Accurate SOP prediction of supercapacitor using fractional calculus framework

Real-time information of state of power (SOP) of a supercapacitor (SC) is crucial for determining its capability about power delivery or absorption. The dynamics of SOP is intricately coupled with the present state of charge (SOC), and depends on various operating limits including voltage limits. In essence, better SOP prediction is highly dependent on the estimated value of SOC as well as the physical model that captures the electrical dynamics of SC. In this context, this paper proposes an accurate SOP prediction scheme which utilizes an accurate device model and SOC estimation scheme based on fractional order calculus. Within this proposed framework, SOP has been predicted in real-time based on the derived value of maximum possible input/output current without violating the device voltage, current, and SOC limits. This maximum current is derived by using instantaneous voltage estimated through a fractional order model (FOM) and instantaneous SOC estimated through fractional order extended Kalman filter (FOEKF), along with the aforementioned device constraints. The FOM is identified based on the experimental data obtained using a commercial Maxwell 5F SC. As SC performance suffers from the leakage current, especially in low duty cycle applications, the effect of leakage current variation on the SOP prediction is investigated. Furthermore, the impact of prediction horizon on SOP prediction has been studied. Overall, these studies collectively show that the effectiveness of the proposed framework.