## 3 Results
### Analysis of Cell Behaviour  
After finishing the pre-tests and the reference schedules using a similar-sized cell and a calorimetric test alternative, the decisive test matrix covering the SOC and temperature dependency was carried out. This involved repeating the standard test procedure at the different cell states, investing five SOCs, starting at a minimum value of 20% and increasing \begin{table}
\begin{tabular}{l c c} \hline \hline  & **46 Ah HP Cell** & **60 Ah HE Cell** \\ \hline Time constant \(\tau\) [s] & 2092 & 2312 \\ Thermal conductivity \(\lambda_{\perp}\) [W/(m\(\cdot\)K)] & 0.47 & 0.40 \\ Specific heat capacity \(\zeta_{p}\) [J/(g\(\cdot\)K)] & 1.25 & 1.09 \\ Specific heat capacity reference test \(\zeta_{p}\) [J/(g\(\cdot\)K)] & 1.23 & 1.19 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Resulting data for the 46 Ah and the 60 Ah cell at \(T_{amb}\) = 25 \({}^{\circ}\)C and SOC = 50%. Figure 9: Comparison of the Nyquist plot for different cell types at the same conditions (\(T_{amb}\) = 25 \({}^{\circ}\)C, SOC = 50% and \(I\) \(\simeq\) 2C). in 15% steps. Also, the test matrix stretched further, covering five temperature measurement points from 10 \({}^{\circ}\)C to 45 \({}^{\circ}\)C per SOC. In Figure 10, the parameter adaptation is compared. On the left-hand side, in Figure 10a, the SOC differs at a standard temperature of 25 \({}^{\circ}\)C, while in the right plot (Figure 10b), the temperature varies at fixed SOC of 50%. Here, the temperature impact appears to be more influential to the battery cell. In contrast, the SOC shows nearly no particular significance, while the impedance spectrum becomes larger when increasing the ambient temperature. That impact results from the smaller total heat generated due to a decreasing ohmic resistance of the cell when increasing the temperature. The results show that neither the specific heat capacity nor thermal conductivity indicate a significant dependency on the SOC [12; 18; 27; 28]. The model approach in Figure 5 is simplified to extract the parameter from the calculated spectra. In this paper, the relevant values for the heat capacity and thermal resistance are fitted using a first-order Cauer model, representing a single RC element, as shown in the upper graphic in Figure 11b. The thermal resistance is then converted to the cross-plane thermal conductivity, further described in Section 2.3. Figure 11a compares a first- and second-order fit to the data points. The fit shows good overall accordance with the data. Furthermore, it shows only insignificant changes in the resulting values comparing a first-order model (Figure 11b, top) to a second-order model (Figure 11b, bottom). Here, the second-order model simulates the time delay caused by the temperature sensor and other surroundings. Given the minor influence of that additional time constant, the fitting algorithm is not adapted to that behaviour. Figure 12 presents both values as a function of SOC for all temperature measurement points. The thermal conductivity in Figure 12b shows nearly constant values, while the specific heat capacity in Figure 12a shows slightly different behaviour for the higher two temperatures. The specific heat capacity scarcely increases with SOC at higher temperatures. This can be caused by the rising negative real part of the Nyquist diagram (Figure 10b), which is not a part of the general RC fit in this work. Here, the influence of the sensor and different surroundings are more significant. Overall, the average specific heat capacity values differ from 1.22 J g\({}^{-1}\) K\({}^{-1}\) (SOC = 50% and T = 25 \({}^{\circ}\)C) to 1.35 J g\({}^{-1}\) K\({}^{-1}\) (SOC = 80% and T = 35 \({}^{\circ}\)C), showing a maximum spread of approximately 10%. The average value inside the test matrix is 1.27 J g\({}^{-1}\) K\({}^{-1}\).