Accelerated battery lifetime simulations using adaptive inter-cycle extrapolation algorithm

Abstract

We propose algorithms to speed up physics-based battery lifetime simulations by one to two orders of magnitude compared to the state-of-the-art. First, we propose a reformulation of the Single Particle Model with side reactions to remove algebraic equations and hence reduce stiffness, with 3x speed-up in simulation time (intra-cycle reformulation). Second, we introduce an algorithm that makes use of the difference between the `fast' timescale of battery cycling and the `slow' timescale of battery degradation by adaptively selecting and simulating representative cycles, skipping other cycles, and hence requires fewer cycle simulations to simulate the entire lifetime (adaptive inter-cycle extrapolation). This algorithm is demonstrated with a specific degradation mechanism but can be applied to various models of aging phenomena. In the particular case study considered, simulations of the entire lifetime are performed in under 5 seconds. This opens the possibility for much faster and more accurate model development, testing, and comparison with experimental data.

Differential voltage analysis for battery manufacturing process control

“…The differential voltage analysis method may be repeated on full cell voltage datasets collected over the course of a cycle life or calendar aging test for the aged cell system. Taking { Q′ n , Q′ p , Q′ Li } to be model outputs from the aged cell, the following familiar quantities can be defined (Sulzer et al, 2021):…”

“…In this equation, the first two terms represent lithium trapped inside lithiated but electrically-isolated positive and negative electrode particles, the third term represents the lithium trapped in the negative electrode SEI (Sulzer et al, 2021), and the last term represents dead lithium lost to lithium plating (Yang et al, 2017). It is important to recognize that differential voltage analysis cannot be used to decompose Q Li or LLI into their constituent parts.…”

"Knees" in lithium-ion battery aging trajectories

“…87,88 A richer picture emerges in models that capture the shifts in electrode stoichiometry with cycling. Lin et al 26 and Kindermann et al 90 89 Initially, all variables (LLI, LAM ne , and LAM pe ) increase linearly with cycle number. Around cycle 600, the maximum stoichiometry in the positive electrode reaches unity, i.e., the electrode saturates.…”

“…Electrode saturation causes a knee in the capacity curve despite nearly linear rates of LAM and LLI. Note that LAM ne and LAM pe do not directly correspond to LAM of lithiated or delithiated electrode sites; see Sulzer et al 89 for more information.…”