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982 ⏐⏐⏐ POLYPHASE SYSTEMS
C
B
E CN
E BN
N
Fixed point P
E AN
Rotation
FIG. 22.9
Determining the phase sequence from the
phase voltages of a three-phase generator.
C
B
E CA
E BC
P
E AB
Rotation
FIG. 22.10
Determining the phase sequence from the line
voltages of a three-phase generator.
A
A
ECA
(a)
E BN
30°
E CN
120°
30°
120°
120°
E BC
30°
E AN
FIG. 22.8
(a) Phasor diagram of the line and phase voltages of a three-phase generator;
(b) demonstrating that the vector sum of the line voltages of a three-phase
system is zero.
22.4 PHASE SEQUENCE (Y-CONNECTED
GENERATOR)
The phase sequence can be determined by the order in which the phasors
representing the phase voltages pass through a fixed point on the
phasor diagram if the phasors are rotated in a counterclockwise direction.
For example, in Fig. 22.9 the phase sequence is ABC. However,
since the fixed point can be chosen anywhere on the phasor diagram,
the sequence can also be written as BCA or CAB. The phase sequence
is quite important in the three-phase distribution of power. In a threephase
motor, for example, if two phase voltages are interchanged, the
sequence will change, and the direction of rotation of the motor will be
reversed. Other effects will be described when we consider the loaded
three-phase system.
The phase sequence can also be described in terms of the line voltages.
Drawing the line voltages on a phasor diagram in Fig. 22.10, we
are able to determine the phase sequence by again rotating the phasors
in the counterclockwise direction. In this case, however, the sequence
can be determined by noting the order of the passing first or second
subscripts. In the system of Fig. 22.10, for example, the phase sequence
of the first subscripts passing point P is ABC, and the phase sequence
of the second subscripts is BCA. But we know that BCA is equivalent to
ABC, so the sequence is the same for each. Note that the phase
sequence is the same as that of the phase voltages described in Fig.
22.9.
If the sequence is given, the phasor diagram can be drawn by simply
picking a reference voltage, placing it on the reference axis, and
then drawing the other voltages at the proper angular position. For a
sequence of ACB, for example, we might choose E AB to be the reference
[Fig. 22.11(a)] if we wanted the phasor diagram of the line voltages,
or E NA for the phase voltages [Fig. 22.11(b)]. For the sequence
indicated, the phasor diagrams would be as in Fig. 22.11. In phasor
notation,
⎪
⎬
⎪
⎭
E AB
E BC
(b)
EAB � EAB �0° (reference)
Line
ECA � ECA ��120°
voltages
EBC � EBC ��120°
⎫
E CA
E AB