Environmental Engineering Reference
In-Depth Information
j100 Ω
j0.50 Ω
A
10 Ω
B
132:11 kV
Figure 2.22
Simple multi-voltage network
the low voltage value. Hence the impedance values must be increased by a factor of
n 2 to ensure that the power dissipations are as before. The total effective impedance
between A and B is thus
j100 þ n 2
ð 10 þ j0 : 50 Þ¼ð 1440 þ j172 Þ W= phase
This effective impedance may be expressed in per unit. Taking an MVA base
of 100 and a kilovolt base of 132, this gives
MVA b
kV b ¼ð 8 : 264 þ j0 : 987 Þ pu
If we now change the voltage base in proportion to the turns ratio of any
transformer encountered, the voltage bases will be 132 and 11 kV. The MVA base
will remain the same throughout the network, giving a per unit impedance of
Z AB ¼ð 1440 þ j172 Þ
100
132 2 þð 10 þ j0 : 50 Þ
100
11 2 ¼ð 8 : 264 þ j0 : 987 Þ pu
Z AB ¼ j100
as required.
Use of the second method, based on modification of the base voltage with
transformer turns ratios, is of little benefit in this simple case. However, it is much
more convenient than the first method - referring all impedances to a single voltage
level - for more realistic power network studies.
2.4.9.2 Conversion to a common MVA base
A common MVA base is required when using the per unit system. Plant impe-
dances Z p are usually quoted in per unit (or per cent) to the MVA rating of that
particular item, say MVA p . If the plant is to be included in a system study with a
common system base of MVA s , then the per unit impedance must be modified. It
may be seen from (2.18) that the per unit impedance is directly proportional to
MVA. Hence the per unit impedance for the plant will become
MVA s
MVA p
for use in the system study.
Z 0 p ¼ Z p
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