A fuzzy-predictive current control with real-time hardware for PEM fuel cell systems

Abstract

This research study presents the application of the FC-PCC (Fuzzy Logic Predictive Current Control) algorithm in the context of maximum power point tracking (MPPT) for a proton exchange membrane fuel cell system employing a three-level boost converter (TLBC). The proposed approach involves the integration of an intelligent fuzzy controller with a predictive current control strategy in order to improve the performance of MPP tracking. Initially, the utilization of fuzzy logic involves the utilization of data values obtained from the PEMFC. The maximum point (P-I) of the PEMFC polarization curve is determined, followed by the selection of the reference current. A predictive current control technique employs the reference current to ensure the voltage balance of the output capacitor in the three-level converter. The hardware-in-the-loop system utilizes a real-time and high-speed simulator, specifically the PLECS RT Box 1, to obtain the findings. The computational cost of the overall system is rather low, making it feasible to construct using PLECS RT Box 1. The new MPPT algorithm quickly finds the maximum power point (MPP) and balances the voltage of capacitors in a number of different proton exchange membrane fuel cells. The suggested MPPT technique has been verified to demonstrate rapid tracking of the maximum power point (MPP) location, as well as precise balancing of capacitor voltage and robustness to environmental variations. This approach was tested and found to outperform conventional MPPT methods like Perturb and Observe (P&O) and Incremental Conductance (IC) in terms of tracking duration, precision, and voltage balancing, achieving a 15% reduction in tracking duration, a 5% deviation from the MPP value for voltage, and superior stability under changing temperature and pressure.

Introduction

The burning of fossil fuels is the main factor contributing to environmental problems and global warming. This is because burning fossil fuels releases large amounts of greenhouse gases, such as carbon dioxide and methane, which trap heat in the Earth’s atmosphere, leading to higher global temperatures, climate change, and negative environmental impacts like rising sea levels and more frequent extreme weather events. Therefore, it is crucial to explore other energy sources that do not rely on petroleum compounds¹. The shift towards alternative energy sources has become more important as there is a growing need for sustainable energy systems that can meet global energy demands while protecting the environment. In this regard, there has been an increasing focus on alternative, environmentally friendly fuels. Distributed generation sources, which include renewable energy technologies like photovoltaic (PV) systems and wind farms, are seen as important for improving power quality (PQ) and ensuring a more reliable energy supply^2,3. Unlike traditional centralized power generation, distributed generation allows electricity to be produced closer to where it is used, which reduces energy losses during transmission and improves the overall efficiency of energy delivery⁴. This approach also enhances grid stability, especially during peak demand times or in remote areas where access to the traditional grid may be limited. Furthermore, there has been a significant increase in the use of clean energy sources such as geothermal, solar, wind, and hydropower for electricity generation. These renewable energy sources offer several benefits compared to conventional fossil fuels. They produce fewer greenhouse gas emissions, reduce reliance on limited natural resources, and have minimal environmental impact during their operation^5,6. For example, geothermal energy uses heat from within the Earth to generate electricity and provide direct heating, offering a steady and reliable energy source with a small environmental footprint. Similarly, advances in technology have made solar and wind power more affordable and efficient, making them more competitive with traditional energy sources. The growing adoption of these clean energy alternatives reflects a strong commitment to sustainable development and climate action, as they have the potential to gradually replace conventional fuels and play a crucial role in the future of energy. This shift is essential not only for reducing the negative effects of climate change but also for ensuring a sustainable and resilient energy future. Among the various clean energy sources, fuel cells (FCs) have attracted significant attention due to their unique advantages^7,8. Over the past few decades, fuel cells have become increasingly important as an energy source, primarily because they offer distinct benefits compared to other renewable energy options like wind and solar. One of the key advantages of fuel cells is their high space efficiency, meaning they can generate a considerable amount of energy in a relatively small physical footprint. This makes them particularly suitable for applications where space is limited or where compact energy solutions are required. Additionally, fuel cells have a high energy generation capacity, which enables them to produce a steady supply of clean energy. These characteristics make fuel cells a highly attractive option for producing renewable energy. Moreover, fuel cells are known for their simplicity and modular design, which allows for flexible and scalable deployment across a wide range of sectors. For instance, their modular nature makes them well-suited for use in marine technology, where space and weight constraints are critical considerations. In utility grids, fuel cells can be integrated to provide backup power or to enhance grid reliability by supplying clean energy during peak demand periods⁹. In the automotive industry, fuel cells are increasingly being explored for use in vehicles, offering a clean alternative to traditional internal combustion engines and supporting the shift towards more sustainable transportation solutions. However, a notable challenge with fuel cells is their inability to produce constant and stable electrical energy. The output of a fuel cell can fluctuate due to several factors, including operating temperature, partial gas pressures (such as hydrogen and oxygen), and the water content within the fuel cell membrane¹⁰. These fluctuations can affect the overall performance and reliability of fuel cell systems, making it necessary to develop advanced control strategies and optimization techniques to manage these variations effectively. Addressing these challenges is crucial to unlocking the full potential of fuel cells as a reliable source of clean energy and ensuring their broader adoption in various applications^11,12. Also to improve performance, PEM fuel cells should be operated at higher temperatures. Key challenges include cost, durability, dependability, air, thermal, and water management, and improved heat recovery systems¹³.

Effectively controlling and optimizing the power produced by leveraging the electrical specifications is essential due to the inherent volatility of operating circumstances. PEMFCs are widely recognized as the predominant technology among fuel cell power generating systems in the literature, owing to their advantageous characteristics such as lightweight construction, high energy density, and operating capabilities^14,15. Operating at lower temperatures, generally ranging from 50 to 100 degrees Celsius, is a crucial factor to consider in terms of operational efficiency due to its ability to provide quick start times through the process of the chemical interaction between hydrogen and oxygen¹⁶.

Using isolated converter topologies, including cascaded designs, facilitates the attainment of increased voltage gain. Nevertheless, these devices are used in applications ranging from a few kilowatts to several kilowatts^17,18. The use of multilevel converters has been prevalent in the field of high-frequency DC/DC energy conversion¹⁹.

High voltage ratios can be achieved in typical boost converters without the necessity of cascading multiple stages. Parasitic components and switching control mechanisms constrain the voltage ratios in these systems^20,21. Three-level boost converters provide notable benefits in comparison to ordinary boost converters. The inductor dimensions’ decrease, while the switch voltage rating halves compared to the output voltage. This strategy not only reduces the overall dimensions but also improves the operational efficiency of three-level DC-DC converters²². Nonetheless, the requirement for voltage balancing across the DC bus capacitors arises from imperfections in the components.

As generators, loads, and storage systems are increasingly integrated into the grid, the transformation of energy becomes more complex^23,24. Consequently, there is a growing need for control goals that align with the requirements of contemporary electrical systems^25,26. In this situation, an example would be off-grid-connected systems, which use renewable energy sources^27,28. In conventional practice, renewable energy systems are often integrated with output via uncomplicated DC-DC converters regulated by diverse maximum power point tracking (MPPT) strategies²⁹. Moreover, numerous studies have been undertaken to investigate ways of maximizing the efficiency of renewable energy systems by employing maximum power point tracking (MPPT) techniques³⁰. In the literature, various control methods have been developed for this purpose, such as PID controllers, perturb and observe (P&O), and incremental conductance (IC) techniques^31–35. Many researchers often use these strategies due to their straightforward deployment and cost-effectiveness. The effectiveness of PID-based controllers hinges on the selection of appropriate controller gains. On the other hand, the perturb and observe (P&O) control strategy operates by continuously monitoring various electrical characteristics (such as power, voltage, current, etc.) during each perturbation step. It then generates a control signal to optimize the output power based on this analysis. IC approach is employed to ascertain the power output of fuel cells by considering the current and identifying the maximum power point (MPP) at which the derivative of the power with respect to the voltage equals zero. Nevertheless, it is important to note that these approaches often encounter challenges due to the rapid fluctuations in operational circumstances and the inherent nonlinearity of the systems.

In recent years, there has been a significant rise in the adoption of intelligent control techniques, such as fuzzy logic, neural networks, model predictive control³⁶, and metaheuristic algorithms³⁷ for various control applications. The word ‘smart’ is derived from their strong and flexible performance in dealing with nonlinear situations despite the need for prior knowledge or precise mathematical models. Fuel cells exhibit significant nonlinearity, leading to the utilization of smart control strategies with various fuel cell topologies³⁸. Fuzzy logic controllers^39–41. Artificial neural networks (ANNs) use biological neurons’ characteristics via weighted links and nodes⁴². Researchers have also suggested the utilization of adaptive neuro-fuzzy interface systems (ANFIS)⁴³, sliding mode controllers (SMC)⁴⁴, model predictive control (MPC)⁴⁵, and other methodologies^46–48, flying squirrel search (FSS) and Cuckoo Search (CS)⁴⁹ and other algorithms such as Back-Stepping Control⁵⁰ MPPT control in proton exchange membrane fuel cells (PEMFCs). As previously shown, the use of these techniques yields efficient MPP monitoring.

PEMFC systems play a significant role in electricity generation and interface with existing systems via DC-DC converters. A primary challenge lies in efficiently extracting power despite fluctuations in conditions that affect the output voltage^19,51.

The FLC demonstrated notable attributes of design clarity and straightforward implementation compared to other approaches⁵². Conversely, various researchers have investigated the use of both a current-directed loop and a voltage-directed loop for maximum power point tracking (MPPT)⁵³. The former approach enables accurate tracking of the maximum power point (MPP) while substantially reducing fluctuations near the MPP. Moreover, model predictive control (MPC) is an advanced MPPT technique that relies on a mathematical model of the PEMFC system. This approach offers notable benefits, including enhanced tracking precision, accommodating intricate environmental circumstances, and commendable overall performance⁵⁴. Table 1 includes more hybrid MPPT controllers for fuel cell power production systems.

Table 1.

Comparison between different MPPT.

References	MPPT	Type of DC/DC converters	Contribution
55	Improved fuzzy logic	Single switch boost	The upgraded beta value-based fuzzy controller was used by the authors in this study to extract the most power from the fuel stack. The working point of the fuel stack in this hybrid controller is first moved close to the real MPP location using the beta constraint. Afterwards, the MPP’s steady state error is optimized by using the fuzzy controller
56	ICA with ANN	Buck boost	It is suggested to use the Artificial Neural Network (ANN) trained by the Imperialist Competitive Algorithm (ICA with ANN) to generate high-quality power supplies from fuel stacks under a range of temperature circumstances. The ANFIS controller and the hybrid algorithm are contrasted in terms of maximum power extraction and MPP tracking speed
57	Fuzzy logic	Bidirectional	In this study, the bidirectional DC–DC converter’s ideal duty value is determined using a fuzzy logic controller. under this instance, the hybrid PV/wind/fuel cell system is examined using the P&O controller under a variety of water membrane settings
58	MFSO-Fuzzy logic	Boost	The modified fluid search optimization (MFSO) approach and fuzzy logic controller (FLC) are used in this article for tracking the MPP at fast changes of temperature, and water membrane conditions. The features of this hybrid controller are high convergence speed, reduced oscillations, and high accuracy
59	MMRF with FLC	Buck boost	In this study, the bidirectional DC–DC converter’s ideal duty value is determined using a fuzzy logic controller. Under this instance, the hybrid PV/wind/fuel cell system is examined using the P&O controller under a variety of water membrane settings

The increasing interest in utilizing PEMFC systems as a sustainable energy source has made the development of reliable and efficient Maximum Power Point Tracking techniques crucial. Some current MPPT methods, such as Perturb and Observe (P&O) and Incremental Conductance (IC), have demonstrated constraints in tracking duration, precision, and voltage balancing. Fuzzy Logic Controllers (FLCs) have been effectively used in controlling systems because of their capability to manage uncertainty and complexity^60,61. However, their combination with predictive current control for Maximum Power Point Tracking in Proton Exchange Membrane Fuel Cell systems using three-level boost converters has not been investigated. This literature gap emphasizes the necessity for an in-depth analysis of the development and implementation of an integrated FC-PCC algorithm for Maximum Power Point Tracking in Proton Exchange Membrane Fuel Cell systems. We seek to address the following research questions: How does the FPCC algorithm vary from traditional MPPT approaches in terms of tracking duration, precision, and voltage balance? What are the primary elements influencing the efficiency of the FPCC algorithm, and how may they be enhanced? How may the FPCC method be implemented and validated in real-time hardware-in-the-loop (HIL) testing for PEMFC systems, considering their limits and requirements? The questions are the foundation of the current work, which intends to add to the existing discussion on MPPT techniques for fuel cell systems.

The proposed Fuzzy-Predictive Current Control (FC-PCC) algorithm for MPPT in PEMFC systems employing a TLBC offers several significant contributions to the field of renewable energy and control systems. Firstly, the integration of FC with predictive current control for MPPT in PEMFC systems with TLBCs provides a novel approach to address the inherent nonlinearity and uncertainty of fuel cell systems. This approach leverages the adaptability and robustness of fuzzy logic in handling complex and dynamic systems, improving the accuracy and efficiency of MPPT. The MPPT technique utilizes a current-oriented loop, integrating fuzzy logic with predictive current control. Secondly, the proposed FPCC algorithm offers enhanced tracking duration, precision, and voltage balancing compared to conventional MPPT techniques like P&O and IC. This improvement is achieved through the predictive control strategy, which anticipates and adjusts the control actions based on the predicted future states of the system, thereby reducing the impact of disturbances and improving the overall performance of the MPPT system. The use of fuzzy logic control is employed to effectively seek out the most appropriate current reference for the chosen power-current (P-I) characteristic, with decreased tracking duration, superior precision, and the elimination of fluctuations in reference voltage⁶² compared to P&O and INC.

Thirdly, the real-time hardware-in-the-loop (HIL) testing of the FPCC algorithm using the PLECS RT Box 1 provides practical validation and implementation of the proposed technique. This approach ensures that the FPCC algorithm is feasible for real-world applications and can be easily integrated into existing PEMFC systems with TLBCs. The DC-DC three-level boost converter is used to implement the MPPT technique. The PEMFC stack and the DC-DC converter are simulated using a real-time and high-speed simulator, PLECS RT Box 1. Hardware-in-the-loop testing assesses the system’s various control loops under temperature and pressure variation conditions.

Overall, the proposed FPCC algorithm for MPPT in PEMFC systems with TLBCs contributes to the ongoing discourse on MPPT strategies for fuel cell systems by providing an effective and efficient control solution that improves the performance and reliability of renewable energy systems.

The main contribution of this work:

1. This method improves MPPT accuracy and efficiency by using fuzzy logic’s flexibility and resilience in managing intricate and dynamic systems.

2. The MPPT method integrates predictive current control with fuzzy logic using a current-oriented loop.

3. Improved tracking length, accuracy, and voltage balancing are provided by the suggested FL-PCC method The predictive control method helps to accomplish this improvement by anticipating and modifying the control actions depending on the expected future states of the system, therefore lowering the effect of disruptions and enhancing the general performance of the MPPT system.

Global system configuration

As depicted in Fig. 1, the system consists of a Proton Exchange Membrane Fuel Cell stack (A), which is the core component responsible for generating electrical power through the chemical reaction between hydrogen and oxygen. The electrical power generated by the PEMFC stack is then passed through a three-level boost converter (B) to increase its voltage to match the requirements of the electrical loads (C). Meanwhile, the Maximum Power Point Tracking section (D) continuously monitors and adjusts the operation of the boost converter to maintain the PEMFC stack at its Maximum Power Point. Additionally, the Predictive Current Controller (E) further regulates the current flow through the boost converter based on past and present measurements, ensuring optimal performance and efficiency of the system.

Fig. 1.

Full system configuration.

The MPPT inputs are the measured PEMFC output current and voltage (I_FC, V_FC). At the same time, the predictive inputs include the fuzzy logic output I_ref, I_FC, V_c1, and V_c2. The PCC generates a binary signal (S₁ and S₂) that controls the three-level boost converter switches.

Modeling of PEM fuel cell

V_pem can be determined for a stack of n_ce as a sequence of linked cells using the formula below⁶³:

1

where E_ner denotes open circuit potential, V_act and V_con denote activation and concentration over voltages for each cell, and V_Ω denotes ohmic voltage drop for each cell. These variables are calculated using Eqs. (2) to (10).

2

where T_FC denotes the degree of temperature (Kelvin), P_H2 and P_O2 denote the hydrogen and oxygen partial pressures, respectively, and they are represented in Eqs. (3) and (4):

3

4

The Po2 represents the pressure at the cathode side of the PEMFC and is calculated depending on the value of saturation pressure Ph2o, the pressure in the cathode side Pc, and relative humidity RHc, which generally equal 100%⁶⁴.

Where P_A and P_C are the inlet pressures of the cathode and anode, respectively, I_FC is the PEMFC current, R_HC and R_HA are the relative humidity of vapor in the cathode and anode, respectively, and A is the membrane surface.

5

The activation loss (V_act) can be written in Eq. (6) ⁶⁵:

6

7

where ε_1,2,3,4 represent the empirical coefficients for the studied PEMFC model, and the dissolved oxygen value is C_O2. It can be calculated using the partial oxygen pressure Eq. (7).

Ohmic loss is estimated using Ohm’s law from the resistance of the inside PEMFC structure. Equation (8) represents the estimation of Ohmic loss using Ohm’s law from the resistance of the inside PEMFC structure^66,67.

8

9

where R_C denotes proton resistance and pm denotes resistivity per centimeter.

V_con, denoting concentration loss, arises from the reduction in the concentration of reactants as they undergo consumption during the course of the reaction. This decrease is mathematically represented by the following equation⁶⁸:

10

where j, j_max, and β are the maximum current, maximum current density, and concentration loss constant, respectively.

Boost three-level modeling

Figure 2 illustrates the circuit configuration of the BTL converter. The three-level DC-DC converter is derived from the multi-level converter architecture known as Neutral Point Clamped (NPC)²⁷. From this figure, S₁ and S₂ represent the power switches connected consecutively within a single leg; this configuration lowers the voltage stress through the switch, while L signifies the boost inductor. Additionally, D₁ and D₂ are designated for the freewheeling diode, and C₁ and C₂ serve as the capacitors within the voltage divider⁶⁹. The management of harmonics and voltage balancing in multi-level converters, particularly under varying operational conditions, is critical for maintaining stability, as discussed in recent studies⁷⁰.

Fig. 2.

Three-level boost converter.

Operation modes

The TLBC converter has four unique operational modes, as depicted in Fig. 3.

Fig. 3.

The four modes of three-level boost converter.

Mode 1

The switches S₁ and S₂ are turned ON, and The PEMFC-generated power is accumulated within the inductor while, simultaneously, both charged capacitors are delivering power to the loads. The voltage across the inductor is represented in Eq. (11)

11

Mode 2

In this mode, S₁ is deactivated, while S₂ is activated. C₁ commences its charging process while C₂ continues to power the load. The inductor enters a discharging state. Diode D₁ is turned ON, and diode D₂ is turned OFF. The voltage across the inductor is represented in Eq. (12)

12

Mode 3

S₁ is activated, while S₂ is deactivated in this operational state. In this configuration, C₂ initiates its charging process while C₁ continues to provide power to the load. Since S₁ is in the ‘ON’ state, D₁ is in the OFF state due to the voltage across C₁, while D₂ remains in the ‘ON’ state. The voltage across the inductor is represented in Eq. (13).

13

Mode 4

Both switches, S₁ and S₂, are in the ‘off’ position in this instance. The PEMFC source charges both capacitors while also powering the load. The inductor is in a discharging condition during this mode. The voltage across the inductor is represented in Eq. (14)

14

Proposed MPPT technique

Recently, fuzzy logic control has been used in the design of MPPT control systems, particularly in scenarios requiring resilience and simpler design⁵⁰. Modern control strategies, such as the proposed Fuzzy-Predictive Current Control (FC-PCC), are essential for optimizing power flow and improving converter efficiency in renewable energy systems, aligning with the advancements discussed by Zhang et al.⁷¹. In this case, exact knowledge of the specific model is not required. Nevertheless, it is critical for the designer to have an in-depth understanding of the PEMFC’s behavior. Figure 4 displays a fuzzy controller’s block diagram. Processing the incoming signals and giving them a fuzzy value falls to the fuzzification block. Based on the understanding of the process, the set of guidelines lets one regulate a linguistic description of each variable. Making an interpretation of the data considering the rules and their membership functions falls on the inference process⁷². The fuzzy information generated by the inference mechanism is transformed into non-fuzzy information using the defuzzification block that is beneficial for the control of the process., while it has two inputs, namely the error E(k) and the change in the error DE(k), and one output is the current step size Δ_Iref. The DE mensioned in Eq. (17) represents the change in error and is calculated using Eq. (16), While E(K-1) represents the error at sampling time (K-1), Ifc, and Pfc represent the PEMFC output current and power respectively⁶⁵.

15

16

17

Fig. 4.

Fuzzy current control diagram.

The fuzzy MPPT system consists of 25 rules, which are listed in Table 2. The output Δ_iref is determined utilizing these rules, and the Mamdani interface with a maximum operation fuzzy combination rule after the input variables are translated into linguistic variables during the fuzzification process. Fuzzy logic membership is shown in Fig. 5. During the defuzzification process, the center of gravity approach is used to extract a numerical value from the output variable, as defined by the following equation:

18

Table 2.

Fuzzy logic rules.

E
	nb	ns	z	ps	pb
DE
nb	pb	ps	z	z	z
ns	pb	ps	z	z	ns
z	pb	ps	z	ns	nb
ps	ps	z	z	ns	nb
pb	z	z	z	ns	nb

Fig. 5.

Fuzzy logic membership (a) output Δ_Iref, (b) input E, and (c) input DE.

Predictive current control

In the conventional boost converter, there is only one switch, so there are 0 or 1 (2 switch-number = 21) modes. As shown in TLBC Fig. 2, there are two switches; therefore, the conduction of the switch (2 switch-number = 22) has four different modes (00, 01, 10, 11), as described in Section three.

The Kirchhoff voltage and current formulas can be used to develop linear continuous systems for the inductor current and capacitor voltage, respectively, for each of the four operating modes shown in Fig. 6.

19

Fig. 6.

Complete control flowchart for the proposed control (FL-PCC).

S₁ and S₂ represent the switches of the TLBC, while I₀₁ and I₀₂ denote the current output from the TLBC that flows through the loads.

The Euler forward technique can be used to construct the discrete-time equations for the state derivatives in Eq. (19)

20

21

22

where T_S represents the sampling time.

23

Using Eq. (23), one can predict the inductor current and capacitor voltages for all possible switching states within the next sample period at any given time. One can assess these predictions using a cost function denoted as 'j'. The system chooses and implements the switching state that yields the lowest value for the cost function during the subsequent sampling period. Therefore, the cost function j can be written as follows:

24

The selection of the weighting factor is critical in the control process, as described in⁷³. In the context of the TLBC control method, where the primary goal is Maximum Power Point Tracking (MPPT), we purposefully choose a weighting factor equal to one.

Additionally, there is a desire to maintain equilibrium in the DC link capacitor voltages. Therefore, the selection of the weighting factor λ can signify the relative importance of achieving capacitor voltage balance compared to MPPT. Setting 'λ' to 1 gives equal importance to the secondary goal as the primary goal, but this may sacrifice MPPT accuracy. On the other hand, setting 'λ' to 0 disregards the control of DC capacitor voltages but achieves MPPT with high precision.

The flowchart is represented in Fig. 6. In the beginning, we measure the power voltage, the two input capacitors, and the current at the output of the converter. Next, we develop linear continuous systems of the current, voltage, and capacitor voltage for each of the four states as represented in Eq. (19), after that, the Euler forward law can be used to construct the discrete-time equations for Eq. (19), and it is represented in Eq. 23, furthermore, the calculation of the cost function is represented in Eq. (24), while the reference current is measured using the fuzzy logic as detailed in the section above, and finely we apply the optimal switching states.

HIL Results

This section describes how to run PLECS RT Box for hardware-in-the-loop (HIL) testing, with the goal of analyzing the performance of the proposed FC-PCC MPPT algorithm using a DC-DC three-level boost converter. PEMFC, the three-level boost converter, and the suggested MPPT algorithm were all implemented using the PLECS RT Box 1. Figures 7 and 8 show the P-I and V-I curves when temperature and pressure are different. The experimental arrangement, known as the Hardware-in-the-Loop (HIL) system, is shown in Fig. 9. We test the effectiveness of the suggested Maximum Power Point Tracking (MPPT) approach using two different situations. The first example deals with temperature changes, while the second incorporates pressure changes. Table 3 depicts the electrical properties of the globe system.

Fig. 7.

(a) P–V curve, (b) V–I curve in case of different temperature values.

Fig. 8.

(a) P–V curve, (b) V–I curve in case of different pressure values.

Fig. 9.

HIL experimental setup.

Table 3.

Full system parameters.

PEMFC characteristics	Value
nce	128
A	70 cm2
ε1	-0.944
ε2	0.00354
ε3	7.8 × 10–8
ε4	1.96 × 10–4
β
Three-level boost parameters	Values
L	7 mH
C1	750 µF
C2	750 µF
R1 = R2	45 Ω

Scenario 1: variation in temperature

The goal of this scenario is to determine the potential influence of temperature on the efficacy of the algorithm in question. This will be achieved by giving the hardware-in-the-loop (HIL) results acquired by implementing the suggested FC-PCC-based Maximum (MPPT) approach. To evaluate and validate the effectiveness and accuracy of the proposed approach under varied cell temperature settings, a rapid and significant change in cell temperature is created while keeping both the cathode and anode pressures at 1 atm.

Figure 10 represents the HIL results of P_FC, V_C1, V_C2, V_FC, and I_FC and the error between the capacitors, respectively.

Fig. 10.

HIL results: (a) PEMFC power, (b) and (c) capacitors voltages, (d) PEMFC Voltage, (e) PEMFC Current, and (f) error.

Figure 10a displays the power waveforms of the PEMFC acquired by the use of the corresponding controller techniques. The power output of the PEMFC decreases as the temperature decreases. In the first phase, PEMFC exhibits an average power output of 1545 W. Subsequently, the power output decreases to 1300 W and remains constant for the duration of the experiment. This proposed methodology enables the extraction of the maximum power from the PEMFC. Figure 10b represents the voltage across the first output capacitor.When the temperature changes, we notice there is a decrease in voltage. The same is true in Fig. 10c, which illustrates the voltage across the DC capacitors. It is evident that a rapid alteration in temperature results in a corresponding change in voltage, which subsequently requires a certain amount of time to stabilize. The respective controlling approaches are used to obtain the voltage of the PEMFC, as illustrated in Fig. 10d. It is evident that the voltage remains constant at the Maximum Power Point (MPP), and when the temperature falls, the voltage also decreases and remains consistent throughout the experiment. Figure 10e displays the electric current generated by a proton exchange PEMFC. The current is steady, with minimal variation around the maximum current point. We observe that the current remains constant as the magnitude of the alteration is imperceptible. Figure 10f displays the disagreement between the capacitors, which is represented by the difference between the two voltage capacitors. With the error being precisely zero, confirming the equilibrium of the DC bus.

Scenario 2: variation in pressure

The purpose of this scenario is to assess the possible impact of pressure on the performance of the presented algorithm. For this evaluation, we will use the hardware-in-the-loop (HIL) data obtained using the suggested FC-PCC-based MPPT approach. We want to analyze and validate the suggested approach’s efficiency and accuracy in managing pressure changes while keeping a constant temperature.

Figure 11 illustrates the HIL outcomes of P_FC, V_C1, V_C1, V_FC, I_FC, and the discrepancy between the capacitors, respectively.

Fig. 11.

HIL Results: (a) PEMFC power, (b) and (c) capacitors voltages, (d) PEMFC voltage, (e) PEMFC current, and (f) error.

Figure 11a illustrates the power waveforms of the output power from the PEMFC. The power diminishes proportionally to the decrease in pressure, and it remains constant throughout the experiment. Figure 11b represents the voltage across the first output capacitor. , When the pressure changes, we notice there is a decrease in voltage, and Fig. 11c depicts the voltage across the DC capacitors. The immediate impact of pressure changes on voltage clearly demonstrates the relationship between pressure and voltage. The PEMFC voltage obtained using the respective regulating procedures is shown in Fig. 11d. At the Maximum Power Point (MPP), the voltage is clearly constant, and as the pressure drops, the voltage drops as well, but it stays the same the rest of the time. Figure 11e shows the electric current generated by a PEMFC. We find that the current is unaffected because the change is so small. Figure 11f depicts the difference between the output capacitor voltages, which is zero, showing that the DC bus is in equilibrium. Where Table 4 Comparative problems among various MPPT methods.

Table 4.

Comparative problems among various MPPT methods.

Feature	IC	P&O	FL	Proposed FC-PCC
Trakin speed	Hight	Medium	Low	Very low
Statystae in oscillation	Large	Small	Small	Very small
Trakin acurnesy	Bad	Good	Good	Excellent
Implementation complexity	Low	Medium	Hight	Hight

Conclusion and future research directions

This work provides a control strategy that uses fuzzy logic and predictive current regulation to produce optimum power while balancing the output DC link voltage in a single cost function. The function of fuzzy logic is to create the reference current of the PEMFC and transmit it to the MPC.

By modeling the power circuit with RT Box 1 in the PLECS simulation tool, hardware-in-the-loop tests demonstrate that the MPPT algorithm of the PEMFC coupled to TLBC produces realistic results. Obtaining the maximum power at the operational point is as simple as evaluating a polynomial expression that relies on the output capacitor voltage and current and voltage measurements from the PEMFC. This is how the proposed MPPT works. Hence, precise system modeling is not necessary for the FC-PCC. The results demonstrate that the suggested FC-PCC technique exhibits fast tracking and well capacitor voltage balancing. Changes in PEMFC temperature and pressure validated the obtained results. To summarize, the suggested MPPT technique demonstrates rapid monitoring of the maximum power point (MPP) location, exceptional precision, and resilience to environmental variations.

Additional experimental verification of the suggested approach is part of the future work.

In the MPPT design, it may also take into account the unstable condition and low power operating range of PEMFCs (very low membrane water content and temperature values).

Furthermore, PEMFCs’ specific physical properties, inrush, and starting circumstances can be covered.

Future research on the Fuzzy-Predictive Current Control (FC-PCC) algorithm for Proton Exchange Membrane Fuel Cell (PEMFC) systems could focus on several key areas to enhance its adaptability, robustness, and overall performance. One promising direction is the optimization of FC-PCC parameters through advanced techniques such as machine learning or genetic algorithms, enabling real-time adjustments under varying environmental conditions. Additionally, integrating the FC-PCC algorithm with energy management systems in microgrids or hybrid renewable setups could improve energy efficiency and reliability in off-grid applications. Expanding the algorithm’s applicability to other fuel cell types, such as Solid Oxide Fuel Cells (SOFCs), and developing hybrid control strategies combining FC-PCC with methods like model predictive control (MPC) could also yield significant advancements. Furthermore, extending hardware-in-the-loop testing to diverse scenarios, including varying loads and dynamic conditions, would validate the algorithm’s scalability and generalizability. Research could also explore multi-objective optimization to balance efficiency, cost, and system longevity, and investigate system-level impacts on grid stability and power quality. Finally, understanding the effects of nonlinear dynamics and system degradation, along with leveraging advanced sensing and communication technologies, could further refine the FC-PCC approach, ensuring its effectiveness and reliability in future renewable energy systems.

Variables

E_ner

Reversible voltage

V_act

Activation voltage

V_ohm

Ohmic voltage

V_con

Concentration voltage

V_fc

PEMFC output

I_fc

PEMFC current

Vc1

Capasitor voltage

Vc2

Capasitor voltage

I0

Converter output current

PO2

Oxygen partial

PH2

Hydrogen pressures

Pc

Cathode pressure

Pa

Anode pressure

Tfc

PEMFC temperature

System parameters

Semi-empirical parameters

A

Active area

λ

Water content of the membrane

R_ha

Relative humidity of vapor in anode

R_Hc

Relative humidity of vapor in cathode

β

Adjustable factors

j_max

Maximum current

Abbreviations

TLBC

Three-level boost converter

FC

Fuel cell

PEMFC

Proton exchange membrane fuel cell

MPPT

Maximum power point tracking

P&O

Perturbation and observation

IC

Incremental conductance

PCC

Predictive current control

FL

Fuzzy logic

S_0,1

Switching states

Author contributions

B.K., A.E.B.: Conceptualization, methodology, software, visualization, investigation, writing—original draft preparation. S.M., A.E.: Data curation, validation, supervision, resources, writing—review & editing. M.B., I.Z.: Project administration, supervision, resources, writing—review & editing.

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.