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.
Search WWH ::




Custom Search