Environmental Engineering Reference
In-Depth Information
fraction expansion of the short term model (similar to Figure 10.50) admittance
function as described in Reference 44. The ultra-capacitor cell model investigated
by researchers at MIT captured the phenomenological behaviour of the highly
distributed
RC
network that is an ultra-capacitor. The model consists of a three time
constant equivalent circuit shown in Figure 10.57.
I
cell
R
f
R
m
R
s
V
cell
R
leak
C
m
C
f
C
s
Figure 10.57 Ultra-capacitor short term model (courtesy MIT)
The short term equivalent circuit for an ultra-capacitor cell is found to have the
parameter values listed in Table 10.13 for a commercially available component.
Table 10.13 Ultra-capacitor short term model parameters*
Fast branch
Medium branch
Slow branch
Leakage
R
f
0.68 m
W
R
m
0.8
W
R
s
2.9
W
R
lk
3k
W
C
f
2,600 F
C
m
250 F
C
s
560 F
t
f
1.768 s
t
m
200 s
t
s
1,624 s
*To be used in making network equivalent models (courtesy MIT for 2,500 F,
0.68 m
W
EDLC)
Application of the short term cell model to an
N
-cell module results in a
complex circuit for simulation consisting of a string of the equivalent circuits
shown in Figure 10.58. In this configuration the time constants of the three
I
module
V
module
Cell 1 Cell 2 Cell 3 Cell
N
Figure 10.58
N
-cell module equivalent circuit using short term cell models
