An adaptive sigma-point Kalman filter with state equality constraints for online state-of-charge estimation of a Li(NiMnCo)O2/Carbon battery using a reduced-order electrochemical model

•A new SOC estimation algorithm based on a reduced-order model is proposed.•An adaptive algorithm with state equality constraints is incorporated.•A comparative study of nonlinear filters show the advantages of the proposed method.•The proposed method is tested in real-time using a battery-in-the-loop test station.•Significant improvements are achieved in reducing the voltage and SOC error. A new SOC estimation method is proposed based on a reduced-order electrochemical model using an adaptive square-root sigma-point Kalman filter (ASR-SPKF) with equality state constraints. The constraints derived from the principle of charge conservation are introduced to improve the accuracy of both anode and cathode SOC estimations. Furthermore, the cathode SOC is estimated to represent the cell SOC for its fast convergence speed, which is due to the high magnitude of the cathode equilibrium potential. Approaches used to adaptively updating the covariance parameters of the filter based on the covariance matching method are also incorporated. As a result, the covariance matrix of process noise is adjusted automatically. Comparative studies of three nonlinear filters concerning estimation accuracy, error bounds, recovery time from an initial offset, and computational time revealed that the ASR-SPKF has the most outstanding performance. That is, 30% more accurate and 88% shorter the convergence time than the AEKF, and, computationally, 23% and 19% faster than the AEKF and ASPKF, respectively. Then, the proposed method was tested at different temperatures using a large-format lithium-ion battery with a nominal capacity of 42 Ah where the voltage and SOC error remained less than 22 mV and 2%, respectively. Finally, the proposed method was implemented in a battery-in-the-loop test station using a fast charging and a driving cycle profile, and the estimated voltage and SOC were compared with the experimental results.