Identifiability and Parameter Estimation of the Single Particle Lithium-Ion Battery Model

Abstract

This paper investigates the identifiability and estimation of the parameters of the single particle model (SPM) for lithium-ion battery simulation. Identifiability is addressed both in principle and in practice. The approach begins by grouping parameters and partially non-dimensionalising the SPM to determine the maximum expected degrees of freedom in the problem. We discover that, excluding open circuit voltage, there are only six independent parameters. We then examine the structural identifiability by considering whether the transfer function of the linearised SPM is unique. It is found that the model is unique provided that the electrode open circuit voltage functions have a known non-zero gradient, the parameters are ordered, and the electrode kinetics are lumped into a single charge transfer resistance parameter. We then demonstrate the practical estimation of model parameters from measured frequency-domain experimental electrochemical impedance spectroscopy (EIS) data, and show additionally that the parametrised model provides good predictive capabilities in the time domain, exhibiting a maximum voltage error of 20 mV between model and experiment over a 10 minute dynamic discharge. NOMENCLATURE Roman A Electrode surface area, m 2 a i Specific active surface area, m −1 c e Electrolyte lithium concentration, mol m −3 c i Lithium concentration (active material), mol m −3 c 0 i Initial lithium concentration, mol m −3 c max i Maximum lithium concentration, mol m −3 c s iSurface lithium concentration, mol m −3 D i Electrode active material diffusivity, m 2 s −1 F Faraday's constant, C mol −1 H 0 SPM transfer function, Ω H d i Diffusion model transfer function, A −1 I Applied current, A i 0,i Exchange current density, A m −2 j i Reaction rate, mol m −2 s −1 k i Reaction rate constant, m 2.5 mol −0.5 s −1 L j Single DoD loss function, Ω 2 L Combined DoDs loss function, Ω 2 N ω Number of data points per EIS measurement N DoD Number of EIS datasets at different DoDs J-H Kim is with the Energy Lab,

An Asymptotic Derivation of a Single Particle Model with Electrolyte

“…We identify (20) as the dimensionless form of the SPM [15,28]. The name refers to the requirement to only solve a diffusion equation in one particle in each electrode, rather than solving a diffusion equation a particle at every macroscopic point as in the DFN model.…”

“…For these applications and others, physics-based models that are simpler than the DFN model are desired. The simplest of these, the SPM, has been employed in several settings in recent years [10,11,12,13,31]. There has also been a number of papers that provide justification for the SPM and suggest correction terms that may increase the accuracy of the predicted voltage [14,15,16,17,18,19].…”

Optimal Design of Experiments for a Lithium-Ion Cell: Parameters Identification of an Isothermal Single Particle Model with Electrolyte Dynamics

“…On the other side, the parameters identifiability of the SPM has been discussed by e.g. Bizeray et al 20 In this work, the output voltage has been linearized around an equilibrium and the parameters grouped into hyper-parameters that can be experimentally identified. A different simplified electrochemical model has been considered in Schmidt et al, 21 where a Fisher Information approach in combination with a sensitivity analysis has been used to estimate the identifiability of the parameters.…”

“…The structural identifiability and ill-conditioning sources of the DFN model have been analyzed by many authors (see e.g. Bizeray,7 where Table 1.1. reports a summary of the literature on the parameter estimation of electrochemical lithium-ion battery models).…”

Gaussian Process Regression for <italic>In Situ</italic> Capacity Estimation of Lithium-Ion Batteries

“…These Authors approaches have been successfully applied in many studies; however, they all require the provision of an accurate battery model. Moreover, for high fidelity models, parameter identifiability can be a major challenge [15].…”