Page 107 - Electrical Equipment Handbook _ Troubleshooting and Maintenance

AC MACHINE FUNDAMENTALS

5.8 CHAPTER FIVE

e ind 2υBl sin
Since angle t,, the induced voltage can be rewritten as
e
e ind 2υBl sin t
e
Since the cross-sectional area A of the turn is 2rl and the velocity of the end conductors is
given by υ r , the equation can be rewritten as
m
e ind 2(r )Bl sin t
m
e
(2rl)B sin t
m e
AB sin t
m
e
The maximum flux passing through the coil is AB. For a two-pole stator
m e
, the induced voltage is
e ind sin t

This equation describes the voltage induced in a single-turn coil; if the coil (phase) has N
c
turns of wire in it, the total induced voltage will be
e ind N sin t
e

The Induced Voltage in a Three-Phase Set of Coils
Figure 5.7 illustrates three coils each of N turns placed around the rotor magnetic field. The
c
voltage induced in each has the same magnitude but differs in phase by 120°. The result-
ing voltages in the three phases are
e (t) N sin t V
aa' c
e (t) N sin ( t 120°) V
bb'
c
e (t) N sin ( t 240°) V
cc' c
Therefore, a set of three-phase currents generates a rotating uniform magnetic field within
the stator of the machine, and a uniform magnetic field induces a set of three-phase volt-
ages in such a stator.

The RMS Voltage in a Three-Phase Stator
The peak voltage in any phase is
E N
max c
Since 2 f, the rms voltage in any phase is
2
E N f
A
c
2

Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)
Copyright © 2004 The McGraw-Hill Companies. All rights reserved.
Any use is subject to the Terms of Use as given at the website.