0195136047.pdf

4.1 THREE-PHASE SOURCE VOLTAGES AND PHASE SEQUENCE 199

rotor carries a field winding excited by the dc supply through brushes and slip rings. When the
rotor is driven at a constant speed, voltages of equal amplitude but different phase angle will be
generated in the three phases in accordance with Faraday’s law. Each of the three stator coils
constitutes one phase of this single generator. If the field structure is so designed that the flux is
distributed sinusoidally over the poles, the flux linking any phase will vary sinusoidally with time,
and sinusoidal voltages will be induced in the three phases. These three induced voltage waves
will be displaced by 120 electrical degrees in time because the stator phases are displaced by 120°
in space. When the rotor is driven counterclockwise, Figure 4.1.2(a) shows the wave forms and
Figure 4.1.2(b) depicts the corresponding phasors of the three voltages. The time origin and the
reference axis are chosen on the basis of analytical convenience. In a balanced system, all three
phase voltages are equal in magnitude but differ from each other in phase by 120°. The sequence
of voltages in Figure 4.1.2(b), corresponding to that of Figure 4.1.2(a), is known as thepositive
sequence(a–b–c). On the other hand, if the rotor is driven clockwise, then Figure 4.1.2(c) shows
the corresponding phasor of the three voltages; the sequence of voltages in Figure 4.1.2(c) is
known asnegative sequence(a–c–b). Notice that in positive sequenceE ̄bb′lagsE ̄aa′by 120°,
andE ̄cc′lagsE ̄bb′by 120°; in negative sequence, however,E ̄cc′lagsE ̄aa′by 120°, andE ̄bb′lags
E ̄cc′by 120°.
The stator phase windings may be connected in either wye (also known as star or symbolically
represented as Y) or delta (also known as mesh or symbolically represented as ), as shown
schematically in Figure 4.1.3. Almost all ac generators (otherwise known as alternators) have
their stator phase windings connected in wye. By connecting together either all three primed
terminals or all three unprimed terminals to form theneutralof the wye, a wye connection
results. If a neutral conductor is brought out, the system is known as afour-wire, three-phase
system; otherwise it is athree-wire, three-phase system. A delta connection is effected for the
armature of the generator by connecting terminalsa′tob, b′toc, andc′toa. The generator
terminalsA, B, C(and sometimesNfor a wye connection) are brought out as shown in Figure
4.1.3. In the delta-connection, no neutral exists, and hence only a three-wire, three-phase system
can be formed. Note that a phase is one of the three branch circuits making up a three-phase circuit.
In a wye connection, a phase consists of those circuit elements connected between one line and
neutral; in a delta circuit, a phase consists of those circuit elements connected between two lines.

A-Phase

Armature

or

stator

Armature

Coil sides

Field

winding

Field

systen

or rotor

Rotation

c′ b′

a′

b c

a

NS

Figure 4.1.1Elementary three-phase, two-

pole ac generator.