Environmental Engineering Reference
In-Depth Information
In (10.73) the Cauer I resistive elements in the ladder network are the coeffi-
cients of
s
0
in the continued fraction expansion and the shunt branch elements are
coefficients of
s
1
as admittances (i.e. a capacitor).
10.7 Exercises
Q1:
For the EESU described in Example 1, and using the given information,
determine the percentage of maximum interface current at cell level when
the terminal voltage is reduced to
U
mx
/2 in the presence of a 150 kW power
pulse.
Given:
J
Al_fuse
¼
112.7 A/mm
2
;
N
c
¼
31.335
10
6
cells;
U
mx
¼
3.5 kV
and
J
Al_op_mx
¼
1.17% of
J
Al_fuse
.
A1:
J
Al_op
/
J
Al_fuse
¼
0.00171%
Q2:
Given an electrochemical capacitor with symmetric activated carbon elec-
trodes in organic electrolyte (AN), calculate the electrostatic pressure (in
pascal) at the electrode compact layer. The ultra-capacitor is fully charged to
U
mx
¼
2.7 V and has the electrode capacitance given in Example 2.
Given: Debye length from (10.24), activated carbon surface area from
(10.25) and using relative dielectric constant of AN of
e
r
¼
37.5.
(a) Find the electrostatic pressure at the compact layer.
Hint:
Apply the definition of electrostatic force between charges and take the ratio
of this force to the electrode area. Use
q
¼
C
elec
U
elec
q
2
4
pe
r
e
0
d
c
A
F
A
¼
P
¼
P
¼
1.862
10
10
GPa
(b) Think of how such enormous pressure can be stabilized at the com-
pact layer since no known material can tolerate such levels without collapse.
For example, some materials with very high Young's modulus,
E
y
, are
BaTiO3:
E
y
¼
67 GPa
Diamond:
E
y
¼
1
103 GPa
Single wall CNT:
E
y
¼
1.2
103 GPa
A2:
Q3:
The following three exercises refer to the case of using ultra-capacitors
as engine cold starting aides. In this case a 14 L compression ignition,
direct injected (CIDI) engine at room temperature is used. The system is
modelled using a starter motor having a torque constant,
k
t
¼
0.0085 Nm/A,
gear ratio pinion to ring, gr
¼
60:1 and a 6S
1P
3,000 F ultra-capacitor
module.
Given the following simulated voltage waveform of the ultra-capacitor
pack during the cranking event, determine the ultra-capacitor cell ESR.