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the RC model and the actual performance increase as the power level approaches its
maximum value.
1
0.9
0.8
E dis / E del
0.7
0.6
0.5
0.4
0.3
0.2
0.1
Electrochemical
Capacitor
Series
RC
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
P ave / P max
Figure 29 Energy dissipated as a function of power for series RC circuit versus a typical
electrochemical capacitor
A rule of thumb for capacitor operation, where efficiency or self-heating is important, is
to restrict operation to a P ave
/P max
ratio of less than 0.1. At this power level, ~90% of the
stored energy can be extracted from the capacitor. There are some applications where
operation at higher power levels is appropriate. These applications generally are not
cyclic in nature since operating at such high levels does cause a temperature rise within
the capacitor.
Two-Terminal Response
The behavior of a typical electrochemical capacitor cell can be represented by the
equivalent circuit model shown in Figure 30. Circuit elements include a series resistance,
R s
, and a capacitor, C, in parallel with a leakage current source. The equilibrium leakage
current has exponential voltage dependence, which is observed for all electrochemical
capacitors. The series resistance of a cell, R s
, is responsible for establishing the voltage of
that cell in a series string during transient operation. During steady state operation, the
leakage current element establishes the voltage in a cell. During intermediate rate
operation, that is during charge/discharge cycling, all three elements can play a role in
establishing the voltage of each cell.
Electrochemical Capacitors 59