Download International Electrical Engineering Journal (IEEJ) Vol. 5 (2014) No.9, pp. 1545-1552

International Electrical Engineering Journal (IEEJ)
Vol. 5 (2014) No.9, pp. 1545-1552
ISSN 2078-2365
http://www.ieejournal.com/
Performance and Analysis of Switching
Function Based Voltage Source Inverter
Fed Induction Motor
Khadim Moin Siddiqui, Kuldeep Sahay, V.K. Giri
[email protected]

Abstract— In industries, the three phase squirrel cage
induction motor is widely used due to its simple construction,
robust design and low operational costs. The exploitation of
squirrel cage induction motor with power semiconductor
devices based inverters presents the greater advantages on cost
and energy efficiency, compared with other industrial solutions
for varying speed applications. Since, Inverter fed-induction
motors are gathering great attractiveness for multi-megawatt
industrial drive applications these days. In the present paper,
an extensive simulation has been carried out for open and
closed loop models of 3HP, 50 Hz, 1430 RPM switching
function based voltage source inverter fed into induction motor.
The transient analysis has been carried out by both models. The
analysis has been carried out in the recent MATLAB/Simluink
environment. The open and closed loop models give
encouraging results and observed that the closed loop model
gives better results as compared to open loop model with
reduced harmonics. Six motor signatures are used for analysis
purpose; these are stator current, rotor current, rotor speed,
electromagnetic torque, q-axis rotor flux and q- axis stator flux
respectively. Though, it has been seen that the stator current
parameter has been widely used parameter in last two decades
with Motor Current Signature Analysis (MCSA). Therefore, in
the harmonic analysis only stator current parameter is used.
The torque control method is used for controlling the induction
motor in closed loop due to its advantages over vector or fieldcontrol method.
Index Terms— Squirrel Cage Induction Motor (SCIM),
Voltage Source Inverter (VSI), Pulse Width Modulation
(PWM), Direct Torque Control, Open/Closed Loop,
MATLAB/Simulink.
I. INTRODUCTION
The three phase squirrel cage induction motor is simple,
efficient and robust asynchronous motor and often a natural
choice as a drive for industries with a very competitive
pricing. Induction motors are the most extensively used
electric motors for appliances, industrial control, automation
Khadim et. al.,
and transportation. These electric motors frequently called the
“workhorse” of the Motion Industry [1-4].
Initially, the induction motors named as constant speed
asynchronous motors. But, in the present time a lot of
applications require variable speed operations. For example, a
washing machine may utilizes different speeds for each wash
cycle. Historically, mechanical gear systems were widely
employed to achieve variable speed. Recently, electronic
power and control systems such as PWM inverter have
grown-up to allow these components to be used for motor
control in the place of mechanical gears [8-9].
The PWM inverter is not only control the motor's speed but
can also provide improve motor’s dynamic and steady state
characteristics. In addition, these devices can reduce the
system's average power consumption and noise generation of
the induction motor. The exploitation of static frequency
inverters are comprehends presently the most efficient
method to control the speed of induction motors. Voltage
Source Inverters (VSI) Inverters transform a constant
frequency constant amplitude voltage into a variable
(controllable) frequency-variable (controllable) amplitude
voltage. The discrepancy of the power frequency supplied to
the motor leads the discrepancy of the rotating of field speed,
which modifies the mechanical speed of the induction motor
[6,10].
The induction motor is being used these days in several
important applications in the place of D.C. motors. The most
significant feature which asserts induction motor as a tough
competitor to D.C. motor in the drives field is that its cost per
KVA is approximately one fifty of its counterpart and it seizes
higher appropriateness in antagonistic atmosphere [5,7-8].
Since, the modeling of induction motor has continuously
attracted the attention of the researchers because such
machines are made and used in leading number of
applications. These machines give varied modes of operation
in both under dynamic and steady state[12-13].
In electric drive system elements, these machines is a part
of the control system elements, which is to be controlled by
the dynamic behavior of Induction Motor (IM) then the
dynamic model of IM has to be preferred. The dynamic model
1545
Performance and Analysis of Switching Function Based Voltage Source Inverter Fed Induction Motor
International Electrical Engineering Journal (IEEJ)
Vol. 5 (2014) No.9, pp. 1545-1552
ISSN 2078-2365
http://www.ieejournal.com/
considers the instantaneous effects of varying voltage,
currents, stator frequency and torque disturbance [8-9].
In the present paper, the open and closed loop switching
function based voltage source inverter fed into induction
motor model has been developed in the recent
MATLAB/Simulink environment. These models are derived
by using d and q variables in a stationary rotating reference
frame. From these simulation models the transient behavior of
the used induction motor has been observed by stator current,
rotor current, rotor speed, electromagnetic torque and q-axis
stator and rotor fluxes.
II. MATHEMATICAL MODELLING of the MOTOR
The direct-quadrature-zero (dq0) transformation or
zero-direct-quadrature (0dq) transformation is a mathematical
tool which is used to simplify the analysis of three phase
circuits in the electrical engineering. For balanced three phase
circuits, the dq0 transform converts three AC quantities into
two imaginary DC quantities. Further, simplified calculations
can then be carried out on these imaginary DC quantities
before performing the inverse transform to recover the actual
three-phase AC results. It is frequently used in order to
simplify the analysis of three phase induction motors or to
simplify calculations for the control of three-phase inverters.
The mathematical modeling of used induction motor is as
shown in fig.1.
d qs
 ds ,
dt
d ds
Vds  Rs ids 
  qs ,
dt
Vqs  Rs iqs 
(1)
(2)
The q-axis and d-axis rotor voltage equations are given in
equation (3) and (4).
V qr  R r i qr 
d qr
 (  r ) dr ,
dt
d dr
V dr  R r i dr 
 (  r ) qr ,
dt
(3)
(4)
The flux linkage of q-axis and d-axis for stator and rotor are as
given in equations (5 to 8).
 qs  Ls iqs  Lmi qr
(5)
ds  Lsids  Lmi dr
 qr  L r i qr  Lmiqs
 dr  L r i dr  Lmids
(6)
(7)
(8)
The total stator inductance is given in equation (9)
Ls  L1s  Lm
(9)
The total rotor inductance is given in equation (10)
L r  L 1r  Lm
(10)
The Electromagnetic Torque is given in equation (11)
Te  1.5 p( ds iqs  qs ids )
(11)
The rotor acceleration equation is given in equation (12)
dm
1

(Te  Fm  Tm )
dt
2H
(12)
The angular velocity of the rotor is given in equation (13)
(a)
d m
 m
dt
(13)
The quadrature d-axis and q-axis are obtained from abc to dq
conversion
A.
abc to dq Reference Frame
The abc-to-dq reference frame transformation applied to
the induction machine phase-to-phase voltages by equations
(14) & (15).
(b)
Fig.1 (a) q-axis diagram of IM, (b) d-axis diagram of IM
The q-axis and d-axis stator voltage equations are given in
equation (1) and (2).
Vabs 
V 
 bcs 
Vqs  1  2 cos 
  
Vds  3  2sin 
cos   3 sin  

sin   3 cos 
V qr  1
 =
V dr  3
cos   3 sin  

sin   3 cos  
 2 cos 
 2sin 

V abr 
V 
 bcr 
(14)
(15)
1546
Khadim et. al.,
Performance and Analysis of Switching Function Based Voltage Source Inverter Fed Induction Motor
International Electrical Engineering Journal (IEEJ)
Vol. 5 (2014) No.9, pp. 1545-1552
ISSN 2078-2365
http://www.ieejournal.com/
In the previous equations, the angular position of the
reference frame is θ and the difference between the position of
the reference frame and the position (electrical) of the rotor is
β = θ - θr. Since, the machine windings are connected in a
three-wire Y configuration and there is no homopolar (0)
component. This justifies that the two line-to-line input
voltages are used inside the model instead of three
line-to-neutral voltages.
B. dq to abc Reference Frame
Equations (16) and (17) illustrate the dq-to-abc reference
frame transformations applied to the induction machine phase
currents.
cos 

ias  
i  =   cos   3 sin 
 bs  
2

cos 

 ar  
  =   cos   3 sin 
 br  
2

ics  ias  ibs
sin 


 3 cos   sin  

2
iqs 
 
ids 
(16)
sin 

  qr 
 3 cos   sin    

  dr 
2
(17)
III. PROPOSED OPEN LOOP SWITCHING
FUNCTION BASED VSI FED INDUCTION MOTOR
The induction machine block available in the
MATLAB/Simulink operates either in generator mode or
motor mode. The modes depend upon the sign of the load
torque. If torque is positive motor usually operates in
motoring mode if negative generator mode. The mechanical
torque is applied on the motor shaft.
The proposed open loop switching function based VSI
simulation model of the three phase squirrel cage induction
motor is as shown in Fig 2. The applied mechanical rated
torque on the shaft is 15 N-m as the full load torque.
The 3 HP, 50Hz, 1430 RPM SCIM is fed into a switching
function based VSI PWM inverter has been considered for
analysis purpose. The fundamental motor frequency is set at
50 Hz. The base frequency of the reference wave is 50 Hz
while the triangular carrier wave's frequency is set to 1650 Hz.
This corresponds to a frequency modulation factor mf of 33.
The maximum time step has been limited to 10 μs due to high
switching frequency of the inverter. The switching function
based VSI inverter is built entirely with standard Simulink
blocks and available in MATLAB/Simulink.
(18)
i cr  i ar  i br
(19)
Where, ias, ibs, ics are the stator currents in different phases. íar,
íbr, ícr are the rotor current in different phases.
TABLE I. MACHINE BLOCK PARAMETERS REFERRED TO THE
STATOR SIDE
Rs ,Lls : Stator resistance and Vqs , iqs: q axis stator voltage and
leakage inductance
current
Rr ,Llr : Rotor resistance and
leakage inductance
Ψqs , Ψds: Stator q and d axis fluxes
Ψqr , Ψdr: Rotor q and d axis fluxes
Lm:
Magnetizing inductance
p: Number of pole pairs
Ls, Lr : Total stator and rotor
inductances
ωm :Angular velocity of the rotor
Tm: Shaft mechanical torque
θm: Rotor angular position
V qr , iqr: q axis rotor voltage and
current
ωr : Electrical angular velocity
(ωm x p)
Vds , ids: d axis stator voltage and
current
θr: Electrical rotor angular
position (θm x p)
Vdr , idr: d axis rotor voltage and
current
Te: Electromagnetic torque
J: Combined rotor, load inertia
constant
Fig. 2 Simulation Model of Open Loop Switching Function Based VSI Fed
Induction Motor
The machine's rotor is kept short-circuited for SCIM. Its
stator leakage inductance L1s is set to twice its actual value to
simulate the effect of smoothing reactor placed in between the
inverter and the induction machine. In spite the use of
smoothing reactor, electromagnetic torque waveform (Te) is
still obtained noisy. This noise is introduced by the inverter.
Though, the motor's inertia prevents this noise to appear in the
motor's speed.
Since, the reference frame plays a vital role in the conversion
of abc to dq transformations. It is used to convert input
voltages (abc reference frame) to the dq reference frame and
output currents (dq reference frame) to the abc reference
frame in the present paper. The analysis has been carried out
1547
Khadim et. al.,
Performance and Analysis of Switching Function Based Voltage Source Inverter Fed Induction Motor
International Electrical Engineering Journal (IEEJ)
Vol. 5 (2014) No.9, pp. 1545-1552
ISSN 2078-2365
http://www.ieejournal.com/
current reaches 96 A peak( 68 A RMS) whereas its steady
state value is 12.25 A( 8.66 A RMS).
The electromagnetic torque waveform shows that it is
reached in the stable condition after 0.4 sec. It has also been
observed that the strong oscillations of the electromagnetic
torque at starting. If it is zoom in on the torque in steady state,
it will be observed a noisy signal with a mean value of 15 N.m,
corresponding to the load torque at nominal speed.
100
80
60
<Stator current is_a (A)>
in the stationary reference frame. Therefore, the value of rotor
angle is set to 0 and the value of β is set to - θr.
We can choose one among the following reference frame
transformations as per our requirement.
i) Rotor reference frame (Park transformation)
ii) Stationary reference frame (Clarke or αβ transformation)
iii) Synchronous reference frame
The complete mathematical modeling of the used induction
motor and corresponding equations of the model has already
been explained. The selection of reference frame affects the
waveforms of all dq variables. It also affects the simulation
speed and in definite cases the accuracy of the results. The
following guidelines have been suggested in [5] for choosing
the reference frame as follows:
i) Use the stationary reference frame if the stator voltages are
either unbalanced or dis-continuous and the rotor voltages are
balanced (or 0).
ii) Use the rotor reference frame if the rotor voltages are either
unbalanced or discontinuous and the stator voltages are
balanced.
iii) Use either the stationary or synchronous reference frames
if all voltages are balanced and continuous.
The brief description about the induction motor parameters is
as shown in Table: II.
40
20
0
-20
-40
-60
-80
0
0.1
0.2
0.3
0.4
0.5
0.6
Time (seconds)
0.7
0.8
0.9
1
(a)
100
80
Rotor Type: Squirrel Cage
Motor: 3 HP
Frequency: 50 Hz
Rotor Resistance: 0.816 Ω
No. of Pole: 4
Reference Frame: Stationary
DC Voltage: 400V
Stator Resistance: 0.435 Ω
Mutual Inductance: 69.31 ×10 -3 H
Speed: 1430 RPM
<Rotor current ir_a (A)>
60
TABLE: II Brief Description of Motor Parameters
40
20
0
-20
-40
-60
-80
-100
0
0.1
0.2
0.3
0.4
0.5
0.6
Time (seconds)
(b)
0.7
0.8
0.9
1
0.7
0.8
0.9
1
:
1600
1400
1200
Rotor Speed(RPM)
A. Simulation Results of Open Loop Model
The simulation results in symmetrical (or called healthy
mode) motor condition of the motor are as shown in Fig. 3.
Six motor signatures have been considered for analysis
purpose, these are stator current, rotor current, rotor speed,
electromagnetic torque, q-axis stator/rotor flux. The slip and
load torque are set 1 and 15 N-m receptively in the healthy
condition.
In the healthy condition of the motor the slip is set at 1(s=1)
and input mechanical torque is 15 N-m. The obtained results
clearly show, all the motor parameters have been reached in
the steady state condition after 0.4 seconds. It has been
observed that in the starting of the motor, the first peak of the
stator current and electromagnetic torque waveforms has
highest amplitude when it is decreased and reached in the
stable condition.
The model is simulated for 1 sec for clear visualization of
transient
characteristics.
Therefore,
the
transient
characteristics of the motor may be clearly observed and
analysed.
The motor starts and reaches its steady state speed 1430
rpm, after 0.4 sec. At starting, the magnitude of the 50 Hz
1000
800
600
400
200
0
-200
0
0.1
0.2
0.3
0.4
0.5
0.6
Time (seconds)
(c)
1548
Khadim et. al.,
Performance and Analysis of Switching Function Based Voltage Source Inverter Fed Induction Motor
International Electrical Engineering Journal (IEEJ)
Vol. 5 (2014) No.9, pp. 1545-1552
ISSN 2078-2365
http://www.ieejournal.com/
140
IV. PROPOSED CLOSED LOOP SWITCHING
FUNCTION BASED VSI FED INDUCTION MOTOR
<Electromagnetic torque Te (N*m)>
120
100
80
60
40
20
0
-20
-40
0
0.1
0.2
0.3
0.4
0.5
0.6
Time (seconds)
0.7
0.8
0.9
1
(d)
1
0.8
The closed loop switching function based VSI fed
induction motor simulation model is as shown in Fig .4. The
torque control method has been used with inverter for
controlling the induction motor. The field oriented control or
vector control method can also be used with PWM inverter
and can obtain same flexibility in the speed and torque control
like DC machines. The field control technique is an attractive
control technique but it faces serious problem that it relies
heavily on precise acquaintance of the motor parameters. The
rotor time constant is particularly complicated to measure
precisely, and to make stuff inferior because it varies with
temperature. Since, the torque control method is efficiently
controls the induction motor. It estimates the stator flux and
electric torque in the stationary.
<Stator flux phis_q (V s)>
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
0
0.1
0.2
0.3
0.4
0.5
0.6
Time (seconds)
0.7
0.8
0.9
1
(e)
0.6
<Rotor flux phir_q (V s)>
0.4
0.2
Fig. 4 Simulation Model of Closed Loop Switching Function Based VSI Fed
Induction Motor
0
reference frame and terminal measurements. The equations
associated with closed loop simulation model are as follows:
-0.2
-0.4
-0.6
-0.8
0
0.1
0.2
0.3
0.4
0.5
0.6
Time (seconds)
0.7
0.8
0.9
 ds   (Vds  Rs ids )dt
(20)
 qs   (Vqs  Rs iqs )dt
(21)

 s  ( 2 ds  2 qs )  tan 1 ( qs )
 ds
(22)
1
(f)
Fig.3 (a) Stator Current, (b) Rotor Current, (c) Rotor Speed, (d)
Electromagnetic Torque, (e) q-axis Stator Flux, (f) q-axis Rotor Flux
If we zoom on the three motor currents, we may observe
that all the harmonics (multiple of the 1650 Hz switching
frequency) are filtered by the stator inductance. Hence we can
say that the 50 Hz component is dominant.
If we observed q-axis stator and rotor flux, it gives
perfectly sinusoidal flux after 0.4 sec. Therefore, it can be
concluded that the proposed model give excellent results as
expected.
Te  1.5 p( ds iqs  qs ids )
(23)
The estimated stator flux and electric torque are controlled
directly by comparing them with their respective demanded
values using the hysteresis comparators. The outputs of the
two comparators are used as input signals of an optional
switching table. The rotor speed is fed back and directly
1549
Khadim et. al.,
Performance and Analysis of Switching Function Based Voltage Source Inverter Fed Induction Motor
International Electrical Engineering Journal (IEEJ)
Vol. 5 (2014) No.9, pp. 1545-1552
ISSN 2078-2365
http://www.ieejournal.com/
140
connected to the shaft. The value of the feedback constant k is
6.693 × 10-4.
<Electromagnetic torque Te (N*m)>
A. Simulation Results of Closed Loop Model
100
80
60
<Stator current is_a (A)>
120
40
20
100
80
60
40
20
0
0
-20
-20
-40
0
0.1
0.2
0.3
-40
0.8
0.9
1
(d)
0.8
0
0.1
0.2
0.3
0.4
0.5
0.6
Time (seconds)
0.7
0.8
0.9
1
0.6
<Stator flux phis_q (V s)>
(a)
100
80
60
<Rotor current ir_a (A)>
0.7
1
-60
-80
0.4
0.5
0.6
Time (seconds)
40
20
0.4
0.2
0
-0.2
0
-0.4
-20
-0.6
-40
-0.8
-60
0
0.1
0.2
0.3
0.4
0.5
0.6
Time (seconds)
0.7
0.8
0.9
1
(e)
-80
0.6
-100
0
0.1
0.2
0.3
0.4
0.5
0.6
Time (seconds)
0.7
0.8
0.9
1
0.5
(b)
0.4
<Rotor flux phir_q (V s)>
1600
1400
Rotor Speed(RPM)
1200
1000
800
0.3
0.2
0.1
0
-0.1
-0.2
600
-0.3
400
-0.4
200
0
-200
0
0.1
0.2
0.3
0.4
0.5
0.6
Time (seconds)
(c)
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
0.6
Time (seconds)
0.7
0.8
0.9
1
(f)
Fig. 5 (a) Stator Current, (b) Rotor Current, (c) Rotor Speed, (d)
Electromagnetic Torque, (e) q-axis Stator Flux, (f) q-axis Rotor Flux
V. HARMONIC ANALYSIS of OPEN and CLOSED
LOOP MODELS
The Total Harmonic Distortion (THD) analysis for open
and closed loop simulation models has been discussed for its
stator current and input line-to-line voltage. The waveforms
of stator current for 1000Hz maximum frequency is as shown
in Fig. 6 and Fig. 7 for open loop and closed loop
respectively. In this THD analysis, we have sampling
frequency 2 KHz.
1550
Khadim et. al.,
Performance and Analysis of Switching Function Based Voltage Source Inverter Fed Induction Motor
International Electrical Engineering Journal (IEEJ)
Vol. 5 (2014) No.9, pp. 1545-1552
ISSN 2078-2365
http://www.ieejournal.com/
Therefore, a DC voltage of 400 V and a modulation factor
of 0.90 yields the 220 Vrms output line-to-line voltage, which
is the required voltage of the induction motor.
Selected signal: 50 cycles. FFT window (in red): 1 cycles
50
0
-50
0
0.1
0.2
0.3
0.4
0.5
Time (s)
0.6
0.7
0.8
0.9
1
Selected signal: 50 cycles. FFT window (in red): 1 cycles
Fundamental (50Hz) = 61.43 , THD= 4.28%
50
4
0
Mag (% of Fundamental)
3.5
-50
3
0
0.1
0.2
0.3
0.4
2.5
2
1
12
Mag (% of Fundamental)
14
0.5
0
0
100
200
300
400
500
600
Frequency (Hz)
700
800
900
1000
(a)
Selected signal: 50 cycles. FFT window (in red): 1 cycles
0.7
0.8
0.9
1
800
900
1000
0.9
1
90
100
10
8
6
4
2
0
0
100
200
300
400
500
600
Frequency (Hz)
700
(a)
0
0.1
0.2
0.3
0.4
0.5
Time (s)
0.6
0.7
0.8
0.9
Selected signal: 50 cycles. FFT window (in red): 1 cycles
1
400
200
0
-200
-400
-600
-800
Fundamental (50Hz) = 312.1 , THD= 79.35%
30
25
0
0.1
0.2
0.3
0.4
0.5
Time (s)
0.6
0.7
0.8
20
Fundamental (50Hz) = 312.1 , THD= 79.35%
15
30
10
Mag (% of Fundamental)
Mag (% of Fundamental)
0.6
Fundamental (50Hz) = 72.34 , THD= 2.31%
1.5
400
200
0
-200
-400
-600
-800
0.5
Time (s)
5
0
0
10
20
30
40
50
60
Harmonic order
70
80
90
100
(b)
Fig. 6 Results of THD in Open Loop (a) Stator Current, (b) Input
Line-to-Line Voltage
m
3
 Vdc = m  0.612 Vdc
2
2
Khadim et. al.,
20
15
10
5
0
The THD in open loop stator current is more in comparison
to closed loop but for the line-to-line voltage, THD is same in
both the cases (open/close). It is because we are not
controlling input line-to-line voltage. Therefore, PWM
inverter output voltage will be unchanged in open loop as well
as closed loop. It has been observed that if the inverter is fed
into induction motor then line voltage will be disturbed
consequently rise in THD for input-line-to-line voltage but
THD in the stator current will be less.
The fundamental component and Total Harmonic
Distortion (THD) of the Vab voltage are displayed above the
spectrum window. The magnitude of the fundamental of the
inverter voltage (312.1 V) is compared well with the
theoretical value of m=0.9(312.1V) as shown in Fig.6(b) and
Fig.7(b). The line-to-line RMS voltage is a function of the DC
input voltage and of the modulation index m as given by the
following equation:
VLLrms 
25
(24)
0
10
20
30
40
50
60
Harmonic order
70
80
(b)
Fig. 7 Results of THD in Closed Loop (a) Stator Current, (b) Input
Line-to-Line Voltage
Harmonics are displayed in percent of the fundamental
component in fig. 6(b) and fig. 7(b). It has been expected that
the harmonics will occur around multiples of carrier
frequency (n×33±k). The Highest harmonics around (30 %)
appear at 31 and 35 harmonics as expected. It is noted that the
THD value for voltage (79.35 %) has been computed for the
specified 0 to 5000 Hz frequency range.
V. CONCLUSIONS
In the present paper, the extensive simulation has been carried
out in the recent MATLAB/Simulink environment for 3 HP,
4 pole, 50 Hz open and closed loop induction motor
connected with switching function based inverter. It has been
observed that the closed loop model has given better results as
compare to open loop model with reduced harmonics. The
torque control method has been used for induction motor
controlling purpose over field-oriented control technique due
to its advantages. From both models, the transient behavior of
the used induction motor has been observed. It has also been
observed that the switching function based inverter influences
the motor performance and might introduce disturbances into
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Performance and Analysis of Switching Function Based Voltage Source Inverter Fed Induction Motor
International Electrical Engineering Journal (IEEJ)
Vol. 5 (2014) No.9, pp. 1545-1552
ISSN 2078-2365
http://www.ieejournal.com/
the main power line. But precisely designed interface system
would be very useful in drive control applications. These
models may be used in various power electronics and drives
applications in industry.
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ACKNOWLEDGMENT
Authors acknowledge Technical Education Quality
Improvement Program Phase-II, Institute of Engineering &
Technology, Lucknow for providing financial assistantship to
carry out the research work.
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Performance and Analysis of Switching Function Based Voltage Source Inverter Fed Induction Motor