Environmental Engineering Reference
In-Depth Information
Figure 10.60 Network equivalents of ultra-capacitor short term model
Table 10.14 Network equivalent circuit parameter values of ultra-capacitor
Fast
Medium
Slow
Foster II
Cauer I
Foster II
Cauer I
Foster II
Cauer I
ESR
0
0.68 m
W
ESR
0
0.68 m
W
R
m
0.8
W
R
d
1
0.6268
W
R
s
2.9
W
R
d
2
3.729
W
C
f
2,600 F
C
f
2,600 F
C
m
250 F
C
d
1
246.75 F
C
s
560 F
C
d
2
563 F
It is intriguing to find that the parameter values found by moving from a Foster II
network model to its Cauer I equivalent model are very similar. Although the Cauer I
model structure is more insightful of ultra-capacitor distributed resistance and
capacitance, the Foster II model appears to be more suitable for laboratory char-
acterization of behaviour. The model parameters in the Cauer I network repre-
sentation are found according to (10.73) written in terms of the Foster II model
parameters as derived from the MIT short term model:
C
f
s
3
þ½ða
m
þa
s
Þ
C
f
þ
1
=
R
m
þ
1
=
R
s
s
2
þða
m
a
s
C
f
þa
s
=
R
m
þa
m
=
R
s
Þ
s
Y
ð
s
Þ¼
s
2
þða
m
þa
s
Þ
s
þa
m
a
s
10
2
s
2,600
s
3
þ
16
:
197
s
2
þ
1
:
0502
Y
ð
s
Þ¼
þ
5
:
616
10
3
s
þ
3
:
08
10
6
s
2
1
Y
ð
s
Þ¼
2600
s
þ
1
0
:
6268
þ
1
246
:
75
s
þ
1
563
s
3
:
729
þ
ð
10
:
73
Þ
