State of Charge Estimation for Lithium-Ion Battery Based on Fractional-Order Kreisselmeier-Type Adaptive Observer

For the safe and efficient use of lithium-ion batteries, the state of charge (SOC) is a particularly important state variable. In this paper, we propose a method for the online estimation of SOC and model parameters based on a fractional-order equivalent circuit model. Firstly, we constructed a fractional-order battery model that includes pseudo-capacitance and determined the values of the circuit elements offline using the least squares method from actual input–output data based on the driving profile of an automobile. Compared to the integer-order battery model, we confirmed that the proposed fractional-order battery model has higher accuracy. Secondly, we constructed a fractional-order Kreisselmeier-type adaptive observer as an observer that performs state estimation and parameter adjustment simultaneously. Applying the general adaptive law to the battery model results in a redundant design with many adjustable parameters, so we proposed an adaptive law that reduces the number of adjustable parameters without compromising the stability of the observer. The effectiveness of the proposed method was verified through numerical simulations. As a result, the high estimation accuracy and convergence of the proposed adaptive law were confirmed.