State of charge estimation for lithium-ion batteries based on fractional order multiscale algorithm

Abstract

The accuracy of state of charge (SoC) plays a critical role in lithium-ion batteries management system, whereas it gradually reduces as ohmic internal resistance growing and maximum available capacity decreasing with battery aging, which is still an open and challenging problem in SoC estimation. To tackle this issue, a multi-scale estimation algorithm is proposed by incorporating fractional order adaptive extended Kalman filter and variable forgetting factor recursive least square (FOAEKF-VFFRLS). Firstly, in order to describe the physicochemical reactions inside battery accurately, a fractional order model of lithium-ion battery with its discrete form is introduced, and the resistor-capacitor (RC) values as well as the order of capacitors are obtained by employing ant colony algorithm (ACA). Secondly, for enhancing SoC estimation accuracy, a fractional order adaptive extended Kalman filter algorithm (FOAEKF) is proposed to continuously modify the noise statistical characteristics while utilizing observation data information. Thirdly, to predict ohmic internal resistance and maximum available capacity for battery, a variable forgetting factor recursive least square algorithm (VFFRLS) is established based on the fact that forgetting factor determined by individual data error would be suddenly changes in the case of inaccurate or perturbed data. Besides, to further improve the accuracy of SoC estimation, a multi-scale estimation approach is proposed in light of the slow variation of battery internal resistance and the fast change of SoC. Finally, through comparative experiments, it is proved that the proposed approach has comprehensive strengths. First, the minimum root mean square error (RMSE) of SoC estimation error is controlled within 0.52 %. Second, terminal voltage error is kept small while limiting SoC errors within narrow ranges. Third, favorable robustness in terms of SoC estimation is achieved despite SoC initial value is mis-initialized.