MODELING AND SIMULATION OF INDUCTION MACHINE AND ITS APPLICATION IN ELECTRIC DRIVES

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MODELING AND SIMULATION OF INDUCTION MACHINE AND ITS APPLICATION IN ELECTRIC

DRIVES PRAJOF P

edited bySarath S Nair



CONTENTS• Introduction• Dynamic d-q modeling• Synchronous and stationary reference frame

equations• Simulation of induction machine• Vector control• Simulation of vector control• Sensor less control • Simulation of sensor less vector control• Conclusions


INTRODUCTION• Motion control is required in large number of

industrial and domestic applications like transportation systems, rolling mills, machine tools, fan, pumps, robots, washing machines etc.

• Electric drives are used for motion control.• AC and DC machines used in drives• AC motors have several advantages- high robustness,

reliability, low price and high efficiency.• Latest ac machine drive technology –VECTOR

CONTROL and sensor less control. These are studied with the help of dynamic d-q modelling.


DYNAMIC d-q MODEL OF INDUCTION MACHINE

• In an adjustable speed drive transient behavior has to be

taken into consideration

• The conventional mathematical modeling are complex

• In d-q modeling 3-φ machine parameters can be

represented by an equivalent 2-φ (d-q)

• A change of variables can be used to reduce the complexity

of machine differential equations.


CONTD…

The following assumptions are made to derive the

dynamic model:

• Uniform air gap.

• Balanced rotor and stator windings, with sinusoidal

distributed mmf.

• Saturation and parameter changes are neglected.


• It is used to transform the machine variables to a frame of reference that rotate at arbitrary angular velocity

AXES TRANSFORMATION

6

abcsssqd fKf 0

,)(, 00 sdsqsT

sqd fffwhere f

,)( csbsasT

abcs ffff

,

21

21

21

)3

2sin()3

2sin(sin

)3

2cos()3

2cos(cos

32

sK

.

1)3

2sin()3

2cos(

1)3

2sin()3

2cos(1sincos

1

sK

).0()(0

t

dtt


• Voltage equation of an induction machine can in synchronously rotating reference frame can be written as follows:

SYNCHRONOUSLY ROTATING REFERENCE FRAME–DYNAMIC MODEL (KRON EQUATION)

7

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STATIONARY FRAME–DYNAMIC MODEL

9

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SIMULATION OF MODELING OF INDUCTION MACHINE


• Rotor reference frame is used• Electrical equations for squirrel cage induction

motor is given by

• But for MATLAB simulation we use


• The electromagnetic torque and mechanical speed is given by

• Rotor speed and position is given by

• Magnetizing current, im is defined as


VECTOR CONTROL- PRINCIPLE

• Vector Control is similar to control of separately exited DC motor, with independent control of flux and torque and with superior dynamic response.

• Vector control is done by resolving stator current• The magnitude of iqs should be controlled to

adjust the torque and the magnitude of ids should be controlled to adjust the rotor flux


CONTD…• Assumption made - the position of the rotor flux linkage

phasor, ƛr , is know

• The current phasor is produces rotor flux ƛr and the torque Te


CLASSIFICATION OF VECTOR CONTROL

Vector control is classified on according to how the field angle is acquired. They are as follows:

1. Direct vector control

2. Indirect vector control


• Field angle is generated in feed forward manner• This method uses the model equations of the machine with

easily measurable quantities as inputs• Derived from synchronously rotating reference frames

INDIRECT VECTOR CONTROL

20


• The resultant rotor flux linkages, ƛr,, is assumed to be on direct axis

• The field, stator and slip angles can be obtained as followsθf = θsl + θr

θs = θf + θT 21


INDIRECT VECTOR CONTROL SCHEME

• The command values are given by as follows


SIMULATION OF VECTOR CONTROL- INDIRECT VECTOR CONTROL


SENSORLESS CONTROL

• Meaning-Control without any speed sensor• Speed sensor - Incremental shaft mounted

speed encoder • Speed encoder is undesirable in a drive

because it adds cost and reliability problems, besides the need for a shaft extension mounting arrangement


CONTD…

• Estimate the speed signal from machine terminal voltages and currents with help of a DSP

• Estimation is normally complex and heavily dependent on machine parameters

• Parameter variation problem particularly near zero speed imposes a challenge in the accuracy of speed estimation.


Induction motor speed estimation techniques

• Slip calculation• Direct synthesis from state equations• Model referencing adaptive system (MRAS)• Extended Kalman filter• Slot harmonics• Injection of auxiliary signal on salient rotor


DIRECT SYNTHESIS FROM STATE EQUATIONS

• The q and d stator voltages in the stator reference frame are obtained from the phase voltages as

• Similarly, the current are obtained in the same way


CONTD…

• From equation (I) and (II) we can find ƛdrs and ƛqr

s


CONTD…

• The field angle can be calculated as


SIMULATION OF SENSORLESS SPEED ESTIMATOR


Actual speed of the machine


Speed from machine parameters


CONCLUSION• The d-q modeling of induction machine was explained• MATLAB simulation of induction machine modeling was done

and the variations in speed and torque was observed• Two applications of d-q modeling ,namely – vector control

and sensor less control was discussed• Vector allows direct control of flux and torque, making torque

limiting and field weakening possible.• Decoupling between flux and torque is effective even under

dynamic conditions.• It was seen from MATLAB simulation that Vector Control

provides excellent dynamic response.• It is very complicated and requires the usage of powerful

processors• The controllers process dc quantities in the steady state


• Precise and smooth speed operations and used obtain high performance drives

• The basic principle of Sensor Less vector control of induction motor was explained

• MATLAB simulation was done on sensor less estimation of speed and compared with actual speed of the machine


REFERENCES1. M. Satyendra Kumar Shet and Uday Kumar R. Yaragatti, ‘’Design of computer

application for 3 phase vector control induction motor drive’’, IET-UK International Conference on Information and Communication Technology in Electrical Sciences (ICTES 2007),Dr. M.G.R. University, Chennai, Tamil Nadu, India. Dec. 20-22, 2007. Pp.315-322.

2. G. R. Slemon, “Modeling of induction machines for electric drives, “IEEE Tram. Onlnd. App. Vol. 25, No. 6, pp. 1126-1131, 1989.

3. Tsugutoshi Ohtani, Noriyuki Takada and Koji Tanaka, ‘Vector Control of Induction Motor without Shaft Encoder,’’ IEEE Transaction on Industry Applications, Vol. 28, No. 1, Jan-Feb 1992.

4. B.K. Bose. “Modern Power Electronics and AC Drives”. Upper Saddle River, NJ: Prentice Hall Pvt ltd, 2002.


5. R.Krishnan.”Electric Motor Drives Modeling, Analysis and Control” PHI Learning private limited New Delhi-110008, 2008.

6. Gopal. K. Dubey, ‘Fundamentals of Electric Drives’, 2nd Ed. Narosa

Publishing House, New Delhi, 2007

7. V. T. Ranganathan, ‘Induction Motors’, Course Notes on Electric

Drives, IISc, Bangalore.

8. Krause, P.C.: Analysis of Electric Machinery, New York, McGraw-

Hill, 1986.

9. Yen Shin Lai, “Modeling and vector control of induction machine-

A new unified approach’’, IEEE Tram. Onlnd. App. 0-7803-4403-01,

1998.

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MODELING AND SIMULATION OF INDUCTION MACHINE AND ITS APPLICATION IN ELECTRIC DRIVES

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