**5. Conclusions**

In this work, a study to replace the existing lead-acid battery UPS by applying a metal-air battery was extended. The thermodynamic model is refined by simulating each cell in the stack module. Based on this, we proposed an optimizing algorithm that controls the flow of the fan that blows air to each cell in the module, decreasing its temperature. Because metal-air batteries use oxygen from the air as a fuel, it is difficult to study the correlation between the flow and the battery performance. Additionally, because the battery model is based on a chemical model, it is challenging to apply DP, which is a theory calculated with discrete points. To solve this problem, we developed a 1.5-dimensional DP suitable for zinc-air batteries.

An RHC model using DP is proposed to find the optimal cost function in the Δ*Wprediction* window, which was estimated in the range of several tens of seconds of electrical load. The load power of the proposed model is more stable than that of the existing control strategies constantly controlling the fans, and it shows excellent performance in terms of overall zinc consumption. Although not globally optimal, appropriate control inputs can be calculated and applied to the oxygen concentration and temperature of each step.

**Author Contributions:** "Conceptualization, B.G. and G.-Y.C.; methodology, B.G.; software, H.L., D.S.; validation, S.L., S.Y. and S.K.P.; formal analysis, H.L.; investigation, C.K.; resources, S.Y.; data curation, S.K.P.; writing—original draft preparation, B.G.; writing—review and editing, N.K.; supervision, S.W.C. All authors have read and agreed to the published version of the manuscript."

**Funding:** "This research received no external funding."

**Acknowledgments:** This work was supported by the Technology Innovation Program (20002762, Development of RDE DB and Application Source Technology for Improvement of Real Road CO2 and Particulate Matter) funded by the Ministry of Trade, Industry and Energy (MOTIE, Korea), and partially supported by the National Research Foundation of Korea (NRF) gran<sup>t</sup> funded by the Korea governmen<sup>t</sup> (Ministry of Science and ICT) (No. NRF-2019R1A4A1025848, No. NRF-2019R1G1A1100393).

**Conflicts of Interest:** "The authors declare no conflict of interest."
