Computational modelling of lithium ion batteries for electric vehicle applications: analysis, design and implementation

Abstract

The realisation of Physics-Based Models (PBMs) of lithium ion cells in the Battery Management Systems (BMSs) of electric vehicles is studied through a three-pronged strategy – analysis, design and implementation. The survey of literature undertaken in the backdrop of this broad landscape reveals a dearth of model-based designs for automotive-grade pouch cells, which is therefore addressed in this work. Perusal of prior art in reduced-order battery modelling provides key guidance on topics meriting further investigation viz. the Discrete-Time Realisation Algorithm (DRA) scheme and the electrolyte-enhanced Single Particle Model (SPM) which are therefore carefully analysed here from the perspective of their embedded implementation. Owing to its familiarity and wide-spread popularity among relevant stakeholders, the Pseudo Two-Dimensional (P2D) implementation of the Doyle-Fuller-Newman (DFN) model is used as the PBM underpinning all research presented herein.

A computational framework to optimise the number of electrochemical layers within a pouch cell is developed. The chosen optimality criterion specifically addresses the two most pertinent issues that currently hinder the mass-market adoption of electric vehicles – range anxiety and fast charging. Driven by the need for a balanced capacity loading at both electrodes, a deterministic criterion for computation of electrode thicknesses is formulated. The search space of layer choices across all thermal scenarios is traversed with the least operation count through a novel application of the binary search algorithm. Numerical simulations of a lumped thermal model coupled with the P2D electrochemical model in conjunction with judiciously chosen exit conditions help to inform the number of layers needed to maximise the cell's usable capacity whilst simultaneously satisfying the power requirements of fast charging. The P2D model is reformulated to accord it with the innate ability to accept power inputs. The model-led optimal layer design procedure thus developed is plating-aware, facilitating the extension of pack lifetimes whilst helping to bypass expensive empirical prototyping.

Owing to its simplicity, the SPM family of models is deemed to be the most promising Reduced Order Model (ROM) candidate that can usher in the use of PBMs in electric vehicles. An in-depth analysis of the SPM reveals an inherent mismatch between the accuracies of its voltage and State of Charge (SOC) predictions, thereby rendering it unsuitable as the plant model in state-estimation tasks. A comprehensive evaluation of the salient electrolyte-enhanced SPMs from literature reveals that most solutions are either mathematically intractable or overly simplistic. For the ionic concentration in the electrolyte, analysis of the quadratic approximation model, which straddles the boundary between computational complexity and mathematical tractability, reveals a poor temporal performance particularly at the current collector interfaces. However, it is capable of delivering acceptable levels of accuracy in computing the spatial profile of ionic concentration. Application of the Multi-Gene Genetic Programming (MGGP) technique exposes that the causal factor for this mediocre temporal performance is the equation deficiency of the underlying P2D model.

From an implementation perspective, the discrete-time formulation of SPMs is presented using the matrix exponential approach and its advantages over its continuous-time counterparts enumerated. Despite its inherent shortcomings, it is deemed that operating within the confines of the well-established foundations of the P2D dynamics represents a definitive step forward in bringing into fruition the goal of incorporating PBMs into vehicular BMSs. Therefore, the existing quadratic approximation model is retained for the electrolyte spatial concentration, whilst advocating the novel application of a system identification method for its temporal dynamics. After establishing linearity and time-invariance of the subsystems under consideration, discrete-time transfer functions of the number of moles per unit area of lithium ions in each electrode region is identified for the pertinent range of applied currents. The identified transfer functions are then employed in a composite SPM which demonstrates superior accuracy compared to the incumbent state of the art electrolyte-enhanced SPM, thereby demonstrating a substantial accomplishment from an implementation viewpoint. Although the advancements herein are reported for an isothermal implementation of the models, future enhancement through thermally coupled model derivations is advocated. Finally, the importance of parametrisation of the underlying PBM is acknowledged as a crucial unsolved aspect which needs the collective effort of the battery research community.