Parameterisation of a Coupled Thermal-Electrochemical Model for Lithium-Ion Batteries
Authors: O'Regan Kieran , Kendrick Emma , Widanage Widanalage Dhammika , Brosa Planella Ferran , Chen Chang-Hui , Gastol Dominika 
Published: December 2020

To develop better thermal-electrochemical models of lithium-ion batteries it is essential to obtain parameter sets that accurately describe the system. Parameters sets of commercial cells provide more utility to the research community as they are relevant in real-world applications that consequently require improved battery management systems. However, this proves challenging as the manufacturer reveals little information about the cell or its components. To characterise the electrodes, they must be extracted from the cell in a manner that does not impact behaviour. This has led to the requirement to develop better parameterization strategies. Through cell teardown and a suite of physical, electrochemical, and thermal analytical techniques it is possible to quantify battery behaviour.
The efficacy of our parameterisation strategy has been demonstrated on the M50, a cell manufactured by LG Chem. Through careful teardown and electrochemical testing we were able to show minimal loss in performance. The subsequent post-mortem chemical analysis revealed the composition of this cell to be NMC811 and graphite-SiOx. Geometric parameters including particle size distribution, volume fractions, and tortuosity were evaluated using microscopy. Electrochemical impedance spectroscopy (EIS) and galvanostatic intermittent titration technique (GITT) enabled the determination of the kinetic and thermodynamic properties of each electrode. These properties are influenced significantly by temperature and state of lithiation, though these dependencies are often neglected in modelling due to the scope of most parameter sets available in literature.
To provide new insights into how parameter values change throughout battery operation, their dependency on state of lithiation and temperature was mapped by evaluating their value at various lithium stoichiometries and the related activation energies. State of lithiation has a significant effect on the electrochemical parameters, while models can utilise functions to describe the entropic term, diffusion coefficients, and open circuit voltages, these parameters are still regarded as constant in many simulations as determining these functions requires dedicated experiments. The thermophysical properties of cell components, including current collectors, electrodes, and separator, vary with temperature, mapping these dependencies gives us a better understanding of how heat transport can change within a battery. Describing these relationships for a commercial cell gives modellers a parameter set that can be utilised to simulate cell behaviour with greater resolution than before.
The electrochemical parameter set has been validated using both Doyle-Fuller-Newman (DFN) and single-particle-model with electrolyte (SPMe) model definitions. The validations datasets replicate various scenarios including standardised drive cycles, in each case demonstrating good approximation. The thermal parameters have been validated using a lumped thermal model and simulating the temperature of the cell. Coupling this behaviour with the electrochemical model to evaluate battery discharge at various temperatures.
Relevant electrochemical parameters and their temperature dependencies have been uploaded into the open source software Python Battery Mathematical Modelling (PyBaMM) to provide access to the modelling community; a parameter set that has been determined directly for a commercial cell and validated in various scenarios. This is contrast to literature where parameter sets are often synthesised from various cells – neglecting the compositional and microstructural differences that have significant influence on the resulting electrochemical and thermal properties. This parameter set is becoming more robust over time as parameters are updated and expanded upon to capture new behaviours and cater to new model definitions. Additionally, the methodologies developed here act as a benchmark for accurate and reproducible battery characterisation, irrespective of chemistry or format.