Transient Behavior Modeling-Based Hysteresis-Dependent Energy Estimation of Ultracapacitor

The rough and porous structure of the electrode and electrolyte interface in ultracapacitors results in hysteresis between the excitation current and corresponding terminal voltage. The hysteretic behavior causes an increment in terminal voltage even after the removal of input excitation current, referred to as remnant voltage. The design and operation of any ultracapacitor-based energy system should necessarily take into account the hysteretic behavior and the associated remnant voltage for optimal utilization of ultracapacitor as a storage device. Proper modeling of hysteresis allows for determining the optimal excitation profile for charging the ultracapacitor, such that proper balance between the load demand and energy storage is achieved. Motivated by the effectiveness of fractional calculus in representing the long-term memory effect and charge diffusion phenomena in ultracapacitors, this article proposes a fractional calculus-based approach for modeling the hysteresis and estimating the related remnant voltage and associated energy availability after the completion of periodic charging excitations. Analytical expressions for ultracapacitor voltage and energy storage have been formulated for different hysteresis levels using fractional calculus. The formulation helps in quantifying the hysteresis as a function of the excitation magnitude/duration and ultracapacitor model parameters, thus providing a platform for improving the energy efficiency of the ultracapacitor-based energy management applications by optimal charging. The derived expressions have been experimentally validated for varying dynamics of current excitation.