A reduced-order electrochemical model for coupled prediction of state of charge and state of health of lithium ion batteries under constant current-constant voltage charging conditions

Accurate and fast prediction of the remaining useful life of lithium (Li) ion batteries is an important requirement for successful electrification of automobiles. Consequently, there is a growing interest in the development of reduced-order models. The existing reduced-order electrochemical models can be used to predict battery performance (state of charge [SoC], terminal voltage) when the current through the battery is known a priori. Therefore these models cannot be used for studying the constant voltage (CV) mode of the constant current-CV (CC-CV) charging protocol, which is a common battery charging mechanism. In this work, we propose a reduced-order electrochemical model to estimate the battery SoC under CC-CV charging conditions, along with an analytical expression to approximate the CV mode charging time. We further propose a framework that accounts for the influence of the battery state of health (SoH) on the battery SoC during an operating cycle and vice-versa. The proposed framework for estimating the battery SoC and SoH in a coupled manner shows good comparison with a first principles electrochemical model for CC-CV charging conditions. This model can be used to study battery ageing and it can find applications in real-time state estimation, charge protocol optimization, and battery design.