# Simulation Of Induction Motor Modelling In MATLAB Software

DOI : 10.17577/IJERTV2IS4886

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#### 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 three-phase to two-phase, 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.

1. 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 de-coupling 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.

2. Induction Motor Modelling

In Induction Motor Modelling the three-phase supply is converted to two-phase supply. This conversion is done with the help of Parks Transformation Matrix. After conversion, one phase is known as d-axis and the other phase is known as q-axis.

Fig. 1. Equivalent (q-axis) 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 (d-axis) 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 d-q 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, direct-axis and quadrature-axis 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 d-axis votages Vqr, Vdr – q and d-axis voltages

Fmq and Fmd – q and d-axis 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 q-axis 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 two-phase 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 de-coupling 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 three-phase supply is converted into two-phase 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. d-q axis currents which are 90 apart

1. Conclusion

Induction Motor Modelling helps us to de-couple 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 direct-axis 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.

2. References

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