Comparison of Li-ion battery degradation models for system design and control algorithm development

Within electrified vehicle powertrains, lithium-ion battery performance degrades with aging and usage, resulting in a loss in both energy and power capacity. As a result, models used for system design and control algorithm development would ideally capture the impact of those efforts on battery capacity degradation, be computationally efficient, and simple enough to be used for algorithm development. This paper provides an assessment of the state-of-the-art in lithium-ion battery degradation models, including accuracy, computational complexity, and amenability to control algorithm development. Various aging and degradation models have been studied in the literature, including physically-based electrochemical models, semi-empirical models, and empirical models. Some of these models have been validated with experimental data; however, comparisons of pre-existing degradation models across multiple experimental data sets have not been previously published. Three degradation models, a 1-d electrochemical model (AutoLion ST, or ALST), a semi-empirical model (from the National Renewable Energy Laboratory) and an empirical model (published in the literature), are compared against three published experimental data sets for a 2.3-Ah commercial graphite/LiFePO
₄
cell. The results show that the physically-based model is best able to capture results across all three representative data sets with an error less than 10 %, but is 24× slower than the empirical model, and 4000× slower than the semi-empirical model, making it unsuitable for powertrain system design and model-based algorithm development. Despite being computationally efficient, the semi-empirical and empirical models, when used under conditions that lie outside the calibration data set, exhibit up to 60% error in capacity loss prediction. Such models require expensive experimental data collection to recalibrate for every new application. Thus, in the author's opinion, there exists a need for a physically-based model that generalizes well across operating conditions, are computationally efficient for model-based design, and simple enough for control algorithm development.