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Batteries experience capacity offset where available charge depends on therate at which this charge is drawn. In this work we analyze the capacity offsetof a 4.8 A h lithium nickel-cobalt-aluminium oxide battery using an equivalentcircuit model of a fractional capacitor in series with a resistor. In thiscase, the available charge, in theory, becomes infinite in the limit ofinfinitesimal rate. We show that the fractional properties of the capacitor canbe extracted from the charge against rate plot. We then use a network of RCelements to represent the fractional capacitor in order to simulate the datawith 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 impedanceversus frequency plot, although the fractional capacity does not. Such anapproach demonstrates the importance of a fractional description for capacityoffset even when an element is nearly a pure capacitor and is valuable forpredictions of state-of-charge when low currents are drawn.

Charge capacity characteristics of a Lithium Nickel-Cobalt-Aluminium Oxide battery show fractional-derivative behavior