Analysis of the Uncertainty of EIS Battery Data Fitting to an Equivalent Circuit Model

In this work an analysis of the uncertainty on electrochemical impedance spectroscopy (EIS) of batteries is presented. Four-wire impedance measurements are performed by using a low-complexity and low-cost approach. EIS data are fitted to an equivalent circuit model through a non-linear least-square regression algorithm. Two equivalent circuit models, with 6 and 9 parameters respectively, are scrutinized. The 9-parameters model is chosen as being more accurate. The uncertainty on extracted parameters is evaluated as the sample standard deviation over repeated measurement of the complex impedance, and by error propagation on the least-square estimator for each observation of a single impedance curve. Results of both approaches are compared, and even though there is a significant difference, they are shown to be equivalent for all practical purpose, i.e. for a hypothetical online battery monitoring system testing a battery when it is in use, extracting equivalent circuit parameters and their uncertainty from a single observation. Also the uncertainty is estimated for three different values of the injected current. The high relative uncertainty on some of the parameters suggests a sensitivity of the model restricted to a limited set of the parameters. The analysis of the sensitivity is left as an open problem for future investigations.