Modeling and Simulation of VSI Fed Induction Motor Drive in Matlab/Simulink

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 7, No. 2, April 2017, pp. 584~595
ISSN: 2088-8708, DOI: 10.11591/ijece.v7i2.pp584-595  584
Journal homepage: http://iaesjournal.com/online/index.php/IJECE
Modeling and Simulation of VSI Fed Induction Motor Drive in
Matlab/Simulink
D. Uma, K. Vijayarekha
Department of Electrical and Electronics Engineering, SASTRA University, Thanjavur, Tamilnadu- 613 401, India
Article Info ABSTRACT
Article history:
Received Nov 11, 2016
Revised Feb 20, 2017
Accepted Mar 4, 2017
The theory of reference frames and switching functions are effective in
analyzing the performance of the induction motor fed from VSI (Voltage
Source Inverter). In this work, mathematical model of Adjustable Speed
Drive (ASD) is developed by taking synchronous reference frame equations
for induction motor, switching function concept for VSI and non-switching
concept for diode bridge rectifier. Simulation model of induction machine is
implemented using dq0 axis transformations of the stator and rotor variables
in the arbitrary reference frame. The corresponding equations are given in the
beginning and then the developed model is implemented using
MATLAB/Simulink. In this work, the proposed model is implemented using
basic function blocks. The performance of induction motor is analysed for
different frequencies. The developed model is tested for the steady state
behavior of machine drive. The proposed mathematical model is validated by
the simulation results.
Keyword:
Converters
Frequency conversion
Inverters
Power conversion
Pulse width modulation
converters
Copyright © 2017 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
D. Uma,
Department of Electrical and Electronics Engineering ,
SASTRA University ,
Thanjavur, Tamilnadu- 613 401, India.
Email: umavijay@eee.sastra.edu
1. INTRODUCTION
In many industrial applications Adjustable speed drives (ASD) are most commonly seen
workhorses. In order to supply the motor with variable AC voltage or AC current with variable frequency
Variable Frequency Drives (VFD) are employed. ASDs are used in pumping applications, in sugar cane
industries, conveyor applications etc. The common VFD consists of a three phase diode bridge rectifier, dc
link and a pulse width modulated inverter. It is necessary to develop a model for VFD for power system
dynamic studies. In literature, for the three phase diode bridge rectifier dq impedance model is employed [1].
State-space averaging method is used for modeling a three phase four wire diode bridge rectifier [2].
Dynamic average value modeling methods are utilized for conventional three phase diode bridge rectifier and
are validated [3]. This can capture the steady-state and transient characteristics of the diode bridge rectifier.
An approximate switching function of the diode bridge rectifier is used in order to obtain the estimating
function for the fundamental current harmonics [4].This method is proven to be effective in finding out the
input current harmonic content. A switching function model for voltage source inverter is derived and also it
is validated using MATLAB/Simulink [5].
Modulation function theory is effectively utilized for deriving the Pulse Width Modulated (PWM)
inverter which makes use of the Iterative Harmonic and Interharmonics Analysis (IHIA) [6]. Space vector
pulse width modulation method is employed for inverter and the method is validated using
MATLAB/Simulink [7]. A three phase boost dc-ac converter is used to supply the induction motor [8]. AC
output voltage that is greater than the input dc voltage is obtained without the need of additional boost
converter.

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The effects of low switching frequencies in inverter fed ac drive are analyzed [9]. Both the
simulation and experimental results are discussed. Model predictive current control method is employed for
load current control [10]. The effectiveness of the method is validated by simulation using two level inverter.
MATLAB /Simulink model is developed for a three phase inverter with PID controller and hardware is
implemented using digital signal processor [11]. Total Harmonic Distortion (THD) is less for inverter with
PID controller. A mathematical modeling of induction motor is derived and validated using
MATLAB/Simulink [12]. Fifth order differential equations are used for modeling induction motor in
synchronously rotating reference frame theory [13]. A dynamic model of three phase induction motor with
double windings in the stator has been derived using space vector theory [14]. The derived model is
simulated in Simulink and the steady state and dynamic characteristics are compared with the standard three
phase induction motor. Three various approaches are used to obtain the squirrel cage induction motor
characteristics. They are, (a) stator resistance measurement, (b) details from the motor plate and (c) induction
motor modeling [11]. This is simple and cost effective approach [15]. Modeling of induction motor based on
object oriented methodology is employed [16]. This model is validated on a faulty squirrel cage induction
motor. A dynamic model of variable frequency drive is obtained which has the capability to ride through the
fault [17]. The same is verified using case studies. Several other models for induction motor
[18-19], voltage source inverter [20-21] and diode bridge rectifier [22] are available in the literature. In
literature, separate models are available for the converters and induction motor.
In modern industrial applications as the induction motor is fed from switching converters, the motor
model developed must be valid for arbitrary applied voltage and current waveforms. Therefore a complete
model is required for power system dynamic studies and for harmonic analysis. Also, the machine model
must include the essential elements of both electromagnetic and mechanical system for both steady state and
transient operating conditions. Considering this, in this work an accurate model for induction motor is
developed using d-q reference frame equations. Switching function concept is used for developing a model
for voltage source inverter (VSI) and a non-switching concept is employed for uncontrolled rectifier. Thereby
a complete and an accurate model of VFD which is required for power system dynamic studies and harmonic
analysis is developed. The accuracy of the developed model has been verified through simulation in
MATLAB/Simulink.
2. MODELING OF VARIABLE FREQUENCY DRIVE
2.1. Modeling of Induction Motor
The steady state equivalent circuit is derived from the principle of operation of induction motor. The
steady state response of variable speed induction motor drive is evaluated based on the equivalent circuit. For
validation of the design of the motor-drive system, the dynamic simulation is one of the important steps. This
eliminates inadvertent mistakes in the design and resulting errors in prototype model. Therefore dynamic
models are required for the induction motor [23]. The dynamic model of the induction motor is obtained from
the fundamentals. The dqo model makes use of two windings for the rotor and stator of the induction motor.
Transformation of abc to dqo axes employed for deriving the dynamic model is based on simple
trigonometric relationship. Used in the derivation of various dynamic models are based on simple
trigonometric relationships. Since the mathematical equations of induction motor are involving differential
equations that are varying with respect to time which helped to choose synchronous reference frame as the
scope of this work in modeling.
The assumptions that are made in order to derive the dynamic model of induction motor are as
follows,
(1) Air gap is uniform
(2) Stator and rotor windings are balanced, with the mmf being distributed sinusoidally
(3) Inductance versus rotor position is sinusoidal; and
(4) Saturation and changes of parameter are neglected.
Three particular cases for the induction machine in arbitrary reference frames are,
(1) Stator reference frames model;
(2) Rotor reference frames model;
(3) Synchronously rotating reference frames model.
The model of induction motor can be done effectively using the reference frames mentioned as
in [18]. Induction motor can be modeled by taking one of the generalized arbitrary reference frames, they are
stator reference frame, rotor reference frame, synchronous rotating reference frames. In this work we
considered implanting synchronous rotating reference frame method. Why, because the steady nature of this
stator d-axis current makes this reference frame useful when a computer is used in simulation and one of
advantages of this frame is speed and angular position can be taken into consideration at any instant of time.

IJECE ISSN: 2088-8708 
Modeling and Simulation of VSI Fed Induction Motor Drive in Matlab/Simulink (D. Uma)
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Since the mathematical equations of induction motor are involving differential equations that are varying
with respect to time which helped to choose synchronous reference frame as the scope of this work in
modeling. The model equations are derived from dqo equivalent circuit of induction motor given in Figure 1.
Figure 1. dqo equivalent circuit of three phase induction motor
The flux linkage equations which are written below are obtained by applying KVL and KCL to
above equivalent circuit







ls
s
ds
b
e
qsb
qs
X
R
V
dt
d





(1)







lsX
sR
qs
b
e
dsVbdt
dsd





(2)









lrX
rR
dr
b
re
qsVbdt
qrd





(3)









lrX
rR
qr
b
re
qsVbdt
drd





(4)
where,









lrX
qr
lsX
qs
MLXmq

 (5)







lrX
dr
lsX
ds
MLXmd

 (6)







lrXlsXMXMLX
111
/1 (7)
Current can be found by substituting flux linkages
 mqqs
lsXqsi  
1
(8)
 mdds
lsXdsi  
1 (9)

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 mqqr
lrXqri  
1 (10)
 mddr
lrXdri  
1 (11)
Torque equation in terms of modified flux linkages and currents is given by
( )dsiqs-qsids
e
1
2
P
2
3
=eT 

(12)
2.2. Modeling of Voltage Source Inverter
In order to describe the function that needs to be done by the circuit, transfer function is derived. A
dependent variable can be calculated in terms of its respective independent variable by using transfer
function. In Pulse Width Modulation (PWM) the dependent variable is the modulated waveform and the
independent variable is the waveform to be modulated. General expression of the transfer function is,
TD = VD/ VI (13)
where, VD is the dependent variable and
VI is the independent variable.
There are several advantages by modelling the VSI using transfer function model.
1. Power conversion circuit can simplified into output and input variables
2. Converter topologies can be derived easily by transfer function approach
3. The strategy to implement gating pulses will become much simpler
4. Various parameters like current and voltage, load current can be calculated easily
5. For a power conversion circuits there is no need of forming real power electronic models and state
equations
A particular transfer function has a particular switching function. The relationship between output
variable and input variable is obtained by employing switching function theory. So to have a detailed account
of the static power converters, a proper switching function must be obtained. Based on the theory of transfer
function, in the VSI, the independent variables are the input voltage Vd and output current IA, IB, and IC and
the dependent variables are input current Ii and output voltage VAB, VBC, VCA. Therefore, the output and
input variables can be related as
[ ] )dV(TF=CAV,BCV,ABV (14)
[ ]CI,BI,AITF=iI (15)
where TF is the Transfer Function of VSI which can expressed in the form of various switching functions.
 nSFSFSFSFTF ........,, 321 (16)
( )( )∑
∞
1=n
tnsinnA=1SF  (17)
For three phases VSI the switching function can be classified as SF1A, SF1B, SF1C and expressions are given
below
  



1
1 sin
n
nA tnASF  (18)
  



1
1 120sin
n
nB tnASF  (19)

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  



1
1 240sin
n
nC tnASF  (20)
By the use of switching functions SF1A, B, C the voltages are found by
  









1
sin
2 n
n
d
AO tnA
V
V  (21)
  









1
120sin
2 n
n
d
BO tnA
V
V  (22)
  









1
240sin
2 n
n
d
CO tnA
V
V  (23)
Line voltages of the inverter is found by,
  











1
30sin
2
3
n
ndBnAnAB tnAVVVV  (24)
  











1
90sin
2
3
n
ndCnBnBC tnAVVVV  (25)
  











1
150sin
2
3
n
tnnAdVAnVCnVCAV  (26)
From the above mentioned theory the required variable for modeling of VSI is formed and can be
realized readily.
2.3. Modeling of Three Phase Diode Bridge Rectifier
The ac input power is converted into dc output power by the use of three phase diode bridge
rectifier. The circuit condition determines the instant at which the diode starts conducting. The input voltages
VA, VB and VC for the balanced condition can be written as follows:
)tsin(mV=AV  (27)
)°120-tsin(mV=BV  (28)
)°240-tωsin(mV=CV (29)
where, Vm is the voltage magnitude. For this voltages, the fundamental switching functions are
expressed as same as voltage source inverter SF1A, B, C as mentioned in the modeling of voltage source
inverter. The correlation input and output of the diode bridge rectifier are given as
Vd = (SF) T
VABC (30)
IABC = (SF) Id (31)
A synchronously rotating dq frame is considered with d-axis aligned with the voltage vector. By the
use of transformation matrix, three phase variables FABC hence, the three phase variables FABC are expressed
in terms of such dq frame.
Fdq = T (FABC) (32)

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     
     








120sin120sinsin
120cos120coscos
ttt
ttt
T


(33)
Combining (30) and (33) following equation can be yielded
( ) 2/12
qV+2
dV
π
33
=dV (34)
where Vd and Vq are d & q axes voltage components. The equations (30) to (34) represent the non-
switching model of diode rectifier
3. MATLAB/SIMULINK IMPLEMENTATION
In this section, MATLAB/Simulink is used for the simulation of three phase induction motor
model [24]. The corresponding equations which are used to implement this model have been discussed in
Section 1. Figure 2 shows the Simulink model of the induction motor.
Figure 2. Matlab/Simulink model 3-phase induction motor
3.1. Simulink Implementation of Voltage Source Inverter
Simulink model of the voltage source inverter (VSI) is shown in Figure 3 which is implemented
using the concept of switching function.
Figure 3. Voltage Source Inverter model in Matlab/Simulink

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3.2. Simulink Implementation of Uncontrolled Rectifier
The switching behaviour of the diode bridge rectifier is not included in the functional modelling
definition [20], thus development is based on the non switching model, as discussed previously. The equation
(34) has been implemented in Simulink as shown in Figure 4. Here abc to dqo transformation is done using
synchronous reference frame concept.
Figure 4. Matlab/Simulink model of uncontrolled rectifier
4. RESULTS AND DISCUSSION
The overall Matlab/Simulink model of VFD is given in Figure 5.
Figure 5. VFD model in Matlab/Simulink
This VFD can be operated at different frequencies ranging from 10Hz to 50Hz. Motor speed and
torque for a drive operating frequency of fo=50Hz are shown in Figure 6.

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Figure 6. Motor speed and torque at fo = 50Hz.
Stator current waveforms at fo = 50Hz are shown in Figure 7.
Figure 7. Stator current waveforms at fo = 50Hz
Rotor current waveforms at fo= 50Hz is shown in Figure 8.
Figure 8. Rotor current waveforms at fo = 50Hz
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
50
100
150
200
250
300
350
speed vs time
Time in seconds
Speed
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-50
-40
-30
-20
-10
0
10
20
torque vs time
Time in seconds
Torque
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
-40
-20
0
20
40
Time in seconds
PhAcurrent
Stator Currents for Phase a
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
-40
-20
0
20
40
Time in seconds
PhBcurrent
Stator Currents for Phase b
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
-40
-20
0
20
40
Time in seconds
PhCcurrent
Stator Currents for Phase c
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
-20
-10
0
10
20
Time in seconds
PhARotorcurrent
Rotor Currents for Phase a
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
-20
-10
0
10
20
Time in seconds
PhBrotorcurrent
Rotor Currents for Phase b
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
-20
-10
0
10
20
Time in seconds
PhCrotorcurrent
Rotor Currents for Phase c

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Motor speed and torque for a drive operating frequency of fo = 40 Hz are shown in Figure 9.
Figure 9. Motor speed and torque at fo = 40Hz.
Stator current waveforms at fo =40Hz are shown in Figure 10.
Figure 10. Stator current waveforms at fo = 40Hz
Rotor current waveforms for fo= 40Hz is shown in Figure 11.
Figure 11. Rotor current waveforms at fo =40Hz
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
50
100
150
200
250
300
Time in seconds
Speed
speed vs time
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-50
-40
-30
-20
-10
0
10
20
Time in seconds
Torque
torque vs time
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
-20
-10
0
10
20
Time in seconds
PhARotorcurrent
Rotor Currents for Phase a
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
-20
-10
0
10
20
Time in seconds
PhBRotorcurrent
Rotor Currents for Phase b
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
-20
-10
0
10
20
Time in seconds
PhCrotorcurrent
Rotor Currents for Phase c

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The machine specifications are given in Table 1
Table 1. Machine Specifications
Machine Specifications
AC Source
Source Frequency fs 50Hz
Source Voltage (line to line) 415 V
Rectifier
Six-Pulse Uncontrolled
PWM Inverter
Carrier Frequency fc 1000Hz
Modulation frequency, fi 10Hz to 50 Hz
Amplitude Modulation Ratio, M 0.8
Induction Motor
Rated Power Input 3.7 kW
Voltage Rating 415 V
Rated Current 7.5A
Resistance of stator, R, 4.9 Ω
Resistance of rotor, Rr 3.63 Ω
Leakage Inductance of stator LI, 10 mH
Leakage Inductance of rotor, LIr 10 mH
Mutual (Magnetizing) Inductance, Lm 20 mH
Pairs of Poles, P 4
Operating Frequency of motor, fo 10 Hz to 50 Hz
Rated Speed rad/sec 314 r/s
5. CONCLUSION
In this work the mathematical model of VSI Fed Induction motor with front end diode bridge
rectifier is developed and described elaborately. The developed model is tested with the specifications that
are obtained by conducting suitable tests on the motor with the mentioned rating. The speed and torque
characteristics for different load frequencies are shown in the results. The performance of induction motor is
analysed for different frequencies. The developed model is tested for the steady state behavior of machine
drive. The proposed model is validated by the simulation results. Thus it can be concluded that
Matlab/Simulink is reliable and easiest way to assess the behavior of ASDs using reference theory, switching
function concept.
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BIOGRAPHIES OF AUTHORS
Mrs. D.Uma was born in India on January 24, 1974. She received B.E. degree in Electrical and
Electronics Engineering from Azhagappa Chettiyar College Of Engineering And Technology in
1995, India. She completed M.E degree in Power Electronics And Drives from Shanmuga
College Of Engineering in 1999, India. At present She is working as Senior Assistant Professor
in Electrical and Electronics Engineering department at SASTRA University, India. 7 papers are
published in various international journals. Her research interests include Power quality,
Electrical Drives, FACT devices and Integrated Renewable Energy Systems.

 ISSN:2088-8708
595
Lt. Dr. K. Vijayarekha was born in India. She received B.E. degree in Electrical and
Electronics Engineering from Azhagappa Chettiyar College Of Engineering And Technology in
1990, India. She completed M.E degree in Power Systems Engineering from REC, Trichy. In
1992, India. She obtained Ph. D degree from CEERI/CSIR, Chennai, in the year 2008. At
present She is working as Associate Dean in Electrical and Electronics Engineering department
at SASTRA University, India. 62 papers are published in various international journals. Her
research interests include Control Systems, Machine vision techniques, Image Processing, Multi-
variate Image Analysis, Hyper-spectral Imaging, Non Destructive Testing, Pattern Recognition,
Imaging in other modalities like ultra sound. Her ongoing research on Enhanced Defect
Characterization and Classification through Ultrasonic signal and Image Analysis & Neural
Networks.

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