Handbook of Energy Storage for Transmission or ... - W2agz.com

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better represents the dynamic behavior of the capacitor. The fastest response time is the
discharge of C1 through R1, the second fastest is the discharge of C2 through R1 + R2,
and so on. Because of the distributed charge storage with distributed resistances, the
capacitor can release only a small fraction of its total stored energy in very short times.
This is evident in the 2500 F example type II capacitor response shown in Figure 32. At
longer times, more of the stored energy becomes available until, at very long times, all of
the stored energy can be accessed. Impedance data is commonly used to derive multiple
time constant equivalent
100
% Total Capacitance
80
60
40
20
0
0.01 0.1 1 10
Time Constant (s)
Figure 32 Type II design, 2500F capacitor demonstrates dynamic characteristics of increased
capacity with reduced loading and longer discharge times.
Electrochemical capacitor response often has a second effect due to the porosity of the
electrodes themselves. Although particles in the electrode are typically large, interstitial
space between these particles in thick electrodes creates multiple-time-constant behavior.
Consequently, an upper limit on the electrode thickness is usually established by the
desired time response of the capacitor.
Symmetric and Asymmetrical Electrodes
Figure 33 summarizes some basic differences between the symmetric and the asymmetric
capacitor designs using aqueous electrolytes. The symmetric capacitor uses the same
material for both positive and the negative electrodes in approximately the same quantity,
and produces two identical capacitances, each C o
. Since these two capacitors are
connected in series, the total capacitance is 1/2 C o
.
In contrast, the asymmetric electrochemical capacitors, as shown on the right side of
Figure 33, have positive and negative electrodes comprised of different materials. In fact,
the positive electrode stores charge more like a battery (Faradaic processes) so although
physically smaller, its capacity is greater than the opposing double layer charge storage
electrode. There is enough space for the negative electrode to be sized for the total
capacitance 2 C o
in the single electrode. And, since it is mated with a much larger series
capacitor, the total capacitance of this design is 2 C o
. This difference, 1/2 C o
for the
symmetric and 2 C o
for the asymmetric, gives a four-fold volumetric capacity advantage
to the asymmetric designs.
The voltage versus charge curve for each electrode is also shown in Figure 33. It
provides information on the exact operation of the capacitor. As charge is delivered to
Electrochemical Capacitors 61