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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.
3
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
4
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)
6
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
7
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”.
8
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
9
(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.
11
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
12
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
13
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.
14
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.
Table 2.2: 120° Conduction Mode Six Switching Patterns
Interva
lDuration Conducting Devices During Interval
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
15
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:
Fig. 2.6: 120° Conduction Mode (a) Gating Signals (b) Line-to-Center Voltages (c) Line-to-Line Voltages (d) Neutral Point Voltage (e) Phase Voltages
16
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)
17
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:
Table 3.1: 150° Conduction Mode Six Switching Patterns
Interva
lDuration Conducting Devices During Interval
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
18
11 π/6 T6 T1 T2
12 π/6 T1 T2
3.3 Gating Pulses and Output Voltage Waveforms
19
Fig. 3.1: 150° Conduction Mode (a) Gating Signals (b) Line-to-Center Voltages (c) Line-to-Line Voltages (d) Neutral Point Voltage (e) Phase Voltages
3.4 Fourier Analysis of Output Voltage Waveform
20
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.
21
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.
22
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
23
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.
24
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.
25
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
26
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
3 Pulse Generator (G2) -
Pulse Type: Time BasedTime (t): Use Simulation TimeAmplitude = 10Period (secs) = 3e-3Pulse Width (% of period) = 41.667Phase delay (secs) = 0.5e-3
4 Pulse Generator (G3) -
Pulse Type: Time BasedTime (t): Use Simulation TimeAmplitude = 10Period (secs) = 3e-3Pulse Width (% of period) = 41.667Phase delay (secs) = 1e-3
5 Pulse Generator (G4) -
Pulse Type: Time BasedTime (t): Use Simulation TimeAmplitude = 10Period (secs) = 3e-3Pulse Width (% of period) = 41.667Phase delay (secs) = 1.5e-3
6 Pulse Generator (G5) -
Pulse Type: Time BasedTime (t): Use Simulation TimeAmplitude = 10Period (secs) = 3e-3Pulse Width (% of period) = 41.667Phase delay (secs) = 2e-3
27
S.No Block Type Parameters
7 Pulse Generator (G6) -
Pulse Type: Time BasedTime (t): Use Simulation TimeAmplitude = 10Period (secs) = 3e-3Pulse Width (% of period) = 41.667Phase delay (secs) = 2.5e-3
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
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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
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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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