State of charge estimation for LiFePO4 batteries joint by PID observer and improved EKF in various OCV ranges

LiFePO4 batteries are increasingly utilized in electric vehicles due to their superior safety. Accurate state estimation is the basis for the safe and reliable application of LiFePO4 batteries. However, the flat voltage characteristics of LiFePO4 batteries lead to state estimation closed-loop correction as its inherent contradiction. To address this challenge, a model-based SOC estimation method combining proportional-integral-differential (PID) observer and improved extended Kalman filter (EKF) is developed according to different open-circuit-voltage (OCV) ranges, specific processes include: First, an exponentially weighted moving average algorithm with a temperature compensation factor is presented to compensate for the errors in the identified OCV. Secondly, the combination of the PID observer and EKF is chosen adaptively to update SOC within distinct OCV ranges, differentiated by the identified OCV. To achieve optimization of the PID parameters and temperature compensation factors across varying temperatures, an enhanced whale optimization algorithm is developed. To validate the developed method, a series of experiments are performed across a range of temperatures and with multiple driving profiles. The results show that the developed method not only guarantees maximum absolute error of <3 %, but also can converge quickly in the early stage.