**1. Introduction**

Instead of a diesel generator [1], the proton-exchange membrane fuel cell (PEM FC) system could be used as a backup green energy source [2] for an FC hybrid power system (FC HPS) to mitigate the load variability by the load-following (LF) control [3–5]. A hybrid energy storage system (ESS) using batteries and ultracapacitors is mandatory to dynamically compensate the power flow balance [6,7]. The most used ESS topologies are the active and semi-active topologies, using two and one bidirectional DC-DC converters integrated into a multiport topology, respectively [8–10]. An active topology with two bidirectional DC-DC converters is more flexible as a control structure compared to a semi-active topology [9]. The two control references will be generated by the energy management strategies

(EMS), usually to regulate the DC voltage and mitigate the load pulses via the bidirectional DC-DC converters for the batteries and ultracapacitors stacks [5,7,11,12]. The EMS has an important role in the optimal and safe operation of the FC system [13,14]. The control objectives for PEM FC system are as follows [15–17]: (1) minimization of the fuel consumption; (2) supplying the dynamic loads with energy, such as FC vehicles; (3) safe operation by using appropriate control loops to mitigate the load pulses, to limit the FC current slope, and to avoid fuel starvation.

The first objective can be ensured using a real-time optimization (RTO) strategy based on different optimization functions, which integrate performance indicators related to fuel consumption such as FC net power, FC lifetime, and cost [18–20].

The equivalent consumption minimization strategy (ECMS) is a well-known strategy applied to FC vehicles, which converts the energy difference in battery charging (at the start and end of a load cycle) into additional fuel consumption, to compensate this loss of energy by discharging the battery [21]. In last decade, several algorithms searching for the global optimum using different optimization functions have been proposed in the literature [22–24]. Intelligent concepts are usually involved in these algorithms [25–27]. In this study, the global extremum seeking (GES) algorithm is used due to the good performance reported in the previous work for FC systems [28–31], photovoltaic (PV) systems [22,23,32], and wind turbine (WT) systems [33,34].

The objective of this paper is to use the sensitivity approach to identify the best value of the parameters used by the optimization function and control loops. Except the tuning parameters of the GES algorithm, which will be designed to ensure the imposed performance and stability of the tracking loops, the dither's frequency *fd* is the most important parameter that could dynamically affect the performance of the GES algorithm.

The GES algorithm must search the optimization function's optimum in real-time, which is defined in this study as a weighted function of the FC net power and the fuel consumption efficiency using the weighting parameters *knet* and *ke*ff. So, if *knet* = 1, then it is important to know the value of the weighting parameter *ke*ff, where the best fuel economy is obtained. So, the sensitivity approach in this study will be performed using the parameters *fd* and *ke*ff.

The structure of the paper is as follows. The FC HPS architecture and LF control and optimization loops are briefly presented in Section 2. The EMS based on LF control and optimization loops is detailed in Section 3. The obtained results are presented and discussed in Section 4. Section 5 concludes this study.
