Electrical Power Systems

5.3 THE PER-UNIT (pu) SYSTEM
Power System Components and Per Unit System 99
Power system quantities such as current, voltage, impedance and power are often expressed in
per-unit values. or example, if base voltage if 220 KV is specified, then the voltage 210 KV is
210/220 = 0.954 pu. One major advantage of the per-unit is that by properly specifying base
quantities, the equivalent circuit of transformer can be simplified. When expressed in per-unit
values, the equivalent impedance of a transformer whether referred to primary or secondary,
is the same. Another advantage of the per-unit system is that the comparison of the characteristics
of the various electrical apparatus of different types and ratings is facilitated by expressing the
impedances in per-unit based on their ratings. When all the quantities are converted in per-unit
values, the different voltage levels disappear and power network involving synchronous
generators, transformers and lines reduces to a system of simple impedances.
Per-unit quantities are calculated as follows:
Let us define,
per-unit quantity =
S pu = S
S B
actual quantity
base value of quantity
, Vpu = V
, Ipu =
VB I
IB and Z pu = Z
Z B
...(5.2)
...(5.3)
where, S (apparent power), V(voltage), I(current) and Z(impedance) are phasor or complex
quantities and denominators (i.e., S B , V B , I B and Z B ) are always real numbers. To completely
define a per-unit system, minimum four base quantities are required.
Two independent base values can be arbitrarily selected at one point in a power system.
Usually, the three-phase base volt-ampere S B or (MVA) B and the line-to-line base voltage V B or
(kV) B are selected. The base value has the same units as the actual quantity and hence making
the per-unit quantity dimensionless. Then, in order for electrical laws to be valid in the per-unit
system, following relations must be used for other base values:
IB = (MVA) B
3 ( KV)
( )
and ZB = KV B
I
B
Now substituting for I B from eqn. (5.4), the base impedance becomes
2
( KV) B
ZB =
(MVA)
B
B
3
...(5.4)
...(5.5)
...(5.6)
Note that phase and line quantities expressed in per-unit values are the same, and the
circuit laws are valid, i.e.,
*
Spu = Vpu · Ipu Here S pu = per-unit complex power = P pu + j Q pu
V pu = per-unit voltage
*
Ipu = complex conjugate of per-unit current Ipu
...(5.7)