This paper presents a reduced-order electrochemical battery model designed for the online implementation of battery control systems. The model is based on porous-electrode and concentrated-solution theory frameworks and is able to predict voltage as well as the internal electrochemical variables of a battery. The reduction of the model leads to a physics-based one-dimensional discrete-time state-space reduced-order model (ROM), which is especially beneficial for online systems. Models optimized around different operational setpoints are combined to predict cell variables over a wide range of temperatures and state of charges (SOCs) using the output-blending method. A sigma-point Kalman filter is further used to manage inaccuracies generated by the reduction process and experimental-related issues such as measurement error (noise) in the current and voltage sensors. The state-estimation accuracies are measured against a full-order model (FOM) developed in COMSOL. The whole system is able to track the internal variables of the cell, as well as the cell voltage and SOC with very high accuracy, demonstrating its suitability for an online battery control system.

Physics-based electrochemical models of lithium-ion cells require knowledge of electrode open-circuit potential (OCP) as a function of stoichiometry. To determine the OCP relationships for a cell built from unknown active materials, we might run low-rate constant-current laboratory tests on half cells built from harvested electrodes to collect related discharge and charge data. However, processing data from these tests must overcome three problems: the “data-quality problem,” the “missing-data problem,” and the “inaccessible-lithium problem.” This paper introduces a simple histogram-based method to overcome the data-quality problem and compares five different approaches to overcome the missing-data and inaccessible-lithium problems. These methods rely in part on a physics-based thermodynamic model for multiple-species multiple-reaction (MSMR) systems, which is flexible enough to accommodate different cell chemistries and simple enough to be utilized in real-time battery management systems. The five methods are validated in simulations and are then applied to physical half-cell data to produce OCP estimates for graphite and NMC electrodes from a commercial cell.

Battery-management systems require mathematical models of their cells to be able to compute estimates of state-of-charge, state-of-health, state-of-power or -function, and state-of-energy. These models may be empirical in nature, like equivalent-circuit models. Alternately, they may be based on physical principles, and we believe that such physics-based models provide benefits over empirical models in terms of their ability to be leveraged by battery-management-system algorithms to enhance battery safety, lifetime, and performance. A roadblock to using physics-based models is the difficulty in determining their parameter values to model a physical cell accurately and inexpensively. This paper proposes a method to identify a subset of the physics-based model parameter values that can be performed with the kind of equipment found in many battery labs and which does not require teardown of the cell. It applies a very short duration pulse to the cell to measure instantaneous resistance as a function of state of charge and amplitude. These resistances are then fit to a reduced-complexity physical model to determine model parameter values. The method is first applied to a virtual cell in simulation to explore its features and limitations, and is then applied to estimate parameter values for a commercial automotive lithium-ion cell.