# Adaptive Feedback Control for Four-Phase Interleaved Boost Converter Used with PEM Fuel Cell +
## 1 Introduction  
As industrial processes continue to advance, fossil fuels remain a significant component of the energy landscape, projected to account for approximately 70% of the energy structure by 2050 [1]. However, the overuse and combustion of fossil fuels in transportation have raised concerns regarding excessive greenhouse gas emissions, energy shortages, and resource allocation issues [2]. While electrification of transportation presents a viable solution to reduce carbon dioxide emissions, if the electricity used is generated from fossil fuels such as coal, significant carbon dioxide emissions will still occur. Therefore, it is essential to highlight that renewable energy sources, despite their intermittency and fluctuations,play a key role in powering these systems. In this context, hydrogen energy can serve as a medium to store excess energy from renewables and bridge the gap in load fluctuations, thus enabling fuel cell hybrid vehicles [3]. Fuel cell electric vehicles (FCEVs), which use hydrogen combined with PEM fuel cell technology, have garnered attention as a promising solution for sustainable transportation [4]. PEMFC offer zero emissions, high power output, and adaptability to varying temperature conditions compared to traditional batteries [5]. The production of hydrogen from diverse sources, particularly renewable ones, further enhances their appeal as a clean energy option [6]. However, it is important to consider the advantages of combining fuel cells with lithium-ion batteries rather than relying solely on one or the other. While hydrogen fuel cells offer zero carbon dioxide emissions, lithium-ion batteries also present a similar environmental benefit when sourced from renewable energy. Furthermore, when the performance of onboard batteries fails to meet electric vehicle (EV) mileage and safety standards, many retired batteries require urgent treatment. Second-use applications for retired EV batteries represent an optimal solution to effectively avoid energy waste and utilize the remaining value of these batteries. Nevertheless, long-term performance testing for second-use applications can increase costs, and the standard classification criteria (such as battery capacity or internal resistance) do not ensure the consistency of regrouped retired batteries. This inconsistency may accelerate battery performance degradation, as highlighted in the literature [7]. The proton-exchange membrane fuel cell (PEMFC) technology is recognized as one of the primary solutions for transportation applications, particularly in the automotive field, due to its excellent performance and high environmental adaptability [8]. In these applications, multiple cells are connected in series and parallel to meet the power and voltage requirements. However, the fuel cell voltage is unstable due to uneven reactions occurring within the cell, as well as other contributing factors such as temperature variations and the management of humidity and water. Therefore, a DC-DC converter is necessary to provide a stable voltage and increase the voltage of the fuel cell stack to the desired level for direct use in practical applications. Among the types of DC-DC converters most commonly used in the industrial world, two categories stand out with voltage boosting functions: isolated and non-isolated converters. The advantages of isolated converters include galvanic isolation and a theoretically very high voltage boost ratio. Applications that are not sensitive to size and require a high voltage ratio have favored isolated converters, particularly in the field of fuel cells [9; 10], such as in photovoltaic applications. However, for size, cost, and power density-sensitive applications like automobiles, isolated converters become less attractive. Theoretically, a standard boost converter, as the simplest and least expensive non-isolated solution, could be used in fuel cell vehicles. However, its simple structure limits its use due to the lack of redundancy and limited ability to suppress current ripple [11].