Application of Variable-Order Fractional Calculus to the Modeling of Calendar Aging in Lithium-Ion Batteries

Abstract

Battery aging is one of the key challenges that electrochemical energy storage faces. Models for both cycling and calendar aging are valuable for quantitatively assessing their contribution to overall capacity loss. Since batteries are stored and employed under varying conditions of temperature and state of charge in their real-life operation, the availability of a suitable model to anticipate the outcome of calendar aging in lithium-ion batteries under dynamic conditions is of great interest. In this article, we extend a novel model to predict the capacity loss due to calendar aging by using variable-order fractional calculus. For this purpose, some theoretical difficulties posed by variable-order definitions are discussed and compared by applying them to fit experimental results with a multi-parameter optimization procedure. We show that employing a variable-order model allows for a significant improvement in accuracy and predictive ability with respect to its constant-order counterpart. We conclude that variable-order models constitute an interesting alternative for reproducing complex behavior in dynamical systems, such as aging in lithium-ion batteries.