Main Induction Motor Characteristics ;

, …….. (1)

…….. (2)

…….. (3)

…….. (4)

Note : Torque – slip curve is depending on 3 of the variables; Stator Voltage, Stator frequency and Rotor Resistance.

To get an idea about the torque curve we may find the slip value for which torque is maximum. Actually to find maximum torque, the torque equation can be derived with respect to slip(s) and the derivation is equated to zero and corresponding slip value will be the maximum torque slip. However, it is too complicated. Another way to find the maximum slip is Rule of Maximum Power

Transfer, maximum torque is satisfied when the maximum power is transfered to R2/s resistance. To get maximum power to R2/s ;

…….. (5)

With this equation;

…….. (6)

…….. (7)

Note : The equations 6 and 7 shows that maximum torque is not depending on rotor resistance and the slip value at torque maximum increases with increasing rotor resistance. Thus the torque – speed curves when an external resistance added to the rotor terminals are as below.

Characteristics of Scherbius Machine;

Scherbius Machine is actually a polyphase commutator machine with 3 phase stator exciting windings and a commutator set in armature. The rotor is wounded single phase but designed to give 3 phase voltage ;therefore, three sets of commutator carbon brushes placed 120 degrees apart electrically to for 3 phase operation.

The stator excitor winding is energized with the rotor current of the main induction machine. The excitor induced emf magnitude can be calculated with the following well known formula;

…….. (8)

Note : The actual signal is a sine wave with frequency f, this formula gives the magnitude.

Similarly induced emf in rotor commutators will be

…….. (9)

where

Ns is effective number of turns in stator windings

Nr is effective number of turns in rotor windings

is flux per pole

f is the frequency of stator exciting voltage

Note : Please see the topology for rotor and stator connections. Rotor and stator terminals are connected each other via an autotransformer with changing turns ratio say Kt.

Thus;

…….. (10)

Please notice that the frequency is totally depending on Kt , since pole number and number of turns values are constant. Moreover, since the Scherbius machine rotor is coupled with an auxiliary induction machine the n value will be nearly constant ( only very small slip changes). Thus, the frequency is determined by the transformer tap postion.

Note : If the Scherbius Machine was a slip ring machine, the rotor frequency will be f –fr. However, commutators changes the reference frame to synchronously rotating reference frame with speed fr, which will in turn gives the output frequency f (same as the one for stator side).

Note : The recovered energy from main motor is converted to mechanical torque at the rotor of Scherbius Machine, which returns the energy to the mains with the help of aux induction machine.

Note : The topology provides a closed loop control of rotor current such that the required speed is always constant with adjusted autotransformer tap position.

REFERENCE : Adkins B., Gibbs W. J. Polyphase Commutator Machines. 1951