World Academy of Science, Engineering and Technology 42 2008
Analysis of Variable Frequency Three Phase
Induction Motor Drive
Thida Win, Nang Sabai, and Hnin Nandar Maung
Abstract— AC motor drives are widely used to control the speed
of conveyor systems, blower speeds, pump speeds, machine tool
speeds, and other applications that require variable speed with
variable torque. 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, this will, in turn, feed the PWM
inverter. The PWM inverter is controlled to produce a desired
sinusoidal voltage at a particular frequency, which is filtered by the
use of an inductor in series and capacitor in parallel and then through
to the squirrel cage induction motor.
II. PROCEDURE FOR FREQUENCY CONTROLLED INDUCTION
MOTOR DRIVE
A. Variable Frequency AC Motor Drive
The traditional variable-frequency drive (known as a voltsper-hertz (V/Hz) changes the motor’s frequency and voltage
using solid-state control units.
Keywords—Pulse-width modulated inverter, diode rectifier,
three-phase induction motor.
Fig. 1 A block diagram of a variable-speed-control system
I. INTRODUCTION
A
modern adjustable speed AC machine system is equipped
with an adjustable frequency drive that is a power
electronic device for speed control of an electric machine. It
controls the speed of the electric machine by converting the
fixed voltage and frequency of the grid to adjustable values on
the machine side. There are many types of inverters, and they
are classified according to number of phases, use of power
semiconductor devices, commutation principles, and output
waveforms.
This research interest in three-phase inverter circuit that
changes DC input voltage to a three-phase variable-frequency
variable-voltage output. Three-phase inverters are also used in
applications in which AC with a controllable frequency is
required. In this application, three-phase AC is rectified into
DC and then filtered to minimize the ripple content. The DC
link is generally used for this purpose. This is a variable DC
obtained by employing three-phase full controlled power
transistors bridge. This controlled DC is converted into
controlled pulses by means of as voltage to frequency
converter. These controlled pulses are fed to the inverter
bridge for producing the variable voltage variable frequency
output. This output is fed to the three-phase induction motor
for controlling its speed.
The basic steps for this process are shown in the block
diagram of Fig. 1, and the circuit is known as a DC link
converter. The first step is to convert 60-Hz AC into DC
power. The second step is to convert this DC power back into
AC at the desired frequency.
B. Transistor Based Variable-Frequency Induction Motor
Drives
The modern strategy for controlling the AC output of such a
power electronic converters is the technique known as PulseWidth Modulation (PWM), which varies the duty cycle of the
converter switch(es) at a high switching frequency to achieve a
target average low frequency output voltage or current. In
principle, all modulation schemes aim to create trains of
switched pulses which have the same fundamental volt–second
average as a target reference waveform at any instant. The
major difficulty with these trains of switched pulses is that they
also contain unwanted harmonic components which should be
minimized.
Three main techniques for PWM exist. These alternatives
are:
1. Switching at the intersection of a target reference
waveform and a high frequency triangular carrier
(Double Edged Naturally Sampled Sine-Triangle
PWM).
2. Switching at the intersection between a regularly
sampled reference waveform and a high frequency
triangular carrier (Double Edged Regular Sampled
Sine-Triangle PWM)).
Thida Win is with the Electrical Power Engineering Department,
Mandalay
Technological
University,
Myanmar
(e-mail:
malthida80@gmail.com).
Nang Sabai was with the Electrical Power Engineering Department,
Mandalay
Technological
University,
Myanmar
(e-mail:
:nangsabai@gmail.com).
Hnin Nandar Maung is with the Electrical Power Engineering Department,
MandalayTechnologicalUniversity,
Myanmar
(email:hninnandarmg@gmail.com).
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World Academy of Science, Engineering and Technology 42 2008
3.
Switching so that the amplitude and phase of the
target reference expressed as a vector is the same as
the integrated area of the converter switched output
over the carrier interval (Space Vector PWM).
loss and the stator copper loss, and produce a high pitch
accoustic noise.
While any increase in flux beyond the rated value is
undesirable from the consideration of saturation effects, a
decrease in flux is also avoided to retain the torque capability
of the motor. Therefore, the variable frequency control below
the rated frequency is generally carried out by reducing the
machine phase voltage, V, along with the frequency in such a
manner that flux id maintained constant. Above the rated
frequency, the motor is operated at a constant voltage because
of the limitation imposed by stator insulation or by supply
voltage limitations.
And per unit frequency k is
K = f / f rated
Where
Fig. 2 Basic circuit topology of pulse-width modulated inverter drive
f = operating frequency
f rated = rated frequency of the motor
Fig. 4 Single-phase equivalent circuit of polyphase induction motor
D. Operation below the Rated Frequency (K< 1)
It is generally preferred to operate the motor at a constant
flux. The motor will operate at constant flux if Im is maintained
constant at all operation points. From Fig. 3 can write the
equation at the rated condition of motor operation:
Fig. 3 Regular asymmetrically sampled pulse width modulation
C.
Variable Frequency Control of Induction Motor
Synchronous speed,
Ns
Where, f = supply frequency
p = poles
Im =
=120f/p
E rated
E rated
1
=
.
Xm
f rated 2π L m
Where Lm= magnetiziting inductance
When the motor is operated at a frequency f, then
Synchronous speed is directly proportional to the supply
frequency. Hence, by changing the frequency, the synchronous
speed and motor speed can be control below and above the
normal full-load speed. The voltage induced in the stator,E, is
proportional to the product of the slip frequency and air gap
flux. The motor terminal voltage can be considered
proportional to the product of the frequency and the flux, if the
stator drop is neglected. Any reduction in the supply frequency
without a change in the terminal voltage causes an increase in
the air-gap flux. Induction motors are designed to operate at
the knee point of the magnetization characteristics to make full
use of the magnetic material. Therefore the increase in flux
will saturate the motor. This will increase the magnetizing
current, distort the line current and voltage, increase the core
Im=
E
E
1
=
.
K.X m K . f rated 2πLm
By the comparison of Equations, Im will stay constant at a
value equal to its rated value if
E = K. E rated
So the flux will remain constant if the back emf changes in
the same ratio as the frequency, in other word, when (E/f )
ratio is maintained constant.
Motor operation for a constant (E/f) ratio and at a frequency
f,
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World Academy of Science, Engineering and Technology 42 2008
K.E rated
I2 =
=
2
 R2 
2

 + (KX 2 )
 S 
Where
S=
when the machine is loaded. From Equation, a constant value
of (KS) implies the motor operation at a constant slip speed ωs.
So, it becomes clear that for any value of T, the drop in the
motor speed from its no-load speed (Kωs) is the same for all
frequencies. Hence, the machine speed-torque characteristics
for 0 < s < Sm are parallel curves. The natures of speed-torque
curves for the variable frequency operation at a constant flux
are shown in Fig. 4 both for motoring and braking operations.
E rated
R 2 2 / (KS) + X 2 2
2
K.ω s − ω r
Kω s
Note that ωs is the synchronous speed at the rated frequency.
Now the developed torque is
T=
3 2
I 2 R 2 /S
Kω s
T=
3  E 2rated R 2 (KS) 


ω s  R 22 / (KS)2 + X 22 
Now, E is maintained constant for a given frequency. The
power transferred across the air-gap will be maximum at a slip
Sm for which
K.X2 =± R2 / Sm
(or)
Fig. 5 Speed – torque curves with variable frequency control
R2
Sm = ±
KX 2
E. Test and Result of the drive
3 E 2rated
Tmax=±
.
2ω s X 2
So , for a variable frequency control at a constant flux, the
breakdown torque remain constant for all frequencies, both
during motoring and regenerative breaking .Also, the
examination of Equations shows that for a constant (SK),the
_
rotor current I2 and torque T are constant . Now, if
E is take
_
as a reference vector, then the phase lag of
I 2 is given by
Fig. 6 Complete block diagram of the drive
Qr=tan-1(K.s.X2/R2)
The pulse width modulated (PWM) inverter for variable
speed drive of induction motor circuit drives small induction
motors up to about 0.5 horse power, 380 volts, variable
frequencies. The frequency may be adjusted from 16 Hz to 60
Hz. So, the motor speed can be varied from 464 rpm to 1740
rpm. The complete system of this thesis consists of an AC
voltage input that is put through a diode bridge rectifier to
produce a DC output which across a shunt capacitor, this will,
in turn, feed the PWM inverter. The PWM inverter is
controlled to produce a desired sinusoidal voltage at a
particular frequency to the squirrel cage induction motor.
Since Qr is also constant for a given (SK), the motor
current will also be constant. Thus, the motor operates at
constant value of torque, I1 and I2 when the flux and (KS) are
maintained constant.
The physical significance of SK ,
SK =
Kω s − ω r ω ss
=
ωs
ωs
Where
Note that
ωs
ω ss = Kω s − ω r
1. Laboratory Test Arrangement
Performance test and results of variable frequency drive of
three-phase induction motor are expressed as follows:
is the speed, which is the difference in the
frequency f (or synchronous speed Kωs) and the rotor speed ωr.
Wss is the drop in motor speed from its no-load speed (Kωs)
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Supply voltage
380 volts
Supply frequency
50 Hz
World Academy of Science, Engineering and Technology 42 2008
Motor rating
0.5 hp
Number of poles
4
Normal speed
1450 rpm
Number of speed up step
45
Maximum speed
1740 rpm
Minimum speed
464 rpm
Maximum frequency
60 Hz
Minimum frequency
16 Hz
TABLE I
SPEED-UP TESTING OF VARIABLE FREQUENCY DRIVE OF THREE-PHASE
INDUCTION MOTOR
No. of Step
Frequency (Hz)
Speed (rpm)
1
16
464
2
25
725
3
32
928
4
45
1305
5
50
1450
6
60
1740
Fig. 8 Photo of the Completed Drive Circuit
2.Output Voltage Waveform of the Inverter Circuit
The output voltage waveform of the inverter circuit is
shown in Fig. 7. This forms step sine waves, with 120 degrees
phase shift to each other. When the drive is tested with the
digital scope, the output frequency of the drive is 55 Hz and
the output voltage is 227 V. The drive is adjusted with the
frequency to control the speed of the induction motor.
Fig 9 Output voltage waveform of PIC18F452 controller circuit
Fig. 7 Photo of Output voltage waveform of Inverter
Fig. 10 Output voltage waveform of gate driver circuit
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World Academy of Science, Engineering and Technology 42 2008
III. CONCLUSION
To control the speed of a three-phase induction motor in
open loop, supply voltage and frequency need to be varied
with constant ratio to each other. The author of this paper
directly contributed to the electronics design of the inverter
and controller. Also the author implemented the system in its
entirety and experimentally verified its operation at a wide
range of speed.
ACKNOWLEDGMENT
The author would like to express her deep gratitude to her
teacher, Professor Dr. Khin Aye Win, Yangon Technological
University, Myanmar for her guidance, help, support and
sharing ideas. The author is deeply grateful to her supervisor
Dr. Salai Tluang Za Thang, Lecturer of Electrical Power
Engineering Department, Mandalay Technological University,
Myanmar for his closed guidance, accomplished supervision
and suggestion for this paper.
REFERENCES
[1]
[2]
[3]
[4]
[5]
R.Krishnan, 2001. Electric Motor Drives (Modeling, Analysis, and
Control), Prentice Hall, Inc.
Ned Mohan, Torre M. Undeland, William P. Robbins, 1995, Power
Electronics Converters, Applications and Design, Wiley, New York.
Richard Valentine, 1998. Motor Control Electronic Handbook,
McGraw-Hill, New York.
Sigh, M. D. and Khanchandani, K. B. 2000. Power Electronic, Tata
McGraw-Hill Publishing Company Limited, Newdelhi.
Ham N. J., Hammerton C. J. and Sharples. D. , 2000. Power
Semiconductor Applications, Tata McGraw-Hill Publishing Company
Limited, Newdelhi.
Thida Win received her B.E degree in Electrical Power Engineering from
Mandalay Technological University and M.E degree in Electrical Power
Engineering from Yangon Technological University, Myanmar, then
following three years teaching in Technological University, Myanmar. Her
interests include Power Electronic Devices and its applications.
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