**4. Results**

We experimented the proposed RHC algorithm using two-parameter settings. RHC #1 used ΔWsolver = 10 and ΔWprediction = 200, and RHC #2 used ΔWsolver = 20 and ΔWprediction = 100. We also simulated the UPS model with full DP control which assumes that we know the entire electrical load cycle. This control means globally optimal potential of the UPS model for comparison. In total the simulations were run controlling the fan by RHC, DP control, and constant fan flow. Electrical load cycle #2, which used the DP control, showed a distinct difference, and the resulting cell temperature of the entire module is shown in Figure 7.

**Figure 7.** Cell temperature on electrical load cycle #2 by DP control.

As mentioned in Section 3.5, the temperature of the cell at the end of the module is significantly lower than that of the other cells during the entire simulation time. This is caused by the natural air-cooling of the module. Additionally, the temperature difference increases with time. By comparing with electrical load cycle #2 of Figure 6, it can also be seen that the temperature increases rapidly because of the large heat generated when the electrical load increases rapidly.

To compare the different controls, i.e., RHC #1, RHC #2, DP, and constant fan flow (1%, 2%, ... , 100% of the maximum fan flow), the state variables based on electrical load cycle #2 were used, leading to the result shown in Figure 8.

**Figure 8.** State variables as simulation result in electrical load cycle #2 by different fan control: (**a**) cell temperature; (**b**) oxygen concentration.

The cell temperature reported in Figure 8a indicates that the influence of the fan flow is not significant at first. However, it increases accumulating over time, resulting in a large di fference between the controls. In the case of the oxygen concentration of Figure 8b, the e ffect of electrical load cycle #2 of Figure 6 is critical, because the oxygen concentration by all controls except DP vibrates under electrical load. Particularly in the case of the DP control, the optimal oxygen concentration of the whole cycle drops below 10%. Additionally, the constant fan flow control shows that the oxygen concentration increases gradually as the oxygen consumption decreases with increasing temperature. However, in the case of RHC, the initial oxygen concentration can be maintained through the cycle despite the temperature di fference. Because the oxygen concentration hardly drops within a single prediction window, the locally optimal path of the control input is near the high oxygen concentration. The controls which maintained oxygen concentration as high unnecessarily using much electric energy. These trends of the variables by RHC will be similar in di fferent situation because RHC has characteristic to find local optimal regardless of condition of the system and circumstances.

Looking at the fan flow for each control of Figure 9, it is seen that, in RHC, it is di fferent from the DP control, though it gradually follows DP one with a time because of the optimal algorithm. Additionally, the fan flow of the RHC #1 control tends to be lower than that of RHC #2. When Δ *Wpredict* and Δ *Wsolver* were respectively increased and decreased (RHC #2 → RHC #1), we found that this control input is better than the DP one. This is usually attributed to low flow in the boundary condition.

**Figure 9.** Fan flow control for the di fferent algorithms.

The zinc consumption in all electrical load cycles is shown in Figure 10, using consumption of DP as reference (100%). Here, a grey bar indicates that the simulation stopped because a boundary condition, such as the state-of-charge of the battery, temperature, and oxygen concentration, was met before the total simulation time had passed. The RHC proposed in this study is represented in purple. The results confirm that the RHC control is e ffective in reducing the zinc consumption of metal-air battery-based UPSs increasing its operation time. In particular, RHC #1 showed stable and excellent performance, in contrast to other constant fan flow controls that fail or consume excessive zinc. Compared to the low-speed flow (that of less than 1–10% of the maximum fan flow), the zinc consumption of RHC #1 is not lower. However, in the case of the low-speed flows, the battery failed because of a poor cooling forced by the fans. Instead, compared with the other controls, RHC #1 displayed a maximum 6–10% di fference in zinc consumption.

**Figure 10.** A comparison of increased zinc consumption by fan controls according to: (**a**) the electrical load cycles #1; (**b**) the electrical load cycles #2; (**c**) the electrical load cycles #3; (**d**) the electrical load cycles #4; (**e**) the electrical load cycles #5.

In most cycles, the zinc consumption is lower for weaker fan flow, though it is seldom very high in these cases either. However, because the simulation time was determined from the available operation time, all of the zinc metal was consumed, as indicated by the gray bars.

RHC #2 showed a slightly lower performance than RHC #1. However, it displayed a relatively low computing cost, approximately 1/5 of the original cost of RHC #1. As a matter of fact, RHC #1 cannot be used for real-time control because its simulation time is 4–5 times higher in a generic PC (i7-4790 CPU, 16GB RAM). In contrast, RHC #2, which needs a longer prediction range, needs a simulation time similar to the actual UPS running time. Thus, in principle, applying RHC #2 as real-time control in UPS is possible. If the current UPS model is simplified through data mapping, or the RHC control algorithm is optimized further, real-time control can be applied in industry. Additionally, the scenario of the facilities connected to the UPS in the event of a main power outage can be determined. In this case, the DP algorithm can be applied to increase the performance of the UPS as the potential with the predicted overall electrical load cycle.
