Co-estimation of state of charge and state of health of sodium-ion batteries based on fractional-order model and improved double unscented Kalman filter

Abstract

Sodium-ion batteries (SIBs) are projected to become a commercially viable alternative to lithium-ion batteries in the future because of their abundant reserves, high energy density, and enhanced safety. Accurate estimation of the state of charge (SOC) and state of health (SOH) is crucial for ensuring safe battery operation, prolonging lifespan, and optimizing energy management in SIBs. This study proposes a collaborative estimation method for battery SOC and SOH based on the FO-MISVDRUKF-UKF algorithm. First, a fractional-order model (FOM) is adopted to characterize the complex ion dynamics in SIBs, achieving terminal voltage prediction errors within 0.08 V. Secondly, to address the limitations of conventional unscented Kalman filter (UKF) algorithms—including low precision, computational complexity, and weak robustness—three key enhancements are implemented: (1) Replacing Cholesky decomposition with singular value decomposition (SVD) ensures algorithm stability when the covariance matrix P lacks positive semi-definiteness; (2) Integration of H-infinity filtering effectively suppresses unknown noise interference; (3) Multi-innovation (MI) theory leverages historical data to further improve estimation accuracy. Furthermore, real-time parameter updating and SOH monitoring are achieved through recursive UKF adaptation, mitigating model parameter drift effects on SOC estimation. Experimental validation under varying temperatures and dynamic load conditions demonstrates the superior performance of the proposed algorithm. At temperatures of 25 °C, 45 °C, and 60 °C, SOC estimation errors remain below 0.34% (mean) and 0.75% (maximum), while SOH errors are constrained within 0.29% (mean) and 0.58% (maximum)—significantly outperforming conventional methods. These results confirm the high accuracy and robust performance of the proposed framework.