Davide Clerici
The state of charge of lithium-ion batteries reflects the concentration of lithium ions in the respective electrodes. Since this quantity cannot be directly measured during operation, the state of charge can only be inferred through indirect measurements (voltage and current traditionally) and estimation algorithms. This inevitably introduces uncertainty, arising from sensor errors and from the limited accuracy of the algorithms under varying operating conditions. These limitations are particularly severe in chemistries such as LFP, where the flat voltage profile limits the effectiveness of voltage-based algorithms, as well as under conditions where voltage model parameters vary, such as changes in operating temperature or aging. Lithium intercalation induces volumetric changes in the electrodes, leading to measurable thickness variations at the cell level. Since this deformation is directly proportional to lithium concentration, it provides a direct physical proxy for state of charge. Based on these considerations, deformation measurements emerge as a promising alternative for state of charge estimation, especially in conditions where voltage-based methods are less effective. Building on this principle, this work proposes a deformation-based state of charge estimation framework, consisting of an extended Kalman filter capable of processing deformation, voltage, or both signals in a hybrid configuration. A mechanical equivalent circuit model is also introduced to simulate the battery deformation response to current profiles, similarly to conventional electrical circuit models. The proposed methods are validated on commercial LFP, NMC and LCO cells under dynamic stress test and drive cycle conditions. Deformation-based estimation yields slightly higher accuracy (RMSE ≈ 1.7 % ) than voltage-based approaches (RMSE ≈ 2.2 % ), while requiring fewer model parameters. More importantly, it maintains robustness under temperature variations and aging without parameter adaptation, whereas voltage-based estimation suffers significant accuracy loss (RMSE up to 12%) due to resistance changes. The hybrid approach further improves performance by combining both signals when the respective covariances are tuned accordingly. • Battery deformation is proportional to SOC during charge/discharge cycles. • SOC can be estimated through deformation inversion under dynamic conditions. • Hybrid methods provide robust SOC estimates by combining voltage and deformation data. • Deformation measurements improve SOC estimation in lithium-ion batteries. • Deformation-based algorithms improve upon voltage-based ones, especially as cells age.