Civil Engineering Reference
In-Depth Information
FIGURE 10-3
Equivalent electrical circuit of the battery showing internal voltage and resistance.
FIGURE 10-4
Battery source line intersecting with load line at the operating point.
line
in
Figure 10-4
,
and operating point is the intersection of the source line and
the load line (point P). The power delivered to the external load resistance
is I
The terminal voltage drops with increasing load as shown by the V
b
.
In fast discharge applications, such as for starting a heavily loaded motor,
the battery may be required to deliver the maximum possible power for a
short time. The peak power it can deliver can be derived using the maximum
power transfer theorem in electrical circuits. It states that the maximum
power can be transferred from the source to the load when the internal
impedance of the source equals the conjugate of the load impedance. The
battery can deliver maximum power to a DC load when R
R
2
L
= R
. This gives
L
i
the following:
2
E
R
P
=
i
(10-2)
max
4
i
Since E
and R
vary with the state of charge, the P
also vary accordingly.
i
i
max
The internal loss is I
R
. The efficiency at any state of charge is therefore:
2
i
