Description of the characteristics of Scherbius drive

1. Main InductionMotor Characteristics ;
jXth jX2
Rth
i2
+
R2/s
Vth
-
jXm
Vth V 1 , Zth ( R1 jX 1) / / jXm …….. (1)
R1 j ( X 1 Xm)
Vth
I2 …….. (2)
R2
( Rth ) j ( Xth X 2)
s
Vth 2
I 22 …….. (3)
R2 2
( Rth ) ( Xth X 2) 2
s
3Vth 2 R2 1
…….. (4)
R2 2
( Rth ) ( Xth X 2) 2 s 2 fs
s
Note :Torque – slip curve is depending on 3 of thevariables; Stator Voltage, Stator frequencyand
Rotor Resistance.
Toget an idea aboutthetorquecurvewemayfindthe slip valueforwhichtorque is maximum.
Actuallytofindmaximumtorque, thetorqueequation can be derivedwithrespectto slip(s)
andthederivation is equatedtozeroandcorresponding slip valuewill be themaximumtorque slip.
However, it is toocomplicated. Anotherwaytofindthemaximum slip is Rule of Maximum Power

2. Transfer, maximumtorque is satisfiedwhenthemaximumpower is transferedto R2/s resistance.
Togetmaximumpowerto R2/s ;
R2
abs( Rth j ( Xth X 2)) …….. (5)
s
Withthisequation;
R2
st max …….. (6)
Rth 2 ( Xth X 2) 2
3Vth 2
max …….. (7)
2 s ( Rth Rth 2 ( Xth X 2) 2 )
Note :Theequations 6 and 7 showsthatmaximumtorque is not depending on rotor resistanceandthe
slip value at torquemaximumincreaseswithincreasing rotor resistance. Thusthetorque –
speedcurveswhen an externalresistanceaddedtothe rotor terminalsare as below.

3. Characteristics of Scherbius Machine;
Scherbius Machine is actually a polyphasecommutatormachinewith 3 phase stator
excitingwindingsand a commutator set in armature.The rotor is woundedsinglephase but
designedtogive 3 phasevoltage;therefore, threesets ofcommutatorcarbonbrushesplaced 120 degrees
apart electricallytofor 3 phaseoperation.
The stator excitorwinding is energizedwiththe rotor current of the main inductionmachine.
Theexcitorinducedemfmagnitude can be calculatedwiththefollowingwellknownformula;
e 4.44 * * Ns * f …….. (8)
Note :Theactualsignal is a sine wavewithfrequency f, thisformulagivesthemagnitude.
Similarlyinducedemf in rotor commutatorswill be
p
E 4.44 * * Nr * n * …….. (9)
2
where
Ns is effectivenumber of turns in stator windings
Nr is effectivenumber of turns in rotor windings
isfluxperpole
f is thefrequency of stator excitingvoltage
Note : Pleaseseethetopologyfor rotor and stator connections. Rotor and stator
terminalsareconnectedeachothervia an autotransformerwithchangingturnsratio say Kt.
Thus;
E
KT
e
Nr n p
KT …….. (10)
Ns f 2
Nr n p
f
Ns KT 2
Pleasenoticethatthefrequency is totallydepending on Kt , sincepolenumberandnumber of
turnsvaluesareconstant. Moreover, since theScherbiusmachine rotor is coupledwith an
auxiliaryinductionmachinethe n valuewill be nearlyconstant ( onlyverysmall slip changes). Thus,
thefrequency is determinedbythetransformer tap postion.

4. Note :IftheScherbius Machine was a slip ring machine, the rotor frequencywill be f –fr.However,
commutatorschangesthereferenceframetosynchronouslyrotatingreferenceframewithspeedfr,
whichwill in turngivestheoutputfrequency f (same as theonefor stator side).
Note :Therecoveredenergyfrom main motor is convertedtomechanicaltorque at the rotor of
Scherbius Machine, whichreturnstheenergytothemainswiththehelp of auxinductionmachine.
Note :Thetopologyprovides a closedloopcontrol of rotor currentsuchthattherequiredspeed is
alwaysconstantwithadjustedautotransformer tap position.
REFERENCE :Adkins B.,Gibbs W. J. PolyphaseCommutatorMachines. 1951