  Batteries experience capacity offset where available charge depends on the
rate at which this charge is drawn. In this work we analyze the capacity offset
of a 4.8 A h lithium nickel-cobalt-aluminium oxide battery using an equivalent
circuit model of a fractional capacitor in series with a resistor. In this
case, the available charge, in theory, becomes infinite in the limit of
infinitesimal rate. We show that the fractional properties of the capacitor can
be extracted from the charge against rate plot. We then use a network of RC
elements to represent the fractional capacitor in order to simulate the data
with Matlab. We find that the fractional exponent alpha obtained in this way,
0.971, agrees with that obtained in a more traditional manner from an impedance
versus frequency plot, although the fractional capacity does not. Such an
approach demonstrates the importance of a fractional description for capacity
offset even when an element is nearly a pure capacitor and is valuable for
predictions of state-of-charge when low currents are drawn.
