Pulse Polarization for Li-Ion Battery under Constant State-of-Charge: Part II. Modeling of Individual Voltage Losses and SOC Prediction

Abstract

A Li-Ion battery, as most batteries, is an unsteady state system. In order to generate polarization curves under constant state of charge (SOC), an experimentally tedious task, we used a pulse discharge method where the initial SOC was adjusted such that at the end of the pulse and during the relaxation the SOC is pre-determined and constant. In this paper the pulse discharge data were simulated using Newman's model, allowing the identification of individual overpotentials under various discharge times, C-rates, and SOC. The agreement between the model and experimental results allowed the construction of pulse polarization curves (PPC) and the identification of individual overvoltages: charge transfer kinetics, ionic mass transport, and solid-state diffusion. The pulse polarization curves converged by the 240 seconds pulse discharge, forming a quasi steady-state polarization curve for the battery, which can be used to determine the SOC of a battery by measuring its steady voltage and current density. In electric cars this method can resolve the driver's range anxiety associated in accurately determining the SOC, especially at low SOC. In a previous paper, 1 we experimentally explored the pulse dis-charge method in Lithium Ion Battery (LIB) and the ability to gener-ate pulse polarization curves (PPC) from that data at discrete states of charge (SOC) and various pulse durations. As mentioned 1 studying battery voltage vs current density 1–6 remains difficult, in part since the SOC changes as the battery is used. Previous work experimen-tally evaluates a voltage vs current density relationship at a constant SOC. 1 In this paper, we use the Newman model 2,3 and COMSOL Multiphysics 4,5 to expand predictions about PPC behavior as pulse times increase reaching pseudo steady state polarization. Bernardi and Go 6 also utilized a pulse discharge method to gather data and a similar model to analyze the performance and voltage evolution, and the modeled results matched very well with their experimental data. In contrast, this work compared the voltages at the end of the pulse discharge and after the battery had returned to an equilibrium at rest state. This allowed us to expand the SOC testing to 10%, 40%, and 70%, from previously reported 6 range of 35% and 65%. Additionally, this model relied on fewer calculated parameters, and could only fit the kinetic rate constant and diffusion in the active particles of the electrode materials. While this involved more experimental results for a battery archetype, the resulting model was usable over a wider range of SOC and performance scenarios than previously demonstrated. This allowed the study of what conditions would allow a battery to achieve a quasi steady state, which is useful for performance analysis and SOC prediction. From a conceptual point of view, a short pulse discharge exhibits voltage losses most attributed to charge transfer kinetic and ohmic losses. As the pulse discharge times increase, the voltage losses in-creasingly depend on the Li + concentration gradient forming first in the electrolyte, and then during Li solid-state diffusion. Therefore, it is expected that the PPCs generated from discrete pulse discharge times will converge once these lithium concentration gradients have been fully formed. As pulse duration increases the unsteady state PPC approaches a quasi steady state polarization curve. The advantage of a computer model based on experimental data includes being able to quickly predict cell performance and its SOC across a wide range of conditions. The modeling of these conditions requires minutes or