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# Advances in Electrolyzer Emulators: A Comprehensive Review

Hoda El Assal, Mамadou-Baïlo Camara, Damien Guilbert

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Hoda El Assal, Mамadou-Baïlo Camara, Damien Guilbert. Advances in Electrolyzer Emulators: A Comprehensive Review. Electronics, 2025, 14 (23), pp.4576. 10.3390/electronics14234576. hal-05377677

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Review

# Advances in Electrolyzer Emulators: A Comprehensive Review

Hoda El Assal* ID, Mamadou-Baïlo Camara ID and Damien Guilbert ID

Groupe de Recherche en Electrotechnique et Automatique du Havre (GREAH), Université le Havre Normandie (ULHN), 76600 Le Havre, France; mamadou-bailo.camara@univ-lehavre.fr (M.-B.C.); damien.guilbert@univ-lehavre.fr (D.G.)

* Correspondence: hoda.el-assal@etu.univ-lehavre.fr

## Abstract

Electrolyzers (ELs) have become pivotal technologies for the production of green hydrogen, a clean energy carrier that facilitates renewable energy sources and supports the energy transition from fossil-based to a zero-carbon energy system. However, challenges such as high costs, maintenance requirements, and hydrogen storage issues still hinder large-scale deployment. To address these obstacles, EL emulators have emerged as low-cost and safe alternatives for system development and testing. These emulators have gained worldwide interest, supporting the design and validation of EL-based systems, without the risk of damaging real units. However, despite their increasing relevance in research and development, dedicated studies on EL emulators remain relatively scarce. This article provides a detailed overview of the main characteristics and various studies on emulators. The review starts by examining the existing literature on EL emulators and identifying gaps in current research. Special attention is paid to the electrical models adopted to reproduce their characteristics, as well as to the control strategies implemented to ensure accurate operation. This analysis highlights the importance of emulator-based studies in accelerating the development, optimization, and integration of diverse EL technologies into future energy systems.

**Keywords:** electrolyzer; emulators; modeling; control; power electronics; power-hardware-in-loop

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### check for updates

Academic Editor: Fabio Corti

Received: 16 October 2025

Revised: 12 November 2025

Accepted: 20 November 2025

Published: 22 November 2025

**Citation:** El Assal, H.; Camara, M.-B.; Guilbert, D. Advances in Electrolyzer Emulators: A Comprehensive Review. *Electronics* 2025, 14, 4576. https://doi.org/10.3390/electronics14234576

**Copyright:** © 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## 1. Introduction

Global progress in hydrogen energy, including its generation, storage, and delivery methods, is becoming a cornerstone in the transition toward a clean and decarbonized future energy system [1,2]. It directly contributes to reducing dependence on fossil fuels and enhancing the resilience of the energy supply to challenges posed by climate change [3–5]. With the increasing integration of renewable energy sources (RESs), the advancement of storage systems has become crucial, as these resources continue to face challenges related to intermittency [6]. Water electrolysis addresses this challenge by converting surplus electricity into chemical energy [7,8], which can be stored for extended periods and converted back to electricity through fuel cells to meet the grid’s energy demand, creating a flexible and efficient energy system. Hydrogen is increasingly being used for many applications, particularly energy storage, as a result of its high mass energy density and long-term storage capability, offering advantages over conventional batteries [9]. Thus, the development of efficient storage systems capable of accommodating surplus renewable electricity is needed.
Electrolyzers (ELs) have emerged as a promising technology that facilitates the conversion of electrical energy to chemical energy by splitting water into hydrogen and oxygen through an electrochemical process [10], which is the reverse of fuel cell operation. While fuel cells generate electricity by combining hydrogen and oxygen to produce water, ELs consume electricity to decompose water into its components [11]. Green electrolysis, driven by RES, has become increasingly important in recent years. The scalability of this system facilitates various applications, ranging from small- to large-scale plants integrated with the grid. This hydrogen can be used for residential heating, energy storage, fuel stations, and a variety of industrial applications [12]. In addition, hydrogen can be reconverted into electricity by using fuel cells as needed. A schematic representation of hydrogen production through electrolysis and its main applications is presented in Figure 1.

<figure><img src="image_4.png" /><figcaption>**Figure 1.** Applications of green hydrogen produced by electrolysis.</figcaption></figure>

With advancements in technology, numerous manufacturers now offer a wide range of EL types. ELs are classified primarily into alkaline water electrolyzers (AWEs), proton exchange membrane (PEM), anion exchange membrane (AEM), and solid oxide electrolysis cells (SOECs), each with distinct characteristics suited for various applications [11,13].

On one hand, PEMEL offers significant advantages in terms of current density, differential pressure operation, and dynamic operating capability, which make it well-suited for integration with RES [14–16]. Although AWE still represents about 60 % of the market [17], PEMEL is experiencing rapid growth driven by its improved operational flexibility and compatibility with variable RES. On the other hand, SOECs deliver efficiency higher than that of PEMEL through high-temperature operation but suffer from dynamic operation limitations and low lifetime. AEM technology remains in the research stage; yet, it presents a promising, low-cost, and flexible option [18].

Despite these benefits, widespread commercialization of different types of ELs is hindered by their reliance on rare and costly materials, particularly noble-metal catalysts such as platinum and iridium at the anode and cathode [19–21]. In addition, the availability of pure water is a problem, as water contaminants increase voltage, which reduces efficiency, increases energy consumption, and negatively affects cell performance and durability, as mentioned in [22]. Their limited scalability for large-scale (MW) applications also poses a significant challenge. To address this, a thorough analysis and further research are required to validate the performance characteristics of large-scale units and to assess their lifespan.

However, experimental hardware is ignored when only simulation is used, even though this hardware is important for studying the EL behavior in a complete system or when integrated into the microgrid. Hardware that is capable of accurately imitating the EL behavior is essential for allowing experiments to be conducted under controllable conditions, offering advantages such as repeatable tests, performance validation, and a
realistic representation of system behavior without the use of a real unit, at least during
the initial experimental stages. In this regard, this hardware system is known as an emula-
tor [23]. An emulator can take the place of a real EL, allowing for study and examination.
After performance validation, it can be replaced with a real EL, helping to save time and
money while avoiding the risk of damaging the real one. An emulator is a combination
of hardware and software designed to mimic the behavior of a real system. It provides a
trade-off between precision and speed, offering a practical alternative [24], since it utilizes
a component-based architecture, thus improving scalability and adaptability for various
applications. An emulator is a physical or digital system designed to reproduce the input-
output behavior of any device in real-time. Unlike a purely mathematical model, which
provides a theoretical or computational description of system dynamics, an emulator allows
for experimental validation, controller testing, and hardware-in-the-loop (HIL) studies by
interacting directly with power electronics and control hardware.

Accurate modeling is essential for the efficient control of hydrogen systems based on RES [25]. Numerous models in the literature emulate the static and dynamic behavior of EL, with some based on thermodynamic principles to illustrate the physical, thermal, and electrochemical processes that take place within the system [15,26–39]. Other models apply electrical laws, such as Kirchhoff’s, and account for membrane capacitance resulting from charge accumulation on both sides [40–49]. An additional EL model uses empirical data and fitted parameters [10,50,51]. In [39], a real-time fault diagnosis system was developed to advance PEM water electrolysis. Its model integrates both the stack and the balance of plant (BoP) components. Furthermore, the study in [52] presents a comprehensive PEMEL model for microgrid applications, integrating electrochemical and thermal dynamics. Using the Partial Reinforcement Optimizer (PRO), model parameters are identified under varying temperature and pressure. The model should reflect the behavior of PEMEL to examine the interactions with power converters reported in the literature [53–55].

In [20,21], the dynamic behavior of PEMELs was investigated by developing an equiv-
alent electrical circuit (EEC) model. Specifically, in [21], Guilbert and Vitale addressed the
limitations of steady-state models by introducing capacitive effects into the EEC framework.
In contrast, in [20], Yodwong et al. proposed a model validated against a 400 W commercial
PEMEL designed for the testing of DC-DC converters and control systems. For emula-
tor validation, a PEMEL emulator using a DC-DC boost converter has been successfully
implemented in [56–59], along with a comparative analysis of data from a real PEMEL
using the power-hardware-in-loop (PHIL) system. A high-power (405 A) PHIL simulator
was presented in [58,59], allowing accurate analysis under real conditions. Furthermore,
in [57], Zhou and Francois created a control-oriented model for hydrogen production
within a hybrid system. Moreover, the model in [56] accurately replicates the nonlinear
polarization curve, eliminating the need for complex auxiliary systems. An analog EEC
based on a Maxwell derived from electrochemical impedance spectroscopy (EIS) data from
a commercial reversible solid oxide electrolyzer cell (RSOEC) stack was developed in [60].
A PHIL-based load emulator was developed to replicate the electrical behavior of an AWE
EL using an EEC model, allowing rectifier testing [61].

In recent years, numerous review papers have been published, including those that
focused on PEM water electrolysis modeling and technology, such as in [10,25,48,62-66]
and fuel cell emulators [23,67,68]. However, based on this brief summary of the state-of-
the-art, this review is driven by the lack of a comprehensive study that focuses on the
concept of EL emulators, despite their growing relevance in microgrids today and in testing
applications. Its originality lies in presenting the different types of emulators mentioned
in the literature, followed by circuit design, which offers a clear reference for researchers
working on EL emulators.
This paper is organized into six sections. The introduction outlines the current state-of-the-art related to this review, followed by Section 2, a coherent explanation of basic construction, the operating principles of water electrolysis, along with a comparison between the different types of EL. After that, a comparison of various EL emulators discussed in the literature is presented in Section 3. In Section 4, the mathematical models are discussed along with the design of the electric circuits. The integration of EL in a power grid is presented in Section 5. Finally, in Section 6, a discussion is given, and Section 7 concludes the work presented in this review.

## 2. Basic Operation and Comparison of EL Types

### 2.1. *Basic Operation of Water Electrolysis*

The transition to a hydrogen-based economy, supported by RES, is significantly dependent on electrolysis that transforms green electricity into hydrogen. Electrolysis refers to the method of applying an electric current to dissociate water into hydrogen and oxygen gas, as shown in Figure 2.

<figure><img src="image_5.png" /><figcaption>**Figure 2.** General scheme for water electrolysis.</figcaption></figure>

A fundamental water electrolysis cell scheme consists of a DC source, an electrolyte, and two electrodes: a cathode attached to the negative pole, where hydrogen is obtained because of the reduction reaction, and an anode attached to the positive pole, where oxidation reactions and the production of oxygen occur. These elements then converge at the cathode to form hydrogen, thereby converting electrical energy into stored chemical energy. The EL stack is made up of several electrolysis cells arranged in a series configuration. Each cell comprises three essential components: the anode compartment, the cathode compartment, and the membrane electrode assembly (MEA) [69]. The resulting oxygen gas permeates the current collector electrode, spreads throughout the gas diffusion layer, and exits through the channels of the flow field plate. At the same time, the free electrons travel through the external circuit to the negative terminal of the power supply. Positively charged hydrogen protons move across the membrane towards the cathode, where they combine with free electrons in the catalyst layer to produce hydrogen gas [70,71]. The hydrogen generated subsequently travels through the porous layers and the gas diffusion layer, arriving at the flow field plate, which directs it to the hydrogen outlet at a predetermined pressure.

Hydrogen production by AWE is a well-established technology capable of operating on a megawatt scale for commercial applications. It was first introduced by Troostwijk and Diemann in 1789 [13]. In the 1960s, General Electric (GE) Company pioneered the first PEMEL as a solution to the deficiencies inherent in AWE technology [72]. Moreover, SOEC was first introduced by Donitz and Erdle in 1980 [73], and in this decade, AEM began to be applied in water electrolysis [74].
Electrochemical water electrolysis technologies can be classified primarily according to the nature of the electrolyte and the ionic agents transported between electrodes, as illustrated in Figure 3.

<figure><img src="image_6.png" /><figcaption>**Figure 3.** Schematic diagrams of operation principles for different EL types: (a) Proton exchange membrane (PEM). (b) Alkaline water electrolyzers (AWEs). (c) Solid oxide electrolysis cells (SOECs). (d) Anion exchange membrane (AEM).</figcaption></figure>

PEMEL (Figure 3a) uses a solid polymer membrane, such as Nafion, that conducts H⁺ ions from the anode to the cathode, where pure hydrogen is produced [13]. In contrast, AWE (Figure 3b) operates with a liquid KOH electrolyte and a porous diaphragm, allowing OH⁻ ion transport in the opposite direction from the cathode to the anode. At high temperatures, SOEC (Figure 3c) employs a ceramic electrolyte, typically yttria-stabilized zirconia (YSZ), which conducts O²⁻ ions, achieving high efficiency through thermal assistance [75]. Finally, AEM (Figure 3d) combines the characteristics of PEMEL and AWE systems, using a solid polymer that transfers OH⁻ ions and allows operation with low-cost, non-noble catalysts.

## 2.2. Reaction Equations

The anode and cathode reactions are typically identified as the oxygen evolution reaction (OER) and hydrogen evolution reaction (HER), respectively. These equations of the four EL types are shown in the table below, Table 1. Meanwhile, Equation (1) illustrates the comprehensive reaction that results from the summation of the two electrochemical half-reactions that occur at the electrodes within an acidic environment, which requires a DC power supply to facilitate the process [10].

$$ \text{Global reaction: } (H_2O)_l \rightarrow (H_2)_g + \frac{1}{2}(O_2)_g \quad (1) $$

<table><caption>**Table 1.** Comparison of chemical reactions in different types of water electrolysis [76–78].</caption><thead><tr><th></th><th>Anode Reaction</th><th>Cathode Reaction</th></tr></thead><tbody><tr><td>PEM</td><td>H<sub>2</sub>O → <sup>1</sup>&frasl;<sub>2</sub>O<sub>2</sub> + 2H<sup>+</sup> + 2e<sup>-</sup></td><td>2H<sup>+</sup> + 2e<sup>-</sup> → H<sub>2</sub></td></tr><tr><td>AWE</td><td>2OH<sup>-</sup> → <sup>1</sup>&frasl;<sub>2</sub>O<sub>2</sub> + H<sub>2</sub>O + 2e<sup>-</sup></td><td>2H<sub>2</sub>O + 2e<sup>-</sup> → H<sub>2</sub> + 2OH<sup>-</sup></td></tr><tr><td>SOEC</td><td>O<sup>2-</sup> → <sup>1</sup>&frasl;<sub>2</sub>O<sub>2</sub> + 2e<sup>-</sup></td><td>H<sub>2</sub>O + 2e<sup>-</sup> → H<sub>2</sub> + O<sup>2-</sup></td></tr><tr><td>AEM</td><td>2OH<sup>-</sup> → <sup>1</sup>&frasl;<sub>2</sub>O<sub>2</sub> + H<sub>2</sub>O + 2e<sup>-</sup></td><td>2H<sub>2</sub>O + 2e<sup>-</sup> → H<sub>2</sub> + 2OH<sup>-</sup></td></tr></tbody></table>
## 2.3. Comparison of EL Types

In general, water electrolysis, such as AWE, AEM, PEM, and SOEC, presents a promising avenue for hydrogen production that holds diverse applications in the fields of renewable energy and catalysis [79]. The table below Table 2 compares the key operational parameters, performance metrics, and characteristics of four major hydrogen production technologies of the four types of EL, including PEM, AWE, SOEC, and AEM.

AWE is the most mature technology, uses non-noble catalysts [80–82], and has a low capital cost (500–800 €/kW). It is better adapted for large-scale hydrogen production when low cost is the priority over rapid response (slow start-up times of 1–2 h). It has a long lifetime (60,000–80,000 h) and low degradation (0.25–1.5%/year). SOEC and AEM are newer technologies that show promise, but they are still in the research phase, and challenges remain [83]. They can produce green hydrogen from renewable energy with high efficiency and zero carbon emissions. SOECs have the highest operating temperature (700–850 °C) and low pressures (~1 bar), and are applicable when the most important application is very high temperatures; they are suitable for industrial applications. They have very high capital costs, slow start-up, low flexibility, and high degradation rates (3–50%/year), which limit current commercial use [84]. Finally, AEM is an emerging technology that offers low cost, fast cold start (5–10 min), and high operational flexibility (0–100%). Although promising for RES applications, their durability is still uncertain, and the current stability is limited to around 10,000 h [74]. This comparison shows that PEMELs are becoming increasingly relevant as a result of their performance compared to traditional ELs. PEMELs operate at high current densities (1–6 A/cm²). They offer rapid start-up (<10 s), excellent dynamic response, and high hydrogen production rates, making them highly flexible for variable operation [10,81,84]. However, they rely on expensive noble materials (platinum, iridium), have moderate degradation (0.5–2.5%/year), and relatively limited lifetimes (30,000–40,000 h) under acidic conditions.

<table><caption>**Table 2.** Technical comparison of different ELs technologies [12,17,22,70,74,81,84–87].</caption><thead><tr><th></th><th>PEM</th><th>AWE</th><th>SOEC</th><th>AEM</th></tr></thead><tbody><tr><td>Operation temperature, °C</td><td>50–80</td><td>70–90</td><td>700–850</td><td>60–80</td></tr><tr><td>Cell pressure, bar</td><td>&lt;50</td><td>&lt;30</td><td>1</td><td>&lt;35</td></tr><tr><td>Typical current density range, A·cm<sup>-2</sup></td><td>1–6</td><td>0.2–0.8</td><td>0.3–1.0</td><td>0.2–2.0</td></tr><tr><td>Voltage range, V</td><td>1.4–2.3</td><td>1.4–3</td><td>1.0–1.5</td><td>1.4–2.0</td></tr><tr><td>System efficiency range, %</td><td>46–60</td><td>51–60</td><td>76–81</td><td>&lt;75</td></tr><tr><td>System specific energy consumption range, kWh·Nm<sup>-3</sup></td><td>4.53–6.1</td><td>4.0–5.47</td><td>3.7–3.9</td><td>4.2–5.5</td></tr><tr><td>Stack efficiency range (based on LHV *), %</td><td>60–68</td><td>63–71</td><td>~100</td><td>60–83</td></tr><tr><td>Stack specific energy consumption range, kWh·Nm<sup>-3</sup></td><td>4.3–5.8</td><td>3.8–5.2</td><td>3</td><td>3.95–5.2</td></tr><tr><td>Max * stack power, MW</td><td>6.5</td><td>5</td><td>&lt;0.01</td><td>2</td></tr><tr><td>Max * hydrogen production, Nm<sup>3</sup>·h<sup>-1</sup></td><td>1110</td><td>1050</td><td>&lt;10</td><td>462</td></tr><tr><td>Lifetime range, kh</td><td>30–40</td><td>60–80</td><td>8–20</td><td>&lt;2</td></tr><tr><td>Degradation rate, % per year</td><td>0.5–2.5</td><td>0.25–1.5</td><td>3–50</td><td>–</td></tr><tr><td>Capital cost, €/kW</td><td>1400–2100</td><td>500–800</td><td>&gt;2000</td><td>200</td></tr><tr><td>Environmental impact</td><td>Moderate</td><td>Lowest</td><td>Highest</td><td>Potentially low</td></tr><tr><td>Renewable energy compatibility</td><td>Excellent</td><td>Low</td><td>Low</td><td>Potentially high</td></tr><tr><td>Technology maturity</td><td>Commercialized</td><td>Mature</td><td>R&D</td><td>Emerging</td></tr><tr><td>Application</td><td>Mobility, Large-scale</td><td>Industrial Large-scale</td><td>Industrial High temperature</td><td>Industrial, Mobility potential</td></tr></tbody></table>

The key benefits and drawbacks of PEM, AWE, SOEC, and AEM are presented in Table 3 below.

<footnote>* LHV: Lower Heating Value. Max: Maximum.</footnote>
<table><caption>**Table 3.** Advantages and disadvantages of four EL technologies [12,13,70,71,74,75,78,81,87–89].</caption><thead><tr><th>ELs</th><th>Advantages</th><th>Disadvantages</th></tr></thead><tbody><tr><td>PEM</td><td><ul><li>High current density</li><li>Fast system response</li><li>Greater hydrogen production rate</li><li>High dynamic operation</li><li>Excellent operational flexibility (0–100%)</li><li>Rapid cold and hot start (&lt;10 s)</li></ul></td><td><ul><li>High cost of noble materials (iridium and platinum)</li><li>Moderate degradation rate (0.5–2.5%/year)</li><li>Limited lifetime (30,000 h–40,000 h)</li><li>Operates in acidic environment</li></ul></td></tr><tr><td>AWE</td><td><ul><li>Most mature and well-established technology</li><li>Non-noble electrocatalysts</li><li>Longer lifetime &gt;60,000 h</li><li>Low degradation rate (0.25–1.5%/year)</li><li>Low capital cost</li></ul></td><td><ul><li>Low current density (0.25–0.8 A/cm²)</li><li>Corrosive electrolyte</li><li>Slow start-up time (1–2 h)</li><li>Lower load flexibility for RES</li></ul></td></tr><tr><td>SOEC</td><td><ul><li>Very high efficiency</li><li>High temperatures</li><li>RES integration with heat</li></ul></td><td><ul><li>Still in research phase</li><li>High degradation rate (3–50%/year)</li><li>Low flexibility (–100/+100)</li><li>Very high capital cost</li><li>Slow start-up time</li></ul></td></tr><tr><td>AEM</td><td><ul><li>Low cost</li><li>Excellent operational flexibility (0–100 %)</li><li>Fast cold start (5–10 min)</li></ul></td><td><ul><li>Emerging technology</li><li>Durability remains uncertain</li><li>Stability up to 10,000 h</li></ul></td></tr></tbody></table>

### 3. Emulator Fundamentals

EL emulation becomes essential, as it enables broader research opportunities and supports advances in EL performance, as well as their grid integration. Furthermore, an emulator of an electrical system, treated as a dipole [20], serves as a substitute that replicates the voltage and current behavior of the actual source. This experimental setup allows measurements and tests to be conducted as if they were on the real system. In fact, EL must be connected to a power converter for proper operation, and an equivalent model enables the entire system to be simulated and tested. Emulators are used in RES applications as practical substitutes for real systems. This is because real energy generation setups can be quite costly to construct and maintain, often require strict safety regulations, utilize chemical substances, and can exhibit complex or unpredictable behavior. Using emulators, researchers can test and develop control strategies or system responses without the risks and costs associated with full-scale implementation [23]. It is intended to replicate the specific characteristics of this type of ELs. Furthermore, studies and experiments on these characteristics have been conducted to simulate actual performance under various operating conditions at a low cost without the need to damage a real EL. In addition, the lifespan of an emulator can be influenced by various factors, including the quality of the components, frequency of use, maintenance practices, and the surrounding environment.

The assessment considers four main factors such as price, accuracy, simplicity, and accessibility. Price refers to the emulator's cost, accuracy reflects how closely it replicates the electrical behavior of the EL cell or stack, simplicity considers the ease of construction, and accessibility addresses the requirement for specialized laboratory equipment. Thus, greater emphasis is placed on accuracy and accessibility. This kind of system is composed of two main parts: the power electronic stage, which provides the necessary power to the EL, and the control stage, which is responsible for managing the power electronic device and emulating the behavior of the ELs through mathematical modeling.
## 3.1. Proposed Emulators in the Literature

Among the reviewed literature, EEC-based emulators are found in [20,21,56,60,61]. In contrast, the second emulator proposed in the literature is based on a power electronic circuit implemented specifically using a DC-DC boost converter, as in [56–58].

### 3.1.1. EEC-Based Emulator

EEC emulators are simply based on an equivalent passive circuit to mimic EL behavior, including anode, cathode, and membrane. EEC is the model that uses electrical components, such as electric voltage/current sources and passive elements such as resistors, inductors, and capacitors, to construct an electrical circuit that can emulate the behavior of a typical machine or device [25,43,90].

Typically, the EL cell voltage can be represented by the summation of the four overvoltages (reversible voltage, ohmic, activation, and concentration overvoltage) from an electrical point of view. Furthermore, it is notable that some EECs incorporate consideration of the electric double layer (EDL) within the EL, as in [20,21], instead of activation and concentration overvoltage, as illustrated in Figure 4. This double-layer effect refers to the occurrence of charge accumulation on both sides of the membrane, which is accompanied by an opposing charge on the surfaces of the electrodes, resulting in capacitive effects at both the anode and cathode sides of the membrane. However, it is fundamentally composed of two parallel RC circuits representing the dynamics of the reactions occurring at both the anode and cathode, reversible voltage models hydrogen production, and a resistor that accounts for the membrane’s ohmic overpotential. Meanwhile, electrical circuit models play an inevitable role in the design and analysis of the different components of the system and associated control techniques. Additional clarification regarding the previously mentioned overvoltage components and the electric circuit design proposed from the reviewed literature will be presented in the following section.

<figure><img src="image_7.png" /><figcaption>Figure 4. PEMEL equivalent electrical circuit.</figcaption></figure>

### 3.1.2. DC-DC Boost Converter-Based Emulators

#### (A) Power electronics stage:

The power electronics of the emulator typically include a DC power supply stage, a conversion stage, such as boost converters, and a terminal stage, which can be implemented as a grid interface or a reversible DC power source, depending on the objectives of each study, as shown in Figure 5. The supply stage provides the DC voltage required to feed the emulator. The conversion stage modifies voltage and current levels to emulate the EL’s electrical behavior, while the grid interface ensures secure bidirectional power exchange with the electrical grid, typically supported by filtering components for power quality and stability. The foundation of this emulator is centered on a DC-DC boost converter that serves as the main component of ELs [56–59,91]. This converter is ideally suitable for considering low-voltage and high-current needs. In addition, it can be used to transfer power from the low-voltage side of the emulator to the higher-voltage DC link. This allows the emulator to behave as a variable impedance that can reflect the dynamic characteristics
of an actual EL. However, it must be controlled to ensure the overall stability of the system and maintain accurate current tracking through the converter inductance [56].

<figure><img src="image_8.png" /><figcaption>Figure 5. Emulator based on a DC-DC boost converter.</figcaption></figure>

### (B) Control stage:

The control strategies currently implemented in emulators fall into two distinct categories: traditional control or advanced control. Traditional control strategies, such as proportional-integral controllers (PI), which have been implemented in [91], have been used due to their simplicity, reliability, and effectiveness in regulating the current, and they reduce steady-state error, making them suitable for real-time control. Moreover, advanced control strategies, including model predictive control (MPC) and sliding mode controller (SMC), are strategies that significantly improve control accuracy and response time, but with more complex structures. The supertwisting sliding mode controller (ST-SMC) has been used in [56], valued for its robustness against system uncertainties. CompactRIO (cRIO) has been used in [59]. It consists of a real-time controller chassis, reconfigurable IO modules (RIO), a field-programmable gate array (FPGA) module, and an Ethernet expansion chassis. Model-Based Control with Causal Ordering Graph (COG) illustrates the relationships among the physical quantities that have been implemented in [57]. However, control strategies and implementation methods are essential for validating EL emulators, and several reported approaches have been investigated, each having its own strengths and limitations. Thus, the ones that have been performed with the ELs emulator reported in the literature [48,56,57,61,92,93] are summarized in Table 4 below.

<table><caption>Table 4. Advantages and disadvantages of different control strategies for EL emulators.</caption><thead><tr><td>Classical Used Controller</td><td>Advantages</td><td>Limitations</td></tr></thead><tbody><tr><td>PI</td><td><ul><li>Simple and well-known, easy to design and implement</li><li>Reliable for current regulation</li><li>Reduces steady-state error and ensures accurate tracking</li></ul></td><td><ul><li>Limited robustness to system uncertainties</li><li>Performance may degrade under nonlinear dynamics or parameter variations</li><li>Poor tuning may cause oscillations or steady-state error</li><li>Slower dynamic response than advanced controllers</li></ul></td></tr><tr><td>ST-SMC</td><td><ul><li>High robustness against uncertainties and disturbances</li><li>Ensures overall stability</li><li>Provides precise current tracking through the inductor</li></ul></td><td><ul><li>Control discontinuity may induce chattering</li><li>Requires careful design of sliding surface and control law</li><li>Increased complexity compared to linear controllers</li></ul></td></tr></tbody></table>
## 3.2. Model Verification Based PHIL Concept

Verification of electrical circuit models occurs primarily through a comparison of the model results with the experimental EL tests. The model's ability to accurately replicate both the static and dynamic behaviors is significantly influenced by the model parameters, which are typically acquired via curve-fitting techniques. In other words, the accuracy and efficiency of the curve-fitting method used will have a direct impact on the model's accuracy and its capability to replicate the behavior of the electrolyzer. Therefore, other parameterization techniques need to be developed to accurately estimate and validate the behavior of the EEC.

The PHIL method represents a simulation technique that links software models of various component systems with the hardware being tested, as shown in Figure 6. The PHIL simulator presents several important advantages for emulators. It supports high-power operation up to tens of kilowatts, enabling realistic testing on an industrial scale. It enables the study of the dynamics and efficiency of industrial-scale EL supply electronics under actual load conditions. Another key strength is its flexibility within energy systems, as it can be incorporated into a Power-to-Gas production chain [58], using RES as input and producing liquid or gaseous fuels as output. The use of commercial converters also improves the robustness and allows the emulation of any type of water electrolysis or other DC loads without necessitating hardware modifications. Moreover, this simulator enables one to study different power supplies and current waveforms, with the option to easily replace the power supply module. Furthermore, it provides a safety-oriented alternative, eliminating the need for supplementary components such as water supply, cooling systems, hydrogen tanks, etc., making it a cost-effective and reliable option for smart grid testing.

<figure><img src="image_9.png" /><figcaption>Figure 6. PHIL configuration.</figcaption></figure>

## 3.3. Comparison of Existing EL Emulator

EL emulation has become an essential tool for testing, design validation, and integration of renewable energy systems. The literature reveals a wide range of approaches and implementations. Table 5 summarizes the different EL emulator designs, showing the type of EL, the utilization of hardware and software platforms, experimental validation, grid integration capability, and the achieved accuracy. The error represents the difference between the experimental and simulated voltage values, which shows how accurately the model reproduces the real behavior. However, the accuracy metrics vary depending on the evaluation method, test conditions, and reference models used in each study. In addition, variations in modeling assumptions, such as ideal components or simplified electrochemical behavior, further affect the reported results. Table 6 will highlight the practical applications, advantages, and limitations of these emulators.
<table><caption>**Table 5.** Comparison of EL emulator studies grouped by EL type.</caption><thead><tr><th>Study No.</th><th>Ref.</th><th>EEC</th><th>Boost Conv.</th><th>PHIL</th><th>Exp.*</th><th>Grid Int.*</th><th>Software</th><th>Accuracy Metric</th></tr></thead><tbody><tr><td colspan="9"><strong>PEM Studies</strong></td></tr><tr><td>1</td><td>[20]</td><td>✓</td><td>✗</td><td>✗</td><td>✓</td><td>✗</td><td>MATLAB/Simulink</td><td>Max error 8.75% (transient), ≤10% (steady-state)</td></tr><tr><td>2</td><td>[21]</td><td>✓</td><td>✗</td><td>✗</td><td>✓</td><td>✗</td><td>MATLAB/Simulink</td><td>Max error ≈ 4%</td></tr><tr><td>3</td><td>[56]</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>MATLAB/Simulink, dSPACE</td><td>Dynamic error &lt; 4% &amp; &gt;15% in static models</td></tr><tr><td>4</td><td>[58,59,94]</td><td>✗</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>LabVIEW, CompactRIO</td><td>&lt;5% deviation in V-I curves</td></tr><tr><td>5</td><td>[95]</td><td>✓</td><td>✗</td><td>✗</td><td>✗</td><td>✗</td><td>MATLAB/Simulink</td><td>Voltage error ≈ 0.1 V, Current error ≈ 1–2 A</td></tr><tr><td colspan="9"><strong>AWE Studies</strong></td></tr><tr><td>1</td><td>[57]</td><td>✗</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>MATLAB/Simulink, DSP</td><td>Good tracking of power and hydrogen flow references</td></tr><tr><td>2</td><td>[61]</td><td>✓</td><td>✗</td><td>✓</td><td>✓</td><td>✗</td><td>PLECS</td><td>Close track of V-I behavior</td></tr><tr><td colspan="9"><strong>RSOEC Studies</strong></td></tr><tr><td>1</td><td>[60]</td><td>✓</td><td>✗</td><td>✗</td><td>✓</td><td>✗</td><td>MATLAB/Simulink, dSPACE</td><td>&lt;5% deviation in static V-I curves</td></tr><tr><td colspan="9"><strong>Not specified</strong></td></tr><tr><td>–</td><td>[91]</td><td>✗</td><td>✓</td><td>✗</td><td>✗</td><td>✓</td><td>–</td><td>–</td></tr></tbody></table>

Exp.*: Experimental; Int.*: Integration; ✓: Yes; ✗: No.

<table><caption>**Table 6.** Comparison of EL emulation papers based on application, advantages, and limitations.</caption><thead><tr><th>Study No.</th><th>Ref</th><th>Application</th><th>Advantages</th><th>Limitation</th></tr></thead><tbody><tr><td colspan="5"><strong>PEM Studies</strong></td></tr><tr><td>1</td><td>[20]</td><td>- Testing new DC-DC converters and controls.<br/>- Modeling dynamic behavior with supercapacitors.</td><td>- Uses low-cost, common components and a linear circuit to reproduce the physical model.<br/>- Avoids parasitic switching interference.</td><td>- Voltage errors during current decrease.<br/>- Trade-off needed to reduce transient errors.</td></tr><tr><td>2</td><td>[21]</td><td>- Emulation of PEMEL dynamic behavior.<br/>- Testing power electronics converters.<br/>- Tests EL design and performance.</td><td>- Validated with experimental data.<br/>- Incorporation of double-layer capacitance effects.<br/>- Efficient analysis of losses, efficiency, and hydrogen production.</td><td>- Limited to a small current range.<br/>- Assumes constant parameters.</td></tr><tr><td>3</td><td>[56]</td><td>- Performance evaluation in smart grids.<br/>- Develops a DC-DC boost converter-based hardware emulator that replicates PEMEL dynamic behavior.</td><td>- New EEC developed using the PSO algorithm.<br/>- Cost-effective testing.<br/>- Seamless integration with smart grid emulators.</td><td>- Parameter accuracy might not reflect EL characteristics.<br/>- Model comparison needed for further validation.<br/>- No smart grid testing to assess performance yet.</td></tr><tr><td>4</td><td>[58]</td><td>- Emulates industrial-scale EL in smart grid setups.<br/>- Analyzes EL power supply electronics.</td><td>- Higher power capability than previous systems.<br/>- Enables testing under real industrial load conditions.<br/>- Robust and cost-effective using commercial converters.</td><td>- Inability to fully exploit available PV power.<br/>- Hydrogen production is lower due to limited current changes in the stack.</td></tr></tbody></table>
<table><caption>**Table 6. Cont.**</caption><thead><tr><th>Study No.</th><th>Ref</th><th>Application</th><th>Advantages</th><th>Limitations</th></tr></thead><tbody><tr><td>5</td><td>[95]</td><td>- Development of digital real-time models focuses on error analysis from discretization methods.</td><td>- Provides systematic comparison of discretization methods.</td><td>- Only static model and no experimental validation.</td></tr><tr><td colspan="5"><strong>AWE Studies</strong></td></tr><tr><td>1</td><td>[57]</td><td>- Hydrogen production process.<br>- Integration with wind energy systems.<br>- Real-time control testing.</td><td>- Characterizes relations among physical quantities.<br>- Regulates power and hydrogen flow.</td><td>- Constant temperature assumption.<br>- Pressure control fails with fast power changes.<br>- Limited power slope reduces flexibility.</td></tr><tr><td>2</td><td>[61]</td><td>- Testing of rectifiers for electrolysis in the context of RES.<br>- Scalable platform to test control strategies and rectifier designs.</td><td>- Enables testing under various grid/rectifier conditions.<br>- High dynamic performance.</td><td>- Oscillations occur when the current drops to zero.<br>- Experimental validation only at a small scale (5 kW).</td></tr><tr><td colspan="5"><strong>RSOEC Studies</strong></td></tr><tr><td>1</td><td>[60]</td><td>- Rapid prototyping of power electronic converters for cyclic operation.</td><td>- Low-cost, accessible, simple, suitable for rapid prototyping.</td><td>- Component tolerances cause minor deviations.</td></tr><tr><td colspan="5"><strong>Not specified</strong></td></tr><tr><td>-</td><td>[91]</td><td>- Design of emulators for fuel cells and EL used for PV application.</td><td>- Show hydrogen and oxygen production/consumption.</td><td>- Simulation results may not fully reflect real-world behavior.</td></tr></tbody></table>
First, Ref. [57] developed a PHIL-based AWE emulator using a DC-DC boost converter integrated with wind energy. This system tracks power and hydrogen flow, but is limited by constant temperature assumptions and a slow pressure response. In the PEMEL emulator reported in [20,21], the system emulates a 400 W PEM stack (NMH2 1000, HELIOCENTRIS, Berlin, Germany) operating within 4.2–8 V and 0–50 A. It relies on EEC to reproduce dynamic behaviors, often validated against experimental data. These emulators are used to test DC-DC converters, but with limited grid integration capability, they achieve low errors. Ref. [56] proposed both a novel EEC, a DC-DC boost converter, and an experimentally validated PHIL configuration to emulate the behavior of PEMEL in smart grid setups with a rated power of approximately 300 W. However, the polarization curve was reproduced from an experimentally validated study found in the literature. This design achieves dynamic errors below 4%, while static models show deviations above 15%, demonstrating a trade-off between dynamic fidelity and static accuracy.

Industrial-scale EL emulators, exemplified by the work of [58,59,94], present a significantly larger-scale emulator capable of handling voltages greater than 600 V, continuous currents up to 405 A, and providing power of 250 kW. Using DC-DC boost converters and PHIL setups provides deviations below 5% in VI curves and enables robust testing under real-world high-power conditions with full grid integration and minimal hardware adjustments. Experimental data from a 4.5 kW commercial PEMEL were proportionally scaled to emulate a higher-capacity system featuring multiple stacks arranged in series and parallel within the PHIL simulator. A PHIL-based load emulator for AWE was reported in [61], which was in strong agreement with the simulations, was experimentally validated at 5 kW, and is mainly intended for rectifier development. The RSOEC emulator focuses on rapid converter prototyping in [60], with a nominal power of 4.5 kW for electrolysis and 1.5 kW for fuel cell operation, showing that static V-I curves match within <5% deviation, although some component tolerances introduce small errors. In [95], a 5 kW PEMEL-based emulator model is presented that analyzes the discretization errors in real-time simulation. This approach is based on the manufacturer's I-V curve, with the stack operating within 22.5–31.1 V and 7.5–150 A. Other approaches, such as the study reported in [91], with a power level of 1 kW, focus on simpler simulation-based emulators without experimental validation or PHIL, emphasizing theoretical replication rather than practical deployment and demonstrating power management strategies to balance generation and consumption.

Throughout various studies, EL emulators serve as cost-effective platforms for the validation of control strategies, testing of power electronics, and integration with RES. However, common challenges include the precise replication of transient responses, limitations in parameter estimation, restricted operational ranges, and incomplete representation of hydrogen production in dynamic scenarios. In summary, the combination of hardware configurations, software implementations, and experimental validations highlights the growing importance of EL emulators for both research and industrial applications, while also pointing out potential areas for future improvements and standardization.

## 4. Mathematical Model of ELs

Numerous modeling approaches are available in the literature, and each study is based on the defined objectives, typically adopting a specific modeling strategy. As in [39], system failure diagnosis techniques were investigated using a detailed stack model, including representations of the anode, cathode, membrane, and voltage model. In addition, system-level models and BoP components can be implemented, such as the water pump, reservoir, and heat exchanger model [96–101]. BoP includes all auxiliary subsystems required to ensure efficient, safe, and continuous hydrogen production. Typical BoP components include the power supply subsystem, the water management subsystem, the hydrogen pro-
duction subsystem, the thermal management subsystem, and the control subsystem [102]. Moreover, BoP is essential for sustaining optimal electrolysis conditions, which encompass temperature, pressure, and aid in the extraction and purification of gas products. Effective coordination among the different components of BoP, including pumps, heat exchangers, gas-liquid separators, condensers, and purification systems, is crucial [103], and improving it will positively affect stack operation [102]. The interactions between the BoP and the stack are significantly coupled and play an essential role in overall performance and durability.

To accurately emulate the EL, it is crucial to have a detailed representation of its electrochemical and thermal characteristics. Consequently, the developed electrical model is the most important model that serves as a vital tool for performance evaluation, specifically in the context of the integration of RES and smart grid applications [104–107]. This section presents the mathematical models used in EL simulations based on power electronics circuits.

## 4.1. EL Voltage According to the Current Density

The polarization curve, commonly known as the V-I characteristic, serves as the primary method to assess the performance of the ELs, illustrating the correlation between current density and voltage during steady-state operation. It consists of three distinct regions, as illustrated in Figure 7. First, the activation region follows directly after the reversible voltage; second, the ohmic region, which is the dominant area of operation; third, the concentration region, which becomes noticeable at high current densities.

<figure><img src="image_10.png" /><figcaption>Figure 7. Typical polarization curve.</figcaption></figure>

The EL voltage is defined as the sum of the reversible voltage and the three overpotentials. Given the insufficient generation of hydrogen from a single EL cell to satisfy demand, several cells are joined to create a stack [108–111]. Consequently, the EL stack voltage can be mathematically expressed as follows:

$$V_{stack} = N_{cell} \cdot V_{cell} \qquad (2)$$

With $N_{cell}$ indicating the number of EL cells in the stack, and $V_{cell}$ referring to the voltage assigned to a single cell, which can be mathematically formulated as follows:

$$V_{cell} = E_{rev} + V_{ohm} + V_{act} + V_{con} \qquad (3)$$

where $E_{rev}$ is the reversible voltage, $V_{act}$, $V_{ohm}$, and $V_{con}$ are the activation, ohmic, and concentration overpotential, respectively. Most authors adopt similar expressions as
in [10,15,112]. Since ELs usually do not work at high current density, this expression excludes mass transport losses.

### 4.1.1. Reversible Voltage

The reversible voltage, also known as the open-circuit voltage, signifies the minimum voltage required to begin electrolysis. It also signifies the voltage utilized by the reversible reaction, which facilitates the production of hydrogen. This voltage generally fluctuates with alterations in operating temperature and pressure. However, several studies consider it a constant in EEC models, frequently emulating it with a constant DC voltage battery. When an additional overpotential is incorporated into this reversible potential and adjusted for concentration effects using the Nernst equation, a real system is formed [113–116].

The reversible voltage that can be determined by the Nernst equation is the lowest electrical potential needed to begin the process of splitting water into hydrogen and oxygen. Numerous publications in the literature use this equation or similar ones [39,56,59]:

$$E_{rev} = E_{rev}^{0} + \frac{TR}{2F} \ln\left(\frac{p_{H_2} p_{O_2}^{1/2}}{p_{H_2O}^{sat}}\right) \quad (4)$$

$E_{rev}^{0}$ denotes the reversible voltage at standard pressure ($p_{std}$ = 1 atm), which is highly influenced by temperature, as described in Equation (5). With $T$ referring to the operating temperature of EL in Kelvin ($k$), the coefficients $R$ and $F$ represent the constant ideal gas and the Faraday constant, respectively, and their respective values are 0.0821 atm/Kmol and 96,485.33 C/mol.

The values $p_{H_2}$, $p_{O_2}$ refer to the partial pressures of hydrogen and oxygen, respectively. They can be calculated using Dalton's law, as shown in (6) and (7). Then $p_{H_2O}$ is the partial pressure of the water, and can be calculated using the August–Roche–Magnus formula, as described in (8), which is based on three assumptions: hydrogen and oxygen behave like ideal gases, only water and oxygen vapor are present at the anode, only water and hydrogen vapor are present at the cathode, and the solubility of hydrogen and oxygen in water is assumed to be negligible.

$$E_{rev}^{0} = 1.229 - 8.5 \times 10^{-4}(T - 298.15) \quad (5)$$

$$p_{H_2} = p_{cat} - p_{H_2O}^{sat} \quad (6)$$

$$p_{O_2} = p_{an} - p_{H_2O}^{sat} \quad (7)$$

$$p_{H_2O}^{sat} = 6.1078 \times 10^{-3} \exp\left[17.694 \times \frac{T - 273.15}{T - 34.85}\right] \quad (8)$$

The pressures on the cathode ($p_{ca}$) and the anode ($p_{an}$) were measured from the gas separator.

### 4.1.2. Activation Overpotential

The activation voltage corresponds to the energy needed for the protons and electrons to pass through the EL membrane during the electrochemical reaction. In the context of an electrolytic process, both the anode and cathode reactions play a role in determining the total activation polarization of the system.

The Butler–Volmer equation is used to derive the activation voltage mathematically, as is used by numerous authors [10,52,112], as shown in the equation below:

$$V_{act} = \frac{RT}{\alpha_{an}F} \arcsinh\left(\frac{i}{2i_{0,an}}\right) + \frac{RT}{\alpha_{cat}F} \arcsinh\left(\frac{i}{2i_{0,cat}}\right) \quad (9)$$
With i being the current density in the EL cell, $i_{0,an}$ and $i_{0,cat}$ are the exchange current density at the anode and cathode, respectively, and $\alpha_{an}$ and $\alpha_{cat}$ represent the anode and cathode charge transfer coefficients, respectively.

Several authors have adopted a similar expression, integrating a factor of 2 associated with the charge transfer coefficient [112,117–119], while others have chosen a simplified one [26,65,69,120,121]. These review papers [25,62,122] present a comprehensive set of equations used in the literature.

The literature presents significantly varying values for the exchange current density coefficients. Consequently, some researchers opted to select values that fit better with their models. These values tend to rise with temperature; therefore, an equation relating to the temperature is beneficial to use to express the exchange current density. Thus, this equation is applicable to both the anode and cathode:

$$i_0 = i_0^{ref} \exp \left[ \frac{-E_{act}}{R} \left( \frac{1}{T} - \frac{1}{T_{ref}} \right) \right] \quad (10)$$

where $i_0^{ref}$ is the exchange current density under reference temperature $T_{ref}$ and $E_{act}$ is the activation energy of the electrodes.

### 4.1.3. Ohmic Overpotential

The ohmic overpotential primarily arises from the resistance of various components and can be categorized into two principal factors: protonic resistance across the membrane and electrical resistance encountered through current collectors, electrode surfaces, and bipolar plates. However, manufacturing techniques significantly contribute to the reduction in this overpotential. Mathematically, $V_{ohm}$ can be expressed as follows [10]:

$$V_{ohm} = R_{Ohm} I = \frac{\delta}{A_{mem}\sigma} I \quad (11)$$

Here, $\delta$ is the thickness of the membrane in (cm), $\sigma$ is the conductivity of the membrane, which can be expressed as shown in (12), $A_{mem}$ is the area of the membrane, and $\lambda$ is the water content of the membrane between 12 and 14, as in [123].

$$\sigma = (0.005139\lambda - 0.00326) \exp \left[ 1268 \left( \frac{1}{303} - \frac{1}{T} \right) \right] \quad (12)$$

In the calculation of ohmic overpotential, manufacturing factors such as membrane geometry and material influence the voltage drop across the cell. For instance, Ruuskanen et al. [59] employed a proton-conducting membrane with a thickness ranging from 50 to 250 µm, whereas Koundi et al. [56] reported values between 324 and 347 µm, depending on the stack configuration and operating conditions. These reported values illustrate the typical range encountered in commercial PEM electrolyzer systems.

### 4.1.4. Concentration Overpotential

The concentration overpotential arises when high current densities hinder the accessibility of reactants to active sites because of the excessive presence of reacting molecules, consequently reducing the reaction rate. The concentration overpotential, commonly known as the mass transport or diffusion overpotential, is a significant factor that affects the efficiency of EL. The generated oxygen gas creates bubbles on the membrane surface, obstructing the electrolysis of the reactant (water). However, such effects are generally absent in electrolytic hydrogen production, which commonly operates at moderate current densities of 1.6 A/cm². Then, limiting the current density is vital to reach high efficiency.
It can be estimated using a modified form of the Nernst equation; in particular, ref. [56] employed an expression that involves the limiting current density that represents the maximum current that the EL can sustain, thus indicating the maximum allowed production rate of the system.

$$V_{\text{cons}} = \frac{RT}{2a_{an}F} \ln\left(\frac{i_{\text{Lim}}}{i_{\text{Lim}} - i}\right) \qquad (13)$$

Here, $i_{lim}$ represents the maximum current density where diffusion occurs and $a_{an}$ is an empirical coefficient.

## 4.2. Efficiency

Efficiency can be defined as the multiplication of Faraday and voltage efficiencies, as demonstrated in Equation (14). Because of the minimal voltage losses, the Faraday efficiency significantly influences the overall efficiency of electrolysis.

$$\eta_{EL} = \eta_{F} \times \eta_{V} \qquad (14)$$

Faraday efficiency $\eta_F$: Faraday efficiency indicates the percentage of hydrogen actually produced compared to the theoretical amount based on the electrical energy input. In practice, mainly at low current densities, some hydrogen may leak through the membrane. However, many researchers assume that it can be limited to 1% or less under standard operating conditions. The efficiency is given as a percentage and calculated using the following formula:

$$\eta_{F} = \frac{m_{H_{2}actual}}{m_{H_{2}theo}} \times 100 \qquad (15)$$

$m_{H_2theo}$ represents the theoretical mass of hydrogen, while $m_{H_2actual}$ indicates the actual mass of hydrogen.

Voltage efficiency $\eta_V$: The thermoneutral voltage represents the lowest voltage necessary to split water into hydrogen and oxygen without energy losses. The measure of voltage efficiency reflects the losses that take place during electrolysis, which leads to a requirement for a voltage that exceeds the thermoneutral voltage. It is the ratio of the thermoneutral voltage to the actual voltage used.

$$\eta_{V} = N_{cell} \frac{V_{th}}{V_{cell}} \qquad (16)$$

$V_{th}$ denotes the thermoneutral voltage, while $V_{cell}$ signifies the cell voltage.

## 4.3. Overview of EEC Representation of EL

EL modeling is essential for power electronics and control systems, particularly in the design of electric circuits. To accurately replicate its real behavior in both static and dynamic operations, its electrical characteristics need to be analyzed. This section, focusing on electric circuit design, provides a summary of various modeling approaches based on the literature. Table 7 below presents the EEC of ELs that have been proposed in the literature.

The operating voltage of an EL cell is the total of the reversible voltage and all irreversibilities that occur within the cell (including activation overvoltage, ohmic overvoltage and concentration overvoltage) [10]. However, at low current densities, the influence of concentration overvoltage is ignored [124,125]. Modeling can begin with basic ohmic losses, and then incorporate activation overvoltages, and after that, concentration losses can be added. Advanced models separate the effects of anode and cathode, with the most detailed models using Warburg impedance to represent concentration losses [126]. It is crucial to note that according to the review of literature, there has not yet been a proposed EEC model for SOEC [89], which is in fact related to its high-temperature operation, which requires
different modeling approaches. The complex interaction of thermal and electrochemical phenomena in SOECs, influenced by kinetics, thermodynamics, and material behavior, makes their modeling challenging [127].

The simplest approach to model an EL, as shown in Table 7 No. 1, involves representing it as a voltage source $E_{rev}$ corresponding to the reversible potential, in series with a resistor $R_{ohm}$ that accounts for the ohmic losses. This basic model successfully illustrates the electrical power transferred to the PEMEL. The accuracy of the model is enhanced when the dynamics of the system are taken into account. This dynamic behavior is the result of the effects of the EDL. This effect is caused by an electrical charge layer that forms between the electrode and the electrolyte, which acts as a capacitor $C_{EDL}$. This leads to a delayed response of the activation overvoltages at the anode and cathode to current fluctuations, while the ohmic overvoltage reacts without delay. As illustrated in Table 7 No. 2, the EEC is made up of a reversible voltage in series with a resistance that compensates for ohmic losses, along with an additional resistance $R_{act}$ in series for activation overpotentials that is parallel to the EDL capacitor. However, concentration losses are modeled as an additional resistance $R_{conc}$ placed in parallel with a capacitor, as shown in No. 3.

The EEC of AWE is presented in Table 7, No. 4, where the activation behavior at both electrodes is modeled using current sources connected in parallel with capacitors, representing the double-layer effect that occurs at the interface between the electrodes and the electrolyte. The internal resistances associated with the anode, cathode, membrane, and electrolyte are included to account for the different ohmic losses within the cell. An inductance is introduced to account for the delay in response, as shown in No. 5. The PEMEL and AWE model design, adapted from previous literature as in No. 6, effectively represents the dynamic behavior by integrating both fast and slow time responses associated with the EDL at the electrode-electrolyte interface. No. 7 in Table 7 presents the concentration losses represented by a Warburg impedance, which provides a more accurate depiction of the diffusion-related phenomena. No. 8 further develops the model by dividing the total losses, ohmic, activation, and concentration into separate contributions from the anode and cathode sides, with the losses represented by resistances. Finally, No. 9 shows a more advanced equivalent circuit in which the contributions of anode and cathode are modeled using Warburg impedance rather than simple resistances, offering a more detailed description of the dynamic behavior of the PEMEL.

<table><caption>**Table 7.** EEC of ELs proposed in the literature.</caption><thead><tr><th>No.</th><th>Ref.</th><th>EL Type</th><th>EEC Representation</th></tr></thead><tbody><tr><td>1</td><td>[66,126]</td><td>PEM</td><td><img src="image_1.png" alt="Electrode with an anode and cathode, connected to a voltage source (v<sub>el</sub>) and a resistor (R<sub>ohm</sub>) in series. The resistor is connected to a voltage source (v<sub>rev</sub>) through a series of capacitors (C<sub>EDL</sub>) and a load (i<sub>el</sub>)."></td></tr><tr><td>2</td><td>[66]</td><td>PEM</td><td><img src="image_2.png" alt="Electrode with an anode and cathode, connected to a voltage source (v<sub>el</sub>) and a resistor (R<sub>ohm</sub>) in series. The resistor is connected to a voltage source (v<sub>rev</sub>) through a series of capacitors (C<sub>EDL</sub>) and a load (i<sub>el</sub>)."></td></tr></tbody></table>
<table><caption>Table 7. *Cont.*</caption><thead><tr><th>No.</th><th>Ref.</th><th>EL Type</th><th>EEC Representation</th></tr></thead><tbody><tr><td>3</td><td>[19,25]</td><td>PEM</td><td><img src="" alt="EEC representation of a PEM cell with an external load and reverse bias current flow."></td></tr><tr><td>4</td><td>[128,129]</td><td>AWE</td><td><img src="" alt="EEC representation of a AWE cell with an external load and reverse bias current flow."></td></tr><tr><td>5</td><td>[126,130,131]</td><td>AWE</td><td><img src="" alt="EEC representation of a AWE cell with an external load and forward bias current flow."></td></tr><tr><td>6</td><td>[21,25,26,130,132,133]</td><td>PEM, AWE</td><td><img src="" alt="EEC representation of a PEM cell with an external load and forward bias current flow."></td></tr><tr><td>7</td><td>[25]</td><td>PEM</td><td><img src="" alt="EEC representation of a PEM cell with an external load and reverse bias current flow."></td></tr><tr><td>8</td><td>[126]</td><td>PEM</td><td><img src="" alt="EEC representation of a PEM cell with an external load and reverse bias current flow."></td></tr><tr><td>9</td><td>[126]</td><td>PEM</td><td><img src="" alt="EEC representation of a PEM cell with an external load and forward bias current flow."></td></tr></tbody></table>

## 5. Integration of EL in a Power-Grid-Based Renewable Energy System

Since the EL operates using only direct current, it is necessary to first adjust the input power, either through an AC-DC or DC-DC converter, depending on the source, as shown
in Figure 8. When an EL is powered by the electrical grid or a wind farm, it requires the use of an AC-DC converter to transform the AC into a DC that is compatible with the operating voltage of the EL [57]. This conversion is crucial for effective integration into various energy systems, particularly those that use RE [134], as it ensures voltage compatibility and operational flexibility. As in [58,59,94], the EL emulator operated as a variable impedance using a boost converter, was connected to the grid via a diode bridge rectifier and a buck converter that is able to decrease the voltage level to be suitable for the EL, with power returned to the grid via an inverter and isolation transformer. However, when an EL is powered by a photovoltaic (PV) solar farm, a DC-DC converter is employed. This converter not only manages voltage levels, but also facilitates Maximum Power Point Tracking (MPPT), which is a vital function in PV systems [91]. MPPT continuously modifies the electrical operating point of solar panels to optimize energy extraction under fluctuating environmental conditions, thus improving the overall efficiency of the solar-to-hydrogen conversion process.

However, the use of such converters introduces current and voltage ripple. Low-frequency ripple usually originates from the rectifier, while high-frequency ripple is produced by the switching action of the DC-DC stage [20]. Previous studies have shown that ripple can influence the performance and operational lifetime of the EL but has no impact on the hydrogen production rate [135–140].

The connection of the power electronic converter in such systems plays a critical role in ensuring stable operation and efficient integration with the grid [141]. Research on PEMEL has explored its operation as a grid-responsive load, evaluating transformer and converter configurations to optimize efficiency and power control [46], while comprehensive reviews have examined electrical modeling, DC/DC converter topologies, and control approaches [48]. Practical implementations include the design of stack interleaved buck converters (SIBCs) [54] and synchronous buck DC/DC converters [142], which address challenges such as current ripple, voltage overshoot, and low-voltage operation. In parallel, control strategies for AWE have been surveyed, revealing that classical PID and model-predictive controllers dominate, highlighting the need for advanced control techniques that consider nonlinear EL behavior and variable RES inputs [143]. These works provide a foundation for designing high-performance, reliable, and renewable-integrated EL systems.

ELs play an increasingly important role in modern electricity grids, capable of providing a wide range of ancillary services such as voltage regulation, grid balancing, congestion management, black-start support [144,145], and frequency control due to their fast dynamic response [146]. Both small- and large-scale installations can enhance grid stability, outperforming conventional generators in speed and flexibility. Case studies and simulations demonstrate their effectiveness in providing primary and secondary frequency reserves, improving reliability, and supporting the economic viability of hydrogen production while participating in ancillary service markets. Electrolyzer systems are scalable and adaptable, with small units providing localized frequency control at the distribution level [147], and large installations supporting broader grid stability at transmission or substation levels [43,148]. Case studies and pilot projects, particularly in Europe [144], have demonstrated that ELs can improve grid reliability, create additional revenue streams through participation in ancillary service markets, and simultaneously produce green hydrogen, enhancing both economic feasibility and environmental sustainability[149]. Their scalability and adaptability make them suitable for a variety of applications, from localized microgrids to large utility-scale installations, underscoring their increasing significance in the shift towards robust and decarbonized energy systems [43]. Therefore, power electronics are critical in a water electrolysis hydrogen production system, as they facilitate
accurate control of voltage and current, enhance power quality, and regulate energy flow.
Accurate control of this phase allows the system to adjust the power supplied, which is
critical to maintaining efficiency and maximizing hydrogen production.

<figure><img src="image_11.png" /><figcaption>Figure 8. Power-electronics converter integration for EL applications using various energy sources.</figcaption></figure>

**6. Discussions**

The diagram presented in Figure 9 illustrates the interaction framework between the EL model, the emulator, the control system, and the validation process using PHIL, and the final comparison against real experimental data. For electrical emulators, controllers and mathematical models (simulation) need to be connected to them to obtain reliable measurements. This high-fidelity model incorporates electrochemical reactions and polarization characteristics to represent the real system as closely as possible. Simulating it across a wide range of operating conditions is essential to generate data that can reflect the dynamic responses of ELs, such as voltage, current, temperature, and pressure. Using these data, a real-time emulator will be developed that retains the essential dynamic characteristics but is optimized for execution on real-time platforms such as dSPACE. However, such models are typically too complex and computationally intensive for real-time applications. The control algorithms are responsible for regulating current, voltage, and power, and send control inputs to both the model and the emulator, guaranteeing consistent testing conditions.

In this setup, the controller sends commands to the emulator as if it were operating
a real EL, and the emulator responds in real time. To ensure the required performance
of the system and its control, a test bench could be developed using PHIL to make it
possible to test and compare the electrical behavior of different EL technologies under
real-time constraints. Finally, the results are compared to real system data obtained from
experimental measurements of real physical ELs, enabling safe and cost-effective testing, validation, and optimization of control strategies under realistic and repeatable conditions without the risks or costs associated with the use of real EL hardware during the early development stages.

In general, the combined insights from hardware configurations, software implementations, and experimental validations underscore the growing importance of EL emulators for both research and industrial applications, while also highlighting areas for further improvement, standardization, and improved predictive accuracy.

<figure><img src="image_12.png" /><figcaption>**Figure 9.** Diagram of the interactions of EL emulators with their components for proper operation.</figcaption></figure>

Table 8 shows that many modeling approaches were applied both at the cell/stack level and the BoP level for EL simulations and emulators. It highlights that while there is a wide variety of models for simulating EL behavior, only a limited number of these models have been implemented in practical emulators. This emphasizes that although emulator implementations are currently more limited, the adoption of multiphysics models that encompass thermal, fluidic, and mass transfer models is increasingly essential. Such multimodel approaches allow all relevant parameters to be accurately considered, avoiding oversimplified assumptions, and enhance the accuracy, reliability, and predictive capabilities of real-time emulators used for control, testing, and power management applications.

<table><caption>**Table 8.** Model references.</caption><thead><tr><th></th><th>EL Simulations</th><th>EL Emulators</th></tr></thead><tbody><tr><td><strong>Cell/Stack Level</strong></td><td></td><td></td></tr><tr><td>Electrical model</td><td>[52,112,119,123,125,150–155]</td><td>[20,21,57–61,91,94,95]</td></tr><tr><td>Thermal model</td><td>[52,112,117,119,123,150,153,155]</td><td>–</td></tr><tr><td>Fluidics model</td><td>[118,156]</td><td>[57]</td></tr><tr><td>Mass transfer model</td><td>[123,153,157]</td><td>–</td></tr><tr><td><strong>System level</strong></td><td></td><td></td></tr><tr><td>BoP considerations</td><td>[39,118,154,158]</td><td>[57]</td></tr></tbody></table>

## 7. Conclusions

EL emulators are key tools for the development of hydrogen production systems, specifically during the early stage of research. These emulators deliver several benefits, as they help in lowering experimental costs, reducing the overall complexity of the setup, and minimizing safety threats connected to actual EL operations, all while providing a flexible and controllable testing environment.
This review has provided a comprehensive overview of ELs, their basic operation and fundamental structure, and a comparison between the different types of EL. It has compared various emulation approaches found in the literature, highlighting key mathematical models used to replicate EL behavior. These models represent the simulated part of the system and, together with the emulator, it is possible to obtain complete and reliable measurements of the entire system. In addition, it examined the design and implementation of associated electronic circuits to show the electrical components needed to build an electrical emulator (resistors, capacitors, and voltage sources). Through this analysis, the review highlights the importance of emulators as practical tools for testing, validating, and integrating EL systems into power electronic platforms, thereby supporting their further advancements in RES applications.

Although all the features of the emulator are present, the research acknowledges certain limitations. Recent studies indicate that an accurate emulator design necessitates not only robust electrical modeling but also the implementation of advanced control strategies to guarantee reliable performance. Therefore, future research should aim to extend the scope of EL emulation, moving beyond stack-level representation toward comprehensive system-level representation to achieve greater fidelity. Despite the contributions of electrical models to EL emulation, accurately accounting for temperature and pressure effects remains a challenge, since the effect of these parameters on the stack efficiency can be significant. Therefore, this highlights the need for integrated multiphysics simulation platforms to capture electrochemical, thermal, and fluidic effects. Another key direction is the emulation of BoP dynamics, where auxiliary components such as pumps, compressors, valves, and cooling systems play an important role in efficiency, safety, and providing more realistic testing environments. Model-based fault diagnosis research is currently being conducted actively within the field of fuel cell technology. However, it is still limited in the field of water electrolysis, and the maturity of the technology is not high. Finally, validation should be performed within smart grid environments to assess interoperability, resilience, and dynamic stability in RES applications. Using approaches such as real-time comparison with experimental data and PHIL configurations can enhance both credibility and practical relevance. By addressing these gaps, future research can improve emulator accuracy and yield more flexible and reliable tools to integrate EL into RES and hydrogen infrastructures while also supporting the design and validation of advanced control strategies for sustainable energy applications.

**Author Contributions:** Methodology, H.E.A., M.-B.C. and D.G.; formal analysis, H.E.A.; writing—original draft preparation, H.E.A.; writing—review and editing, H.E.A., M.-B.C. and D.G.; supervision, M.-B.C. and D.G. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by a scholarship from the University of Le Havre Normandie.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data are contained within the article.

**Acknowledgments:** This work was carried out at the GREAH Laboratory of the University of Le Havre Normandie, particularly by the Renewable Energy and Storage Systems (MERS) research team. The authors thank the University of Le Havre Normandie for their continuous support. All individuals mentioned in this section have provided their consent to be acknowledged.

**Conflicts of Interest:** The authors declare no conflict of interest.
## Abbreviations

The following abbreviations are used in this manuscript.

<table><tr><td>ELs</td><td>Electrolyzers</td><td>RES</td><td>Renewable energy source</td></tr><tr><td>GHG</td><td>Greenhouse gas</td><td>CO<sub>2</sub></td><td>Carbon dioxide</td></tr><tr><td>PEMEL</td><td>Proton exchange membrane electrolyzer</td><td>AWE</td><td>Alkaline water electrolyzers</td></tr><tr><td>AEM</td><td>Anion exchange membrane</td><td>SOEC</td><td>Solid oxide electrolysis cells</td></tr><tr><td>EEC</td><td>Equivalent electrical circuit</td><td>PHIL</td><td>Power-hardware-in-loop</td></tr><tr><td>EIS</td><td>Electrochemical impedance spectroscopy</td><td>RSOEC</td><td>Reversible solid oxide electrolysis cells</td></tr><tr><td>BoP</td><td>Balance-of-plant</td><td>PRO</td><td>Partial reinforcement optimizer</td></tr><tr><td>GE</td><td>General Electric</td><td>MEA</td><td>Membrane electrode assembly</td></tr><tr><td>DC</td><td>Direct current</td><td>SPE</td><td>Solid polymer electrolyte</td></tr><tr><td>OER</td><td>Oxygen evolution reaction</td><td>HER</td><td>Hydrogen evolution reaction</td></tr><tr><td>EDL</td><td>Electric double layer</td><td>PI</td><td>Proportional-integral</td></tr><tr><td>ST-SMC</td><td>Supertwisting sliding-mode control</td><td>cRIO</td><td>CompactRIO</td></tr><tr><td>FPGA</td><td>Field-programmable gate array</td><td>COG</td><td>Causal ordering graphs</td></tr><tr><td>MPPT</td><td>Maximum power point tracking</td><td>PV</td><td>Photovoltaic</td></tr></table>

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