Environmental Engineering Reference
2.4.8 Equivalent single-phase
Three-phase real and reactive power are given by
p V L I L cos f
p V L I L sin f
For balanced conditions it is convenient to define an equivalent single-phase
system with voltage and current as follows:
V ¼ V L
p I L
Equivalent single-phase power and reactive power are then given by
P ¼ VI cos f
Q ¼ VI sin f
It is always possible to retrieve the actual line current by dividing by
However, we are more likely to be interested in quantities such as (1) voltage
profile, (2) real and reactive power flow and (3) losses/efficiency.
These quantities may be obtained directly from the equivalent single-phase
2.4.9 The per unit system
The per unit system has been devised to remove two difficulties:
The large numbers that would occur in power systems work if we restrict
ourselves to volts, amperes and ohms.
The analysis of networks with several voltage levels.
For example, it is more meaningful to say that a 275 kV system node voltage is
1.05 per unit (pu) than 289 kV line-to-line. The per unit number tells us immediately
that the voltage is 5 per cent above nominal - often that is all we need to know.
Per unit quantities may be expressed as 1.05 pu, or just 1.05 if it is obvious that
it is a per unit quantity.
The basis of the per unit system is that we choose voltage, current and impe-
dance bases such that
V b ¼ Z b I b
We can see immediately that only two of these bases can be chosen independently.
The per unit quantities are then
V pu ¼ V = V b
I pu ¼ I = I b
Z pu ¼ Z = Z b