Fractional calculus-based modeling and state-of-charge estimation of supercapacitor

Supercapacitors (SCs) are becoming a well-accepted energy storage device in many industrial applications for their high power density and remarkably long life span. The SC-powered systems require an accurate estimation of the state of charge (SOC) to ensure the proper energy management of the system. SOC estimation accuracy is significantly affected by SC leakage current, particularly in low-duty cycle applications like wireless sensor nodes. Considering the memory effect of the electrochemical energy storage systems, the fractional calculus-based SC model accurately characterizes the device's electrical dynamics. This paper proposes a fractional order (FO) equivalent circuit model of SC considering the leakage effect of the device. The model parameters are experimentally identified, considering the commercially available 5F Maxwell SC cell. Based on the proposed model, a fractional order Extended Kalman Filter (FOEKF) has been designed and implemented to estimate the SOC of the SCs. A state initialization method has been proposed to address the convergence issue of the estimator under unknown initial conditions. The performance of the proposed estimation scheme has been illustrated through simulation and experimental studies. Finally, the performance of the proposed fractional order estimation has been compared with the integer-order approach.