Accounting for the Effects of Probabilistic Uncertainty During Fast Charging of Lithium-ion Batteries

TL;DR

This work tackles the problem of fast charging Li-ion batteries under probabilistic uncertainty in ambient temperature and model parameters within the Porous Electrode Theory framework. It employs non-intrusive polynomial chaos expansion to efficiently propagate uncertainty across $24$ input parameters, constructing a surrogate model that enables rapid assessment of degradation risks under a CC-CV charging strategy. A key finding is that ambient temperature and 11 of the parameters dominate degradation-related constraints (voltage, temperature, lithium plating), and that probabilistic analysis can reveal constraint violations that nominal analyses miss; Monte Carlo verification confirms the surrogate's accuracy while offering substantial computational savings. The study demonstrates how adjusting charging constraints, such as $V_{ ext{max}}$ or the CC-CV transition timing, can reduce the probability of degradation while maintaining fast charging, providing a scalable framework for robust, probabilistic charging protocols.

Abstract

Batteries are nonlinear dynamical systems that can be modeled by Porous Electrode Theory models. The aim of optimal fast charging is to reduce the charging time while keeping battery degradation low. Most past studies assume that model parameters and ambient temperature are a fixed known value and that all PET model parameters are perfectly known. In real battery operation, however, the ambient temperature and the model parameters are uncertain. To ensure that operational constraints are satisfied at all times in the context of model-based optimal control, uncertainty quantification is required. Here, we analyze optimal fast charging for modest uncertainty in the ambient temperature and 23 model parameters. Uncertainty quantification of the battery model is carried out using non-intrusive polynomial chaos expansion and the results are verified with Monte Carlo simulations. The method is investigated for a constant current--constant voltage charging strategy for a battery for which the strategy is known to be standard for fast charging subject to operating below maximum current and charging constraints. Our results demonstrate that uncertainty in ambient temperature results in violations of constraints on the voltage and temperature. Our results identify a subset of key parameters that contribute to fast charging among the overall uncertain parameters. Additionally, it is shown that the constraints represented by voltage, temperature, and lithium-plating overpotential are violated due to uncertainties in the ambient temperature and parameters. The C-rate and charge constraints are then adjusted so that the probability of violating the degradation acceleration condition is below a pre-specified value. This approach demonstrates a computationally efficient approach for determining fast-charging protocols that take probabilistic uncertainties into account.

Figures (5)

• Figure 1: Schematic of the uncertainty propagation during fast charging.
• Figure 2: Total Sobol' indices for three degradation conditions for 2.2C CC-CV charging: (a) voltage, (b) temperature, (c) lithium-plating overpotential.
• Figure 3: Nominal values and CI for three degradation conditions in 2.2C CC-CV: (a) voltage, (b) temperature, (c) lithium-plating overpotential. QoI comparison by MC and PCE at 600 seconds: (d) voltage, (e) temperature, (f) lithium-plating overpotential.
• Figure 4: Nominal values and CI for three degradation conditions in 2.0C CC-CV (V$_{\max}$ = 4.08 V): (a) voltage, (b) temperature, (c) Li-plating overpotential.
• Figure 5: Probability distribution and by and at 800 seconds in 2.0C charging.