Induction Machine Modelling

Induction Machine ModellingPrepared by:Kishan M. Darji16 March 20151

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ContentsIntroductionList of SymbolsMachine Rating & ParametersList of SubsystemsSimulationSimulation ResultsConclusionReferences16 March 20152

IntroductionModelling means mathematical representation of a system.Here, induction motor is modelled using MATLAB Simulink.16 March 20153

List of Symbols16 March 20154Ls -stator inductanceLm-mutual inductanceLr -rotor inductanceRs -stator resistanceRr -rotor resistanceRc -cable resistancew -rotor speedP -pole numberVds, Vqs -d-axis and q-axis components of the stator voltage vector VsVdr, Vqr -d-axis and q-axis components of the rotor voltage vector Vrids, iqs -d-axis and q-axis components of the stator current vectors isidr, iqr -d-axis and q-axis components of the rotor current vectors irJ -moment of inertia of rotorJL -moment of inertia of loadT-generated torqueTL-load torqueRc-cable resistance

Machine Rating & Parameters7.5 kWY-connectedSquirrel CageRs=0.288 /phLs=0.0425 /phLr=0.0418 /phJL=0.4 kg-m2Rr=0.158 /phLm=0.0412J=0.4 kg-m2P=6 polesTL=20 N-mF=60 HzRc=0.2 16 March 20155

List of SubsystemsElectrical Sub-model: To implement the 3 phase to 2-axis transformation of stator voltage and current calculation.Torque Sub-model: To calculate developed electromagnetic torque.Mechanical Sub-model: To yield the rotor speed.Stator current output sub-model: To calculate the voltage drop across supply cable.Power supply sub-model: To provide 3-phase supply to the induction motor.16 March 20156

Simulation16 March 201571. Induction Motor Simulink Model

Electrical sub-model of the induction motor: The three-phase to two-axis voltage transformation is achieved using the following equation:

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In the two-axis stator reference frame, the current equation of an induction motor can be written as:

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2. Electrical Subsystem16 March 201510

3. Modelling of Matrix C using Fcn blocks16 March 201511

Torque Sub-model of Induction Motor: In the two-axis stator reference frame, the electromagnetic T is given by:

4. Torque Subsystem

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Mechanical Sub-model of Induction Motor: From the torque balance equations and neglecting viscous friction, the rotor speed w may be obtained as follows:

5. Mechanical Subsystem

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Stator Current Output Sub-model: The stator current output sub-model is used to calculate the stator current amplitude according to the following equation:

6. Stator Current Modelled using Fcn block

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The electrical sub-model in Fig. 1, the torque sub-model in Fig. 3, the mechanical sub-model in Fig. 4, and the stator current output sub-model are grouped together to form the induction motor model as shown below:

7. Interconnection of Subsystems

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Power Supply Sub-model: The voltage supply block consists of a three-phase sinusoidal voltage generator and a terminal-voltage calculation block which accounts for the voltage drop in the supply cable. The three-phase sinusoidal voltage generator is based on Equation and one of the three phase voltages is modelled as shown below:

Due to the voltage drop in the supply cable, the terminal voltage is given by Equation:

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8. Single phase voltage supply model16 March 201517

9. Cable drop Model16 March 201518

10. 3-phase voltage supply subsystem

Simulation Results

16 March 20151911. Torque v/s Speed Graph

12. Terminal Voltage & Stator Current16 March 201520

ConclusionHence, MATLAB is very powerful tool to model any electrical machine in detail.We can incorporate as many variables as they exist in physical induction motor and check its performance under different circumstances.16 March 201521

ReferencesMODELLING AND SIMULATION OF THE THREE-PHASE INDUCTION MOTOR USING SIMULINK - K. L. SHI, T . F. CHAN, Y. K. WONG and S. L . Head Of Department of Electrical Engineering, Hong Kong Polytechnic University, Hong KongKrause, P. C., Simulation of symmetrical induction machinery, IEEE Trans. Power Apparatus Systems, Vol. PAS-84, No. 11, pp. 10381053 (1965)16 March 201522

Thank you16 March 201523