Fractional variable-order observer-based method for state-of-charge estimation of lithium-ion batteries

In most fractional-order equivalent circuit models (ECM) of lithium-ion batteries (LIB), the order of the constant phase element is fixed, which usually translates into inaccuracies when describing the strongly nonlinear behavior of the voltage–current (U–I) characteristics of the batteries. In this paper, the problem is addressed by a novel fractional variable-order ECM (FVO-ECM) of LIB, where the order of the capacitor is a function of the state-of-charge (SOC). An improved chaotic adaptive fractional-order particle swarm optimization (CAFPSO) algorithm is designed to identify the FVO-ECM parameters, and its accuracy is verified with different models, parameter identification methods and under sub-zero cold environments. Then, a fractional variable-order observer (FVOO) is proposed for SOC estimation, and the dynamics of the error system are proven to be stable in the sense of Lyapunov. Finally, the proposed SOC estimation scheme is assessed using LIB experimental data, revealing its robustness under different test cycle conditions and temperatures. The experimental results show that the new method can work normally under various test cycles and different temperatures, exhibiting higher accuracy than existing alternative methods. The SOC estimation error is limited to a narrow band of $\pm 0.02$, and the root mean square error (RMSE) can be kept within 1 %. Moreover, the proposed approach can overcome the divergence caused by incorrect initial SOC values and random noise interference, revealing good robustness.