## 4 Optimization Results
### Case B: Abnormal Mode with Fixed Priorities  
In this case, the optimal solutions of the optimization problem were investigated during emergency conditions, i.e., main generator outages. Also, the priorities of loads were considered only based on their interruption penalty, i.e., \(W_{j,t}^{pen}\). It means the higher interruption penalty of a load caused it to be shed later during an outage. The value of \(W_{j,t}^{pen}\) for the high priority loads, medium priority loads and low priority loads were considered \(10^{3}\), \(10^{2}\) and \(10\), respectively. Tables 3 and 4 contain the connection status of loads during three generators outages and for \(\beta=0\) (i.e., without considering hydrogen cost, we named this the load importance mode) and for \(\beta=0.5\), respectively. The simultaneous disconnection of three generators is an extremely critical state, so the solutions of optimization problem can be robust in this case. It was assumed that the outages time was in time slot 15. As can be seen from Table 3, the high priority load ECS and the low priority galleys are interrupted at time slot 15 because of their high power magnitude (see Table 1). Table 5 contains the Pareto results for the proposed two-objective optimization problem. The optimal results of load shedding and PEMFCS power are shown at the beginning time of different generators outages. We can see for \(\beta=0\) and three generators outage, the PEMFCS optimum size was 300 kW and the optimum amount of interrupted load is 440 kW which was equal to the sum of ECS and galleys. This optimum size of PEMFCS, although it prevents a greater amount of load shedding, according to Figure 8, weighs 377 kg, which is heavy. We expect that by increasing the weighting parameter \(\beta\), the size and weight of the PEMFCS will decrease, and more load will be cut off. The contents of Table 4 are similar to Table 3, with the difference that the results are reported for \(\beta=0.5\) (we name this the compromise mode) in Table 4. As it turns out, in addition to the previous loads, the Forward Cargo AC was interrupted too. So, based on Table 5, the total load shedding was 500 kW and also the optimum size of PEMFCS was 180 kW. This size of PEMFCS has less weight (225 kg according to Figure 8) and looks more suitable for vehicles applications such as aircraft. So, as Table 5 turns out, by increasing \(\beta\) the PEMFCS optimum size was decreased and the total load shedding was increased. For \(\beta=1\) (we name this the hydrogen economy mode) all the loads were interrupted and the PEMFCS power was zero because it was the most attention to minimizing the hydrogen consumption. Figure 7: The SoC of ESS during normal mode. The weight of PEMFCS was an important factor to select the best choice. Given this factor and according to Table 5, it can be said that the power of 279 kW for \(\beta=0.6\) in the event of four generators outage was a good choice. Because, according to Figure 8, this size for PEMFCS had 340 kg weight. This amount of power and weight compared to 300 kW and 377 kg was a more appropriate choice. The amount of 279 kW for the PEMFCS as an emergency power unit led to interruption of 660 kW loads in the case of four generators outage. Which is, of course large, but the probability of simultaneous outages of four generators is also very small. If this value is selected, in the case of three generators outage, 500 kW will be cut off. With the outage of two generators, this PEMFCS power (i.e., 279 kW) leads to interrupt the load below 180 kW. Also, if only one generator is disconnected, then the 279 kW PEMFCS will not interrupt loads at any time. Figure 9 shows the changes in the SoC of ESS during emergency modes (time slots 15-20). As it shows, the ESS released more energy in the compromise mode (i.e., for \(\beta=0.5\)). In this case, the battery was discharged to 30% whereas it was discharged to 60% in the load importance and hydrogen economy modes (i.e., for \(\beta=0,\ \beta\)= 1).