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Lecture 12
Per unit in 3
φ
systems
In 1
φ
systems we defined 2 base quantities for each 1
φ
device: V
B
, S
B
. For example, I =
1.1 pu implies that it is 10% above the rated current. In addition we have seen that the
transformers can be replaced by solid wires yielding the following relations,
1_
2_
p
up
u
p
u
VV
II
=
=
Hence the analysis is simpler without the transformers. The rationale behind the
definition of the base quantities was to maintain KCL, KVL, and Ohm’s laws invariant to
the new set of functions. Therefore if
VI
Z
=
in SI units and
p
u
pu
Z
=
.
In 3
φ
systems the same rationale is applied. Consider the 3
φ
power consumed by a 3
φ
balanced load. We have seen that
3
3c
o
s
PV
I
φ
=
.
Figure 1  3f load
Recall that,
0,
120,
120,
,
120,
120
ab
c
c
φφ
=∠
−
−
−−
−+
.
Note that V is the rms value of the phase to ground voltage. Be aware that in 3
φ
systems
voltages are rated phase to phase
3
=
.
Example. A 3
φ
motor is rated at 1000 V implies that V
φφ
= 1000V, therefore
1000/ 3
V
=
Volts.
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 Spring '09
 FRANCISCODGALIANA

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