Novel Table-based Kalman Filter for State of Charge Estimation of Batteries

This paper considers the problem of state of charge (SOC) estimation in rechargeable batteries. Traditionally, the SOC is estimated based on quantifiable measures such as current, voltage, or both. The current and voltage-based approaches are, in general, susceptible to several uncertainties as well as practical limitations. Meanwhile, the fusion of both approaches through nonlinear filtering techniques tends to preserve respective benefits and improves the overall SOC estimation process. However, there are no general solutions to the nonlinear filtering problem but only sub-optimal approximations, which compels the selection of appropriate filter to be a concern while designing SOC algorithms. Additionally, practical implementation of filter-based approaches would require high-precision storage systems to store the model parameters. For restrictive computational scenarios, the round-off errors could induce numerical instabilities. Therefore, this paper presents a novel table-based Kalman filter (TKF) that describes the usual nonlinear functional relationship between the open-voltage voltage (OCV) and the SOC through inflection points of the OCV-SOC curve. The table-based approximation is advantageous as the system model can be described linearly in terms of the table components. The resulting linear system model would allow us to apply the Kalman filter directly rather than its computationally expensive nonlinear variants. The results show that a 16-point table can have a maximum error of approximately 0.01. Further, it highlights that the TKF with 32 points has a comparable error performance to the state-of-the-art nonlinear filtering approach.