A linear framework for low-complexity SoC estimation in lithium-ion batteries validated with real data

The use of lithium-ion batteries requires careful monitoring, especially regarding the estimation of key internal parameters. Among these, the state of charge (SoC) is particularly important since it cannot be measured directly, requiring the development of reliable estimators. Model-based approaches are widely used for this purpose, with equivalent circuit models (ECMs) being especially popular due to their ability to intuitively represent battery dynamics using electrical analogs. Despite their low complexity, ECMs typically exhibit nonlinear output equations that must be properly handled to ensure accurate estimation. In this context, the present work proposes a SoC estimator based on a second-order ECM with a linearized output. The proposed formulation is derived from an immersion-based transformation that increases the system order, yielding in a model with a linear output and state-affine dynamics containing a current-dependent parameter. The main difference in this approach is that the basis transformation exactly converts the originally non-linear system into a linear parameter varying (LPV) model. This allows the use of low-complexity estimators for estimating the SoC, such as the classic Kalman filter in this work. An observability analysis is conducted to guarantee estimation convergence, and a Kalman Filter (KF) is designed for SoC estimation. Results using real data obtained in an electromobility use case demonstrate that the proposed approach achieves a root mean square error (RMSE) below 1.2% under different initial conditions.