## 1 Introduction  
Fuel cells, with the advantages of high energy conversion efficiency, low noise, clean air, and low carbon, have been gradually applied to transportation, aerospace, and distributed generation [1, 2]. Fuel cell research and development are fully consistent with the strategic approach to renewable and sustainable energy development. Proton exchange membrane (PEM) fuel cells are the most promising fuel cells because of their low operating temperature and portability [3]. Currently, PEM fuel cells are available in a variety of structural forms to meet the output power requirement, including low-power single-stack fuel cell systems (SFCSs) and high-power multi-stack fuel cell systems (MFCSs) [4, 5, 6, 7]. The rated power of large-scale power equipment typically ranges from several hundred kilowatts to several megawatts. However, current SFCS technology is not advanced enough to support such a high-power demand [8, 9]. Therefore, in facing this demand, the decision to create a high-power MFCS using technologically mature stacks from the market or to develop a new high-power SFCS is a crucial issue that needs to be addressed. This decision is primarily related to the efficiency, availability, durability, and cost of PEM fuel cell power systems [10]. The development of high-power single-stack fuel cell systems leads to an increase in minimum output power as the power rating increases. In this case, there is no advantage of SFCS power coverage compared to MFCS. [PERSON] et al. [11] investigated the dynamic and transient characteristics of a DC/DC-free sub-healthy fuel cell multi-stack system and found the fuel cell system current and voltage characteristics of series and parallel structures. MFCSs, consisting of multiple fuel cells, are mainly available in integrated and distributed configurations. [PERSON] et al. [12] proposed the concept of multi-stack association in fuel cell systems, after which MFCSs have evolved considerably in the intervening decades. Since then, [PERSON] et al. [13] proposed the concept of a modular fuel cell system. The combination of modular fuel cell systems into MFCSs is clearly an effective solution for dealing with the power output of large-scale devices. [PERSON] et al. [14] developed a power management strategy and designed a triple-stack configuration applied in a vehicle; this PEM fuel cell system could prolong the lifetime and cut the stack cost. [PERSON] et al. [15] proposed a 240 kW MFCS with 30 kW per stack based on an average split-stack scheme in a ship-like environment, and they identified a management procedure for performance optimization. [PERSON] et al. [16] built a dual-stack fuel cell system and proposed an improved overall efficiency maximization strategy based on this MFCS; the results show that this system and control strategy can improve system efficiency and economy. [PERSON] et al. [17] proposed a fault-tolerant control strategy for energy allocation and considered the global switching sequence calculation in an MFCS, resulting in lower hydrogen consumption and a longer service life. [PERSON] et al. [7] proposed a co-optimized power allocation strategy based on the maximum efficiency range, which aims to improve the efficiency and economy of multi-stack fuel cell systems at different altitudes. [PERSON] et al. [18] used a cooperative independent Q-learning algorithm for energy management of vehicles with multi-stack fuel cell systems, defined a comprehensive reward function including hydrogen consumption and degradation, and demonstrated its superior performance relative to other online strategies. [PERSON] et al. [19] used a multi-agent reinforcement learning method for energy management of multi-stack fuel cell hybrid vehicles and transplanted the method to an actual controller for online operation. In summary, MFCSs offer the practicality of a longer service life, energy efficiency, and economy in high-power application scenarios.