Generalised single particle models for high-rate operation of graded lithium-ion electrodes: Systematic derivation and validation

Abstract

A derivation of the single particle model (SPM) is made from a porous electrode theory model (or Newman model) of half-cell (dis)charge for an electrode composed of uniformly sized spherical electrode particles of a single chemistry. The derivation uses a formal asymptotic method based on the disparity between the size of the thermal voltage and that of the characteristic change in overpotential that occurs during (de)lithiation. Comparison is made between solutions to the SPM and to the porous electrode theory (PET) model for NMC, graphite and LFP. These are used to identify regimes where the SPM gives accurate predictions. For most chemistries, even at moderate (dis)charge rates, there are appreciable discrepancies between the PET model and the SPM which can be attributed to spatial non-uniformities in the electrolyte. This motivates us to calculate a correction term to the SPM. Once this has been incorporated into the model its accuracy is significantly improved. Generalised versions of the SPM, that can describe graded electrodes containing multiple electrode particle sizes (or chemistries), are also derived. The results of the generalised SPM, with the arXiv:1907.09410v1 [physics.chem-ph] 26 Jun 2019 correction term, compare favourably to the full PET model where the active electrode material is either NMC or graphite.

DandeLiion v1: An Extremely Fast Solver for the Newman Model of Lithium-Ion Battery (Dis)charge

“…In [11] it has been compared to (vi) an approximate, simplified, reduced-order battery cell model, showing very good agreement between the two different approaches, even for relatively high discharge rates up to around 12C. An example comparison between PyBaMM, experiment and DandeLiion is shown below in §5 and further work [11,22] also verify DandeLiion against other experiments and simulations. The DandeLiion solver works very much faster than: (i) our previous MATLAB implementation of a DFN solver (which is based on ode15s with the analytic Jacobian pattern provided for the solver for increased speed); (ii) the implementation of the model in the Dymola Battery Library [18]; (iii) the implementation in COMSOL Multiphysics [19]; and (iv) than the open source implementation PyBaMM [20].…”

“…For the cross-verification with Dymola, the code was parametrised using the same model and battery properties as described in [21]. In [11] it has been compared to (vi) an approximate, simplified, reduced-order battery cell model, showing very good agreement between the two different approaches, even for relatively high discharge rates up to around 12C. An example comparison between PyBaMM, experiment and DandeLiion is shown below in §5 and further work [11,22] also verify DandeLiion against other experiments and simulations.…”

“…This results in a fivedimensional problem that is extremely compuationally challenging. Various approaches are adopted to reduce the complexity of this problem including equivalent circuit modelling of the cell and more recently systematic (single particle) asymptotic reductions of the DFN model which reduce the dimension of the DFN model by one, see [11,12]. Rather than simplify the model, our approach here is to tailor highly-efficient numerical methods to the DFN model and thereby reduce the computational time to a level that is acceptable for the type of computations that we might wish to perform.…”

Potentiometric MRI of a Superconcentrated Lithium Electrolyte: Testing the Irreversible Thermodynamics Approach

“… 86 Although shorter interelectrode distances reduce the barriers to high-rate operation by raising the mass-transfer-limited current, physics-based simulations similar to the one deployed here have shown that practical cell geometries are susceptible to severe concentration gradients that can swing from the equilibrium composition by ±100% under reasonable power loads. 87 …”

Asymptotic Reduction of a Lithium-Ion Pouch Cell Model

“…This in turn informs practical design choices for key cell parameters (such as current collector thickness or tab placement) in order that the cell discharge uniformly. Our systematic analysis also makes clear that the simplifications are independent of the model used for the through-cell current, so that they can be combined with other through-cell asymptotic simplifications (e.g., reducing the DFN to the single particle model with electrolyte [23,32]) in a systematic and mathematically consistent way. This idea is exploited in [24], in which further model reductions are considered in various interesting and physically relevant limits.…”