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986 ⏐⏐⏐ POLYPHASE SYSTEMS
C
I fg
+
I fg
–
Ef A
N
+
E f
–
–
I fg
Ef +
B
E L
E L
E L
I L
I L
I L
For a balanced load,
c
V f
+
I fL
FIG. 22.14
Y-connected generator with a D-connected load.
–
Z 3
Z 1 � Z 2 � Z 3
(22.9)
The voltage across each phase of the load is equal to the line voltage
of the generator for a balanced or an unbalanced load:
V f � E L
(22.10)
The relationship between the line currents and phase currents of a
balanced D load can be found using an approach very similar to that
used in Section 22.3 to find the relationship between the line voltages
and phase voltages of a Y-connected generator. For this case,
however, Kirchhoff’s current law is employed instead of Kirchhoff’s
voltage law.
The results obtained are
I L � �3�I f
(22.11)
and the phase angle between a line current and the nearest phase current
is 30°. A more detailed discussion of this relationship between the
line and phase currents of a D-connected system can be found in Section
22.7.
For a balanced load, the line currents will be equal in magnitude, as
will the phase currents.
EXAMPLE 22.2 For the three-phase system of Fig. 22.15:
a. Find the phase angles v2 and v3. b. Find the current in each phase of the load.
c. Find the magnitude of the line currents.
Solutions:
a. For an ABC sequence,
v2 � �120° and v3 � �120°
–
I fL
Z 2
V f
a
+
+
Z 1
I fL
V f
–
b