Predicting Local Lithium Plating Based on a Variable Discrete Electro-Chemical Electrode Model
Authors: Hahn Markus , Plank Christian , Mößle Patrick , Danzer Michael A. 
Published: December 2020

Besides the limited driving range of battery electric vehicles, the insufficient fast charging capability of lithium-ion batteries is the major drawback hindering electric vehicles to be fully competitive to combustion vehicles. However, fast charging is kinetically and thermodynamically limited: When the surface potential of the anode particles drops below 0 V vs. Li/Li+, Li-ions will deposit on the particles’ surface instead of intercalating into the active material. Thermodynamically, this lithium plating side reaction starts, when the anode material is fully lithiated and no more lattice sites for ions are available. Kinetically, the sum of charge transfer and diffusive overpotential may be higher than the open circuit voltage (OCV), which also leads to a negative surface potential vs. Li/Li+. The latter is supported by high charging rates and low temperature. This behavior is unavoidable. The limits in which safe operation is possible, can be widened by cell and electrode design.
Identifying and especially approaching these limits without damaging the cell is not trivial. Up to date, 0D equivalent circuit (EC) models are used to predict and control the overpotential to avoid plating in real-time battery management systems (BMS). As these models lack spatial information, e.g. local degree of lithiation within the electrode or the current distribution, these models are inaccurate and cannot provide additional information. To conserve the lifetime of the battery a large safety margin has to be applied, in many cases charge currents might get limited more than actually needed. In contrast, electrochemical models offer 1D to 3D information about degree of lithiation, concentrations, potentials and currents. Furthermore, due to the large number of parameters and variables, these models cannot be parametrized unambiguously and are only valid in a very limited operational range.
As a result, discrete electrochemical models based on a transmission line (TLM) or mixed conducting network structure have become of interest. These models provide spatial information by a distribution of interfacial processes, i.e. charge transfer, solid electrolyte interphase (SEI) and solid-state lithium transport, alongside the current collector’s normal. As displayed in the Figure, these distributed elements are segregated by ionic resistances, while the conductivity of the electrode itself is assumed to be very large. The lithium transport within the particle is described by a TLM as well, consisting of charge dependent voltage sources representing the OCV and diffusion resistances. The model, discretized into n electrode and m particle elements, results in a 2n (m +1)-1-dimensional differential-algebraic equation (DAE) system, which is solved using a linear implicit method. For sufficiently large n and m, the model has been proven to be real-time capable at a sample time of 10 ms. Moreover, with eight parameters, which is the same as in an EC model containing an ohmic resistance, two RC and a Warburg element, it can easily be parametrized in time and frequency domain by pulse and impedance spectroscopy measurement. Hence, this is a large benefit compared to the electrochemical models which also allows the application of the model for a large number of applications.
In this study, we introduce a non-equally distributed discretization, allowing for a high resolution at the separator-electrode-interface, where lithium plating is proven to begin. Simulating the lithiation of a graphite electrode at various charging currents, the sensitivity of the discrete electrochemical model with and without unequally spaced discretization, which could enable an increased precision, is compared to a standard EC model. The time until plating starts and the degree of lithiation is investigated. The influence of the discretization is shown. The non-equally distributed resolution is beneficial as expected as with a constant dimension of the equation system, the precision increases and with constant precision, the equation system may be chosen smaller. The latter is of high interest regarding the application in BMS as a smaller DAE system strongly decreases the computational effort and hence computational time. Compared to the EC, the TLM is significantly more sensitive in detecting local lithium plating, especially at intermediate currents between 1C and 3C which are most relevant for fast charging applications. This is caused by the spatially distributed degree of lithiation, which increases at the separator interface more rapidly than at the current collector interface. Hence, this inhomogeneity leads to different SOCs and OCVs across the electrode and consequently the plating criterion is reached significantly earlier. In future, this model could not only be used for simulation and analysis, but also for battery management: for state estimation and for charge control optimizing the charge time while aging due to lithium plating is avoided.

Figure 1