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Electrochemical Supercapacitors for Energy Storage and Delivery
In normal situations, CDCs are performed by applying a constant cell current, during which the cell voltage is recorded as a function of charging or
discharging time. Constant cell voltage mode can also be applied for characterization of supercapacitor properties. In this case, cell current is continuously measured as a function of charging and discharging time, but this
technique is seldom used. This section will cover only supercapacitor CDCs
using constant current mode.
7.4.1 Capacitance, Maximum Energy and Power Densities,
and Equivalent Series Resistance Measurements
As discussed in Chapter 2, immediately after charging starts (charging time
t ≥ 0), the supercapacitor charging voltage (V cell ) can be expressed as Equation
(7.21) if the two-electrode test cell and the constant current (I cell ) charging
modes are employed:
V = I R + I R (1− exp( −
t )) (charging process)
(7.21)
cell
cell esr
cell p
R C
p T
where R esr is the equivalent series resistance, and R p is the equivalent faradic
leakage resistance, which is an electrode potential-dependent parameter. In
Chapter 2, for simplifying the mathematics, this parameter was treated as a
constant. Actually, with an electrochemical leakage reaction, a more complicated equation should be applied (please see our recent work [7]). If there is
no parallel leakage reaction, R p → ∞. Thus, Equation (7.21) can be simplified as
V = I R + I
t (charging process)
(7.22)
cell
cell esr
cell C T
Equation (7.22) suggests that cell voltage has a linear relationship with charging time. After the supercapacitor is charged to a cell voltage of (V cell ) max , a
discharging process using a constant current (I cell ) can be started immediately. The cell voltage (V cell ) can be expressed as
V = −I R + (V ) − I
t (discharging process)
(7.23)
cell
cell esr
cell max
cell C T
Figure 7.8 shows the CDC using a two-electrode test cell in which both
electrodes are identical (symmetric cells) [7]. According to Equations (7.22)
and (7.23), these data can be simulated to obtain several parameters such
as capacitance (C T ), maximum cell voltage ((V cell ) max ), and equivalent series
resistance (R esr ). In the case shown in the figure, the simulated capacitance
Electrochemical Supercapacitors for Energy Storage and Delivery
In normal situations, CDCs are performed by applying a constant cell current, during which the cell voltage is recorded as a function of charging or
discharging time. Constant cell voltage mode can also be applied for characterization of supercapacitor properties. In this case, cell current is continuously measured as a function of charging and discharging time, but this
technique is seldom used. This section will cover only supercapacitor CDCs
using constant current mode.
7.4.1 Capacitance, Maximum Energy and Power Densities,
and Equivalent Series Resistance Measurements
As discussed in Chapter 2, immediately after charging starts (charging time
t ≥ 0), the supercapacitor charging voltage (V cell ) can be expressed as Equation
(7.21) if the two-electrode test cell and the constant current (I cell ) charging
modes are employed:
V = I R + I R (1− exp( −
t )) (charging process)
(7.21)
cell
cell esr
cell p
R C
p T
where R esr is the equivalent series resistance, and R p is the equivalent faradic
leakage resistance, which is an electrode potential-dependent parameter. In
Chapter 2, for simplifying the mathematics, this parameter was treated as a
constant. Actually, with an electrochemical leakage reaction, a more complicated equation should be applied (please see our recent work [7]). If there is
no parallel leakage reaction, R p → ∞. Thus, Equation (7.21) can be simplified as
V = I R + I
t (charging process)
(7.22)
cell
cell esr
cell C T
Equation (7.22) suggests that cell voltage has a linear relationship with charging time. After the supercapacitor is charged to a cell voltage of (V cell ) max , a
discharging process using a constant current (I cell ) can be started immediately. The cell voltage (V cell ) can be expressed as
V = −I R + (V ) − I
t (discharging process)
(7.23)
cell
cell esr
cell max
cell C T
Figure 7.8 shows the CDC using a two-electrode test cell in which both
electrodes are identical (symmetric cells) [7]. According to Equations (7.22)
and (7.23), these data can be simulated to obtain several parameters such
as capacitance (C T ), maximum cell voltage ((V cell ) max ), and equivalent series
resistance (R esr ). In the case shown in the figure, the simulated capacitance