Environmental Engineering Reference
In-Depth Information
I CA
I AB
I BC
I A
Figure 2.21
Phasor relationship between line and phase currents for a delta-
connected load
It follows from (2.16) that reactive power in a balanced three-phase system is
given by
p V L I L sin f
Q ¼
The quoted voltage for a three-phase system is the line value.
2.4.6 Some useful conventions
For the most part we will be considering power transmission systems under
balanced conditions. This embraces balanced three-phase faults as well as normal
operation. Three key simplifications are:
1.
The complex VA product.
2.
The equivalent single-phase approach.
3.
The per unit system.
2.4.7 The complex VA product
We now introduce complex power, defined as
S ¼ P þ j Q
where the real and reactive power, for a single-phase system, are given by
P ¼ VI cos f
Q ¼ VI sin f
It is important to note at this point that the sign of active power P is the same
whether current leads or lags voltage by an angle f , that is, cos( f ) ¼ cos( f ). This
reflects the nature of active power - it is a real quantity corresponding to a flow of
energy in a particular direction during each electrical cycle.
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