86
Electrochemical Supercapacitors for Energy Storage and Delivery
(2
avera
E
( )
P
M
m
=
.76)
ge
t
Limitations in cell performance will manifest as a reduction in discharge
time (lower energy output) and reduced effective V
o
sc (due to IR drop) as
power levels are increased. It is possible for a cell to produce higher power
for a short burst at the cost of irreversible cell damage and increased ESR.
Using multiple tests, devices are monitored for sustainable average output power and average energy density to determine a stable peak power
rating and identify failure modes. In practice, the constant power method
is underutilized because it requires a capacitor test system that can output
a high level of amperage (high power materials) and the response rate of
the current must be fast enough to maintain constant power as the voltage
quickly drops (low capacitance prototypes).
2.6.3 Ragone Plot: Relationship of Energy Density and Power Density
In applications, the specific energy density and power density are the
most important factors determining the performance of electrochemical
supercapacitors. The higher the densities, the better a device should perform. Unfortunately, for all electrochemical devices including batteries,
fuel cells, and supercapacitors, higher energy densities do not necessarily
mean high power densities. The relationship of energy and power densities is illustrated using a Ragone plot [55] on which the specific power
density is plotted against the specific energy density. These plots are often
used to evaluate and compare the performances of electrochemical energy
storage devices.
Figure 2.20 shows Ragone plots for various electrochemical energy storage
and conversion devices including batteries, fuel cells, and supercapacitors.
The figure demonstrates that supercapacitors have higher power densities
and lower energy densities than other types of devices. Therefore, overcoming the challenge of low energy density is currently the major focus in supercapacitor research and development.
To obtain the relationship shown in the Ragone plot, assuming the external
load of a supercapacitor cell is R L , the entire system is shown schematically
in Figure 2.21. It is assumed that the leakage current does not exist (r → ∞) in
mathematical treatment.
In Figure 2.21, due to the presence of an ESR, the specific energy density
(E L ) available for the load can be expressed as:
1
(
o
)
2
R L
( )
R
E = C s p V
= E
L
L
s c
m
(2.77)
2
R + R
max
L
esr
R L + R esr
Electrochemical Supercapacitors for Energy Storage and Delivery
(2
avera
E
( )
P
M
m
=
.76)
ge
t
Limitations in cell performance will manifest as a reduction in discharge
time (lower energy output) and reduced effective V
o
sc (due to IR drop) as
power levels are increased. It is possible for a cell to produce higher power
for a short burst at the cost of irreversible cell damage and increased ESR.
Using multiple tests, devices are monitored for sustainable average output power and average energy density to determine a stable peak power
rating and identify failure modes. In practice, the constant power method
is underutilized because it requires a capacitor test system that can output
a high level of amperage (high power materials) and the response rate of
the current must be fast enough to maintain constant power as the voltage
quickly drops (low capacitance prototypes).
2.6.3 Ragone Plot: Relationship of Energy Density and Power Density
In applications, the specific energy density and power density are the
most important factors determining the performance of electrochemical
supercapacitors. The higher the densities, the better a device should perform. Unfortunately, for all electrochemical devices including batteries,
fuel cells, and supercapacitors, higher energy densities do not necessarily
mean high power densities. The relationship of energy and power densities is illustrated using a Ragone plot [55] on which the specific power
density is plotted against the specific energy density. These plots are often
used to evaluate and compare the performances of electrochemical energy
storage devices.
Figure 2.20 shows Ragone plots for various electrochemical energy storage
and conversion devices including batteries, fuel cells, and supercapacitors.
The figure demonstrates that supercapacitors have higher power densities
and lower energy densities than other types of devices. Therefore, overcoming the challenge of low energy density is currently the major focus in supercapacitor research and development.
To obtain the relationship shown in the Ragone plot, assuming the external
load of a supercapacitor cell is R L , the entire system is shown schematically
in Figure 2.21. It is assumed that the leakage current does not exist (r → ∞) in
mathematical treatment.
In Figure 2.21, due to the presence of an ESR, the specific energy density
(E L ) available for the load can be expressed as:
1
(
o
)
2
R L
( )
R
E = C s p V
= E
L
L
s c
m
(2.77)
2
R + R
max
L
esr
R L + R esr