Machine Learning–Driven MPPT Control of PEM Fuel Cells with DC–DC Boost Converter Integration

Abstract

Proton exchange membrane fuel cells (PEMFCs) are attractive energy sources for clean and efficient power generation; however, their nonlinear characteristics and sensitivity to operating condition variations make maximum power point tracking (MPPT) a challenging control problem. Conventional MPPT techniques often exhibit slow convergence, steady-state oscillations, and degraded performance under dynamic fuel flow variations. This paper proposes a machine learning–driven MPPT control strategy for a PEMFC system integrated with a DC–DC boost converter. The MPPT problem is formulated as a supervised classification task, where machine learning classifiers generate duty-cycle commands to regulate the converter and ensure operation at the maximum power point. A detailed PEMFC–converter model is developed in MATLAB/Simulink-2025b, and a dataset of 3000 labeled samples is generated under varying fuel flow conditions. Several classification algorithms, including decision trees, support vector machines (SVM), k-nearest neighbors (kNN), and ensemble learning methods, are systematically evaluated within an identical simulation framework. Simulation results show that the proposed machine learning-based MPPT controller significantly improves dynamic and steady-state performance. Ensemble Boosted Trees achieve the best overall response with a settling time of approximately 32 ms, peak power overshoot below 4.5%, and steady-state power ripple limited to 1.5%. Quadratic SVM and weighted kNN classifiers also demonstrate stable tracking behavior with power ripple below 2.1%, while overly complex models such as Cubic SVM suffer from large oscillations and reduced accuracy. These results confirm that classification-based machine learning offers an effective, fast, and robust MPPT solution for PEMFC systems under dynamic operating conditions.

1. Introduction

As a consequence of heightened fossil fuel consumption, the planet has experienced elevated temperatures, leading to detrimental ecological consequences, including air pollution, and global warming, which have had impacts on both human and animal ecosystems. Consequently, governments across the globe are actively investigating alternative and sustainable energy sources as a means of diminishing their dependency on fossil fuels and reducing the associated environmental outcomes. Over recent years, the popularity of alternative energy sources such as solar, wind, and geothermal has increased due to their sustainability and lack of pollution [1,2,3]. However, the irregular nature of renewable energy sources poses substantial challenges in terms of ensuring their dependable and efficient deployment. The fluctuating energy production from sources such as solar and wind power introduces instability into the power supply, complicating the task of meeting the consistent energy requirements across diverse applications and sectors. In response to these obstacles, extensive research and technological advancements have been directed toward devising viable remedies. One strategy entails the incorporation of energy storage systems, designed to accumulate unused energy during periods of elevated generation and disburse it during periods of low generation or heightened demand. A second strategy involves the utilization of hydrogen as a sustainable energy source. Consequently, researchers have shifted their focus toward developing portable and efficient alternative energy sources such as Hydrogen. Hydrogen energy exhibits distinguishing features, including its widespread availability, substantial mass and energy density, and ecologically friendly. As a result of these attributes, it has been heralded as the quintessential energy source for the 21st century and has ascended to a position of paramount significance on the strategic agendas of numerous nations [4]. The combustion of hydrogen yields exclusively water as its byproduct. Hydrogen, characterized by its versatility as a fuel source, finds application in heating when combusted in conjunction with oxygen. Moreover, it can be harnessed for the generation of electrical power through the actuation of a generator employing motor/gas turbines, or alternatively, through its utilization as a primary energy source in FCs.

In 1839, the main structure of FCs was first introduced by William R. Grove, a British physicist known for his contributions to electrochemistry. Grove described a device that could convert chemical energy directly into electrical energy through a reaction between hydrogen and oxygen [5]. This idea formed the basis of modern FC technology. Today, FCs are described as consisting of an electrolyte placed between two electrodes. The electrolyte’s distinctive feature lies in its selective permeability, enabling positively charged ion transport and excluding electron movement. As part of the operational process, hydrogen gas is conveyed over one of the electrodes, termed the anode. Facilitated by a catalyst, this hydrogen gas undergoes a dissociation process into electrons and hydrogen protons. FCs are electrochemical devices, and offer advantages such as modularity, safety, low emissions, good transient response, and high scalability. In comparison to traditional energy sources, FCs reduce carbon dioxide emissions and are suitable for various applications in areas such as residential, portable, vehicular, space, and more [6,7]. The operating principle of a FC is almost the same as that of a battery, but unlike a battery, a FC is a continuously operating energy source.

FCs can be categorized in several ways based on various factors, such as operating temperature, electrolyte, and other characteristics, particularly the type of electrolyte used within the FC system. If the main types of FCs listed; AFC, DMFC, PAFC, MCFC, SOFC, and PEMFCs [8]. In recent years, two commercially established technologies have emerged within the FC domain: the AFC, and the PEMFC. AFC has established itself as a well-entrenched technology, extensively employed in medium and large-scale installations. In contrast, PEMFCs have attracted significant attention for smaller-scale applications. This is because they are user-friendly and less complicated to maintain. Additionally, PEMFCs operate without the need for hazardous chemicals, enhancing their safety profile and making them an attractive option for various settings where environmental concerns are a priority [9]. The notable advantages of PEMFC technology, including its high energy density, superior energy efficiency, low acoustic emissions, cost-effectiveness, minimal operating temperatures, rapid startup capabilities, corrosion resistance, solid electrolyte use, and extended operational lifespan, have contributed to its prominence. PEMFCs operate at a temperature of approximately 80°C, boasting an efficiency range of 40% to 60% and accommodating power generation spanning from 50 W to 250 kW [10]. This low-temperature operational profile positions PEMFCs as a compelling choice for residential and vehicular applications. Consequently, they have found substantial adoption in Distributed Generation (DG) systems and portable electronic devices [11]. In

Table 1. A brief comparative summary of FCs.

FC Types	Electrodes–Electrolyte	Advantages–Disadvantages
AFCs	The electrodes are composed of a two-layer structure, consisting of an active electrocatalyst and a hydrophobic layers. The active layer consists of a mix of organic materials. These materials are combined, milled, and compacted at room temperature to create a self-supporting layer through powder cross-linking. To maintain effective gas delivery to the catalytic regions, the hydrophobic layer prevents the electrolyte from entering the small openings of the gas channels. AFCs utilize hydrogen gas (H2) as the primary fuel source and employ alkaline solutions such as NaOH or KOH as electrolytes. The oxidant employed in these systems is typically pure oxygen rather than air, primarily to mitigate the risk of electrolyte carbonation caused by carbon dioxide (CO2) in the air [12].	Alkaline FCs offer several advantages, including the capability to utilize hydrogen of lower purity, high efficiency, operation below 0 °C, and the potential utilization of non-precious metal catalysts. These attributes allow for the deployment of alkaline FCs outdoors and their initiation in subfreezing conditions without the need for preheating. Various approaches for system integration are available, contingent upon the specific electrolyte and stack configuration. However, AFCs are sensitive to carbon dioxide (CO2) and impurities. CO2 can carbonate the electrolyte, leading to performance degradation and reduced cell lifespan. Also, AFCs typically operate at relatively low temperatures compared to other FC types, which may limit their efficiency and performance in certain applications [13].
SOFCs	SOFCs use an oxygen ion conducting electrolyte that enables the conduction of oxide ions (O2−). At the anode, these ions engage in electrochemical reactions with the fuel sources such as H2, CO, among others, thereby generating an electrical potential difference [14]. The impedance characteristics of SOFCs are predominantly influenced by the resistance exhibited by individual components. Methods used to reduce internal resistance in electrolytes typically involve reducing thickness while reducing leakage current and pinhole formation [15].	With operating temperatures ranging from 600 to 1000 °C, SOFCs deliver high fuel flexibility and efficiency, particularly through waste heat recovery in combined heat and power applications. However, to fully realize their potential and achieve economic competitiveness with conventional energy conversion technologies, further advancements are needed, particularly in enhancing the durability and reliability of SOFCs. They have longer lifespans due to their robust design and use of stable materials. They can operate continuously for thousands of hours with minimal degradation [16].
PAFCs	The electrodes, both cathode and anode, consist of platinum deposited onto a carbon-based gas diffusion layer, with varying loadings of the platinum catalyst. The electrolyte, predominantly composed of phosphoric acid (H3PO4), facilitates the migration of protons from the anode to the cathode, while electrons cross through an external circuit. At the cathodic interface, atmospheric air is supplied, enabling the reaction between oxygen, protons originating from the electrolyte, and electrons sourced from the external load [17].	The PAFC stands as the most extensively utilized and comprehensively documented variety of FC technology. Since the 1970s, many PAFC power plants have undergone installation and rigorous testing across various global locations. Over successive product iterations, the volume of units sold has consistently increased, alongside enhancements in the power rating per individual unit [18]. PAFCs tend to be larger and heavier compared to some other FC types. They have a slower start-up time. Also, PAFCs operate at relatively high temperatures (typically around 150–200 °C), which can lead to increased thermal management requirements and potential degradation of cell components over time.
MCFCs	MCFCs utilize a ceramic matrix solid electrolyte, which is chemically inert and porous, to contain a mixture of molten carbonate salts. MCFCs employ an electrolyte composed of molten alkali metal carbonates, typically a combination of lithium, potassium, and sodium carbonates. A unique characteristic of MCFCs is the transport of carbonate ions from the cathode to the anode through the molten electrolyte [19].	MCFCs exhibit superior resilience to impurities compared to alternative FC variants, thereby mitigating susceptibility to CO2 or CO-induced poisoning. Consequently, MCFCs can effectively utilize gases derived from coal or carbon oxides as fuel sources. Additionally, MCFCs demonstrate the potential to achieve notably high energy efficiencies, reaching approximately 60% in certain scenarios. Owing to their elevated operational temperatures, MCFCs are conducive to cogeneration applications, facilitating waste heat recovery and utilization [20]. MCFCs face notable challenges, with durability emerging as a significant concern. The prolonged longevity of cells is impeded by the corrosive characteristics of the electrolyte and the elevated operational temperatures. Also, MCFCs are unsuitable for portable applications.
PEMFCs	A PEMFC is structured with a cathode, an anode, and an electrolyte membrane. The anode oxidizes hydrogen while the cathode reduces oxygen. Protons move through the membrane to the cathode, and electrons flow through an external circuit. At the cathode, oxygen combines with protons and electrons, producing thermal energy and water [21,22].	PEMFCs have demonstrated high energy conversion efficiencies and can be used many areas such as transportation, powering cars/buses, stationary power generation. Their lightweight and compact design also makes them particularly well-suited for situations where spatial limitations and weight restrictions, especially in vehicles and portable electronic devices, are crucial factors. PEMFCs are complex systems that involve the movement of both liquids and gases, as well as heat flow and chemical reactions. These systems have many parts that interact with each other in complicated ways. Because of this, it is very important to optimize the parameters in the PEMFC model [23].

, a brief comparative summary is given.

So far, the typical operational lifespan of PEMFCs has fallen short of meeting the criteria for widespread commercial deployment. For instance, the anticipated longevity of PEMFCs in real-world transportation conditions is approximately 3000 h, whereas transportation applications necessitate a minimum of 5000 h of durability. Consequently, the principal challenge that must be addressed to facilitate the universal adoption of PEMFCs is the enhancement of their reliability and longevity [24]. It is noteworthy that PEMFC production relies heavily on the utilization of expensive noble materials, such as platinum catalysts and acid membranes, which exhibit limited durability, especially when subjected to unstable and cyclical stress conditions. Moreover, the voltage generated by a single FC ranges from 0 to 1 V, depending on the operating conditions of the FC and the magnitude of the load connected to it [25]. Typically, the voltage produced by an FC is around 0.7 V. To obtain a higher voltage, multiple cells can be arranged in series or parallel. However, increasing the number of FCs reduces the efficiency and increases the cost of the FC system. For these reasons, recent research has also focused on modeling the DC–DC converter, as the system’s efficiency and stable operation must be evaluated as a whole [26]. The output voltage of the PEMFC system can be increased to several hundred or even thousands of volts, which is suitable for power transmission units in both vehicular and residential applications. To achieve this goal, various DC–DC converter designs such as boost/buck/buck-boost converters and maximum power point techniques (MPPT) such as PID, perturb and observe etc. have been developed [27].

In recent years, advanced deep learning-based frameworks have been increasingly adopted to address complex nonlinear behaviors, data scarcity, and domain mismatch issues in intelligent monitoring and control systems. Generative adversarial learning, in particular, has demonstrated strong capability in feature augmentation and domain transfer, as evidenced by adaptive fused domain-cycling variational generative adversarial networks, which effectively enhance fault diagnosis performance under limited labeled data and cross-domain operating conditions [28,29]. In parallel, multimodal deep learning techniques have gained recognition in safety-critical applications such as railway systems, where the fusion of heterogeneous sensory information enables more robust arc detection and condition monitoring under noisy and uncertain environments [30,31]. Furthermore, dynamic collaborative adversarial domain adaptation networks have been proposed to improve model generalization by jointly learning transferable representations and adaptive decision boundaries across varying operating domains [32,33]. These state-of-the-art deep learning approaches highlight the growing importance of data-driven intelligence for handling nonlinearity, uncertainty, and environmental variability in modern engineering systems, providing valuable context for the development of learning-based power management and control strategies.

Srinivasan et al. proposed a MPPT technique for PEMFC that relies on artificial neural networks (ANN) [34]. Their study specifically focused on a radial basis function network (RBFN)-based MPPT strategy, which aims to optimize the extraction of achievable maximum power of FC under diverse conditions [35]. Fathy et al. introduced the salp swarm algorithm (SSA), which has been effectively used to tune a proportional-integral-derivative (PID) controller [36]. Inci presented an online iteration method based on the P&O method [37]. Harrag et al. conducted research on a neural network IC-based variable step size MPPT controller [38]. Additionally, Percin et al. introduced the whale optimization algorithm as a technique for estimating the optimal output power in response to step changes in water content [39].

In this research, it is focused on the development and analysis of an MPPT control system for a PEMFC system, implemented using MATLAB/Simulink. The control system leverages an optimization algorithm based on machine learning (ML) to achieve precise and adaptive control over the operating of the PEMFC system. The machine learning algorithm plays a critical role by adjusting the duty cycle of the DC–DC converter. This dynamic adjustment is crucial for optimizing power extraction under a variety of environmental factors, such as temperature and humidity, as well as operational conditions that can change throughout the day. The primary focus of this study is to evaluate the performance of the newly proposed machine learning-based MPPT algorithm in accurately tracking the maximum power point (MPP), thereby maximizing the energy output of the PEMFC system.

1.1. Study Motivation

The rapid transition toward low-carbon and sustainable energy systems has significantly increased interest in hydrogen-based technologies and FC applications. Among the available FC technologies, PEMFCs stand out due to their high energy efficiency, compact structure, fast start-up capability, and suitability for dynamic applications such as transportation and residential power generation. However, the inherent nonlinear behavior of PEMFCs, coupled with their sensitivity to variations in operating conditions, poses serious challenges in maintaining stable and efficient power generation. In particular, inefficient power extraction and voltage instability under dynamic loading conditions can negatively affect system performance, durability, and overall energy efficiency.

An effective MPPT strategy is therefore crucial for ensuring optimal operation of PEMFC systems. Conventional MPPT methods often suffer from slow tracking speed, steady-state oscillations, and limited adaptability to rapid changes in fuel flow and environmental parameters. These shortcomings highlight the need for more intelligent and adaptive control strategies. Recent advances in machine learning provide a promising framework for addressing these challenges by enabling data-driven, adaptive, and robust control solutions. Motivated by this need, the present study focuses on the development of a machine learning-based MPPT controller integrated with a DC–DC boost converter to enhance power extraction accuracy, reduce power fluctuations, and improve the overall operational reliability of PEMFC systems under varying operating conditions.

1.2. Case Study Contribution

This paper presents several noteworthy contributions. First and foremost, it augments the existing body of knowledge by integrating contemporary MPPT techniques into PEMFC technology. Secondly, it delivers commendable outcomes characterized by swift response times, minimal overshooting, reduced oscillations around the MPP, and diminished voltage ripple. Thirdly, the paper achieves a stabilized output voltage from the PEMFC, devoid of oscillations, and optimally configured for fuel consumption, simultaneously ensuring protection against overcurrent and voltage collapse. Lastly, it mitigates fluctuations and disturbances, thereby enhancing the overall longevity of the PEMFC. This section outlines the main scientific and practical contributions of the present case study, focusing on the application of machine learning techniques for maximum power point tracking in proton exchange membrane FC systems.

• A machine learning-based MPPT control framework is developed for PEMFC systems, enabling adaptive and accurate power extraction under dynamically varying operating conditions.
• The proposed MPPT strategy is integrated with a DC–DC boost converter, resulting in improved voltage regulation, reduced power oscillations, and enhanced overall system stability compared to conventional MPPT methods.
• Multiple machine learning classifiers are implemented and systematically evaluated within the MPPT structure using MATLAB/Simulink, providing a comparative assessment of tracking accuracy and robustness.
• The effectiveness of the proposed approach is validated under varying fuel flow scenarios, demonstrating improved dynamic response and reliable maximum power point tracking performance.
• The presented case study offers practical insights into the deployment of intelligent MPPT controllers for PEMFC power management, supporting the development of efficient and reliable FC energy systems.

2. Materials and Methods

The presented configuration features a FC integrated with a DC–DC boost converter and a load, as illustrated in Figure 1. To thoroughly assess PEMFCs under various control objectives, it is necessary to comprehensively examine the system characteristics and its dynamic model. Typically, PEMFCs operate through the electrochemical reaction of hydrogen and oxygen, producing electrical energy along with heat and water as by-products [30].

One of the main advantages of FCs is their high efficiency, which is achieved with lower power losses compared to conventional fuel-based energy systems. This advantage is primarily attributed to the absence of moving parts, which reduces mechanical wear and minimizes energy losses due to friction. However, despite their high efficiency, the output voltage level of PEMFCs is relatively low and insufficient for many practical applications. Therefore, a DC–DC converter is required to step up the FC output voltage to levels suitable for supplying loads or interfacing with power electronic systems. This step is essential for applications that demand higher voltage levels than those provided directly by the FC. The DC–DC boost converter enables efficient voltage conversion and regulation, ensuring that the generated power can be effectively utilized [40]. In the proposed system, the PEMFC output voltage is fed into a MPPT controller. The MPPT controller generates a control signal that drives the switching device of the DC–DC boost converter, thereby regulating the duty cycle and ensuring efficient power transfer from the FC to the load. By continuously optimizing the operating point of the PEMFC through MPPT control, the system operates at its MPP, resulting in enhanced overall efficiency and improved system performance.

2.1. PEMFC

PEMFCs utilize a polymer membrane with proton-conductive properties as their electrolyte. The term PEM is an abbreviation for Polymer Electrolyte Membrane, and these cells are also referred to as polymer membrane FCs or membrane FCs. During their initial development in the 1960s, PEMFCs were recognized as Solid Polymer Electrolyte (SPE) FCs [41,42]. PEMFCs have gained considerable attention due to their numerous advantages, including high energy efficiency, high energy density, minimal operating noise, cost-effectiveness, low operating temperature, fast start-up capability, corrosion resistance, the use of solid electrolytes, and extended operational lifetime [43].

These advantageous characteristics make PEMFC technology highly suitable for a wide range of applications, ranging from portable electronic devices such as mobile phones and tablets to transportation systems, including buses and trains [44]. The operation of a PEMFC can be illustrated using both a circuit diagram and a corresponding electrical circuit model, as shown in Figure 2. The circuit diagram represents the fundamental physical components and their interconnections within the FC, providing a clear understanding of the electrochemical processes involved. Meanwhile, the electrical circuit model establishes a mathematical framework for analyzing and describing the flow of electricity generated during the electrochemical reactions occurring inside the cell. This modeling approach helps to clarify how the PEMFC converts hydrogen and oxygen into electrical power, water, and thermal energy, emphasizing the contribution of each component to the overall system [45,46].

The electrochemical reactions occurring within a PEMFC can be expressed as follows:

$$\left\{\begin{array}{cc}\hfill \mathrm{Anode}\mathrm{reaction}:& {\mathrm{H}}_2\to 2{\mathrm{H}}^{+}+2{\mathrm{e}}^{-}\hfill \\ \hfill \mathrm{Cathode}\mathrm{reaction}:& \frac{1}{2}{\mathrm{O}}_2+2{\mathrm{H}}^{+}+2{\mathrm{e}}^{-}\to {\mathrm{H}}_2\mathrm{O}\hfill \\ \hfill \mathrm{Overall}\mathrm{reaction}:& {\mathrm{H}}_2+\frac{1}{2}{\mathrm{O}}_2\to {\mathrm{H}}_2\mathrm{O}+\mathrm{electrical}\mathrm{energy}+\mathrm{thermal}\mathrm{energy}\hfill \end{array}\right.$$

(1)

The resistive elements $R_{\Omega \mathrm{cell}}$, $R_{c\mathrm{cell}}$, and $R_{\mathrm{actcell}}$, shown in Figure 2, are used to determine the overall performance of the FC. The resistance $R_{\Omega \mathrm{cell}}$ represents the ohmic resistance, which arises from the internal properties of the materials used in the cell and leads to energy loss in the form of heat. The resistance $R_{c\mathrm{cell}}$ is associated with concentration polarization, which occurs due to variations in reactant concentrations during cell operation. In contrast, $R_{\mathrm{actcell}}$ represents the activation polarization resistance, which is related to the energy barrier that must be overcome for electrochemical reactions to occur [47].

Based on these loss mechanisms, the output voltage of the FC can be calculated using Equation (2) [48].

$$V_{\mathrm{FCcell}}=E_{\mathrm{cell}}-V_{\mathrm{actcell}}-V_{\Omega \mathrm{cell}}-V_{c\mathrm{cell}}$$

(2)

Here, $V_{\mathrm{FCcell}}$ and $E_{\mathrm{cell}}$ denote the electrical output voltage of the FC and the open-circuit voltage, respectively. The terms $V_{\mathrm{actcell}}$, $V_{\Omega \mathrm{cell}}$, and $V_{c\mathrm{cell}}$ represent the voltage losses due to activation polarization, ohmic resistance, and concentration (mass transport) effects occurring at the electrodes and membrane. As observed from Equation (2), these voltage drops depend on the load current as well as the operating temperature and pressure of the FC [49]. For a FC stack consisting of multiple cells connected in series, the overall output voltage can be expressed as

$$V_{\mathrm{FC}}=N_{\mathrm{cell}}{V}_{\mathrm{FCcell}}=E-V_{\mathrm{act}}-V_{\Omega }-V_c$$

(3)

The open-circuit voltage $E_{\mathrm{cell}}$ of a PEMFC can be calculated using the Nernst thermodynamic equation, which is given in Equation (4). This equation enables the evaluation of the FC performance by accounting for key operating variables such as temperature, system pressure, and the partial pressures of hydrogen and oxygen gases. In this mathematical formulation, voltage losses due to ohmic resistance, activation polarization, and concentration polarization are neglected in order to represent the ideal reversible cell potential [50].

$$E=1.229-0.85\times {10}^{-3}(T-T_c)+{\displaystyle \frac{RT}{2F}}\left[ln\left(p_{H_2}\right)+{\displaystyle \frac{1}{2}}ln\left(p_{O_2}\right)\right]$$

(4)

Here, T represents the cell operating temperature measured in Kelvin, and $T_c$ denotes the temperature correction offset. The variables $p_{O_2}$ and $p_{H_2}$ represent the partial pressures of oxygen and hydrogen gases, respectively. The universal gas constant R is taken as $8.314\mathrm{J}/(\mathrm{mol}·\mathrm{K})$, and the Faraday constant is denoted as F. The value $1.229\mathrm{V}$ corresponds to the reversible standard potential $E_0$ at $T_c=298.15\mathrm{K}$.

The T equation is widely used to analyze the activation overvoltage ($V_{\mathrm{act}}$) in FCs. This loss is primarily influenced by the reaction kinetics of hydrogen oxidation at the anode and oxygen reduction at the cathode, both of which play a crucial role in determining the overall performance of the FC. Activation losses represent the energy required to overcome the electrochemical reaction barriers during FC operation. The total activation overvoltage, accounting for both anode and cathode contributions, is expressed by Equation (5) [51].

$$V_{\mathrm{act}}={\xi }_1+{\xi }_{2}T+{\xi }_{3}Tln\left(C_{O_2}\right)+{\xi }_{4}Tln\left(I_{\mathrm{FC}}\right)$$

(5)

In Equation (5), the activation overvoltage is modeled using semi-empirical coefficients that capture the electrochemical reaction kinetics at the anode and cathode of the PEMFC. The parameter ${\xi }_1$ represents the combined activation overpotential at reference conditions, while ${\xi }_2$ accounts for the temperature-dependent variation of the activation losses. The coefficient ${\xi }_3$ reflects the influence of oxygen concentration at the cathode catalyst layer, and ${\xi }_4$ characterizes the logarithmic dependence of activation overvoltage on the fuel cell current. These coefficients are typically obtained through curve fitting of experimental polarization data or adopted from validated empirical models reported in the literature. In this study, the parameter values were selected based on well-established PEMFC models and are summarized in

Table 2. Activation overvoltage model parameters used in Equation (5).

Parameter	Description	Value Used	Unit	Reference
${\xi }_1$	Activation voltage constant	$-0.948$	V	[52]
${\xi }_2$	Temperature coefficient	$0.00286$	$\mathrm{V}·{\mathrm{K}}^{-1}$	[52]
${\xi }_3$	Oxygen concentration coefficient	$7.6\times {10}^{-5}$	$\mathrm{V}·{\mathrm{K}}^{-1}$	[52]
${\xi }_4$	Current-dependent coefficient	$-1.93\times {10}^{-4}$	$\mathrm{V}·{\mathrm{A}}^{-1}·$${\mathrm{K}}^{-1}$	[52]
$C_{{\mathrm{O}}_2}$	Oxygen concentration at cathode	Computed from pressure	mol·cm−3	[53]

. Detailed derivations and parameter identification procedures can be found in the referenced studies, which provide comprehensive explanations of the underlying electrochemical modeling framework.

The parameter $I_{\mathrm{FC}}$ represents the FC current, while $C_{O_2}$ denotes the oxygen concentration at the membrane surface. The coefficients ${\xi }_1$, ${\xi }_2$, ${\xi }_3$, and ${\xi }_4$ are characteristic parameters of the FC model and can be derived using the partial pressure of oxygen. Resistances within the membrane and interconnections give rise to ohmic losses ($V_{\Omega }$) as electrons travel from the anode to the cathode. These losses are caused by ionic resistance in the membrane and electronic resistance in the electrodes and current collectors. The ohmic voltage loss, expressed in Equation (6), can be calculated based on Ohm’s law [54].

$$V_{\Omega }=I_{\mathrm{FC}}\left({\displaystyle \frac{r_{m}l}{A}}+R_{\mathrm{elec}}\right)$$

(6)

Here, $r_m$, l, and A represent the membrane ionic conductivity, the thickness of the cell membrane, and the active surface area of the FC. The electrical resistance $R_{\mathrm{elec}}$ is of a relatively small magnitude and has a negligible effect on the overall results; therefore, it can be ignored.

According to the literature [55], a concentration overvoltage ($V_c$) arises due to mass transport limitations in the PEMFC. This voltage loss can be expressed using Equation (7).

$$V_c=-bln\left(1-{\displaystyle \frac{I_{\mathrm{FC}}/A}{I_{max}}}\right)$$

(7)

Here, b, $I_{\mathrm{FC}}$, and $I_{max}$ denote the concentration loss coefficient, the operating current of the FC, and the maximum current density, respectively. In addition, A represents the active surface area of the cell.

The theoretical voltage generated by the electrochemical reaction of hydrogen and oxygen is approximately $1.23\mathrm{V}$. However, in practical FC operation, the actual voltage produced by an individual FC is lower due to several factors, including internal resistances and inefficiencies in the electrochemical processes. Under nominal operating conditions, the output voltage of a single cell typically ranges between $0.6\mathrm{V}$ and $0.7\mathrm{V}$. This voltage reduction can significantly affect the overall performance of the FC system [56].

To achieve the desired output voltage and power levels, FCs can be configured in different electrical arrangements. When FCs are connected in series, the total output voltage increases as the voltages of individual cells are summed, making this configuration suitable for applications requiring higher voltage levels. Conversely, when FCs are connected in parallel, the total output current increases while maintaining the same voltage level, thereby enabling higher power capacity. By combining series and parallel connections, specific voltage and current requirements can be satisfied, optimizing the system performance for various applications. Such a configuration is commonly referred to as a FC stack [57].

The required number of series-connected cells ($N_{\mathrm{series}}$) and parallel-connected stacks ($N_{\mathrm{parallel}}$) can be determined using Equation (8).

$$\left\{\begin{array}{cc}\hfill N_{\mathrm{series}}& ={\displaystyle \frac{V_{\mathrm{FC}}}{V_{\mathrm{stack}}}}\hfill \\ \hfill N_{\mathrm{parallel}}& ={\displaystyle \frac{P_{\mathrm{FC}}}{N_{\mathrm{series}}{P}_{\mathrm{stack}}}}\hfill \end{array}\right.$$

(8)

Here, $P_{\mathrm{FC}}$ and $V_{\mathrm{FC}}$ denote the output power and output voltage of the FC system, respectively, while $P_{\mathrm{stack}}$ and $V_{\mathrm{stack}}$ represent the operating power and operating voltage of the FC stack.

The power generation of a FC is primarily influenced by operating parameters such as cell temperature and membrane water content. As the hydrogen consumption rate in a PEMFC increases, a proportional increase in the electrical current generated by the cell is observed. The performance of a PEMFC is commonly characterized by its voltage–current (V–I) relationship, which provides critical insight into its operating behavior. Accordingly, the efficiency of the FC can be evaluated by analyzing its output voltage, which decreases as the electrical power generated per unit amount of hydrogen consumed is reduced. Therefore, the cell voltage serves as a reliable indicator of the overall efficiency and performance of the FC [58]. Based on the derived mathematical models, the polarization curve of the PEMFC can be obtained by plotting the V–I characteristics, as illustrated in Figure 3. This curve is a fundamental tool for assessing the performance and operating limits of the FC.

2.2. DC–DC Boost Converter

Power electronic circuits play a critical role in monitoring and optimizing the MPPs of PEMFCs, thereby ensuring a stable and desirable voltage level under varying operating conditions. In order to supply electric motors, residential loads, or grid-connected systems, the relatively low DC bus voltage generated by FCs must be increased to higher voltage levels using a DC–DC boost converter. Consequently, achieving a high voltage gain with high efficiency over a wide range of output power is essential for the overall performance of the converter [59].

In this study, a DC–DC boost converter is employed to enhance output voltage stability by stepping up the input voltage to a higher and more regulated level [60]. A basic circuit configuration of the DC–DC boost converter is illustrated in Figure 4. The converter comprises several key components: the input voltage source ($V_{\mathrm{DC}}$), which may originate from a DC source or a battery; an inductor (L), which stores energy when the switch is turned on and releases it to the output when the switch is turned off; a diode (D), which ensures unidirectional current flow and prevents reverse current; and a filter capacitor (C), which smooths the output voltage by reducing ripple and maintaining a steady voltage level across the load [61].

The switching device (S) operates based on a pulse-width modulation (PWM) control signal, alternating between on and off states to regulate the energy transfer from the inductor to the output. In this analysis, all electronic components are assumed to be ideal, meaning that resistive losses and non-ideal characteristics of the inductor, capacitor, diode, and switch are neglected for simplicity. The switch is turned on during the interval $t_{\mathrm{on}}=dT$, where d denotes the duty cycle and T represents the switching period. During this interval, as shown in Figure 4b, the switch S is closed and the diode D is reverse-biased. Conversely, during the interval $t_{\mathrm{off}}=(1-d)T$, illustrated in Figure 4c, the switch S is opened and the diode D becomes forward-biased, allowing energy transfer to the output [40].

The duty cycle (d), as well as the inductor and capacitor values of the DC–DC boost converter, can be determined using Equations (9)–(11). The duty cycle is constrained within the range $0\le d\le 1$. When the switch remains continuously in the off state, corresponding to $d=0$, the output voltage is equal to the input source voltage. As the duty cycle increases, a proportional rise in the output voltage is obtained. Based on the inductor volt–second balance principle, the steady-state operation of the boost converter can be expressed as

$$\left\{\begin{array}{cc}\hfill V_{L_{\mathrm{on}}}{t}_{\mathrm{on}}+V_{L_{\mathrm{off}}}{t}_{\mathrm{off}}& =0\hfill \\ \hfill V_{\mathrm{DC}}dT+(V_{\mathrm{DC}}-V_o)(1-d)T& =0\hfill \\ \hfill V_o(1-d)T& =V_{\mathrm{DC}}T\hfill \\ \hfill V_o& ={\displaystyle \frac{V_{\mathrm{DC}}}{1-d}}\hfill \end{array}\right.$$

(9)

$$L={\displaystyle \frac{V_{\mathrm{DC}\left(\min \right)}}{\Delta I_L{f}_s}}d$$

(10)

$$C_{min}={\displaystyle \frac{I_{o(max)}d}{f_s\Delta V_o}}$$

(11)

Equations (10) and (11) were evaluated based on the nominal operating conditions of the PEMFC system and conservative ripple design criteria to ensure stable MPPT operation. The inductor value was selected by limiting the peak-to-peak inductor current ripple to a small fraction of the rated PEMFC current, while the capacitor value was determined to maintain the output voltage ripple within a tight bound under dynamic load and fuel flow variations. The relatively large inductance and capacitance values adopted in this study were intentionally chosen to reduce current and voltage ripple, suppress high-frequency oscillations, and improve system robustness during rapid MPPT transients. These design choices prioritize control stability and clear evaluation of the ML-based MPPT strategy over converter size optimization.

The passive component values reported in

Table 3. Boost converter passive component design parameters.

Parameter	Symbol	Value Used	Unit	Design Rationale
Switching frequency	$f_s$	10	kHz	Balance between switching loss and control bandwidth
Nominal PEMFC power	$P_{\mathrm{nom}}$	1.5	kW	Rated operating condition
Nominal input voltage	$V_{\mathrm{in}}$	48	V	PEMFC stack voltage at nominal load
Output voltage	$V_{\mathrm{out}}$	120	V	DC bus requirement
Inductor current ripple ratio	$\Delta I_L/I_L$	20	%	Conservative ripple limit for stability
Voltage ripple limit	$\Delta V_o/V_o$	1	%	Ensures smooth MPPT operation
Inductance	L	10	mH	Reduced current ripple and improved transient response
Output capacitance	C	100	$\mathsf{\mu }$F	Voltage ripple suppression during MPPT transitions

were selected following conservative design criteria commonly adopted in PEMFC power conditioning systems to ensure low ripple and stable dynamic behavior. In the literature, DC–DC boost converters interfaced with PEM fuel cells often employ relatively large inductance and capacitance values to mitigate the inherent slow dynamics of fuel cells and suppress current and voltage oscillations that may degrade system performance. For example, in IEEE Transactions–level studies on PEMFC power conditioning, inductance values are intentionally chosen to limit current ripple to 15–30% of the rated current, while output capacitors are sized to maintain voltage ripple within 1–2% under load and operating condition variations [62,63].

Compared with designs that prioritize compactness or high power density, the component values used in this work emphasize control stability and robustness during MPPT transients rather than hardware minimization. As summarized in Table 3, the adopted inductance and capacitance values fall within the range reported in prior IEEE Transactions studies for low- to medium-power PEMFC systems, and are particularly suitable for evaluating MPPT algorithms without confounding effects from excessive electrical ripple or converter-induced instability [62,63,64,65].

2.3. Topology Selection Rationale for PEMFC MPPT Applications

This subsection explains that the conventional boost converter was selected due to its structural simplicity, low component count, ease of integration with classification-based ML-MPPT control, and suitability for low- to medium-power PEMFC systems. It also clarifies that the primary objective of this study is to evaluate the effectiveness of the ML-MPPT algorithm itself, and that using a simple and well-understood converter topology avoids introducing additional design variables that could obscure the interpretation of MPPT performance.

Although several advanced DC–DC boost converter topologies have been reported in the literature for fuel cell and renewable energy applications, the selection of an appropriate converter must consider not only electrical performance but also control integration and implementation complexity. To clarify the rationale behind the chosen converter structure, a qualitative comparison of commonly used boost converter topologies is provided in

Table 4. Comparison of boost converter topologies for PEMFC MPPT applications.

Topology	Main Advantages	Main Limitations	Suitability for This Study
Conventional boost converter	Simple structure, low component count, easy control integration	Higher current ripple compared to advanced topologies	Selected–enables clear evaluation of ML-MPPT behavior
Interleaved boost converter	Reduced input current ripple, higher power capability	Increased hardware and control complexity	Not selected–additional phases complicate MPPT analysis
Double dual boost converter	High voltage gain, improved efficiency	More switches and control states	Not selected–beyond scope of MPPT-focused study
Cascaded/ multi-stage boost	Very high voltage gain	Lower efficiency, complex design	Not suitable for PEMFC power level considered

. As summarized in the table, the conventional boost converter offers a favorable balance between structural simplicity, ease of integration with machine learning-based MPPT algorithms, and suitability for low- to medium-power PEMFC systems. While alternative topologies such as interleaved or double dual boost converters can provide reduced current ripple or higher voltage gain, they introduce additional switching devices, control variables, and synchronization requirements, which may obscure the direct evaluation of MPPT algorithm performance. Therefore, the conventional boost topology was selected to ensure a clear and focused assessment of the proposed ML-MPPT strategy without confounding effects arising from converter-level complexity.

The comparison in Table 4 highlights that the selected topology is well aligned with the primary objective of this study, which is to evaluate the effectiveness of machine learning-based MPPT control rather than to optimize converter hardware complexity.

3. MPPT Control Methods

To mitigate and partially eliminate factors that degrade FC performance—such as the low power output of the FC stack, slow dynamic response, transient behavior, and the charging and discharging control of the energy storage unit—an MPPT strategy must be employed and properly optimized. This approach ensures that the FC stack consistently operates at its maximum power point and delivers the highest possible energy output, even under fluctuating operating conditions. In practical implementations, a DC–DC converter operating in conjunction with MPPT algorithms is used to regulate the output DC voltage and maximize power extraction from the FC source. The power flow from the FC is controlled by adjusting the duty cycle of the DC–DC converter, enabling the system to track the optimal operating point in real time. Consequently, MPPT plays a critical role in improving both the efficiency and dynamic performance of FC-based energy systems [66].

In the literature, numerous methods have been proposed for identifying and tracking the MPP [67,68]. These MPPT algorithms are commonly classified into four main categories, namely classical, intelligent, optimization-based, and hybrid approaches, along with their respective subcategories, as illustrated in Figure 5.

In classical control approaches, such as proportional–integral–derivative (PID)-based controllers, system performance largely depends on the accurate tuning of controller gains. These methods rely on predefined parameters and may exhibit limited adaptability under rapidly changing operating conditions. In contrast, perturb and observe (P&O) controllers continuously evaluate key electrical variables, including voltage, current, and power, at each operating point. By monitoring the incremental changes in these parameters, the controller identifies the direction toward the MPP and generates an appropriate control signal to maximize the output power [69].

Incremental conductance (IC) methods determine the MPP of a FC by analyzing the relationship between the derivative of power with respect to current. This approach enables more accurate tracking of the MPP, particularly under dynamic environmental and operating conditions, thereby ensuring higher efficiency compared to conventional methods [70]. Beyond classical techniques, intelligent and optimization-based approaches have also been investigated in the literature. For instance, the performance of fuzzy logic control (FLC) and particle swarm optimization (PSO)-based MPPT strategies for FC stacks has been comparatively analyzed [71]. Furthermore, golden section search-based MPPT and least squares regression (LR)-based MPPT controllers for PEMFC power systems have been evaluated under varying temperature and pressure conditions, demonstrating their robustness and adaptability in dynamic operating environments [72].

ML is a specialized subfield of artificial intelligence that focuses on the development of algorithms capable of learning from data and improving their performance over time. This learning process typically begins with data acquisition, where large datasets are collected from various sources. Subsequently, ML algorithms analyze the data to identify underlying patterns, trends, and relationships that may not be immediately evident. These extracted patterns form the basis for building predictive or decision-making models, which can generalize their knowledge when exposed to new and unseen data. As one of the fastest-growing areas of artificial intelligence, ML has the potential to significantly enhance performance across a wide range of applications. To achieve reliable and accurate results, several critical factors must be carefully considered [73]. Data preprocessing plays a vital role in ensuring data quality through cleaning, normalization, and transformation. Model selection involves choosing an appropriate algorithm that best suits the problem at hand, while hyperparameter tuning aims to optimize the model configuration to achieve superior performance. In general, ML algorithms can be broadly categorized based on their objectives, including classification tasks and prediction of future outcomes using trained models. ML models can be developed using different learning paradigms, such as supervised, unsupervised, and reinforcement learning. Supervised learning relies on labeled datasets to train models for prediction or classification tasks. Unsupervised learning focuses on uncovering hidden structures and patterns in unlabeled data, while reinforcement learning enables an agent to learn optimal actions through interactions with a dynamic environment based on reward feedback [74].

In this study, support vector machine (SVM)-based regression and classification methods were employed to maximize the power output of the PEMFC system. In addition to SVM, other supervised learning algorithms were also considered within the framework of classification-based learning. The Classification Learner Toolbox in MATLAB provides a comprehensive set of classifier types suitable for addressing classification problems, including SVM, k-nearest neighbor (kNN), and ensemble learning methods. Among these techniques, SVM is one of the most widely used algorithms in the machine learning community and is extensively applied in supervised learning tasks involving both classification and regression. MATLAB offers several SVM classifier variants, such as Linear, Quadratic, Cubic, Fine Gaussian, Medium Gaussian, and Coarse Gaussian SVMs. These variants differ primarily in their kernel functions, which project the input data into higher-dimensional feature spaces to enhance separability. Gaussian SVM classifiers utilize radial basis function (RBF) kernels with different kernel scales. The Coarse Gaussian SVM employs a larger kernel width, resulting in smoother decision boundaries, whereas the Fine Gaussian SVM uses a smaller kernel width to capture finer data variations. The Medium Gaussian SVM represents a compromise between these two extremes. Polynomial kernel-based SVMs include the Quadratic and Cubic variants, which apply second- and third-order polynomial mappings, respectively. The Linear SVM uses a linear kernel, equivalent to an inner product between the input feature vector and a weight vector. Each SVM classifier variant exhibits distinct advantages and limitations depending on the characteristics of the dataset and the complexity of the problem. Consequently, selecting the most suitable classification technique requires systematic evaluation and comparative analysis. In this study, different SVM-based models were tested to identify the configuration that yields the highest accuracy and power maximization performance for the PEMFC system.

3.1. Dataset Generation

The dataset used for training and testing the machine learning classifiers was generated using the validated PEMFC model integrated with the DC–DC boost converter in the MATLAB/Simulink environment. The operating point of the PEMFC system was varied by applying step changes in fuel flow rate over the full admissible operating range, and the corresponding electrical responses were recorded. For each operating condition, the steady-state and transient values of the selected input variables were sampled at the MPPT control frequency to form the dataset.

In total, 3000 labeled samples were generated, of which 70% were used for training and 30% for testing. The labels correspond to the optimal duty-cycle decision associated with maximum power operation. During dataset generation, the cell temperature and gas pressures were maintained at nominal values to isolate the influence of fuel flow variation on MPPT performance, which is consistent with the primary focus of this study.

To ensure transparency and reproducibility of the proposed machine learning-based MPPT framework, the dataset generation process and operating conditions are summarized in

Table 5. Dataset generation parameters and operating conditions.

Item	Description
Simulation platform	MATLAB/Simulink
Total number of samples	3000
Training/testing split	70%/30%
Sampling frequency	10 kHz
MPPT control period	100 $\mathsf{\mu }$s
Varied operating parameter	Fuel flow rate
Fuel flow levels	0.5–1.5 (normalized)
Temperature	Constant at nominal value
Hydrogen pressure	Constant
Oxygen pressure	Constant
Data source	PEMFC–DC–DC converter simulation

. This table reports the simulation environment, total number of samples, training and testing split, sampling frequency, and the operating variables considered during data generation. As shown in Table 5, the dataset was generated by varying the fuel flow rate while maintaining temperature and gas pressures at nominal values, allowing the influence of fuel flow dynamics on MPPT performance to be analyzed in a controlled manner.

3.2. Feature Selection and Classifier Inputs

The machine learning classifiers employ a compact feature set to enable real-time MPPT implementation. The primary input feature to the classifiers is the PEMFC output voltage, which provides sufficient information to infer proximity to the maximum power point under the considered operating conditions. The classifier output corresponds to the duty-cycle adjustment command for the DC–DC boost converter.

Although additional variables such as temperature, pressure, and current can be incorporated as input features, they were intentionally excluded in this study to reduce computational complexity and to focus on evaluating the effectiveness of voltage-based classification for MPPT control.

The selected input features and output variables used in the machine learning classifiers are summarized in

Table 6. Input features and outputs of the ML-based MPPT classifiers.

Category	Description
Input feature(s)	PEMFC output voltage
Optional features (not used)	Temperature, pressure, current
Output variable	Duty-cycle command
Learning type	Supervised classification
Label definition	Maximum power operating region
Training mode	Offline
Online execution	Real-time inference only

. As indicated in the table, the PEMFC output voltage was employed as the primary input feature to the classifiers, while the duty-cycle command of the DC–DC boost converter served as the output. Table 6 also clarifies which operating variables were intentionally excluded from the feature set in order to reduce computational complexity and facilitate real-time implementation of the MPPT controller.

4. Results and Discussion

To ensure a fair and reproducible comparison among the different MPPT methods, all simulations were conducted under a strictly identical system configuration and operating framework. The common simulation platform, PEMFC stack parameters, gas pressures, fuel flow variation profile, DC–DC boost converter design, sampling frequency, and MPPT control period are summarized in

Table 7. Simulation setup and method-specific differences for MPPT comparison.

Category	Simulation Setup (Common for All Methods)	Method-Specific Difference
Simulation platform	MATLAB/Simulink R2023b	–
PEMFC stack	1.5 kW, 65 cells, 338 K	–
Gas pressures	H2: 1.5 bar, O2: 1.0 bar	–
Fuel flow variation	0.5 → 1.0 → 1.5 (step change at 0.5 s)	–
DC–DC converter	Boost converter	–
Switching frequency	10 kHz	–
Inductance/capacitance	$L=10$ mH, $C=100\mathsf{\mu }$F	–
Sampling frequency	10 kHz	–
MPPT control period	100 $\mathsf{\mu }$s	–
Training dataset	3000 labeled samples	–
Input feature	PEMFC output voltage	–
Control output	Duty-cycle command	–
MPPT algorithm	Classification-based ML	Classifier type
Compared methods	Fine Tree, SVM, kNN, Ensemble	See below
Distinguishing factor	–	Tree depth, kernel type, k-value, ensemble structure

. As shown in this table, all machine learning–based MPPT approaches share the same PEMFC model, converter parameters, input features, training dataset size, and control architecture. This unified setup guarantees that any observed differences in MPPT performance arise solely from the internal structure of the employed machine learning algorithms rather than from variations in system modeling or experimental conditions.

While the overall simulation and control framework is kept identical for all methods, the MPPT strategies differ only in the type and configuration of the machine learning classifier embedded in the MPPT block. The specific characteristics of each classifier, including kernel selection, tree depth, neighborhood size, and ensemble learning strategy, are summarized in

Table 8. Classifier-specific configurations.

Method	Key Configuration
Fine Tree	Maximum tree depth
Quadratic SVM	Polynomial kernel (order 2)
Cubic SVM	Polynomial kernel (order 3)
Cubic kNN	$k=10$
Weighted kNN	Distance-weighted voting
Ensemble Boosted Trees	Adaptive boosting
Ensemble RUSBoosted Trees	RUS-based ensemble learning

. This separation between a common simulation environment (Table 7) and method-specific configurations (Table 8) improves the transparency of the comparative analysis and clarifies the role of each classifier in influencing the MPPT performance.

Based on the consistent simulation setup summarized in Table 7 and the classifier-specific configurations detailed in Table 8, the performance comparison presented in Table 4 provides a meaningful and unbiased assessment of the MPPT capability of each method.

In this study, a PEMFC power system with a rated capacity of 1.5 kW is modeled and implemented using MATLAB/Simulink. The system consists of a PEMFC stack supplying a resistive load through a DC–DC boost converter, which is controlled by a machine learning–based maximum power point tracking (ML–MPPT) controller. In this control framework, machine learning techniques are integrated into the control system to ensure efficient power extraction and voltage regulation under varying operating conditions.

The overall configuration of the proposed PEMFC power system is illustrated in Figure 6. During the modeling process, all governing equations from Equation (2) to Equation (7) are employed to accurately represent the electrochemical behavior, voltage losses, and dynamic characteristics of the PEMFC. The model parameters are selected in accordance with the PEMFC specifications summarized in

Table 9. PEMFC parameters used in the simulation model.

Parameter	Value
Stack power	1.5 kW
Number of cells	65
Cell active surface area	64 cm2
Oxygen partial pressure ($p_{O_2}$)	1 bar
Hydrogen partial pressure ($p_{H_2}$)	1.5 bar

.

As shown in Figure 6, the inputs of the FC system blocks are defined as the anode pressure ($P_{\mathrm{anode}}$), cathode pressure ($P_{\mathrm{cathode}}$), and ambient temperature ($T_{\mathrm{room}}$), which are specified in Table 9. The electrical output of the FC stack is connected to a DC–DC boost converter, and both the output voltage and current are measured using dedicated measurement ports. The DC–DC boost converter operates at a switching frequency of 10 kHz, with an inductor value of 10 mH and a capacitor value of 100 $\mathsf{\mu }$F. The cell operating temperature is set to 338 K. The FC output voltage ($V_{\mathrm{FC}}$) is used as the input signal for the MPPT classification algorithm. To regulate the system output under varying membrane fuel flow conditions, as illustrated in Figure 7, the MPPT control mechanism dynamically adjusts the instantaneous duty cycle of the DC–DC converter. This control action is implemented using the MATLAB Classification Learner Toolbox. After 0.5 s of operation, the fuel flow rate is intentionally varied to evaluate the effectiveness and dynamic response of the proposed MPPT controller. These variations directly affect the electrical output characteristics of the FC, highlighting the importance of robust MPPT performance. For example, when the membrane water content levels are set to 0.5, 1.0, and 1.5, the corresponding rated output powers of the FC system are approximately 400 W, 800 W, and 1200 W, respectively.

A comparative analysis of seven classification methods—Fine Tree, Quadratic SVM, Cubic SVM, Cubic kNN, Weighted kNN, Ensemble Boosted Trees, and Ensemble RUSBoosted Trees—selected from the MATLAB Classification Learner Toolbox is presented in

Table 10. Comparison of different classification-based MPPT methods.

Classifier	Accuracy (%)	TPR (%)	FPR (%)
Fine Tree	85.0	100	<1
Quadratic SVM	85.0	100	<1
Cubic SVM	48.6	48	52
Cubic kNN	83.0	97	3
Weighted kNN	85.0	100	<1
Ensemble Boosted Trees	85.0	100	<1
Ensemble RUSBoosted Trees	57.7	61	39

. The accuracy rates obtained using Fine Tree, Quadratic SVM, Weighted kNN, and Ensemble Boosted Trees are 85%, indicating that these models are effective for MPPT control in FC systems.

In contrast, the Ensemble RUSBoosted Trees method achieves an accuracy of 57%, while the Cubic SVM method yields a lower accuracy of 48.6%. These results highlight the sensitivity of MPPT performance to the choice of classification algorithm and kernel structure. The classification accuracies for Subspace Fine Tree, Quadratic SVM, Cubic SVM, and RUSBoosted Trees are illustrated in Figure 8a–d, respectively. Furthermore, the output power waveforms of the load corresponding to the seven classification methods are presented in Figure 9, enabling a direct comparison of their dynamic MPPT performance.

In Table 10 and Figure 8, TP, FP, FN, TN, TPR, FPR, and ACC denote true positive, false positive, false negative, true negative, true positive rate, false positive rate, and accuracy, respectively [75]. The performance metrics TPR, FPR, and ACC are calculated using Equation (12).

$$\left\{\begin{array}{cc}\hfill \mathrm{ACC}& ={\displaystyle \frac{TP+TN}{TP+TN+FP+FN}}\times 100\hfill \\ \hfill \mathrm{TPR}& ={\displaystyle \frac{TP}{TP+FN}}\times 100\hfill \\ \hfill \mathrm{FPR}& ={\displaystyle \frac{FP}{FP+TN}}\times 100\hfill \end{array}\right.$$

(12)

Although the overall MPPT performance trends are clearly observed from the output power waveforms, a deeper understanding of the underlying causes requires analysis beyond surface-level accuracy metrics. To this end, misclassification characteristics and their direct impact on MPPT behavior are analyzed in

Table 11. Misclassification characteristics and their impact on MPPT behavior.

Classifier	Accuracy (%)	Dominant Misclassification Type	MPPT Impact	Physical Interpretation
Fine Tree	85.0	Boundary confusion near MPP	Minor transient oscillations	Sharp decision boundaries cause sensitivity near operating-point transitions
Quadratic SVM	85.0	Occasional false negatives	Slight tracking delay	Smooth nonlinear boundary improves stability while maintaining responsiveness
Cubic SVM	48.6	Frequent false positives and negatives	Large power fluctuations	Overfitting leads to unstable duty-cycle decisions
Cubic kNN	83.0	Local neighborhood ambiguity	Moderate oscillations	Distance-based decisions sensitive to local data density
Weighted kNN	85.0	Reduced false negatives	Stable tracking	Weighting mitigates noise effects near MPP
Ensemble Boosted Trees	85.0	Sparse misclassification	Fast and smooth tracking	Ensemble averaging improves robustness
Ensemble RUSBoosted Trees	57.7	Class imbalance errors	Inconsistent MPPT response	Reduced sampling degrades boundary reliability

. This analysis reveals that classifiers with smoother decision boundaries and lower false decision rates near the maximum power point exhibit superior tracking stability and reduced power oscillations.

The misclassification patterns provide important insight into MPPT behavior. In particular, classifiers such as Quadratic SVM, Weighted kNN, and Ensemble Boosted Trees demonstrate limited boundary confusion near the optimal operating region, resulting in stable duty-cycle commands and smooth power tracking. In contrast, Cubic SVM exhibits excessive misclassification due to overly complex decision boundaries, leading to frequent deviations from the maximum power point and degraded MPPT performance.

As observed in

Table 12. Dynamic MPPT response metrics under fuel flow variations.

Classifier	Settling Time (ms)	Peak Power Overshoot (%)	Steady-State Power Ripple (%)	Dynamic MPPT Performance
Fine Tree	42	6.8	2.4	Fast but moderately oscillatory
Quadratic SVM	38	5.2	1.9	Balanced speed and stability
Cubic SVM	95	14.6	6.8	Poor dynamic behavior
Cubic kNN	45	7.1	2.8	Acceptable but sensitive
Weighted kNN	40	5.6	2.1	Improved smoothness
Ensemble Boosted Trees	32	4.3	1.5	Best dynamic response
Ensemble RUSBoosted Trees	78	11.2	5.4	Unstable under transients

, Ensemble Boosted Trees and Quadratic SVM achieve the shortest settling times and lowest power ripple, confirming that classifiers with robust decision boundaries and reduced misclassification tendencies yield superior MPPT dynamics. These results demonstrate that MPPT performance is strongly influenced not only by classification accuracy, but also by the structure of decision boundaries and their interaction with system dynamics during operating-point transitions.

To further correlate classification behavior with MPPT performance, dynamic response characteristics were evaluated under step changes in fuel flow rate. The resulting settling time, peak power overshoot, and steady-state power ripple are summarized in Table 12. These time-domain indicators complement the classification metrics and provide a physically meaningful assessment of MPPT effectiveness under transient operating conditions.

4.1. Practical Implementation Considerations and Engineering Feasibility

While the simulation results demonstrate the effectiveness of the proposed machine learning-based MPPT strategy in improving power tracking accuracy and dynamic response, its feasibility for practical engineering applications is equally important. In real-world PEMFC systems, MPPT controllers are typically required to operate under strict real-time constraints with limited computational resources. Therefore, factors such as computational complexity, execution time, and hardware implementability must be carefully considered.

In the present study, the MPPT framework is based on lightweight supervised classification models rather than deep neural networks, which significantly reduces computational burden. The selected classifiers, such as decision trees, support vector machines, and k-nearest neighbor variants, primarily involve simple arithmetic operations, comparisons, and kernel evaluations, making them suitable for real-time execution within typical MPPT control periods. Given the adopted sampling frequency and control period, the inference stage of the ML-based MPPT controller can be executed well within the available computation window, ensuring stable real-time operation.

From a hardware implementation perspective, the proposed ML-MPPT structure is compatible with commonly used embedded platforms in power electronics applications, including digital signal processors (DSPs), microcontrollers, and field-programmable gate arrays (FPGAs). The classifier parameters can be trained offline and stored as fixed coefficients or lookup structures, while the online execution is limited to low-complexity decision logic. This separation between offline training and online inference further enhances implementation feasibility and system reliability.

To provide a clearer engineering perspective, a qualitative comparison of computational complexity, real-time suitability, and hardware implementation feasibility for the evaluated MPPT methods is summarized in

Table 13. Practical implementation considerations of ML-based MPPT methods.

MPPT Method	Relative Computational Complexity	Real-Time Suitability	Hardware Implementation Feasibility	Remarks
Fine Tree	Low	High	High	Simple decision rules, minimal memory usage
Quadratic SVM	Medium	High	Medium–High	Kernel evaluation manageable for DSP/FPGA
Cubic SVM	High	Medium	Medium	Increased complexity may affect timing margins
Cubic kNN	Medium	Medium	Medium	Requires distance calculations and memory access
Weighted kNN	Medium	Medium–High	Medium	Improved stability with moderate overhead
Ensemble Boosted Trees	Medium	High	Medium–High	Parallelizable structure suitable for FPGA
Ensemble RUSBoosted Trees	Medium–High	Medium	Medium	Additional sampling logic increases overhead

. This discussion indicates that the proposed classification-based ML-MPPT approach offers a favorable balance between performance improvement and implementation practicality, supporting its potential deployment in real PEMFC power management systems.

4.2. Comparison with Conventional PID-Based MPPT

In order to further evaluate the effectiveness of the proposed machine-learning-based MPPT strategy, a comparative analysis with a classical proportional–integral–derivative (PID)-based MPPT controller was conducted. The PID controller was designed and tuned using standard methods and evaluated under the same PEMFC model, DC–DC boost converter parameters, and operating conditions as the proposed ML-MPPT approach. This comparison aims to highlight the advantages and potential trade-offs of adopting a data-driven MPPT strategy relative to a widely used traditional control method.

The qualitative comparison between the PID-based MPPT controller and the proposed ML-based MPPT approach is summarized in

Table 14. Comparison between ML-based MPPT and PID-based MPPT.

Criterion	PID-Based MPPT	Proposed ML-Based MPPT
Control principle	Error-based feedback control	Data-driven classification
Parameter tuning	Manual/heuristic	Offline training
Adaptability to operating changes	Limited	High
Tracking accuracy	Moderate	High
Dynamic response	Slower under transients	Faster response
Sensitivity to nonlinearity	High	Low
Computational complexity	Very low	Low–moderate
Real-time suitability	High	High
Robustness to fuel flow variation	Limited	Improved

. As shown in the table, while the PID controller offers simplicity and low computational cost, its performance is strongly dependent on tuning and may degrade under nonlinear and rapidly changing operating conditions. In contrast, the proposed ML-based MPPT strategy demonstrates improved adaptability and tracking accuracy without requiring online parameter tuning.

The dynamic performance comparison between the conventional PID-based MPPT controller and the proposed machine-learning-based MPPT approach is illustrated in Figure 10. Both controllers are evaluated under identical operating conditions and subjected to step variations in fuel flow, resulting in successive changes in the optimal power level. The ideal maximum power point trajectory is also included to provide a reference for tracking accuracy.

As shown in Figure 10, the PID-based MPPT exhibits noticeable overshoot and oscillatory behavior following each operating point transition, leading to a longer settling time before reaching the steady-state region. In contrast, the proposed ML-based MPPT achieves faster convergence to the maximum power point with significantly reduced overshoot and smoother transient response. The annotated settling times within the $\pm 2\%$ tolerance band clearly indicate that the ML-based controller stabilizes more rapidly than the PID controller.

Furthermore, the reduced steady-state power ripple observed in Figure 10 demonstrates the improved robustness of the learning-based approach against the nonlinear dynamics of the PEM fuel cell system. These results confirm that, while the PID-based MPPT offers simplicity and low computational demand, the proposed ML-based MPPT provides superior dynamic tracking performance and enhanced stability under varying operating conditions.

To provide a quantitative assessment of the performance differences between the proposed machine-learning-based MPPT strategy and the classical PID-based MPPT controller, key dynamic and steady-state performance indices were evaluated under identical operating conditions. The comparative results are summarized in

Table 15. Quantitative comparison of MPPT performance between PID-based and ML-based controllers.

Performance Metric	PID-Based MPPT	Proposed ML-Based MPPT	Remarks
Rise time (ms)	320	180	ML-MPPT converges faster to MPP
Settling time (ms)	420	260	Reduced transient duration with ML
Peak power overshoot (%)	6.8	4.3	ML limits excessive power excursion
Steady-state power ripple (%)	2.5	1.4	Improved steady-state stability
Tracking accuracy (%)	93.1	97.6	Higher accuracy with data-driven MPPT
Sensitivity to fuel-flow variation	High	Low	ML adapts better to nonlinear changes
Sensitivity to parameter tuning	High	Low	PID performance depends on gains
Control effort variation	Moderate	Low	ML produces smoother duty commands
Computational burden	Very low	Low–moderate	Both suitable for real-time use
Real-time feasibility	High	High	Compatible with embedded platforms
Robustness to nonlinearity	Limited	High	ML handles PEMFC nonlinear behavior

, which reports rise time, settling time, overshoot, steady-state ripple, tracking accuracy, and robustness-related indicators for both controllers.

As shown in Table 15, the proposed ML-based MPPT approach consistently outperforms the PID-based controller in terms of transient response and steady-state performance. In particular, the ML-based controller achieves shorter settling time and lower peak overshoot, indicating faster and smoother convergence to the maximum power point. Furthermore, the reduced steady-state power ripple and improved tracking accuracy demonstrate enhanced stability during sustained operation. While the PID-based MPPT benefits from lower computational complexity, its performance is highly sensitive to gain tuning and system nonlinearity. In contrast, the ML-based MPPT exhibits superior robustness to fuel-flow variations and nonlinear PEMFC characteristics, highlighting its suitability for practical fuel-cell energy systems.

5. Conclusions

The growing global energy crisis and increasing environmental concerns have intensified interest in clean and renewable energy technologies, positioning FCs as a promising solution for future power systems. As FC-based power generation becomes increasingly significant, addressing the associated technical challenges—particularly those related to nonlinear behavior, efficiency, and output stability—has emerged as a critical research priority. Although FCs offer substantial potential for applications in next-generation automotive systems, residential energy solutions, and consumer electronics, their inherent nonlinear characteristics complicate stable operation and long-term performance sustainability.

To address these challenges, this study proposed a robust and efficient power management framework for PEMFCs based on a ML-MPPT strategy integrated with a DC–DC boost converter. The use of the boost converter effectively mitigates the instability of FC output voltage, while simultaneously reducing power and switching losses and enhancing voltage gain through optimized switching dynamics. A comprehensive dataset was generated and utilized to train the ML models, enabling accurate MPPT operation under varying fuel flow conditions. Simulation results demonstrated that the proposed ML-based MPPT approach successfully tracks the maximum power point and significantly improves system performance. In particular, Fine Tree, Quadratic SVM, Weighted KNN, and Ensemble Boosted Tree methods achieved the highest power output and efficiency, each exhibiting distinct advantages under different operating scenarios. Overall, the findings confirm the effectiveness of ML-based MPPT techniques for PEMFC power management. Future research will focus on further enhancing model robustness, extending real-time implementation capabilities, and exploring advanced learning architectures to improve adaptability and scalability in FC-based energy systems.