Analytical Model Based Prediction of State-of-Charge (SoC) of a Lithium-Ion Cell under Time-Varying Charge/Discharge Currents

Abstract

Real-time State of Charge (SoC) estimation of a Li-ion cell is necessary for an accurate estimation of the state of the cell, and to ensure safety and efficient performance by avoiding overcharge or overdischarge. While past papers have presented analytical models for predicting voltage and SoC for constant-current conditions, there is a need for analytical models that account for time-varying charge/discharge currents representative of realistic conditions. This paper presents an analytical SPM-based model to predict the terminal voltage and SoC of a Li-ion cell operating under a general time-dependent current profile. Concentration distributions in the positive and negative electrodes are determined analytically using Green’s function approach, followed by determination of the electrode voltages as functions of time using the Butler–Volmer kinetic equation. The analytical model is validated through good agreement with numerical simulations and past experimental data for a number of different operating conditions. Cell voltage and SoC are predicted for a variety of time-varying currents, including drive cycles representative of realistic driving conditions. It is expected that the analytical model developed here will help improve the performance of battery management systems by obtaining more accurate information about the internal state of the cell in realistic charge/discharge conditions.