8.0
7.0
6.0
5.0
R L = R esr
4.0
Logarithmic Specific
Power Density, W/kg
3.0
2.0
1.0
0.0
R L = 0
1.2
1.3
1.4
1.5
1.6
1.7
Logarithmic Specific Energy Density, Wh/kg
88
Electrochemical Supercapacitors for Energy Storage and Delivery
⎛
⎞
1
E L = ( )
E m
⎜
P
1
⎟
+ 1 −
L
2
max ⎜
P
⎟
( )
(2.79)
⎝
m max ⎠
The plot of
⎛
⎞
1
P L ⎟
2
( )
E
⎜
m
1+ 1 −
max ⎜
P
⎝
( )
m max
⎟
⎠
versus P L creates the Ragone plot shown in Figure 2.21.
Figure 2.22 indicates that when increasing the load or reducing the load
resistance (R L ), the available specific energy will be reduced, leading to a
higher specific power density until the load resistance reaches the ESR (R L =
R esr ). Likewise, further increasing the load or further reducing (R L ) will lead
to a decrease in the power density. Therefore, there is a trade-off between
power density and energy density.
Note that both the specific power and energy densities shown in
Figure 2.22 should be considered the maximum available densities for a
double-layer supercapacitor, that is, they are the values at the moment the
supercapacitor starts to discharge (t = 0). After discharging starts, both their
magnitudes will gradually decrease. This situation is only for supercapacitors whose discharge voltages are monotonically decreased by increasing
the discharging time. When the Ragone plot is used for supercapacitors, it is
necessary to indicate the plot for its maximum energy and power densities.
FIGURE 2.22
Calculated Ragone plot according to Equation (2.75) using V 0 = 2.5 V, C sp = 45 F.g –1 , and R esr =
sc
0.05 Ω.cm 2 . The magnitude of R l is set to change from 1.0 × 10 –6 to 0.91 Ω.cm 2 .
7.0
6.0
5.0
R L = R esr
4.0
Logarithmic Specific
Power Density, W/kg
3.0
2.0
1.0
0.0
R L = 0
1.2
1.3
1.4
1.5
1.6
1.7
Logarithmic Specific Energy Density, Wh/kg
88
Electrochemical Supercapacitors for Energy Storage and Delivery
⎛
⎞
1
E L = ( )
E m
⎜
P
1
⎟
+ 1 −
L
2
max ⎜
P
⎟
( )
(2.79)
⎝
m max ⎠
The plot of
⎛
⎞
1
P L ⎟
2
( )
E
⎜
m
1+ 1 −
max ⎜
P
⎝
( )
m max
⎟
⎠
versus P L creates the Ragone plot shown in Figure 2.21.
Figure 2.22 indicates that when increasing the load or reducing the load
resistance (R L ), the available specific energy will be reduced, leading to a
higher specific power density until the load resistance reaches the ESR (R L =
R esr ). Likewise, further increasing the load or further reducing (R L ) will lead
to a decrease in the power density. Therefore, there is a trade-off between
power density and energy density.
Note that both the specific power and energy densities shown in
Figure 2.22 should be considered the maximum available densities for a
double-layer supercapacitor, that is, they are the values at the moment the
supercapacitor starts to discharge (t = 0). After discharging starts, both their
magnitudes will gradually decrease. This situation is only for supercapacitors whose discharge voltages are monotonically decreased by increasing
the discharging time. When the Ragone plot is used for supercapacitors, it is
necessary to indicate the plot for its maximum energy and power densities.
FIGURE 2.22
Calculated Ragone plot according to Equation (2.75) using V 0 = 2.5 V, C sp = 45 F.g –1 , and R esr =
sc
0.05 Ω.cm 2 . The magnitude of R l is set to change from 1.0 × 10 –6 to 0.91 Ω.cm 2 .