This document presents the modeling equations for induction machines. It introduces three reference frames for modeling: arbitrary, stationary, and synchronously rotating. It then derives the voltage, flux linkage, and torque equations in the d-q rotating reference frame. The voltage equations transform stator voltages to the d-q frame. Flux linkage equations relate the stator and rotor fluxes. Torque equations express torque as a function of flux linkage and current. In conclusion, the arbitrary reference frame allows the easiest mathematical modeling of induction machines while permitting saturation effects to be simulated.

1. INDUCTION MACHINE
MODELLING
EQUATIONS
PREPARED BY :
UPADHYAY RAKSHITA R.
Er No : 140370707018
Roll No : 24

2. Contents..
 Introduction
 Voltage equations
 Flux linkage equations
 Torque equations
 Conclusion
 References
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3. Introduction
 Types of reference frames :
1) Arbitrary reference frame : rotating at speed of w in the
direction of rotor.
2) Stationary reference frame theory : w=0
3) Synchronously rotating reference frame : w= we
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4. Voltage equations
1) Convert the Vabc to Vqdo
Where ,
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5. 2 ) Voltage equations in qd0 frame:
from transformation we can write,
And finally we can write
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6. Flux linkage equations
1) Flux linkage equations in qdo frame
qdo stator flux equation
qdo rotor flux equation
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By combining both stator and rotor flux linkage we get
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8. Torque equations
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1) Instantaneous input power of all 6 winding
In terms of qdo quantities:
Putting value of voltages we get

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Using flux linkage relationship we can write
Finally torque equations can be written as

10. Conclusion
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 The arbitrary reference frame is the easiest way to
express induction machine mathematically and also
permits effect of saturation to be readily simulated.

11. References
 Dynamic Simulation of Electric Machinery using
MATLAB by ONG, Chee-Mun - Prentice Hall PTR
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