Lithium-ion battery electrochemical model for high-current control applications: extended single particle model

Abstract

Large battery management systems require accurate but simple battery models to meet high performance expectations while maintaining the cell’s safety.In special, Single Particle Models (SPM) are electrochemical models that are usually valid on low current applications. First, the model developed in this study is inspired on the SPM assumption, and it is developed from a volume-averaged partial differential equation (PDE) first-principles electrochemical model to maintain physical significance. Next, empirical algebraic estimators are developed and used to recover the concentration variation over the spatial dimension. A reduced order ESPM (RESPM), composed of ordinary differential equations (ODE), is also developed to be used specifically at control applications.The RESPM contains only four states divided in two de-coupled systems composed of two ODEs each. These models further extend the usable range of SPM by addressing the electrolyte concentration and electrolyte potential variation over space, thus being named Extended SPMs (ESPMs). Using a PDE solver for lithium diffusion over the electrodes, the ESPM and RESPM obtain at least 78.1\% and 60.5\% reduction of the RMS error, respectively, when compared to the SPM using a PDE solver on pulse current simulations (C/4 to 8C). The steady state response, simulated on the range of full discharge/charge at -2C to 2C, also obtains a similar performance for most of the SoC range, with inaccuracies becoming significant only at the end of discharge, where the open-circuit potential functions are highly nonlinear. The RESPM is designed for BMS control and estimation applications for its reduced number of states, and its full ODE nature may employ the vast array of tools already developed for ODE control and estimation. Further improvements of the model may include a treatment for thermal behavior or better development of the estimators used to recover the concentration profiles from average concentration values.