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