Environmental Engineering Reference
In-Depth Information
power) divided by the capacitors rated discharge rate. This is expressed mathe-
matically in (10.48):
P
pk
g
P
b
m
b
h
c
g
P
c
m
c
¼
ð
kg
Þ
ð
10
:
48
Þ
Next, expressing the energy available from the ultra-capacitor as greater than
or equal to the required energy to meet the specification leaves
1
3,600
ð
P
pk
t
m
t
m
g
P
b
m
b
Þ
Wh
Þ
s
2
h
c
ð
1
Þ
g
E
c
m
c
ð
10
:
49
Þ
Then, substituting for ultra-capacitor mass,
m
c
, in (10.49) from (10.48) yields
an expression that can be used to find the relationship of specific power to specific
energy for the ultra-capacitor or its
P
/
E
limit. Making the necessary substitutions
and solving reduces (10.49) to
g
P
c
g
E
c
3,600
ð
1
s
2
Þ
(h
1
)
ð
10
:
50
Þ
t
m
Representative values for specific energy of an ultra-capacitor range from 2 to
6 Wh/kg and specific power values can be in the range of 1,000 W/kg to 2,500 W/kg.
For these representative values, (10.50) predicts that ultra-capacitor
P
/
E
for an
independent power processor architecture will be in the range of 167-500. These
are entirely reasonable values for an ultra-capacitor.
When an independent power processor is used to buffer the ultra-capacitor in
combination with a battery, the capacitor voltage swing can now be more extreme
leading to extraction of most of its energy. The resulting question is this: Can
the combined mass of the ultra-capacitor plus its power processor be less than the
battery mass saved so that a net mass and perhaps cost benefit accrues? The voltage
swing ratio,
s
, is set equal to 0.3 and all remaining parameters in (10.46) for battery
mass and (10.47) for ultra-capacitor mass are left unchanged. This means the target
pulse power remains at 40 kW given a pulse duration of 10 s. When these expressions
are solved, the following results are obtained:
m
b
¼
1
:
472
m
c
¼
49
:
05
m
I
¼
12
:
868
M
stor
¼
63
:
39
ð
kg
Þ
ð
10
:
51
Þ
Equation (10.51) introduces a new component, the power processor. Power
electronics for automotive applications today reveals that these units have a typical
specific power density,
g
PI
, of about 5 kW/kg with recent power MOSFET plus SiC
diode units reaching 12 and 25 kW/L using interleaved converter stages. The
