Civil Engineering Reference
In-Depth Information
In order to minimize losses in an existing line, the current flowing along it must
be kept as low as possible while ensuring that the active power
P
required by the
loads can still flow.
A constant amount of power
P
at constant voltage can be carried by keeping the
product
I
φ
φ
cos
constant. The higher the power factor cos
, the lower the current
will be and in consequence line losses.
In electric circuits, this means that electric active power is transferred with the
reactive power intrinsically needed by the majority of electric loads such as motors
and transformers. If the reactive power is fed in nodes along the network, generally
by means of capacitors, the excess of current, which flows downstream the node
itself because of the reactive power demand, will be reduced upstream.
Electric utilities usually charge for a part of the reactive energy consumed. This
reactive energy
E
Q
must be paid for, since the utility has to provide plants of
sufficient size to generate and transmit both the active and reactive power required
by end users and the active power corresponding to line losses.
If
E
Q
¼
0.5
E
p
then cos
φ¼
0.9.
This value, cos
0.9, represents a situation that is generally accepted
by the utility companies in the delivering node. At lower cos
φ
¼
values,
φ
corresponding to
E
p
, a charge must be paid for each kvarh
exceeding 0.5 kWh; at higher cos
E
Q
>
0.5
values, corresponding to
φ
E
q
<
0.5
E
p
there are no charges.
values exceeding unity, which may occur when
capacitors remain in operation even with low load rates, because of overvoltages
along the lines upstream. Consequently, every site must install control equipment or
manual procedures in order to avoid this problem. The same procedures must be
used to protect internal distribution lines, if capacitors are installed at the end-user
nodes.
The capacitor power (kvar) needed to raise cos
Utilities do not accept cos
φ
to a set value can be calculated
with reference to the mean reactive and active power over a set period (
Q
φ
¼
E
Q
/
operating hours,
P
E
P
/operating hours) as follows (see also Fig.
7.3
):
- Reference situation:
¼
cos atan
Q
0
Q
0
,
P
0
, and cos
φ
0
¼
P
0
.
- Final situation (cos
φ
1
>
cos
φ
0
)
cos atan
Q
1
Q
1
,
P
0
, and cos
φ
1
¼
P
0
.
Δ
Q
¼
Q
0
Q
1
¼
power of capacitors to be installed.
- If the final situation must be cos
φ
1
¼
0.9
atan
Q
1
cos
φ
1
¼
0.9 corresponds to
φ
1
¼
P
0
¼
atan 0.5.
