*2.1. Prior Research*

As previously mentioned, we developed a 64 kW UPS system using small-sized stacks of metal-air batteries in a previous study [9]. The research represents an important experimental trial to develop a UPS system based on metal-air batteries. The major point of the prior research was to determine the entire composition of the system and a hybrid system using lithium-ion battery. Thermodynamic and electromechanical analyses were performed assuming that the properties of the cells in each module of the UPS system are uniform:

$$T\_1 = T\_2 = \dots = T\_n \tag{1}$$

$$\mathbb{C}p\_{\text{module}} = \mathbb{C}p\_{\text{case}} + \mathbb{C}p\_{\text{electrolyte}} + \sum\_{k=1}^{n} \mathbb{C}p\_{\text{cell},k} \tag{2}$$

where *T* is the temperature, *Cp* is the heat capacity, and *n* is the number of cells in a module. The parameters of the previous UPS model were also used in this study. Table 1 shows the parameters of the iterative simulation and mechanical calculation used. A total of 20 fans that supply oxygen and cool the module were located at the 20 inlet, and 20 fans at outlet. The flow rate of these fans was constant value in the previous study, i.e.:

$$Q\_1^t = Q\_{N\_2,1}^t + Q\_{O\_2,1}^t = Q\_2^t = \dots = Q\_m^t = \text{const} \tag{3}$$

where *Qtm* is the flow rate at time *t* on *mth* fan, *<sup>Q</sup>tN*2,*m*, *<sup>Q</sup>tO*2,*<sup>m</sup>* is the flow rate of gas except oxygen, and the flow rate of oxygen gas.


**Table 1.** Values of the parameters in the UPS module.

The parameters were designed to satisfy the required specification of up to2hruntime under maximum electrical load with a simple constant flow control. The2hruntime was the minimum required specification of the UPS until the main source is connected again. Though the simple constant flow control showed good performance under static load power, it was not optimized for different environments like changing electrical loads. Therefore, it did not show stable control performance in this case, because it did not meet the electrical load and boundary conditions of a metal-air battery.
