Journal of Robotics, Networking and Artificial Life
Vol. 7(3); December (2020), pp. 170–174
DOI: https://doi.org/10.2991/jrnal.k.200909.006; ISSN 2405-9021; eISSN 2352-6386
https://www.atlantis-press.com/journals/jrnal

Research Article

Simulation of SPWM Fed Three-phase Induction Motor
Drive Mathematical Model Using MATLAB Simulink
Amir Rasyadan1,*, Sazali bin Yaacob1, Pranesh Krishnan1, Mohamed Rizon2, Chun Kit Ang2Intelligent Automotive Systems Research Cluster, Electrical Electronic and Automation Section, University Kuala
Lumpur Malaysian Spanish Institute, Kulim, Kedah 09000, Malaysia2
Faculty of Engineering, Technology and Build Environment, UCSI University, No 1, Jalan Menara Gading, Taman Connaught, Kuala Lumpur 56000, Malaysia
1ARTICLE INFOABSTRACT

Article History

Three-phase induction motors are used in a vast area of applications mainly due to their simplicity, ruggedness and highreliability. With recent advancement in semiconductor technologies, the use of fixed speed induction motor drive is becoming
obsolete, majority of the applications now requires inverter-based drives for variable speed operation. In the study of induction
motor drive operation, mathematical models are often used to simulate the steady state and transient behavior of induction
motor. However, developing such models are not as simple. One must develop the understanding of the mathematical equations
to be used and also having the knowledge to solve the equations with the use of computer simulation software. To address thisissue, this work presents an approach to implement the mathematical model of a Sinusoidal Pulse Width Modulation (SPWM)
fed three-phase induction motor drive in MATLAB Simulink. The sub models include induction motor direct quadraturemodel and a voltage source inverter fed by SPWM signal generator. The presented model implementation is able to simulate thedynamic behavior of an induction motor operation, this mathematical model implementation would be useful for further studies
on the development of induction motor drive system.

Received 06 November 2019
Accepted 17 April 2020
Keywords
Three-phase induction motor
DQ-modelvoltage source inverter
SPWM© 2020 The Authors. Published by Atlantis Press B.V.
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

1. INTRODUCTION
Recent advancement in semiconductor technologies have furtherextended the capability of induction motors from the traditional
fixed speed to the modern variable speed operation with the use ofPulse Width Modulation (PWM) fed inverter-based drives. Someof the applications include industrial pumps, crane lifters, drillingmachines, traction applications such as in electric vehicles, andmany others. Developing elaborate models have now become crucial in the designing process of induction motor drive system as
the application complexity increases. The model should be able topredict and simulate operational characteristics and performances
which would be useful to validate the design process and minimize
designing error1. However, building such model is not a straightforward task, knowledge of the machine basic electric, magnetic,
and mechanical behaviors and also some experience in using
computer simulation software are required.
Several available literatures have published their respective
induction motor mathematical model implementation approach.
Some of the works suggest the use of Simulink’s-function [1,2],
others use Simulink’s mathematic operation blocks [3,4], andthere are also works that have proposed a solution to avoid
MATLAB/Simulink [5] where the motor are modeled completelyusing C++ programming language. Their works however does
Corresponding author. Email: amir.kelana22@s.unikl.edu.my*

not focused on modeling of the Sinusoidal PWM (SPWM) signal
and the inverter equations. This paper chooses SPWM control
method because it is one simplest. With this, a better understanding on the fundamentals can be developed without the needto dive into the other complex control method. The overview
of the equations needed to mathematically model an induction
motor drive and the approach to implement them in computer
simulation software specifically using MATLAB Simulink arepresented here. Three main components of the induction motordrive system are included in this work which are the induction
motor DQ-model, the three-phase voltage source inverter [6],and the SPWM signal generator for Voltage Source Inverter(VSI) switching [7,8].
The model be entirely built by writing MATLAB programmingcode from ground up, or one can use Simulink which provides abetter system representation in block diagram form as an alternative. The main advantage of Simulink is that it uses functional
blocks instead of programming code.

2. MODEL IMPLEMENTATION
The model describe in this work include the Induction motor
Direct Quadrature (DQ)-model, the SPWM model, and the voltage source inverter model. Each of the sub model is presented asfollows.

A. Rasyadan et al. / Journal of Robotics, Networking and Artificial Life 7(3) 170–174

2.1. Induction Motor Direct
Quadrature-Model		 F = x é Fds + Fdr ù (8)úmdml êë xls xlr ûThis is the very first step of modeling an induction motor, it
involves reference frame transformation of the three-phase supply(Vas, Vbs, Vcs) voltage into two-phase voltage [9,10]. To simplify later
implementation in Simulink, it is convenient to first transform thethree-phase voltage using Eq. (1) into a two-phase voltage in stationary reference frame (Vds, Vqs), then from the stationary reference frame to the arbitrary reference frame using Eq. (2).
1é1 év ù 2 ê2		 êv ú = 3 êê0 - 3ë ûêë21ù- ú évas ù2 êv úú
3 ú ê bs ú (1)
ë vcs û2 úûsqssds

évqs ù écosq		 ê ú = êëvds û ë sinq-sinq ù évqss ùê ú (2)cosq úû êëvdss úû

The DQ model can be then be calculated once vds and vqs areobtained. Implementations of the DQ-model are divided into threeparts as follows.

2.1.1. Flux linkages
The first set of equations to be solve part is on the flux linkage as
defined in Eqs. (3)–(6):   x* R  x*w
= w b uqs −Fds + s  ml Fqr +  ml − 1 Fqs   (3)dtwbxls  xlr
 xls
  


dFqs


 x*
 R  x*
w= w b uds −Fqs + s  ml Fdr +  ml − 1 Fds   (4)  dtwbxls  xlr
 xls
  

dFqs

  

dFqr
dt

 (w − w r )x R x
= w b 0 − e
Fdr + r  ml Fqs +  ml − 1 Fqr   (5)wxxx  

blr lslr**

 (w − w r ) x* dFR  x*   dr = w b 0 − e
Fqr + r  ml Fds +  ml − 1 Fdr   (6)wbdt
x lr  x ls
 x lr  

		 xml =1
(9)é 1
11 ù+ úê +
ë xm xls xlr û

From there, the stator and rotor current (A) in the arbitrary reference frame can be solved as follows.
1iqs = (Fqs - Fmq ) 		 xls

(10)

1ids = (Fds - Fmd ) (11)		 xlswhere:
iqs, ids : stator current (A) of quadrature and direct axis
xls : leakage reactance (W) of stator
Fqs, Fds : stator flux linkage (Wb-t) of quadrature and direct axis

2.1.3. Electromagnetic torqueand rotor speed
The final set of equations calculate the electromagnetictorque Te (Nm) and rotor speed wr (rad/s) outputs as shown inEqs. (12) and (13).
3 æ pö 1		 Te = ç ÷(Fdsiqs - Fqsids ) 2 è 2 ø wb(12)		 dw r = p (T - T ) (13)ldt
2J e
where p is the number of poles, J (Kg/m2) is the moment of inertiaand Tl (Nm) is the input load torque.

2.2. Sinusoidal Pulse Width Modulation

where:wb : Motor angular base frequency
we : Electrical supply angular frequency
wr : Rotor angular frequency (rad/s)
vqs, vds : Stator voltages (V) of q and d-axis
vqr, vdr : Rotor voltages (V) of q and d-axis

2.1.2. Magnetizing flux
The second part calculates the magnetizing flux with the equation
shown by Eqs. (7) and (8):é Fqs Fqr ùFmq = xml ê + ú 		  ë xls xlr û171

(7)

Three-phase VSI is typically made up of six power switches thatrequires proper switching sequence to transform the DC voltage supply into a variable frequency three-phase PWM voltage
output. As mentioned, the SPWM is used in this work. To model
the three-phase SPWM switching signals, three sinusoidal reference signals which are set 120° phase apart from each other; Vref_nwhere n represents the three phase a, b, c, the signals are thencompared with a high frequency triangular signal VT. The changing of the reference signal frequency fref changes the inverter
frequency which then changes the speed of the induction motor[11]. Hence, this relation provides a simple control over the speedof induction motor. However, to produce the varying frequency
reference signal, the standard sine function as shown in Eq. (14)is not applicable.		  
vrefn (t ) = sin(2p * f ref * t ) (14)A. Rasyadan et al. / Journal of Robotics, Networking and Artificial Life 7(3) 170–174

172

Since the sin function takes argument of angles, simply changing
fref by time will not produce a smooth frequency transition, jitter
will be seen in the output as the results of jumping phase from one
point of the waveform. To solve this issue, the use of phase accumulator is proposed with the Eq. (15) described below:		 vrefn (t ) = sin(2p * ò f ref (t ) dt ) (15)The phase accumulator can be built using the Backward Euler
Method with Eq. (16) and modeled using Simulink’s User-Defined
Function block.

abc

vrefn[n] = sin(2p * ((Vrefn[k - 1]) + ((t[k]) - t[k - 1]) * f ref [n])) (16)The fref can now be varied as intended, even in discontinuous ways,
the phase will still change smoothly by time, producing a continuous variable frequency sinusoid.

d2.3. Voltage Source Inverter
One way of modeling a three-phase inverter is described by Bosein his book [6] based on the relation of phase voltages and pole
voltages as in Eqs. (17)–(19).
112		 van = vao - vbo - vco (17)33
3
112		 vbn = vbo - vao - vco (18)33
3
1
12vcn = vco - vao - vbo (19)		 333where:
van, vbn, vcn : Phase voltages
vao, vbo, vco : Pole voltages
With the voltage source inverter mathematical model is implemented, all the components required are completed and simulation
can be run.
To validate the mathematical model implementation, the resultsof the model described in Section 2 is compared with theSimulink’s preset asynchronous machine drive which is alreadybuilt and made available by MATLAB in its Simulink library.
During simulation, both the mathematical and the Simulink’spreset model use the same 5 Hp motor with parameters asshown in Table 1.
The results of both models output are presented in the next section.
Table 1 | Induction motor parameter for mathematical modeling
Parameter
Rotor resistance
Stator resistance
Rotor inductance
Stator inductance
Magnetizing inductanceNo. of poles
Moment of inertia

Abbreviation

Value

Unit

RrRs
LrLs
Lm
PJ

1.083
1.115
5.974E-03
5.974E-03
0.2037
40.02

Ohm
Ohm
Henry (H)Henry (H)Henry (H)kg/m2

Figure 1 | Side by side Mathematical and Simulink’s preset modelcomparison of (a) load torque applied, (b) rotor speed, (c) phase currents,(d) electromagnetic torque.

3. RESULTS
The induction rotor speed, phase current, and electromagnetic
torque response are as presented in Figure 1 showing side-by-side
comparison of the mathematical model and the Simulink’s presetmodel outputs with the applied load torque profile.
From the results shown, the mathematical model and the Simulink’spreset model yield similar response behavior. During starting, transient conditions are observed before the motors got into a steadystate condition at time 0.3 s. When the load torque is increased from
7 to 28 Nm, both the model responds with decrease in rotor speed,
increase in phase currents amplitude, and increase electromagnetic
torque, transient region can also be observed whenever load torquechange occurred before getting back into steady state condition.

4. CONCLUSION
This work has presented an approach to implement an SPWM fed
three-phase induction motor drive. The model was built in Simulink
entirely based on the equations described in Section 2. The implementation process is also presented in a step-by-step approach so that thework can be easily followed. The results produced by this model haveshown similar behavior to that of Simulink’s preset induction motordrive model, which validates that the mathematical model implementation is working as expected. This model implementation would be
useful for future development of induction motor drive systems.

NOTE
The complete Simulink model implementation described in thispaper can be referred at MATLAB Central File Exchange: https://www.mathworks.com/matlabcentral/fileexchange/73260-dq-­
model-of-3-phase-induction-motor-drive.

A. Rasyadan et al. / Journal of Robotics, Networking and Artificial Life 7(3) 170–174

CONFLICTS OF INTEREST
The authors declare they have no conflicts of interest.

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AUTHORS INTRODUCTION
Mr. Amir Rasyadan

Prof. Dr. Sazali Yaacob
He received Master of Engineering
Technology degree from University ofKuala Lumpur in 2019. His researchinterests include industrial automation,
digital signal processing, and powerelectronics.

He completed his PhD and MS degrees
from the University of Southampton andthe University of Surrey, United Kingdom
respectively. He has published over 300
articles in conferences and journals. Heis a life member of Institute of Engineers
and recipient of a number of awards.

Dr. Pranesh Krishnan

Dr. Mohamed Rizon

He is currently serving as a Post-Doctoral
Researcher at Malaysian Spanish Institute,
Universiti Kuala Lumpur, Kulim, Malaysia.
He completed his Masters (Mechatronics)
and PhD (Mechanical) from Universiti
Malaysia Perlis, Malaysia. He obtained
his Bachelors (Information Technology)
degree from Anna University, India. He
is a member of IEEE, and a Graduate
Technologist from MBOT. His research interests include Signal
Processing, Driver Drowsiness and Machine Learning.

He graduated Doctor of Engineering at
Department of Computer Science andIntelligence System in Oita University,
Japan. He was a Professor of Biomedical
Technology in King Saud University,
Saudi Arabia in 2010. He served atMIEC, Fuzhou University, China in 2019.
Currently, he is a Professor at Department
of Electrical and Electronics, UCSI University, Malaysia.

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A. Rasyadan et al. / Journal of Robotics, Networking and Artificial Life 7(3) 170–174

Dr. Chun Kit Ang
He received his Bachelor ofEngineering Degree with First Class
Honors in Mechatronic Engineeringfrom University of UCSI, Malaysia
in year 2010. In end of year 2010, hewas attached with Universiti Putra
Malaysia for his PhD in Mechanicaland Manufacturing Engineering andgraduated in year 2014. Currently, heis the Dean for Faculty of Engineering
Technology and Built Environment,UCSI University. He is interested inartificial intelligence, soft computing, robotics, and mechatronics. He has published many papers which related to the application of Artificial Intelligence in recent years.