Optimal Charging Profile Design for Attaining Desired State of Charge in Symmetric Electrochemical Capacitor With Efficiency Analysis

The optimal utilization of ultracapacitor (symmetric electrochemical capacitor) for vehicular applications demands continuous monitoring and maintenance of its state of charge (SOC). The online estimation of SOC plays a vital role in the effective utilization of the energy storage capacity of ultracapacitors. In addition to monitoring SOC, high reliability in vehicle operation requires a predefined SOC level, as per the dynamic load requirement. For the ultracapacitor undergoing series of charge-discharge cycles, proper regulation of the SOC in accordance with the vehicle drive profile, increases the ultracapacitor life by avoiding possible stress due to undercharging/overcharging. Achieving the desired SOC in real-time warrants a mechanism for the optimal charging of the ultracapacitor. In this regard, the present article proposes an optimal charging scheme to attain a predefined SOC from any initial value, within a given time-frame. The proposed noniterative fractional calculus-based approach allows for analytically representing the charging current as a function of the desired SOC, charging duration and ultracapacitor model parameters. The scheme has been extensively validated experimentally for its effectiveness in attaining the desired SOC. Further, the appropriateness of the derived charging profiles for different operating scenarios has also been analyzed in terms of maintaining a tradeoff between faster charging and high charging efficiency.