A Case Study to Compare the Methods of SOC Estimation for Lithium-ion Batteries Using Second-order RC Circuit Model

Since the State of Charge (SOC) of lithium-ion battery cannot be directly measured, accurately and precisely estimating SOC has become a significant challenge in the field of new energy vehicles. This paper presents a comparison of several SOC estimation methods, with the finding that the method coupled by Variable Forgetting Factor Recursive Least Squares and Unscented Kalman Filter (UKF) algorithm is the best to estimate SOC.First, a second-order RC model is used to establish a physical model for SOC estimation. The Open Circuit Voltage (OCV) - SOC expression is derived. Subsequently, following the logic of increasing identification accuracy and improving dynamic performance, the parameters of the physical model are identified. The Ohmic internal resistance \(\:{R}_{0}\), electrochemical polarization resistance \(\:{R}_{1}\), concentration polarization resistance \(\:{R}_{2}\), electrochemical polarization capacitance \(\:{C}_{1}\), and concentration polarization capacitance \(\:{C}_{2}\) are sequentially derived based on the Recursive Least Squares (RLS) method, the Forgetting Factor Recursive Least Squares (FF - RLS) method, and the Variable Forgetting Factor Recursive Least Squares (VFF - RLS) method. Then, an algorithm with a variable forgetting factor is adopted. After substituting it into the model, the values of \(\:{R}_{0}\), \(\:{R}_{1}\), \(\:{R}_{2},\:\) \(\:{C}_{1}\) and \(\:{C}_{2}\) are obtained as 0.00015 Ω, 0.00351 Ω, 0.01290 Ω, 320 F and 14995 F respectively, which are quite consistent with the real situation.Finally, in the order of increasing applicability for SOC estimation, the mathematical principles of the Kalman Filter (KF) algorithm, the Extended Kalman Filter (EKF) algorithm, and the Unscented Kalman Filter (UKF) algorithm are considered. The parameter identification results are substituted into the EKF and UKF estimation models as initial values for iteration, and the SOC estimation results are obtained. The simulation results show that when the algorithm is stable, the error range of the UKF for SOC estimation is within 2%, proving that the UKF has higher estimation accuracy and robustness.