0195136047.pdf

12.2 emf PRODUCED BY WINDINGS 517

and(a 2 ,−a 2 ), connected in series by their end connections. The span of each coil is one-half
wavelength of flux, or 180 electrical degrees for the full-pitch coil. Since the generated voltage
now goes through two complete cycles per revolution of the rotor, the frequency is then twice the
speed in revolutions per second, consistent with Equation (12.2.8).
The field winding may be concentrated around the salient poles, as shown in Figures 12.2.1(a)
and 12.2.2, or distributed in slots around the cylindrical rotor, as in Figure 12.2.1(b). By properly
shaping the pole faces in the former case, and by appropriately distributing the field winding in
the latter, an approximately sinusoidal field is produced in the air gap.
A salient-pole rotor construction is best suited mechanically for hydroelectric generators
because hydroelectric turbines operate at relatively low speeds, and a relatively large number
of poles is required in order to produce the desired frequency (60 Hz in the United States),
in accordance with Equation (12.2.9). Salient-pole construction is also employed for most
synchronous motors.
The nonsalient-pole (smooth or cylindrical) rotor construction is preferred for high-speed
turbine-driven alternators (known also as turbo alternators or turbine generators), which are
usually of two or four poles driven by steam turbines or gas turbines. The rotors for such machines
may be made either from a single steel forging or from several forgings shrunk together on the
shaft.
Going back to Equation (12.2.6), the maximum value of the induced voltage is
Emax=ωNφ= 2 πf N φ (12.2.11)

and the rms value is

Erms=

2 π

√

2

fNφ= 4. 44 fNφ (12.2.12)

which are identical in form to the corresponding emf equations for a transformer. The effect of
a time-varying flux in association with stationary transformer windings is the same as that of the
relative motion of a coil and a constant-amplitude spatial flux-density wave in a rotating machine.
The space distribution of flux density is transformed into a time variation of voltage because of the
time element introduced by mechanical rotation. The induced voltage is a single-phase voltage
for single-phase synchronous machines of the nature discussed so far. As pointed out earlier, to
avoid the pulsating torque, the designer could employ polyphase windings and polyphase sources
to develop constant power under balanced conditions of operation.

Magnetic flux path

+

+

+

+

S

S

a 1 N N

−a 1

a 2

−a 2

Figure 12.2.2Elementary single-

phase, four-pole synchronous machine.