13.1 ELEMENTARY CONCEPTS OF ROTATING MACHINES 555satisfyingωs=ωm±ωr, which relates electrical and mechanical angular speeds, exist, giving
rise to the names by which the machines are generally known, synchronous, induction, or dc
machines.
Elementary Synchronous Machines
The polyphase synchronous machine operates with direct current supplied to the field winding
(assumed to be on the rotor, which is usually the case) through two slip rings and with polyphase
alternating current supplied to the armature (assumed to be on the stator). The rotor mmf, which is
obtained from a dc source, is stationary with respect to the rotor structure. When carrying balanced
polyphase currents, as shown in Section 12.3, the armature winding produces a magnetic field in
the air gap rotating at synchronous speed [Equation (12.2.9) or (12.2.10)], as determined by the
system frequency and the number of poles in the machine. But the field produced by the dc rotor
winding revolves with the rotor. To produce a steady unidirectional torque, the rotating fields of
stator and rotor must be traveling at the same speed. Therefore, the rotor must turn precisely at
thesynchronous speed.Such conditions satisfy the second possibility for the development of a
constant torque suggested in the discussion following Equation (12.4.32). The resulting physical
system is shown in Figure 13.1.2.
Thepolyphase synchronous machineis one in which the rotor rotates in synchronism with
and in the same direction as the rotating mmf wave produced by the stator. Thus for synchronous
machines with polyphase stator winding, the following equation relating mechanical and electrical
angular speeds is satisfied:
ωm=ωs=2 πf
P/ 2(13.1.1)or alternatively, the steady-state speed at which the machine operates is known as thesynchronous
speed, given by
RotorFs
FFrωsωm = ωsωsωsδrδAxis of stator fieldAxis of resultant fieldSSNNAxis of rotor fieldAir gapStatorFigure 13.1.2Simplified two-pole
synchronous machine with non-
salient poles.