Supercapacitor sizing based on desired power and energy performance

In this paper, instantaneous power and energy capabilities of supercapacitor (SC) connected to a power element are derived for an arbitrary power profile, given either in analytical or statistical distribution form. A class of applications is considered where the device is used as deeply cycled energy storage with significant capacity, absorbing/supplying the whole power flow or its significant component rather than shaving low-energy high-frequency peaks. The analytical derivation of SC behavior is based on simple RC model with parameters taken from a manufacturer datasheet. It is shown that the commonly adopted 'state-of-charge' indication based on terminal voltage only is insufficient to reflect the energy balance for both charging and discharging; hence an alternative definition of 'state-of-energy' is proposed for each direction of energy flow, depending on both instantaneous power and terminal voltage. A simplified quick noniterative sizing procedure is proposed at the expense of a slightly oversized SC. Comprehensive example is provided in order to reinforce the proposed method of analyzing SC performance and demonstrate sizing procedure.