Energy storage and loss in fractional-order circuit elements


The efficiency of a general fractional-order circuit element as an energy storage device is analysed. Straightforward expressions are derived for the proportions of energy that may be transferred into and then recovered from a fractional-order component by either constant-current or constant-voltage charging and discharging. For a half-order element, it is shown that the efficiency of the charging part of the cycle is equal to the potency of the discharging phase. The results demonstrate the duality of the fractional capacitive and inductive parts, in that the efficiency of one under constant-current cycling is the same because the potency of the opposite under constant-voltage cycling, and vice-versa.

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