Equivalent circuit models (ECMs) are used widely in the battery and vehicle industry today in battery management systems or for battery system simulation. Low accuracy can cost performance, reduce accuracy in state estimation and influence further parameters in a negative manner. Therefore, one places accuracy goals on the models which are developed.
But of course, there are limits to those accuracy goals since one might overfit, e.g. measurement uncertainty coming from the inputs used to fit the ECM. There is noise and offset on current, voltage, temperature, and the battery capacity, which are all necessary during the fitting process. On top in practical applications, you typically have sampling time, which might limit the dynamics one can fit.

The goal of the work is to quantify the resulting uncertainties in the model’s prediction based on those inputs. The authors apply the principal of the “Guide to the expression of uncertainty in measurement” (GUM) to the problem [1]. Due to the nonlinear behavior of a battery cell a Monte Carlo method is developed employing a P2D model. The quantified uncertainties are then e.g. used to compare reference predictions for typical operating conditions (e.g. quick charge, driving cycles) to decide at which point the measurement setup needs to be improved, before real gains in model quality can be reached or to assess if the results from simulation are able to resolve the desired effects in e.g. system or cell design.

Two examples shall be mentioned here: In the first example a C/3 capacity test with the assumption of standard test equipment results in an accuracy of about 0.8 %. Therefore, measures in the system design resulting in capacity deviations of smaller 1 % are difficult to resolve in simulations. The second example shows how the fitting process of an RC model itself is affected by measurement uncertainty. In a race track simulation the impact of the measurement error during the parameterization process alone results in slightly more than 8 mV uncertainty. Additional errors like temperature gradients or low operating temperatures, insufficient degrees of freedom of RC models compared to P2D models and an insufficient fitting process are coming on top.

This shows that limitations in the modelling process need to be understood better. The measurement equipment used during the parameterization procedures already limits the accessible accuracy in practical applications.

[1] JCGM 100:2008: Evaluation of measurement data – “Guide to the expression of uncertainty in measurement”