Model Simplification Techniques for Li-Ion Battery Thermal-Electrochemical Models
Authors: Brosa Planella Ferran , Chen Chang-Hui , Li Liuying , Kendrick Emma , Marco James , Widanage Widanalage Dhammika 
Published: February 2020

The pseudo two-dimensional (P2D) model proposed by Fuller, Doyle and Newman [1] has taken a predominant role in the modelling of lithium-ion batteries. This model gives accurate predictions of the electrochemical behaviour over a wide range of C-rate conditions but requires further development when simulating the cell voltage with temperature dependences, for characterisation or control of batteries. This is mainly due to the complex system of partial differential equations required for the simulation. For this reason, it is important to develop simplified models which capture the relevant features of the physical system but allow faster and simpler simulations.
Here we present an asymptotic reduction and compare model order reduction techniques as one way of model simplification. The asymptotic method allows us to systematically reduce a full P2D thermal-electrochemical model down to much simpler model (in some cases a system of three ordinary differential equations). This method has the advantage of keeping only the phenomena (and thus the parameters) that are relevant and, therefore, provides insight to the experimentalists on which experiments to focus. Within the model reduction methods the residue grouping method is compared with the balance truncation method to reduce the order of a single partial model with electrolyte (SPMe). The residue grouping method can be applied either analytically (from a transcendental transfer function) or numerically (from a finite element model). Residues with similar eigenvalues are grouped together to reduce the model order. The simplified and reduced order model can be used for model based state estimation, and optimal fast charging control. Such simplifications of the model, which are complementary techniques, will also allow more efficient data fitting methods that lead to faster and more accurate characterisations as well as the possibility of running real-time simulations for control purposes.
Obtaining a valid set of parameters is crucial for the model development and validation. One problem the models can suffer is the lack of accuracy in parameters, as values are often obtained from literature, and the experiments are not necessarily designed for the parameterisation of the specific battery of interest. In this work, we have chosen a commercially available cylindrical battery, LG M50, to obtain a full set of parameters, specifically for the asymptotic reduction model. The combination of electrochemical testing together with material characterization provides a powerful tool to understand the physical-chemical properties of the cells. We believe that the methods introduced in this work are not only valuable for the model simplifications developed herein, but will also provide valuable insights to the parameterization of other P2D models.

References:

[1] T. F. Fuller, M. Doyle, and J. S. Newman, “Simulation and Optimization of the Dual Lithium Ion Insertion Cell,” J. Electrochem. Soc., vol. 141, no. 1, pp. 1–10, 1994.