Parametric estimation of arbitrary fractional order models for battery impedances⁎

Electrochemical impedance spectroscopy (EIS) is a widely-used non-invasive technique for estimating the impedance of a battery from current and voltage measurements. While EIS is commonly used as a nonparametric, purely data-driven estimation method, this article proposes a parametric, physics-informed alternative. As an underlying parametric model, we use an equivalent circuit model for the battery impedance with a Warburg element to model the low-frequency diffusion. This fractional order impedance model is linear in all the parameters except one, namely the fractional order itself. Hence, we present a separable total least squares estimator, which first eliminates the linear parameters using their total least squares solution, and then minimises the resulting nonlinear least squares problem over the fractional order. Measuring multiple periods of the signals allows to weigh the problem with the noise variances, thus making the estimation consistent. The parametric estimation method is validated on simulations and applied to measurement data of commercial Samsung 48X cells.