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Degradation in lithium-ion cells results from internal mechanisms whose effects can be partially observed through input/output data. In particular, we notice that when a cell experiences calendar aging, its voltage decays over time along with its capacity/power. This work aims to establish a mathematical model to describe these observations. Since calendar-life aging involves both reversible and irreversible aspects, we combine a simple solid-electrolyte-interface (SEI) growth model to describe irreversible lithium loss and a redox-shuttle model to describe reversible loss. We also propose a reduced-order model framework for fast computations. The models are parameterized using six-month self-discharge data gathered at different ambient temperatures from a commercial cell. We find that while SEI growth leads to permanent capacity loss and some voltage decrease, the redox-shuttle can dominate voltage decay during self-discharge. Therefore, it is important to include a redox-shuttle component in a model of voltage decay during calendar-life aging.

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.