To estimate the state of health, charge, power, and safety (SoX) of lithium-ion batteries (LiBs) in real time, battery management systems (BMSs) need accurate and efficient battery models. The full-order partial two-dimensional (P2D) model is a common physics-based cell-level LiB model that faces challenges for real-time BMS implementation due to the complexity of its numerical solver. In this paper, we propose a method to discretise the P2D model equations using the Finite Volume and Verlet Integration Methods to significantly reduce the computational complexity of the solver. Our proposed iterative solver uses novel convergence criteria and physics-based initial guesses to provide high fidelity for discretised P2D equations. We also include both the kinetic-limited and diffusion-limited models for Solid Electrolyte Interface (SEI) growth into an iterative P2D solver. With these SEI models, we can estimate the capacity fade in real time once the model is tuned to the cell–voltage curve. The results are validated using three different operation scenarios, including the 1C discharge/charge cycle, multiple-C-rate discharges, and the Lawrence Livermore National Laboratory dynamic stress test. The proposed solver shows at least a 4.5 times improvement in performance with less than 1% error when compared to commercial solvers.

Lithium-ion batteries (LiBs) are used as the main power source in electric vehicles (EVs). Despite their high energy density and commercial availability, LiBs chronically suffer from non-uniform cell ageing, leading to early capacity fade in the battery packs. In this paper, a non-invasive, online characterisation method based on deep learning models is proposed for cell-level SoH estimation. For an accurate measurement of the state of health (SoH), we need to characterize electrochemical capacity fade scenarios carefully. Then, with the help of real-time monitoring, the control systems can reduce the LiB’s degradation. The proposed method, which is based on convolutional neural networks (CNN), characterises the changes in current density distributions originating from the positive electrodes in different SoH states. For training and classification by the deep learning model, current density images (CDIs) were experimentally acquired in different ageing conditions. The results confirm the efficiency of the proposed approach in online SoH estimation and the prediction of the capacity fade scenarios.

The pseudo-two-dimensional (P2D) model is a full-order physics-based model for lithium-ion batteries (LiBs), capable of providing accurate predictions of battery behavior. However, parameterizing the P2D model is complex due to its extensive parameter space, making parameter estimation (PE) particularly challenging. Thus, this research presents a novel, multistage, noninvasive algorithm to efficiently and accurately estimate these parameters. The algorithm operates in three stages. First, it defines essential inputs such as battery chemistry, parameter boundaries, and reference data. The second stage focuses on PE using a unique global-local search strategy. Here, particle swarm optimization (PSO) explores the global parameter space, followed by a novel parallel implementation of simulated annealing (SA) for refined local optimization. Finally, the third stage is a validation process that selects the output parameter set with the lowest prediction error across both estimation and validation stages. The proposed algorithm achieves a root-mean-square error under 17 mV, estimating 18 high-sensitivity parameters with an average error of 30%, and a rapid processing time of 52 min on average—among the fastest on record. This PE algorithm offers researchers and engineers a highly efficient, precise open-source tool for P2D model parameterization, potentially enhancing battery management and performance in practical applications.

Simulated electrochemical impedance spectroscopy (sEIS) is a powerful technique for non-invasive analysis of lithium-ion batteries (LiBs). It virtually replicates experimental EIS by applying small-signal current perturbations to a physics-based LiB model to observe the resulting impedance response, enabling applications like model parameterisation and degradation characterisation. To advance this area of sEIS research, this work proposes a MATLAB-based solver to simulate a full-order physics-based model called the Electrochemical-Ageing-Capacitance (EAC) model. The contributions of this work are threefold. First, the equations of the EAC model are transformed from a set of coupled partial-differential-equations (PDEs) and ordinary-differential-equations (ODEs) into a coupled ODE-only system. Second, a custom-built 'ODE+iterative' solver framework is proposed to accurately and efficiently compute the EAC model equations. To benchmark performance, the solver is compared with state-of-the-art solvers in both MATLAB and PyBaMM. It demonstrates < 1% prediction error for most EAC model variables. When computing sEIS impedance spectra, the solver also achieves a 4x improvement in solving performance compared to MATLAB, and competitive performance compared to PyBaMM. Finally, we present a case study for the use of sEIS, to quantitatively characterise degradation in the EAC model. The solver is provided open-source, offering researchers a validated and efficient tool for high-fidelity sEIS simulations.

Simulated Electrochemical Impedance Spectroscopy (sEIS) is a powerful technique for non-invasive analysis of lithium-ion batteries (LiBs). It virtually replicates experimental EIS by applying small-signal current perturbations to a physics-based LiB model to observe the resulting impedance response, enabling applications like model parameterisation and degradation characterisation. To advance this area of sEIS research, this work proposes a novel solver to simulate a full-order physics-based model called the Electrochemical-Ageing-Capacitance (EAC) model. The contributions of this work are threefold. First, the equations of the EAC model are transformed from a set of coupled partial-differential-equations (PDEs) and ordinary-differential-equations (ODEs) into a coupled ODE-only system. Second, a novel ‘ODE+iterative’ solver framework is proposed to accurately and efficiently compute the EAC model equations. To benchmark performance, the solver is compared with state-of-the-art solvers in both MATLAB and PyBaMM. It demonstrates <1% prediction error for most EAC model variables. When computing sEIS impedance spectra, the solver also achieves a 4x improvement in solving performance compared to MATLAB, and competitive performance compared to PyBaMM. Finally, we present a novel demonstration of using sEIS to quantitatively characterise degradation in the EAC model. The solver is provided open-source, offering researchers a validated and efficient tool for high-fidelity sEIS simulations.