This contribution presents the results of our recent publication [1]. Capacity and internal resistance are key properties of batteries determining energy content and power capability. However, they change over time due to battery aging, hence requiring a reliable diagnosis. We present a novel algorithm (see Figure 1) for estimating the absolute values of capacity and internal resistance from operando voltage and current data. The algorithm is based on voltage-controlled models (VCM) [2]: Experimentally-measured voltage is used as input variable to an equivalent circuit model (see Figure 2). The simulation gives current as output, which is compared to the experimentally-measured current.
We show that capacity loss and resistance increase lead to characteristic fingerprints in the current output of the simulation. In order to exploit these fingerprints, a theory is developed for calculating capacity and resistance from the difference between simulated and measured current. The findings are cast into an algorithm for operando diagnosis of batteries operated with arbitrary load profiles.
The algorithm is demonstrated using cycling data from 20 Ah NMC/graphite lithium-ion pouch cells operated on full cycles, shallow cycles, and dynamic cycles typical for electric vehicles. Capacity and internal resistance of a “fresh” cell was estimated with high accuracy (mean absolute errors of 0.9 % and 1.8 %, respectively) (see Figure 3). For an “aged” cell, the algorithm required adaptation of the model’s open-circuit voltage curve in order to obtain high accuracies.
As overall conclusion, we show that the diagnosis of battery capacity and internal resistance is possible with high accuracy using a novel and numerically simple algorithm based on voltage-controlled models.

[1] W. G. Bessler, “Capacity and resistance diagnosis of batteries with voltage-controlled models,” J. Electrochem. Soc. 171, 080510 (2024), https://doi.org/10.1149/1945-7111/ad6938 . Research data on Zenodo, https://zenodo.org/doi/10.5281/zenodo.10965654
[2] J. A. Braun, R. Behmann, D. Schmider, and W. G. Bessler, „State of charge and state of health diagnosis of batteries with voltage-controlled models,“ J. Power Sources 544, 231828 (2022), https://doi.org/10.1016/j.jpowsour.2022.231828, research data on Zenodo, https://doi.org/10.5281/zenodo.6817725