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INTRODUCTION TO INVERTERS

1.1 Inverters

Inverters are power electronic circuits that convert a direct current into an

alternative current power of desired magnitude and frequency. The inverters find their

application in modern ac motor and uninterruptible power supplies.

1.2 Classification of Inverters

1. Based on the source used

Voltage source inverter

Current source inverter

2. Based on switching methods

Pulse width modulation inverters

Square wave inverters

3. Based on switching devices used

Transistorized inverter

Thyristorized inverter

4. Based on the inversion principle

Resonant inverter

Non- Resonant inverter

1.3 Pulse Generator

The main controlling unit of the proposed system is the pulse generator. In

practice, a microcontroller (or) a Digital Signal Processor (DSP) will be used for this

purpose.

A microcontroller consists of a powerful CPU tightly coupled with memory 1

[RAM,ROM or EPROM],various I/O features such as serial ports, parallel ports

,timer/counters, interrupt controller ,data requisition interface , Analog to digital

converter[ADC],digital to analog converter, everything integrated into a single silicon

chip. It does not mean that any microcontroller should have all the above said features on

a single chip, depending on the need and area of application for which it is designed, the

on chip features present in it may or may not include all the individual section said above.

Any microcomputer systems requires memory to store a sequence of instructions

making up a program ,parallel port or serial port for communicating with an external

system timer/counter for control purpose like generating time delay. Similarly, a DSP

consists of memory [RAM,ROM or EPROM],various I/O features such as serial ports,

parallel ports ,timer/counters, interrupt controller ,data requisition interface , Analog to

digital converter[ADC],digital to analog converter, everything integrated into a single

silicon chip. The unique feature of DSP is its speed which makes it suitable for many

applications.

1.4 Semiconductor Devices

The power semiconductor device act as switching device in the power electronic

converters. In general, the characteristics of the device are utilized in such a way that it

acts as a short circuit when closed. In addition to, an ideal switch also consumes less

power to switch from one state to other. Semiconductor is defined as the material whose

conductivity depends on the energy (light, heat, etc.,) falling on it. They don’t conduct at

absolute zero temperature. But, as the temperature increases, the current conducted by the

semiconductor increases as it gets energy in the form of heat. The increase in current is

proportional to the temperature rise. Semiconductor switches are diodes, SCR, MOSFET,

IGBT, BJT, TRIAC etc.

1.4.1 Classification of Semiconductor Devices

1. Based on controllability

Un-controlled switching device

Semi controlled switching device

Fully controlled switching device

2. Based on control modes

2

Current controlled devices (SCR ,BJT)

Voltage controlled device (MOSFET ,IGBT)

3. Based on current direction

Unidirectional device (SCR,MOSFET ,IGBT)

Bidirectional device (TRIAC)

1.5 Advantages of Inverters

Small leakage current during off stage.

Low voltage drop during ON stage.

Faster turn ON and turn OFF.

Small control power to switch from one state to other.

High forward current and blocking voltage capabilities.

High dv/dt and di/dt ratings.

1.5.1 Applications of Inverters

Adjustable Speed AC Drives.

UPS.

Static VAR Compensators.

Active filters.

Flexible AC Transmission System

In all vehicle for lightning.

Now also used for driving electric vehicle.

1.6 MOSFET

The component that is used as the switch in the inverter unit is the

MOSFET which is a voltage controlled device. They are the power semiconductor

devices that have a fast switching property with a simple drive requirement.

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Fig 1.1 MOSFET symbol

Vdss= 500 V

Rds (on) = 0.27 ohm

Id= 20 A

This MOSFET provides the designer with the best combination of fast switching, rugged

device design, low on-resistance and cost-effectiveness. This package is preferred for

commercial and industrial applications where higher power levels are to be handled.

1.6.1. MOSFET Operating Principle

1.6.1.1 Construction

N Channel depletion type N Channel enhancement type

S G D S G D

1.6.1.2 N Channel Depletion:

The N channel depletion type of MOSFET is constructed with p -Substrate. it has

two n doped regions , which forms the drain and source. It has sio2 insulating layer

Metal contacts

Sio2 layer

Channel Substrate

Metal contact

Sio2 layer

No Channel Substrate

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between the channel and the metal layer. Thus it has three terminals namely drain source

and gate.

When negative voltage applied between the gate and source (VGS), the positive

charge induced in the channel and the channel is depleted of electrons. Thus there is no

flow of current through this terminal.

When appositive voltage is applied between the gate and source, more electros are

induced in the channel by capacitor action. So there is a flow of current from drain to

source. As the gate source voltage increases, the channel gets wider by accumulation of

more negative charges and resistance to the channel decreases. Thus more current flows

from drain to source. As there is a current flow through device for zero Gate Source

Voltage, it is called as normally ON MOSFET.

1.6.1.3 N Channel Enhancement

The N channel enhancement MOSFET is similar to the depletion type in the

construction except that there is no physical existence of the channel when it is unbiased.

When the positive voltage is applied between the gate and the source, the electron

get accumulated in the channel by capacitive induction in the channel formed out of

electrons allowing the flow of current. This channel gets widened as more positive

voltage is applied between gate and source. There will not be any condition through the

device if the gate source voltage is negative.

Setting “VGS” to a constant value, varying VDS and nothing the corresponding

changes into give the drain characteristic. VGS ≤0, the device does not conduct drain

current and the device is considered to be in the off state. In this state, the entire voltage

gets drop across the device i.e., between drain and source.

In the ON state of the device, gate source voltage is positive and the drain current

is increased with the increase in the gate source voltage. It is understood clearly in the

transfer characteristics.

As the enhancement type MOSFET conduct only after applying positive gate

voltage, it is also called as normally OFF MOSFET. For this reason it becomes easily

controllable and is used in power electronics as a switch.5

VOLTAGE SOURCE INVERTERS

2.1 Introduction to Voltage Source Inverters (VSI)

Voltage Source Inverter (VSI), as the name indicates, receive DC voltage at one

side and convert it to AC voltage on the other side. The AC voltage and frequency may be

variable (or) constant depending on the application. A VSI should have stiff voltage

source at the input, that is, its Thevenin impedance should be ideally zero. A large

capacitor can be connected at the input if the source is not stiff. The DC voltage may be

fixed (or) variable, and may be obtained from a utility line (or) rotating AC machine

through a rectifier and filter. It can also be obtained from a battery, fuel cell, (or) solar

photovoltaic array. The block diagram of various VSIs is shown below:

Fig. 2.1: Block diagram of a VSI

2.1.1 Applications of Voltage Source Inverters

AC Motor Drives

AC Uninterruptable Power Supplies (UPS)

Induction Heating

AC Power Supply from Battery, Photovoltaic Array (or) Fuel Cell

Static VAR Generator (SVG) (or) Static VAR Compensator (SVC)

Active Harmonic Filter (AHF)

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2.1.2 Types of Voltage Source Inverters

1. Based on Type of Output Voltage

Single Phase VSI

Three Phase VSI

2. Based on Shape of Output Voltage

Square Wave VSI

Sine Wave VSI

PWM Wave VSI

Stepped Wave VSI

Quasi Square Wave VSI

2.2 Single Phase VSI

2.2.1 Types of Single Phase VSI

Based on Circuit Configuration

Half-Bridge Inverter

Full-Bridge Inverter

2.2.2 Half-Bridge Inverter

One of the simplest possible inverter configurations is the single-phase, half-

bridge inverter as shown in the figure below:

Fig 2.2: (a) Half-Bridge Inverter Circuit (b) Output Voltage and Current Waveforms

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The circuit consists of a pair of power semiconductor devices Q1 and Q2 connected

across the DC supply, and the load is connected point “a” and the center point of a split-

capacitor power supply. The Snubber across the device is omitted for simplicity. The

devices Q1 and Q2 are closed for 180° angle to generate the square-wave output as shown

above. In fact, a shot gap, or lock-out time (td), is maintained, as indicated, to prevent any

short circuit or “shoot-through” fault due to turn-off switching delay. The load is usually

inductive and assuming perfect filtering, the sinusoidal load current will lag the

fundamental voltage by angle “Φ” as shown above.

2.2.3 Full-Bridge (or) H-Bridge Inverter

Two half-bridges can be connected to construct a Full (or) H-Bridge inverter as

shown in the figure below:

Fig. 2.3: (a) Full-Bridge Inverter Circuit (b) Output Voltage and Current Waveforms

The split-capacitor supply is not needed in this case, and the load is connected

between the center points “a” and “b”. In the square-wave operation mode, the device

pairs “Q1Q3” and “Q2Q4” are switched alternatively to generate output as shown above.

The load is usually inductive and assuming perfect filtering, the sinusoidal load current

will lag the fundamental voltage by angle “Φ” as shown above. In active mode, the load

current will be carried by the “Q1Q3” or “Q2Q4” pair, whereas the feedback current will

flow through “D1D3” or “D2D4” pair. Both the diodes and IGBTs are designed to

withstand the supply voltage “Vd”.

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2.3 Three Phase VSI

The three-phase Voltage Source Inverter (VSI) is widely used in AC motor drives and

general purpose AC power supplies. The three-phase Voltage Source Inverter (VSI) is as shown

in the figure below:

Fig. 2.4: Three Phase VSI Circuit Configuration

The circuit consists of three half-bridges, which are mutually shifted by 120° angle to

generate the output three phase voltages. The voltage source for the inverter is made up from a

rectifier and the so-called dc link, composed of a capacitor, C, and inductor, L. If the ac machine

fed from the inverter operates as a motor (i.e., in the first or third quadrant), the average input

current is positive. However, the instantaneous input current, may assume negative values,

absorbed by the dc-link capacitor which, therefore, is necessary. The capacitor also serves as a

source of the high-frequency ac component, so that it is not drawn from the power system via the

rectifier. In addition, the dc link capacitor smoothes and stabilizes the voltage produced by the

rectifier. The optional dc-link inductor is less important, being introduced to provide an extra

screen for the power system from the high-frequency current drawn by the inverter.

2.4 Fourier Series Analysis of Inverter Output Voltages

The Fourier series coefficient are given by

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(2.1)

For all n, the Fourier series is given as

(2.2)

Hence,

(2.2.1)

Finally, the Fourier series of the quarter-wave symmetric parallel connected

Multilevel waveform is written as follows:

(2.3)

Where, “αk” is the switching angles, which must satisfy the following condition

(2.3.1)

Where,

“s” is the number of H-bridge cells.

“n” is odd harmonic order.

and “E” is the amplitude of dc voltages.

2.4.1 Total Harmonic Distortion (THD) Calculation

The total harmonics distortion (THD) of the output voltage waveform is

mathematically given by,

10

(2.4)

Where

“H1” is the amplitudes of the fundamental component, whose frequency is “w0”

and “Hn” is the amplitudes of the nth harmonics at frequency “nw0”

The amplitude of the fundamental and harmonic components of the quarter-wave symmetric multilevel waveform can be express as:

(2.4.1)

(2.4.2)

(2.4.3)

Therefore, output voltage THD of the presented waveform can be calculated.

Theoretically, to get exact THD, infinite harmonics need to be calculated. However, it is

not possible in practice. Therefore, certain number of harmonics will be taken into

account. It relies on how precise THD is needed. Usually, n = 63 is reasonably accepted.

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2.5 Conventional Conduction Modes of Three Phase VSI

A three-phase VSI can be operated conventionally in two modes of operation.

They are:

180 Degree Conduction Mode

120 Degree Conduction Mode

2.5.1 180 Degree Conduction Mode

This is the most common type of transistors firing, in which, one transistor, per

inverter leg, conducts for 180°. So, three transistors remain on at any instant of time. For

phase "a", when transistors T1 is switched on, phase "a" is connected to the positive

terminal of the dc input voltage, + V/2. When transistor T4 is switched on, phase "a" is

connected to the negative terminal of the dc source, -V/2. The same sequence occurs in the

other two phases "b" and "c". Six patterns of operation are available in the 2π-cycle,

where the interval of each pattern is 60°. The conducting transistors during each distinct

interval are shown in Table 2.1, where the rate of sequencing theses patterns specifies the

bridge output frequency.

For three-phase star-connected balanced load controlled with 180° conduction

mode, Fig. 2.4 (a-e) shows respectively, transistors gating signals, instantaneous line-to-

center and line-to-line quasi-square output voltage waveforms, neutral point voltage, and

line-to-neutral (phase) output voltages. The gating signals are shifted from each other by

60° to get three-phase balanced voltages. The phase voltage waveform contains four

voltage levels of dc bus (± V/3, ±2 V/3). The six switching patterns for 180° conduction

mode is shown in the following table:

Table 2.1: 180° Conduction Mode Six Switching Patterns

Interva

lDuration Conducting Devices During Interval

1 π/3 T1 T2 T3

2 π/3 T2 T3 T4

3 π/3 T3 T4 T5

4 π/3 T4 T5 T6

5 π/3 T5 T6 T1

6 π/3 T6 T1 T2

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2.5.1.1 Output Voltage Waveforms for 180° Conduction Mode

The various waveforms related to 180 degree conduction mode are shown below:

Fig. 2.5: 180° Conduction Mode (a) Gating Signals (b) Line-to-Center Voltages (c) Line-to-Line Voltages (d) Neutral Point Voltage (e) Phase Voltages

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2.5.1.2 Fourier Series of Output Voltage

The line-to-line voltage, Vab, is expressed in Fourier series, recognizing that the

even harmonics are zeros, and n is the harmonic order, as

(2.5)

The line-to-neutral voltage, Van, is expressed in Fourier series, recognizing that

the even harmonics are zeros, and n is the harmonic order, as

(2.6)

2.5.1.3 Disadvantages of 180 Degree Conduction Mode

The main drawbacks in 180° conduction mode are:

The magnitude of the nth harmonic is “1/n” of the fundamental.

Two switches across the voltage rail (e.g. T1 and T4) may conduct

simultaneously, causing short circuit on the dc bus. This is due to the absence of

any time-delay between the on-switching signal edge of transistor T4 and the off-

switching signal edge of transistor T1.

The poor voltage and current qualities obtained, especially in line-to-line voltage,

dictates the requirement of large filters to be inserted between the converter and

the motor. These values can be decreased by increasing switching frequency, but

switching losses increase.

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2.5.2 120 Degree Conduction Mode

In this mode of operation, each switch conducts for 120°. As a result, at any

instant, only two switches conduct. Table 2.2 and Fig. 2.5 (a-e) show the available six-

conduction patterns, and output voltage waveforms, respectively. In the first interval

(number 1), both of T1 and T2 transistors are conducting. So, phase "a" voltage is picked

up to + V/2, where phase "c" voltage is picked up to - V/2. Unlike the 180° conduction

mode, during this period, the third phase "b" is open, i.e. it is a floating point. The phase

voltage waveform contains three voltage levels, which are; 0, ± Vd/2.

For three-phase star-connected balanced load controlled with 180° conduction

mode, Fig. 2.4 (a-e) shows respectively, transistors' gating signals, instantaneous line-to-

center and line-to-line quasi-square output voltage waveforms, neutral point voltage, and

line-to-neutral (phase) output voltages. The gating signals are shifted from each other by

60° to get three-phase balanced voltages. The phase voltage waveform contains four

voltage levels of dc bus (0, ± Vd/2). The six switching patterns for 180° conduction mode

is shown in the following table.


Interva


1 π/3 T1 T2

2 π/3 T2 T3

3 π/3 T3 T4

4 π/3 T4 T5

5 π/3 T5 T6

6 π/3 T6 T1

The main advantage of this mode is the existence of a 60° dead-time between two

series switches conducting (e.g. T1 turning-off edge, and T4 turning-on edge), thereby, a

safety margin, against simultaneous conduction of the two series devices across the dc

supply, is provided. Unfortunately, this safety margin is obtained at the expense of lower

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devices utilization, since each transistor conducts only for 1200. The output voltages

comprise same harmonic contents given by n=6 r±1. This mode is rarely used in industry.

2.5.2.1 Output Voltage Waveforms for 120° Conduction Mode:

The various waveforms related to 120 degree conduction mode are shown below:


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2.5.2.2 Fourier Series of Output Voltage

The line-to-line voltage, Vab, is expressed in Fourier series, recognizing that the

even harmonics are zeros, and n is the harmonic order, as

(2.7)

The line-to-neutral voltage, Van, is expressed in Fourier series, recognizing that

the even harmonics are zeros, and n is the harmonic order, as

(2.8)

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150° CONDUCTION MODE OF THREE PHASE VSI

3.1 Introduction to 150° Conduction Mode

In this conduction mode of operation, each switch conducts for 150°. Hence,

twelve switching patterns are required per cycle, with each pattern of duration 30°. Three

transistors conduct in one interval, while only two transistors conduct in the next one, as

in 180° and 120°, respectively. Due to this switching pattern, the output phase voltages

will have seven levels of DC bus voltage (0, ±V/2, ±V/3, ±2V/3) and the line voltages

will have five levels of DC bus voltage (0, ±V/2, ±V).

3.2 Switching Pattern for 150° Conduction Mode

There are twelve switching patterns that are required per cycle in 150° conduction mode.

The duration of each switching pattern is 30°. The switching pattern is shown in the

following table:


Interva


1 π/6 T1 T2 T3

2 π/6 T2 T3

3 π/6 T2 T3 T4

4 π/6 T3 T4

5 π/6 T3 T4 T5

6 π/6 T4 T5

7 π/6 T4 T5 T6

8 π/6 T5 T6

9 π/6 T5 T6 T1

10 π/6 T6 T1

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11 π/6 T6 T1 T2

12 π/6 T1 T2

3.3 Gating Pulses and Output Voltage Waveforms

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3.4 Fourier Analysis of Output Voltage Waveform

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The Fourier series coefficient are given by

(3.1)

For all n, the Fourier series is given as

(3.2)

Hence,

(3.3)

Finally, the Fourier series of the quarter-wave symmetric parallel connected

Multilevel waveform is written as follows:

(3.4)

Where, “αk” is the switching angles, which must satisfy the following condition

(3.5)

Where,

“s” is the number of H-bridge cells.

“n” is odd harmonic order.

and “E” is the amplitude of dc voltages.

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By applying Equations (3.1), (3.2), (3.3), (3.4) and (3.5) to the output voltage waveform, the expression for line-to-neutral voltage is given by,

(3.6)

3.4 Advantages of 150° Conduction Mode

The 150° conduction mode has the following advantages:

Increases the RMS values of output voltages, compared to 120° mode, to almost

those obtained by 180° mode (Table 6).

Provides a 300 safety margin period, which is large enough, to avoid short circuit

on dc supply.

Produces seven level phase-voltage waveforms, (0, ±V/3, ± V/2, ±2V/3),

compared to only four or three levels in 180° and 120° modes, respectively.

Highly reduces the THD and DF of output voltage wave shapes, by presenting 12-

step waveforms, which are closer to the sinusoidal waveform compared to the

original 6-step ones.

Almost eliminates the low order harmonics that has “1/n” of fundamental

magnitude in previous modes, by improving the “l/n” undesired magnitude

relation.

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SIMULATION OF 150° CONDUCTION MODE OF VSI USING MATLAB/SIMULINK

4.1 INTRODUCTION TO SIMULATION

Simulation is an effective tool by which we can experience the practical results

through the software. There are number of simulation software available and the most

efficient tool is the MATLAB. There are number ways in which MATLAB software can

be used for simulation of electrical circuits. We employ the Simulink part of the

MATLAB for the simulation of three-phase VSI operating in 150° conduction mode.

4.2 What Is MATLAB?

MATLAB is a high-performance language for technical computing. It integrates

computation, visualization, and programming in an easy-to-use environment where

problems and solutions are expressed in familiar mathematical notation. Typical uses

include

• Math and computation

• Algorithm development

• Data acquisition

• Modeling, simulation, and prototyping

• Data analysis, exploration, and visualization

• Scientific and engineering graphics

• Application development, including graphical user interface building

MATLAB is an interactive system whose basic data element is an array that does

not require dimensioning. This allows you to solve many technical computing problems,

especially those with matrix and vector formulations, in a fraction of the time it would

take to write a program in a scalar non-interactive language such as C or FORTRAN. The

name MATLAB stands for matrix laboratory. MATLAB was originally written to

provide easy access to matrix software developed by the LINPACK and EISPACK

projects. Today, MATLAB engines incorporate the LAPACK and BLAS libraries,

embedding the state of the art in software for matrix computation. MATLAB has evolved

over a period of years with input from many users. In university environments, it is the

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standard instructional tool for introductory and advanced courses in mathematics,

engineering, and science. In industry, MATLAB is the tool of choice for high

productivity research, development, and analysis.

4.2.1 Toolboxes

MATLAB features a family of add-on application-specific solutions called toolboxes.

Very important to most users of MATLAB, toolboxes allow you to learn and apply

specialized technology. Toolboxes are comprehensive collections of MATLAB functions

(M-files) that extend the MATLAB environment to solve particular classes of problems.

Areas in which toolboxes are available include signal processing, control systems, neural

networks, fuzzy logic, wavelets, simulation, and many others.

4.2.2 The MATLAB System

The MATLAB system consists of five main parts:

Development Environment: This is the set of tools and facilities that help you use

MATLAB functions and files. Many of these tools are graphical user interfaces. It

includes the MATLAB desktop and Command Window, a command history, an editor

and debugger, and browsers for viewing help, the workspace, files, and the search path.

The MATLAB Mathematical Function Library: This is a vast collection of

computational algorithms ranging from elementary functions, like sum, sine, cosine, and

complex arithmetic, to more sophisticated functions like matrix inverse, matrix Eigen

values, Bessel functions, and Fast Fourier Transforms (FFT).

The MATLAB Language: This is a high-level matrix/array language with control flow

statements, functions, data structures, input/output, and object-oriented programming

features. It allows both “programming in the small” to rapidly create quick and dirty

throw-away programs, and “programming in the large” to create large and complex

application programs.

Graphics: MATLAB has extensive facilities for displaying vectors and matrices as

graphs, as well as annotating and printing these graphs. It includes high-level functions

for two-dimensional and three-dimensional data visualization, image processing,

animation, and presentation graphics. It also includes low-level functions that allow you

to fully customize the appearance of graphics as well as to build complete graphical user

interfaces on your MATLAB applications.

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The MATLAB Application Program Interface (API): This is a library that allows you

to write C and FORTRAN programs that interact with MATLAB. It includes facilities for

calling routines from MATLAB (dynamic linking), calling MATLAB as a computational

engine, and for reading and writing MAT-files.

4.3 What Is Simulink?

Simulink is an interactive environment for modeling, simulating, and analyzing

dynamic, multi-domain systems. It lets you build a block diagram, simulate the system’s

behavior, evaluate its performance, and refine the design. Simulink integrates seamlessly

with MATLAB, providing you with immediate access to an extensive range of analysis

and design tools. These benefits make Simulink the tool of choice for control system

design, DSP design, communications system design, and other simulation applications.

Blocksets are collections of application-specific blocks that support multiple

design areas, including electrical power-system modeling, digital signal processing, fixed-

point algorithm development, and more. These blocks can be incorporated directly into

your Simulink models.

Real-Time Workshop® is a program that generates optimized, portable, and

customizable ANSI C code from Simulink models. Generated code can run on PC

hardware, DSPs, microcontrollers on bare-board environments, and with commercial or

proprietary real-time operating systems.

4.4 Simulink Model of Three-Phase VSI with 150° Conduction Mode

The various components required for creating a MATALB/SIMULINK model of

a three phase VSI are obtained from different libraries available in SIMULINK. It is very

important to know about various libraries available in SIMULINK from which required

components can be gathered. The required components are added to a new model file.

The following table explains various components required for creating a model and the

library in which they are available.

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Table 4.1: Components Required for Simulation

S.No Component Required Library Block

1 DC Voltage Source Sim Power Systems Electrical Sources

2 MOSFET Sim Power Systems Power Electronics

3 Pulse Generator Commonly Used Blocks Sources

4 Series RLC Branch Sim Power Systems Elements

5 Voltmeter Sim Power Systems Measurements

6 Ammeter Sim Power Systems Measurements

7 Scope Commonly Used Blocks Sinks

8 Workspace Commonly Used Blocks Sinks

4.4.1 Simulink Model

Vin

v+-Vdc

Van1

simoutVan

v+-

Vab1

simout 1

Vab v+ -

S6

gm

DS

S5

gm

DS

S4

gm

DS

S3

gm

DS

S2

gm

DS

S1

gm

DS

Input and Output Voltages

Gate Pulses

G6

G5

G4

G3

G2

G1

CBA

Fig. 4.1: Simulink Model of Three-Phase VSI

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4.4.2 Parameters of Simulink Blocks

The parameters of various blocks used in the simulink model shown in figure 4.1 are

explained in the following table:

Table 4.2: Simulink Block Parameters

S.No Block Type Parameters

1 DC Voltage Source Ideal Amplitude(V) = 100

2 Pulse Generator (G1) -

Pulse Type: Time BasedTime (t): Use Simulation TimeAmplitude = 10Period (secs) = 3e-3Pulse Width (% of period) = 41.667Phase delay (secs) = 0


Pulse Type: Time BasedTime (t): Use Simulation TimeAmplitude = 10Period (secs) = 3e-3Pulse Width (% of period) = 41.667Phase delay (secs) = 0.5e-3


Pulse Type: Time BasedTime (t): Use Simulation TimeAmplitude = 10Period (secs) = 3e-3Pulse Width (% of period) = 41.667Phase delay (secs) = 1e-3




Pulse Type: Time BasedTime (t): Use Simulation TimeAmplitude = 10Period (secs) = 3e-3Pulse Width (% of period) = 41.667Phase delay (secs) = 2e-3

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S.No Block Type Parameters



8 MOSFET -

FET resistance Ron (ohms) = 0.1Internal diode inductance Lon (H) = 0Internal diode resistance Rd (ohms) = 0.01Internal diode forward voltage Vf(V) = 0Initial current Ic (A) = 0Snubber resistance Rs (ohms) = 1e5Snubber capacitance Cs (F) = inf

9 Series RLC Branch RResistance (ohms) = 10

10 Voltmeter --

11 Ammeter --

12 Scope --

13 Workspace --

4.4.3 How to run simulation?

After creating the simulink model for a three phase VSI shown in figure (4.1), set

the configuration parameters of various blocks as shown in the table (4.2). Then, select

the “Simulation” option available in the toolbar and click on “Configuration Parameters”.

Set the start time and stop time for simulation. Then, run the simulation by selecting

“Start” option available under “Simulation” in toolbar. After the simulation is completed,

click on the “Scope” to see the output waveforms.

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4.4.4 Switching Pulses Waveforms for 150° Conduction Mode

Fig. 4.2: Switching Pulse Waveforms for 150° Conduction Mode

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4.4.5 Output Voltage Waveforms for 150° Conduction Mode

Line-to-Line Voltages

Fig. 4.3: Output Line-to-Line Voltages of Three-Phase VSI in 150° Conduction Mode

(a) Vab (b) Vbc (c) Vca

30

Line –to-Neutral Voltages

Fig 4.4: Output Line-to-Neutral Voltages of Three-Phase VSI in 150° Conduction Mode

(a) Van (b) Vbn (c) Vcn

31

RESULTS AND COMPARISONS

5.1 Fourier Analysis

Fourier series is the theory behind frequency analysis of signals. Fourier is the

basic tool for representing periodic functions which play major role in many applications.

Fourier series are the infinite series designed to represent any general periodic function in

terms of simple ones, namely, cosines and sines.

Any periodic function is made up of the sum of single frequency components.

These components consist of fundamental frequency component and multiples of

fundamental frequency called the harmonics along with a bias term which represents the

average off-set from zero.

The Fourier series for a periodic function “f(t)” is given by,

The Fourier series for a periodic function “f(t)” in amplitude and phase form is given by,

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5.2 Total Harmonic Distortion (THD)

The stepped wave output voltage of an inverter when operated in various

conducting modes consists of fundamental components and several harmonic

components. The purpose of analyzing the output of an inverter is to determine the

harmonics in the output voltage waveform.

Total Harmonic Distortion (THD) is the general harmonic index that is used. THD

is a measure of harmonic content in the output voltage waveform. THD is defined as the

Root Mean Square (RMS) of the harmonics expressed as the percentage of the

fundamental component. THD is also known as Harmonic Factor (HF).Greater the value

of THD, greater the harmonic content and greater is the distortion of the output voltage.

THD is given by the formula,

The expressions for line-to-neutral voltages of various conducting modes can be

used for determining the THD. These expressions are given by,

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5.3 Comparison of THD

H.Order 180 Degree 120 Degree 150 Degree

5 20 20 1.436

7 14.285 14.285 1.026

11 9.091 9.091 9.091

13 7.692 7.692 7.692

17 5.882 5.882 0.422

19 5.263 5.263 0.378

23 4.348 4.348 4.348

25 4.000 4.000 4.000

29 3.448 3.448 0.248

31 3.225 3.225 0.232

35 2.857 2.857 2.857

37 2.703 2.703 2.703

41 2.439 2.439 0.175

43 2.325 2.325 0.167

47 2.128 2.128 2.128

49 2.041 2.041 2.041

5.4 Comparison of Various Conducting Modes

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The various conducting modes of a 3-phase six switch inverter are compared and

tabulated in the following table.

Criteria 180 Degree 120 Degree 150 Degree

Tn 6 6 6

Dn 6 6 6

LOH 5th 5th 11th

DF-LLV (%) 0.856 0.856 0.107

THD-LLV (%) 31.17 31.04 16.88

Switch Utilization 0.159 0.137 0.148

VL /Vd 0.816 0.707 0.764

Vph /Vd 0.471 0.408 0.441

THD-LL.Ct 37.64 31.86 12.85

THD-Ph.Ct 37.83 32.22 12.74

Tn – Number of Transistors

Dn - Number of Diodes

LOH – Lower Order Harmonic

DF-LLV – Distortion Factor of Line-to Line Voltage

THD-LLV – Total Harmonic Distortion of Line-to-Line Voltage

THD-LL.Ct – Total Harmonic Distortion of Line Current

THD-Ph.Ct – Total Harmonic Distortion of Phase Current

CONCLUSIONS

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This project presents a new conduction mode for the most common, simple, and

well-known three-phase six-switch Voltage Source Inverter. Each transistor conducts for

150° and so, a seven-level, 12-step output voltage waveforms, which resembles the

sinusoidal wave shape, are obtained by the inverter. Consequently, the harmonic contents

involved in both current and voltage waveforms are highly reduced, without any

additional weight, size, or cost. The number of switches and diodes remain the same in all

the conducting modes of operation. But, the utilization of each switch is more in 180°

mode of operation when compared to the 120° and 150° modes of operation.

The lower order harmonic (LOH) shifts to 11th in150° conduction mode where as

LOH is 5th in 120° and 180° modes of operation. The Total Harmonic Distortion (THD)

in line-to-line voltage, line current and phase current is more in 180° conduction mode

when compared to 120° and 150° conduction modes. The Distortion Factor (DF) in line-

to-line voltage is more in 180° conduction mode when compared to 120° and 150°

conduction modes.

The 150° mode of conduction increases the RMS values of output voltages,

compared to 120° mode, to almost those obtained by 180° mode. The 150° mode of

conduction provides a 30° safety margin period, which is large enough, to avoid short

circuit on dc supply. It produces seven level phase-voltage waveforms, (0, ±V/3, ± V/2,

±2V/3), compared to only four or three levels in 180° and 120° modes, respectively.

Highly reduces the THD and DF of output voltage wave shapes, by presenting 12-step

waveforms, which are closer to the sinusoidal waveform compared to the original 6-step

ones. The 150° mode of conduction almost eliminates the low order harmonics that has

“1/n” of the fundamental magnitude in previous modes, by improving the “1/n” undesired

magnitude relation.

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