## 3 Results
### Effect of C-Rate at Constant Temperature Conditions
#### 3.1.2 SoH Estimation for Batteries at Different C-Rates under 25 \({}^{\circ}\)C Ambient  
We perform a similar study as in the previous section to estimate SoH for batteries tested at two C-rates and 25 \({}^{\circ}\)C, and the results are shown in Tables 7 and 8. Batteries tested under 25 \({}^{\circ}\)C shows lower degradation rate at both 1 C-rate and 3 C-rate when compared with batteries tested at 55 \({}^{\circ}\)C as  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Cycles Selected for k’s Values Extraction** & **\% Estimation Error** \\ \hline
100, 200, 300 & 3.14 \\
125, 225, 325 & 3.68 \\
150, 250, 350 & 3.52 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Percentage estimation error of SoH for a different set of three cycles in the k’s values extraction.  
Figure 5: The estimation error between different discharge current under 55 \({}^{\circ}\)C. % value on top of the bar represents the % error in estimation.  
expected. Also, the degradation rate is slower for 1 C-rate as expected. Sample using 1 C-rate still have 89.76% SoH after 800 cycles, while the 3 C-rate sample reaches the cut-off point at around 700 cycles.  
Again, the k's values obtained from one battery is applied to obtain the SoH of same battery as well as other battery tested at other C-rate and the error percentage is computed between the Experimental and Estimated SoH. The percentage error results for estimating SoH are shown in Figure 6.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Cycle Number** & **1 C** & **3 C** \\ \hline
1 & 100\% & 100\% \\
100 & 97.38\% & 96.28\% \\
200 & 94.91\% & 93.00\% \\
300 & 94.26\% & 91.30\% \\
400 & 93.14\% & 88.21\% \\
500 & 92.48\% & 84.48\% \\
600 & 91.88\% & 83.80\% \\
700 & 90.81\% & 80.41\% \\
800 & 89.76\% & - \\ \hline \hline \end{tabular}
\end{table}
Table 7: Calculated SoH at 25 \({}^{\circ}\)C based on the Qm computed from the ECBE model.  
Figure 6: The estimation error between 1 and 3 C-rate at 25 \({}^{\circ}\)C. The % value on top of each bar represent the % error of estimation.  
In comparing the % errors for C\({}^{\prime}\) and A\({}^{\prime}\), and that for D\({}^{\prime}\) and B\({}^{\prime}\), we can see that the % error is larger for the case of 25 \({}^{\circ}\)C. Such larger error is due to the inaccuracy of the temperature of 25 \({}^{\circ}\)C as the testing was done in the laboratory ambient, and the ambient temperature has a small fluctuation over the span of measurement period. The temperature varies between 24 to 26 \({}^{\circ}\)C during our test.  
In Figure 6, the largest percentage error obtained is around 8.49 % for the case when k's values from battery tested at 3 C is applied to obtain SoH for battery tested at 1 C under 25 \({}^{\circ}\)C. In comparison to D\({}^{\prime}\), although the difference in the C rate between the cells are the same, the large % error for the case of C\({}^{\prime\prime}\) is expected to be attributed by the temperature difference between the cell of interest and the reference cell, which is approximately 8 \({}^{\circ}\)C as can be seen in Table 9. Table 9 shows the temperatures of the LiB when discharged at different C rates at different temperatures.  
The increase in the cell temperature as shown in Table 9 is expected according to the work by [PERSON] et al. [22], and the rise in temperature during discharge depends on the Peltier heat as a result of the entropy change, the discharge current, heat capacity and weight of a battery as well as its thermal design and the ambient temperature [22]. As the different C rate and cell temperature can affect the estimation accuracy, we further investigate the effect of temperature on the accuracy of the estimation using the SECF model.