Properly Lumped Lithium-ion Battery Models: A Tanks-in-Series Approach

Abstract

This article introduces a lumped electrochemical model for lithium-ion batteries. The governing equations of the standard ‘pseudo 2-dimensional’ (p2D) model are volume-averaged over each region in a cathode-separator-anode representation. This gives a set of equations in which the evolution of each averaged variable is expressed as an overall balance containing internal source terms and interfacial fluxes. These quantities are approximated to ensure mass and charge conservation. The averaged porous domains may thus be regarded as three ‘tanks-in-series’. Predictions from the resulting equation system are compared against the p2D model and simpler Single Particle Model (SPM). The Tanks-in-Series model achieves substantial agreement with the p2D model for cell voltage, with error metrics of <15 mV even at rates beyond the predictive capability of SPM. Predictions of electrochemical variables are examined to study the effect of approximations on cell-level predictions. The Tanks-in-Series model is a substantially smaller equation system, enabling solution times of a few milliseconds and indicating potential for deployment in real-time applications. The methodology discussed herein is generalizable to any model based on conservation laws, enabling the generation of reduced-order models for different battery types. This can potentially facilitate Battery Management Systems for various current and next-generation batteries.

An Efficient Electrochemical Tanks-in-Series Model for Lithium-Sulfur Batteries

“…In the tank model, each region is approximated as a tank connected in series. Previously, our group has developed and validated this approach for Lithium-ion batteries 20 , and one of the key differences and challenges is the dynamic porosity within lithium sulfur batteries. The equations are spatially integrated over the two regions, the cathode and the separator.…”

Lithium Plating Detection Methods in Lithium-Ion Batteries

“…White has applied various methods such as orthogonal decomposition [133] , state-space reformulation [134,135] , reducing the system of partial differential equations to ordinary differential equations [135,136] , and applying polynomial representations of the Li ion concentration in the solid phase [137] . In recent years, the popularity of these models [138][139][140][141][142][143][144][145][146][147][148][149] has increased due to their relative speed and accuracy.…”

A Model Predictive Control Scheme for Fast Charging via Accurate Quadratic Battery Models

“…Other researchers have modeled the cathode, anode, and separator as tanks in series, allowing for inference of lumped internal states while maintaining low computational complexity for multiple chemistries. [29], [30] Additionally, the equivalent hydraulic electrochemical model has been used in conjunction with a reference governor to develop a fast charging strategy [31]. Nevertheless, these models, which contain 10 ordinary differential equations, still require substantially more computational power than a comparable ECM, and thus have not seen wide adoption.…”