K
R esr
C
T
dl
R L
(V
o )
V L
sc
87
Fundamentals of Electrochemical Double-Layer Supercapacitors
10
7
Capacitors
10
–2
10
–1
10
0
10
1
10
2
10
3
Supercapacitors
Batteries
Fuel
cells
10 6
10
5
10
4
10
3
Specific Power (W/kg)
10
2
10
1
10
0
Specific Energy (Wh/kg)
FIGURE 2.20
Ragone plots for electrochemical energy storage and conversion devices including batteries,
fuel cells, and supercapacitors along with conversional capacitors. (Source: Winter, M. 2004.
Chemical Reviews, 104(10). With permission.)
The specific power density (P L ) available to the external load is:
2
2
o
o
V
2
V sc R L
V sc
L
4 4R R
P
L esr
L =
=
( ) = ( )
= P
4R R
L esr
(2.78)
mR L m R
( L + R
2
m max
2
esr
( )
) 4R m
esr
( R L + R esr )
( R L + R esr )
By combining Equations (2.77) and (2.78), the Ragone plot can be obtained.
FIGURE 2.21
Electrochemical supercapacitor cell with external load (R l ) and output voltage V l .
R esr
C
T
dl
R L
(V
o )
V L
sc
87
Fundamentals of Electrochemical Double-Layer Supercapacitors
10
7
Capacitors
10
–2
10
–1
10
0
10
1
10
2
10
3
Supercapacitors
Batteries
Fuel
cells
10 6
10
5
10
4
10
3
Specific Power (W/kg)
10
2
10
1
10
0
Specific Energy (Wh/kg)
FIGURE 2.20
Ragone plots for electrochemical energy storage and conversion devices including batteries,
fuel cells, and supercapacitors along with conversional capacitors. (Source: Winter, M. 2004.
Chemical Reviews, 104(10). With permission.)
The specific power density (P L ) available to the external load is:
2
2
o
o
V
2
V sc R L
V sc
L
4 4R R
P
L esr
L =
=
( ) = ( )
= P
4R R
L esr
(2.78)
mR L m R
( L + R
2
m max
2
esr
( )
) 4R m
esr
( R L + R esr )
( R L + R esr )
By combining Equations (2.77) and (2.78), the Ragone plot can be obtained.
FIGURE 2.21
Electrochemical supercapacitor cell with external load (R l ) and output voltage V l .