Lithium-ion batteries are the dominant electrochemical energy storage device and are a key enabler of portable electronics and electric vehicles. However, the technology is often criticized for its use of rare metals. Extending the lifetime of lithium-ion batteries can allow for more time to develop rare metal recycling efforts but this requires accurate knowledge of the battery's state-of-health.

The state-of-health is affected by degradation mechanisms that cause a fade in capacity and power over time, which eventually leads to end-of-life. A common way to track capacity fade is to compare state-of-charge values with changes in charge across a time period. The change in charge can be found by accumulating current, while state-of-charge can be tracked using estimation frameworks that use equivalent circuit models to mirror battery behavior. These models require a relationship between state-of-charge and open-circuit voltage to link the cell's internal state with the observed voltage. However, establishing this relationship is a time-consuming process.

Furthermore, the battery voltage partly depends on the direction of current, i.e. whether the battery is being charged or discharged. This hysteresis effect is highly nonlinear and persists when no current is applied. In past lithium-ion cell chemistries, voltage hysteresis was often neglected but recent developments have introduced silicon doping, which improves energy density, leading to a higher range for electric vehicles, but also increases the magnitude of the hysteresis effect. This degrades the accuracy of model-based estimation frameworks that neglect hysteresis. To improve state-of-charge estimation accuracy for silicon-doped cells, battery models can be extended with additional complexity to match the effect of hysteresis and improve the accuracy of state estimates.

This work combines the Plett hysteresis model with a single RC-pair equivalent circuit, the RC-H model, and uses a joint unscented Kalman filter to identify model parameters and estimate the state-of-charge during different dynamic testing profiles performed on an NMC/Si-C lithium-ion battery. A second version of the model replaces the predetermined OCV function with a simplification of the SOC-OCV relationship that is adaptively estimated using the Kalman filter, the A-RC-H model. Both models are benchmarked against a single RC-pair model, with a predetermined SOC-OCV relationship and no hysteresis component.

The results show that the RC-H model produces lower SOC errors, but comes at the cost of additional complexity and lower robustness to initial SOC error. While the A-RC-H model produces reasonable SOC estimations and can reconstruct the main OCV trend, the RMSE and MAE are only close to the RC model when the initial SOC error is small.

Future work could be aimed at understanding typical initial SOC errors and uncertainties in practical scenarios, improving the filter tuning by adapting noise covariances online, and reducing computational cost by separating states and parameters into two filters running at different frequencies. Furthermore, the different frameworks should be combined with capacity estimation methods to confirm the hypothesis that higher SOC accuracy leads to improved estimation accuracy of the total capacity.