

The circuit uses standard power supply comprising of a step-down

transformer from 230Vto 12V and 4 diodes forming a bridge rectifier that delivers

pulsating dc which is then filtered by an electrolytic capacitor of about 470μF to 1000Μf.

3.2.1.2 RECTIFIER

A rectifier is an electrical device that converts alternating current (AC),

which periodically reverses direction, to direct current (DC), current that flows in only

one direction, a process known as rectification. Rectifiers have many uses including as

components of power supplies and as detectors of radio signals. Rectifiers may be made

of solid state diodes, vacuum tube diodes, mercury arc valves, and other components.



The output from the transformer is fed to the rectifier. It converts A.C. into pulsating

D.C.

Fig 3.2.1.2 Bridge rectifier

3.2.1.3 FILTER

Fig 3.2.1.3 Capacitor filter

Capacitive filter is used in this project. It removes the ripples from the

output of rectifier and smoothens the D.C. Output received from this filter is constant



until the mains voltage and load is maintained constant. However, if either of the two is

varied, D.C. voltage received at this point changes. Therefore a regulator is applied at its

output .

3.2.1.4 MULTILEVEL INVERTER

This is the main part of the proposed system. It consists of ten high power

switches, which can be operated both in high frequency and low frequency regions. The

switches used here are MOSFETs which have fast switching characteristics. Among the

ten switches six of them take part in level generation process while other four will work

as the polarity generation process. The desired 7 levels are generated from the level

generation part and they are fed into the polarity generation part to reverse its polarity if

needed.

3.2.1.5 PIC MICROCONTROLLER

Fig 3.2.1.5 PIC16F877A Microcontroller

PIC stands for Peripheral Interface Controller

given by Microchip Technology to identify itssingle-chip

microcontrollers. These devices have been very successful in 8-bit

microcontrollers



Fig 3.2.1.5.1 pin out

PIC 16F877A Specification: PIC16F877 is a 40 pin microcontroller. It has 5 ports port A,

port B,

port C, port D, port E. All the pins of the ports are for interfacing input output devices.

Port A: It consists of 6 pins from A0 to A5

Port B: It consists of 8 pins from B0 to B7

Port C: It consists of 8 pins from C0 to C7

Port D: It consists of 8 pins from D0 to D7

Port E: It consists of 3 pins from E0 to E2



The rest of the pins are mandatory pins these should not be used to connect input/output

devices.

Pin 1 is MCLR (master clear pin) pin also referred as reset pin.

Pin 13, 14 are used for crystal oscillator to connect to generate a frequency of about

20MHz.

Pin 11, 12 and31, 32 are used for voltage supply Vdd(+)and Vss (-).

3.2.1.6 DRIVER CIRCUIT

It is used to provide 9 to 20 volts to switch the MOSFET

Switches of the inverter. Driver amplifies the voltage from microcontroller which

is 5volts. Also it has an opto coupler for isolating purpose. So damage to

MOSFET is prevented. The driver circuit forms the most important part of the

hardware unit because it acts as the backbone of the inverter because it gives the

triggering pulse to the switches in the proper sequence. The diagram given above gives

the circuit operation of the driver unit.

Fig 3.2.1.6 Driver circuit

+

1000uF/25V

12

1K

D22

LED

IN4007

IC

TLP250

1

2

3

4 5

6

7

8

560E100E

220E

2N2222

31

2

FR 10712

18V ZENER

12

G

0.1uF

12

CK100

31

2

12

GND

Pulse

1K

LED

SW112

S

(230-12)V

V1



3.2.1.7 CRO

Fig 3.2.1.7 CRO

The cathode ray oscilloscope is an instrument which we use in laboratory

to display measure and analyze various waveforms of various electrical and electronic

circuits. In this project the output waveform of seven level is obtained on the CRO.

3.2.1.8 WORKING

The single phase Ac supply is given to a step down transformer and

therefore 230 V is step down to 12V ac. These are then fed into a bridge rectifier and

filter circuit so that a 12V dc supply is obtained at its output. Another step down

transformer of 230/12v is placed for providing supply for the driver circuit. The driver

circuit will amplifies the voltage from microcontroller which is 5 V. The microcontroller

is supplied by using a 230/9V step down transformer .Since microcontroller works on 5V

supply a 7805 voltage regulator is used to power the controller.



3.3 CIRCUIT DIAGRAM

Fig 3.3 Circuit diagram

3.3.1 CIRCUIT GENERAL DESCRIPTION

This is a hybrid multilevel topology which separatesthe output voltage

into two parts. One part is named level generation part and is responsible for level

generating in positive polarity. This part requires high-frequency switches to generate the

required levels. The switches in this part should have high-switching-frequency

capability. The other part is called polarity generation part and is responsible for

generating the polarity of the output voltage, which is the low-frequency part operating at

line frequency. The proposed system combines the two parts (high frequency and low

frequency) to generate the multilevel voltage output.



In order to generate a complete multilevel output, the positive levels are

generated by the high-frequency part (level generation), and then, this part is fed to a full-

bridge inverter (polarity generation), which will generate the required polarity for the

output. This will eliminate many of the semiconductor switches which were responsible

to generate the output voltage levels in positive and negative polarities.

3.3.2 SWITCHING SEQUENCE

In Table I, the numbers show the switch according to Fig.3.3 should be

turned on to generate the required voltage level. According to the table, there are six

possible switching patterns to control the inverter. It shows the great redundancy of the

topology. However, as the dc sources are externally adjustable sources (dc power

supplies), there is no need for voltage balancing for this work. In order to avoid unwanted

voltage levels during switching cycles, the switching modes should be selected so that the

switching transitions become minimal during each mode transfer. This will also help to

decrease switching power dissipation. According to fig.1 the aforementioned suggestions,

the sequences of switches (2–3-4), (2-3-5), (2-6-5), and (1, 5) are chosen for levels 0 up

to 3, respectively. These sequences are shown in Fig. 3. As can be observed from Fig.

3.3.2, the output voltage levels are generated in this part by appropriate switching

sequences. The ultimate output voltage level is the sum of voltage sources, which are

included in the current path that is marked in bold. In order to produce seven levels .

Table 1Switching sequences for each level



Fig 3.3.2 Switching sequence for different level generation

The step form of seven levels of the output waveform is obtained by the

equation 2(N+1) where N is the number of dc sources. So by increasing the number of

sources the level can also be increased. Here three dc sources of 5 V is used in the circuit.

Fig 3.3.2 indicates that for generating the 0 level output only the switches 2,3,5 are turned

on and in the polarity generation part the switches 7 and 10 will be in the on position. For

obtaining the 5 v output level one of the dc source is active in the circuit and the

switches 2,3,5,7,10will be in the ON position.



For obtaining 10V output step level two of the dc sources will be active and

the switches 2,6,5,8 and 9 will be active. For generating the 15 V level three of the dc

sources will adds up its voltage and the switches 1,5 ,7 and 10 will be active and

therefore desired output level is generated .Similarly for generating the negative polarity

output voltage levels the switches 8 and 9 will be ON in the polarity generation part of

the circuit .

Fig 3.3.2.1 gate signals for level generation

The ON and OFF period of the switches are controlled by generating pulse

signals by PWM technique.Fig 3.3.2.1 shows how the delay time and on period are

calculated. Here there are 12 states for completing one cycle of the wave. So the total

time required for completion one cycle is equal to .02s. So for one switch the time period

is .02/12 which is equal to .00166s.there for the ON percentage is calculated by

(.0016/.02)*100 which is equal to.8333%.



3.3.3 LIST OF COMPONENTS

The following are the components used in the circuit,

3.3.3.1 INVERTER CIRCUIT DIAGRAM

Bridge rectifier-5Amps

MOSFET IRF840

2 pin PTP

3.3.3.2 CONTROLLERS

PIC16F877A

AC socket

Bridge rectifier 1 amps

Capacitor 470microfrad/25v

Voltage regulator LM7805

LED resistor 330 ohm

Reset switch

Resistor 100 ohm

3.3.3.3 DRIVER BOARD

Diode IN4007

Capacitor 1000microfrad/25v

Transistor(PNP) CK100

Transitor(NPN) IN2222

Resistor 100 ohm

Resisitor 1 k

IC opto coupler MCT2E

Buffer Ic wCD4050



Zener diode

3.3.4 DECRIPTION OF COMPONENTS

3.3.4.1 MOSFET IRF840

This N-Channel enhancement mode silicon gate power field effect

transistor is an advanced power MOSFET designed, tested, and guaranteed to withstand a

specified level of energy in the breakdown avalanche mode of operation. All of these

power MOSFETs are designed for applications such as switching regulators, switching

converters, motor drivers, relay drivers, and drivers for high power bipolar switching

transistors requiring high speed and low gate drive power. These types can be operated

directly from integrated circuits.

3.3.4. 2 LM7805

FIG 3.3.4.2 LM7805

This series of fixed – voltage integrated-circuit voltage regulators are

designed for a wide range of applications .This applications include on-card regulation

for elimination of noise and distribution problems associated with single point

regulation .Each of these regulators can deliver upto 1.5A of output current.



The internal current-limiting and thermal shutdown features of these

regulators essentially make them immune to overload. In addition to use asfixed –

voltage regulators ,these devices can be used with external component to obtain

adjustable output voltages and currents, and also can be used as the power- pass

element in precision regulators.

3.3.4.3 OPTOCOUPLER

Optocoupler is also termed as optoisolator. Optoisolator a device

which contains a optical emitter, such as an LED, neon bulb, or incandescent bulb, and an

optical receiving element, such as a resistor that changes resistance with variations in

light intensity, or a transistor, diode, or other device that conducts differently when in the

presence of light. These devices are used to isolate the control voltage from the

controlled circuit.

3.3.4.4 BUFFER IC CD4050

The CD4049UBC and CD4050BC hex buffers are monolithic

complementary MOS (CMOS) integrated circuits constructed with N- and P-channel

enhancement mode transistors. These devices feature logic level conversion using only

one supply voltage (VDD). The input signal high level (VIH) can exceed the VDD

supply voltage when these devices are used for logic level conversions. These devices are

intended for use as hex buffers, CMOS to DTL/ TTL converters, or as CMOS current

drivers, and at VDD =5.0V, they can drive directly two DTL/TTL loads over the full

operating temperature range.



3.3.4.5 IN4007

Diodes are used to convert AC into DC these are used as half wave rectifier

or full wave rectifier. The number and voltage capacity of some of the important diodes

available in the market are as follows: Diodes of number IN4001, IN4002, IN4003,

IN4004, IN4005, IN4006 and IN4007 have maximum reverse bias voltage capacity of

50V and maximum forward current capacity of 1 Amp.

3.3.4.6 RESISTORS

A resistor is a two-terminal electronic component designed to oppose an

electric current by producing a voltage drop between its terminals in proportion to the

current, that is, in accordance with Ohm's law: V = IR Resistors are used as part of

electrical networks and electronic circuits. They are extremely commonplace in most

electronic equipment. Practical resistors can be made of various compounds and films, as

well as resistance wire (wire made of a high resistivity.



CHAPTER 4

PROJECT PLAN

4.1 OUTPUT FOR PROJECT

The feasibility of the proposed approach is verified using computer

simulations. A model of the seven-level inverter is constructed in MATLAB-Simulink

software. Output waveform is created, resulting in the production of the desired voltage

waveform of the multilevel inverter .The waveform of the proposed multilevel inverter

with an output voltage is 600v peak-peak of a resistive load is 100 Ω is obtained. The

resulting output voltage THD was 34.44% .

Fig 4.1 output waveform



4.2 DESIGN PROCEDURES

4.2.1 VOLTAGE REGULATOR

As we require 5v we need to use LM 7805 IC

LM 7805 IC ratings:

Input voltage : 7v-35v

Current rating : 1A

Output voltage range : V (max)=5.2v V(min)=4.8v

4.2.2 RECTIFIER CIRCUIT

IN 4007 diodes are used as it is capable of withstanding high reverse voltage.

4.2.3 FILTER CIRCUIT

Let the maximum ripple factor of capacitor input filter be 3%.

Theoretical value of r= 1/(43 f RC)

Power supply frequency f=50 Hz. Assume R=1k,

Then, C=100F, PIC used is 16F877A

4.2.4 MOSFET

IRF840 MOSFETs are used since it can withstand currents upto 8A.



4.3 TRAINING KNOWLEDGE AND SKILLS NEEDED

MATLAB (matrix laboratory) is a multi-paradigm numerical computing

environment and fourth-generation programming language. Developed by MathWorks,

MATLAB allows matrix manipulations, plotting of functions and data, implementation

of algorithms, creation of user interfaces, and interfacing with programs written in other

languages, including C, C++, Java, Fortran and Python. Although MATLAB is intended

primarily for numerical computing, an optional toolbox uses the MuPADsymbolic

engine, allowing access to symbolic computing capabilities. An additional package,

Simulink, adds graphical multi-domain simulation and Model-Based Design for dynamic

and embedded systems.

4.4 SCHEDULE OF THE PROJECT

SL NO: SCHEDULE OF WORK MONTH

1 Project selection August

2 Design of circuit August

3 Basic introduction to MATLAB August - September

4 Simulation September - October

5 Further improvements in circuit design December-January

6 Hardware implementation February Table 1 Schedule of the project



4.5 PROTOTYPE COST

SL

NO

COMPONENT NAME

COST(in Rs)

INVERTER CIRCUIT DIAGRAM

1 P2 pin PTP-1 connector 4

2 Bridge rectifier-5Amps 98

3 MOSFET IRF840 26

4 2 pin PTP 4

CONTROLLERS

5 PIC16F877A 250

6 AC socket 40

7 Bridge rectifier 1 A 52

8 Capacitor 479 micro farad/25V 5

9 Voltage regulator LM7805 35

10 LED resistor 330 ohms 2

11 Reset switch 2

12 Resistor 100 ohms 2

DRIVER BOARD

13 Diode IN4007 4

14 Capacitor 5

15 Transistor (NPN) IN2222 5

16 Resistor 100 ohm 2

17 Resistor 1k 2

18 IC MCT2E 34

19 Buffer IC WCD4050 65

20 Zener diode 7

21 PCB layout board for PIC microcontroller 750

22 PCB layout board for driver board 870

23 Transformer 230/12V 220



24 General purpose soldering board 50

TOTAL 2534

Table 2 prototype cost



CHAPTER 5

CURRENT STATUS OF THE PROJECT

5.1 CURRENT STATUS OF THE PROJECT

The feasibility of the proposed approach is verified using computer

simulations. A model of the seven-level inverter is constructed in MATLAB-Simulink

software. Output waveform is created, resulting in the production of the desired voltage

waveform of the multilevel inverter.

Simulation completed

Designed Multilevel inverter



CHAPTER 6

APPLICATIONS

1. DC power source utilization

An inverter converts the DC electricity from sources such as batteries or

fuel cells to AC electricity.

2. Uninterrupted powers source utilization

An uninterruptible power supply (UPS) uses batteries and an inverter to

supply AC power when main power is not available. When main power is restored, a

rectifier supplies DC power to recharge the batteries.

3. Electric motor speed control

Inverter circuits designed to produce a variable output voltage range are

often used within motor speed controllers. The DC power for the inverter section can be

derived from a normal AC wall outlet or some other source. Control and feedback

circuitry is used to adjust the final output of the inverter section which will ultimately

determine the speed of the motor operating under its mechanical load.

4. Power grid

Grid-tied inverters are designed to feed into the electric power distribution

system. They transfer synchronously with the line and have as little harmonic content as

possible. They also need a means of detecting the presence of utility power for safety

reasons, so as not to continue to dangerously feed power to the grid during a power

outage.



5. Solar

A solar inverter is a balance of system (BOS) component of a

photovoltaic system and can be used for both, grid-connected and off-grid systems. Solar

inverters have special functions adapted for use with photovoltaic arrays, including

maximum power point tracking and anti-islanding protection.

6. HVDC

With HVDC power transmission, AC power is rectified and high voltage

DC power is transmitted to another location. At the receiving location, an inverter in a

static inverter plant converts the power back to AC. The inverter must be synchronized

with grid frequency and phase and minimize harmonic generation.



CHAPTER 7

CONCLUSION

In this project, a new inverter topology has been proposed which has

superior features over conventional topologies in terms of the required power switches

and isolated dc supplies, control requirements, cost, and reliability. It is shown that this

topology can be a good candidate for converters used in power applications such as

FACTS, HVDC, PV systems, UPS, etc. In the mentioned topology, the switching

operation is separated into high- and low-frequency parts. This will add up to the

efficiency of the converter as well as reducing the size and cost of the final prototype. In

this phase of the project the feasibility of the prototype model has been designed using

MATLAB and the desired output level of seven levels for a resistive load of 100 ohms

is obtained.



CHAPTER 8

REFERENCES

[1] EhsanNajafi, Member, IEEE, and Abdul Halim Mohamed Yatim, Senior Member,

IEEE,“Design and Implementation of a New Multilevel Inverter Topology”, IEEE

TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 11, NOVEMBER

2012.

[2] K. Jang-Hwan, S.-K. Sul, and P. N. Enjeti, “A carrier-based PWMmethod with

optimal switching sequence for a multilevel four-leg voltagesource inverter,” IEEE

TRANS. IND. APPL., VOL. 44, NO. 4, PP. 1239–1248,JUL./AUG. 2008.

[3] X. Yun, Y. Zou, X. Liu, and Y. He, “A novel composite cascade multilevel

converter,” IN PROC. 33RD IEEE IECON, 2007, PP. 1799–1804.

Documents

Final Report (3) (1) PDF