How does model reduction affect lithium-ion battery state of charge estimation errors? theory and experiments

This article examines the impact of unmodeled dynamics on the accuracy of model-based lithium-ion battery state of charge (SOC) estimation. The article is motivated by the need for accurate SOC estimation for online battery diagnostics and control. Reduced-order battery models can lessen the computational cost of online SOC estimation. However, this comes at a price: model reduction is known to cause an estimation bias, in addition to the estimation noise typically induced by sensor measurement noise. This article derives analytic expressions for the expected estimation bias for two lithium-ion battery models: a nonlinear equivalent circuit model (ECM), and a nonlinear electrolyte enhanced single particle model. This derivation assumes a least squares SOC estimation law, but can be extended to other estimation laws. The article validates the analytic SOC estimation error expressions using both Monte Carlo simulation and experiments, for two different commercial lithium-ion batteries: a LiFePO₄ battery and a LiNi_xCo_yMn_zO₂ battery. The end result is, to the best of the authors’ knowledge, the first body of experimentally-validated analytic expressions for the expected SOC estimation errors resulting from lithium-ion battery model reduction.