State of charge estimation of lithium-ion batteries using fractional order sliding mode observer

•A fractional order RC equivalent circuit model for the lithium-ion battery is developed.•Fractional calculus is applied to model the battery.•The fractional order sliding mode observers for state of charge estimation are designed.•The stability conditions of the sliding mode observers are proved by Lyapunov stability theory.

This paper presents a state of charge (SOC) estimation method based on fractional order sliding mode observer (SMO) for lithium-ion batteries. A fractional order RC equivalent circuit model (FORCECM) is firstly constructed to describe the charging and discharging dynamic characteristics of the battery. Then, based on the differential equations of the FORCECM, fractional order SMOs for SOC, polarization voltage and terminal voltage estimation are designed. After that, convergence of the proposed observers is analyzed by Lyapunov's stability theory method. The framework of the designed observer system is simple and easy to implement. The SMOs can overcome the uncertainties of parameters, modeling and measurement errors, and present good robustness. Simulation results show that the presented estimation method is effective, and the designed observers have good performance.