Environmental Engineering Reference
In-Depth Information
In Figure 10.31 it is interesting to note that the ultra-capacitor alone is unable
to meet the peak power target. The battery alone is marginally capable of supplying
the peak power when it has the total system mass available. In combination the pair
meets the power target for ultra-capacitor mass of 50 kg or less. This represents the
energy limited solution since in combination the battery plus ultra-capacitor meet
the system peak power target, but most likely would not meet the energy require-
ment to sustain this peak power for
t
m
seconds. The available energy of the direct
parallel combination is now considered to determine whether this combination of
storage component masses is optimal. Equation (10.43) restates the system energy
for the direct parallel combination:
P
pk
t
m
3,600
E
stor
¼
E
c
-
avail
þ
E
b
¼ h
c
ð
1
s
2
Þg
E
c
m
c
þ g
E
b
m
b
¼
ð
10
:
43
Þ
The energy values given in (10.43) are translated to equivalent specific power
values to be consistent with the example construction in progress using the Ragone
plot empirical relations for NiMH battery and ultra-capacitor given by (10.29) and
(10.31), respectively. Solving (10.40) and (10.43) by eliminating
m
c
and after some
rearranging of coefficients, the battery mass in terms of storage system parameters
is given as
m
b
¼
ð
P
pk
t
m
g
P
c
=
3,600
Þ
P
pk
g
E
c
h
c
ð
ð
kg
Þ
ð
10
:
44
Þ
g
E
b
g
P
c
g
E
c
g
P
b
Þ
When the Ragone characteristic parameters are substituted into (10.44), the
battery mass computes to 1.472 kg. The Ragone plot characteristic parameters used
for the NiMH battery and ultra-capacitor are
k
1
c
¼
3
k
2
c
¼
0
:
00127
k
1
b
¼
50
k
2
b
¼
0
:
035
ð
10
:
45
Þ
Making the substitution for battery specific energy,
g
E
b
, and ultra-capacitor
specific energy,
g
E
c
, (10.45) becomes
ð
P
pk
t
m
g
P
c
=
3,600
Þð
k
1
c
k
2
c
g
P
c
Þ
P
pk
h
c
½ð
m
b
¼
ð
kg
Þ
ð
10
:
46
Þ
k
1
b
k
2
b
g
bc
Þ
g
P
c
ð
k
1
c
k
2
c
g
cb
Þ
g
P
b
Figure 10.32 is the result of balancing energy available with energy required of
the system. In this plot the energy required to meet the discharge pulse duration is
given as the trace with circles; the capacitor energy (solid unmarked trace) clearly
rises linearly as the fraction of ultra-capacitor mass increases, whereas the battery
energy decreases since the battery is oversized to a high mass target initially. The
