558 ROTATING MACHINES
Elementary Induction Machines
In the discussion that followed Equation (12.4.32), the third possible method of producing constant
torque was to cause the mmf axes of stator and rotor to rotate at such speeds relative to their
windings that they remain stationary with respect to each other. If the stator and rotor windings
are polyphase and carry polyphase alternating current, then both the stator mmf and the rotor
mmf axes may be caused to rotate relative to their windings. Such a machine will have polyphase
stator ac excitation atωs, polyphase rotor ac excitation atωr, and the rotor speedωmsatisfying
ωm=ωs−ωr (13.1.5)
Let us consider the rotor speed given by Equation (13.1.5) and the same phase sequence of
sources. A rotating magnetic field of constant amplitude, rotating atωsrad/s relative to the
stator, is produced because of polyphase stator excitation. A rotating magnetic field of constant
amplitude, rotating atωsrad/s relative to the rotor, is also produced because of polyphase rotor
excitation. The speed of rotation of the rotor magnetic field relative to the stator isωm+ωr,or
ωs, if the rotor is rotating with a positive speed of rotationωmin the direction of the rotating
fields. If so, the condition for energy conversion at constant torque is satisfied. Such a situation
is illustrated diagrammatically in Figure 13.1.5. Under these conditions the machine is operating
as a double-fed polyphase machine. Normally, in an induction machine with polyphase stator
and rotor windings, only a source to excite the stator is employed, and the rotor excitation at
the appropriate frequency is induced from the stator winding. The device is thus known as an
induction machine.
In an induction machine, the stator winding is essentially the same as in a synchronous
machine. Equation (12.2.13) and the considerations leading to it hold here as in the case of a
synchronous machine. When excited from a balanced polyphase source, the polyphase windings
produce a magnetic field in the air gap rotating at a synchronous speed determined by the number
of poles and the applied stator frequency given by Equation (12.2.9). On the rotor, the winding is
electrically closed on itself (i.e., short-circuited) and often has no external terminals.
The induction machine rotor may be one of two types: thewound rotoror thesquirrel-cage
rotor.The wound rotor has a polyphase winding similar to and wound for the same number of
poles as the stator winding. The terminals of the rotor winding (wye- or delta-connected, in the
case of three-phase machines) are brought to insulated slip rings mounted on the shaft. Carbon
brushes bearing on these slip rings make the rotor terminals available to the circuitry external toRotorFs Frωsωmωm + ωr = ωsδSSNNStatorFigure 13.1.5Mmf axes of an induction machine.