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The PerUnit System
1
Introduction and Motivation
Power system quantities like power, voltage, current, and impedance are often given in
per unit
or
percent of speciFed base values. ±or instance, if a base voltage of 735 kV is speciFed then the voltage
765 kV is 765
/
735 = 1
.
04 per unit or 104%.
Advantages of the perunit system are many. ±irst, by specifying appropriate base quantities, the
transformer equivalent circuit can be simpliFed by eliminating the ideal transformer winding. As a
result, voltages, currents, external impedances and admittances expressed in perunit do not change
when referred either to the primary or the secondary winding. This is a signiFcant advantage when
analyzing power systems of even moderate size, where hundreds of transformers can be found. The
perunit system avoids us the possibility of making many serious calculation errors when referring
from one transformer side to the other. Another advantage of the perunit system is that the perunit
impedances of electrical equipment of similar type usually lie within a narrow numerical range when
the equipment ratings are used as base values. Thus, perunit impedance data can be checked rapidly
for gross errors by someone familiar with the perunit quantities. Moreover, manufacturers normally
specify the impedances of machines and transformers in perunit or percent of nameplate rating.
Perunit quantities are calculated as:
Perunit quantity =
Actual quantity
Base value of quantity
,
(1)
where the
actual quantity
is the value of the quantity in the actual (SI) units. The base value has the
same units as the actual quantity, therefore making the perunit quantity dimensionless. In addition,
the base value is always a real number. Thus, the angle of the perunit quantity is identical to the
angle of the actual quantity.
2
PerUnit System for SinglePhase Circuits
Two independent base values can be arbitrarily selected at one point of a power system. Usually
for singlephase systems the base voltage,
E
base
, and the base singlephase complex power,
S
base
, is
selected. Then, in order for electrical laws to be valid in the perunit system, the next relationships
must be used for other base values:
P
base
=
Q
base
=
S
base
,
(2)
I
base
=
S
base
E
base
,
(3)
Z
base
=
R
base
=
X
base
=
E
base
I
base
=
E
2
base
S
base
,
(4)
Y
base
=
G
base
=
B
base
=
1
Z
base
.
(5)
By convention, we adopt the following two rules for base quantities:
1. The value of
S
base
is the same for the entire power system being studied.
1
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This note was uploaded on 01/10/2011 for the course ECSE 486 taught by Professor Gezajoos during the Winter '10 term at McGill.
 Winter '10
 GezaJoos

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