Combination of Stochastic State Estimation with Online Identification of the Open-Circuit Voltage of Lithium-Ion Batteries

Abstract

Typical equivalent circuit models for Lithium-ion batteries are represented in the form of the so-called Thévenin form. These models comprise a state of charge (SOC) controlled voltage source as well as lumped elements such as series resistances as well as at least one RC subnetwork to describe dynamic effects by the terminal current and voltage as input and output of the battery. In classical state estimation approaches, these characteristics are assumed to be identified beforehand, while aging of battery cells is related to a loss of the total capacity, changes in the charging/discharging efficiency, an increase of the Ohmic cell resistance, and/or changes of the time constants of the above-mentioned RC networks. Such variations can be estimated by means of additional parameters that are included in the system's state vector. However, the typically applied approaches do not allow for a direct identification of the nonlinear dependencies of the circuit elements on the SOC and other influence factors such as currents or the cell temperature. Therefore, this paper proposes a real-time capable, two-stage identification of these dependencies on the example of the open-circuit voltage by means of an Unscented Kalman Filter (UKF) approach. In the first stage, the state variables of the dynamic system model are estimated together with a lumped disturbance term (an additive correction of the open-circuit voltage). In the second stage, this disturbance term is used to correct the a-priori knowledge of the open-circuit voltage and to simultaneously express the identification quality in terms of covariances for the coefficients of its piecewise polynomial approximation in each temporal discretization step. The efficiency of the proposed methodology is demonstrated in simulations for an experimentally validated system model.