# Identifiability and parameter estimation of the single particle lithium-ion battery model

## TL;DR

This paper analyzes the identifiability and parameter estimation of the single particle model for lithium-ion batteries, revealing only six independent parameters and demonstrating practical estimation from impedance data with good predictive accuracy.

## Contribution

It provides a comprehensive analysis of the model's identifiability and introduces a practical method for parameter estimation from experimental data.

## Key findings

- Only six independent parameters in the model.
- Model is structurally identifiable under certain conditions.
- Estimated model predicts voltage with a maximum error of 20 mV.

## 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.