Mathematical Modelling of a Lithium-Ion Battery in Steady-State Charge and Discharge Modes

This paper describes a mathematical model of a lithium-ion battery based on the Shepherd equation, and presents the results of its validation; describes a methodology for calculating the equation coefficients, and presents the results of experimental studies; provides coefficient adjustments for both the discharge and charge characteristics of the batteries. The work outlines the applicability limits of the described methods, and steps to ensure sustainability and scalability models. The aim of this study is to develop a simulation mathematical model of a lithium-ion battery, followed by verification using experimental data obtained during electric vehicle battery testing on a discharge-charge bench. A mathematical model of a battery will enable developers to conduct computational studies and analyse electric vehicle systems at the design stage. The simulation model is created using the MATLAB & Simulink software suite. Experimental studies are conducted using a measuring rig to record the discharge and charge characteristics of batteries. The novelty of this work lies in using a combined calculation method based on the Shepherd equation with additional coefficient adjustments to improve the convergence of the calculated and experimental data. The obtained results of convergence between the described method and the experiment (standard deviation < 0.02 V) indicate the high level of the model development and the appropriately selected calculation methods. The presented mathematical equation for the voltage dependence of a lithium-ion battery with known current characteristics on the current and the methods for calculating the coefficients of this equation can be used by engineers and developers specializing in modelling AC batteries of different application. Since the classical Shepherd equation does not account for temperature limitations, changes in internal resistance, and other battery parameters during discharge and charge, the developed mathematical model requires individual approaches to a battery type, which is expressed in correcting coefficient equation and its modifications. The presented mathematical battery model with calculated coefficients is convenient and sufficiently accurate basis for simulating lithium-ion battery operation in steady-state operating modes.