ESE Seminar – Venkat Subramanian: “Model-based Battery Management Systems – Where Solvers Fail”

Abstract
Fast charging is being heavily researched for the widespread implementation of lithium-ion batteries for electric vehicles. However, charging at high currents accelerates several parasitic reactions that lead to the degradation of the cell, affecting its lifetime. It is possible to study material degradation mechanisms and predict their impact on capacity loss under several operating conditions using physics-based multi-scale battery models. These models can be integrated with battery management systems (BMSs) to control the cell’s performance and to design novel charging protocols that enable safe and optimal cell performance and suppress cell degradation. Our group has successfully applied BMS2,3 based on a physics-based battery model to improve life and reduce charging time for different batteries (as shown in Figure 1). This seminar will present some results from our group for cells, modules, and packs. The talk will also include the theoretical development of pulse profiles as predicted by optimal control of phase-field models.4

Figure 1: Implementation of MPC in batteries.

Model-based BMS algorithms require fast and efficient production codes that can predict and estimate battery parameters in real-time and control the battery’s performance under different loads. The theory is reasonably well developed and defined for one or all of (a) ordinary differential equations (ODEs), (b) elliptic partial differential equations (PDEs) with homogenous boundary conditions, and (c) well-conditioned linear equations. Solvers, optimizers, and software have been well developed for the same by optimizing/utilizing one or all of (a) high-performance computing, (b) GPU acceleration, (c) adaptive time stepping, (d) adaptive mesh refining, (e) estimation, (f) parallel computing, (g) efficient Jacobian/Hessian/adjoint calculation, and (h) sparse linear algebra. When physics-based models are taken to BMS – solvers and optimizers can (and often) fail. A Google search (aided by Generative AI) on “where solvers fail” returns four common scenarios (not all of them are accurate or relevant).
1. Numerical issues & convergence issues – Inaccurate/inconsistent models, stiff problems, inconsistent problems, tolerances, nonunique solutions, mesh quality.
2. Model complexity & structure – High nonlinearity, rigid body motion, unconstrained bodies, missing contacts/fixtures.
3. Solver-related issues – Limitations, bugs/errors, infeasible solutions.
4. Other-potential issues – Results/folder permissions, corrupt study, installation issues.
Our efforts to alleviate some of these issues for battery models will be presented. Challenges, benefits, and pitfalls of disguising Differential Algebraic Equations (DAEs)5 as ODEs, advective phase-field/level set PDEs as elliptic PDEs,6 unconstrained optimization problems as constrained optimization problems, immersed-interface approach to solving moving boundaries, multi-phase problems will be presented.
Bio
Professor Venkat R. Subramanian is currently the Ernest Dashiell Cockrell II Professor of Mechanical Engineering and Materials Science Engineering at the University of Texas at Austin. Subramanian is an elected ECS Fellow and is a past elected chair of the IEEE Division of the Electrochemical Society. He is also a former elected technical editor of the Electrochemical Society, and a former elected chair of Area 1e: (Electrochemical Engineering) of AIChE.
Subramanian’s group aims to be visible in the area of model-based Battery Management System (BMS) and model-based design of current and next-generation energy storage devices. He is a co-founder and CTO of Battgenie Inc., a student startup aiming to commercialize model-based BMS algorithms.
Disclaimer & References
1. https://wheresolversfail.blogspot.com/. Venkat hopes to write (update) and maintain a blog on “Where Solvers Fail.” He plans to write a book on this topic. The title is inspired by the movie “Where Eagles Dare” (without any political affiliation). The importance/relevance/pitfalls of disguise and deception carry over to simulation/optimization and control of electrochemical systems and batteries.
2. M. Pathak, D. Sonawane, S. Santhanagopalan, R. D. Braatz, and V. R. Subramanian, “Analyzing and Minimizing Capacity Fade through Optimal Model-based Control – Theory and Experimental Validation”, ECS Trans., 75 (23), 51-75 (2017).
3. S. B. Lee, R. S. Thiagarajan, V. R. Subramanian, and Simona Onori, “Advanced Battery Management Systems: Modeling and Numerical Simulation for Control”, 2022 American Control conference (ACC), Atlanta, USA, June 8-10, 2022.
4. T. K. Telmasre, A.C. Concepción, S. Kolluri, L. Mishra, R.S. Thiagarajan, A.N. Matam, A. Subramaniam, T.R. Garrick, and V. R. Subramanian, “Perspective—Moving Next-Generation Phase-Field Models to BMS Applications: A Case Study that Confirms Professor Uzi Landau’s Foresight”, J. Electrochem. Soc., 171, 063507 (2024).
5. L. Petzold, “Differential/Algebraic Equations are not ODE’s”, SIAM Journal on Scientific and Statistical Computing 3 (3), 367 (1982).
6. T. Jang, L. Mishra, S. A. Roberts, B. Planden, A. Subramaniam, M. Uppaluri, D. Linder, M. P. Gururajan, J. Zhang, and V. R. Subramanian, “BattPhase—A Convergent, Non-Oscillatory, Efficient Algorithm and Code for Predicting Shape Changes in Lithium Metal Batteries Using Phase-Field Models: Part I. Secondary Current Distribution”, J. Electrochem. Soc., 169, 080516 (2022).