Environmental Engineering Reference
In-Depth Information
Fig. 5.10 Lead-acid cell
voltage discharge for a con-
stant current discharge as a
function of time
2,2
2,0
Voltage
drop
1,8
1,6
0
2
4
6
8
10
Discharge time [h]
Fig. 5.11 Discharging
equivalent circuit for a
battery
R
1
I
+
-
Electric
Load
V
BATT
E
o
The operative working condition of a battery can be represented by simple
equivalent circuits, which are only valid for charging or discharging operations
without considering the current transient phenomena. The discharging equivalent
circuit of a battery is shown in Fig.
5.11
.
In this case, the battery is represented by a fixed voltage E
o
connected in series
with a resistance R
1
. The voltage V
batt
at the terminals of the battery is different
from the open circuit voltage E
0
, because of the drop in voltage caused by the
internal resistance R
1
. Thus, if I is the current flowing out of the battery, as shown
in Fig.
5.11
, the terminal voltage of the battery is expressed by the following
equation:
V
batt
¼
E
o
R
1
I
:
ð
5
:
1
Þ
If I = 0, obviously the terminal voltage equals the open circuit voltage:
V
batt
¼
E
0
:
ð
5
:
2
Þ
The internal resistance R
1
for electric vehicle batteries should be evidently as
low as possible. The charging equivalent circuit of a battery is shown in Fig.
5.12
.
The difference with the discharging equivalent circuit is the resistance R
2
and
the switch S. The resistance R
2
takes in account the charging losses, which start to
