 Open Access
 Total Downloads : 2667
 Authors : Radhika Priyadarshini, Lekshmi M
 Paper ID : IJERTV2IS4058
 Volume & Issue : Volume 02, Issue 04 (April 2013)
 Published (First Online): 16042013
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Dynamic Performance of ThreePhase Induction Motor
Radhika Priyadarshini, M.Tech, 2nd semester, EEE, ACIT, Bangalore Lekshmi M, Associate Professor, EEE, ACIT, Bangalore
Abstract A dynamic model of an induction motor considers the instantaneous effects of varying voltage/currents, stator frequency, and torque disturbances. The dynamic model is derived, using a three phase motor in direct and quadrature axes. Theory of reference frames has been used to analyze the performance of induction machines. Reference frames gives a unique view of the system as well as simplification of system equation. In this paper relevant equations are stated, and then a generalized model of a three phase induction motor is developed and implemented in Simulink. The simulated results provide the steadystate behavior of the induction machine.
Keywords Dynamic performance, transformation, abcdq0 model, twothree phase transformation, Simulink implementation.

INTRODUCTION
The voltage and torque equations that describe the dynamic behavior of an induction motor are timevarying. It is successfully used to solve such differential equations and it
advantage over other machine simulators in modeling the induction machine using dq0 axis transformation .It can be a powerful technique in implementing the machine equations as they are transferred to a particular reference frame. Thus, every single equation among the model equations can be easily implemented in one block so that all the machine variables can be made available for control and verification purposes. In this paper, Simulink is used to simulate the dynamic performance of an induction motor model whose stator and rotor variables are referred to an arbitrary reference frame. The implementation process is given for all the stated equation. The equivalent circuit of the induction machine in the arbitrary reference frame is shown in Fig. 1 above.

INDUCTION MOTOR MODEL
Driving the model equations can be generated from the dq0 equivalent circuit of the induction machine shown in Fig.1. The flux linkages equations associated with this circuit can be found as follows [3]:
may involve some complexity. A change of variables can be
=
+ (
) . (1)
used to reduce the complexity of these equations by eliminating all timevarying inductances. By this approach, a
poly phase winding can be reduced to a set of two phase
= + ( ) (2)
windings (qd) with their magnetic axes formed in quadrature.
In other words, the stator and rotor variables (voltages,
=
( )
+ (
) . (3)
currents and flux linkages) of an induction machine are transferred to a reference frame, which may rotate at any
angular velocity or remain stationary. Such a frame of
= ( ) + ( ) (4)
reference is commonly known in the generalized machines analysis as arbitrary reference frame [1, 2]
Where
+
+
– + +
=
+ ………….(5)
( )
– – =
+
…(6)
1
=
=
1 + 1 + 1
.(7)
+ +
– +
+
( )
– – Then substituting the values of the flux linkages to find the current are given below;
+ 0 +
= 1
( ) (8)
0
– –
= 1
(
)
. (9)
Fig.1 The dq0 equivalent circuit of an induction motor
The dynamic analysis of the symmetrical induction machines in the arbitrary reference frame has been intensively used as a standard simulation approach from which any particular mode of operation may then be developed. Simulink has an
= 1
= 1
( (
) (10)
). (11)
Based on the above equations, the torque and the rotor speed can be determined as follows:
2 2
2 2
= 3 1 ( ) (12)
2
2
= ( ). (13)
Fig. 2 depicts the complete Simulink scheme of the described induction machine model [4, 5 and 6].
In this model the simulation starts with generating a three phase stator voltages according to the equations (1418) and then transforming these balanced voltages to two phase voltages referred to the synchronously rotating frame using Clarke and Park transformation as in equations .
Where P: number of poles;J:moment of inertia (Kg/m2). For squirrel cage induction motor, the rotor voltages and in the flux in the flux equations are set to zero since the rotor cage bars are shorted. After driving the torque and speed equations in term of dq flux linkages and currents of the stator, the dq axis transformation should now be applied to
the machine input (stator) voltage.
v as vq
A
v bs vd
B
Vqs
Vds
iqs ids iqr idr
wr
iqs
ids
iqr
ias ibs
ics s
iar
ibr
The threephase stator voltages of an induction machine under
v cs vo TL
0
0
Te
idr
icr r
balanced conditions can be expressed as:
= 2 sin . (14)
C
abcdq
Terminator TL
induction motor dq model
Te/wr
23 ph
3
3
= 2 sin 2 (15)
3
3
= 2 sin + 2 . (16)
These threephase voltages are transferred to a synchronously
Fig.2 The 3phase induction motor Simulink model
Fig. 3 illustrates the internal structure of the threephase to two phase transformation, which represents the equations (14 to 18).
1
rotating reference frame in only two phases (dq axis transformation). This can be done using the following two equations.
vas
2
vbs
2
vd
K*u 1
vq
1 1 1
Gain
3
= 2 2 2 (17) vo
3 0 3
2
3 2
3
vcs
Fig. 3 internal structure of abc to dq model
Then, the direct and quadrature axes voltages are
= cos sin (18)
Fig. 4 illustrates the internal structure of the induction machine dq model by which the flux linkages, currents,
sin cos
torque and the rotor angular speed are calculated.
The instantaneous values of the stator and rotor currents in threephase system are ultimately calculated using the following transformation:
Fmq

Vqs
Vqs
Fqr
Fqs
Fqr
Fqs
Fmq iqr iqs
3
iqr
1
iqs
=
cos sin sin cos
. (19)

Vds
Vds
wr
Fmd
Fds
<>Fdr
current cal
Fds ids idr
iqs
2
ids
4
Fqs
Te 6
Fds Te
ids
1 0
1 0
flux linkage calculation
Fdr
Fmd
idr
Subsystem1
=
1
3
3
2 2
3 2
…. (20)
current cal1
TL
wr 5

Te wr
TL
TL
1
2
3
2
Subsystem
III SIMULINK IMPLEMENTATION
In this section, the three phase induction machine model is simulated by using the Simulink. The Model is implemented using the same set of equations provided above in sections II.
Fig. 4 The internal structure of the 3 phase induction motor dq model
3
Fds
The Simulink model to find the flux linkages stated in equations (1) to (4) is shown in Fig. 5.
1
iqs
2
K 1
Te
Fqs
4
ids
2
Vqs
1
Fds Vqs Fmq
Fqs
2
Fqs
3
Vds
5
Fmd
Fqs Vds Fmd
Fds
3
Fds
Fig. 7 the implementation of the torque equation Te (12)
1
s
1
s
2
Fmq 2
1
4
wr
Te
1
TL
K 1
wr
wr
Fmq Fqr Fdr
3
1
Fqr
Fmd wr Fqr
4
Fdr
4
Fdr
Fig. 8 the implementation of the angular speed equation (13)
Fig.9 shows the internal structure of the blocks (1 4) in Fig. 4 in which the equations (1)(4) are implemented in Simulink
Fig. 5 The internal structure of the block to calculate the flux linkages
Fig. 6 show the Simulink blocks used to calculate the currents according to the equations (8) (11)and also flux linkages in equations (5),(6). Fig. 7 & 8 show the implementation of torque Te and angular speed as expressed in equations (12),
(13) respectively.
format.
2
Vds
377
1
Fqs
3
Fmd
K
K
K 1
s
1
Fds
2
Fqs
1
Fqr
Fqs
Fmq Fqr
Fqs
iqs Fmq
Fmq
iqr
Fqr
3
iqs
1
Fmq
2
iqr
2
Vds
377 K
1
Fqs
K 1
s
1
Fds
3
Fmd K
1
Fds
2
Fdr
Fds
Fmd Fdr
1
ids
3
Fmd
377
377
1 wr
3
Fdr
Fds
ids Fmd
Fds
ids Fmd
K
K 1
s
1
Fqr
Fmd
idr
Fdr
Fmd
idr
Fdr
2
idr
Fig. 6 The internal structure of the block to calculate the currents and fluxes
2
Fmq
K
377
2
wr
K
K 1
s
1
Fdr
1
Fmd
K
1
idr
3
Fqr
1 K Fmd
Fig. 9 The implementation of the equation (1)(4)
2
Fdr
Fig. 11 The implementation of dq current equations
Fig. 12 represents the implementation of 2 phase to 3 phase conversion
Fig. 10 presents the implementation of the flux linkages found in Fig. 6. Also, Fig. 11 depicts how the current equations are constructed.
2
ids
1
K*u
1
ias 2
ibs 3
1
Fds
K
K
1
Fmd
iqs
4
ics
4
2
Fdr
1
Fqs
K
K
idr
3
iqr
K*u
Fig .12 The implementation of dqabc model
iar 5
ibr 6
icr
2
Fqr
K
K
1
Fmq
Finally, the machine parameters should be defined to the simulated machine system in order to complete the simulation process. There are many ways to input the required data. The input is given and the results are observed.
Fig.10 The calculation of the flux linkages Fmq and Fmd
1
Fqs

SIMULINK RESULTS
An induction motor is tested in this simulated model. The results of the simulation are given for the induction motor with the following specifications:
2
Fmq
1
Fmq
2
Fqr
1
Fds
2
Fmd
K
K
K
1
iqs
1
iqr
1
ids
Hp = 3; VL = 220; f = 60; Rs = 0.435; Xls = 0.754; P = 4;
Rr = 0.816; Xlr = 0.754; J = 0.089; Xm = 26.13; rpm = 1710
Fig.13 The stator currentsv/s time
Fig. 14 The rotor currents v/s time
Fig.15 v/s time & Te v/s tome

CONCLUSIONS

In this paper, an implementation and dynamic modeling of a threephase induction motor using Simulink are presented in a stepbystep manner. The dynamic model of a three phase induction machine is derived from the two phase machine by establishing equivalence between three and two phase and then, two phase motor in direct and quadrature axis. The model was tested for given ratings of a small induction motor. Satisfactory outputs are observed. This concludes that the Simulink is a reliable and sophisticated way to analyze and predict the behavior of induction motors using the theory of reference frames.
REFERENCES

P. C. Krause, Analysis of Electric Machinery, McGraw
Hill Book Company, 2012

R. Krishnan, Electric motor drives, Prentice Hall, 2001 [3]CheeMunOng, Dynamic Simulation of Electric machinery using Simulink/Matlab, Prentice hall PTR, 1998
Vol PAS87, No 11, November 1969
[6]Burak Ozpinei,Simulink implementation of Induction Motor model.