A fractional-order model for calendar aging with dynamic storage conditions

Due to the increasing importance of lithium-ion batteries in electric vehicle and renewable energy applications, battery aging is a subject of intense research. Although many laboratory experiments are performed under well-controlled static conditions, batteries are stored and operated under varying conditions of temperature and state of charge in their real-life performance, so that a suitable model for predicting the effects of calendar aging in lithium-ion batteries with dynamic conditions is highly desirable. In this paper, we review previous models to calculate capacity loss due to calendar aging under variable temperature and state-of-charge conditions according to experimentally observed power-law behavior, and propose a novel model based on fractional calculus. To validate the new model, we compare its predictions with experimental results showing that it can reproduce the non-monotonic behavior that is observed when the state of charge or the temperature change significantly. This is an interesting application of fractional calculus since this characteristic is not obtained with non-fractional models.