Electrochemical-Thermal Tanks-in-Series Models for Lithium-Ion Batteries

Abstract

The safe and efficient operation of lithium-ion batteries assumes substantial significance with their increasing prevalence in electric transportation and grid-scale storage.1,2 To this end, mathematical models play a critical role in predicting battery state and dynamics, which informs optimization and real-time control strategies. 3 Prediction of thermal dynamics is key to ensure safe operation, in view of deleterious phenomena such as overheating, non-uniform capacity degradation, and potential thermal runaways.4,5 The choice of battery model is typically a trade-off between physical detail and computational speed, due to which various reduced-order and reformulated models have been employed. Reduced order battery models are typically based on the Single Particle Model (SPM) and other simplifications of macrohomogeneous electrochemical models with lumped descriptions of thermal dynamics.1,6,7 This restricts their accuracy to specific operating regimes and parameter combinations. Reformulated models for coupled electrochemical-thermal dynamics have been demonstrated, but computational efficiency is likely to be compromised for certain form factors, cycling simulations, and large cell stacks.4,8 Moreover, parameterization of these models is a non-trivial task. The tanks-in-series approach was introduced previously as being more accurate than SPM, but easier to parameterize than reformulated models.9 This work extends the isothermal tanks-in-series model to incorporate thermal effects. Energy balances based on porous electrode theory10, including heat conduction and generation terms, are volume-averaged for each region in a cathode-separator-anode sandwich. The original tank model is thus augmented by an energy balance equation in each region, containing source terms and interfacial heat fluxes that are approximated accordingly. Voltage-time and temperature predictions from this model are evaluated against a one-dimensional electrochemical-thermal model under different operating conditions. The impact of different flux approximations on prediction accuracy is also examined, in addition to performance in simulating different series-parallel configurations. An additional goal is the application of the volume-averaging methodology to cylindrical cells, characterizing accuracy and computational performance vis-à-vis both full-order and lumped models. Acknowledgements The authors acknowledge financial support from the Battery500 Consortium. Financial support from the Department of Chemical Engineering and the Clean Energy Institute at the University of Washington is also acknowledged. References H. E. Perez, S. Dey, X. Hu, and S. J. Moura, Proc. Am. Control Conf., 2016–July, 4000–4005 (2016).M. Pathak, D. Sonawane, S. Santhanagopalan, R. D. Braatz, and V. R. Subramanian, ECS Trans., 75, 51–75 (2017).T. R. Tanim, C. D. Rahn, and C.-Y. Wang, J. Dyn. Syst. Meas. Control, 137, 011005 (2014).S. Kosch, Y. Zhao, J. Sturm, J. Schuster, G. Mulder, E. Ayerbe, and A. Jossen, J. Electrochem. Soc., 165, A2374–A2388 (2018).K. E. Thomas and J. Newman, J. Electrochem. Soc., 150, A176–A192 (2003).C. Forgez, D. Vinh Do, G. Friedrich, M. Morcrette, and C. Delacourt, J. Power Sources, 195, 2961–2968 (2010).M. Guo, G. Sikha, and R. E. White, J. Electrochem. Soc., 158, A122–A132 (2011).P. W. C. Northrop, V. Ramadesigan, S. De, and V. R. Subramanian, J. Electrochem. Soc., 158, A1461–A1477 (2011).A. Subramaniam, S. Kolluri, C. D. Parke, M. Pathak, S. Santhanagopalan, and V. R. Subramanian, Meet. Abstr., MA2019-01, 1157–1157 (2019).K. Kumaresan, G. Sikha, and R. E. White, J. Electrochem. Soc., 155, A164–A171 (2008).