 Open Access
 Total Downloads : 4275
 Authors : Naintara Wasnik, Prof. M. V. Palandurkar
 Paper ID : IJERTV2IS4886
 Volume & Issue : Volume 02, Issue 04 (April 2013)
 Published (First Online): 26042013
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Simulation Of Induction Motor Modelling In MATLAB Software
Naintara Wasnik
Department of Electrical Engineering,Shri Ramdeobaba College of Engineering and Management, Nagpur, Maharashtra, India.
Prof. M. V. Palandurkar
Department of Electrical Engineering,Shri Ramdeobaba College of Engineering and Management, Nagpur, Maharashtra, India.
Abstract
Induction Motor has inherent coupling effect due to its construction. Any changes made in the stator or rotor parameters changes the other parameters also. For
The supply current is in the stationary reference frame. Hence, the after the conversion from threephase to twophase, the two axis currents is also in stationary reference frame. It is made into rotating reference frame by adding unit vectors to the equation.
example; both torque and flux are the function of
iqs
Lls Llr
iqr
voltage or current and frequency. This means that when
torque is increased, flux tends to decrease. Therefore, change of one parameter affects the other parameter
Rs Rr
which is not desirable. This paper presents the decoupling of parameters termed as Induction Motor Modelling. Induction Motor Modelling helps to control each parameter separately.

Introduction
Induction motor is used in every industry. Therefore, its performance characteristics improvement will prove to be very beneficial. By performing Induction Motor Modelling, the parameters which were earlier inter
Vqs
eds e rdr
qsLm qr
Vqr
dependent due to coupling effect, now become independent due decoupling of parameters. By proper controlling of these parameters the current or voltage, frequency, output torque, speed can be controlled. Therefore, Induction Motor Modelling helps in controlling the parameters which will give the desired results in the output.

Induction Motor Modelling
In Induction Motor Modelling the threephase supply is converted to twophase supply. This conversion is done with the help of Parks Transformation Matrix. After conversion, one phase is known as daxis and the other phase is known as qaxis.
Fig. 1. Equivalent (qaxis) circuit of induction motor
b
b
qs Fqs
b
b
qr Fqr
ds Fds
b
dr Fdr
b
Lls Ls Lm
Llr Lr Lm
The above equations shows the flux linkages and mutual inductances of induction motor.
sine to convert the two phases in synchronously rotating reference frame.
ids
Lls Llr
idr
Rs Rr
eqs
e rqr
Vds
ds
Lm dr
Vdr
Fig. 2. Equivalent circuit (daxis) of induction motor Parks Transformation matrix in Simulink:
Fig. 3. Implementation of Parks Transformation in Simulink
Equations in the form of flux linkages:
dFqs
bVqs
e Fds
Rs
Rs
Fmq Fqs
2 1
1
dt
b Xls
Van 3 3 3Va 0
dFds e Rs
V 1 2 1 V
bVds Fqs Fmd Fds
bn
3 3
3
b0
dt
b Xls
Vcn
1
1 2Vc0
dFqr
e r
Rr
3 3
3
But the above matrix is in simple form, therefore cannot be implemented. It needs unit vectors to convert
bVqr
dt
b Fdr
Xlr
Fmq Fqr
the dq axis in synchronously rotating reference frame.
dFdr
bVdr
e r
Fqr
Rr
Rr
Fmd Fdr
dt
b Xlr
Vs qs
s
1
0
0
1
0 Van
1 Vbn
Mutual Flux linkages are calculated as given below:
V ds
3 3 V
cn
Fmq Xml Fqs
Xls
Fqr
Xlr
Vqs Vs qs.cose Vs ds.sin e
Fmd Xml Fds
Fdr
s s
Vds V qs.sin e V ds.cos e
Xls
Xlr
The above matrix is used in Simulink to get the d and q axis voltage with the help of unit vectors, cose and
Once, the flux linkages are known, directaxis and quadratureaxis currents can be formulated as given below:
iqs 1 Fqs Fmq
Xls
Fig. 4. Simulation implementation of mutual flux
ids
1 Fds Fmd
Xls
iqr
1 Fqr Fmq
Putting these equations we get:
Xlr
idr
1 Fdr Fmd
dFqs e
Rs Xml
Xml
Xlr
bVqs
Fds
Fqr
1Fqs
dt b
dFds e
Xls Xlr
Rs Xml
Xls
Xml
Where,
d – direct axis
bVds
Fqs
Fdr
1Fds
dt
dFqr
b
e r
Xls Xlr
Rr Xml
Xls
Xml
q – quadrature axis s – stator variable r – rotor variable
b
Fdr
Fqs
1Fqr
F – flux linkages
dt
dFdr
b
e r
Xlr Xls
Rr Xml
Xlr
Xml
Vqs, Vds – q and daxis votages Vqr, Vdr – q and daxis voltages
Fmq and Fmd – q and daxis magnetizing flux linkages
b Fqr
Fds
1Fdr
dt b
Xlr Xls
Xlr
Xls stator leakage reactance Xlr rotor leakage reactance
Fig. 6. Simulation implementation of qaxis current equation
Finally the torque can be calculated as:
Te 3 P 1
Fds.iqs Fqs.ids
Fig. 5. Simulation implementation of flux equation.
Similarly, rest of the flux equations can be implemented.
2 2 b
Where, Te is electromagnetic torque
Tl – load torque
e stator angular electrical frequency
b motor angular electrical base frequency r rotor angular electrical speed
Fig. 7. Simulation implementation of torque equation
The speed calculation is calculated as given below:
Te Tl J 2 dr
converted into vqs and vds. Depending upon these voltages, self flux linkages are found. Then with the help of these flux linkages, mutual flux linkages are obtained. The twophase currents, iqs and ids are calculated with the help of these mutual flux linkages. These two currents gives final torque Te i.e. electromagnetic torque.
Here the current ids is oriented in the direction of flux and the current iqs is oriented in the direction of torque. Since the variation of flux gives sluggish response,it is kept constant. Therefore, to control the output torque, current iqs is controlled. This is the major benefit of Induction Motor Modelling which gives decoupling effect and also the parameters can be independently controlled.
4. Simulation results
Figure shown below shows the electromagnetic torque and the load torque. The load torque is given as step input. This step input acts as a variable load torque.
P dt
Fig. 8. Simulation implementation of speed equation
3. Simulation diagram
Fig. 9. Simulation diagram of induction motor Modelling
The threephase supply is converted into twophase supply by Parks Transformation, i.e. va, vb and vc is
Fig. 10. Simulation results of electromagnetic torque matching the load torque
Here, the electromagnetic torque is matching the load torque, after the initial transients. Therefore, Induction Motor Modelling provides the facility of independent control over the parameters to get the desired outputs. Also any additional control technique can be applied to the input side of induction motor after the Induction Motor Modelling is done for better and independent control of parameters.
Fig. 11. Simulation result of speed of induction motor
Fig. 12. Simulation results of Parks Transformation matrix, i.e. dq axis currents which are 90 apart

Conclusion
Induction Motor Modelling helps us to decouple the parameters. It gives the advantage of independent control over the parameters. Also any advance control technique can be applied to Induction Motor Modelling to enhance the performance of induction motor considering Induction Motor Modelling as the base technique.
In this modelling, we find directaxis and quadrature axis currents. This shows that id and iq are 90 apart from each other, id lies in the direction of flux and iq lies in the direction of torque. Therefore the parameters are easily accessible for control which was not possible without this technique. Hence, parameters become independent variables because of which change of one parameter does not affect the other parameters.

References

Dal Y. Ohm, Dynamic Model of Induction Motors forn Vector Control.

Burak Ozpineci & Leon M. Tolbert, Simulink Implementation of Induction Machine Model A Modular Approach, 0780378172/03/$17.00 Â©2003 IEEE

A A Ansari, and D M Deshpande, Mathematical Model of Asynchronous Machine in MATLAB Simulink, A. Ansari et. al. / International Journal of Engineering Science and Technology 1 Vol. 2(5), 2010, 12601267.

Sifat Shah, A. Rashid, and MKL Bhatti, Direct Quadrate (DQ) Modeling of 3Phase Induction Motor Using MatLab / Simulink, Canadian Journal on Electrical and Electronics Engineering Vol. 3, No. 5, May 2012

M. V. Palandurkar, J.P. Modak and S. G. Tarnekar, Elimination of a Flywheel in a Process Machine by Controlling Power Frequency of the Main Drive, M. V. Palandurkar et al. / International Journal of Engineering Science and Technology (IJEST), ISSN : 09755462 Vol. 3 No. 4 April 2011

Lionel Hutt, Donald Vollrath and Casey Carey, Modern VVVF Drives, Educational Focus: Elevator Drive Systems

Dong Hwa Kim, Kaoro Hirota, Vector control for loss minimization of induction motor using GAPSO, Applied soft computing, Volume 8, Issue 4, September, 2008.

Paul C. Krause, Oleg Wasynczuk and Scott D. Sudhoff, Analysis of Electric Machinery and Drive Systems, Second Edition, IEEE Press

Bimal K. Bose, Modern Power Electronics and AC Drives, Prentice Hall PTR, Â© 2002.

R. Krishnan, Electric Motor Devices, modeling, Analysis and control,PrenticeHall, Inc., New Jersy, Â©2001.