Real Time Terminal Voltage Prediction and State-of-Charge Estimation for Supercapacitors Using Fractional Order Model

An accurate state-of-charge estimation is highly important for the reliable application of supercapacitor in the field of electric vehicles and powertrains. This paper presents a dynamic approach to supercapacitor modeling and state of charge estimation using a fractional-order model. Analytical expressions for charging, discharging, and rest characteristics of supercapacitors are formulated and validated through experimental results. The proposed parameter estimation technique dynamically optimizes the fractional order model parameters by using least squares technique that updates parameters at each stage of operation, which are then used in the implementation of a Kalman Filter used for state of charge estimation. This dynamic parameter optimization, coupled with dedicated rest period dynamics modeling, enables accurate real time SOC estimation, achieving <3% error in state of charge and <50mV voltage error. The method's effectiveness is demonstrated across multiple supercapacitor types (360F, 480F, and 3000F) under varied operating stages. Qualitative comparison with recent literature shows our approach uniquely combines explicit rest period modeling with computationally efficient dynamic parameter estimation, suitable for real-time embedded applications.