# Water Electrolysis Hydrogen Damping Improvement by Hamiltonian Based Control

Burin Yodwong, Pongsiri Mungporn, Yaowaret Maiket, Damien Guilbert, Matheepot Phattanasak, Uthen Kamnarn, Melika Hinaje, Gianpaolo Vitale, Phatiphat Thounthong

► To cite this version:

Burin Yodwong, Pongsiri Mungporn, Yaowaret Maiket, Damien Guilbert, Matheepot Phattanasak, et al.. Water Electrolysis Hydrogen Damping Improvement by Hamiltonian Based Control. IEEE Transactions on Industry Applications, 2025, pp.1-11. 10.1109/TIA.2025.3645003. hal-05428656

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# Water Electrolysis Hydrogen Damping Improvement by Hamiltonian Based Control

Burin Yodwong, *Senior Member, IEEE*, Pongsiri Mungporn, *Member, IEEE*, Yaowaret Maiket, Damien Guilbert, *Senior Member, IEEE*, Matheepot Phattanasak, *Senior Member, IEEE*, Uthen Kamnarn, Melika Hinaje, *Member, IEEE*, Gianpaolo Vitale, *Senior Member, IEEE*, and Phatiphat Thounthong, *Senior Member, IEEE*.

**Abstract**— This paper presents an improved damping control strategy based on the Hamiltonian control law (HCL) for a two-phase interleaved buck converter in water electrolysis applications. The transient induced by renewable sources energy variation is still a challenge for hydrogen production. The proposed approach is designed to enhance the stability and efficiency of a proton exchange membrane (PEM) electrolyzer powered by a photovoltaic (PV) source. By leveraging HCL energy conservation principles, the control method enhances system stability, mitigates oscillations, and improves dynamic response under various operating conditions. The performance of the proposed control strategy was experimentally validated using a laboratory-scale PEM electrolyzer system. Comparative tests between HCL and conventional PI control were conducted under varying electrolyzer current reference. Results demonstrated that HCL control achieved superior damping characteristics, reducing voltage and current overshoot and improving settling time as compared to PI control. Additionally, the proposed method exhibited higher steady-state accuracy and better disturbance rejection, ensuring stable hydrogen production efficiency.

***Index Terms***—Damping control; Hamiltonian energy-based control; Proton Exchange Membrane Electrolyzer; Interleaved Buck Converter; Renewable Energy Integration.

## I. INTRODUCTION

HYDROGEN production systems leaning on the use of renewable energy sources (RES) supplying the water electrolysis process, offer a sustainable pathway for generating clean fuel, thereby significantly reducing

carbon footprints and advancing the global transition towards carbon neutrality [1].

A recent review work [2] has highlighted the contribution of proton exchange membrane (PEM) electrolyzers in electricity grid flexibility by coupling them with RES. However, the intermittent and instability nature of RES have an impact on the accelerated aging of the PEM electrolyzer, while affecting the safety and efficiency of the hydrogen production system [3], [4], [5]. For this reason, the development of power electronics (AC-DC and DC-converters) and their controls are the key to coping with degradation, safety, and efficiency issues assuring the best trade-off between achieving a fast response and avoiding voltage overshoots [6], [7].

Over the last decade, many works have been reported in the literature regarding the interaction between RES and electrolyzers by using suitable DC-DC converters and controllers [8], [9], [10], [11], [12], [13], [14]. In [8], the authors have designed a proportional-integral controller applied to a synchronous DC-DC buck converter interfacing a photovoltaic (PV) system and an electrolyzer. Simulations and experiments have been conducted to verify the performance of the controller. More recently, Baraean et al. [9] have devised a controller based on adaptive backstepping terminal sliding mode control (ABTSMC) applied to a basic DC-DC buck converter within a DC microgrid. The electrolyzer load is modelled as an equivalent electrical circuit model considering both static and dynamic operating conditions. The controller performance has been validated using a hardware-in-the-loop implementation. In [10], Mas et al. have investigated the coupling between a PV system and an electrolyzer with the use

This study received partial funding from the International Research Partnership "Electrical Engineering – Thai French Research Center (EE-TFRC)" within the Lorraine Université d'Excellence (LUE) framework, a joint between Université de Lorraine and King Mongkut's University of Technology North Bangkok. It was also supported in part by the in part by National Science, Research and Innovation Fund (NSRF), and King Mongkut's University of Technology North Bangkok (Project no. KMUTNB-FF-69-B-35, in part by the National Research Council of Thailand (NRCT) under Research Team Promotion Grant (Senior Research Scholar Program) under Grant No. N42A680561, and in part by the NSRF via the Program Management Unit for Human Resources & Institutional Development, Research and Innovation under Research project Grant No. B41G680025. (Corresponding author: Burin Yodwong).

Burin Yodwong and Pongsiri Mungporn are with the Renewable Energy Research Centre, Thai-French Innovation Institute, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand (e-mail: burin.y@tfii.kmutnb.ac.th and pongsiri.m@tfii.kmutnb.ac.th).

Yaowaret Maiket is with the Chemical Process Engineering Technology, Faculty of Engineering and Technology, King Mongkut's University of Technology North Bangkok (Rayong), Thailand (e-mail: yaowaret.m@eat.kmutnb.ac.th).

Damien Guilbert is with the Groupe de Recherche en Electrotechnique et Automatique du Havre (GREAH), Université Le Havre Normandie, 76600 Le Havre, France (e-mail: damien.guilbert@univ-lehavre.fr).

Matheepot Phattanasak and Phatiphat Thounthong are with the Renewable Energy Research Centre, Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand (e-mail: matheepot.p@fte.kmutnb.ac.th; phatiphat.t@fte.kmutnb.ac.th).

Uthen Kamnarn is with Department of Electrical Engineering, Rajamangala University of Technology Lanna, Chiang Mai, 50300, Thailand (e-mail: uthen@rmutl.ac.th).

Melika Hinaje is with the Laboratoire Réactions et Génie des Procédés, CNRS, Université de Lorraine, Nancy F-54000, France (e-mail: melika.hinaje@univ-lorraine.fr).

Gianpaolo Vitale is with ICAR, Institute for high performance computing and networking, Italian National Research Council of Italy, Palermo, 90146, Italy (e-mail: gianpaolo.vitale@icar.cnr.it).

Color versions of one or more of the figures in this article are available online at http://ieeexplore.ieee.org
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of two different DC-DC converter topologies: basic buck converter and quadratic buck converter. These converters are controlled by a sliding mode controller; however, only simulations have been performed to validate the proposed controller. In addition, Liu et al. [11] have studied an off-grid PV-PEM electrolyzer system consisting of a multi-stack parallel configuration via the use of several basic DC-DC buck converters. This configuration allows facing the intermittency and instability of the photovoltaic system by controlling the power allocation to each PEM electrolyzer stack; only simulation results are provided to confirm the effectiveness of the control strategy. Li et al. [12] have proposed an LCC-resonant-type current-fed-out three-port DC-DC converter for an off-grid PV-electrolyzer system integrated with energy storage. This topology enables simultaneous power delivery to both the electrolyzer and energy storage system, improving conversion efficiency and reducing current ripple at the electrolyzer port. Experimental validation on a 500 W prototype confirms high voltage step-down gain and zero-voltage switching across a wide operating range.

More recently, Renaudineau et al. [13] proposed a PV-to-electrolyzer system using a two-stage DC-DC converter combining a partial power converter and a resonant DCX stage. This architecture improves efficiency and provides high voltage step-down with soft switching. Experimental results on a 1 kW prototype confirmed its effectiveness under dynamic PV conditions. Martínez et al. [14] have proposed a Passivity-Based Control (IDA-PBC) for power converters control within a DC microgrid representing a typical structure of electric-hydrogen hybrid refueling station. The converter to interface the electrolyzer and the DC microgrid is a non-isolated half-bridge circuit; the controller effectiveness is validated only by simulations.

In addition to advanced control strategies, several converter topologies specifically tailored for electrolyzer applications have been proposed. For example, [15] and [16] introduced novel high step-down, low-ripple DC-DC converters designed for hydrogen production systems, achieving efficient voltage regulation and compact form factors. In [17], a reconfigurable quadratic converter topology was developed to enable flexible integration within DC microgrids. On the control front, [18] implemented a backstepping strategy augmented with an extended state observer (ESO) for three-level converters, enhancing system robustness and dynamic response. In [19], presented an adaptive PID control approach for small-scale hydrogen systems, demonstrating improved voltage tracking under fluctuating solar input conditions.

Recent work has also explored more sophisticated control frameworks in related dynamic systems. Abbas et al. [20] proposed a self-adaptive fractional-order PID controller for regulating particle velocity in a pneumatic conveying system, highlighting the benefits of fractional-order strategies for managing nonlinear and time-varying dynamics. Similarly, Li et al. [21] introduced a PD-type iterative learning consensus control approach for electromechanical actuator-based multiagent systems, showing promising results in improving tracking and coordination across multiple agents. A control approach that could inspire distributed or coordinated control in future hydrogen-based microgrids.

While these contributions represent notable progress in converter design and control for hydrogen energy systems, many focus predominantly on single-phase configurations, employ conventional control methods, or lack a comprehensive energy-based stability framework. Moreover, the explicit treatment of current ripple mitigation and interleaved phase balancing remains limited in the current literature.

In this work, the interaction between a PV system and a PEM electrolyzer is investigated by using a step-down DC-DC converter with high current capability. Additionally, pivotal features such as low output current ripple, minimal step-down conversion gain, reliability, high efficiency, and low capital cost are considered. As a result, the multi-leg interleaved buck converter is proposed for this work. Although the PV generator is characterized by relatively slow power variations due to the variation of solar radiation during the day, it also must face fast variations due to partial shading. Such variations can occur at any point of operation and with fluctuations that sweep the entire power range of the PV source. For this reason, compared with conventional control, the proposed system always ensures the absence of overvoltages that can be harmful to the electrolyzer [22]. Compared to the current state-of-the-art, the main contributions of the paper are summarized below:

1. A novel enhanced damping control strategy is proposed for a two-phase interleaved buck converter. It builds on a Hamiltonian-based control (HCL) framework and incorporates an integral current-balancing term to improve current ripple reduction and inter-phase current sharing.

2. The proposed approach guarantees global asymptotic stability and improved damping performance through energy-shaping and passivity-based control principles.

3. The controller demonstrates robustness against PV input fluctuations and accurately captures the nonlinear dynamics of a real PEM electrolyzer assuring a constant hydrogen production.

4. The proposed strategy is experimentally validated using a real-time dSPACE platform in conjunction with an actual PEM electrolyzer, confirming its practical viability and performance.

The structure of this paper is organized as follows: Section I introduces motivation and key contributions. Section II describes the system configuration, including the interleaved buck converter, PEM electrolyzer, hydrogen flow model, and Hamiltonian formulation. Section III presents the design of the improved HCL, along with set-point generation and a stability analysis. Section IV outlines the experimental setup. Section V discusses the results, including steady-state performance, dynamic behavior under current reference and input voltage variations, and a comparison with optimized PI controllers to highlight the performance with constant output power. Section VI concludes the study and suggests future research directions to enhance robustness and scalability.

## II. SYSTEM DESCRIPTION AND MODELING

### A. Description and modeling of the two-phase interleaved buck converter

In this paper, an interleaved buck converter (IBC) is employed to interface a PV system with a PEM electrolyzer to
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<figure><img src="image_2.png" /><figcaption>**Fig. 1.** Studied low-carbon hydrogen production system.</figcaption></figure>

produce low-carbon hydrogen, as shown in Fig. 1. The converter reduces the high voltage from the PV system to a lower voltage suitable for the electrolyzer, while featuring low current ripple, high efficiency, and improved reliability, which makes it ideal for this application. In general, the converter's structure includes multiple power switches $S_1, S_2$ and $S_N$ that regulate each phase, and key inductors $L_1, L_2$, and $L_N$ that manage energy storage and smooth the current, with currents denoted as $i_{L1}, i_{L2}$ and $i_{LN}$, respectively. Diodes $D_1, D_2$, and $D_N$ ensure proper current flow by preventing reverse currents. The output capacitor $C_O$ stabilizes the output voltage $V_{el}$ supplied to the electrolyzer, which is the current $i_{el}$ to produce hydrogen ($H_2$) from water ($H_2O$).

A two-phase IBC (N = 2) has been selected for this work; it allows for a 180° phase shift control signal, which can be easily implemented using a prototyping dSPACE board for experimental purposes, maintaining a low ripple and good reliability. This circuit is able to minimize the current ripple assuring a good efficiency conversion with a high step-down ratio, as it will be shown in the paper; however, this approach can be generalized to multi-phase converters.

The differential equations governing the operation of this two-phase IBC in continuous conduction mode (CCM) can be expressed as follows:

$$L_1 \frac{di_{L1}}{dt} = d_1 \cdot v_{PV} - R_{L1} \cdot i_{L1} - v_{el} \quad (1)$$

$$L_2 \frac{di_{L2}}{dt} = d_2 \cdot v_{PV} - R_{L2} \cdot i_{L2} - v_{el} \quad (2)$$

$$C_O \frac{dv_{el}}{dt} = i_{L1} + i_{L2} - i_{el} \quad (3)$$

where: $d_1$ and $d_2$ denote the duty cycles for the pulse width modulation (PWM) of the two-phase IBC. The equivalent series resistances (ESRs) of the inductors, $R_{L1}$ and $R_{L2}$ are assumed to be known values.

## B. The Studied PEM electrolyzer

The studied low-carbon hydrogen production through water electrolysis utilizes a commercial PEM electrolyzer, model QL2000. The key specifications of the PEM electrolyzer are summarized in Table I. The system is designed to operate within a voltage range of 0–18 V and a current range of 0–35 A, making it suitable for integration with photovoltaic systems. The device features a hydrogen flow rate of 2000 cm³/min at an output pressure between 0.01 and 4 bar, ensuring stable hydrogen generation under controlled conditions. The electrolyzer operates at an electrical power of less than 1000 W, making it a viable option for small- to medium-scale hydrogen production applications.

Additionally, to gain a deeper understanding of the static electrical behavior of the electrolyzer under varying operating

<table><caption>**TABLE I.** SPECIFICATIONS OF THE QL-2000 PEM ELECTROLYZER.</caption><thead><tr><td>Parameters</td><td>Value</td><td>Unit</td></tr></thead><tbody><tr><td>Rated electrical power</td><td>&lt;1000</td><td>W</td></tr><tr><td>Stack operating voltage</td><td>0-18</td><td>V</td></tr><tr><td>Stack current range</td><td>0-35</td><td>A</td></tr><tr><td>Delivery output pressure</td><td>0.01-4</td><td>bar</td></tr><tr><td>Hydrogen flow rate</td><td>2000</td><td>cm³.min<sup>-1</sup></td></tr></tbody></table>

<figure><img src="image_3.png" /><figcaption>**Fig. 2.** The static voltage-current curve of the PEM electrolyzer.</figcaption></figure>

conditions and to establish a detailed characterization for system optimization, an experiment was conducted. The procedure involved gradually increasing the input current while measuring the corresponding output voltage of the electrolyzer. This process enabled the characterization of the system's steady-state voltage-current (V-I) behavior. The collected data was used to generate the static V-I curve, as illustrated in Fig. 2, providing insights into the electrolyzer's internal resistance and efficiency.

## C. Hydrogen Flow Rate

Hydrogen production in a PEM electrolyzer is directly related to the electrolyzer current. According to Faraday's law of electrolysis, the amount of hydrogen generated is proportional to the amount of charge passed through the electrolyzer. The molar flow rate of hydrogen ($\dot{N}H_2$) is given by:

$$\dot{N}H_2 = \frac{\eta_F \cdot n_C \cdot i_{el}}{z \cdot F} \quad (4)$$

-$\eta_F$ is the Faraday efficiency (assumed to be 1),

-$n_C$ the number of cells in the electrolyzer (in this case,

$n_c = 8$),

-$i_{el}$ is the electrolyzer current (A).

-$z = 2$ is the number of electrons required to produce one mole of hydrogen,

-$F = 96,485$ (C/mol) is Faraday's constant.

To express the hydrogen flow rate in standard liters per minute (slpm), the molar flow rate is converted using the molar volume at standard conditions, as follows:

$$\dot{V}H_2 = V_m \cdot 60 \cdot \dot{N}H_2 \quad (5)$$

where $V_m = 23.65$ L/mol is the molar volume at standard temperature and pressure (STP: pressure at 1 bar and temperature at 15°C).
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### III. HAMILTONIAN-BASED CONTROLLER DESIGN

#### A. Hamiltonian Control Law

The typical Hamiltonian representation of the system describes the differential equation governing a controlled network as follows [23]:

$$ \dot{\mathbf{x}}=[\mathbf{J}(\mathbf{x})-\mathbf{R}(\mathbf{x})] \cdot \frac{\partial \mathbf{H}(\mathbf{x})}{\partial \mathbf{x}}+\mathbf{g}(\mathbf{x}) \cdot \mathbf{u}+\xi \quad (6) $$

In this equation, $\xi$ represents external disturbances, $\mathbf{u}$ is the control variable vector, $\mathbf{H}(\mathbf{x})$ is the system's Hamiltonian energy store function, $\mathbf{R}(\mathbf{x})$ is the dissipation matrix (with $\mathbf{R}(\mathbf{x})=\mathbf{R}(\mathbf{x})^{\mathrm{T}} \geq 0$), $\mathbf{J}(\mathbf{x})$ is the interaction matrix $\mathbf{g}_{(\mathbf{x})}$ is the input matrix and $\mathbf{x}$ denotes the system state vector.

For the closed-loop system, the controlled Hamiltonian is defined as [14]:

$$ [\mathbf{J}_d(\mathbf{x}) - \mathbf{R}_d(\mathbf{x})] \cdot \frac{\partial \mathbf{H}_d(\mathbf{x})}{\partial \mathbf{x}} = \mathbf{0} \quad (7) $$

Here, $\mathbf{H}_d(\mathbf{x})$ is the desired Hamiltonian energy function, $\mathbf{R}_d(\mathbf{x})$ is the desired dissipation matrix (with $\mathbf{R}_d(\mathbf{x})=\mathbf{R}_d(\mathbf{x})^{\mathrm{T}} \geq 0$), and $\mathbf{J}_d(\mathbf{x})$ is the control interaction matrix (with $\mathbf{J}_d(\mathbf{x})=-\mathbf{J}_d(\mathbf{x})^{\mathrm{T}}$).

The integrated control strategy for the dynamic system is formulated by aligning the plant model with the control model, as shown in equations (6) and (7), resulting in:

$$ [\mathbf{J}_d(\mathbf{x}) - \mathbf{R}_d(\mathbf{x})] \cdot \frac{\partial \mathbf{H}_d(\mathbf{x})}{\partial \mathbf{x}} = [\mathbf{J}(\mathbf{x}) - \mathbf{R}(\mathbf{x})] \cdot \frac{\partial \mathbf{H}(\mathbf{x})}{\partial \mathbf{x}} + \mathbf{g}(\mathbf{x}) \cdot \mathbf{u} \quad (8) $$

Hence, the control input $\mathbf{u}$ can then be determined using equation (8).

#### B. Improved Hamiltonian Control Approach

The Hamiltonian control law is improved by incorporating an integral term ($\lambda_1$) to ensure equal inductor currents in each phase ($i_{L1} = i_{L2}$). This can be expressed as:

$$ \lambda_1 = K_1 \int (i_{L2} - i_{L1}) dt \quad (9) $$

where $K_1$ is the integral gain used to improve current sharing between phases 1 and 2, thereby reducing ripple, with $K_1 > 0$.

Accordingly, the differential equations of the two-phase IBC, including the integral term, can be represented in the Hamiltonian framework (6) as follows:

$$ \mathbf{x}=[x_1 \quad x_2 \quad x_3 \quad x_4]^\mathrm{T}=[i_{L1} \quad i_{L2} \quad v_{el} \quad \lambda_1]^\mathrm{T} \quad (10) $$

$$ \mathbf{u}=[u_1 \quad u_2]^\mathrm{T}=[d_1 \quad d_2]^\mathrm{T} \quad (11) $$

As a result, $\xi$ and $\mathbf{g}_{(\mathbf{x})}$ can be identified as:

$$ \xi = \begin{bmatrix} 0 \\ 0 \\ -\frac{i_{el}}{C_O} \\ 0 \end{bmatrix}, \quad \mathbf{g}(\mathbf{x}) = \begin{bmatrix} \frac{v_{PV}}{L_1} & 0 \\ 0 & \frac{v_{PV}}{L_2} \\ 0 & 0 \\ 0 & 0 \end{bmatrix} \quad (12) $$

Afterwards, the system's Hamiltonian energy function can be expressed as:

$$ \mathbf{H}(\mathbf{x})=\frac{1}{2} \mathbf{x}^{\mathrm{T}} \mathbf{Q} \mathbf{x} \quad (13) $$

$$ \text{with } \mathbf{Q}=\mathrm{diag}\{L_1, L_2, C_1, K_1^{-1}\} \quad (14) $$

As a result, the Hamiltonian function $\mathbf{H}(\mathbf{x})$ is given by:

$$ \mathbf{H}(\mathbf{x})=\frac{1}{2}\left(L_1 \cdot \mathbf{x}_1^2+L_2 \cdot \mathbf{x}_2^2+C_B \cdot \mathbf{x}_3^2+K_1^{-1} \cdot \mathbf{x}_4^2\right) \quad (15) $$

This Hamiltonian function $\mathbf{H}(\mathbf{x})$ captures the system's total energy. Its design allows shaping the system dynamics by injecting desired damping properties, which are key for robust control under transient conditions.

Following this, the gradient of $\mathbf{H}(\mathbf{x})$ can be calculated as:

$$ \frac{\partial \mathbf{H}(\mathbf{x})}{\partial \mathbf{x}}=[L_1 \cdot \mathbf{x}_1 \quad L_2 \cdot \mathbf{x}_2 \quad C_1 \cdot \mathbf{x}_3 \quad K_1^{-1} \cdot \mathbf{x}_4]^\mathrm{T} \quad (16) $$

Consequently, the matrix J-R can be determined as follows:

$$ \mathbf{J-R} = \begin{bmatrix} -\frac{R_{L1}}{L_1^2} & 0 & -\frac{1}{L_1 C_O} & 0 \\ 0 & -\frac{R_{L2}}{L_2^2} & -\frac{1}{L_2 C_O} & 0 \\ \frac{1}{L_1 C_O} & \frac{1}{L_2 C_O} & 0 & 0 \\ \frac{K_1}{L_1} & -\frac{K_1}{L_2} & 0 & 0 \end{bmatrix} \quad (17) $$

To design the Hamiltonian control law, the error variable (e) and the desired reference ($x_d$) are defined as follows:

$$ e=[e_1 \quad e_2 \quad e_3 \quad e_4]^\mathrm{T} \quad (18) $$

$$ x_d=[x_{1d} \quad x_{2d} \quad x_{3d} \quad 0]^\mathrm{T} \quad (19) $$

with $e = x_d - x$ and $x_{4d} = 0$.

The desired Hamiltonian energy function $\mathbf{H}_d(e)$ is expressed as:

$$ \mathbf{H}_d(e)=\frac{1}{2} \mathbf{e}^{\mathrm{T}} \mathbf{Q} \mathbf{e} \quad (20) $$

$$ \mathbf{H}(e)=\frac{1}{2}\left(L_1 \cdot \mathbf{e}_1^2+L_2 \cdot \mathbf{e}_2^2+C_O \cdot \mathbf{e}_3^2+K_1^{-1} \cdot \mathbf{e}_4^2\right) \quad (21) $$

With $x_{4d}$ is set to zero, the gradient $\mathbf{H}_d(x_e)$ is calculated as:

$$ \frac{\partial \mathbf{H}_d(e)}{\partial e}=[L_1 \cdot e_1 \quad L_2 \cdot e_2 \quad C_O \cdot e_3 \quad K_1^{-1} \cdot x_4]^\mathrm{T} \quad (22) $$

The desired dissipation matrix $\mathbf{R}_d$ and the control interaction matrix $\mathbf{J}_d$ in equation (7) are defined $\mathbf{J}_d = -\mathbf{J}_d^{\mathrm{T}}$ and $\mathbf{R}_d = \mathbf{R}_d^{\mathrm{T}} \geq 0$. They are specified as follows:

$$ \mathbf{R}_d=\begin{bmatrix} \frac{(K_{R1}+R_{L1})}{L_1^2} & 0 & 0 & 0 \\ 0 & \frac{(K_{R2}+R_{L2})}{L_2^2} & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{bmatrix} \quad (23) $$

$$ \mathbf{J}_d=\begin{bmatrix} 0 & 0 & -\frac{(K_j+1)}{L_1 C_O} & -\frac{K_1}{L_1} \\ 0 & 0 & -\frac{(K_j+1)}{L_2 C_O} & \frac{K_1}{L_2} \\ \frac{(K_j+1)}{L_1 C_O} & \frac{(K_j+1)}{L_2 C_O} & 0 & 0 \\ \frac{K_1}{L_1} & -\frac{K_1}{L_2} & 0 & 0 \end{bmatrix} \quad (24) $$
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By substituting equations (10)-(12), (16)-(17), and (22)-(24) into equation (8), a set of four equations is formulated through algebraic manipulation. Solving these equations, it reveals three unknown variables ($u_1$, $u_2$, and $K_j$) which can be approximated using two constant tuning controller gains: $K_r$, and $K_I$. The resulting expressions are as follows:

$$K_j = -(x_{1d} - i_{el} + x_{2d}) / (x_1 + x_2 - x_{1d} - x_{2d}) \quad (25)$$

$$u_1 = (x_{3d} - x_4 - K_j \cdot x_3 + K_j \cdot x_{3d} - K_{R1} \cdot x_1 + K_{R1} \cdot x_{1d} + \dots \\ R_{L1} \cdot x_{1d}) / v_{PV} \quad (26)$$

$$u_2 = (x_4 + x_{3d} - K_j \cdot x_3 + K_j \cdot x_{3d} - K_{R2} \cdot x_2 + K_{R2} \cdot x_{2d} + \dots \\ R_{L2} \cdot x_{2d}) / v_{PV} \quad (27)$$

### C. Set-Point Generation

To protect the real electrolyzer during high-current operation and extend its lifespan [22], the desired electrolyzer voltage ($v_{eld}$ or $x_{3d}$) is generated based on its V-I characteristic curve, as shown in Fig. 2. From the curve, it is observed that at 0 A, the voltage is approximately 12 V, which corresponds to the reversible voltage (E) of the electrolyzer. This value can be used as the initial voltage setting. For current values between 1 A and 35 A, the V-I curve demonstrates a nonlinear relationship. However, this section can be approximated using polynomial regression to define the desired electrolyzer voltage ($x_{3d}$). Polynomial regression is employed to approximate the nonlinear behavior of the PEM electrolyzer's V-I characteristics, ensuring safe voltage tracking during large current variations and extending the device's lifespan. The desired electrolyzer voltage ($x_{3d}$) can be expressed by the following equations:

$$x_{3d} = 0.0001 i_{elREF}^3 + 0.0155 i_{elREF}^2 + 0.5767 i_{elREF} + 11.72 \quad (28)$$

with $i_{elREF} = x_{1d} + x_{2d}$

Finally, the block diagram illustrating improved damping control based on Hamiltonian control law for the studied low-carbon hydrogen production system, as detailed in the previous subsection, is shown in Fig. 3.

### D. Stability Proof

To verify the global stability of the closed-loop system, the desired Hamiltonian energy function is selected as a Lyapunov candidate. This approach guarantees that the total system energy decreases over time under the proposed control law, thereby ensuring asymptotic convergence to the equilibrium. The desired Hamiltonian energy function $H_d(x)$ as presented in equation (20), serves as the total energy of the closed-loop system. It also fulfills the requirements of a Lyapunov candidate function, denoted here as $V$. Thus, the candidate Lyapunov function is given by:

$$V = H_d(x) \geq 0 \quad (29)$$

The time derivative of $V$ is expressed as:

$$\dot{V} = \left( \frac{\partial H_d(x)}{\partial x} \right)^T \frac{dx}{dt} \quad (30)$$

<figure><img src="image_4.png" /><figcaption>Fig. 3. Proposed control algorithm diagram for studied converter.</figcaption></figure>

By substituting the system dynamics into (30), the derivative simplifies to:

$$\dot{V} = - \left[ \left( \frac{\partial H_d(x)}{\partial x} \right)^T R_d \frac{\partial H_d(x)}{\partial x} \right] < 0 \quad (31)$$

This implies that $\dot{V} < 0$ for all $x \neq 0$ provided that $R_d$ is positive semi-definite. Therefore, the following stability conditions hold:

$$V > 0, \dot{V} < 0 \quad (32)$$

Thus, the Lyapunov function $V$ remains positive, while its derivative is strictly negative, which ensures global asymptotic stability of the system governed by the Hamiltonian-based passivity control framework.

## IV. EXPERIMENTAL SETUP

To validate the effectiveness of the proposed improved damping control applied to the two-phase IBC for PEM electrolyzer applications, an experimental test rig was set up, as depicted in Fig. 4. The setup consists of a two-phase interleaved buck converter (1) responsible for regulating the current supplied to the electrolyzer, a DC power supply (2) simulating input voltage from a PV (implementing a four-parameter model for the photovoltaic source model under varying solar irradiance conditions [24]), a QL 2000 PEM electrolyzer (3) used for hydrogen generation, a 4-channel oscilloscope (4) for capturing and analyzing key signals such as current and voltage, a dSPACE MicrolabBox (5) serving as the real-time control hardware for executing the proposed control algorithm, and a dSPACE Control Desk (6) acting as the graphical interface for monitoring, tuning, and managing the control process during the experimental validation.

A real PEM electrolyzer is used for validation to accurately realistic nonlinear dynamics and slow response does not present in electronic loads. This ensures practical relevance, highlights the controller's robustness under transient conditions, and avoids reliance on emulators or simplified models, thereby demonstrating the feasibility of the proposed control strategy.

The improved damping control, designed using the HCL, was initially developed in MATLAB-Simulink environment. It was then deployed onto the DS1202 dSPACE MicroLabBox real-time controller. The model was discretized with a fixed-step size corresponding to a predefined sampling period and a fixed switching interval. Utilizing MATLAB and dSPACE software, the control algorithm was automatically converted
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<figure><img src="image_5.png" /><figcaption>**Fig. 4.** Experimental platform of the studied low-carbon hydrogen production systems.</figcaption></figure>

<table><caption>**TABLE II.** SYSTEM SPECIFICATIONS.</caption><thead><tr><td>Parameters</td><td>Value</td><td>Unit</td></tr></thead><tbody><tr><td>Photovoltaic voltage range, v<sub>PV</sub></td><td>70-150</td><td>V</td></tr><tr><td>Electrolyzer voltage range, v<sub>el</sub></td><td>0-18</td><td>V</td></tr><tr><td>Inductor L<sub>1</sub> = L<sub>2</sub></td><td>334</td><td>μH</td></tr><tr><td>Output Capacitors C<sub>0</sub></td><td>520</td><td>μF</td></tr><tr><td>Switching Frequency, f<sub>s</sub></td><td>25</td><td>kHz</td></tr></tbody></table>

<table><caption>**TABLE III.** CONTROLLER PARAMETER.</caption><thead><tr><td>Parameters</td><td>Value</td></tr></thead><tbody><tr><td>K<sub>R1</sub> = K<sub>R2</sub></td><td>1.55 Ω</td></tr><tr><td>K<sub>1</sub></td><td>3350</td></tr><tr><td>K<sub>Max</sub></td><td>2</td></tr></tbody></table>

into executable code and programmed into the digital controller within the dSPACE MicroLabBox for real-time implementation. Additionally, the control parameters are given in Table III.

## V. RESULTS AND DISCUSSION

To evaluate the effectiveness of the improved damping control strategy, experimental testing was carried out under one steady-state condition and two dynamic operating conditions, each designed to reflect real-world scenarios in PEM electrolyzer applications.

### A. Steady-State Operation

Firstly, in the steady-state test, the objective was to verify that the improved damping control could accurately regulate the electrolyzer current to follow its reference while maintaining equal current sharing between the two interleaved inductors and minimizing ripple. The input voltage ($V_{PV}$) was set to 100 V, and the electrolyzer current reference ($i_{elREF}$) was set to 30 A. The experimental results are shown in Fig. 5, which displays the following waveforms: Ch1: inductor current of phase 1 ($i_{L1}$), Ch2: inductor current of phase 2 ($i_{L2}$), Ch3: electrolyzer current ($i_{el}$), and Ch4: electrolyzer current reference ($i_{elREF}$), with the time scale 20 us per division.

The experimental results illustrate the system's steady-state performance under the proposed improved damping control. Ch3 shows the actual electrolyzer current ($i_{el}$) precisely tracking the reference current (Ch4), both equal to 30 A, confirming accurate current regulation and ripple cancellation. On the other side, Ch1 and Ch2 represent the inductor currents of phase 1 and 2 respectively, which exhibit consistent and balanced ripple patterns, validating equal current sharing between phases.

<figure><img src="image_6.png" /><figcaption>**Fig. 5.** Test bench results: steady-state behavior of the studied converter at $i_{elREF}$ = 30 A and $V_{PV}$ = 100 V</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Fig. 6.** Test bench results: transient behavior of $i_{L1}$, $i_{L2}$, $i_{el}$ and $v_{el}$ during the change of $i_{elREF}$ from 5 A to 30 A and vice versa.</figcaption></figure>
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## B. Change in Current Reference (Hydrogen Production Rate)

Secondly, to evaluate the performance of the proposed control law under varying current references, dynamic operating conditions were applied to the hydrogen generation system by adjusting the electrolyzer current reference ($i_{elREF}$) from 5 A to 30 A, corresponding to a hydrogen flow rate ranging from 0.295 slpm to 1.774 slpm, as calculated from Eq. 5. During the test, the input voltage ($v_{PV}$) was maintained at 100 V. It represents a step variation of the required hydrogen production, with constant solar radiation on the PV source. Additionally, this dynamic test was performed twice to highlight the converter's performance during both transient and long-cycle operations. The experimental results, presented in Fig. 6 and Fig. 7, demonstrate the system's dynamic response using the same signal assignments: Ch1 represents the inductor current of phase 1, Ch2 the inductor current of phase 2, Ch3 the electrolyzer current, and Ch4 the electrolyzer voltage. Fig. 6 shows the response with a time scale of 200 ms per division for transient behavior, while Fig. 7 presents long-cycle performance with a time scale of 40 s per division.

The results shown in Fig. 6 illustrate the transient behavior of the inductor currents ($i_{L1}$ and $i_{L2}$), which closely follow each other, indicating proper current sharing between both converter phases. Meanwhile, the actual electrolyzer current ($i_{el}$) accurately tracks the reference without significant overshoot or delay. The electrolyzer voltage ($v_{el}$) also adjusts smoothly in response to the change in current demand, further validating the stability and responsiveness of the control strategy during sudden load variations. However, the studied PEM electrolyzer does not immediately reach its steady-state value.

On the other hand, Fig. 7 presents the long-cycle behavior of the same variables over an extended time frame. These results demonstrate the controller's long-term robustness and effectiveness during sustained operation and periodic current reference changes. Notably, the electrolyzer voltage ($v_{el}$) increases sharply with some overshoot and then gradually settles to a steady-state value of approximately 18 V (see Fig. 2).

This behavior is attributed to the electrochemical reaction dynamics inside the PEM electrolyzer when subjected to a large step change in current. Particularly, Fig. 6 presents the short-term dynamics immediately after the current step (in seconds), where only the fast cathodic response dominates, the transient is just started, and no overshoot is visible; Fig. 7 covers a much longer timescale (hundreds of seconds), so that both cathodic and anodic dynamics, as well as the overshoot and the subsequent relaxation processes, can be appreciated.

Both Fig. 6 and Fig. 7 show that the HCL revealed able to manage two different time constants: the smaller (tens of milliseconds) is responsible of the first transient, the bigger (tens of seconds) regulates asymptotic behavior over long periods of time.

## C. Step Change in Input Voltage (Simulated PV Fluctuation)

Third, the effectiveness of the proposed control law under fluctuating input voltage was assessed by applying dynamic conditions to the hydrogen generation system, where the input voltage ($v_{PV}$) was intentionally varied to mimic the characteristics of a RES. In this test, the step DC input voltage

<figure><img src="image_8.png" /><figcaption>**Fig. 7.** Test bench results: long-cycle behavior of $i_{L1}$, $i_{L2}$, $i_{el}$ and $v_{el}$ during the change of $i_{elREF}$ from 5 A to 30 A and vice versa.</figcaption></figure>

($v_{PV}$) was changed from 100 V to 150 V, simulating a sudden change in solar irradiance, and then back to 100 V, while maintaining a constant electrolyzer current reference ($i_{elREF}$) at 30 A. It corresponds to a step variation of solar radiation maintaining constant hydrogen production. The results of this test are illustrated on Fig. 8, which exhibits the following signals: Ch1: inductor current of phase 1 ($i_{L1}$), Ch2: inductor current of phase 2 ($i_{L2}$), Ch3: electrolyzer current ($i_{el}$), and Ch4: input voltage ($v_{PV}$), with the time scale 200 ms per division.

The waveforms demonstrate that, despite the sudden change in input voltage ($v_{PV}$), the electrolyzer current ($i_{el}$) remains close to the set reference value, and consequently the produced hydrogen, confirming the effective regulation by the proposed control method. The inductor currents of both phases ($i_{L1}$ and $i_{L2}$) show synchronized and stable behavior throughout the voltage transitions, with only minor transient deviations.
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<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 8. Test bench results of stepping the DC input voltage from 100 V to 150 V vice visa with a constant inductor current reference ($i_{elREF}$) at 30 A.</figcaption></figure>

During the step-up test where the input voltage is increased from 100 V to 150 V, the experimental results show that the proposed HCL maintains the electrolyzer current precisely at the 30 A reference level. No overshoot or transient fluctuation is observed in the electrolyzer current ($i_{el}$), and the each inductor currents inductor $i_{L1}$ and $i_{L2}$ remain perfectly balanced. This indicates that the HCL effectively decouples the output dynamics from input-side disturbances, providing smooth and stable operation under dynamic voltage variations, which are common in photovoltaic-driven systems.

Similarly, during the step-down event from 150 V to 100 V, the electrolyzer current ($i_{el}$) continues to track the 30 A reference with no observed undershoot or oscillation. The balanced inductor current sharing is maintained throughout the transition, validating the reliability and stability of the HCL even when the available input energy is suddenly reduced. These results confirm that the proposed controller ensures uninterrupted, precise and constant hydrogen production under

both increasing and decreasing input voltage conditions, thereby demonstrating its effectiveness and suitability for renewable-energy-based hydrogen generation applications.

## D. Performance Comparison of Improved Damping Control Based on Hamiltonian Control Law with Optimized PI

A performance evaluation of the improved damping control based on HCL approach was conducted by comparing it with the traditional Proportional-Integral (PI) controller. The PI controller was used for regulating the electrolyzer current, and its mathematical representation is given as follows:

$$d_1 = k_{p1}(i_{L1REF} - i_{L1}) + k_{I1} \int (i_{L1REF} - i_{L1}) dt$$

$$d_2 = k_{p2}(i_{L2REF} - i_{L2}) + k_{I2} \int (i_{L2REF} - i_{L2}) dt$$

where:

$$\dot{i}_{elREF} = i_{L1REF} + i_{L2REF}$$

$k_{p1} = k_{p2}$ denote the proportional gain

$k_{I1} = k_{I2}$ denote the integral gain

To ensure a fair and comprehensive comparison between the proposed HCL and the conventional PI controller, the PI parameters were carefully tuned for optimal performance. Two parameter sets were evaluated: (1) $k_{p1} = k_{p2} = 0.008$ and $k_{I1} = k_{I2} = 10$ and (2) $k_{p1} = k_{p2} = 0.015$ and $k_{I1} = k_{I2} = 10$. For the proposed HCL, the damping gain $k_r$ was set to 1.55 and 1.25 to assess performance sensitivity.

### 1) Step Current Reference Response Test

In the first scenario, the performance of the proposed HCL and the PI controller was assessed under a fixed input voltage of 100 V. A step change in the electrolyzer current reference ($i_{elREF}$) from 10 A to 25 A was applied to observe the dynamic behavior. The experimental results shown in Fig. 9 and summarized in Table IV. It can be observed that, the HCL with a damping gain $k_r=1.55 \Omega$ achieves the fastest settling time of approximately 1.4 ms, followed by the $k_r=1.25 \Omega$ variant at 2.4 ms. In contrast, both PI controllers settle more slowly, between 4.8–5.0 ms. Although the HCL exhibits a higher overshoot (36%) compared to the PI controller (20%), it remains within acceptable limits and does not cause any voltage variation in the PEM electrolyzer. Moreover, this is offset by enhanced damping and a faster transient response. This experiment also serves as a sensitivity analysis of the damping gain $k_r$. Both values demonstrate stable and effective system performance, validating the robustness and adaptability of the proposed HCL approach for PEM electrolyzer control systems.

### 2) Step Input Voltage Disturbance Test

In the second test, the input voltage was stepped from 100 V to 150 V while maintaining a constant current reference of 25 A; it corresponds imposing constant the output power or the hydrogen production. This scenario emulates fluctuating photovoltaic input conditions to assess control robustness. The results are presented in Fig. 10.

In this test, both versions of the proposed HCL maintain excellent current regulation, with minimal deviation from the reference current, showcasing strong disturbance rejection and rapid recovery. In contrast, the PI controllers exhibit visible current deviations, slower response and takes a longer time to stabilize the HCL demonstrates resilience and fast adaptation, confirming its superiority in maintaining electrolyzer stability
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<figure><img src="image_11.png" /><figcaption>**Fig. 9.** Comparison of electrolyzer current response between PI and improved damping control based on HCL</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Fig. 10.** Electrolyzer current response under a step input voltage from 100 V to 150 V at 25 A reference, comparing HCL and PI controllers.</figcaption></figure>

<table><caption>**TABLE IV.** QUANTITATIVE AND QUALITATIVE PERFORMANCE COMPARISON BETWEEN IMPROVED DAMPING CONTROL BASED ON HCL AND CONVENTIONAL PI CONTROLLER</caption><thead><tr><td>Performance Metric</td><td>Proposed HCL</td><td>PI Controller</td></tr></thead><tbody><tr><td>Settling Time (ms)</td><td>1.4 – 2.4</td><td>4.8 – 5.0</td></tr><tr><td>Overshoot (%)</td><td>36%</td><td>20%</td></tr><tr><td>Current Sharing</td><td>Excellent (due to integral current-balancing term)</td><td>Moderate</td></tr><tr><td>Control Robustness</td><td>Robust to PV and load changes</td><td>Sensitive to fluctuations</td></tr><tr><td>Response Speed</td><td>Faster</td><td>Slower</td></tr><tr><td>Hydrogen Production Stability</td><td>Maintained under dynamic conditions</td><td>Adequate under steady conditions</td></tr></tbody></table>

<table><caption>**TABLE V.** QUANTITATIVE COMPARISON OF RMSE AND CURRENT RIPPLE BETWEEN HCL AND PI CONTROLLERS UNDER PV VOLTAGE VARIATION</caption><thead><tr><td>Controller</td><td>RMSE (A)</td><td>RMSE (%)</td><td>Max Current Ripple (A)</td></tr></thead><tbody><tr><td>HCL ($k_r$ = 1.55 Ω)</td><td>0.095</td><td>-</td><td>0.4</td></tr><tr><td>HCL ($k_r$ = 1.25 Ω)</td><td>0.142</td><td>49.5 %</td><td>0.6</td></tr><tr><td>PI ($k_p$ = 0.015)</td><td>0.285</td><td>200 %</td><td>1.2</td></tr><tr><td>PI ($k_p$ = 0.008)</td><td>0.356</td><td>274 %</td><td>1.5</td></tr></tbody></table>

and hydrogen production consistency under real-world operating conditions. The higher current peak does not correspond to voltage overshoot since the electrolyzer operates at constant voltage (Fig. 2), preserving its reliability.

Finally, Table V compares the Root Mean Square Error (RMSE) and current ripple under PV voltage variation. Using HCL with $k_r$=1.55 Ω as the reference, other controllers show higher RMSE, up to 274% more, and greater current ripple. This confirms the superior performance of the proposed HCL in dynamic conditions.

## VI. CONCLUSION AND FUTURE WORK

The nonlinear behavior of a PEM electrolyzer can be effectively managed through a control strategy based on the Hamiltonian control law (HCL). By integrating a two-phase interleaved buck converter with a PEM electrolyzer and renewable energy sources, the proposed system mitigates oscillations and enhances overall system stability during transient operations. Experimental results validate the effectiveness of the control strategy, demonstrating optimal performance of the PEM electrolyzer under both steady-state and dynamic conditions, while ensuring hydrogen production in accordance with the current reference. As expected, the proposed HCL control achieved best performance when a constant output power is required; besides, it provides faster dynamic response compared to PI controller. Furthermore, the improved reliability and operational robustness offered by the proposed control approach underscores its potential for large-scale green hydrogen production applications. This work contributes to the advancement of hydrogen production technologies by addressing challenges posed by renewable energy intermittency and electrolyzer degradation. Future work will focus on integrating a state observer to estimate unmeasured internal states of the system, further enhancing control accuracy, fault detection capability, and system resilience.

## ACKNOWLEDGMENT

The authors would like to express their heartfelt gratitude to the Research, Development, and Technological Transfer Department at the Thai-French Innovation Institute of KMUTNB for their research equipment.

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<figure><img src="image_13.png" /></figure>

**Burin Yodwong** (Senior Member, IEEE) was born in Chiang Rai, Thailand, in 1990. He received his B.S. and M.S. degrees in electrical engineering from King Mongkut's University of Technology North Bangkok (KMUTNB), Bangkok, Thailand, in 2014 and 2016, respectively. Subsequently, he

earned a Ph.D. in electrical engineering from Université de Lorraine (UL), Longwy, Lorraine, France, in 2022. Currently, he serves as a researcher and head of the Research, Development, and Technological Transfer Department at the Thai-French Innovation Institute, King Mongkut's University of Technology North Bangkok. His current research interests include power electronics and their control laws for electrolyzer applications, renewable energy source systems, electric vehicle applications, and the modeling of proton exchange membrane electrolyzers.

<figure><img src="image_14.png" /></figure>

**Pongsiri Mungporn** (Member, IEEE) received his B.S. and M.E. degrees in electrical engineering from King Mongkut's University of Technology North Bangkok (KMUTNB), Bangkok, Thailand. He is currently pursuing his doctoral degree in electrical engineering at King Mongkut's

Institute of Technology Ladkrabang, Bangkok, Thailand. His current research interests lie in the field of power electronics, encompassing areas such as fuel cells, solar cells, batteries, and supercapacitors.
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<figure><img src="image_15.png" /></figure>

**Yaowaret Maiket** was born in Nonthaburi, Thailand, in 1993. She received her B.S., M.S., and Ph.D. degrees in Industrial Chemistry from King Mongkut's University of Technology North Bangkok (KMUTNB), Bangkok, Thailand, in 2015, 2017, and 2022,

respectively. Currently, she is a lecturer in Division of Chemical Process Engineering Technology, Faculty of Engineering and Technology, King Mongkut's University of Technology North Bangkok (Rayong campus), Thailand. Her current research interests include fuel cells, energy storage, materials for energy application, and energy simulation.

<figure><img src="image_16.png" /></figure>

**Damien Guilbert** (Senior Member, IEEE) was born in Paris, France, in 1987. He received an M.Sc. degree in electrical engineering and control systems and a Ph.D. degree in electrical engineering from the University of Technology of Belfort-Montbéliard (UTBM), France, in 2011 and 2014, respectively. Between September 2016

and August 2023, he was Associate Professor at the University of Lorraine (France) and a permanent member of the GREEN (Group of Research in Electrical Engineering of Nancy) laboratory. In June 2022, he obtained the HDR (habilitation à diriger des recherches) in electrical engineering at the University of Lorraine. Since September 2023, he has been Full Professor at the University of Le Havre Normandy and a permanent member of the GREAH (Group of Research in Electrotechnics and Automatic of le Havre). His current research interests include power electronics for electrolyzer applications, electrolyzer modeling and emulation, and energy management of multisource systems relying on renewable energy sources and hydrogen technologies.

<figure><img src="image_17.png" /></figure>

**Matheepot Plattanasak** (Senior Member, IEEE) received a B.Sc. and M.E. degrees in electrical engineering from King Mongkut's Institute of Technology North Bangkok (KMITNB), Bangkok, Thailand, in 1996 and 2004, respectively, and a Ph.D. degree in electrical engineering from Université de

Lorraine, Nancy-Lorraine, France, in 2012. Currently, he is a Full Professor in the Department of Teacher Training in Electrical Engineering (TE), King Mongkut's University of Technology North Bangkok (KMUTNB). His current research interests include power electronics and their controllers.

<figure><img src="image_18.png" /></figure>

**Uthen Kamnarn** was born in Uttaradit, Thailand, in 1974. He received his B.Eng. in Electrical Engineering from Rajamangala Institute of Technology (RIT), Thanyaburi, Pathum Thani, Thailand, in 1996, his M.Eng. and Ph.D. in Electrical Engineering from King Mongkut's Institute of Technology North

Bangkok (KMITNB), Thailand, in 2002 and 2007, respectively. Currently, he is an Associate Professor in the Department of Electrical Engineering, Faculty of Engineering, Rajamangala University of Technology Lanna (RMUTL), Chiang Mai, Thailand. His main research interests include the field of power electronic circuits and control, power factor correction, power module, dc microgrid, distributed power systems and harmonics on power systems.

<figure><img src="image_19.png" /></figure>

**Melika Hinaje** was born in Nancy, France, in 1978. She received an M.S. degree in electrical engineering from the University of Nancy, Nancy, France in 2002, and a Ph.D. degree from the National Polytechnic Institute of Lorraine (INPL), Nancy, France, in 2005. Since 2006, she has been an Assistant

Professor at National Polytechnic Institute of Lorraine, Nancy, France. Her research activities in the Laboratoire Réactions et Génie des Procédés concern fuel cells. She defended her Habilitation qualification (accreditation to supervise research) in June 2012. Since 2015, she has been a Professor at the University of Lorraine, Nancy, France. Her main research interests deal with the modeling of fuel cells, including their characterization.

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**Gianpaolo Vitale** (Senior Member, IEEE) was born in Palermo, Italy, in 1964. He received an M.S. degree in electronic engineering from the University of Palermo, Palermo, Italy, in 1988.

He is the Research Director of the Institute for High Performance Computing and Networking (ICAR) belonging to the National Research Council of Italy (CNR). He teaches "Industrial electronics" at the University of Palermo, Department of Engineering, MD electronics engineering. Prof. G. Vitale is the coauthor of two books, two edited books, four book chapters and over one hundred scientific works. He is a senior member of IEEE (Institute of Electrical and Electronics Engineers) and serves as a reviewer for several journals and conferences. His current research interests are in the fields of power electronics, power generation from renewable sources, electromagnetic compatibility and robotics.

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**Phatiphat Thounthong** (Senior Member, IEEE) was born in Phatthalung, Thailand, on December 29, 1974. He received the B.S. and M.E. degrees in electrical engineering from King Mongkut's Institute of Technology North Bangkok (KMITNB), Bangkok, Thailand, in 1996 and 2001, respectively, the

Ph.D. degree in electrical engineering from Institut National Polytechnique de Lorraine (INPL), Nancy-Lorraine, France, in 2005, and the Habilitation à Diriger la Recherche (HDR) from Université de Lorraine, Nancy-Lorraine, France in 2020.

Since 2012, he has been a Full Professor in Department of Teacher Training in Electrical Engineering, King Mongkut's University of Technology North Bangkok. He is the author of 290 scientific papers (including 21 papers in IEEE Transactions/Magazines) published in Scopus with citations = 7,115 times, and h-index= 42. His current research interests include power electronics, electric drives, electric vehicles, electrical devices (fuel cells, photovoltaic, wind turbine, batteries, and supercapacitors), nonlinear controls, and observers.