Joint Estimation of Open Circuit Voltage and Equivalent Circuit Model Parameters Using State-Space Model Optimization

Open circuit voltage (OCV) of the battery is the difference in potential between its positive and negative electrodes. Accurate estimation of OCV during battery usage is crucial for battery management tasks such as state of charge (SOC) estimation, state of power (SOP) estimation, etc. A vast majority of the existing approaches propose to model battery SOC estimation as a nonlinear state estimation problem; these approaches use nonlinear filtering techniques such as the extended Kalman filter (EKF) or particle filter (PF) to estimate SOC. The battery parameters in the nonlinear state-space model also need to be estimated, and are most often combined as a joint estimation problem with SOC. The drawback of using nonlinear filters is that a general solution does not exist, and only sub-optimal approximations will result. Further, nonlinear state estimators also suffers from numerical instabilities in practical applications and tend to diverge over time. The unknown nature of the model parameters makes the problem worse and may fast lead to faster divergence during the estimation process. This paper presents a novel approach to recursively estimate the OCV through a linear state-space formulation. The linearity in the state-space enables the application of the optimal Kalman filter to estimate the desired state, i.e., OCV of the battery. The model parameter estimation is derived as a constrained least-squares estimation problem by making use of the Hamiltonian function. The benefit of the proposed approach is that optimal solution is achievable for this joint state and parameter estimation problem.