## 3 Results and Discussion
### Implications from EIS Parameter Fitting  
With the DRT analysis two processes were identified. The faster process with an initial time constant of \(<\)12.4 ms was attributed to the first semi-circle of the ZARC element. It is detectable as a peak distribution between 100 Hz and 1 Hz of the relaxation time distribution function as depicted in Figure 7. This frequency range is equal to the one stated by [11] for the negative electrode. The second process is represented by the larger peak between 1 Hz and 0.1 Hz and should be mainly influenced by the positive electrode. It would be associated with the RC-element of the representative EEC even though a RC-element would deliver a single peak in the DRT. For both processes, it can be said that with proceeding operation time the time constant increases, which means that the process is slowed down. The resulting fit for \(\tau_{\text{ct,NAM}}\) is depicted in Figure 8.  
Furthermore, the corresponding resistance of the processes increases. This development is also evident for the relative increase of \(R_{\text{ct,NAM}}\) of the ZARC element, which is depicted in Figure 8 as well as the increasing inner resistance \(R_{\text{i}}\). Similar to the impedance reading at about 1 kHz the fitted internal resistance \(R_{\text{i}}\) decreases first and then increases by 8.28 to 13.4%. The relative increase of the fitted \(R_{\text{ct,NAM}}\) is even strong then for \(\mid\!\!\!Z\!\mid\) at 0.1 Hz. The RC-element with higher time constants cannot be fitted reliably as some impedance values at lower frequencies are not meeting the zHit criterion and thus a fit was not always possible.  
Interestingly, the capacitance of the first process is first increasing. This could be an indication for the aforementioned run-in effect with an additional formation of the active mass.  
The increase of \(R_{\text{ct,NAM}}\) and \(\tau_{\text{ct,NAM}}\) would be an indication for water loss. The strong increase at the beginning could be associated with an imperfect recombination cycle. As the efficiency of this cycle increases with a lower saturated AGM the increase rate of the two parameters slows down.  
Figure 6: Increase of the normalized impedance \(\mid\!\!\!Z\!\mid\) measured at four different frequencies (1 kHz, 78 Hz, 10 Hz and 0.1 Hz) with superimposed DC current over time of the test for all check-ups of battery 2-014 of String 2.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Battery No.** & **String No.** & \begin{tabular}{c} **1 kHz μEIS** \\ **-120 DC** \\ \end{tabular} & \begin{tabular}{c} **78 Hz μEIS** \\ **-120 DC** \\ \end{tabular} & \
\begin{tabular}{c} **10 Hz μEIS** \\ **-120 DC** \\ \end{tabular} &
\begin{tabular}{c} **0.1 Hz μEIS** \\ **-120 DC** \\ \end{tabular} \\ \hline
2-014 & 2 & \(+\)5.05\% & \(+\)6.45\% & \(+\)14.23\% & \(+\)30.75\% \\
2-018 & 2 & \(+\)8.42\% & \(+\)10.82\% & \(+\)16.99\% & \(+\)35.45\% \\
2-024 & 2 & \(+\)11.09\% & \(+\)13.51\% & \(+\)17.50\% & \(+\)39.26\% \\
3-004 & 3 & \(-\)1.00\% & \(+\)0.001\% & \(+\)3.11\% & \(+\)16.91\% \\
3-008 & 3 & \(+\)14.13\% & \(+\)15.07\% & \(+\)14.45\% & \(+\)21.96\% \\ \hline \hline \end{tabular}
\end{table}
Table 5: Summary of relative change of the impedances registered by the μEIS over 568 days at different frequencies for all investigated batteries.