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I was working on speed control of induction motors through cascading. Theoretically, in differential cascading of two motors, the speed is given by $$\frac{120f}{P_1-P_2}$$

where \$P_1\$ and \$P_2\$ are number of poles.

What will happen practically when the number of poles of both motors is equal? Will the speed saturate and if yes, then why?

Precisely, if two same induction motors having the same rating and number of poles are cascaded differentially then \$P_1-P_2\$ becomes equal to zero theoretically, giving resultant speed as infinite.

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    \$\begingroup\$ Are you asking about a scheme in which the rotor of a wound-rotor induction motor is connected to supply power to the stator of another induction motor? If you provide a clear description of the scheme, preferably with a diagram, there is some possibility that someone may explain how it works. However there has not been much interest in such schemes for the past 60 to 80 years, so an answer may be difficult to find. \$\endgroup\$
    – user80875
    Apr 13, 2017 at 23:38

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In the case of differential cascaded connection speed control, the main motor and auxillary motor torques are differential (opposite to each other) so their rotating directions are opposite to each other. (Nm = -Na)

When the poles are equal the speeds are equal and opposite so the motor doesn't rotate.

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