*2.1. Heat Generation in Battery Cell*

In battery packing, the battery cells generate heat during the charging and discharging processes. The initial temperature was set according to the ambient temperature. The heat generation of the lithium-ion battery module consisted of two primary sources: the irreversible heat caused by the Joule's heating based on the internal resistance (*Qirr*) and the reversible heat inside the battery (*Qrev*). From these sources, the battery heat generation can be represented by Equation (1) [26].

$$Q = I^2 R\_\varepsilon - I \left[ T \frac{dE}{dT} \right] \tag{1}$$

where *I* is the current flowing through the battery (A), *Re* is the internal resistance (Ω), *T* is the temperature (K), *dE/dT* is the entropy coefficient (V/K), and *Q* is the battery heat generating rate (W). *Re* and *dE/dT* are a function of battery temperature (*T*) and *SOC* as shown in Equations (2) and (3), respectively.

$$R\_{\varepsilon} = \begin{pmatrix} -112 \times \text{SOC}^3 - 0.203 \times \text{SOC}^2 \times T + 0.000737 \times \text{SOC} \times T^2\\ + 0.00000753 \times T^3 + 301 \times \text{SOC}^2 - 0.144 \times \text{SOC} \times T\\ -0.0061 \times T^2 - 188 \times \text{SOC} + 1.28 \times T + 23.6 \end{pmatrix} \times 10^{-3} \tag{2}$$

$$\frac{dE}{dT} = \left(-0.342 + 0.979 \times \text{SOC} - 1.49 \times \text{SOC}^2 + 0.741 \times \text{SOC}^3\right) \times 10^{-3} \tag{3}$$

To model the battery in an extreme condition, we used a current of 2.6 A for 1 C discharge rate, battery temperature of 20 ◦C, *SOC* of 0.1, along with the parameters shown in Table 1. The parameters were under the assumption of operation in a tropical region with the already included ambient temperature. Based on Equations (1) to (3), the lower the *SOC* or the battery temperature, the higher the heat generated from the battery. *SOC* of 0.1 was the limit value used in the experiment by Jiaqiang et al. according to the recommendation of the battery manufacturer [26]. Meanwhile, the battery temperature of 20 ◦C was used as the low temperature in possible operating conditions in a tropical region with an average ambient temperature of 30 ◦C. The heat generation rate of the battery module was calculated with the result of 81.02 W. This value was used for the simulation input for battery cell heat generation.

**Table 1.** The specification of the lithium-ion battery investigated in this study.


<sup>a</sup> Ref. no [26]. <sup>b</sup> Ref. no [32]. <sup>c</sup> Ref. no [33].
