A Fractional-Order State Estimation Method for Supercapacitor Energy Storage

Supercapacitors (SCs) are emerging as a dependable energy storage technology in industrial applications, valued for their high power output and exceptional longevity. In high-power applications, SCs are not used as single cells but are configured in a series–parallel combination to form a bank. Accurate state-of-charge estimation is essential for effective energy management in power systems employing SC banks. This work presents a novel state estimation approach for SC banks. First, a dynamic model of an SC bank is derived by applying a fractional-order Thévenin equivalent circuit to a single-cell SC. Then, an observability analysis is conducted, which reveals that the system is empirically weakly observable. This is the fundamental challenge for state-of-the-art observers to robustly perform state estimation. To address this challenge, an implicitly regularized observer is developed based on generalized parameter estimation techniques. The performance of the proposed observer is benchmarked against a fractional-order extended Kalman filter using experimental data. The results demonstrate that incorporating a regularization law into the observer dynamics effectively mitigates observability limitations, offering a robust solution for the SC bank state estimation.