Environmental Engineering Reference
In-Depth Information
According to (4.21) we calculate that
N
bc
= 400 cells in series per string. From
this and using (4.18) and (4.19) we can state that the battery module will have
maximum and minimum voltage levels of
U
b
min
¼
N
bc
U
c
min
¼
440 V
ð
4
:
22
Þ
U
b
mx
¼
N
bc
U
c
mx
¼
580 V
ð
4
:
23
Þ
For a direct parallel combination of battery and ultra-capacitor, there is no
isolation between the system bus and the ultra-capacitor so that it must function
within the stated voltage swing limits. In this case, as given by (4.20), only 71%
droop is permitted. In a lead-acid system, for example, this droop from maximum
(2.56 V/cell) to minimum (1.75 V/cell) or a ratio of 0.68. This low percentage of
voltage droop will not extract the maximum energy from the capacitor bank.
Typically an ultra-capacitor bank can deliver 75% of its energy for a voltage droop
of 50%. This fact can be verified by substituting the values given in (4.20) and
(4.23) into (4.24):
1
2
C
uc
ð
1
s
u
Þ
U
b
mx
ð
J
Þ
E
uc
¼
ð
4
:
24
Þ
In practical systems the working voltage swing factor,
s
u
, is dictated by the
storage system technology, and the maximum bus voltage,
U
b
mx
, is set by the power
electronics device technology. From (4.24), it can be seen that stored energy in the
ultra-capacitor is maximized when the swing voltage factor is minimal (i.e. 0) and
the bus voltage is as high as possible. When the capacitor energy is determined from
the drive scenario, we will use (4.24) to calculate the required capacitance. Our ultra-
capacitor cells in the resultant string must adhere to the following constraints, just as
the battery cells have limitations on charge and discharge potential extremes. For the
ultra-capacitor, (4.18) and (4.19) become
U
uc
c min
0
ð
V
Þ
ð
4
:
25
Þ
U
uc
cmx
2
:
7
ð
V
Þ
ð
4
:
26
Þ
There is not a nominal open circuit voltage for the ultra-capacitors, so we
define the necessary number of cells per string using the maximum working vol-
tage. Note that there is some tolerance in the maximum working voltage for an
ultra-capacitor cell stated in (4.26). Ultra-capacitors can be operated with
>
3.0 V/
cell for short periods of time. When the voltage across the cell exceeds 4 V, the cell
is strongly in overvoltage and likely to rupture from overpressure. The number of
ultra-capacitor cells in series for the hybrid bus example becomes
U
b
mx
U
uc
cmx
N
uc
¼
ð
4
:
27
Þ