Joint estimation of state of charge and health utilizing fractional-order square-root cubature Kalman filtering with order scheduling strategy

Accurate joint estimation of state of charge (SOC) and state of health is crucial for battery management systems. This paper proposes an innovative method employing a fractional-order model (FOM) in conjunction with a fractional-order filter for effective and precise online joint estimation of SOC and capacity. Motivated by the advantageous characteristics of FOMs in depicting the dynamic behavior of batteries, this paper establishes a first-order FOM. Subsequently, a fractional-order square-root cubature Kalman filter method is proposed for the online estimation of SOC and capacity. This method effectively addresses the potential non-positive definite covariance matrix issue during the iteration process. Additionally, this paper suggests using polynomials instead of binomials to compute fractional derivatives, aiming to further improve simulation accuracy. Besides, motivated by the impact of orders on modeling and state estimation under different battery aging and temperature conditions, through extensive experiments, the following findings are derived: (1) When the order of the state estimator is higher than the model order, it can significantly enhance the precision of state estimation. (2) The optimal order of the state estimator shows a decreasing trend with battery aging and increasing temperature. (3) Based on the experimental results, a order scheduling strategy can be established to provide a reference for the selection of the order. Finally, a comparative analysis is conducted between classical methods and the proposed method. Experimental results demonstrate that the proposed method makes the mean absolute error of SOC estimation about 2% and the capacity estimation errors typically remain below 3%, despite the degree of aging and temperatures.