Interval Observer for SOC Estimation in Parallel-Connected Lithium-ion Batteries

The internal states of Lithium-ion batteries, notably state of charge (SOC), need to be carefully monitored during battery operation to manage energy and safety. In this paper, we propose an interval observer for SOC estimation in an electrically and thermally coupled parallel connection of cells. This is a particularly challenging problem because mathematically cells in parallel yield a system of differential-algebraic equations (DAE), which are more difficult to handle than ordinary differential equations (e.g. a series string of cells). For a large battery pack with thousands of cells, applying an estimation algorithm on each and every cell would be mathematically and computationally intractable. These issues are tackled using an interval observer based on a coupled equivalent circuit-thermal model. The key novelty lies in considering cell heterogeneity as well as state-dependent parameters as unknown, but with bounded uncertainty. The resulting interval observer maps bounded uncertainties to a feasible set of state estimation, and is independent of the number of cells in parallel. Stability and inclusion of the interval observer are proven and validated through numerical studies.