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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