**1. Introduction**

To date, many electrical storage systems (ESS), such as novel types of batteries and ultracapacitors, have been studied and applied to various systems. In particular, these batteries can improve the size or

weight aspects of the storage system making it small-size and easy to move. Large size is required for ESS that optimize economical gain by charging/discharging large amounts of electrical energy and for uninterruptible power supplies (UPS) supporting large electrical systems in emergencies. UPS systems have studied by many researchers because UPS are essential for supporting electrical energy stability. Before being applied to practical commercialization, a UPS is developed and studied through modeling and simulation because of the scale [1–3].

However, UPS are often based on conventional batteries because of their economic convenience and reliability. Among the UPS systems, the hybrid UPS (H-UPS) combines an electrical storage system (ESS) with UPS, using lead-acid batteries as the source of DC voltage [4]. Currently, replacing the batteries with an ultracapacitor is not a ffordable, because of the price of the latter [5]. Lithium-ion batteries, which are mostly used as a secondary battery, are also costly. Additionally, the secondary batteries must be always activated when connected to the main power source. In this aspect, though reliable, lead-acid batteries require frequent maintenance, and therefore they are not a ffordable [6].

Therefore, UPS requires the introduction of new battery technologies, especially high-power UPSs (those of more than 10 kW), which are more challenging. Among the commercially available batteries, metal-air batteries have a high energy density and are inexpensive, when select metal electrodes are used. Thus, they are widely studied as primary or secondary batteries, and small-capacity metal-air batteries have already been commercialized as primary batteries [7,8]. However, they cannot be used as rechargeable batteries, because they support only a few recharging cycles. For this reason, metal-air batteries are suitable for high-power UPSs, which require high capacity and no recharge. In these systems, the initial standby time after triggering can be supplemented by hybridization with a small-sized lithium-ion battery. Thus, modeling and simulation of UPSs using metal-air batteries are needed for their commercialization. In a previous study, we developed UPS model using experimental cell data and theoretical analysis [9]. Simulation includes the controls for UPS and lithium-ion battery which is a secondary battery on standby during normal situation. However, after initial operation, when the primary battery, metal air battery, which is the main battery operates in earnest, only basic control using constant fan flow was applied.

Metal-air batteries are not widely used as energy storage devices in the industry. Thus, previous researches on controlling metal-air batteries have focused on determining their parameters or supplying stable energy [10–12]. However, the performance and lifespan of a battery is directly related to its thermal managemen<sup>t</sup> system that controls the temperature of the battery [13–15]. Unlike other batteries for which the cooling system has already been studied, metal-air batteries have a significant limitations on air cooling because of its their consumption. Furthermore, previous studies have barely covered air-cooling of metal-air batteries because of their unusual properties. Although studies for cooling system control of metal-air batteries are fewer than for other batteries, control strategies for cooling systems of other batteries have been studied [16,17]. Especially, Zhan developed a rule-based control strategy for cooling PEM fuel cells in UPS systems [18].

This study devised a control strategy of air-cooling system for fuel supply using battery cell experimental data. As the optimal control strategy for a cooling system a ffects not only cooling but also oxygen supply, an overall performance improvement of the metal air battery could be expected. To do this, the detailed thermodynamics of metal-air battery among the UPS module were examined, and state variables were calculated for each cell. Because the studies for the UPS system based on metal-air battery are rare, detailed modeling of UPS system can be the first contribution. Though di fficult, we applied the existing discrete dynamic programming (DP) algorithm, optimization theory, considering the characteristics of the metal-air battery. This is the second contribution of this paper and main contents.

The paper is structured in five sections. After this Introduction, Section 2 presents the UPS system modeling using prior research and thermodynamic models. Section 3 provides functions, parameters, and analytical theories to solve the main optimal problem for control modeling and

simulation. Section 4 arrange the result of the simulation and compare that with other control strategies. Section 5 presents concluding remarks and the performance of the suggested control strategy.

## **2. UPS System Modeling**
