Efficient high-fidelity modeling of a nickel-rich silicon-graphite cell enabled by optimal spatial distribution

The development of high-fidelity battery models with a unique set of parameters remains challenging, especially when considering operation at various C-rates as well as relaxation periods, which becomes more complex in the case of cells with silicon-graphite blended anodes. In this paper, we present a general reduced-order modeling framework that allows including blended electrodes, a particle size distribution, and self-heating, based on a discrete transmission line model. The optimal number of spatial nodes in each electrode is determined to be 6 for both electrodes, thereby challenging the volume averaging hypothesis. A particle size distribution is required to match the slower relaxation response observed experimentally; however, self-heating and spatial distribution are also shown to contribute to a faster effective relaxation at higher C-rates. The proposed model provides highly accurate results when validated against experimental data: below 15 mV Root Mean Square (RMS) for discharges from C/2 up to 2C followed by relaxation, below 13 mV RMS for charges at C/2 and 1C, and below 0.35 ∘C RMS for cell temperature in all cases. Finally, the potential risk of lithium plating is discussed, suggesting that the presence of silicon may lead to an earlier onset thereof. In summary, the importance of an appropriate description of spatial distribution is demonstrated for an accurate modeling of a commercial Nickel Manganese Cobalt/Si-Gr (NMC/Si-Gr) cell.