Batteries are electrochemical energy storage devices that exhibit physico-chemical heterogeneity on a continuity of scales. As such, battery systems are amenable to mathematical descriptions on a multiplicity of scales that range from atomic to continuum. In this paper we present a new method to assess the veracity of macroscopic models of lithium-ion batteries. Macroscopic models treat the electrode as a continuum and are often employed to describe the mass and charge transfer of lithium since they are computational tractable and practical to model the system at the cell scale. Yet, they rely on a number of simplifications and assumptions that may be violated under given operating conditions. We use multiple-scale expansions to upscale the pore-scale Poisson-Nerst-Planck (PNP) equations and establish sufficient conditions under which macroscopic dual-continua mass and charge transport equations accurately represent pore-scale dynamics. We propose a new method to quantify the relative importance of three key pore-scale transport mechanisms (electromigration, diffusion and heterogenous reaction) by means of the electric Péclet (Pe) and Damköhler (Da) numbers in the electrolyte and the electrode phases. For the first time, applicability conditions of macroscopic models through a phase diagram in the (Da-Pe)-space are defined. Finally, we discuss how the new proposed tool can be used to assess the validity of macroscopic models across different battery chemistry and conditions of operation. In particular, a case study analysis is presented using commercial lithium-ion batteries that investigates the validity of Newman-type macroscopic models under temperature and current rate of charge/discharge variation. Predictive understanding of battery dynamical behavior still remains a major bottleneck in achieving diagnostic capabilities, safety, optimization and control of battery systems under different operating conditions. Such a difficulty arises from two main factors: i) nonlinearity of lithium-ion transport processes 1 and ii) battery systems multiscale structure that exhibits physicochemical heterogeneity on a continuity of scales (from the nanometer to the meter).2-5 Since the seminal work by Newman and Tiedemann, 6 where macroscopic ion transport equations were first formulated, a plethora of models have spurred in the past decades. They range from fully empirical approaches to generalizations of electrochemical models based on the porous electrode theory to account for concentrated solutions, 7,8 thermal effects 9 and capacity fade due to Solid-Electrolyte Interphase (SEI)-growth, [10][11][12] just to mention a few. In the past decade, ever increasing computational capabilities have fuelled the development of fully molecular/atomistic models and multiscale/multiphysics approaches. 13 For a thorough review on the topic, we refer the reader to Ref. 4. Microscale models 14,15 (e.g. molecular dynamics, kinetic Monte Carlo and pore-scale models) are theoretically robust, but are impractical as a predictive tool at t...

Control-oriented models based on electrochemistry have conventionally been evaluated and designed from the Doyle-Fuller-Newman (DFN) macroscale model. However, the DFN model is susceptible in predicting battery response under certain operating conditions since it is an approximate representation of pore-scale dynamics. This work shows the limitations of the DFN model in predicting voltage response at high temperatures of cell operation. A full homogenized macroscale (FHM) model, developed in previous research, is shown to overcome these limitations. Results indicate that the predictability of the DFN model deteriorates when trying to predict the voltage response at low state of charge for high temperature of operation under 1 C-rate discharge. The influence of parameters on the model states and output is investigated as a means to address parameter identifiability issues, for which, we formulate and resolve sensitivity functions for the partial differential equations (PDEs) of the FHM model. Results show that parameter identifiability is dependent on the battery state of charge.

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