Modeling lithium-ion batteries

Lithium-ion batteries dominate the rechargeable battery market. Their main advantage is their unrivalled energy density, which is constantly evolving. This translates into extended autonomy for the devices they power, from portable electronics to electric vehicles. The evolution of energy density is due to the development of ever more efficient positive electrode materials, mainly made of cobalt, nickel, manganese oxides or iron phosphate and, to a lesser extent, the addition of silicon to the graphite making up the negative electrode.

The second major advantage of lithium-ion batteries is their long service life, compared with that of older water-based technologies. Their third advantage is their ability to deliver high levels of power, enabling the electrification of ground transportation (scooters, cars, trains, etc.).

However, there are also some dark spots. The biggest problem is undoubtedly the safety of goods and people, which can be compromised in the event of manufacturing defects or misuse that could generate smoke, fire or explosion. The cost remains high, due to the criticality of certain materials (cobalt, nickel, lithium) and the complex manufacturing processes required to guarantee user safety. Finally, recycling also remains an area for improvement.

Mathematical modeling of batteries has a history of over half a century. Its aim is to predict their performance by testing hypotheses and theories and comparing them with experimental data. Testing is costly, and having a tool capable of predicting results, without having to test the batteries, means that production can be carried out faster and at lower cost. The approach presented in this article is "multiphysical", i.e. based on different scientific disciplines such as thermodynamics, physics and electrochemistry. There are also empirical and electrical models, as well as more modern tools based on artificial intelligence.

However, we will be concentrating exclusively on a multiphysics approach, as this is the only way to understand the operation of the accumulator and thus optimize it. It also offers the possibility of interpolation and extrapolation, without risk, of accumulator performance at operating points for which we have no validation data.

The modeling of lithium-ion batteries is very rich, as there are as many models as there are applications. Such an undertaking requires a prior acquaintance with the theoretical considerations valid for all batteries. Indeed, we quickly get into more advanced theoretical concepts whose complexity is matched by their effectiveness in representing the properties of these unusual batteries. This is the reason why, despite a fairly extensive modelling community worldwide, there is still...