Environmental Engineering Reference
In-Depth Information
For a carbon based, symmetrical ultra-capacitor system:
g
E
¼
3
0
:
00127
g
P
ð
10
:
31
Þ
The specific power density range used in (10.27) through (10.31) is 300-
500 W/kg except for the lead-acid battery, a valve regulated lead-acid (VRLA)
design for which the data sets are restricted to 20-80 W/kg discharge rates. Ultra-
capacitors modelled by (10.31), on the other hand, have specific power density
values ranging to over 10 kW/kg with newer units now approaching specific energy
values of 6 Wh/kg and specific power densities of 12-15 kW/kg and higher. Dual
mode hybrid (i.e. hybrids having electric-only range) and battery electric vehicles
have characteristically different energy versus power relationships. Advanced
batteries for dual mode operation have the following Ragone relationships:
Lithium ion dual mode battery has the following specific energy versus spe-
cific power (refer (10.28)):
g
E
¼
125
0
:
48
g
P
Similarly, the NiMH dual mode battery is characterized as follows (refer
(10.29)):
g
E
¼
63
0
:
145
g
P
In dual mode application, the ESS battery is designed for higher specific
energy at the expense of power. Consequently, the sensitivity of specific energy to
specific power is dramatically higher. Furthermore, cell design is often tailored to
specific applications with prismatic designs having higher efficiency than cylind-
rical designs. For example, an NiMH cell at 80% SOC and discharged at a
C
/5 rate
will exhibit the following typical efficiencies: cylindrical
¼
82%, prismatic
¼
94%.
In these expressions relating data curve fits within regions of the Ragone plot,
the ranking from top to bottom has been intentionally done in terms of highest to
lowest specific energy density. It is apparent that electrochemical cells are from one
to two orders of magnitude more capable than ultra-capacitor cells, which in turn
are superior to parallel plate capacitors. Today, the utility of Ragone charts is still
appropriate to contrast different energy storage technologies as demonstrated
in Figure 10.23, where the Ragone line is shown intentionally as a band to reflect an
E
(
P
)
¼
E
sto
t
P
ln{
U
i
/
U
f
} characteristic as the storage system capacity changes
from top of charge (
U
i
) to some lower value represented here by
U
f
.
By taking the ratio of
E
/
P
in these log-log Ragone charts, a new set of para-
meters can be inserted that reflect time duration of energy exchange. For example,
an energy storage unit that stores 1 kWh of energy and then discharges this at a rate
of 100 kW will be capable of sustaining this power level for
E
/
P
¼
1 kWh/100 kW
¼
36 s. Consider the Ragone chart in Figure 10.24 that is complete with a set of char-
acteristic time diagonal lines (lower left to upper right slant). Notice here that the
case in point has a
P
/
E
¼
100, which represents a very high power lithium ion cell. In
the Ragone chart below, compiled using manufacturer data (the star points are
