**1. Introduction**

The very fast increase of global energy demand over recent decades calls for a new approach to energy sustainable development based on Hybrid Power Systems (HPS) combining Renewable Energy Sources (RESs) and Fuel Cell (FC) systems [1–3]. Therefore, innovative solutions based on experimental research have been proposed for the implementation of the Fuel Cell Hybrid Power Systems (FCHPS) with or without support from the RESs [4–6].

The state-of-the-art studies in this field have identified the following challenging topics for the next stage of research [7–9]:


In this study, the optimization of the FCHPS is approached using the control mode of the required load power on the DC bus, named the Required-Power-Following (RPF) control-mode of the FC system. The FC system using RPF-control mode will generate, on the DC bus, the needed power to compensate the DC power flow balance for a Hybrid Power System operating with a variable load demand. The RPF-control mode will use one from the three inputs variables of the FC system that can control the FC power: the reference input for the FC boost controller, the air regulator, or the fuel regulator. So, the other two inputs or only one input can be used to optimize the operation of the FC system in order to improve the fuel consumption based on the optimization function chosen. Thus, the RPF-control loop and two optimization loops controlling all three reference inputs of the FC system means three optimization strategies. In addition, beside one needed loop for the RPF-control, only one optimization loop controlling two from the three reference inputs of the FC system means the other four optimization strategies. Consequently, seven optimization strategies can be set for an FC Hybrid Power System to be analyzed.

The real-time searching and tracking of the optimum is mandatory for the optimization algorithm used in this study [52–54]. Furthermore, the optimization function is time-dependent and could become a multimodal type by controlling the FCHPS in different operating modes [55]. So, a Real-Time Optimization (RTO) algorithm must be selected to search the global optimum. The Global Extremum Seeking (GES) scheme proposed in [20] will be considered here, with minor changes of the parameters' values to improve the searching performance.

Summarizing, the novelty of this study is that seven RTO strategies will be analyzed for a FCHPS under the same load profile in order to estimate the fuel consumption compared to that obtained using the Static Feed-Forward (sFF) strategy, which is commercially implemented [56].

The goal of this study is to identify which is the best RTO strategy in full range of load demand or the best two RTO strategies that can be used for high and low values of the load demand, respectively.

The obtained results reveal that the fuel economy is better (in comparison with the sFF strategy) for only two RTO strategies, if the FCHPS is operated using the same strategy in the full range of load demand. If the FCHPS is operated using the best RTO strategy for high values of the load demand and another one which is best in the rest of the load range, then more combinations are possible (which we

refer to as the switching strategies). This is because two RTO strategies are identified as best for high levels of load and two others as best for low load.

The rest of this study is organized as follows. The modeling of the FCHPS, the Energy Management Unit implementing the RPF-control mode and the optimization loops, and setting of the RTO strategies are presented in Section 2. The fuel economy obtained using a RTO strategy for the FCHPS is discussed in Section 3. Th final section concludes the performed study by highlighting the main findings and next work.
