## Appendix A Impedance Spectra without Superimposed DC-Current  
Other research groups working with lead-acid batteries perform _EIS_ without superimposed DC-currents [6; 8; 9; 19]. Therefore, in addition to the presented impedance spectra recorded with superimposed DC-currents, impedance spectra during resting phases were recorded in the aging tests. During _hard AK3.4, EIS_ measurements were performed at the end of the 5 h resting phases after cycling and after charging.  
In Figure 11, the impedance spectra recorded during _hard AK3.4_ on _TC_1 are presented. The verification of the validity of the impedance values was positive for the first half-circle and a part of the following tail of all impedance spectra. However, the data points, which correspond to the charge-transfer process of the negative electrode, cannot be determined clearly in almost all spectra, as the first half-circle is not well recognizable in the spectra. The reason for this is the shape of the first half-circle, which turns into the tail at higher frequencies than in the spectra with superimposed DC-currents. Only for the spectra recorded after charging and at 90 FCE and higher does the shape of the half-circle allow for a clear determination of the data points corresponding to this process. The number of chosen data points for fitting affects the fitting results. In Figure 12, the spectrum of _TC_1 in _hard AK3.4_ recorded after the cycling phase (90 FCE) is shown three times. In every graph, the measured data points and the calculated impedance values of fitted EEC are presented. Different numbers of data points were used for fitting. In Table 11, the corresponding fitting results for \(R_{ohmic}\), \(R_{ct,neg}\), and \(\tau_{neg}\) are presented.  
\begin{tabular}{c c c c} \hline \hline
**Number. of Data Points** & **20** & **23** & **27** \\ \hline \(R_{ohmic}\) & 3.31 m\(\Omega\) & 3.21 m\(\Omega\) & 3.19 m\(\Omega\) \\ \(R_{ct,neg}\) & 12.76 m\(\Omega\) & 18.72 m\(\Omega\) & 18.49 m\(\Omega\) \\ \(\tau_{neg}\) & 0.53 s & 4.75 s & 4.63 s \\ \hline \hline \end{tabular}  
The determined values for \(R_{ohmic}\) differ by not more than \(0.12\,\mathrm{m}\Omega\), while the difference in the \(R_{ct,neg}\) values is \(6\,\mathrm{m}\Omega\). All values are larger than the values determined from spectra with superimposed DC-currents. Additionally, the values for time constants are larger. With the use of three more data points, the determined time constant changes from \(0.53\,\mathrm{s}\) to over \(4\,\mathrm{s}\).  
Figure 14 shows the spectrum of the same test cell recorded after the charging phase (\(30\,\mathrm{FCE}\)). In Table 11, the corresponding fitting results are denoted.  
For the spectrum in Figure 11, the variations of the \(R_{ct,neg}\) and \(\tau_{neg}\) values are even larger, although the variation in the number of data points is smaller. For 22 points, the value for \(\tau_{neg}\) reached the maximum fitting limit.  
These examples depict the difficulty in the processing of the spectra recorded without superimposed DC-currents. The fitting of the EEC used here is not possible, as a correct number of data points could not be determined. The extension of the EEC to describe the whole recorded spectrum is also not a potential solution here, as none of the half-circles have an adequate shape to be used for distinct fitting. Therefore, these spectra were not further considered in this work, and _EIS_ without superimposed DC-currents is not recommended for _SoH_ estimation methods.