## 3 Results and Discussion
### SOC Estimation Results
other cases, the SOC estimation is accurate during the earlier and middle stages, with some deviations towards the end of the discharge cycle. High ambient temperatures generally accelerate electrochemical reactions in lithium-ion batteries, potentially leading to faster discharge and increased errors in SOC estimation models due to thermal effects. At an ambient temperature of 40 \({}^{\circ}\)C, the SOC estimation curves still follow the measured SOC closely, but there are instances where the deviation between the estimated and measured SOC increases, particularly in cases involving significant dynamic variations (Figure 14). The SOC estimation model generally performs well, though the higher temperature appears to introduce more noticeable deviations in some cases, particularly during the middle and later stages of the discharge process. Case 1, Case 4, and Case 7 maintain high accuracy throughout the discharge cycle, indicating that the SOC estimation model is robust under high-temperature conditions for certain battery dynamics. Case 2, Case 5, Case 6, and Case 9 show deviations that become more pronounced in the later stages of the discharge. In Case 3, the model shows overprediction, reflecting that thermal effects at 40 \({}^{\circ}\)C are not fully accounted for, leading to increased errors during periods of dynamic battery behaviour. Figure 12: SOC estimation results for different cases at ambient temperature of \(-10\)\({}^{\circ}\)C.  
Briefly, during the middle and later stages of discharge, the battery experiences a possible increase in internal resistance due to the polarization of active material. This phenomenon is more pronounced in certain cases where the discharge pulses are more aggressive (e.g., higher C-rates, longer discharge pulse times). As the discharge progresses, especially at lower SOC levels, the accumulation of polarization effects creates voltage drops, which lead to deviations between the measured and estimated SOC values. Additionally, as the SOC decreases, the battery approaches its cutoff voltage, and charge transfer resistance increases. This contributes to the observed deviations in the voltage response during the final discharge stages. The operating temperature plays a significant role in the accuracy of SOC estimation, as said before. In cases where the battery is tested at extreme temperatures (e.g., \(-10\)\({}^{\circ}\)C or \(40\)\({}^{\circ}\)C), thermal effects lead to deviations. At low temperatures, the battery's ionic mobility is reduced, leading to slower reaction kinetics and higher internal resistance, particularly during the final stages of discharge when the battery is already under stress. These combined effects cause the battery voltage to deviate more significantly from the expected behaviour. At high temperatures (\(40\)\({}^{\circ}\)C), the battery experiences faster electrochemical reactions and potential thermal degradation, which can cause voltage drifts or inconsistencies in the SOC estimation. The deviations in these cases during the final stages can be attributed to accelerated capacity loss and self-discharge  
Figure 13: SOC estimation results for different cases at ambient temperature of \(25\)\({}^{\circ}\)C.  
at elevated temperatures. Also, the deviations in cases can also be linked to the rest time allowed between pulses. During rest periods, the battery undergoes charge redistribution and voltage recovery as it equilibrates after a high-power discharge. In cases where the rest time is too short, the battery does not fully recover, leading to deviations in the SOC estimation due to an incomplete relaxation of the battery's voltage. Table 5 presents the variation in the measured property across distinct temperature levels (\(-10\)\({}^{\circ}\)C, 25 \({}^{\circ}\)C, and 40 \({}^{\circ}\)C). At \(-10\)\({}^{\circ}\)C, the recorded values span from 0.0167 to 0.0802, with Case 3 exhibiting the highest value, implying a greater sensitivity to lower temperatures.