Traditional state of charge (SOC) estimation algorithm of lithium battery is often based on equivalent circuit model, which has low accuracy and too many parameters. And the application of equivalent circuit model in state of health (SOH) estimation is limited because of the disadvantages. In addition, the capacity attenuation of lithium battery is often ignored to result in poor timeliness of SOC estimation. There is a coupling relationship between SOC and SOH of lithium battery. SOC-SOH joint estimation is an effective means during life cycle, but joint estimation model is relatively complex and imperfect, which doesn’t support the estimation requirements. This paper presented a joint SOC-SOH estimation model with equivalent circuit model and fractional order theory. By adaptive extended Kalman filter (AEKF) algorithm and capacity parameter modification method, the accuracy and the timeliness of the state estimation were improved. Firstly, based on the second order RC model of lithium battery, the state equation was established. Considering the time-varying characteristics of noise covariance, dynamic noise covariance parameter was obtained by calculating the cumulative error, and AEKF algorithm was proposed to estimate the SOC of lithium battery. Secondly, aiming at the of excessive parameters in integer order model, the RC series module was simplified by fractional calculus theory to acquire a fractional order model with high precision and few parameters. The parameters were identified by fuzzy controller. Based on the charging conditions and the polarization characteristics of lithium battery, the interval constant current charging time and the fractional-order model parameters were determined as health factors. Thirdly，by use of SSA to optimize BP neural network for the global optimal solution of the weight, nonlinear relationship between health factors and SOH was analyzed to design SOH estimation model. Finally，considering the capacity attenuation of lithium battery and the measurement accuracy of health factors, SOH estimation value was used to modify the capacity parameters and SOC estimation value was used to determine the initial sampling point of health factor to develop a SOC-SOH joint estimation model. Aging tests, dynamic condition tests of US06 and DST of lithium battery are designed to verify the joint SOC-SOH estimation model. In dynamic tests of US06 and DST, the results show that maximum error of SOC estimation accuracy based on AEKF algorithm and EKF algorithm is less than 1% and more than 3% respectively, which verified the effectiveness of SOC estimation model with AEKF algorithm. In aging tests, the effectiveness of health factors was verified and the influence of accuracy between SOC and SOH estimates was analyzed. The results show that the correlation coefficient between interval constant current charging time and SOH is greater than 0.96, the correlation coefficient between fractional order model parameters and SOH is greater than 0.95, which expressed the strong correlation of the health factors. The maximum errors of SOH estimation based on health factors acquired by AEKF and EKF were less than 1% and more than 2%, respectively, which showed the SOH estimation improvement with health factors acquired by AEKF. By capacity parameter modification, the maximum error of SOC estimation could decrease at less than 1%, while the maximum error of SOC estimation is more than 22% without modification. Meanwhile, with different capacity modification accuracies, the maximum errors of SOC estimation could be ensured to be less than 1.5%, which reduced the estimation errors and improved the timelines with the joint SOC-SOH estimation model. The following conclusions can be drawn from the analysis: (1) Compared with EKF, the actual dynamic noise covariance is considered in AEKF algorithm proposed. It is more appropriate to establish SOC model to effectively improve SOC estimation accuracy. (2) Fractional order model can better reflect the polarization characteristics of lithium battery. With the health factors extracted based on charging conditions and fractional order model parameters, SOH estimation model established can reduce the estimation error. (3) AEKF algorithm is used to adaptively monitor the charging and discharging state of lithium battery to acquire accurate health factors. SOH estimation value is used to modify capacity parameters instead of fixed capacity parameters because of actual capacity attenuation. The joint estimation model designed is more suitable for the actual change. It has stronger timeliness and robustness. © 2023 Chinese Machine Press. All rights reserved.
