**Guoqing Jin 1, Lan Li 2, Yidan Xu 2, Minghui Hu 2,\*, Chunyun Fu 2,\* and Datong Qin <sup>2</sup>**


Received: 20 February 2020; Accepted: 26 March 2020; Published: 7 April 2020

**Abstract:** Accurate estimation of the state of charge (SOC) is an important criterion to prevent the batteries from being over-charged or over-discharged, and this assures an electric vehicle's safety and reliability. To investigate the effect of different operating conditions on the SOC estimation results, a dual-polarization model (DPM) and a fractional-order model (FOM) are established in this study, taking into account the prediction accuracy and structural complexity of a battery model. Based on these two battery equivalent circuit models (ECMs), a hybrid Kalman filter (HKF) algorithm is adopted to estimate the SOC of the battery; the algorithm comprehensively utilizes the ampere-hour (Ah) integration method, the Kalman filter (KF) algorithm, and the extended Kalman filter (EKF) algorithm. The SOC estimation results of the DPM and FOM, under the dynamic stress test (DST), federal urban driving schedule (FUDS), and hybrid pulse power characteristic (HPPC) cycle conditions, are compared and analyzed through six sets of experiments. Simulation results show that the SOC estimation accuracy of both the models is high and that the errors are within the range of ±0.06. Under any operating conditions, the SOC estimation error, based on the FOM, is always lower than the SOC estimation error of the DPM, but the adaptability of the FOM is not as high as that of the DPM.

**Keywords:** lithium-ion battery; dual-polarization model; fractional-order model; SOC estimation; hybrid Kalman filter
