Civil Engineering Reference
In-Depth Information
FIGURE 14-4
Loss components varying with load in typical power equipment.
parts. The other component varies with the current squared, representing
the I
R loss in the conductors. For a constant voltage system, the conductor
loss varies with the load power squared. The total loss is, therefore, expressed
as (
Figure 14-4
)
the following:
2
2
Loss
=+⋅
L
k P
(14-3)
o
where P is the power delivered to the load (output), L
is the fixed loss and
k is the proportionality constant. The efficiency is given by the following:
o
output
input
output
output
P
PL kP
o
η=
=
=
++
(14-4)
2
+
loss
For the efficiency to be maximum at a given load, its derivative with respect
to the load power must be zero at that load. That is as follows:
(
)
(
)
−++
PkPPL
+
kP
2
12
d
dP
η
=
o
=
0
(14-5)
(
)
2
PL kP
++
2
o
. Therefore, the component efficiency is
maximum at the load under which the fixed loss is equal to the variable loss.
This is an important design rule, which can save significant electrical energy
in large power systems.
This equation reduces to
L
=
kP
2
o
