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INDUCTION MOTORsteady-state model(squirrel cage)EL 371ELECTRIC MOTOR CONTROL
Construction abbccaStator 3-phase windingRotor squirrel cage / wound
Construction aaSingle N turn coil carrying current iSpans 180o elecPermeability of iron >> o all MMF drop appear in airgap
Construction Distributed winding coils are distributed in several slots
Nc for each slot
/2-/2-(3Nci)/2(Nci)/2
Construction Distributed winding (full-pitch)The resultant MMF is the total contribution of MMF from each coilConsidering only the space-fundamental component,
Phase a sinusoidal distributed winding Airgap mmfF()2
Sinusoidal winding for each phase produces space sinusoidal MMF and flux Sinusoidal current excitation (with frequency s) in a phase produces space sinusoidal standing wave MMF
Combination of 3 standing waves resulted in MMF wave rotating at:
p number of polesf supply frequency
Rotating flux induced:emf in stator winding (known as back emf)Emf in rotor winding Rotor flux rotating at synchronous frequency Rotor current interact with flux producing torque Rotor ALWAYS rotate at frequency less than synchronous, i.e. at slip speed: sl = s r
Ratio between slip speed and synchronous speed known as slip
Stator voltage equation:
Vs = Rs Is + j(2f)LlsIs + Eag
Eag airgap voltage or back emf
Eag = k f ag
Rotor voltage equation: Er = Rr Ir + js(2f)Llr
Er induced emf in rotor circuit Er /s = (Rr / s) Ir + j(2f)Llr
Perphase equivalent circuitRr/s+
Vs
RsLlsLlr+
Eag
IsIrImLmRs stator winding resistanceRr rotor winding resistanceLls stator leakage inductanceLlr rotor leakage inductanceLm mutual inductances slip
+
Er/s
We know Eg and Er related by
rotor voltage equation becomes
Eg = (Rr / s) Ir + j(2f)Llr Ir Where a is the winding turn ratioThe rotor parameters referred to stator are:
Perphase equivalent circuitRs stator winding resistanceRr rotor winding resistance referred to statorLls stator leakage inductanceLlr rotor leakage inductance referred to statorLm mutual inductanceIr rotor current referred to stator
Power and TorquePower is transferred from stator to rotor via airgap, known as airgap powerLost in rotor windingConverted to mechanical power = (1s)Pag
Power and TorqueMechanical power, Pm = Tem r
But, ss = s - rr = (1-s)s Pag = Tem sTherefore torque is given by:
Power and Torque1 0rsTratedPull out Torque(Tmax)Tem0 rated ssm
Steady state performanceThe steady state performance can be calculated from equivalent circuit, e.g. using Matlab
Steady state performancee.g. 3phase squirrel cage IMV = 460 V Rs= 0.25 Rr=0.2 Lr = Ls = 0.5/(2*pi*50) Lm=30/(2*pi*50)f = 50Hz p = 4
Steady state performance
Steady state performance
Steady state performance