Despite their promising potential, lithium-ion batteries have not witnessed wide adoption in large-scale applications such as electrified propulsion. This is attributed to: a) safety concerns and performance degradation due to aging, and b) lack of a comprehensive understanding of battery behavior. Lithium-ion transport processes are non-linear and span multiple length scales. As such, ion transport can be modeled on a multiplicity of scales. Macroscale battery models describing mass and charge transport are well suited as a reference model for developing model-based control and estimation strategies. The battery research community, for long, has considered the Doyle-Fuller-Newman (DFN) macroscale model [1, 2] as the benchmark to evaluate the predictive ability of reduced-order and simplified electrochemical models. However, macroscale models are approximate representations of micro-scale battery dynamics, and are vulnerable as predictive tools under specific operating conditions. The motivation to pursue this work is driven by the need to develop tools to guide battery researchers on the use of the most appropriate models for predicting battery dynamics. This work specifically identifies the operating temperature conditions that violate the underlying assumptions of the continuum equations of the DFN model, and leads to loss of model predictiveness.

Starting with the Poisson-Nernst-Planck (PNP) micro-scale equations, a multiple-scale expansion is applied to rigorously derive macroscopic equations of mass and charge transport [3]. Physics-based conditions are identified under which classical macroscale models accurately describe lithium-ion micro-scale dynamics with an accuracy prescribed by the homogenization technique. These conditions are represented schematically in the form of phase diagrams. The temperature-dependent dynamics of lithium-ion battery electrodes are examined using the electrolyte phase diagram [4], and the results obtained indicate that standard macroscopic models fail to describe micro-scale processes in batteries that are operated above critical temperature conditions. The results predicted by analytical studies in previous work [4] are confirmed through numerical simulations in the present work. The equations of the full-homogenized macroscale (FHM) model developed in [3] are resolved using the finite element modeling software COMSOL Multiphysics®. Numerical simulations are performed using the FHM model and the DFN macroscale model developed in COMSOL by Plett [5]. The performance of both models is assessed against data from experiments conducted on 18650 cylindrical lithium-ion cells with nickel manganese cobalt oxide cathode at the Battery Aging and Characterization Laboratory at Clemson University.

2A (1 C-rate) constant current discharge experiments are conducted at 5°C, 23°C, 45°C, and 52°C. The measured battery voltage responses are used to assess the predictive ability of the FHM and DFN models. To prevent any bias, the same geometrical and stoichiometric parameters values are used in both models, and kept constant across different temperatures. For each data set, five parameters are identified for both the models as a function of temperature: electrode diffusion coefficients and reaction rate constants, and contact resistance. The results indicate that the DFN model, which predicts battery dynamics accurately at 5°C and 23°C, fails to replicate the same at 45°C and 52°C towards the end of cell discharge. Simulations results for the performance of both models at these temperatures are illustrated in Fig. 1. The FHM model accurately predicts battery response under all temperature conditions. The lack of accuracy of the DFN model at higher temperatures is due to the inability of the electrolyte equations to capture micro-scale dynamics, indicated by a phase diagram study [4]. The outcome of this work will enable the development of physics-based control strategies to prolong battery useful life for battery management system applications.

References

1. Doyle, T. F. Fuller, and J. Newman, “Modeling of galvanostatic charge and discharge of the lithium/polymer/insertion cell”, J. Electrochem. Soc., vol. 140, no. 6, pp. 1526-1533, (1993).
2. Doyle and J. Newman, “The use of mathematical modeling in the design of lithium/polymer battery systems”, Electrochimica Acta, vol. 40, no. 13-14, pp. 2191-2196, (1995).
3. Arunachalam, S. Onori, and I. Battiato, “On veracity of macroscopic Lithium-ion battery models”, J. Electrochem. Soc., vol. 162, no.10, pp. A1940-A1951, (2015).
4. Arunachalam, S. Onori, and I. Battiato, “Temperature-dependent multiscale-dynamics in Lithium-Ion battery electrochemical models”, in Proceedings of the 2015 American Control Conference, pp. 305-310, IEEE, (2015).
5. L. Plett, “Battery Management Systems, Volume I: Battery Modeling”, Artech House, (2015).