B. Conversion efficiency
As it can be seen from (9), the ultra-capacitor losses depend
on three parameters: 1) The resistance Rca, 2) The capacitance
Co and 3) The ultra-capacitor initial voltage. Is it possible to
design the ultra-capacitor for conversion efficiency gi ven as a
design parameter? Let's consider that the ultra-capacitor is
charged from UeoillM toward Ueomax with constant power Pea.
The energy lost during an entire charge period can be defined
as
On another side, the ultra-capacitor resistance Rca depends
on the capacitance Co. The greater capacitance is, the smaller
resistance is.
The graph is plotted for an SOOV custom designed ultracapacitor
module. The module is composed of series/parallel
connected ultra-capacitor cells rated for 2.SV.
The conversion losses as a function on the capacitance Co
and maximum operating voltage are
TJ=T2=2s. Please, note from Fig. S that the efficiency is above
90% for capacitance above 0.2F. Below this capacitance, the
efficiency decreases steeply and reaches 40% at capacitance of
O.OSF. Since the internal series resistance increases
significantly as the capacitance decrease, such pure efficiency
is expected. If high efficiency is the primary design criterion,
the ultra-capacitor Co must be selected from efficiency
criterion (15) instead of using the criterion (7).