## 1 Introduction
### Related Works  
The energy management strategies for different transportation systems have been studied in some research works. In [17], a hybrid configuration for operating a tram without connecting to the main grid including proton exchange membrane fuel cell system (PEMFCS) and ESS was proposed. The equivalent consumption minimization strategy (ECMS) was used to optimize the hydrogen consumption. Different energy management for a fuel cell emergency power unit in an MEA as investigated in [18]. As a result, ECMS method had a better performance in the case of fuel consumption minimization. The specific energy of a fuel cell emergency power unit in an aircraft was maximized in [19] by the proposed optimization of the ratio energy/weight. Also, the feasibility of using PEMFCS in an aircraft was analyzed. Optimizing the size and the hydrogen consumption in a powertrain system was investigated in [20]. This system included typical PEMFCS and their durability was also considered. First, the model was solved by dynamic programming method which had some results for multi-objective optimization as the rules. These rules were named soft-run strategy which helps the fuel cell being stable. A convex model was proposed in [21] to simultaneously optimize the hybrid ESS (battery and supercapacitor) size and the power allocation between hybrid ESS and fuel cell in an electric bus. As a result, the hybrid ESS has less hydrogen consumption rather than battery-only ESS. The stochastic dynamic programming method was used in [22] to minimize costs of the fuel cell, including fuel consumption and degradation. A new hydrogen consumption minimization strategy is proposed in [23] and was compared with ECMS. The proposed model was more robust to change in the load profile in an MEA but had high stress on the ESS. The load management in the MEA system often happens by interrupting the loads or load shedding in order to prevent the main generators from overloading. In this regard, prioritization of different loads has been used repeatedly in some references. A load with a higher priority will be disconnected later. Variable priority method was used in [24] and also in [25] in which each load sends a variable request to a control unit. A load with high request level will be connected earlier. The proposed load management in [26] prevents loads from being reconnected instead of load shedding. Some studies used other methods for load management like the power-sharing, time-sharing and peak-compression which were used in [27] to exploit long responding times of MEA like heater and galleys. However, in some studies, the authors suggest a learning method such as in [28; 29]. Also the authors gave a novel method to optimize the system performance using clustering [30; 31; 32], heuristic [33], genetic [34; 35; 36], evolution [37], and optimization [38] approaches. Other robust methods have also been used for uncertainty removal [39; 40; 41; 42; 43; 44]. Regarding the review of past references, no article has addressed the joint optimization of fuel cell hydrogen consumption (hydrogen economy) and demand-side management in an MEA system. Most of the articles have examined this topic separately. The purpose of this paper is to provide a convex multi-objective optimization model for both hydrogen consumption and also load management in an MEA and examine the effect of load priority during emergency condition in a flight on the hydrogen consumption. Choosing the large size for PEMFCS will increase the hydrogen consumption as well as aircraft's weight, but the probability of load interruption during the emergency condition will decrease (the purpose of optimal size in this paper is to determine the optimal electric power and weight). On the other hand, selecting a small size for the PEMFCS reduces the weight and the hydrogen consumption of aircraft but it also causes more load shedding during emergency conditions. By prioritizing loads in the system, both size of PEMFCS and optimal load shedding can be achieved (Figure 1).