Electrochemical model-based estimation techniques have attracted increasing attention in the past decade due to their inherent insight about the internal battery operating conditions and limits while being able to monitor important li-ion battery states. The applicability of these methods is, however, limited due to the implementation complexity of their underlying models. In order to facilitate online implementation while maintaining the physical insight, a reduced-order electrochemical model is used in this work. This model, which is based on the commonly-used single particle model, is further improved by incorporating the electrolyte-phase potential. Furthermore, an output-injection observer, suitable for online implementation, is proposed to estimate SOC. The observer convergence is proved analytically using Lyapunov theory. Although the proposed observer shows great performance at low C rates, its accuracy deteriorates at high C-rates. To overcome this issue and achieve accurate SOC estimates for such charge/discharge rates, an adaptation algorithm is augmented to the observer. The adaptation algorithm, which can be implemented online, is used to compensate for model uncertainties, especially at higher C rates. Finally, simulation results based on a full-order electrochemical model are used to validate the observer performance and effectiveness.

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