Modelling Of The Three-phase Induction Motor Using Simulink

Modelling of the three-phase Induction Motor using SIMULINK K. L. Shi, T. F. Chan and Y. K. Wong

Department of Electrical Enginedng Hong Kong Polytechnic University,Hunghom, Kowloon Hong Kong Telephone:(+0852)27666148

Facsimile: (+0852)23301544

-

Abstract This paper describes a generalid simulation model of the three-phase induction motor using the SIMULIMC software package of MATLAB. The model is based on two-axis theory of revolving frame transformation. The model takes power source and load torque as inputs and gives speed and electromagnetic torque as outputs. Internal resistance of the power supply and magnetic saturation of the motor may also be accounted for.

A GENERALIZED MODEL OF INDUCTION MOTOR

In this simulation scheme, the model of the induction motor consists of three-phase to two-phase transformation equations, electromechanical equation and load dyna" equation. In Fig.l, the block in dotted line is the induction motor model which may be used alone when the motor operates in the current controlled mode. In addition, a power supply block is included to adapt the model to motor operation on a voltage source (E) or a current source (0.

INTRODUCTION

T

Simulation of the three-phase induction machine is well documented in the literature and digital computer solution can be performed using various methods, such as numeric programming, symbolic programming and the electromagnetic transient program [1*21. With the rapid development in computer hardware and software, new simulation packages which are much faster and more user friendly are now available. This paper discusses the use of one such product, the SWZULINK software of MATLAB,in the dynamic modelling of the induction motor. The dynamic model is based on the two-axis theory of revolving frame transformation. The main advantage of the SIMULINK over other programming sohares is that.,instead of compilation

em)

which performing a specific mathematical operation. Programming efforts are drastically reduced and the iS a model debugging Of errors iS easy. shcx the S-INK operation programmer, the simulation model can be easily developed by addition of new sub-models to cater for various control functions. As a sub-model the induction motor could be incorporated in a complete electric motor drive system. model described in t h i s paper ~ s n "e S the following characteristics; 1. It takes voltage source (E) or current source (I)and load torque as inputs and gives speed and electromagnetic torque as outputs. 2. ~nternal resistance of the power supply may be accounted for. 3. The parameters may be continuously changed. 4.

E or I Fig.1 Block diagram for simulation of induction motor

BASIC EQUATIONS AND THEIR SIMULINK BLO€KS

m e current block is b&

on the w e n t quatiom.

i,

~

=~

~+

~

- 27J3

ibs = dcos(of

+

8)

(

d

(1) (2)

= Acos(wt + 2d3 + @ (3) ~ representation ~ s of one phase supply using the The SIMULINK blocks is shown in Fig.2.

i,

A

' m

Magnetic saturation level of the motor may be set.

The model may be easily expanded and developed. 6. Good user interface. 5.

0-7803-3946-0/97/$10.00 0 1997 IEEE.

Cbck

Fig.:! A SIMULINK block for the power supply of one phase

WB3-6.l

The function blocks in Fig.2 may be grouped together to

create a new subsystem block as shown in Fig.3.

PRODUCT and INTEGMTOR in the SIMULINK library. These blocks can be easily opened in separate windows for modification of their m e t e r s . The completed model is illustrated in FigS.

Fig3 A SIh4ULINK block of the power supply

The 312 transfoxmation block is based on the current equations for phase transformation. COS(@ - 2 ~ 3)/ COS(@ + 2 ~3)/ -sin(cot-2~13) -sin(cut,+2~/3)

The repmentation of 312 transformation by the SlMoLINK blocks is shown in Fig.4. ianerprodua

cosine vector

Fig5 A SIMULINK block of electromechanicalcalculation

i'm

The stator voltage calculation block is based on Eq. (10) and (11). The flux n6~=/Zc,,+j.2', andpleR Can be obtained directly fiom the electromechanical block. (10) j$' = R8ii + (p +jo)TY

Fig4 A SIh4ULINK block Of312 transform

The load dynamics block is ksed on Eq. (12) and is

The electromechanicalblock configuration is based on the following three equations. With the rotor voltage vector normally assumed zero, the torque equation in excitation reference -e is expressxi as[41,

configuredin a similar wdy as shown in Fig.6.

do dt

T-T,

cf

A=_-

(rr=L,R,is the rotor time constant)

J,

@,+

J,

+ JL

Fig.6 A SIMULINK rqpreSentati~nof load djnamics block

To construct a block diagram of the motor, in which components i+DS and ieQSof the stator current vector, i4s , represent the input variables and the torque, T, the output variable, the rotor flux vector components, A'DR and A'QR , appearing in Eq. (7)must be expressed in terms of i4Ds and ~+QS using Eq. (8) and (9). Eq. (7), (8) and (9) describe the dynamic block diagram of an induction motor shown in Fig.5. The diagram illustrates the major difi'iculty encountered in the control of induction motors. The four multipliers make the motor a nonlinear system, and there are two crosscouplings between the D and Q paths. Configuring the eledromechanicalblock in the SIMULINK

only requires the standard blocks of SUM, GAIN,

From Eq.(12), the slip frequency w, can be calculated and fed back into the electromechanical block. @,=@--

P 2 O0

SIMULATION RESILTS

Following are the parameters of the induction motor chosen for the simulation studies. Type: three-phase, wyeannected, squirrelcage induction motor Rated power: HPrd= lOhp(7.46kW)

WB3-6.2

Rated stator voltage: Vs,,z220V Rated frequency:f,,=60Hz Rated speed: nMm= 1164 rpm Number of poles: -6 Stator resistance: RS=0.294!3ph Stator leakage reactance:&=0.524Wph Rotor resistance referred to stator: R,=O. 156Wph Rotor leakage reactance referred to stator: X1,=0.279Wph Magnetizing reactance:X,= 15.457aph Mass moment of inertia of the rotor: J p 0 . 4 kg.m2 Coefficient of friction:' C 0.062 To illustrate the application of the dynamic model of the induction motor to transient motor operation, a simulation study of direct-on-line starting is demonstrated. At the initial instant of time, t = 0, the motor, previously de-energized and at standstill, is connected to a 220 V, 60Hz supply. The power source is simulated by a signal generator block in the SIIWLINK library. The load torque, TL,is assumed to be 50% of the rated torque of the motor, and independent of speed. The mass moment of inertia, JL , of the load equals that ofthe motor. The simulation conditions are: 1. Runge-Kutta method 2. Max step size: 0.01 sec 3. Min step size: 0.0001 sec 4. Tolerance: le-3 Fig.7 and 8 show the results of computer simulation using the SIMULINK model. When the power supply has a large internal resistance, the torque oscillations in the torqudspeed characteristic are r e d u d and damped more rapidly, but the run up time of the motor is longer.

..

o

a5

2

1.5

t

26

..

..

..

..

....

....

.,..

....

..

... 0

0.6

1

1.5

2

"53

3

25

Time (second)

"

"

o

...

...

...

...

...

...

...

...

.

...

"

.

'

a

XI

.

o

.

...

w t m i a

speed (radlsec)

.

..

..

..

..

..

..

..

..

o

m

o

r

m

m

i

a

t

m m(

.. 4

.. ~

.. ~~ 2

.. ~

..

I ~

2

~ d )

Fig8 Simulation results: intemal resistance ofpower supply = 0.05Q.

CONCLUSION

The computer simulation model presented in this paper is effective for transient analysis of the induction motor. Using the SIMULINK software, each block of the model may be connected and modified easily. Some limit conditions such as saturation of magnetic circuit and stator current limit may be easily inserted in the function blocks. Researchers on machine drives will find this method convenient to use as program compilation is not required. In addition, there are many toolboxes of signal processing, neural network, fuzzy logic, identification and control in the SlMuLINK library. As a subsystem, the model may be easily incorporated into a sophisticated control system of the induction motor.

5

Time (second)

speed (radlsec)

REFERENCES 30-

.. i

..

..

,

.

..

...

.

.

...

...

.

.

: -:........:... ...........

..

..

"*.." .

..

. .

...

.

. . ... . ...

...

.

o m o r a l w r

.

U

.

W

i

..

..

l

i i i ....i...".".l.......i ....

. . . . . .. .. . . ... ... . .. . .. . ..

.

W

:

..

I .. .. . . . stitac;rratlofi,(1y:,, -..........-..................... ......-:..........-;.......... .

. . . . . . . .. ... ... ... ...

.

..

:"

iliSHliuailv,,,, ,~.... ...i

........

..

.

e

.

.

2

.

.

.

P 2 4 2 a 2 8 3

TnQ (semri)

Fig7 Simulationresults intemalresistance of power supply'=0.2R.

[l] A D. Jr, Y.Yh,"Single Phase Indudcm Machine Simulation Using the Electromagnetic Transients Program: Theory and Test Cases," LEET Trans. on E n e m Conversion,vol. 9,No.3,pp 535-542,Sept, 1994. [2] P. C. lkause, "Simulatim of Sy"&oal Induai~ Machinery,'?lEEE Trans. on Power apparatus and Systems, vol. PAS-84, No. 11, pp. 1038-1053,NOV.,1965. [3] S. N. G b i , "Digital cornputer Simulation of Threephase Induction Machine Dynamics - A Generalized Approach," IEEE Trans. on Ind. App., vol. 24,No. 1, JauReb., 1988. [4] A M . Tnynadlowki, The Field Orientation Principle in Control of Induction Motors, KLUWER ACADEMIC PUElLISHERS,1994. [SI P. N. Enjeti P. D. Ziagas, J. F. Lindsay and M. H. Rasbid, "A New Current Control Scheme for ac Motor Drives," IEEE. Trans. on Ind. App..,vol. 28,No.4, pp842-849.Jul./Aug., 1992.

WB3-6.3

8

x

3