Environmental Engineering Reference
In-Depth Information
The mass of ultra-capacitor rated to meet required pulse power level stated in
(10.36) is substituted into (10.38) by re-expanding the energy available term, and
the resultant expression is then solved for the ratio of power to energy. The result is
g
P
c
g
E
c
3,600
ð
1
s
2
Þð
P
pk
P
b
Þ
t
m
ð
P
pk
ð
1
=
2
Þ
P
b
Þ
ð
10
:
39
Þ
Equation (10.38) shows that ultra-capacitor (
P
/
E
) is dependent on both avail-
able battery power and working voltage swing. Figure 10.29 is a plot of (10.38) in
per unit quantities.
Ultra-capacitor (
P
/
E
) versus battery powe
r
140.976
200
PE(
i
)
100
3.130296 × 10
-14
0
0
0.5
1
0
1
i
Pb (pu)
Figure 10.29 Power to energy ratio of direct parallel connection versus battery
power
In Figure 10.29 the
P
/
E
ratio varies from 141 when battery power is zero to 92
when the battery provides one-half the specified peak power and zero when the
battery provides all the specified power,
P
pk
. Figure 10.30 is a plot of
P
/
E
for the
direct parallel combination versus voltage swing ratio with battery power as para-
meter. PE20 defines the case when
P
b
¼
20% of
P
pk
and so on.
400
320
PE20(
i
)
PE40(
i
)
PE60(
i
)
200
10
−14
4.567775
×
0
0
0
0.2
0.4
0.6
0.8
1
s
(
i
)
1
Voltage swing ratio
Figure 10.30 Direct parallel connection capacitor
P
/
E
versus voltage swing
