The Influence of Path Dependence on the Degradation of Lithium-Ion Batteries in Electric Vehicles
Authors: Raj Trishna , Howey David Alastair 
Published: February 2020

Gaining understanding into battery ageing is essential, especially for electric vehicles (EVs) where the reliability of the vehicle is dependent on battery performance, capacity and lifetime. Studying the causes of degradation, the conditions that accelerate degradation and the end of life criteria of batteries under realistic EV conditions enables us to make accurate predictions of the lifetime of a cell. During usage, the battery will experience ageing caused by multiple factors, but broadly, these can be grouped into two ageing types: calendar ageing when the cell is at rest and cyclic ageing when it is in use.
Degradation path dependency is the impact on degradation caused by the order in which a cell is exposed to different ageing conditions. The order in which the cell experiences each type of ageing can affect the ageing of a cell by influencing the interactions between degradation mechanisms. Studying path dependency allows us to determine how the interactions between these degradation mechanisms impacts state of health [1].
An experimental study is being conducted which exposes groups of lithium-ion NCA 18650 cells to various blended load profiles consisting of calendar and cyclic ageing in various orders. The ratio of calendar and cyclic ageing in the profiles is constant through the tests to allow comparability between the degradation data collected. The profiles for groups 1 and 3 are designed to expose the cells to 1 day of cyclic ageing followed by 5 days of calendar ageing at C/2 and C/4 respectively. The cells in groups 2 and 4 experience 2 days of cyclic ageing and 10 days of calendar ageing at C/2 and C/4 respectively. The cyclic ageing portion of the profile is conducted using constant current charge/discharge and the calendar ageing portion is conducted at 90% state of charge (SoC). The stress factors that the cell is exposed to are controlled in terms of environmental temperature, depth of discharge, SoC and C-rate. This aims to ensure that the data obtained from this study are an accurate representation of the degradation effects due to path dependency only. Specifically, two groups of cells that are exposed to the same calendar/cyclic ageing in different orders are shown in the supporting image. Although group 1 and group 3 experience the same amount of ageing, the order in which the cell experiences the ageing leads to a difference in state of health in terms of capacity and resistance. The current lifetime estimation models superimpose calendar and cyclic aging however the early indications from the results obtained suggests that path dependency does exist, meaning that existing empirical ageing models may need to be reconsidered or modified in order to account for coupling between different ageing mechanisms [2].
Image Caption: Normalised capacity graphs highlighting the impact of path dependency on capacity fade rate between two groups of cells that are exposed to the same aging conditions in different orders.
[1] M. Dubarry, A. Devie, and K. McKenzie, “Durability and reliability of electric vehicle batteries under electric utility grid operations: Bidirectional charging impact analysis,” J. Power Sources, vol. 358, pp. 39–49, 2017.
[2] M. Schimpe, M. E. von Kuepach, M. Naumann, H. C. Hesse, K. Smith, and A. Jossen, “Comprehensive Modeling of Temperature-Dependent Degradation Mechanisms in Lithium Iron Phosphate Batteries,” ECS Trans., vol. 80, no. 13, pp. 147–170, 2017.

Figure 1