Assessment of Hysteresis Models for LiFePO4
Authors: Triebl Robert , Wurzenberger Johann Christian 
Published: August 2024

The selection of the cathode material is an important task in the design phase of batteries for mobile applications. One material of increasing interest is LiFePO4 (LFP) due to its improved energy density, good thermal stability and durability. In contrast to other commonly used cathode materials, LFP features a clear phase separation between the lithium rich and the lithium poor phase, leading to a pronounced voltage plateau over wide ranges of state of charge (SOC). The level of this plateau also changes for charge and discharge operation, even at very low C-rates. This voltage hysteresis in combination with the wide plateau gives some ambiguity to the correlation between voltage and SOC, which is a challenge for battery management systems. Thus its correct description is crucial if a cell model is meant to serve as virtual twin supporting control function development and calibration. Beyond that, a highly dynamic battery development process requires models that run significantly faster than real-time and parametrization processes which allow for accurate validation and easy adaptation to modified electrodes. A simulation approach complying with these requirements is the electrochemical pseudo-two dimensional (P2D) model, though adaptions to the core model are needed to appropriately capture hysteresis-affected voltage plateau characteristics for phase-separating materials such as LFP.
The goal of this study is to extend an existing P2D framework with two approaches capable of describing hysteresis effects and analyzing these extensions regarding result plausibility, computational cost and effort of parametrization. The first model of interest is based on the one-state hysteresis model proposed by Plett. This approach allows for fast simulation and accurate reproduction of the charge and discharge voltages at low C-rates but lacks deeper physical consideration of the phase-separating origin of the hysteresis and thus might lose accuracy to predict system responses on dynamic pulses. In this approach, the voltage hysteresis is not a simulation result, it is due to the input of two separate open circuit voltages for charge and discharge. The second model of interest applies variable solid diffusion (VSSD) featuring a reduced Fickian diffusion coefficient in the plateau region. Lower diffusion at a given C-rate leads to steeper concentration gradients between lithium rich and lithium poor phase. With this approach, effective phase boundaries within the representative particles can be obtained. In the limiting case, when the Fickian diffusion coefficient becomes zero or even negative at some lithium concentration, phase separation persists also when no current is applied. In this setting, the voltage hysteresis at low C-rates is an emergent phenomenon, it is not an input. The physical basis of the approach also allows to consider mechanical stresses and their impact on the voltage gap between charge and discharge. Concentration gradients cause a mismatch of volume demands and thus lead to local stresses, which in turn alter the chemical potential.
Results emphasizing advantages and disadvantages of the two hysteresis models are presented. Charge and discharge simulations are performed for several C-rates and the voltage hysteresis is extrapolated to infinitely small currents. Furthermore, the effect of resting phases with zero current as in Galvanostatic Intermittent Titration Technique measurements is discussed. As hysteresis models are often tested only on charge/discharge cycles with constant currents over large SOC regions, the responses of the simulation models are also assessed in pulse tests and dynamic profiles giving a realistic picture of automotive applications. Here special focus is put on energetical aspects of the one-state model and on intra-particle concentration profiles for the VSSD model.