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

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 nondimensionalising the SPM to determine the maximum expected degrees of freedom in the problem. We discover that excluding open-circuit voltage (OCV), there are only six independent parameters. We then examine the structural identifiability by considering whether the transfer function of the linearized SPM is unique. It is found that the model is unique provided that the electrode OCV functions have a known nonzero 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 data, and show additionally that the parametrized model provides good predictive capabilities in the time domain, exhibiting a maximum voltage error of 20 mV between the model and the experiment over a 10-min dynamic discharge.