i SIMULATION AND DESIGN OF THREE PHASE ENERGY EFICIENT SPWM BASED VFD Supervisor Dr. Muhammad Ahmad Chaudhary Professor Submitted By Muhammad 08-EE-16 Imtiaz Hussain 08-EE-39 Muhammad Ahtisham Asif 08-EE-46 DEPARTMENT OF ELECTRICAL ENGINEERING FACULTY OF ELECTRONICS AND ELECTRICAL ENGINEERING UNIVERSITYOF ENGINEERING AND TECHNOLOGY TAXILA July 2012
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i
SIMULATION AND DESIGN OF THREE PHASE ENERGY
EFICIENT SPWM BASED VFD
Supervisor
Dr. Muhammad Ahmad Chaudhary
Professor
Submitted By
Muhammad 08-EE-16
Imtiaz Hussain 08-EE-39
Muhammad Ahtisham Asif 08-EE-46
DEPARTMENT OF ELECTRICAL ENGINEERING
FACULTY OF ELECTRONICS AND ELECTRICAL ENGINEERING
UNIVERSITYOF ENGINEERING AND TECHNOLOGY
TAXILA
July 2012
ii
SIMULATION AND DESIGN OF THREE PHASE ENERGY
EFFICIENT SPWM BASED VFD
Supervisor
Dr. Muhammad Ahmad Chaudhary
Professor
Submitted By
Muhammad 08-EE-16
Imtiaz Hussain 08-EE-39
Muhammad Ahtisham Asif 08-EE-46
A Project Report submitted in partial fulfillment of the requirements for the
award of Bachelors Degree in Electrical Engineering
DEPARTMENT OF ELECTRICAL ENGINEERING
FACULTY OF ELECTRONICS AND ELECTRICAL ENGINEERING
UNIVERSITY OF ENGINEERING AND TECHNOLOGY
TAXILA
July 2012
iii
Undertaking
We certify that project work titled “Simulation and Design of Three Phase Energy
Efficient SPWM Based VFD” is our own work. No portion of the work presented in
this project has been submitted in support of another award or qualification either at
this institution or elsewhere. Where material has been used from other sources it has
been properly acknowledged / referred.
_______________
Muhammad
08-EE-16
_______________
Imtiaz Hussain
08-EE-39
_______________
Muhammad Ahtisham Asif
08-EE-46
iv
Acknowledgements
We must express our sincere thanks to Mr. Khalid Azizi, Director at Reverse
Engineering & Product Development Rawalpindi, for his enthusiastic response,
earnest co-operation, and timeliness without which this work could not have been
possible. We offer sincerest gratitude to our supervisor, Dr. Muhammad Ahmad
Chaudhary, who extended his valuable assistance whilst allowing us the room to
work in our own way.
Finally, we are thankful to our families and friends for their continuous
encouragement and moral support.
v
Abstract
Squirrel-cage induction motors are the workhorse of industries for variable speed
applications in a wide power range that covers from fractional watt to megawatts.
However, the torque and speed control of these motors is difficult because of their
non-linear and complex structure. So, there is a need to adjust motor‟s speed in such a
way that enable closer matching of motor output to load and thus results in energy
savings. This can be achieved using variable frequency drive. The complete system
consists of an AC voltage input that is put through a diode bridge rectifier to produce
a DC output which across a shunt capacitor will, in turn, feed the PWM inverter. The
PWM inverter is controlled to produce a desired sinusoidal voltage at a particular
frequency. Simulation is carried out using OrCAD Pspice v10.5 and NI Multisim
v12.0 and in the experimental work a prototype model is built to verify the simulation
results. PIC microcontroller (PIC18f4431) is used to generate the PWM pulses to
drive the 0.5 hp 3-phase Induction Motor.
vi
Table of Contents
Undertaking _______________________________________________________ iii
Acknowledgements ________________________________________________ iv
Abstract ___________________________________________________________ v
Chapter 1 __________________________________________________________ 1
Introduction ________________________________________________________ 1
1.1 Background _____________________________________________________ 1
1.1.1 Cycloconverters ________________________________________________ 1
1.1.2 Variable Frequency Drives ________________________________________ 4
1.2 What is VFD _____________________________________________________ 5
1.3 Why VFD ________________________________________________________ 5
Chapter 2 __________________________________________________________ 7
Variable Frequency Drives __________________________________________ 7
2.1 Induction Motor __________________________________________________ 7
2.1.1 Rotating Fields _________________________________________________ 8
2.1.2 Transformer Action ______________________________________________ 9
2.1.3 Torque Generation (Motor Action) _________________________________ 10
2.1.4 Slip _________________________________________________________ 11
2.1.5 Speed _______________________________________________________ 12
2.1.6 Speed Control ________________________________________________ 12
2.1.7 Generator Action ______________________________________________ 14
2.1.8 Starting ______________________________________________________ 16
2.1.9 Power Factor _________________________________________________ 16
2.1.10 Characteristics________________________________________________ 17
2.1.11 Applications __________________________________________________ 19
2.2 Concept of Variable Frequency Drive _____________________________ 20
2.2.1 Variable Frequency Drive Fundamentals ____________________________ 21
2.2.2 V/HZ vs. Vector Drives __________________________________________ 22
2.2.3 Diode Rectification _____________________________________________ 23
2.2.4 Single-Phase Half-Wave Rectifiers ________________________________ 24
2.2.5 Single-Phase Full-Wave Rectifiers_________________________________ 25
2.2.6 Single Phase Full Wave Bridge Rectifier ____________________________ 27
2.2.7 The DC Link (And Current Distribution) _____________________________ 28
2.2.8 Inverter Section _______________________________________________ 30
2.3 Pulse Width Modulation _______________________________ 34
2.3.1 Duty Cycle ___________________________________________________ 35
2.3.2 Switching Devices for PWM generation _____________________________ 35
2.3.3 Advantages __________________________________________________ 36
2.3.4 Issues related to PWM __________________________________________ 36
2.3.5 Applications of PWM ___________________________________________ 36
vii
2.4 Sinusoidal Pulse Width Modulation _______________________________ 37
2.4.1 Modulation Index ______________________________________________ 39
2.4.2 Advantages of SPWM __________________________________________ 40
Chapter 3 _________________________________________________________ 42
Implementation of Project __________________________________________ 42
3.1 Main Parts of Drive ______________________________________________ 42
3.1.1 Power Supply _________________________________________________ 43
3.1.2 Inverter ______________________________________________________ 43
3.1.3 Control Circuit_________________________________________________ 43
3.2 Power Supply ___________________________________________________ 43
3.3 Transformer ____________________________________________________ 44
3.3.1 Main Components of a transformer ________________________________ 45
3.3.2 Transformer Designing __________________________________________ 45
3.4 Rectifier ________________________________________________________ 48
3.4.1 Full Wave Bridge Rectifier _______________________________________ 49
3.4.2 Bridge Output Voltage __________________________________________ 50
3.4.3 Peak Inverse Voltage (PIV) ______________________________________ 51
3.4.4 PIV Rating of Bridge Rectifier ____________________________________ 52
3.5 Filter ___________________________________________________________ 52
3.5.1 Working _____________________________________________________ 53
3.5.2 Capacitor Input Filter ___________________________________________ 54
3.5.3 Ripple Voltage ________________________________________________ 55
3.5.4 Ripple factor __________________________________________________ 56
3.6 Regulator _______________________________________________________ 57
3.6.1 Fixed Positive linear Voltage Regulators ____________________________ 57
3.6.2 Fixed Negative linear Voltage Regulators ___________________________ 58
3.6.3 Issues with 78XX Regulators _____________________________________ 58
3.7 Inverter _________________________________________________________ 61
3.8 IGBTs __________________________________________________________ 62
3.8.1 Basic Structure ________________________________________________ 63
3.8.2 Output Characteristics __________________________________________ 66
3.8.3 Switching Characteristics ________________________________________ 66
3.9 IR2130 __________________________________________________________ 68
3.9.1 ADVANTAGES ________________________________________________ 69
3.9.2 Applications __________________________________________________ 69
3.10 Control Section _________________________________________________ 71
3.10.1 Architecture of PIC 18f4431 _____________________________________ 71
3.11 LCD Interfacing with Micro Controller _____________________________ 74
3.12 Implementation of Project________________________________________ 75
3.12.1 Single Phase Scheme of VFD ____________________________________ 75
3.12.2 Three Phase Scheme of VFD ____________________________________ 77
3.12.3 Three Phase SPWM based VFD Using PIC 18f4431 __________________ 79
Chapter 4 _________________________________________________________ 81
viii
Simulations and Results ___________________________________________ 81
4.1 Simulation in OrCAD Pspice _____________________________________ 81
4.1.1 Issues _______________________________________________________ 82
4.2 Three Phase Inverter Circuitry ___________________________________ 84
4.2.2 Solution Proposed _____________________________________________ 85
4.2.3 PHASE 01 ___________________________________________________ 87
4.2.4 PHASE 02 (Circuit Optimization) __________________________________ 87
4.3 Issues before Hardware Implementation __________________________ 89
4.4 Three Phase Inverter Simulation using PIC18f4431 ________________ 90
4.5 Transformer Design Simulator ___________________________________ 92
Conclusion ________________________________________________________ 93
Future Recommendations __________________________________________ 94
Appendix _________________________________________________________ 95
A.1 Datasheets _____________________________________________________ 95
A.1.1 INSULATED GATE BIPOLAR TRANSISTOR WITH ULTRAFAST SOFT
RECOVERY DIODE (IRG4BC30UDPbF) ___________________________________ 95
A.1.2 PIC18F4431 _________________________________________________ 97
A.1.3 3-PHASE BRIDGE DRIVER (IR2130) _____________________________ 98
A.2 Transformer designing Tables __________________________________ 100
A.2.1 Table A _____________________________________________________ 100
A.2.2 Table B _____________________________________________________ 102
References _______________________________________________________ 104
ix
List of Figures
Chapter 1 __________________________________________________________ 1
Introduction _______________________________________________________ 1 Figure1.1 Single-phase cycloconverter______________________________________ 2
Figure 1.2 Cycloconverter waveforms_______________________________________ 3
Chapter 2 __________________________________________________________ 7
Variable Frequency Drives __________________________________________ 7 Figure 2.1 Three Phase Induction Motor____________________________________ 9
Figure 2.2 Squirrel Cage Rotor____________________________________________ 10
Figure 2.3 Torque-Speed Curve of Induction Motor____________________________ 17
Figure 2.4 Torque-Speed Curve Keeping V/f ratio constant______________________ 19
Figure 2.5 Concept of VFD_______________________________________________ 21
Figure 2.6 Half wave Rectifier_____________________________________________ 24
Figure 2.7 Current and voltage waveform of Single phase half wave rectification____ 25
Figure 2.8 Full wave rectifier with center tapped transformer_____________________ 26
Figure 2.9 Voltage and current waveform of full wave center tapped transformer____ 27
Figure 2.10 Bridge Rectifier________________________________________________ 28
Figure 2.11 Current and voltage waveforms of full wave bridge rectifier_____________ 28
Figure 2.12 DC Link_____________________________________________________ 29
Figure 2.13 Phasor Diagram of Motor Current_________________________________ 30
Figure 2.14 Inverter Switching Sequence_____________________________________ 31
Figure 2.15 Switching sequence of output transistors___________________________ 33
Figure 2.16 PWM Sine Wave Syntheses_____________________________________ 34
Figure 2.17 Duty Cycles of 75% and 50%____________________________________ 35
Figure 2.18 Comparison of reference signal with carrier signal____________________ 38
Figure 2.19 Resulting Pulses______________________________________________ 38
Figure 2.20 Comparison of three phases with triangular wave_____________________ 39
Figure 2.21 Modulation Index > 1___________________________________________ 40
Figure 2.22 Effect of Over Modulation________________________________________ 40
Chapter 3 _________________________________________________________ 42
Implementation of Project _________________________________________ 42
x
Figure 3.1 Block Diagram of Regulated Power Supply__________________________ 44
Figure 3.2 Full wave bridge rectifier________________________________________ 49
Figure 3.3 Operation of a bridge rectifier_____________________________________ 50
Figure 3.4 Bridge operation during a positive half cycle of voltages________________ 51
Figure 3.5 Peak inverse voltages across diodes during the positive half-cycle_______ 52
Figure 3.6 Full wave rectifier with filter______________________________________ 53
Figure 3.7 Power supply filtering___________________________________________ 53
Figure 3.8 Operation of a half-wave rectifier with a capacitor-input filter____________ 54
Figure 3.9 Vr and VDC determine the ripple factor______________________________ 56
Figure 3.10 Conceptual diagram of 78XX regulator_____________________________ 57
Figure 3.11 Regulator with an external pass transistor for handling currents__________ 59
Figure 3.12 Regulator with an external pass transistor and current limiting circuit______ 60
Figure 3.13 Hex bridge using IGBTs_________________________________________ 61
Figure 3.14 Structure of IGBT______________________________________________ 63
Figure 3.15 Equivalent circuit model of an IGBT________________________________ 64
Figure 3.16 Symbol of IGBT_______________________________________________ 65
Figure 3.17 Output characterisics of an IGBT__________________________________ 66
Figure 3.18 IGBT Switcing Time Test Circuit__________________________________ 67
Figure 3.19 IGBT current and voltage turn-on and turn-off waveforms_______________ 67
Figure 3.20 Pin configuration of PIC18F4431__________________________________ 71
Figure 3.21 Single Phase Scheme of Variable frequency Drive____________________ 76
Figure 3.22 Three phase scheme of variable frequency Drive_____________________ 78
Figure 3.23 Three Phase SPWM based VFD block diagram Using PIC 18f4431_______ 80
Chapter 4 _________________________________________________________ 81
Simulations and Results ___________________________________________ 81
Figure 4.1 Triangular waveform generator circuit______________________________ 81
Figure 4.2 Output of Triangular wave generator circuit__________________________ 81
Figure 4.3 Output of AND and NOT gate using OrCAD Pspice___________________ 82
Figure 4.4 Complete Single Phase inverter circuit_____________________________ 83
Figure 4.5 Simulation results of single phase inverter circuit_____________________ 84
Figure 4.6 Simulation results using OrCAD Pspice____________________________ 85
Figure 4.7 Three phase inverter circuitry_____________________________________ 86
Figure 4.8 Simulation using Multiplier Blocks_________________________________ 87
Figure 4.9 Output waveforms_____________________________________________ 88
Figure 4.10 Simulation results using PIC 18f4431______________________________ 90
Figure 4.11 3-phase schematic using 18f4431 in OrCAD Pspice___________________ 91
Figure 4.12 LabView based Transformer Design Simulator_______________________ 92
1
Chapter 1
Introduction
1.1 Background
Over the last 40 years, a revolution has occurred in the application of electric motors.
The development of solid-state motor drive packages has progressed to the point
where practically any power control problem can be solved by using them. With such
solid-state drives, it is possible to run dc motors from ac power supplies or ac motors
from de power supplies. It is even possible to change ac power at one frequency to ac
power at another frequency.
Furthermore, the costs of solid-state drive systems have decreased dramatically, while
their reliability has increased. The versatility and the relatively low cost of solid-state
controls and drives have resulted in many new applications for ac motors in which
they are doing jobs formerly done by dc machines. DC motors have also gained
flexibility from the application of solid-state drives.[1,2]
1.1.1 Cycloconverters
Before the advent of Variable frequency drives, cycloconverters were used for
converting AC power at one frequency to AC power at another frequency.
Although the details of a cyc1oconverter can become very complex, the basic idea
behind the device is simple. The input to a cyc1oconverter is a three-phase source
which consists of three voltages equal in magnitude and phase-shifted from each other
2
by 120°. The desired output voltage is some specified waveform, usually a sinusoid at
a different frequency. The cycloconverter generates its desired output waveform by
selecting the combination of the three input phases which most closely approximates
the desired output voltage at each instant of time.
To understand the operation principles of cycloconverters, let us consider single-
phase to single-phase cycloconverter (figure 1.1). This converter consists of back-to-
back connection of two full-wave rectifier circuits. Figure 1.2 shows the operating
waveforms for this converter with a resistive load.
Figure 1.1, Single-phase to single-phase cycloconverter connected to a resistive
load
The input voltage, Vs is an ac voltage at a frequency, as shown in figure 1.2(a). For
easy understanding assume that all the thyristors are fired at =0firing angle, i.e.
thyristors act like diodes. Note that the firing angles are named as P for the positive
converter and N for the negative converter.
3
Consider the operation of the cycloconverter to get one-fourth of the input frequency
at the output. For the first two cycles of Vs, the positive converter operates supplying
current to the load. It rectifies the input voltage; therefore, the load sees 4 positive half
cycles as seen in figure 1.2(b). In the next two cycles, the negative converter operates
supplying current to the load in the reverse direction. The current waveforms are not
shown in the figures because the resistive load current will have the same waveform
as the voltage but only scaled by the resistance. Note that when one of the converters
operates the other one is disabled, so that there is no current circulating between the
two rectifiers.[3,4]
Figure 1.2, Single-phase to single-phase cycloconverter waveforms
(a) Input voltage, (b) Output voltage for zero firing angle
Compared to rectifier-inverter schemes, cyc1oconverters have many more SCRs and
much more complex gating circuitry. Despite these disadvantages, cyc1oconverters
can be less expensive than rectifier inverters at higher power ratings.
4
1.1.2 Variable Frequency Drives
The first inverters were made in the 1960‟s. They had a rather limited application due
to the small size and reliability of the solid state devices of the day. When higher
power transistors became widely available in the 1980‟s, larger inverters were made
and many more applications opened up. All of these earlier devices used linear
amplifiers and controls for their basic operation. Small potentiometers and dip
switches were used to set their operating characteristics. In the 1990‟s digital controls
began to be used more and more in Inverters. Solid state devices were also developed
that allowed higher voltage and current ratings. This made it possible for inverters to
be used on larger motors. Microprocessors have also made the Inverter a much more
versatile device. In the last decade or so they have become much more flexible and
reliable. For many applications, the Inverter can be removed from a packing box,
wired to a motor, and turned on and operated without additional set up. Of course, for
some applications, additional effort is needed to program and tune a drive to the
application.[5]
The motors that are usually controlled by VFD‟s are induction motors. A three phase
induction motor is one of the simplest power conversion devices ever made. It has one
moving part. Of course, if the motor has ball bearings, and we call ball bearings
moving parts, then an induction motor with ball bearings does have more than one
moving part. In any case, they are very simple, and hence very reliable. They have a
winding on the stator, or part that stands still, and a winding on the rotor, or the part
that turns. When voltage is applied to the stator, a voltage is induced (Hence –
induction motor) in the stator coil. This causes a current to flow in both the stator and
the rotor. The design of the motor is such that the magnetic fields of the two currents
act against each other to cause a force on the rotor and make it rotate. The designers
5
of these motors have done an excellent job in making motors with a very high
efficiency and power factor. Efficiencies of over 90% and power factors of over 80%
are common at full load. Some larger motors have power factors of up to 90% when
fully loaded. However, lightly loaded AC induction motors typically have low
efficiency and low power factor.
1.2 What is VFD
Every machine consists of three parts: the prime mover, the machine system, and the
transmission system. The prime mover is the motor or engine. The transmission
system consists of gears, shafts or pulley etc. The prime mover and the transmission
system together known as drive which keeps the machine working in motion. Thus
electric drive may be defined as a form of equipment, designed to convert electric
energy input into mechanical energy output or „drive‟ is an arrangement which keeps
the working machine in motion. It also provides control to the machine.
1.3 Why VFD
The primary function of a variable frequency drive is to convert electrical power to
the usable form for controlling speed, torque and direction of rotation of AC motor.
We all know that lot of energy is wasted in fan/pump/blower applications if not
properly designed. When we use conventional motor control system, in which AC
motor is run at full speed, the flow of gases/air /liquid is regulated using the damper
/throttle control. In this process, substantial energy is lost in the damper/throttle. This
waste of energy can be as high as 25 to 30 % of motor rating. Always go for reliable
V/f, variable speed drives to control the speed of fan/pump/blower, which in turn will
6
automatically control the flow. Hence we can eliminate the need of damper/throttle.
Our pay-back period can be even less than one year.
Nowadays, electric drives are being applied in an increasing number of industries due
to following advantages over mechanical drives:
(1) It is simple in construction and has less maintenance cost.
(2) Its speed control is very easy and smooth.
(3) It can be installed at any desired convenient place this affording more
flexibility in the layout.
(4) It can be remotely controlled.
(5) Being compact it requires less space.
(6) It is neat and clean and is free from smoke or flue gases.
(7) It can be started quickly without any loss of time.
(8) It has comparatively longer life.
7
Chapter 2
Variable Frequency Drives
What is Variable Frequency Drive? To understand the answer to this question we
have to understand that the basic function of a variable frequency drive (VFD) is to
control the flow of energy from the mains to the process. Energy is supplied to the
process through the motor shaft. Two physical quantities describe the state of the
shaft: torque and speed. To control the flow of energy we must therefore, ultimately,
control these quantities.
2.1 Induction Motor
One third of the world's electricity consumption is used for running induction motors
driving pumps, fans, compressors, elevators and machinery of various types. The AC
induction motor is a common form of asynchronous motor whose operation depends
on three electromagnetic phenomena:
Motor Action - When an iron rod (or other magnetic material) is suspended in
a magnetic field so that it is free to rotate, it will align itself with the field. If
8
the magnetic field is moving or rotating, the iron rod will move with the
moving field so as to maintain alignment.
Rotating Field - A rotating magnetic field can be created from fixed stator
poles by driving each pole-pair from a different phase of the alternating
current supply.
Transformer Action - The current in the rotor windings is induced from the
current in the stator windings, avoiding the need for a direct connection from
the power source to the rotating windings.
The induction motor can be considered as an AC transformer with a rotating
secondary winding.
2.1.1 Rotating Fields
Rotating magnetic fields are created by poly-phase excitation of the stator windings.
In the example below (figure 2.1) of a 3 phase motor, as the current applied to the
winding of pole pair A (phase 1) passes its peak and begins to fall, the flux associated
with the winding also begins to weaken, but at the same time the current in the
winding of the next pole pair B (phase 2) and its associated flux is rising.
Simultaneously the current through the winding of the previous pole pair C ( phase 3)
and its associated flux will be negative and rising (towards positive). The net effect is
that a magnetic flux wave is set up as the flux created by the stator poles rotates from
one pole to the next, about the axis of the machine, at the frequency of the applied
voltage. In other words, the rotating flux field appears to the stator as the north and
south poles of a magnet rotating about the stator.[4-7]
9
Figure 2.1, Three Phase Induction Motor
2.1.2 Transformer Action
The stator carries the motor primary windings and is connected to the power source.
There are normally no external connections to the rotor which carries the secondary
windings. Instead the rotor windings are shorted.
When a current flows in the stator windings a current is induced in the shorted
secondary windings by transformer action. The magnitude of the rotor current will be
proportional to the flux density B in the air gap (and the relative motion, called the
slip, of the rotor with respect to the rotating field).
Many rotor types are used. The most popular AC motors use "squirrel cage" rotors
which are constructed from copper or aluminium bars fixed between conducting end
rings which provide the short circuit path for the currents induced in the bars.
10
Figure 2.2, Squirrel Cage Rotor with ends short circuited for providing
path for current induced in rotor bars
2.1.3 Torque Generation (Motor Action)
When the motor is first switched on and the rotor is at rest, a current is induced in the
rotor windings (conductors) by transformer action. Another way of seeing this is that
the relative motion of the rotating flux passing over the slower moving (initially
static) rotor windings causes a current to flow in the windings by generator action.
Once current is flowing in the rotor windings, the motor action due to the Lorentz
force on the conductors comes into effect. The reaction between the current flowing in
the rotor conductors and the magnetic flux in the air gap causes the rotor to rotate in
the same direction as the rotating flux as if it was being dragged along by the flux
wave.
Similar to the DC machine, the torque in an induction motor T is proportional to the
flux density B and the induced rotor current I. Thus
T = k1 BI
Where k1 is a constant depending on the number of stator turns, the number of phases
and the configuration of the magnetic circuit.
11
The rotor speed builds up due to the motor action, but as it does so, the relative
motion between the rotating stator field and the rotating rotor conductors is reduced.
This in turn reduces the generator action and thus the current in the rotor conductors
and the torque on the rotor. As the speed of the rotor approaches the speed of the
rotating field, known as the synchronous speed, the torque on the rotor drops to zero.
Thus the speed of an induction motor can never reach the synchronous speed.
2.1.4 Slip
The relative motion between the rotating field and the rotating rotor is called the slip
and is given by:
S = Ns- N
Ns
Where S is the slip, Ns is the synchronous speed in RPM, and N is the rotor speed.
Since the rotor current is proportional to the relative motion between the rotating field
and the rotor speed, the rotor current and hence the torque are both directly
proportional to the slip.
The rotor current is proportional to the rotor resistance. Increasing the rotor resistance
will reduce the current and increase the slip; hence a form of speed and torque control
is possible with wound rotor motors. Increased rotor resistance also has the added
benefit of reducing the input surge current and increasing starting torque on switch on,
but all of these benefits are at the expense of more complex rotor designs and
unreliable slip rings to give access to the rotor windings.
12
2.1.5 Speed
Synchronous speed in RPM is given by:
Ns = 120 (f)
P
Where f is the power line frequency in Hz and P is the number of poles per phase. P
must be an even integer since for every north pole there is a corresponding south pole.
The actual speed of the motor depends on the load it must drive. Increasing the load
on the motor causes it to slow down increasing the slip. The motor speed will settle at
an equilibrium speed when the motor torque equals the load torque. This occurs when
the slip provides just enough current to deliver the required torque.[11,14]
2.1.6 Speed Control
Pole Changing
Early machines were designed with multiple poles to facilitate speed control
by pole changing. By switching in different numbers or combinations of poles
a limited number of fixed speeds could be obtained.
Variable Rotor Resistance
The speed of induction motors can however be varied over a limited range by
varying the rotor resistance as noted in the section on slip but only by using
wound rotor designs negating many of the advantages of the induction motor.
Variable Frequency
Since motor speed depends on the speed of the rotating field, speed control
13
can be affected by changing the frequency of the AC power supplied to the
motor.
As in most machines, the induction motor is designed to work with the flux
density just below the saturation point over most of its operating range to
achieve optimum efficiency.
The flux density B is given by:
f
VkB 2
Where V is the applied voltage, f is the supply frequency and k2 is a constant
depending on the shape and configuration of the stator poles.
In other words if the flux density is constant, the Volts per Hertz is also a
constant. This is an important relationship and it has the following
consequences.
o For speed control, the supply voltage must increase in step with the
frequency; otherwise the flux in the machine will deviate from the
desired optimum operating point. Practical motor controllers based on
frequency control must therefore have a means of simultaneously
controlling the motor supply voltage. This is known as Volts/Hertz
control.
o Increasing the frequency without increasing the voltage will cause a
reduction of the flux in the magnetic circuit thus reducing the motor's
output torque. The reduced motor torque will tend to increase the slip
14
with respect to the new supply frequency. This in turn causes a greater
current to flow in the stator, increasing the IR volt drop across the
windings as well as the I2R copper losses in the windings. The result is
a major drop in the motor efficiency. Increasing the frequency still
further will ultimately cause the motor to stall.
o Increasing the voltage without increasing the frequency will cause the
material in the magnetic circuit to saturate. Excessive current will flow
giving rise to high heat dissipation due to I2R losses in the windings
and high eddy current losses in the magnetic circuit and ultimately
failure of the motor due to overheating. Increasing the voltage will not
force the motor to exceed the synchronous speed because as it
approaches the synchronous speed the torque drops to zero.[7,8]
The variable frequency is normally provided by an inverter.
Since the induced current in the rotor is proportional to the flux density and the flux
density in turn is proportional to the line voltage, the torque, which depends on the
product of the flux density and the rotor current, is proportional to the square of the
line voltage V.
2.1.7 Generator Action
If an induction motor is forced to run at speeds in excess of the synchronous speed,
the load torque exceeds the machine torque and the slip is negative, reversing the
rotor induced EMF and rotor current. In this situation the machine will act as a
generator with energy being returned to the supply.
15
If the AC supply voltage to the stator excitation is simply removed, no generation is
possible because there can be no induced current in the rotor.
Regenerative braking
In traction applications, regenerative braking is not possible below
synchronous speed in a machine fed with a fixed frequency supply. If however
the motor is fed by a variable frequency inverter then regenerative braking is
possible by reducing the supply frequency so that the synchronous speed
becomes less than the motor speed.
AC motors can be microprocessor controlled to a fine degree and can
regenerate current down to almost a stop whereas DC regeneration fades
quickly at low speeds.
Dynamic Braking
Induction motors can be brought rapidly to a stop (and/or reversed) by
reversing one pair of leads which has the effect of reversing the rotating wave.
This is known as "plugging". The motor can also be stopped quickly by
cutting the AC supply and feeding the stator windings instead with a DC (zero
frequency) supply. With both of these methods, energy is not returned to the
supply but is dissipated as heat in the motor. These techniques are known as
dynamic braking. [8,9]
16
2.1.8 Starting
Three phase induction motors and some synchronous motors are not self starting but
design modifications such as auxiliary or "damper" windings on the rotor are
incorporated to overcome this problem.
Usually an induction motor draws 5 to 7 times its rated current during starting before
the speed builds up and the current is modified by the back EMF. In wound rotor
motors the starting current can be limited by increasing the resistance in series with
the rotor windings.
In squirrel cage designs, electronic control systems are used to control the current to
prevent damage to the motor or to its power supply.
Even with current control the motor can still overheat because, although the current
can be limited, the speed build up is slower and the inrush current, though reduced, is
maintained for a longer period.
2.1.9 Power Factor
The current drawn by an induction motor has two components, the current in phase
with the voltage which governs the power transfer to the load and the inductive
component, representing the magnetizing current in the magnetic circuit, which lags
90° behind the load current.
The power factor is defined as cosΦ where Φ is the net lag of the current behind the
applied voltage due to the in phase and out of phase current components. The net
power delivered to the load is VAcosΦ where V is the applied voltage; A is the
current which flows.
17
Various methods of power factor correction are used to reduce the current lag in order
to avoid losses due to poor power factor. The simplest is to connect a capacitor of
suitable size across the motor terminals. Since the current through a capacitor leads
the voltage, the effect of the capacitor is to counter-balance the inductive element in
the motor canceling out the current lag.
2.1.10 Characteristics
One of the major advantages of the induction motor is that it does not need a
commutator. Induction motors are therefore simple, robust, reliable, maintenance free
and relatively low cost. They are normally constant speed devices whose speed is
proportional to the mains frequency. Variable speed motors are also possible by using
motor controllers which provide a variable frequency output.
Typical torque-speed characteristics of induction motor are shown in figure 2.3.
Figure 2.3, Torque-Speed Curve of Induction Motor
Torque-speed curve shows that:
18
The induced torque is zero at synchronous speed.
The curve is nearly linear between no-load and full load. In this range, the
rotor resistance is much greater than the reactance, so the rotor current, torque
increase linearly with the slip.
There is a maximum possible torque that can‟t be exceeded. This torque is
called pullout torque and is 2 to 3 times the rated full-load torque.
The starting torque of the motor is slightly higher than its full-load torque, so
the motor will start carrying any load it can supply at full load.
The expression for the synchronous speed indicates that by changing the stator
frequency it can be changed. This can be achieved by using power electronic circuits
called inverters which convert dc to ac of desired frequency. Power electronic control
achieves smooth variation of voltage and frequency of the ac output. This when fed to
the machine is capable of running at a controlled speed. However, consider the
equation for the induced emf in the induction machine.
V = 4.44 N Φm f
where N is the number of the turns per phase, Φm is the peak flux in the air gap and f
is the frequency. Note that in order to reduce the speed, frequency has to be reduced.
If the frequency is reduced while the voltage is kept constant, thereby requiring the
amplitude of induced emf to remain the same, flux has to increase. This is not
advisable since the machine likely to enter deep saturation. If this is to be avoided,
then flux level must be maintained constant which implies that voltage must be
reduced along with frequency. The ratio is held constant in order to maintain the flux
level for maximum torque capability.[9-10]
The speed torque characteristics at any frequency may be estimated. There is one
curve for every excitation frequency considered corresponding to every value of
19
synchronous speed. The curves are shown in figure 2.4. It may be seen that the
maximum torque remains constant.
Figure 2.4, Torque-Speed Curve Keeping V/f ratio constant
2.1.11 Applications
Three phase induction motors are used wherever the application depends on AC
power from the national grid. Because they don't need commutators they are
particularly suitable for high power applications.
They are available with power handling capacities ranging from a few Watts to more
than 10 Megawatts.
They are mainly used for heavy industrial applications and for machine tools. The
availability of solid state inverters in recent years means that induction motors can
20
now be run from a DC source. They are now finding use in automotive applications
for electric and hybrid electric vehicles. Induction motors are seen as more rugged for
these applications than permanent magnet motors which are vulnerable to possible
degradation or demagnetization of the magnets due to over-temperature or accidental
over-current at power levels over about 5 kW.[11]
2.2 Concept of Variable Frequency Drive
Any variable speed electrical drive system comprises of the following components:
An electronic actuator - the controller.
A driving electrical machine - motor.
A driven machine (load) - pump, fan, blower, compressor…
The task of a variable speed electrical drive is to convert the electrical power supplied
by the mains into mechanical power with minimum loss. To achieve an optimum
technological process, the drive must be variable in speed. This will steep-lessly
adjust the speed of the driven machine. This is ensured by the low loss control using
solid state technology in electronic controllers. The controllers are connected to mains
supply and the electrical machine as shown in figure 2.5.
21
Figure 2.5, Concept of VFD
2.2.1 Variable Frequency Drive Fundamentals
2.2.1.1 Voltage and Frequency Relationship
When the frequency applied to an induction motor is reduced, the applied voltage
must also be reduced to limit the current drawn by the motor at reduced frequencies.
The inductive reactance of an AC magnetic circuit is directly proportional to the
frequency according to the formula
XL = 2 πf L
(Where: π= 3.14, f = frequency in hertz, and L= inductive reactance in
Henrys.)
Variable speed AC drives will maintain a constant volts/hertz relationship from 0-50
Hertz. At low frequencies the voltage will be low, as the frequency increases the
voltage will increase. (Note: this ratio may be varied somewhat to alter the motor
performance characteristics such a providing a low-end boost to improve starting
torque.)
22
Depending on the type of AC drive, the microprocessor control adjusts the output
voltage waveform, by one of several methods, to simultaneously change the voltage
and frequency to maintain the constant volts/hertz ratio throughout the 0-50 Hz range.
On most AC variable speed drives the voltage is held constant above the 50 hertz
frequency. [7]
2.2.2 V/Hz vs. Vector Drives
Modern Variable Frequency drives (VFD or VSD) come in two major formats, V/Hz
and vector drives.
The V/Hz drive is a drive where the voltage applied to the motor is directly related to
the frequency. In the ideal motor, the magnetic circuit would be purely inductive and
keeping a constant V/Hz ratio would maintain a constant flux in the iron. The real
motor has resistance in series with the magnetizing inductance. This has no bearing on
the operation at line frequency, however as the frequency of the drive is reduced, the
resistance begins to become significant relative to the inductive reactance. This causes
the flux to reduce at very low frequencies and so it is difficult to get sufficient torque
at low speeds. For many applications, this low torque is not a problem, but there are
some that do need a high torque from a low speed. Early drives were designed with a
voltage boost to provide a measure of torque increase at low speed.
Vector drives have a mathematical model of the drive in software and by measuring
the current vectors in relation to the applied voltage, they are able to maintain a
constant field at all frequencies below the line frequency. These drives need to be
tuned to the motor and typically include a self tuning algorithm that is enabled at
23
commissioning to determine the component values for the mathematical model. If the
motor is replaced, the drive needs to be re-tuned to learn the characteristics of the new
motors.
Vector drives come in three major formats;
1. Closed loop
2. Open loop
3. Direct torque control
The closed loop controllers were the first vector controllers and are still the best option
for accurate control at zero speed. The open loop vector and DTC are suitable for
applications requiring good control above 3 – 5 Hz.
Quite a number of modern drives can operate as V/Hz, open loop vector or closed
loop vector just by changing a parameter. Closed loop requires a shaft encoder to give
accurate speed feedback.
The major differentiation between modern VSDs are the enclosure, auxiliary
functionality, programming and user interface. Low cost drives are often very poorly
filtered and can create major RFI (EMC) issues. Some drives include no filtering and
must be installed with external filters, and others include all the filtering required. [1]
2.2.3 Diode Rectification
There are two types of single-phase diode rectifier that convert a single-phase ac
supply into a dc voltage, namely, single-phase half-wave rectifiers and single-phase
full-wave rectifiers. In the following subsections, the operations of these rectifier
circuits are examined and their performances are analyzed. For the sake of simplicity
24
the diodes are considered to be ideal, that is, they have zero forward voltage drop and
reverse recovery time. This assumption is generally valid for the case of diode
rectifiers that use the mains, a low-frequency source, as the input, and when the
forward voltage drop is small compared with the peak voltage of the mains.
Furthermore, it is assumed that the load is purely resistive such that load voltage and
load current have similar waveforms.[4]
2.2.4 Single-Phase Half-Wave Rectifiers
The simplest single-phase diode rectifier is the single-phase half-wave rectifier. A
single-phase half-wave rectifier with resistive load is shown in Fig. 2.6. The circuit
consists of only one diode that is usually fed with a transformer secondary as shown.
During the positive half-cycle of the transformer secondary voltage, diode D
conducts. During the negative half-cycle, diode D stops conducting. Assuming that
the transformer has zero internal impedance and provides perfect sinusoidal voltage
on its secondary winding, the voltage and current waveforms of resistive load R and
the voltage waveform of diode D are shown in figure 2.7.
Figure 2.6, Half wave Rectifier
25
Figure 2.7, Current and voltage waveform of Single phase half wave rectification
By observing the voltage waveform of diode D it is clear that the peak inverse voltage
(PIV) of diode D is equal to Vm during the negative half-cycle of the transformer
secondary voltage. Hence the Peak Repetitive Reverse Voltage (VRRM) rating of diode
D must be chosen to be higher than Vm to avoid reverse breakdown. In the positive
half-cycle of the transformer secondary voltage, diode D has a forward current which
is equal to the load current and, therefore, the Peak Repetitive Forward Current (IFRM)
rating of diode D must be chosen to be higher than the peak load current. In addition,
the transformer has to carry a dc current that may result in a dc saturation problem of
the transformer core.[3-6]
2.2.5 Single-Phase Full-Wave Rectifiers
There are two types of single-phase full-wave rectifier, namely, full-wave rectifiers
with center-tapped transformer and bridge rectifiers. A full-wave rectifier with a
center-tapped transformer is clear that each diode, together with the associated half of
26
the transformer, acts as a half-wave rectifier. The outputs of the two half-wave
rectifiers are combined to produce full-wave rectification in the load.
Figure 2.8, Full wave rectifier with center tapped transformer
As far as the transformer is concerned, the dc currents of the two half-wave rectifiers
are equal and opposite, such that there is no dc current for creating a transformer core
saturation problem. The voltage and current waveforms of the full wave rectifier are
shown in figure 2.9. By observing diode voltage waveforms VD1 and VD2 it is clear
that the peak inverse voltage (PIV) of the diodes is equal to 2Vm during their blocking
state. Hence the Peak Repetitive Reverse Voltage (VRRM) rating of the diodes must
be chosen to be higher than 2Vm to avoid reverse breakdown.
During its conducting state, each diode has a forward current that is equal to the load
current and, therefore, the Peak Repetitive Forward Current (IFRM) rating of these
diodes must be chosen to be higher than the peak load current. Employing four diodes
instead of two, a bridge rectifier as can provide full-wave rectification without using a
center-tapped transformer. During the positive half cycle of the transformer secondary
voltage, the current flows to the load through diodes D1 and D2. During the negative
half cycle, D3 and D4 conduct. The voltage and current waveforms of the bridge
rectifier are shown in figure 2.11. [12]
27
As with the full-wave rectifier with center-tapped transformer, the Peak Repetitive
Forward Current (IFRM) rating of the employed diodes must be chosen to be higher
than the peak load current Vm=R. However, the peak inverse voltage (PIV) of the
diodes is reduced from 2Vm to Vm during their blocking state.
Figure 2.9, Voltage and current waveform of full wave center tapped transformer
2.2.6 Single Phase Full Wave Bridge Rectifier
During the first positive half Diode D1 and D3 are forward bias whereas D2 and D4 are
reverse bias. In the next half cycle D1 and D3 are reverse bias whereas D2 and D4 are
forward bias. Bridge rectifier is shown in figure 2.10.
28
Figure 2.10, Bridge Rectifier
Current and voltage waveforms are as follows
Figure 2.11, Current and voltage waveforms of full wave bridge rectifier
2.2.7 The DC Link (And Current Distribution)
The DC link circuit can be regarded as a store where the motor, through the inverter,
can get its energy. The DC link can be built up according to 3 different principles, and
the actual principle used depends on the type of rectifier and inverter used. [2-5]
29
Figure 2.12, DC Link
The constant voltage DC link consists of large electrolytic capacitor(s) and on larger
frequency converters – an inductor (coil). These components form an L-C filter which
smoothes the pulsating voltage from the rectifier. The Jaguar range of frequency
converters use uncontrolled diode bridge rectifiers, and when the L-C filter is applied
the input to the inverter output stage becomes a smooth DC voltage of constant
amplitude.
With this type of DC link, the load determines the size of motor current. The large DC
link capacitor(s) also supplies the magnetizing current for the motor. This is because
the magnetizing current is reactive and if it came from the main power input it would
have to return there. The diodes in the rectifier block prevent this action, so the
capacitor(s) are charged up to the value of peak mains, then discharge into the motor,
out of phase with the main load current by up to 90 degrees, as magnetizing current is
demanded. This is one reason why the output current or current measured on the
motor input wires is always greater than the input current.
Motor manufacturers normally state the cosφ of a motor at rated current. At lower
values of cosφ the rated motor current – at the same voltage and power – will be
higher, as shown in the equation.
30
Figure 2.13, Phasor Diagram of Motor Current
2.2.8 Inverter Section
The AC output inverter for a three phase output stage comprises six solid state
switches. In small low voltage and low current VSDs, the output stages will typically
be MOS FETs and in larger VSDs, they are typically IGBTs.
The output switches operate at a high frequency, typically between 3kHz and 16kHz,
and are controlled to produce a PWM output waveform which causes a sinusoidal
current to flow in the motor. There are many different PWM schemes and algorithms
with different advantages. [1]
2.2.8.1 Inverter Principle
Inverter circuitry generates an alternating current by sequentially switching a direct
current in alternate directions through the load. The illustration (figure 2.14) shows
the generation of a single positive pulse (red) and a single negative pulse (green)
which occurs 180 electrical degrees later. To analyze the circuit assume a
conventional current flow (positive to negative direction). The black arrows on the
emitter of each transistor indicate the direction of conventional current through the
transistors. This is a three-phase drive, so at certain times during the cycle transistors
will be turned on to cause current flow through the A - C and B - C motor windings
but for clarity this is not shown in this illustration. For this analysis also assume that
31
the free-wheeling diodes are non-conducting. Transistors 1A and 2B are turned on
and off by the microprocessor control and current flows from the DC bus positive,
through the motor windings as shown by the red arrows producing the positive (red)
voltage pulse, and back to the DC bus negative. To generate the next half-cycle
transistors 1B and 2A will be turned on and off and the current flow will reverse
through the motor winding as shown by the green arrows which result in the negative
(green) pulse.
Figure 2.14, Inverter Switching Sequence
The figure 2.15 shows the switching sequence of the output transistors, SCR‟s, or
GTO‟s used in a VFD to produce a three-phase AC waveform. Since each these
devices are functioning as solid-state switches, the circuit operation can be easily
visualized by representing these devices as open or closed mechanical switches.
Switches closed to the positive bus are shown in red, switches closed to the negative
bus are shown in black, and open switches are shown in gray. When a particular
32
winding is connected to the same bus potential (either positive or negative) the
voltage across that winding will be zero. If a winding is connected so that the positive
voltage is connected to the first letter of the winding label (for example the A in AB)
the voltage produced across that winding is positive. If a winding is connected so that
the positive voltage is connected to the second letter of the winding label (for example
B in AB) the current flow reverses and the voltage produced across that winding will
be of a negative polarity.
Below each diagram is a table listing of the number of electrical degrees through
which the switches operate and the resultant phase voltage produced.
Note: On a six-step drive the output devices will be closed throughout the listed
operating range; on a PWM drive, pulses will be produced through this range.
33
Figure 2.15, Switching sequence of output transistors
34
2.3 Pulse Width Modulation
Pulse width modulation is a technique for controlling power to inertial electrical
devices.
The term inertial electrical device refer that cannot respond to fast switching of TTL
signal between the high and low state.
So the switching frequency of PWM will depend upon the inertia of load so that it is
faster than the limit to which the device can respond For example:
Several times a minute in an electric stove.
120 Hz in a lamp dimmer.
From few kHz to tens of kHz for a motor drive.
Tens or hundreds of kHz in audio amplifiers and computer power
supplies.
Figure 2.16, PWM Sine Wave Syntheses
PWM can be thought as getting analog results by digital means.
35
2.3.1 Duty Cycle
In PWM an electronic switch between supply and load is turned on and off repeatedly
at very fast speed. In this way power to the circuit is controlled. If switch is in on state
for long time as compared to off time the power delivered to the load will be more
and vice versa. This phenomenon is termed as duty cycle of PWM which may be
defined as;
“Duty cycle describes the proportion of 'on' time to the regular interval or
'period' of time”
For example in the figure 2.17, the upper wave form shows a duty cycle of 75% while
lower shows a duty cycle of 50%.
Figure 2.17, Duty Cycles of 75% (blue) and 50% (red)
2.3.2 Switching Devices for PWM generation
As stated earlier that some sort of electronic switch is required to alter the value from
maximum to minimum at very high speed. Following switching devices are used for
36
this purpose. The switch is chosen on the basis of frequency at which PWM should be
generated, performance required and cost of the switch. These switching devices can
be;
Bipolar junction transistor
MOSFET
IGBT
2.3.3 Advantages
Low Power Loss in switching devices
When a switch is off there is practically no current, and when it is on, there is
almost no voltage drop across the switch. Power loss, being the product of voltage and
current, is thus in both cases close to zero.
2.3.4 Issues related to PWM
The main disadvantages of PWM circuits are the added complexity and the possibility
of generating radio frequency interference (RFI). Locating the controller near the
load, using short leads, and in some cases, using additional filtering on the power
supply leads, may minimize RFI.[4-6]
2.3.5 Applications of PWM
Voltage Regulation
PWM is used in switch mode power supplies and voltage regulators. The
required voltage is achieved by changing the duty cycle. Switching noise is removed
with the help of inductor and capacitors.
37
Power Control
The power to a circuit can also be controlled using pulse width modulation.
High frequency PWM power control systems are easily realizable with semiconductor
switches. As explained above, almost no power is dissipated by the switch in either on
or off state. However, during the transitions between on and off states, both voltage
and current are non-zero and thus power is dissipated in the switches. By quickly
changing the state between fully on and fully off (typically less than 100
nanoseconds), the power dissipation in the switches can be quite low compared to the
power being delivered to the load.
Telecommunications
Digital data transmission can be sent very easily by means of PWM where
90% duty cycle corresponds to logic 1 while 10% duty cycle corresponds to logic 0
2.4 Sinusoidal Pulse Width Modulation
SPWM switching technique is commonly used in industrial applications. SPWM
techniques are characterized by constant amplitude pulses with different duty cycle
for each period. The width of these pulses is modulated in order to obtain inverter
output voltage control and to reduce its harmonic content. Sinusoidal pulse width
modulation or SPWM is the most common method in motor control and inverter
application.
38
“To generate the signal, triangle wave as a carrier signal is compared with the
sinusoidal wave, whose frequency is the desired frequency.”
In the following figures comparison of reference sinusoidal signal of 50Hz is
shown with triangular carrier signal. The resulting pulses are shown below and it can
be seen that there pulse width varies in sinusoidal fashion.
Figure 2.18, Comparison of reference sinusoidal signal of 50Hz with
triangular carrier signal
Figure 2.19, Resulting Pulses
The above figures were for single phase. For three phase SPWM all three phases must
be compared with same triangular wave as shown in the figure 2.20.
39
Figure 2.20, Comparison of three phases with triangular wave
2.4.1 Modulation Index
The term modulation index refers to the ratio between the amplitude of carrier
wave to the amplitude of reference wave
r
c
A
AM
The modulation index should be less than 1 otherwise there will be areas
where there will be no intersection of carrier and reference signal. Some time slight
over modulation is also allowed to achieve higher voltage but it will make the
spectrum worse. [2-4]
40
Figure 2.21, Modulation Index > 1
2.4.1.1 Effect of Over Modulation
Figure 2.22, Effect of Over Modulation
Now the effect of over modulation can be easily seen from figure 2.21 and 2.22. Full
voltage is applied in the portion where there is no intersection of carrier wave with
reference wave.
2.4.2 Advantages of SPWM
The output voltage control is easier with PWM than other schemes and can be
achieved without any additional components.
The lower order harmonics are either minimized or eliminated altogether.
The filtering requirements are minimized as lower order harmonics are
eliminated and higher order harmonics are filtered easily.
It has very low power consumption.
41
The entire control circuit can be digitized which reduces the susceptibility of
the circuit to interference.
By the use of SPWM the frequency of motors can easily be changed hence
their speed while torque remain constant. [4-7]
42
Chapter 3
Implementation of Project
In order to understand VFD, a review of some of the concepts that apply to inverters,
and a description of some of the components that are a part of most Inverters are
given in the following sections.
3.1 Main Parts of Drive
In very general terms the operation of variable frequency drive is as follows.
a. Power first goes into the rectifier, where AC is converted into a
rippling DC voltage. The intermediate circuits then smoothes and
holds the DC Voltage at a constant level or energy source for the
inverter.
b. The inverter uses the DC voltage to pulse the motor with varying levels
of voltage and current depending upon the control circuit.
c. The control circuit provides signals to the switching devices of inverter
to switch them in appropriate manner.
So from above we conclude that there are three main parts of variable frequency drive
43
3.1.1 Power Supply
This portion includes rectification stage and smoothening of the DC voltage. Also the
AC voltage is transformed to desire voltage before rectification to achieve desired
voltage level.
3.1.2 Inverter
This section takes the DC voltage from the intermediate section and, with the help of
the control section, fires each set of (transistors) to the three terminals of the motor. In
three phase drive hex bridge along with its related circuitry (like gate driver IC etc) is
used for this purpose.
3.1.3 Control Circuit
Control circuit provides control signals for proper operation of Hex Bridge. Control
circuit may be built with the help of analog circuitry or with digital devices available
like DSP‟s, FPGA‟s and microcontrollers. In this project we have used
microcontroller PIC18F4431 for this purpose.
Now each of the above section will be discussed in detail. [2-8]
3.2 Power Supply
During the design of variable frequency drive different dc voltages are required at
different places.
Gate pulses of 15V dc to turn on and turn off switching devices (IGBT).
Micro controller operates at 5V.
44
Another isolated 5V dc supply is required to operate serial port so that the
interface with the computer remains intact from the rest of circuitry. In this
way we can avoid any possible damage to computer.
Desired voltage to operate the inverter.
We designed power supply to achieve these voltages for the proper operation of drive.
Most of the power supplies are designed to convert high voltage AC mains electricity
to a suitable low voltage supply for electronic circuits and other devices. A power
supply can be broken down into a series of blocks, each of which performs a
particular function.
A typical block diagram of a 5V DC supply is:
Figure 3.1, Block Diagram of Regulated Power Supply
3.3 Transformer
As shown in above block diagram the first component of power supply is transformer
that converts AC electricity from one voltage to another with little loss of power.
Transformers work only with AC and this is one of the reasons why mains electricity
is AC.
Step-up transformers increase voltage, step-down transformers reduce voltage. Most
power supplies use a step-down transformer to reduce the high mains voltage (220V
in Pakistan) to a safer low voltage.
45
The input coil is called the primary and the output coil is called the secondary. There
is no electrical connection between the two coils. Instead they are linked by an
alternating magnetic field created in the soft-iron core of the transformer. The two
lines in the middle of the circuit symbol represent the core.
Transformers waste very little power so the power out is (almost) equal to the power
in. Note that as voltage is stepped down current is stepped up.
The ratio of the number of turns on each coil, called the turns ratio, determines the
ratio of the voltages. A step-down transformer has a large number of turns on its
primary (input) coil which is connected to the high voltage mains supply, and a small
number of turns on its secondary (output) coil to give a low output voltage.
3.3.1 Main Components of a transformer
1) Iron core stampings (configured either as U/T or E/I, generally the later is used
more extensively).
2) Central plastic or ceramic bobbin surrounded by the iron core stampings.
3) Two windings (electrically isolated and magnetically coupled) using super
enameled copper wire made over the bobbin.
3.3.2 Transformer Designing
As stated earlier that in variable frequency drive different voltages are required at
different places so we have to design transformers that can supply us the required
voltage as the voltages at the mains are fixed.
Designing of transformer consists of different steps which are described in detail
below.
46
3.3.2.1 Calculating the Core Area (CA) of the Transformer
The Core Area is calculated through the formula given below:
CA = 1.152 ×√ (Output Voltage × Output Current).
3.3.2.2 Calculating Turns per Volt (TPV)
It is done with the following formula:
TPV = 1 / (4.44 × 10-4
× CA × Flux Density × AC frequency)
where the frequency will depend on the particular country‟s specifications (either 60
or 50 Hz), the standard value for the flux density of normal steel stampings may be
taken as 1 Weber/sq.m, for ordinary steel material the value is 1.3 Weber/sq.m.
3.3.2.3 Primary Winding Calculations
Basically three important parameters needs to be figured out while calculating the
primary winding of a transformer, they are as follows:
a. Current through the primary winding.
b. Number of turns of the primary winding.
c. Area of the primary winding.
3.3.2.4 Primary Winding Calculations
Primary Current = (Secondary Volts × Secondary Current) ÷ (Primary Volts ×
Efficiency)
47
(The average value for the efficiency of any transformer may be presumed to be 0.9 as
a standard figure).
Number of Turns = TPV × Primary Volts
Primary Winding Area = Number of Turns / Turns per Sq. cm (from the table A given
in appendix. Reading Table A is easy – just find out the relevant figures (wire SWG
and Turns per sq.cm.) by tallying them with the closest matching value of your
selected primary current.
3.3.2.5 Secondary Winding Calculations
As explained above, with the help of Table A we should be able to find the SWG of
the wire to be used for the secondary winding and the TPV simply by matching them
with the selected secondary current.
The Number of turns for the secondary winding is also calculated as explained for the
primary winding, however considering high loading conditions of this winding, 4 %
extra turns is preferably added to the overall number of turns. Therefore the formula
becomes:
Secondary Number of Turns = 1.04 × (TPV × secondary voltage),
Also secondary winding area = Secondary Turns / Turns per sq. cm. (from table A).
3.3.2.6 Calculating the Core Size of Steel Laminations
The core size of the steel stampings to be used may be easily found from Table B
(given in appendix) by suitably matching the relevant information with total winding
area of the transformer.
The Total Winding Area thus needs to be calculated first, it‟s as follows:
48
Total Winding Area = (Primary Winding Area + Total Secondary Winding Area) ×
Space for external Insulation.
The third parameter i.e. the space for the insulation/former etc. may be taken
approximately 25% to 35% of the sum of the first two parameters. Therefore, the
above formula becomes:
Total Winding Area = (Primary Winding Area + Total Secondary Winding
Area) × 1.3
Normally, a core having a square central pillar is preferred and used other factors
involved are also appropriately illustrated in the adjoining figure and calculated as
follows:
Gross Core Area = Core Area from Table B / 0.9 (sq.cm.)
Tongue Width = √Gross Core Area (cm)
After calculating the Tongue Width, it may be used as a reference value and matched
appropriately in Table B to acquire the actual CORE TYPE.
Stack Height = Gross Core Area / Tongue Width.
3.4 Rectifier
After transforming the voltage to the desired level the next step is rectification of AC
voltage into DC voltage. There are many types of rectifiers such as half wave rectifier,
Full wave center tapped rectifier, Full wave Bridge rectifier, Three phase half wave
rectifier, three phase full wave rectifier.
49
We used full wave bridge rectifier in our project so its construction and working is
discussed below in detail.
3.4.1 Full Wave Bridge Rectifier
Figure 3.2, Full wave bridge rectifier
The bridge rectifier uses four diodes connected as shown in figure 3.2. When the input
cycle is positive as in figure 3.3(a), diodes D1 and D2 are forward-biased and conduct
current in the direction shown. A voltage is developed across RL that looks like the
positive half of the input cycle. During this time, diodes D3 and D4 are reverse-biased.
When the input cycle is negative as in Figure 3.3(b), diodes D3 and D4 are forward-
biased and conduct current in the same direction through RL as during the positive
half- cycle. During the negative half-cycle, Dl and D2 are reverse-biased. A full-wave
rectified output voltage appears across RL as a result of this action. [4]
50
Figure 3.3, Operation of a bridge rectifier
3.4.2 Bridge Output Voltage
Bridge Output Voltage A bridge rectifier with a transformer-coupled input is shown in
figure 3.4(a). During the positive half-cycle of the total secondary voltage, diodes D1
and D2 are forward-biased. Neglecting the diode drops, the secondary voltage appears
across the load resistor. The same is true when D3 and D4 are forward-biased during
the negative half-cycle.
Vpout = Vpsec
51
As we can see in figure 3.4(b), two diodes are always in series with the load resistor
during both the positive and negative half-cycles. If these diode drops are taken into
account, the output voltage is
Vpout = Vpsec - 1.4V
Figure 3.4, Bridge operation during a positive half cycle of the primary and
secondary voltages
3.4.3 Peak Inverse Voltage (PIV)
Let's assume that D1 and D2 are forward-biased and examine the reverse voltage
across D3 and D4. Visualizing D1 and D2 as shorts (ideal model), as in figure 3.5(a),
we can see that D3 and D4, have a peak inverse voltage equal to the peak secondary
voltage. Since the output voltage is ideally equal to the secondary voltage. [4]
52
PIV = Vpout
If the diode drops of the forward-biased diodes are included as shown in figure 3.5(b),
the peak inverse voltage across each reverse-biased diode in terms of Vpout is
PIV=Vpout + 1.4V
Figure 3.5, Peak inverse voltages across diodes D3 and D4 in a bridge rectifier
during the positive half-cycle of the secondary voltage.
3.4.4 PIV Rating of Bridge Rectifier
The PIV rating of the bridge diodes is less than that required for the center-tapped
configuration. If the diode drop is neglected, the bridge rectifier requires diodes with
half the PIV rating of those in a center-tapped rectifier for the same output voltage.
3.5 Filter
The third step is smoothing of DC and this is achieved using Filter. The working of a
filter is described below. [3]
53
Figure 3.6, Full wave rectifier with filter
3.5.1 Working
In most power supply applications, the standard 50 Hz ac power line voltage must be
converted to an approximately constant dc voltage. The 50 Hz pulsating dc output of a
half wave rectifier or the 100 Hz pulsating output of a full-wave rectifier must be
filtered to reduce the large voltage variations. Figure 3.7 illustrates the filtering
concept showing a nearly smooth dc output voltage from the filter. The small amount
of fluctuation in the filter output voltage is called ripple.
Figure 3.7, Power supply filtering
54
3.5.2 Capacitor Input Filter
A half-wave rectifier with a capacitor-input filter is shown in figure 3.8. The filter is
simply a capacitor connected from the rectifier output to ground. RL represents the
equivalent resistance of a load. We will use the half-wave rectifier to illustrate the
basic principle and then expand the concept to full-wave rectification.
Figure 3.8, Operation of a half-wave rectifier with a capacitor-input filter. The
current indicates charging or discharging of the capacitor
55
During the positive first quarter-cycle of the input, the diode is forward-biased,
allowing the capacitor to charge to within 0.7 V of the input peak, as illustrated in
figure 3.8(a). When the input begins to decrease below its peak, as shown in figure
3.8(b), the capacitor retains its charge and the diode becomes reverse-biased because
the cathode is more positive than the anode. During the remaining part of the cycle,
the capacitor can discharge only through the load resistance at a rate determined by
the R-L-C time constant, which is normally long compared to the period of the input.
The larger the time constant, the less the capacitor will discharge. During the first
quarter of the next cycle, as illustrated in figure 3.8(c), the diode will again become
forward-biased when the input voltage exceeds the capacitor voltage by
approximately 0.7 V. [4]
3.5.3 Ripple Voltage
As we have seen, that the capacitor quickly charges at the beginning of a cycle and
slowly discharges through RL after the positive peak of the input voltage (when the
diode is reverse-biased). The variation in the capacitor voltage due to the charging and
discharging is called the ripple voltage. Generally, ripple is undesirable; thus, the
smaller the ripple, the better the filtering action.
For a given input frequency, the output frequency of a full-wave rectifier is twice that
of a half-wave rectifier. This makes a full-wave rectifier easier to filter because of the
shorter time between peaks. When filtered, the full-wave rectified voltage has a
smaller ripple than does a half-wave voltage for the same load resistance and
capacitor values. The capacitor discharges less during the shorter interval between
full-wave pulses.
56
3.5.4 Ripple factor
The ripple factor (R) is an indication of the effectiveness of the filter and is defined as
R = Vrpp / Vdc
where Vrpp is the peak-to-peak ripple voltage and Vdc is the dc (average) value of the
filter's output voltage, as illustrated in figure.
Figure 3.9, Vr and VDC determine the ripple factor
The lower the ripple factor, the better the filter. The ripple factor can be lowered by
increasing the value of the filter capacitor or increasing the load resistance.
For a full-wave rectifier with a capacitor-input filter, approximations for the peak-to-
peak ripple voltage, Vrpp and the dc value of the filter output voltage, Vdc, are given
in the following expressions. The variable Vprect is the unfiltered peak rectified
voltage.
57
3.6 Regulator
The final step in designing of power supply is regulation of DC voltage. This purpose
is achieved in smaller power supply as 5V and 15V in our case using electronic
regulators such as LM7805 and LM7815. This group of regulators is called LM78XX
regulators.
While in case of high voltage power supplies as 155V DC power supply in our case
zener diode may be used for regulation purpose.
The LM78XX gives positive voltage while LM79XX gives negative voltage both are
discussed below.
3.6.1 Fixed Positive linear Voltage Regulators
Although many types of IC regulators are available, the 78XX series of lC regulators
is representative of three-terminal devices that provide a fixed positive output voltage.
The three terminals are input, output, and ground as indicated in the standard fixed
voltage configuration in figure 3.10. The last two digits in the part number designate
the output voltage, for example 7805 is a + 5.0 V regulator.
Figure 3.10, Conceptual diagram of 78XX regulator
Capacitors, although not always necessary, are sometimes used on the input and
output. The output capacitor acts basically as a line filter to improve transient
58
response. The input capacitor is used to prevent unwanted oscillations when the
regulator is at some distance from the power supply filter such that the line has a
significant inductance. The 78XX series can produce output currents up to in excess
of 1A when used with an adequate heat sink. The input voltage must be at least 2V
above the output voltage in order to maintain regulation. The circuits have internal
thermal overload protection and short circuit current-limiting features. Thermal
overload occurs when the internal power dissipation becomes excessive and the
temperature of the device exceeds a certain value. Almost all applications of
regulators require that the device be secured to a heat sink to prevent thermal
overload. [3-6]
3.6.2 Fixed Negative linear Voltage Regulators
The 79XX series is typical of three-terminal IC regulators that provide a fixed
negative output voltage. This series is the negative-voltage counterpart of the 78XX
series and shares most of the same features and characteristics.
3.6.3 Issues with 78XX Regulators
3.6.3.1 The External Pass Transistor
As we know a voltage regulator is capable of delivering only a certain amount of
output current to a load. For example 78XX series regulators can handle a peak output
current of 1.3A (more under certain conditions). If the load current exceeds the
maximum allowable value, there will be thermal overload and the regulator will shut
down. A thermal overload condition means that there is excessive power dissipation
inside the device.
59
If an application requires more than the maximum current that the regulator can
deliver, an external pass transistor Qext can be used. Figure 3.11 illustrates a three-
terminal regulator with an external pass transistor for handling currents in excess of
the output current capability of the basic regulator.
Figure 3.11, three-terminal regulator with an external pass transistor for handling
currents
The value of the external current-sensing resistor, Rext determines the value of current
at which Qext begins to conduct because it sets the base-to-emitter voltage of the
transistor. As long as the Current is less than the value set by Rext, the transistor Qext is
off, and the regulator operates normally. This is because the voltage drop across Rext
is less than the 0.7 V base-to-emitter voltage required to turn on Qext. Rext is
determined by the following formula, where Imax is the highest current that the voltage
regulator is to handle internally.
60
When the current is sufficient to produce at least a 0.7V drop across Rext the external
pass transistor Qext turns on and conducts any current in excess of Imax. Qext will
conduct more or less, depending on the load requirements. For example, if the total
load current is 3A and Imax was selected to be 1A, the external pass transistor will
conduct 2A, which is the excess over the internal voltage regulator current Imax.
The external pass transistor is typically a power transistor with a heat sink that must
be capable of handling a maximum power of
Pext = Iext (Vin - Vout)
3.6.3.2 Current limiting
A drawback of the circuit is that the external transistor is not protected from excessive
current, such as would result from a shorted output. An additional current limiting
circuit (Qlim and Rlim) can be added to protect Qext from excessive current and possible
burn out.
Figure 3.12, three-terminal regulator with an external pass transistor and
additional current limiting circuit (Qlim and Rlim)
61
3.7 Inverter
Inverter is the main part of variable frequency drive. As stated earlier it consists of
hex bridge along with related circuitry. Hex bridge consists of six switches arranged
in three legs of inverter as shown below.
Q1
IRG4BC30UD/TO
Q2
IRG4BC30UD/TO
Q3
IRG4BC30UD/TO
Q4
IRG4BC30UD/TO
Q5
IRG4BC30UD/TO
Q6
IRG4BC30UD/TO
Figure 3.13, Hex bridge using IGBTs
These switches should be on and off at a very high speed in variable frequency drive
that is why electronic switches like MOSFET‟s and IGBT‟s are used. We used
IGBT‟s because of its suitability for many applications in power electronics, such as
in Pulse Width Modulated (PWM), servo and three-phase drives requiring high
dynamic range control and low noise. Now the IGBT‟s and its comparison with
MOSFET‟s will be discussed in detail.
62
3.8 IGBTs
The Insulated Gate Bipolar Transistor (IGBT) is a minority-carrier device with high
input impedance and large bipolar current-carrying capability. Many designers view
IGBT as a device with MOS input characteristics and bipolar output characteristic that
is a voltage-controlled bipolar device. To make use of the advantages of both Power
MOSFET and BJT, the IGBT has been introduced. It‟s a functional integration of
Power MOSFET and BJT devices in monolithic form. It combines the best attributes
of both to achieve optimal device characteristics.
The IGBT is suitable for many applications in power electronics, such as in Pulse
Width Modulated (PWM) servo and three-phase drives requiring high dynamic range
control and low noise. It also can be used in Uninterruptible Power Supplies (UPS),
Switched-Mode Power Supplies (SMPS), and other power circuits requiring high
switch repetition rates. IGBT improves dynamic performance and efficiency and
reduced the level of audible noise. It is equally suitable in resonant-mode converter
circuits. Optimized IGBT is available for both low conduction loss and low switching
loss.
The main advantages of IGBT over a Power MOSFET and a BJT are:
It has a very low on-state voltage drop due to conductivity modulation and has
superior on-state current density. So smaller chip size is possible and the cost
can be reduced.
Low driving power and a simple drive circuit due to the input MOS gate
structure. It can be easily controlled as compared to current controlled devices
(thyristor, BJT) in high voltage and high current applications.
63
Wide Safe Operating Area. It has superior current conduction capability
compared with the bipolar transistor. It also has excellent forward and reverse
blocking capabilities.
The main drawbacks are:
Switching speed is inferior to that of a Power MOSFET and superior to that of
a BJT. The collector current tailing due to the minority carrier causes the
turnoff speed to be slow.
There is a possibility of latch up due to the internal PNPN thyristor structure.
3.8.1 Basic Structure
The basic structure of a typical N-channel IGBT based upon the DMOS process is
shown in figure 3.14. This is one of several structures possible for this device. It is
evident that the silicon cross-section of an IGBT is almost identical to that of a
vertical Power MOSFET except for the P+ injecting layer. It shares similar MOS gate
structure and P wells with N+ source regions. The N+ layer at the top is the source or
emitter and the P+ layer at the bottom is the drain or collector. It is also feasible to
make P-channel IGBTs and for which the doping profile in each layer will be
reversed. IGBT has a parasitic thyristor comprising the four-layer NPNP structure.
Turn-on of this thyristor is undesirable.
64
Figure 3.14, Structure of IGBT
Some IGBTs, manufactured without the N+ buffer layer, are called non-punch
through (NPT) IGBTs whereas those with this layer are called punch-through (PT)
IGBTs. The presence of this buffer layer can significantly improve the performance of
the device if the doping level and thickness of this layer are chosen appropriately.
Despite physical similarities, the operation of an IGBT is closer to that of a power
BJT than a power MOSFET. It is due to the P+ drain layer (injecting layer) which is
responsible for the minority carrier injection into the N--drift region and the resulting
conductivity modulation.
Based on the structure, a simple equivalent circuit model of an IGBT can be drawn as
shown in figure 3.15.
65
Figure 3.15, Equivalent circuit model of an IGBT
It contains MOSFET, JFET, NPN and PNP transistors. The collector of the PNP is
connected to the base of the NPN and the collector of the NPN is connected to the
base of the PNP through the JFET. The NPN and PNP transistors represent the
parasitic thyristor which constitutes a regenerative feedback loop. The resistor RB
represents the shorting of the base-emitter of the NPN transistor to ensure that the
thyristor does not latch up, which will lead to the IGBT latchup. The JFET represents
the constriction of current between any two neighboring IGBT cells. It supports most
of the voltage and allows the MOSFET to be a low voltage type and consequently
have a low RDS (on) value. A circuit symbol for the IGBT is shown in Figure below.
It has three terminals called Collector (C), Gate (G) and Emitter (E). [1-4]
Figure 3.16, Symbol of IGBT
66
3.8.2 Output Characteristics
The plot for forward output characteristics of an NPT-IGBT is shown in Figure 3.17.
It has a family of curves, each of which corresponds to a different gate-to-emitter
voltage (VGE). The collector current (IC) is measured as a function of collector-emitter
voltage (VCE) with the gate-emitter voltage (VGE) constant.
Figure 3.17, Output characterisics of an IGBT
A distinguishing feature of the characteristics is the 0.7V offset from the origin. The
entire family of curves is translated from the origin by this voltage magnitude. It may
be recalled that with a P+ collector, an extra P-N junction has been incorporated in the
IGBT structure. This P-N junction makes its function fundamentally different from
the power MOSFET.
3.8.3 Switching Characteristics
The switching characteristics of an IGBT are very much similar to that of a Power
MOSFET. The major difference from Power MOSFET is that it has a tailing collector
67
current due to the stored charge in the N--drift region. The tail current increases the
turnoff loss and requires an increase in the dead time between the conduction of two
devices in a half-bridge circuit. The figures 3.18 and 3.19 shows a test circuit for
switching characteristics and the corresponding current and voltage turn-on and turn-
off waveforms.
Figure 3.18, IGBT Switcing Time Test Circuit
Figure 3.19, IGBT current and voltage turn-on and turn-off waveforms
68
The turn-off speed of an IGBT is limited by the lifetime of the stored charge or
minority carriers in the N--drift region which is the base of the parasitic PNP
transistor. The base is not accessible physically thus the external means cannot be
applied to sweep out the stored charge from the N--drift region to improve the
switching time. The only way the stored charge can be removed is by recombination
within the IGBT. Traditional lifetime killing techniques or an N+ buffer layer to
collect the minority charges at turn-off are commonly used to speed-up recombination
time.
The turn-on energy Eon is defined as the integral of IC. VCE within the limit of 10% ICE
rise to 90% VCE fall. The amount of turn on energy depends on the reverse recovery
behavior of the free-wheeling diode, so special attention must be paid if there is a
free-wheeling diode within the package of the IGBT (Co-Pack).
The turn-off energy Eoff is defined as the integral of IC. VCE within the limit of 10%
VCE rise to 90% IC fall. Eoff plays the major part of total switching losses in IGBT.
3.9 IR2130
To operate hex bridge in proper manner additional circuitry like gate driver IC is
required. We used IR2130 gate driver IC for this purpose. IR2130 MOSFET and
IGBT gate driver IC is the simplest, smallest and low cost solution to drive IGBTs up
to 600V in applications up to 12kW, and can save over 30% in part count in a 50%
smaller PCB area compared to a discrete opto-coupler or transformer based solution.
With the addition of few external components, IR gate driver ICs provide full driver
69
capability with extremely fast switching speeds, designed-in ruggedness and low-
power dissipation.
IR2130 generate the current and voltage necessary to turn MOSFETs or IGBTs on
and off from the logic output of a DSP, micro-controller or other logic device. The
input is typically a 3.3 volt logic-level signal. All IR gate driver ICs are CMOS
compatible, and most are TTL compatible. Output currents are up to 2A.
3.9.1 ADVANTAGES
Dead-time as low as 500ns allows frequency up to 100khz
Increases speed range and torque control of motor drives
Enable rugged gate drive design
Low power dissipation
Doesn't need auxiliary power supply
10X faster delay matching (±50ns)
No degradation of performance over time
Shorter time to signal over-current 1.5µs versus 6µs)
Reduced EMI and voltage spikes
3.9.2 Applications
Motor Drive
Lighting Ballast
Switched Mode Power Supplies
Automotive
Plasma Display Panels
70
3.9.2.1 IR Gate Driver ICs enable rugged driver designs
IR Gate Driver ICs are specifically designed with motor drive applications in mind.
The newest soft-turn-on limits voltage and current spike and reduce EMI. In addition,
they have up to 50V/ns dV/dt immunity and are tolerant to negative voltage transient.
The under-voltage lock-out available for most drivers prevents shoot-through currents
and device failures during power-up and power-down without any additional
circuitry. The output drivers feature a high pulse current buffer stage designed for
minimum driver cross-conduction.
Noise immunity is important for the high-side position which has a floating voltage
and is susceptible to high noise levels, particularly in motor drive applications. Noise
immunity ensures that the MOSFET or IGBT doesn't turn on accidentally. Noise
immunity is obtained by using Schmitt-triggered input with pull-down. Additional
noise immunity is obtained with separate logic and ground pins in some ICs, such as
the 600V ICs in 14-pin packages.
3.9.2.2 IR Gate Driver ICs enable fast switching speeds
IR Gate Drive ICs have ten times better delay matching performance than opto-
coupler-based solutions. Delay matching between the low-side and high-side driver is
typically within ± 50ns (and as low as ± 10ns for some specialty products), allowing
complete dead-time control for better speed range and torque control in motor drive
applications. Fast switching also reduces switching power losses and allows
leveraging the full benefits of the fastest IGBTs available on the market today for
better torque control over a wider speed range.
71
3.10 Control Section
After discussing power supply and inverter section, the third important section of
drive is control section. Control section generates signals to switch IGBT‟s of inverter
in proper manner so that the desired operation is achieved. Variation of frequency and
voltage etc all depends upon the switching sequence and switching rate. The control
circuit can be obtained in several ways but in our project we used PIC18f4431 for this
purpose. Its features like dedicated power control PWM channels along with dead
time control options make it a very useful microcontroller for power applications. A
junk of circuitry can be eliminated by using this microcontroller. [6-9]
3.10.1 Architecture of PIC 18f4431
PIC 18f4431 has architecture which is very similar to rest of micro controllers of
PIC18f series. Here we will discuss only those registers which are very closely related
to Power control PWM generation.
The pin configuration of PIC 18f4431 is shown below in figure
Figure 3.20, Pin configuration of PIC18F4431
72
As evident from figure 3.20 it is a 40 pin IC. Most of the pins are multiplexed and are
capable of performing different functions. There function depends upon the
configuration of registers. For example by configuration of ADCON register the pins
of port A and port E can be used as analog inputs. While at other configuration they
can be used as digital I/O pins.
In our project we use this microcontroller to generate pulses of sinusoidal PWM.
PWM module was used for this purpose. To control PWM module total 22 registers
are used. Eight of them configure the module while remaining registers are necessary
to set the timings for the generation of PWM. The eight configuration registers are as
follow:
• PWM Timer Control Register 0 (PTCON0)
• PWM Timer Control Register 1 (PTCON1)
• PWM Control Register 0 (PWMCON0)
• PWM Control Register 1 (PWMCON1)
• Dead-Time Control Register (DTCON)
• Output Override Control Register (OVDCOND)
• Output State Register (OVDCONS)
• Fault Configuration Register (FLTCONFIG)
Dead Time Control function is very useful because otherwise a lot of circuitry will be
required to generate dead time to avoid short circuit in the inverter.
73
There are also 14 registers that are configured as seven register pairs of 16 bits. These
are used for the configuration values of specific features. They are;
• PWM Time Base Registers (PTMRH and PTMRL)
• PWM Time Base Period Registers (PTPERH and PTPERL)
• PWM Special Event Trigger Compare Registers (SEVTCMPH and
SEVTCMPL)
• PWM Duty Cycle # 0 Registers (PDC0H and PDC0L)
• PWM Duty Cycle # 1 Registers (PDC1H and PDC1L)
• PWM Duty Cycle #2 Registers (PDC2H and PDC2L)
• PWM Duty Cycle #3 Registers (PDC3H and PDC3L)
Above eight registers are used to set the duty cycle of 4 PWM channels with
complementary out puts.
Apart from the PWM generation the microcontroller was used for LCD and Serial
port interface.
74
3.11 LCD Interfacing with Micro Controller
Large numbers of embedded projects require some type of user interface. This
includes displaying numerical, textual and graphical data to user. For very simple
numerical display we can use 7 segment displays. If the requirement is little more
than that, like displaying some alphanumeric text, we can use LCD Modules. They are
cheap enough to be used in low cost projects. They come in various sizes for different
requirement. A very popular one is 16x2 model. It can display 2 lines of 16
characters. Other models are 16x4, 20x4, 8x1, 8x2 etc. In our project we used 20x4
LCD.
A PIC Microcontroller can be easily made to communicate with LCD by using
the built in Libraries of MikroC. Interfacing between PIC and LCD can be 4-bit or 8-
bit. The difference between 4-bit and 8-bit is how data are send to the LCD. In the 8-
bit mode to write an 8-bit character to the LCD module, ASCII data is send through
the data lines DB0- DB7 and data strobe is given through the E line.
But in our project we interfaced the controller using 4-bit mode. It uses only 4 data
lines. In this mode the 8-bit ASCII data is divided into 2 parts which are sent
sequentially through data lines DB4 – DB7 with its own data strobe through the E
line. The idea of 4-bit communication is to save as much pins that used to interface
with LCD. The 4-bit communication is a bit slower when compared to 8-bit. The
speed difference is only minimal, as LCDs are slow speed devices the tiny speed
difference between these two modes is not significant.
75
3.12 Implementation of Project
Before simulating the three phase variable frequency drive we worked on the
simulation of single phase VFD and after that we extended this scheme towards three-
phase VFD.
3.12.1 Single Phase Scheme of VFD
The basic scheme we employed for single phase VFD is that; we generated two types
of the sinusoidal waveforms; one inverted and one non-inverted. Then we compare
these two sinusoidal waveforms with high frequency (typically 5 kHz) triangular
waveform. This triangular waveform is generated from the square waveform
generator.
After comparing two sinusoidal waveforms with triangular waveform we obtain 5 V
PWM pulses. Now these two PWM pulses are AND with continuous square
waveform through an AND gate IC. On coming out from the AND gate we invert one
of the PWM pulses for obtaining the negative cycle of the waveform.
Before giving these PWM pulses to the H-bridge these 5V pulses are amplified to
12V through an optocoupler IC. And thus sinusoidal waveform of variable frequency
can be obtained from the output of the H-bridge.
76
Figure 3.21, Single Phase Scheme of Variable frequency Drive
77
3.12.2 Three Phase Scheme of VFD
After successfully completing the simulation of single phase variable frequency drive,
we extended our work towards the three phase variable frequency drive. The block
diagram of this scheme explaining its methodology of implementation is shown in
figure. The brief explanation of this scheme is that three phase sinusoidal waveforms
are compared with variable frequency reference triangular waveform through a
comparator. Thus SPWM signals are generated.
Each of the comparator has two outputs, one non-inverted through the multiplier
circuit and one inverted through the inverter. Now how this scheme will work for
floating ground issue? The non-inverted pulse will be given at 170V i.e. 15V plus the
DC input of the inverter, to the upper three IGBTs of the inverter. While the inverted
pulses will drive the gates of IGBTs present on the lower side of the inverter.
78
Comparator
1
Comparator
3
Comparator
2
155 VDC
Three Phase Sinusoidal Waveform
Triangular Waveform
Generator
INDUCTION MOTOR LOAD (DELTA
CONNECTED)
Figure 3.22, Three phase scheme of variable frequency Drive
79
3.12.3 Three Phase SPWM based VFD Using PIC 18f4431
The scheme of figure 3.23 is the final scheme of the project. This scheme consists of
three transformers. First transformer steps down 220V (rms) to 18V (rms). Then this
18V will serve as the input for the two regulated power supplies. 5V regulated power
supply for PIC microcontroller and 15V for gate driver IC so that it can convert the
5V SPWM pulses generated from the microcontroller to 15V pulses in order to give to
the gates of the IGBTs.
Another isolated power supply is designed especially for serial port. The reason for
the isolation of this supply is to save our computer from any electrical mishap. So,
second transformer serves as the input for this power supply.
Now as the final stage of this project is DC to AC inverter. To supply 110V rms
motor we require 150V dc. So another DC of 150V is required and this is addressed
by 220V rms to 110V rms transformer.
The brief functions of the components are:
1. LCD will display the running frequency of the motor.
2. PIC microcontroller will generate six 5V spwm pulses.
3. Driver IC will convert the 5V SPWM pulses into 15V pulses plus it will also
take the issues of floating ground & dead time into account automatically.
4. Serial port will handle the two way communication between the computer &
the PIC microcontroller.
80
Figure 3.23, Three Phase SPWM based VFD block diagram Using PIC 18f4431
81
Chapter 4
Simulations and Results
4.1 Simulation in OrCAD Pspice
We started our work with simulation of single phase inverter using OrCAD Pspice.
The methodology was to compare sinusoidal wave form with triangular waveform to
get sinusoidal PWM. The triangular waveform was generated using op amps and
combination of resistors and capacitors as shown in figures 4.1 and 4.2.
Figure 4.1, Triangular waveform generator circuit
Figure 4.2, Output of Triangular wave generator circuit
82
4.1.1 Issues
First problem encountered in the simulation of digital gates using OrCAD Pspice was
that the simulation of digital circuits was not according to scale. Only pulses are
shown in the diagram without any scale of voltage. The output pulses of AND gates
and NOT gates are shown in figure 4.3, It is evident that they are not according to
scale.
Figure 4.3, Output of AND and NOT gate using OrCAD Pspice (not to scale)
Secondly, the opto-coupler or gate driver IC (used to remove the issue of floating
ground) package was not available in Orcad.
So we used multiplier blocks in place of the driver IC before the H-bridge. Moreover
the problem of digital logic gates was also taken account by these blocks.
The complete single phase inverter circuit with simulation results is shown in figures
4.4 and 4.5.
83
0
0
M3
IRF740
M4
IRF740
V-V+
0
U5
LM741
+3
-2
V+7
V-4
OU
T6
OS1
1
OS2
5
0
V32
FREQ
= 50VAM
PL = 1VO
FF = 0
M5
IRF740
0
M6
IRF740
V33
1.5
V10
15.67
U6
LM741
+3
-2
V+7
V-4
OU
T6
OS1
1
OS2
5
0
0
V34
15
0
R14
1k
R15
1k
0
0
U1
LM741
+3
-2
V+7
V-4
OU
T6
OS1
1
OS2
5
U7
LM741
+3
-2
V+7
V-4
OU
T6
OS1
1
OS2
5
0
0
V36
1.5
V37
15
R1
1k
R2
1k
V115Vdc
V215Vdc0
C1100n
0
U2
LM741
+3
-2
V+7
V-4
OU
T6
OS1
1
OS2
5
C2.001u
R3
1meg
R4
100k
R5
10k
V3
12
V4
12
U3
LM741
+3
-2
V+7
V-4
OU
T6
OS1
1
OS2
5
V11
15.67
R6
47k
0
U4
LM741
+3
-2
V+7
V-4
OU
T6
OS1
1
OS2
5
R7
1k
R81k
R9
1kR
10
1k
V5FR
EQ = 50
VAMPL = 8
VOFF = 0
V6
FREQ
= 50VAM
PL = 8VO
FF = 0
0
V9220
R13
50
Figure 4.4, Complete Single Phase inverter circuit
84
Figure 4.5, Simulation results of single phase inverter circuit
4.2 Three Phase Inverter Circuitry
We extended this single phase inverter circuit simulation towards three phase inverter.
We did our simulation in the OrCAD Pspice first but shifted to the MULTISIM 12.0
which is another simulation package available at the NI website.
The reasons behind our shifting were:
1- Unavailability of Load model in OrCAD Pspice 10.5.
2- The logic gate pulses timing diagrams were not satisfactory.
The simulation results in OrCAD Pspice are shown below;
85
Figure 4.6, Simulation results using OrCAD Pspice
4.2.2 Solution Proposed
National Instruments Multisim 12 can easily solve the above stated problems. The
three phase inverter complete circuitry with simulation in the National Instruments
Multisim 12.0 is shown in figure 4.7.
86
V1
7 Vp
k 50 H
z 0°
U4
LM
74
1A
H/8
83
3 2
47
6
51
R1
3
1.0
kΩ
R1
4
1.0
kΩ
V4
15 V
V5
15 V
V2
7 Vp
k 50 H
z 120°
U1
LM
74
1A
H/8
83
3 2
47
6
51
R1
1.0
kΩ
R2
1.0
kΩ
V3
15 V
V6
15 V
U6
LM
74
1A
H/8
83
3 2
47
6
51
R1
5
10
kΩ
V1
01
2 V
V1
11
2 V
R1
71
00
kΩ
R1
81
0kΩ
C
41
0n
F
U7
LM
74
1A
H/8
83
3 2
47
6
51
R1
9
15
kΩ
C5
10
0n
F
R2
0
1kΩ
R5
1kΩ
R6
1kΩ
V12
12 V
V13
12 V
XSC1
AB
Ext Trig+
+
_
_+
_
V16
7 Vp
k 50 H
z 0°
U3
OP
AM
P_5T
_VIR
TU
AL
U8
LM
74
1A
H/8
83
3 2
47
6
51
R9
10
kΩ
V1
71
2 V
V1
81
2 V
R1
01
00
kΩ
R1
11
0kΩ
C
11
0n
F
U9
LM
74
1A
H/8
83
3 2
47
6
51
R1
2
15
kΩ
C2
10
0n
F
R1
6
1kΩ
R2
1
1kΩ
R2
2
1kΩ
V19
12 V
V20
12 V
XSC3
AB
Ext Trig+
+
_
_+
_
U10
OP
AM
P_5T
_VIR
TU
AL
XSC4
AB
Ext Trig+
+
_
_+
_
XSC5
AB
Ext Trig+
+
_
_+
_
U5
LM
74
1A
H/8
83
3 2
47
6
51
R7
10
kΩ
V1
41
2 V
V1
51
2 V
R8
10
0kΩ
R3
01
0kΩ
C
71
0n
F
U1
4
LM
74
1A
H/8
83
3 2
47
6
51
R3
1
15
kΩ
C8
10
0n
F
R3
2
1kΩ
R3
3
1kΩ
R3
4
1kΩ
V25
12 V
V26
12 V
XSC6
AB
Ext Trig+
+
_
_+
_
U15
OP
AM
P_5T
_VIR
TU
AL
U1
1
LM
74
1A
H/8
83
3 2
47
6
51
R2
3
10
kΩ
V2
11
2 V
V2
21
2 V
R2
41
00
kΩ
R2
51
0kΩ
C
31
0n
F
U1
2
LM
74
1A
H/8
83
3 2
47
6
51
R2
6
15
kΩ
C6
10
0n
F
R2
7
1kΩ
R2
8
1kΩ
R2
9
1kΩ
V23
12 V
V24
12 V
XSC8
AB
Ext Trig+
+
_
_+
_
V28
7 Vp
k 50 H
z 240°
U13
OP
AM
P_5T
_VIR
TU
AL
U1
6
LM
74
1A
H/8
83
3 2
47
6
51
R3
5
10
kΩ
V2
91
2 V
V3
01
2 V
R3
61
00
kΩ
R3
71
0kΩ
C
91
0n
F
U1
7
LM
74
1A
H/8
83
3 2
47
6
51
R3
8
15
kΩ
C1
0
10
0n
F
R3
9
1kΩ
R4
0
1kΩ
R4
1
1kΩ
V31
12 V
V32
12 V
XSC10
AB
Ext Trig+
+
_
_+
_
V33
7 Vp
k 50 H
z 120°
U18
OP
AM
P_5T
_VIR
TU
AL
XSC11
AB
Ext Trig+
+
_
_+
_
V7
7 Vp
k 50 H
z 240°
U2
LM
74
1A
H/8
83
3 2
47
6
51
R3
1.0
kΩ
R4
1.0
kΩ
V8
15 V
V9
15 V
U1
9
LM
74
1A
H/8
83
3 2
47
6
51
R4
2
10
kΩ
V2
71
2 V
V3
41
2 V
R4
31
00
kΩ
R4
41
0kΩ
C
11
10
nF
U2
0
LM
74
1A
H/8
83
3 2
47
6
51
R4
5
15
kΩ
C1
2
10
0n
F
R4
6
1kΩ
R4
7
1kΩ
R4
8
1kΩ
V35
12 V
V36
12 V
XSC12
AB
Ext Trig+
+
_
_+
_
U21
OP
AM
P_5T
_VIR
TU
AL
XSC13
AB
Ext Trig+
+
_
_+
_
S2
V3
7
22
0 V
S3
S5
S6
S4
S1
V38
200 V 100 H
z
3PH
A1
1 V/V
0 V
YX
V39
2.4 V
A2
1 V/V
0 V
YX
V40
2.4 V
A3
1 V/V
0 V
YX
V41
2.4 V
A4
1 V/V
0 V
YX
V42
2.4 V
A5
1 V/V
0 V
YX
V43
2.4 V
A6
1 V/V
0 V
YX
V44
2.4 V
XSC2
AB
Ext Trig+
+
_
_+
_
87
This simulation has been completed in two phases.
4.2.3 PHASE 01
In the first phase, the simulation is performed by using the six multiplier blocks
before the Hex-Bridge. These multiplier blocks just convert the 5V 180 degree
conduction pulses, generated by comparing six sinusoidal pulses (three inverted &
three non-inverted) with reference triangular waveform, into 15V conduction pulses
for gate to source firing of IGBTS.
Figure 4.8, Simulation using Multiplier Blocks
4.2.4 PHASE 02 (Circuit Optimization)
In the second phase, we performed the simulation by reducing the number of
multiplier circuits from six to three. The idea behind this optimization was that, we
88
introduced three inverted ICs after three multipliers. We took two outputs from each
multiplier, one inverted and one non-inverted. Three non-inverted pulses (positive)
were applied to the switches present in the upper part of the Hex bridge legs and vice-
versa.
Finally, the three sinusoidal waveforms having 120 degree phase difference, having
155V peak & 110V rms were applied to the load model and simulated as cleared from
the simulation results shown in figure 4.9.
Figure 4.9, Output waveforms
89
4.3 Issues before Hardware Implementation
Now up to this point our simulation was complete and the project was ready for
hardware implementation but there were some issues which are discussed below.
As no practical IC model exists that could generate directly 3-phase sinusoidal
waveform of variable frequency while keeping the phase difference between the
waveforms constant. So, how a three phase sinusoidal waveform of variable
frequency could e generated while keeping the phase difference constant?
1. Capacitive reactance is frequency dependent. As the frequency is changed
its reactance will change so, the solution of phase difference by using RC
phase shifter would also not work on variable frequency.
2. Another advanced solution we found is to answer this issue is to use
AD9833IC. But no simulation package is available for simulating
AD9833.
3. Another solution was proposed was to use EEPROM memory for storing
the sine waveform data and to generate sinusoidal waveform by adding a
Digital to analog converter. But this solution was rejected as the project
would become uneconomical then.
So, by keeping in mind the above solutions we finally decided to move on PIC
microcontroller that is an efficient and cost effective way of generating PWM signals.
We choose PIC 18f4431 for this purpose as it has built in six PWM channels & also it
takes the dead time issue into account automatically.
90
4.4 Three Phase Inverter Simulation using PIC18f4431
By using six PWM channels of PIC 18f4431 we generated six SPWM pulses that
were sent to the gate driver IC IR2130. This IC converts these SPWM pulses to the
required potential and finally sent them to the gates of IGBTs in hex bridge for
switching. This IC eliminates the need of the opto-couplers. The microcontroller
simulation performed in Proteus is shown in figure 4.10.
Figure 4.10, Simulation results using PIC 18f4431
The schematic diagram, drawn in Orcad Pspice is shown in figure 4.11.
91
Figure 4.11, 3-phase schematic using 18f4431 in OrCAD Pspice
92
4.5 Transformer Design Simulator
A snapshot of LabView based transformer designer is shown in figure 4.12. It can
calculate the area of the transformer (VA), number of primary and secondary
transformer turns, area of the wires as well as the area of the bobbin. An additional
feature of this simulator is that it can also tell us the wire gauge. All the formulae used
behind this simulator already explained previously in the transformer design section.
Figure 4.12, LabView based Transformer Design Simulator
93
Conclusion
A PIC microcontroller (18f4431) based PWM controlled inverter fed Induction Motor
drive has been designed and implemented successfully. The simulation and hardware
implementation results are presented to verify the feasibility of the system. The
implementation of the proposed work shows the practical industrial application of
PWM variable frequency drives.
94
Future Recommendations
Feedback loop can be added to make the operation more accurate by using
feedback loop one can easily control the whole frequency drive.
Use of GSM module can extend the distance of operation of drive from
control room.
High voltage variable frequency drives can be designed just by using high
rating components, safety is required to achieve that goal.
Harmonics can be removed by performing detailed harmonic analysis.
95
Appendix
A.1 Datasheets
A.1.1 INSULATED GATE BIPOLAR TRANSISTOR WITH ULTRAFAST
SOFT RECOVERY DIODE (IRG4BC30UDPbF)
Features
UltraFast: Optimized for high operating frequencies 8-40 kHz in hard
switching, >200 kHz in resonant mode
Generation 4 IGBT design provides tighter parameter distribution and
higher efficiency than Generation 3
IGBT co-packaged with HEXFREDTM ultrafast, ultra-soft-recovery anti-
parallel diodes for use in bridge configurations
Industry standard TO-220AB package
Lead-free
96
Benefits
Generation -4 IGBT's offer highest efficiencies available
IGBTs optimized for specific application conditions
HEXFRED diodes optimized for performance with IGBTs . Minimized
recovery characteristics require less/no snubbing
Designed to be a "drop-in" replacement for equivalent
Absolute Maximum Ratings
97
A.1.2 PIC18F4431
(40-Pin Enhanced, Flash Microcontrollers with nanoWatt Technology,
High Performance PWM and A/D)
Microcontroller Features
100,000 erase/write cycle enhanced Flash program memory typical
1,000,000 erase/write cycle data EEPROM memory typical
Flash/data EEPROM retention: 100 years
Self-programmable under software control
Priority levels for interrupts
8 X 8 Single-cycle Hardware Multiplier
Extended Watchdog Timer (WDT)
o Programmable period from 41 ms to 131s
Single-supply In-Circuit Serial Programming™
(ICSP™) via two pins
In-Circuit Debug (ICD) via two pins
o Drives PWM outputs safely when debugging
98
14-bit Power Control PWM Module
Up to 4 channels with complementary outputs
Edge- or center-aligned operation
Flexible dead-band generator
Hardware fault protection inputs
Simultaneous update of duty cycle and period
o Flexible special event trigger output
A.1.3 3-PHASE BRIDGE DRIVER (IR2130)
Features
Floating channel designed for bootstrap operation
Fully operational to +600V
Tolerant to negative transient voltage dV/dt immune
Gate drive supply range from 10 to 20V
99
Undervoltage lockout for all channels
Over-current shutdown turns off all six drivers
Independent half-bridge drivers
Matched propagation delay for all channels
2.5V logic compatible
Outputs out of phase with inputs
Cross-conduction prevention logic
Also available lead-free
Absolute Maximum Ratings
100
A.2 Transformer designing Tables
A.2.1 Table A
The table below helps you to select the gauge and turns per sq. cm of copper wire by
matching them with the selected current rating of the winding appropriately.
SWG------- (AMP) ------- Turns per Sq.cm.
10----------- 16.6 ---------- 8.7
11----------- 13.638------- 10.4
12----------- 10.961------- 12.8
13----------- 8.579--------- 16.1
14----------- 6.487--------- 21.5
15----------- 5.254--------- 26.8
16----------- 4.151--------- 35.2
17----------- 3.178--------- 45.4
18----------- 2.335--------- 60.8
19----------- 1.622--------- 87.4
20----------- 1.313--------- 106
21----------- 1.0377-------- 137
22----------- 0.7945-------- 176
23----------- 0.5838--------- 42
24----------- 0.4906--------- 286
25----------- 0.4054--------- 341
101
26----------- 0.3284--------- 415
27----------- 0.2726--------- 504
28----------- 0.2219--------- 609
29----------- 0.1874--------- 711
30----------- 0.1558--------- 881
31----------- 0.1364--------- 997
32----------- 0.1182--------- 1137
33----------- 0.1013--------- 1308
34----------- 0.0858--------- 1608
35----------- 0.0715--------- 1902
36----------- 0.0586---------- 2286
37----------- 0.0469---------- 2800
38----------- 0.0365---------- 3507
39----------- 0.0274---------- 4838
40----------- 0.0233---------- 5595
41----------- 0.0197---------- 6543
42----------- 0.0162---------- 7755
43----------- 0.0131---------- 9337
44----------- 0.0104--------- 11457
45----------- 0.0079--------- 14392
46----------- 0.0059--------- 20223
47----------- 0.0041--------- 27546
48----------- 0.0026--------- 39706
49----------- 0.0015--------- 62134
50----------- 0.0010--------- 81242
102
A.2.2 Table B
This Table B enables you to make your own transformer design by comparing the
calculated Winding Area with the relevant required Tongue Width and Lamination
Type number.
Type -------------------Tongue----------Winding
No. ---------------------Width-------------Area
17(E/I) -------------------- 1.270------------1.213
12A(E/12I) ---------------1.588-----------1.897
74(E/I) --------------------1.748-----------2.284
23(E/I) --------------------1.905-----------2.723
30(E/I)--------------------2.000-----------3.000
21(E/I)--------------------1.588-----------3.329
31(E/I)--------------------2.223-----------3.703
10(E/I)--------------------1.588-----------4.439
15(E/I)-------------------2.540-----------4.839
33(E/I)--------------------2.800----------5.880
1(E/I)----------------------2.461----------6.555
14(E/I)--------------------2.540----------6.555
11(E/I)---------------------1.905---------7.259
34(U/T)--------------------1/588---------7.259
3(E/I)-----------------------3.175---------7.562
9(U/T)----------------------2.223----------7.865
9A(U/T)----------------------2.223----------7.865
11A(E/I)-----------------------1.905-----------9.072
4A(E/I)-----------------------3.335-----------10.284
103
2(E/I)-----------------------1.905-----------10.891
16(E/I)---------------------3.810-----------10.891
5(E/I)----------------------3.810-----------12.704
4AX(U/T) ----------------2.383-----------13.039
13(E/I)--------------------3.175-----------14.117
75(U/T)-------------------2.540-----------15.324
4(E/I)----------------------2.540----------15.865
7(E/I)----------------------5.080-----------18.969
6(E/I)----------------------3.810----------19.356
35A(U/T)-----------------3.810----------39.316
8(E/I)---------------------5.080----------49.803
104
References
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105
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