International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 3, March 2014)
Normalized Dynamic Simulation of 3-phase Induction Motor
using MATLAB/SIMULINK
Abhinav1, Venu Sangwan2
Electrical department, PEC University of technology Chandigarh-160012, India
Simulink is a useful tool for understanding the
performance, analysis & design of such machines.
Simulink induction machine models are available in
literature [5]-[6], but they appear to be black boxes with
no internal details. Reference [7]-[8] refers to
implementation of dynamic model and simulink of
induction motor in synchronously rotating reference
frame. But, fail in explain the performance of model with
normalized variables.
In this paper, MATLAB/SIMULINK is used to
simulate the dynamic performance of an induction motor
model whose normalized stator and rotor variables are
referred to a synchronous reference frame.
Abstract Power system engineers and design engineers
use normalized values for the variables. This paper presents
dynamic modeling and simulation of 3-phase induction
motor using dq0 axis transformation of normalized stator
and rotor variables in the synchronous reference frame
assisted by MATLAB/SIMULINK. For this purpose, the
relevant electrical differential equations and mechanical
differential equation, known by electrical machine
researchers, are stated at the beginning and then
generalized model in synchronous reference frames of 3phase induction motor is developed and implemented by
using MATLAB/SIMULINK.
KeywordsMATLAB/SIMULINK, induction
normalized value, dynamic modeling, dq0 model.
motor,
II. SYSTEM MODELING
I. INTRODUCTION
Usually, when an electrical machine is simulated in
circuit simulator like PSpice, its steady state model is
used; this implies that all transients are neglected during
load changes and stator frequency variations, but for
electrical drive studies, the transients behaviors is also
important.
In the past, researchers have developed their own
software packages for dynamics modeling of induction
motor. In [9], a software package was developed, using
the FORTRAN programming language, for the steady
state and dynamic simulation of induction motor drives. It
is unnecessary to develop user-written software for
dynamic model of induction motor when you have
proprietary
software
package
such
as
MATLAB/SIMULINK, licensed by MathWorks.
MATLAB/SIMULINK makes simulation design more
efficient and allows other interested parties to understand
the operation of the system more easily than a
programming-language implementation.
MATLAB provides a powerful matrix environment,
the basis of state-space modeling of dynamic systems, for
system design, modeling, and algorithm development.
SIMULINK is an extension to MATLAB and allows
graphical block diagram modeling and simulation of
dynamic systems [10].
The dynamic d-q model is developed using MATLAB
and a simulation is carried out to observe the speed flux,
torque and current waveforms.
Induction motors are called as horsepower of industry.
According to a survey, 75% of motors used in industries
are induction motors due to their high torque to volume
ratio, ruggedness, robustness & low maintenance. The
analysis of induction motor is carried out in steady state
whereby the machine is modelled as a second order
electromechanical system. However for in depth analysis,
dynamic behaviour is accounted whereby machine
dynamics are of fifth order [1].
The dynamic model considers the instantaneous effects
of varying voltages/currents, stator frequency, and torque
disturbance. The dynamic model of the induction motor is
derived by transferring the three-phase quantities into two
phase direct and quadrature axes qualities. The
equivalence between the three phase machine models is
derived from the concept of power invariance [2]. This
approach is desirable because of conceptual simplicity
obtained with two sets of winding, one on the stator and
the other on the rotor.
The following assumptions are made to derive the
dynamics model [3]:
i.
Uniform air gap;
ii.
Balanced rotor and stator windings, with
sinusoidally distributed mmf;
iii.
Inductances vs. rotor position is sinusoidal; and
iv.
Saturation and parameter changes are neglected
d-q model is extensively used in control application as
it has capability to convert sinusoidal variables quantities
to dc quantities using suitable reference theory. By
having the voltage and current quantities in dq frame, it is
possible to control the speed of the machine by
controlling the flux and torque independently. It is also
method of senor less flux measurement.[4]
III. DQ MODELING
The direct and quadrature axis model (d-q model)
based on the space phasor theory is widely used for
simulation the dynamic behaviour of three phase
induction motor.
43
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 3, March 2014)
A. Nomencuture
In a generalize d-q reference frame, the electrical
equation in normalized form of squirrel induction motor
can be found as follows:
d:
direct axis
q : quadrature axis
:
stator
variables
s
r : rotor variables
n : normalized value
Pb
: normalized power
Vb
vasn, vbsn, vcsn : normalized input voltage for phase a, b
and c
vqsn, vdsn
: normalized stator q and d axis voltages
vqrn, vdrn
: normalized rotor q and d axis voltages
iqsn, idsn
: normalized stator q and d axis current
iqrn, idrn
: normalized rotor q and d axis current
qsn, dsn : normalized stator q and d axis modified
flux linkages
qrn, drn : normalized rotor q and d axis modified
flux linkages
b
: base speed
rn
: normalized rotor speed
cn
: normalized angular speed in
synchronous reference frame
Ten
: normalized electromagnetic torque
Tln
: normalized load torque
Rsn
: normalized stator resistance
Rrn
: normalized rotor resistance
Xsn
: normalized stator reactance
Xrn
: normalized rotor reactance
Xmn
: normalized magnetizing reactance
J
: moment of interia
H
: interia constant
P
: number of poles
(1)
(2)
(3)
4)
For squirrel induction motor as in the case of this paper
and
in equation (3) and (4) are set to zero since
rotor cage bars are short circuited.
Modified flux linkages in normalized form are:
(5)
(6)
(7)
(8)
Normalized electromagnetic torque equation in terms
of normalized modified flux linkage and normalized
current form:
(
idsn
wcn*fqsn
(wcn-wrn)*fqrn
(Xrn-Xmn)/wb
Rrn
After driving the torque and speed equations in term of
d-q flux linkages and currents of the stator, the d-q axis
transformation should now be applied to the machine
input (stator) voltages.
The three-phase stator voltages of an induction
machine under balanced conditions can be expressed as:
Xmn/wb
iqsn
Vqsn
Where
idrn
(Xsn-Xmn)/wb
Vdsn
Rsn
(9)
Based on the above equations, normalized rotor speed
can be determined as follows:
B. Equations
Driving the model equations can be generated from the
dq0 equivalent circuit of the induction machine shown in
figure 1.
Rsn
idrn
(Xsn-Xmn)/wb
wcn*fdsn
(wcn-wrn)*fdrn
(Xrn-Xmn)/wb
Rrn
Xmn/wb
Figure 1: The d-q normalized equivalent circuit of an Induction
Motor
44
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 3, March 2014)
These three-phase voltages are transferred to a
synchronously rotating reference frame in only two
phases (d-q axis transformation). This can be done using
the following two equations.
[
][
Figure 3 illustrates the internal structure of the
induction machine d-q model, implemented according to
equations (1-11), through which the flux linkages,
currents, torque and the rotor angular speed are calculated.
f dsn
v dsn
f dsn
vdsn
f drn
v drn
f qsn
vdrn
wrn
Then, the direct and quadrature axes voltages are:
fdsn
fdrn
4
idrn
f qrn
idsn
f dsn
f drn
idrn
idsn
idsn
ten
][
f qsn
f qsn
f dsn
f qsn
f qrn
[ ]
[ ]
fqrn
wrn
tln
tln
3
iqrn
wrn
iqrn
iqsn
v qsn
vqsn
iqsn
Figure 3: The internal structure of the 3-phase Induction Motor dq model
Figures 3 & 4 show the implementation of torque Ten
and angular speed rn as expressed in equations (9), (10)
respectively.
][ ]
ten
fqsn
f qrn
f drn
][ ]
iqsn
9
10
v qrn
vqrn
The instantaneous values of the stator and rotor
currents in three-phase system are ultimately calculated
using the following transformation:
ten
4
iqsn
1
IV. MATLAB/SIMULINK IMPLEMENTATION
fdsn
The inputs of an induction machine are three phase
voltages, their fundamental frequency and the load torque.
The outputs of an induction machine are three-phase
currents, electrical torque, and rotor speed.
Dynamic model of squirrel cage induction motor is
developed by using the equations from (1) (18) in
MATLAB/SIMULINK platform in figure 2.
v qsn
iqsn
iqsn
idsn
idsn
v qsn
idsn
3
fqsn
iqrn
iqrn
idrn
idrn
idsn*fqsn
Figure 4: The implementation of the torque equation Ten
1
ibsn
Scope
tln
1
s
1/(2*H)
ten
2
iarn
v dsn
1
ten
Subtract
iasn
icsn
v dsn
iqsn*fdsn
Add
Gain
Integrator
wrn
ibrn
ten
v qrn
i0n
icrn
Scope1
i0n
wrn
Figure 5: The implementation of the angular speed equation (wrn)
f dsn
v drn
f drn
f qsn
0
TL
The Matlab/Simulink models to find the flux linkages
fqsn, fdsn, fqrn, fdrn are shown below:
Scope4
tln
f qrn
Figure 2: The 3-phase Induction Motor Matlab/Simulink Model
f qsn
In this model the simulation starts with generating a
three-phase stator voltages according to the equations (12,
13, 14), and then transforming these balanced voltages to
two phase voltages referred to the synchronously rotating
frame using Clarke and Park transformation as in
equations (15, 16)
2
fqrn
v qsn
vqsn
iqsn
iqsn
f qsn
f qrn
f dsn
fdsn
2
iqsn
Figure 6: Block for flux linkage fqsn
45
1
fqsn
6
wrn
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 3, March 2014)
1
1
f dsn
vdsn
idsn
vqrn
v dsn
idsn
f dsn
f drn
fdrn
rrn
wb
iqrn
fdsn
1
s
1
fqrn
wcn
f qsn
fqsn
2
Constant
4
wrn
fdrn
idsn
Figure 12: Internal structure of block of flux linkage fqrn
Figure 7: Block for flux linkage fdsn
1
vdrn
v qrn
vqrn
f qrn
iqrn
f qsn
f qrn
f drn
fqrn
fdrn
4
wrn
1
s
1
fdrn
Figure 8: Block for flux linkage fqrn
fqrn
v drn
vdrn
idrn
wrn
The Matlab/Simulink models to show the internal
structure of the blocks shown above for calculation of the
currents iqsn, idsn, iqrn, idrn as stated in equation (5-8)
are shown below:
iqrn
f drn
Constant
4
Figure 13: Internal structure of block of flux linkage fdrn
wrn
1
idrn
f dsn
fdsn
wb
wcn
fqsn
rrn
idrn
iqrn
f qrn
fqrn
3
wrn
xrn
fqsn
f drn
fdrn
1/(xrn*xsn-xmn*xmn)
1
iqsn
xmn
fqrn
wrn
2
Figure 14: Internal structure of block of current iqsn
idrn
Figure 9: Block for flux linkage fdrn
xrn
fdsn
The Matlab/Simulink models to show the internal
structure of the blocks shown above for implementation
of the flux linkages fqsn, fdsn, fqrn, fdrn as stated in
equation (1-4) are shown below:
1/(xrn*xsn-xmn*xmn)
1
idsn
xmn
fdrn
Figure 15: Internal structure of block of current idsn
1
vqsn
rsn
1
s
wb
iqsn
xsn
fqrn
fqsn
1/(xrn*xsn-xmn*xmn)
wcn
Constant
fqsn
1
iqrn
xmn
3
fdsn
Figure 16: Internal structure of block of current iqrn
Figure 10: Internal structure of block of flux linkage fqsn
1
xsn
fdrn
1/(xrn*xsn-xmn*xmn)
vdsn
2
i dsn
rsn
wb
1
s
xmn
1
idrn
fdsn
1
fdsn
wcn
Figure 17: Internal structure of block of current idrn
Constant
3
fqsn
V. MATLAB/SIMULINK RESULTS
Figure 11: Internal structure of block of flux linkage fdsn
The simulations are carried out using the motor data
obtained from no-load test, short circuit test, retardation
test and stator resistance measurement test on the motors.
46
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 3, March 2014)
40hp 60hz 3-phase induction motor has the following
ratings and parameters:-
iarn
5
Rs=0.22
Rr=0.209
Lm=0.04H
Ls=0.0425H Lr=0.043H
2
B=0
Load torque= 0 J=.124kg-m
0
-5
0
0.05
0.1
0.15
0.2
0.25
0.15
0.2
0.25
0.15
0.2
0.25
0.15
0.2
0.25
0.15
0.2
0.25
0.15
0.2
0.25
0.15
0.2
0.25
0.15
0.2
0.25
0.15
0.2
0.25
ibrn
5
The results of the simulation are given for the induction
motor with the following specifications:
0
-5
0
fdsn
1
0.5
0
-0.5
0.05
0.1
icrn
0.05
0.1
0.15
0.2
0.25
fdrn
-5
0.2
0
-0.2
-0.4
0.05
0.1
0.15
0.2
0.05
0.1
0.25
ten
fqrn
0
-0.5
-1
-1.5
2
1
0.05
0.1
0.15
0.2
0.25
fqsn
0.5
0
-0.5
-1
-1
0
0.05
0.1
wrn
0.05
0.1
0.15
0.2
0.25
1
iasn
0.5
5
0
0
-5
0
0.05
0.1
0.15
0.2
0.05
0.1
0.25
iqsn
2
0
-2
-4
-6
ibsn
5
0
0.05
0.1
idsn
6
4
2
0
-2
-5
0
0.05
0.1
0.15
0.2
0.25
icsn
5
0.05
0.1
iqrn
6
4
2
0
-2
0
-5
0
0.05
0.1
0.15
0.2
0.25
0.05
0.1
idrn
2
0
-2
-4
-6
0.05
0.1
Figure 18: Machine variables during free acceleration of a 40-hp
induction motor
47
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 3, March 2014)
Finally, the machine parameters should be defined to
the simulated machine system in order to complete the
simulation process using graphical user interface (GUI)
available in Matlab/Simulink. Figure 19 shows the GUI
of the induction motor model shown earlier in figure 2.
This concludes that the Matlab/Simulink is a reliable
and sophisticated way to analyze and predict the behavior
of induction motors using the theory of reference frames.
REFERENCES
Andrzej
M. Trynadlowski, Control of induction motor
Academic Press: England, 2001.
[2] P. C. Sen, Princibles of Electric Machines and power
electronics, Wily, 2nd edition, 1996.
[3] R. Krishnan, Electrical Motor Drives: modeling, analysis and
control, PHI
[4] Sushma, P. ; Samaga, B.L.R. ; Vittal, K.P. DQ Modeling of
Induction Motor for Virtual Flux Measurement IPEC, 2010
Conference Proceedings , 2010 , pp. 903 908
[5] A Dumitrescu, D.Fodor, T.Jokinen, M.Rosu, and S.Bucurencio,
"Modeling and Simulation of electric drive system using
Matlab/Simulink environments," international Conference on
Electric Machines & Drives (JEMD), 1999, pp.451-453.
[6] M.L.de Aguiar, and M.M.Cad, "The concept of complex transfer
functions applied to the modeling of induction motors," Power
Engineering Society Winter Meeting, 2000, voU, pp.387-39I.
[7] Adel Aktaibi & Daw Ghanim,Dynamic Simulation of a ThreePhase Induction Motor Using Matlab Simulink,
[8] Burak Ozpineci and Leon M. Tolbert, "Simulink implementation
of induction machine model - a modular approach," international
Conference on Electric Machines & Drives (JEMD), 2003, vol.2,
pp.728-734.
[9] J. D. Lavers and R. W. Y. Cheung, A software package for the
steady state and dynamic simulation of induction motor drives,
IEEE Trans..
[10] Wade, S. ; Dunnigan, M.W. ; Williams, B.W. Modeling and
simulation of induction machine vector control with rotor
resistance identification, , Power Electronics, IEEE Transactions,
vol 12, pp. 495 - 506
[1]
VI. CONCLUSIONS
In this paper, an implementation and dynamic
modeling of a three-phase induction motor using
Matlab/Simulink are presented in a step-by-step manner.
The model was tested by 40 hp 60hz 3-phase induction
motors. The simulated machines have given a satisfactory
response in terms of the torque and speed characteristics.
48
