## 1 Introduction
Moreover, in the car propulsion system, these storage devices allow for the absorption of braking energy, thus improving efficiency and also eliminating the requirement for a starting device [19]. The way in which the HPS control strategy is designed has a decisive influence both on its performance [20] and on the economic aspects [21]. System performance control aims to optimize the static and dynamic characteristics and also to maintain a low current fluctuation of FCs [21,22] and a narrow range of charging and discharging depth of the energy storage devices, in order to preserve their lifespan [14,17,19,23]. System economics control often involves improving economic efficiency through several means, such as reducing the fuel [24] and/or energy consumption [25] and maximizing energy efficiency [26]. An EMS aims at finding an optimal solution [27] for the specific system by considering several or all the mentioned aspects [19; 20; 28; 29; 30]. Especially in the last decade, more attention has been paid to different topologies of multisource hybrid electric power systems used in mobility energy supply [31] and in stationary and portable power generation [32]. The major challenges faced by the ongoing research involve the integration of multiple and often conflicting objectives of power management strategy optimization in a real-time control system [33]. The EMS of a fuel cell hybrid power systems should aim at improving the system design (topology, dimensions, weight etc. ), performances (fuel consumption, energy efficiency, lifespan, resilience, etc.) and cost, and at finding an optimal solution for the specific system by considering aforementioned objectives. The main objective of this paper is to carry out a systematic evaluation of four fuel economy EMSs, three of which involves power-following control (PFC). These EMSs are referred to as air/fuel-PFC, air-PFC, fuel-PFC, and static feed-forward (sFF) strategies, and they are assessed in order to identify the best and safest strategy compared to the commercial standard based on the static feed-forward (sFF) control. For this, indicators such as fuel economy and oxygen excess ratio (OER) are used to evaluate the efficient and safe operation of an FC system and battery using power-following control (PFC) for the air regulator or the fuel regulator of the FC system, either separately or switched. The innovative switched mode proposed for the air/fuel-PFC strategy is comparatively analyzed with PFC-based strategies that control separately the air regulator or the fuel regulator of the FC system in order to highlight the fuel economy obtained for FC systems and FC/renewable hybrid power systems (HPSs). Net FC power is generated by PFC-based strategies for battery operation in sustained charging mode, with increased battery lifespan and cost less maintenance of the HPS. Following this objective, the structure of the paper is as follows. The first section details the model of an FC/renewable HPS, a PFC-based fuel economy EMS, and the involved control and optimization loops. The second section presents and comments on the results obtained under dynamic load and variable power from renewable energy sources (RESs). The last two sections discuss the results and conclude the paper respectively.