## 2 Materials and Methods  
4 Panasonic SANYO UR18650E lithium-ion batteries [19] are tested using Bio-Logic BCS-815, which is an 8-channel tester and support 15 A per channel. It is used for charging and discharging of the batteries with test data collection under room temperature, which is approximately 25 \({}^{\circ}\)C. The sampling frequency of the data collection is 1 Hz. The specification of the batteries used here are shown in Table 1 as obtained from the manufacturer. The batteries are tested under different test conditions as shown in Table 2. Only one battery is tested under each condition due to time and resources limitations. However, as the model employed here has been verified in the work by [PERSON] et al. [17] on different charge-discharge cycles for LiB, the results obtained in this work are presented with confidence despite the small sample size. Verification of the model using another 3 cells from the same batch will be performed later. The purpose of this work is to examine the capability and accuracy of this SECF model when ambient temperature and discharge current are considered. More batteries will be tested when resource becomes available. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Battery Characteristics**} \\ \hline Type & Cylindrical \\ Chemical system & NMC \\ Nominal voltage & 3.62 V \\ Typical capacity & 2150 mAh \\ Cut-off voltage Charging & 4.2 V \\ Discharging & 2.75 V \\ Dimensions(mm) & 18.4 \(\times\) 65 \\ Approx. weight & 44.5 g \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Samsung 18,650 battery specification provided by manufacturer [8]. In the experiments, we use CC-CV method for charging the batteries. 1 A constant current (as recommend from the battery's manufacturer datasheet) is used to charge the batteries to its cut-off voltage, and the charging is done with constant voltage until the current drops to 100 mA. When the battery is fully charged, a rest time of 30 min is kept before discharging. One or 3 C-rate is implemented to discharge the batteries until the cut-off voltage of 4.2 V is reached. Figure 1 shows the typical time progression of the terminal voltage of a LiB during charging and discharging. One can see that the voltage is higher when LiB is charging at higher temperature. This is because cell impedance will be higher at higher temperature. The terminal voltage can be modelled as the constant current multiples the cell impedance as the charging is done using CC-CV, and hence a higher terminal voltage results. In fact, the cell impedance of a LiB has been employed to monitor the temperature of LiB by [PERSON] et al. [20]. The discharge curves of all the LiB are analyzed using the ECBE model to calculate the maximum capacity of the cells (Q\({}_{\rm m}\)). This Q\({}_{\rm m}\) is used to compute the corresponding SOH using Equation (1) where Q\({}_{\rm max(fresh)}\) is the Q\({}_{\rm m}\) after the first discharge cycle, and Q\({}_{\  
The SECF model used in this work is shown in Equation (2) [16]. The SoH determined using Equation (2) is termed as Estimated SoH. The parameter k\({}_{1}\) accounts for the capacity losses that increase rapidly during the conditions of cycling at high temperature, and k\({}_{2}\) is a factor to account for capacity losses under the normal conditions of cycling. k\({}_{3}\) accounts for the capacity loss due to C-rate [21]. \[\text{SoH}=1-\left(0.5\text{+}\text{k}_{1}\text{N}^{2}+\text{k}_{2}\text{N} \right)-\frac{\text{k}_{3}}{\text{Q}_{\text{max}(\text{fresh})}}\text{i} \tag{2}\]  
Here, N represents the number of charge-discharge cycles the battery experienced at the time of this SoH calculation and i is discharging current.