## 3 Results and Discussion
### Comparison of Estimation Difference for the Case of an Individual Cell  
To verify the ability of the semi-empirical fading model for estimating the SoH of batteries over the number of cycles tested as shown previously, the percentage difference (which will be termed as difference hereafter) was calculated for each cell between the experimental and estimated SoH and the results are shown in Figure 5.  
It is noticed that the average mean difference was around 1.2%, which is an acceptable difference according to literature. The highest percentage difference was found to be 2.22% of A4, and the  
Figure 4: Charge evaluation for a Li-ion battery using the electrochemistry-based electrical (ECBE) model and Coulomb counting method.  
Figure 5: Comparison result between the estimated and experimental results for the ECBE model verification for each cell after the completion of the test (Cell A1, A2 are tested for 500 cycles, A3, A4 are tested for 550 cycles, A5, A6 are tested for 600 cycles, and A7, A8 are tested for 650 cycles).  
remaining samples were all within the acceptable range of 1.5% which demonstrates the capability of the semi-empirical fading model in accurately estimating the decrease of SoH for all the cells tested for whole cycles ranging. It is also interesting to note that difference for cells A2, A5, and A6 are very low (around 0.5%), which represents the model's effectiveness in determining accurate SoH.  
After verifying the ability of the semi-empirical fading model of a LiB cell, we examined the ability of the extracted k values to estimate the SoH of other cells from the same batch. To verify this, average, k values obtained in our previous steps were calculated, as shown in Table 4, and they were used to estimate the SoH of the batteries over the number of cycles tested.  
The average values in Table 4 were used to estimate the SoH of the batteries over the number of cycles tested, and the comparison results are shown in Figure 6. Cell A2 is used to demonstrate the comparison. It is again observed that the estimation difference is higher for cycle numbers from 1 to 60, as noticed in our previous results. However, the mean difference is still within the range of around 1% in our case.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **k1** & **k2** & **k3** \\ \hline Averaged K-value & \(2.14\times 10^{-7}\) & \(1.25\times 10^{-4}\) & 0.007143 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Averaged K-values.  
Figure 6: Difference comparison between the battery fade model using average parameters and the ECBE model for cell A2.  
Figure 6 shows the differences between the estimated SoH and the experimental SoH for cell A2 using the average k values, and the differences are in acceptable limits at each cycle number, up to 500 cycles. The initial and final part are prone to larger differences, but the actual battery degradation can still be accurately estimated from the trend of semi-empirical fading model (red line). Figure 7 shows the average percentage difference for individual cells when estimated using the average k values, and it is observed that the capacity fading model fitting is in good correlation with the experimental SoH data obtained with the ECBE model with the average k values. The mean difference percentage value is less than 1%, which is even better than the estimations of an individual cell. This shows the robustness of the semi-empirical fading model in estimating SoH for a batch of cells over their respective number of cycles.