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Accurate estimations of battery state of charge (SOC) are great of significance for achieving stable and safe operation of electric vehicles. To meet the requirement of high robustness and real-time, the sliding mode observer with linear time-invariant battery model is usually used to estimate SOC of batteries. However, the observer for state estimation based on the time-varying model is rarely. In addition, there is a lack of stability proof for observers with time-varying systems. The applicability of the observer in different types of batteries is yet to be discussed. The application accuracy of the observer in the battery management system (BMS) needs to be further verified. To solve these issues, an improved observerbased estimation algorithm has been proposed. In this paper, a recursive fitting technology is used to automatically update the variable parameters of the battery, then the time-varying-model-based discrete sliding mode observer (TVDSMO) is proposed to build a SOC estimator. The stability condition is proposed to online evaluate the presented observer. The presented estimator has been verified by LiFePO4 (LFP) and Ni-Mn-Co (NMC) lithium-ion cells under different operating temperatures and working conditions. Finally, a platform based hardware-in-loop is built to verify the proposed method. The result manifests that the maximum estimation errors of SOC are both within 4% for NMC and LFP cells when the erroneous initial value of SOC and capacity are both considered. Additionally, the results from the platform show that the SOC estimation error is less 4.6% which fully meets the application of BMS.INDEX TERMS Lithium-ion battery, state of charge, discrete stability condition, time-varying-model-based discrete sliding mode observer, BMS.

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