65
Fundamentals of Electrochemical Double-Layer Supercapacitors
R esr
C
T
dl
FIGURE 2.13
Equivalent circuit of supercapacitor in presence of equivalent series resistance.
supercapacitor cell, can be expressed as Equation (2.35) if the equivalent
series resistance is expressed as R esr :
j
1
Z ce ll = R esr − j πfC
T
(2.35)
2
dl
where f is the AC frequency in hertz. The magnitude of this Z
j
cell can be
expressed as:
2
2 ⎛ 1 ⎞
Z
j
cell = ( R esr ) + ⎜ ⎜ T ⎟ ⎟
(2.35a)
⎝ 2πfC dl ⎠
Using AC impedance spectroscopy at the high end of AC frequency, the corresponding impedance would be R esr because the second term on the right
side of Equation (2.35a) will be much smaller than the first term. At the low
end of the AC frequency, this second term will become much larger than the
first one and the obtained AC impedance is dominated by this second term
from which C
T
dl can be obtained. This allows R esr and C
T
dl to be obtained
separately. Another way to measure R esr is to use the charging–discharging curve if its magnitude is large enough. This will be discussed in a later
section.
ESR is an important parameter in evaluating a supercapacitor’s performance, in particular its power density, because the ESR restricts the rates at
which the capacitance can be charged or discharged upon application of a
given current or voltage.
2.5.2.1 Thermal Degradation from ESR
The voltage drop created by cell resistance affects both the charge and discharge capacities of a cell. The non-ideal loss limits the effective region for
usable charge storage and thereby limits the charge capacity of the cell. The
lost charge is primarily dissipated as heat. The non-ideal resistive power
losses can generate an unacceptable amount of heat very quickly. Even commercial cells designed to have low resistance, for example, a Maxwell K2 cell
(Table 2.4) can accumulate heat very quickly.
If the cell based on the specifications in the table was operated at the maximum usable power of 1 kW, the current passing through the device would
Fundamentals of Electrochemical Double-Layer Supercapacitors
R esr
C
T
dl
FIGURE 2.13
Equivalent circuit of supercapacitor in presence of equivalent series resistance.
supercapacitor cell, can be expressed as Equation (2.35) if the equivalent
series resistance is expressed as R esr :
j
1
Z ce ll = R esr − j πfC
T
(2.35)
2
dl
where f is the AC frequency in hertz. The magnitude of this Z
j
cell can be
expressed as:
2
2 ⎛ 1 ⎞
Z
j
cell = ( R esr ) + ⎜ ⎜ T ⎟ ⎟
(2.35a)
⎝ 2πfC dl ⎠
Using AC impedance spectroscopy at the high end of AC frequency, the corresponding impedance would be R esr because the second term on the right
side of Equation (2.35a) will be much smaller than the first term. At the low
end of the AC frequency, this second term will become much larger than the
first one and the obtained AC impedance is dominated by this second term
from which C
T
dl can be obtained. This allows R esr and C
T
dl to be obtained
separately. Another way to measure R esr is to use the charging–discharging curve if its magnitude is large enough. This will be discussed in a later
section.
ESR is an important parameter in evaluating a supercapacitor’s performance, in particular its power density, because the ESR restricts the rates at
which the capacitance can be charged or discharged upon application of a
given current or voltage.
2.5.2.1 Thermal Degradation from ESR
The voltage drop created by cell resistance affects both the charge and discharge capacities of a cell. The non-ideal loss limits the effective region for
usable charge storage and thereby limits the charge capacity of the cell. The
lost charge is primarily dissipated as heat. The non-ideal resistive power
losses can generate an unacceptable amount of heat very quickly. Even commercial cells designed to have low resistance, for example, a Maxwell K2 cell
(Table 2.4) can accumulate heat very quickly.
If the cell based on the specifications in the table was operated at the maximum usable power of 1 kW, the current passing through the device would