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This paper presents the current state of mathematical modelling of the electrochemical behaviour of lithium-ion batteries as they are charged and discharged. It reviews the models developed by Newman and co-workers, both in the cases of…

Chemical Physics · Physics 2020-02-04 Giles W Richardson , Jamie M Foster , Rahifa Ranom , Colin P Please , Angel M Ramos

Electrochemical Impedance Spectroscopy (EIS) is a non-invasive technique widely used for understanding charge transfer and charge transport processes in electrochemical systems and devices. Standard approaches for the interpretation of EIS…

Silicon anodes promise high energy densities of next-generation lithium-ion batteries, but suffer from shorter cycle life. The accelerated capacity fade stems from the repeated fracture and healing of the solid-electrolyte interphase (SEI)…

Chemical Physics · Physics 2022-12-01 Lars von Kolzenberg , Arnulf Latz , Birger Horstmann

This work presents analytical solutions for the current distribution in lithium-ion battery packs composed of cells connected in parallel, explicitly accounting for the presence of interconnection resistances. These solutions enable the…

Systems and Control · Electrical Eng. & Systems 2025-08-21 Jaffar Ali Lone , Nilsu Atlan , Simone Fasolato , Davide M Raimondo , Ross Drummond

This study presents a comprehensive Multiphysics model for zinc-ion batteries (ZIBs), incorporating electrochemical aspects. The model integrates the mass transport of Zn2+ ions, charge transfer, and solid diffusion to predict performance…

Materials Science · Physics 2025-05-06 Roya Rajabi , Shichen Sun , Booker Wu , Jamil Khan , Kevin Huang

When participating in electricity markets, owners of battery energy storage systems must bid in such a way that their revenues will at least cover their true cost of operation. Since cycle aging of battery cells represents a substantial…

Optimization and Control · Mathematics 2017-07-27 Bolun Xu , Jinye Zhao , Tongxin Zheng , Eugene Litvinov , Daniel S. Kirschen

Reliable early detection of lithium-ion battery degradation requires health indicators that are physically interpretable and computable from routine cycler telemetry without access to the degradation region. We introduce…

Materials Science · Physics 2026-05-19 Dieter W. Heermann , Hagen Heermann

Lithium-ion batteries exhibit nonlinear voltage dynamics across varying operating conditions and aging states, making accurate modeling essential for estimation, control, and health monitoring. This work compares two data-driven frameworks…

Systems and Control · Electrical Eng. & Systems 2026-05-05 Khalid Mahmud Labib , Inayat Rasool , Shabbir Ahmed

The cycling performance of lithium-ion batteries is closely related to the expansion effect of anode materials during charge and discharge processes. Studying the mechanical field evolution of anode materials is crucial for evaluating…

Instrumentation and Detectors · Physics 2024-07-04 Kaijun Liu , Zhijuan Zou , Guolu Yin , Yingze Song , Zeheng Zhang , Yuyang Lou , Zixuan Zhong , Huafeng Lu , Duidui Li , Tao Zhu

Cycle life is critically important in applications of rechargeable batteries, but lifetime prediction is mostly based on empirical trends, rather than mathematical models. In practical lithium-ion batteries, capacity fade occurs over…

Chemical Physics · Physics 2012-11-27 Matthew B. Pinson , Martin Z. Bazant

The reliability, lower computational complexity, and ease of implementation of control observers make them one of the most promising methods for the state estimation of Li-ion batteries (LIBs) in commercial applications. To pave their way,…

Systems and Control · Electrical Eng. & Systems 2024-12-03 Muhammad Saeed , Arash Khalatbarisoltani , Zhongwei Deng , Wenxue Liu , Faisal Altaf , Shuai Lu , Xiaosong Hu

Non-destructive determination of lithium distribution in a working battery is key for addressing both efficiency and safety issues. Although various techniques have been developed to map the lithium distribution in electrodes, these methods…

Modeling of Li-ion cells is used in battery management systems (BMS) to determine key states such as state-of-charge (SoC), state-of-health (SoH), etc. Accurate models are also useful in developing a cell-level digital-twin that can be used…

Systems and Control · Electrical Eng. & Systems 2024-05-27 Abhijit Kulkarni , Ahsan Nadeem , Roberta Di Fonso , Yusheng Zheng , Remus Teodorescu

The state of health (SOH) estimation plays an essential role in battery-powered applications to avoid unexpected breakdowns due to battery capacity fading. However, few studies have paid attention to the problem of uneven length of…

Machine Learning · Computer Science 2021-09-29 Kate Qi Zhou , Yan Qin , Billy Pik Lik Lau , Chau Yuen , Stefan Adams

Distributions of potential and lithium content inside lithium ion batteries highly affects their performance and durability. An increased heterogeneity of the lithium distribution is expected in thick electrodes with high energy densities…

Modeling lithium-ion battery (LIB) degradation offers significant cost savings and enhances the safety and reliability of electric vehicles (EVs) and battery energy storage systems (BESS). Whilst data-driven methods have received great…

Machine Learning · Computer Science 2025-01-22 James Sadler , Rizwaan Mohammed , Michael Castle , Kotub Uddin

Accurate assessment of lithium-ion battery ageing is challenged by cell-to-cell variability, heterogeneous cycling protocols, and limited transferability of data-driven models across datasets. In particular, robust identification of…

Machine Learning · Computer Science 2026-04-21 Agnieszka Pregowska , Stefan Marynowicz

Under mechanical abuse conditions, the failure of lithium-ion batteries occurs in various stages characterized by different force, temperature and voltage response which require it's in-situ measurements for analysis. Firstly, four sizes of…

Materials Science · Physics 2023-07-06 Vishesh Shukla , Ashutosh Mishra , Jagadeesh Sure , Subrata Ghosh , R. P. Tewari

We present a porous electrode model for lithium-ion batteries using Butler--Volmer reaction kinetics. We model lithium concentration in both the solid and fluid phase along with solid and liquid electric potential. Through asymptotic…

Applied Physics · Physics 2019-06-03 Iain R. Moyles , Matthew G. Hennessy , Timothy G. Myers , Brian R. Wetton

Batteries are ubiquitous today, with applications ranging from smartphones, watches, and laptops to electric cars, drones, and electric aircraft. Lithium-ion batteries are widely used in these applications due to their high energy density,…

Computational Engineering, Finance, and Science · Computer Science 2026-03-03 Vikram C Patil