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MODELING AND SIMULATION OF INDUCTION MACHINE AND ITS APPLICATION IN ELECTRIC
DRIVES PRAJOF P
edited bySarath S Nair
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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
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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.
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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.
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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.
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• 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
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• 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
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• Rotor reference frame is used• Electrical equations for squirrel cage induction
motor is given by
• But for MATLAB simulation we use
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• The electromagnetic torque and mechanical speed is given by
• Rotor speed and position is given by
• Magnetizing current, im is defined as
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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
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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
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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
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• 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
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• 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
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INDIRECT VECTOR CONTROL SCHEME
• The command values are given by as follows
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SIMULATION OF VECTOR CONTROL- INDIRECT VECTOR CONTROL
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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
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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.
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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
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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
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CONTD…
• From equation (I) and (II) we can find ƛdrs and ƛqr
s
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CONTD…
• The field angle can be calculated as
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SIMULATION OF SENSORLESS SPEED ESTIMATOR
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Actual speed of the machine
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Speed from machine parameters
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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
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• 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
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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.
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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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