State of Charge Estimation of Vanadium Redox Flow Battery Based on Sliding Mode Observer and Dynamic Model Including Capacity Fading Factor

State of charge (SOC) of the batteries is a key indicator for battery monitoring and control. Long-term operation of vanadium redox flow batteries may cause ion diffusions across the membrane and the depletion of active materials, which will lead to capacity fading and increase in internal resistance. In previous studies, the capacity fading factor is not considered when designing the SOC estimation observer. This will cause a large error of SOC estimation if the capacity fading is significant. Thus, a selection of an adaptive SOC estimation method considering capacity fading factor is critical. In this paper, an adaptive observer-sliding mode observer-capable of monitoring SOC considering capacity factor is proposed based on a nonlinear electrical model. The observer is designed to adjust the capacity based on the decaying factor and compensate the error caused by the electrical model. A root mean square error of 0.013 V between the measured terminal voltage and estimated voltage is observed while a root mean square error of 0.12 V with the modeled voltage. The mean error between the observed and the modeled capacities is 0.14 Ah. The proposed method shows that the sliding mode observer could accurately estimate SOC with capacity fading.