Journal of C Carbon Research

Review Proton Exchange Membrane Electrolyzer Modeling for Power Electronics Control: A Short Review

Burin Yodwong 1,2 , Damien Guilbert 1,* , Matheepot Phattanasak 2 , Wattana Kaewmanee 2, Melika Hinaje 1 and Gianpaolo Vitale 3

1 Group of Research in Electrical Engineering of Nancy (GREEN), Université de Lorraine, GREEN, F-54000 Nancy, France; [email protected] (B.Y.); [email protected] (M.H.) 2 Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut’s University of Technology North Bangkok (KMUTNB), 1518, Pracharat 1 Road, Bangsue, Bangkok 10800, Thailand; [email protected] (M.P.); [email protected] (W.K.) 3 ICAR, Institute for High Performance Computing and Networking, Italian National Research Council of Italy, 90146 Palermo, Italy; [email protected] * Correspondence: [email protected]



Received: 31 March 2020; Accepted: 6 May 2020; Published: 9 May 2020


Abstract: The main purpose of this article is to provide a short review of proton exchange membrane electrolyzer (PEMEL) modeling used for power electronics control. So far, three types of PEMEL modeling have been adopted in the literature: resistive load, static load (including an equivalent resistance series-connected with a DC voltage generator representing the reversible voltage), and dynamic load (taking into consideration the dynamics both at the anode and the cathode). The modeling of the load is crucial for control purposes since it may have an impact on the performance of the system. This article aims at providing essential information and comparing the different load modeling.

Keywords: PEM electrolyzer; modeling; power electronics; control

1. Introduction Hydrogen is the most innumerable and simplest element on Earth. It can store and deliver usable energy. However, it does not exist by itself in nature and must be made from different elements that contain it. For instance, it can be combined with carbon (e.g., oil, natural gas) and with oxygen in water (H2O) [1]. Hydrogen has the highest specific energy per kilogram of all fuels (i.e., 120–140 MJ/kg), but its energy density is less suitable for storage (i.e., 2.8–10 MJ/L) depending on the physical-based storage (e.g., compressed (350–700 bar), liquid) [2]. On one hand, the global hydrogen production from natural gas, coal, and oil by using the reformation process represents approximately 96%. On the other hand, the use of the water electrolysis process to split the deionized water into hydrogen and oxygen represents around 4% of the global hydrogen production [3]. Albeit hydrogen being an intrinsically clean energy vector, it requires energy to be produced; the kind of adopted source makes the difference. Hydrogen produced by fossil fuels is known as grey hydrogen due to indirect pollution. To supply the water electrolysis process, renewable energy sources (RES) (e.g., wind turbines, photovoltaic) are the most suitable since they can limit the environmental impact. In this way, the so-called green hydrogen is obtained. Blending this kind of hydrogen into the existing natural gas pipeline network has been proposed as a means of increasing the output of renewable energy systems. Delivering blends of hydrogen and methane by pipeline also has a long history; recently, the rapid growth in installed wind power capacity and interest in the near-term market readiness of fuel cell electric vehicles has increased the stakeholder interests [4,5].

C 2020, 6, 29; doi:10.3390/c6020029 www.mdpi.com/journal/carbon C 2020, 6, 29 2 of 20

The water electrolysis process is carried out by an electrolyzer. Nowadays, there are three main types of electrolyzers: alkaline electrolyzer (AEL), proton exchange membrane electrolyzer (PEMEL), and solid oxide electrolyzer (SOEL) [3,6]. Currently, AEL and PEMEL are commercially available, and SOEL is still under research and development. AEL is the oldest technology widespread around the world, commonly used for large-scale systems. The advantage of this technology is its long lifespan and lower capital cost due to the cheaper catalysts based on Nickel material. However, AELs have several drawbacks such as low current density and operational pressures [6]. Besides, their response time in case of dynamic operations is slower compared to PEMELs. Indeed, since AEL is based on a liquid electrolyte leading up to more inertia, the ion transportation is slower compared to PEMEL [7]. This issue is particularly crucial when an electrolyzer has to be operated under fast dynamics, usually met when RES are adopted. Indeed, a RES depends on weather conditions (as solar irradiance or wind speed) that can vary abruptly during the operation. For this reason, this technology is not generally considered to be coupled with RES; conversely, it is employed for high-power stationery operated plants supplied by the grid where the harmonics impact on the grid has to be considered [8–10]. In comparison, PEMELs are generally used for small-scale hydrogen production. Anyway, PEMELs can be connected in series to form a multi-stack electrolyzer for large-scale systems. Furthermore, PEMELs offer some advantages compared to AELs, such as high current densities, high cell voltage efficiency, and fast system response when operating dynamically [3,11], since PEMEL has faster ion transportation due to the solid and thin membrane. As a result, this review article is focused on PEMEL technology since it can be connected with RES to produce hydrogen. On the other side, power converters are mandatory for the hydrogen production system supplied by RES to interface the RES with PEMEL. In these systems, DC–DC converters play a crucial role since most of RESs generate high DC voltage output and PEMELs need to be supplied with low DC voltage input [12]. However, the system needs an AC–DC converter if a wind turbine conversion system or power grid is used [10,13]. Dealing with PEMEL supplied by power converters, it is clear that two systems with their dynamics have to interact with each other. For this reason, the PEMEL model needs a deep investigation; it becomes of the utmost importance when RES is employed since the delivered power can vary with a dynamic that solicits the whole conversion chain. To simulate the hydrogen production system by using PEMEL supplied by RES, it is necessary to know the PEMEL electrical characteristics. The model must replicate the real behavior of PEMEL (i.e., static, dynamic operations) to investigate its interaction with power converters. In the literature, three types of models have been reported (e.g., resistive load, static load, and dynamic load) [14–25]. The last modeling comes from the need to investigate the dynamic of the conversion chain with RES. The main objective of this article is to present each model used for power electronics control and how these models have been developed. Besides, the validity of these models is discussed. Finally, some guidelines are provided to determine the parameters of the proposed models (i.e., static and dynamic). This article is divided into three sections. After the introduction presenting the current state-of-the-art, and the reasons to carry out such review work, Section2 is focused on the proton exchange membrane electrolyzer system for hydrogen production including the DC–DC converter. Finally, a review of proton exchange membrane electrolyzer modeling for control propose and a comparison of the static and dynamic models from the control point of view are provided in Section3.

2. Proton Exchange Membrane Electrolyzer System

2.1. Proton Exchange Membrane Stack The first proton exchange membrane electrolyzer has been developed by the General Electric (GE) Company in the 1960s. This technology aims at overcoming the weaknesses of AEL technology [3]. C 2020, 6, x FOR PEER REVIEW 3 of 21

The first proton exchange membrane electrolyzer has been developed by the General Electric (GE) Company in the 1960s. This technology aims at overcoming the weaknesses of AEL technology [3]. The PEMEL converts the electrical energy directly into chemical energy. The principle of PEMEL is shown in Figure 1. The water is oxidized electrochemically within the anode catalyst layer combine with electricity at the anode side (Wele, including Gibbs energy and energy losses); then water is broken down into oxygen gas, protons, and electrons, and this reaction called oxidation reaction is given by (1). The protons transport across the proton conductive membrane to the cathode side while the electrons move through the outer circuit and also reach the cathode side. The protons and the Celectrons2020, 6, 29 electrochemically react within the cathode catalyst layer and produce hydrogen gases.3 This of 20 reaction, called reduction reaction, and the overall reaction, called redox reaction, are given by (2) and (3), respectively [3]. It has to be remarked that the redox reaction (3) requires energy to be The PEMEL converts the electrical energy directly into chemical energy. The principle of PEMEL performed, whereas the reduction (2) is almost spontaneous; it justifies the need to supply the PEMEL is shown in Figure1. The water is oxidized electrochemically within the anode catalyst layer combine and the different dynamics expected by the two reactions. with electricity at the anode side (W , including Gibbs energy and energy losses); then water is broken Oxidation reaction ele down into oxygen gas, protons, and electrons, and this reaction called oxidation reaction is given + - by (1). The protons transport across2H the2O proton+ Wele conductive→ 4H + 4e membrane + O2 to the cathode side while(1) the electronsReduction move throughreaction the outer circuit and also reach the cathode side. The protons and the electrons electrochemically react within the cathode catalyst layer and produce hydrogen gases. This reaction, + - called reduction reaction, and the overall4H reaction, + 4e → called 2H2 redox reaction, are given by (2) and(2) (3), respectivelyRedox reaction [3]. It has to be remarked that the redox reaction (3) requires energy to be performed, whereas the reduction (2) is almost spontaneous; it justifies the need to supply the PEMEL and the different dynamics expected by the two reactions.2H2O → 2H2 + O2 (3)

Figure 1. PrinciplePrinciple of of proton proton exchange membrane (PEM) electrolyzer.

OxidationIn PEMEL, reaction the key components are bipolar plates with flow channels, current collectors, and + membrane electrode assembly (MEA)2H2O [26].+ W Theseele co4Hmponents+ 4e− + areO2 shown in Figure 2 giving a cross-(1) → sectionReduction of mass reactiontransport in a PEMEL. The bipolar plates are mandatory and have crucial functions in PEMEL operation, such as conducting electrons,+ connecting single cells to realize a stack, arranging 4H + 4e− 2H2 (2) a flow path for pure water-sharing over the current→ collectors, isolating hydrogen and oxygen, supportingRedox reactionthe membrane and electrodes, and bringing thermal conduction to handle the PEMEL temperature [26]. To meet these functions,2H bipolar2O plates2H2 + mustO2 feature specific properties such as high(3) → thermal and electrical conduction, low gas permeability, and high mechanical and corrosion In PEMEL, the key components are bipolar plates with flow channels, current collectors, resistance. Generally, bipolar plates based on Titanium (Ti) material are employed since Ti has a high and membrane electrode assembly (MEA) [26]. These components are shown in Figure2 giving mechanical and corrosion resistance. a cross-section of mass transport in a PEMEL. The bipolar plates are mandatory and have crucial functions in PEMEL operation, such as conducting electrons, connecting single cells to realize a stack, arranging a flow path for pure water-sharing over the current collectors, isolating hydrogen and oxygen, supporting the membrane and electrodes, and bringing thermal conduction to handle the PEMEL temperature [26]. To meet these functions, bipolar plates must feature specific properties such as high thermal and electrical conduction, low gas permeability, and high mechanical and corrosion resistance. Generally, bipolar plates based on Titanium (Ti) material are employed since Ti has a high mechanical and corrosion resistance. C 2020, 6, x FOR PEER REVIEW 5 of 21

meet the requirements of PEMELs, particularly in terms of low conversion gain. The control of the converters differs depending on the source. For grid-connected applications, the available power significantly overcomes the power required by the electrolyzer; hence, it can be regulated based on the quantity of hydrogen to be produced. Differently, a RES requires that all the available power must be converted into hydrogen. For this reason, the converter needs a maximum power point tracking. Furthermore, to increase the input voltage of PEMELs, multi-stack PEMELs can be used, consisting of connecting several PEMELs in series to meet the requirements (i.e., voltage ratio, hydrogen flow rate, energy efficiency). Finally, power converters slightly decrease the overall efficiency. Since the Cefficiency2020, 6, 29 of power converters is generally higher than 92%–95%, the expected lowering of the whole4 of 20 conversion chain (including the PEMEL), is around 2%–6%.

Figure 2. Cross-section of mass transport in a PEM electrolyzer [26]. Figure 2. Cross-section of mass transport in a PEM electrolyzer [26]. In comparison, current collectors are used to move the electrons from the catalyst layer to bipolar plates and to eliminate the gases (i.e., hydrogen, oxygen) from the catalyst layer [26]. It is important to point out that current collectors must operate in the same environment conditions (i.e., acid, high overvoltage) as bipolar plates. Therefore, porosity and electrical conductivity are important requirements in choosing the materials of current collectors. On one hand, in PEM fuel cells, carbon (C) paper or cloth is employed as current collectors (commonly known as gas diffusion layer (GDL)) at both sides of the electrodes. On the other hand, in PEMELs, carbon paper or cloth is not suitable for either the catalyst layer or current collector of the anode side since the anode potential is higher than the cathode potential [26]. This high potential leads to the corrosion of the carbon material during the water electrolysis process. As a result, at the anode side, a material based on Ti is preferred since it features low corrosion even under high anode potential and acid environment. Regarding the cathode side, its potential is smaller than the anode side and close to that for PEM fuel cell operation. Therefore, a material based on carbon is perfectly fit not only for the catalyst layer but also for the current collector. Finally, MEA (i.e., PEM in Figure2) is essential to move the protons from the anode to the cathode side and drive the electrons to migrate around a flow path to the cathode. Moreover, the MEA allows the electrical insulation between the anode and cathode while acting as a reactant barrier against gas crossover [27]. Currently,Figure fluoropolymer 3. PEM electrolyzer (PFSA) system Nafion including membranes power electronics. from DuPont Company are the most widespread in PEMELs, since they feature high thermal stability and proton conductivity (i.e., 1 0.12.2. S AC–DC cm− at and 100 DC–DC◦C) and Converters thin membrane (25–254 µm). The choice of the membrane thickness results in a compromise between the expected operating pressures across the membrane, mechanical resistance, Power converters can be classified based on the type of RES or bus systems configuration (i.e., low gas crossover, and ohmic resistance [27]. Different types of Nafion membranes are available in DC or AC). From the literature, four types of hydrogen production systems including PEMELs the market, such as NafionTM 211, NafionTM 212, NafionTM 115, NafionTM 117, and NafionTM 1110, supplied by solar energy, wind energy, DC microgrid system, and the power grid have been reported. depending on their thickness [28]. Based on previous works reported in the literature [27,29], it has In any case, step-down DC–DC converters are needed to supply PEMELs with a low DC voltage (i.e., been emphasized that very thin membranes allow reducing ohmic losses and operating the membrane less than 10 V) [25,34]. at high pressure due to its high mechanical resistance. However, the higher the operating pressure, the higher the equivalent current of hydrogen crossover [30]. As a result, faradaic losses due to the hydrogen and oxygen crossover increase. Faradaic losses related to Faraday’s efficiency are particularly noticeable at low current densities. Since the energy efficiency of the PEMEL is linked to the Faraday’s efficiency, it leads to a decrease of energy efficiency. This important issue has been discussed in [31]. Furthermore, equivalent currents of hydrogen and oxygen crossover are inversely proportional to the membrane thickness [30]. The higher the membrane thickness, the smaller the currents of hydrogen and oxygen crossover. High currents of hydrogen and oxygen crossover may damage the membrane and cause failures of the PEMEL stack [32]. For this reason, membrane thickness and operating pressures are key issues to enhance the performance of the PEMEL [31]. Currently, PFSA Nafion membranes C 20202020,, 66,, 29x FOR PEER REVIEW 5 of 2021

meet the requirements of PEMELs, particularly in terms of low conversion gain. The control of the suconvertersffer from havingdiffers adepending high cost, andon the their source. performances For grid-connected are strongly dependentapplications, on thethe relativeavailable humidity power (RH)significantly and temperature overcomes (T), the which power impede required their by development the electrolyzer; at large hence, scale it and can market be regulated penetration based [26 on]. Indeed,the quantity these of two hydrogen operating to be parameters produced. play Differentl a key roley, a RES in drying requires or floodingthat all the the available membrane power linked must to itsbe waterconverted content. into Thehydrogen. membrane For mustthis reason, be perfectly the converter hydrated needs to enhance a maximum the move power of protons point tracking. from the anodeFurthermore, and cathode to increase and to the reduce input the voltage gas crossover. of PEMELs, To cope multi-stack with this importantPEMELs can issue be from used, the consisting cost and performanceof connecting point several of view,PEMELs membranes in series basedto meet on the hydrocarbon requirements material (i.e., voltage have much ratio, to hydrogen offer. Indeed, flow thisrate, type energy of membrane efficiency). is Finally, a promising power solution converters to replace slightly Nafion decrease membranes, the overall since efficiency. it presents Since several the 1 advantagesefficiency of such power as converters low-cost, fit is proton generally conductivity higher than (> 8092%–95%, mS cm− the), low expected gas permeation, lowering of and the ablewhole to operate at low RH (<25%) and large temperature range (from 40 C to 120 C) [33]. conversion chain (including the PEMEL), is around 2%–6%. − ◦ ◦ In PEMEL system, the stack is not only the key component. Indeed, PEMEL system includes also several ancillaries such as power conditioning system (i.e., AC–DC and/or DC–DC converter), pure water circulation system (i.e., tanks, circulation pump, and valves), hydrogen processing system (i.e., storage tanks, hydrogen separator, and valves), and cooling system (i.e., cooling pumps, valves) [26]. In Figure3, a PEMEL system is provided showing only the stack and power electronics part. Given that PEMELs operate at low DC voltages, it is not feasible to directly couple them with the power grid or RES in the hydrogen production system. For this reason, power converters are mandatory to meet the requirements of PEMELs, particularly in terms of low conversion gain. The control of the converters differs depending on the source. For grid-connected applications, the available power significantly overcomes the power required by the electrolyzer; hence, it can be regulated based on the quantity of hydrogen to be produced. Differently, a RES requires that all the available power must be converted into hydrogen. For this reason, the converter needs a maximum power point tracking. Furthermore, to increase the input voltage of PEMELs, multi-stack PEMELs can be used, consisting of connecting several PEMELs in series to meet the requirements (i.e., voltage ratio, hydrogen flow rate, energy efficiency). Finally, power converters slightly decrease the overall efficiency. Since the efficiency of power converters is generally higher than 92–95%, the expected lowering of the whole conversion chain (including theFigure PEMEL), 2. Cross-section is around 2–6%. of mass transport in a PEM electrolyzer [26].

Figure 3. Figure 3. PEM electrolyzer system including power electronics. 2.2. AC–DC and DC–DC Converters 2.2. AC–DC and DC–DC Converters Power converters can be classified based on the type of RES or bus systems configuration (i.e., DC orPower AC). Fromconverters the literature, can be classified four types based of hydrogen on the productiontype of RES systems or bus includingsystems configuration PEMELs supplied (i.e., byDC solar or AC). energy, From wind the energy, literature, DC microgridfour types system, of hydrogen and the production power grid systems have been including reported. PEMELs In any case,supplied step-down by solar DC–DC energy, converters wind energy, are neededDC microgrid to supply system, PEMELs and with the power a low DCgrid voltage have been (i.e., reported. less than 10In V)any [25 case,,34]. step-down DC–DC converters are needed to supply PEMELs with a low DC voltage (i.e., less than 10 V) [25,34]. C 2020, 6, x 29 FOR PEER REVIEW 6 of 21 20 C 2020, 6, x FOR PEER REVIEW 6 of 21

First, the hydrogen production systems supplied by solar energy consist of using photovoltaic First,First, the the hydrogen hydrogen production production systems systems supplied supplied by by solar solar energy energy consist consist of of using using photovoltaic photovoltaic (PV) panels, step-down DC–DC converter, and PEMEL. The illustration diagram of this system is (PV)(PV) panels, panels, step-down step-down DC–DC DC–DC converter, converter, and and PEMEL. PEMEL. The The illustration illustration diagram diagram of of this this system system is is presented in Figure 4. The photovoltaic enables harvesting energy from the sun to generate DC presentedpresented in FigureFigure4 .4. The The photovoltaic photovoltaic enables enables harvesting harvesting energy energy from from the sun the to sun generate to generate DC voltage DC voltage and then coupling with the buck (step-down) converter to supply DC current to the PEMEL voltageand then and coupling then coupling with the with buck the (step-down) buck (step-do converterwn) converter to supply to DC supply current DC to current the PEMEL to the to PEMEL produce to produce hydrogen gas. It should be remarked that operating with PV panels, the available power tohydrogen produce gas.hydrogen It should gas. be It remarkedshould be thatremarked operating that with operating PV panels, with thePV panels, available the power available depends power on depends on solar irradiance. To maintain a high efficiency of the conversion chain, all this power has dependssolar irradiance. on solar Toirradiance. maintain To a highmaintain efficiency a high of efficiency the conversion of the chain,conversion all this chain, power all has this to power be used has to to be used to supply the PEMEL. It is guaranteed by the maximum power point (MPPT) algorithm tosupply be used the to PEMEL. supply It the is guaranteed PEMEL. It byis guarant the maximumeed by power the maximum point (MPPT) power algorithm point (MPPT) that both algorithm controls that both controls the step-down converter and supplies the suitable current to the PEMEL. thatthe step-downboth controls converter the step-down and supplies converter the suitableand supplies current the to suitable the PEMEL. current to the PEMEL.

Figure 4. Hydrogen production systems supplied by solar energy. FigureFigure 4. 4. HydrogenHydrogen production production systems systems supplied supplied by by solar solar energy. energy. Second, wind energy systems are composed of the wind turbine, step-down DC–DC converter, Second,Second, wind wind energy energy systems systems are are composed composed of of the the wind wind turbine, turbine, step-down step-down DC–DC DC–DC converter, converter, and PEMEL. However, wind turbines allow exploiting the kinetic energy of the wind to be andand PEMEL. However,However, wind wind turbines turbines allow allow exploiting exploiting the kinetic the kinetic energy ofenergy the wind of tothe be wind transformed to be transformed into AC voltage at the output of a three-phase generator. The system needs a three-phase transformedinto AC voltage into AC at the voltage output at the of aoutput three-phase of a three-phase generator. generator. The system The needs system a three-phaseneeds a three-phase rectifier rectifier AC–DC converter interfacing the wind turbine, and the buck converter. The schematic rectifierAC–DC AC–DC converter converter interfacing interfacing the wind turbine,the wind and tu therbine, buck and converter. the buck The converter. schematic The diagram schematic of this diagram of this system is shown in Figure 5. The wind generation system shows a fast dynamic due diagramsystem isof shown this system in Figure is shown5. The in wind Figure generation 5. The wind system generation shows system a fast dynamic shows a duefast todynamic gusts. due It is to gusts. It is partially mitigated by the DC bus capacitor C1, but it must operate with the power topartially gusts. It mitigated is partially by mitigated the DC bus by capacitor the DC bus C1, butcapacitor it must C1 operate, but it withmust theoperate power with transfer the power to the transfer to the PEMEL. On one hand, if the available power rises abruptly and it is not transferred to transferPEMEL. to On the one PEMEL. hand, On ifthe one available hand, if the power availabl risese abruptlypower rises and abruptly it is not and transferred it is not totransferred the PEMEL, to the PEMEL, the voltage of C1 can overcome its rated voltage with risk of damaging. On the other thethe PEMEL, voltage ofthe C 1voltagecan overcome of C1 can its ratedovercome voltage its withrated risk voltage of damaging. with risk On of thedamaging. other hand, On the powerother hand, the power flowing through the PEMEL has to be varied without voltage overshoots that could hand,flowing the throughpower flowing the PEMEL through has the to PEMEL be varied has without to be varied voltage without overshoots voltage that overshoots could damage that could the damage the same PEMEL. damagesame PEMEL. the same PEMEL.

Figure 5. Hydrogen production systems supplied by wind energy with uncontrolled rectifier as FigureFigure 5. 5. HydrogenHydrogen production production systems systems supplied supplied by by wind wind energy energy with with uncontrolled uncontrolled rectifier rectifier as as passive front-end. passivepassive front-end. front-end. The architecture shown in Figure 55 isis widelywidely usedused forfor permanent magnet synchronous generatorgenerator The architecture shown in Figure 5 is widely used for permanent magnet synchronous generator (PMSG)-based wind wind turbines. The The simple simple diode diode rectifier rectifier on on the the generator side gives a cost-ecost-efficientfficient (PMSG)-based wind turbines. The simple diode rectifier on the generator side gives a cost-efficient solution since active active power power flows flows unidirectionally, unidirectionally, and no reactive reactive power power is is required. required. Unfortunately, Unfortunately, solution since active power flows unidirectionally, and no reactive power is required. Unfortunately, the uncontrolled uncontrolled rectifier rectifier might might cause cause low-frequency low-frequency torque torque pulsation pulsation exciting exciting shaft shaft resonance. resonance. The the uncontrolled rectifier might cause low-frequency torque pulsation exciting shaft resonance. The availabilityThe availability of cheap of cheap controlled controlled power power devices devices and and microprocessor microprocessor platforms platforms allows allows conceiving conceiving more more availability of cheap controlled power devices and microprocessor platforms allows conceiving more complicated schemesschemes withwith better better performance. performance. The The uncontrolled uncontrolled rectifier rectifier can becan substituted be substituted by a PWMby a complicated schemes with better performance. The uncontrolled rectifier can be substituted by a PWMactive rectifier,active rectifier, as in Figure as in6 ;Figure it enables 6; it full enables power full controllability power controllability (four-quadrant (four-quadrant operation). Theoperation). simple PWM active rectifier, as in Figure 6; it enables full power controllability (four-quadrant operation). The simple structure (available as an integrated power module) is robust and reliable. Besides many The simple structure (available as an integrated power module) is robust and reliable. Besides many C 2020, 6, 29 7 of 20

C 2020, 6, x FOR PEER REVIEW 7 of 21 structure (available as an integrated power module) is robust and reliable. Besides many turbines where turbines where the electrical generator is a squirrel cage induction generator (SCIG), a double-fed the electrical generator is a squirrel cage induction generator (SCIG), a double-fed induction generator induction generator (DFIG) is adopted in this scheme in the back-to-back configuration for grid (DFIG)connection is adopted [35–37]. in this scheme in the back-to-back configuration for grid connection [35–37].

FigureFigure 6. 6. HydrogenHydrogen production production systems systems supplied supplied by wi bynd wind energy energy with front-end with front-end based on based active on activerectifier. rectifier.

InIn low-power low-power wind wind turbines turbines with with a PMSG, a PMSG, the three-phase the three-phase high-frequency high-frequency semicontrolled semicontrolled rectifier, shownrectifier, in Figure shown7, in is attractive,Figure 7, is since attractive, it is simple since and it is robust. simple Moreover,and robust. all Moreover, active switches all active are connected switches toare a common connected point, to a andcommon a short-circuit point, and through a short-circuit a leg is through not possible. a leg is A not higher possible. distortion A higher of the distortion generator currentsof the generator results [38 currents]. results [38].

Figure 7. Hydrogen production systems supplied by wind energy with front-end based on FigureFigure 7. 7. HydrogenHydrogen production systems supplied supplied by by wind wind energy energy with with front-end front-end based based on on semicontrolled rectifier. semicontrolledsemicontrolled rectifier. rectifier. A three-level neutral-point diode clamped front-end topology (3L-NPC) gives two DC outputs AA three-level three-level neutral-point neutral-point diodediode clampedclamped front-endfront-end topology (3L-NPC) (3L-NPC) gives gives two two DC DC outputs outputs that can be connected to two electrolyzers; each DC level has one half of the voltage obtained by the thatthat can can be be connected connected to to two two electrolyzers; electrolyzers; eacheach DCDC level has one half half of of the the voltage voltage obtained obtained by by the the two levels of the active rectifier. It is sketched in Figure 8. The 3L-NPC topology is one of the most twotwo levels levels of of the the active active rectifier. rectifier. ItIt isis sketchedsketched inin FigureFigure8 8.. TheThe 3L-NPC3L-NPC topology is is one one of of the the most most commercialized multilevel converters on the market, and it is usually proposed as a back-to-back commercializedcommercialized multilevel multilevel convertersconverters onon thethe market, and it it is usually proposed proposed as as a a back-to-back back-to-back topology in wind turbines. A potential drawback is the midpoint voltage fluctuation of the DC bus; topologytopology in in wind wind turbines. turbines. AA potentialpotential drawbackdrawback is the the midpoint midpoint voltage voltage fluctuation fluctuation of of the the DC DC bus; bus; however, this problem is minimized by the controlling of the redundant switching status [35,36,39]. however,however, this this problem problem is is minimized minimized by by the the controlling controlling ofof thethe redundantredundant switching status [35,36,39]. [35,36,39]. Third, like hydrogen production systems supplied by solar energy, the DC microgrid system is Third,Third, like like hydrogen hydrogen production production systemssystems supplied by solar solar energy, energy, the the DC DC microgrid microgrid system system is is shown in Figure 9 (the input filter is not drawn for the sake of clarity). The input of the buck converter shownshown in in Figure Figure9 (the9 (the input input filter filter is is not not drawn drawn for for the the sake sake ofof clarity).clarity). The input input of of the the buck buck converter converter in this system interfaces with the DC bus in DC microgrid and the output coupling with PEMEL [13]. in this system interfaces with the DC bus in DC microgrid and the output coupling with PEMEL [13]. In this case, the dynamic behavior depends on the need to use the hydrogen as storage depending on In this case, the dynamic behavior depends on the need to use the hydrogen as storage depending on the constraints of the microgrids. the constraints of the microgrids. Finally, the hydrogen production system connected with the utility grid is present in Figure 10. Finally, the hydrogen production system connected with the utility grid is present in Figure 10. This system consists of a delta-star transformer and an AC–DC rectifier interfacing the grid system This system consists of a delta-star transformer and an AC–DC rectifier interfacing the grid system and and PEMEL. Since the current of the electrolyzer must be controlled, thyristors-based rectifiers are PEMEL. Since the current of the electrolyzer must be controlled, thyristors-based rectifiers are generally generally preferred for this purpose [8–10]. In Figure 10, a 6-pulse thyristor bridge rectifier is shown. preferred for this purpose [8–10]. In Figure 10, a 6-pulse thyristor bridge rectifier is shown. Currently, Currently, thyristor-based rectifiers are particularly employed for industrial and power-to-gas thyristor-basedapplications where rectifiers a high are voltage particularly and current employed are required for industrial to supply and power-to-gas electrolyzers. applicationsIn [8–10], 6-pulse where aand high 12-pulse voltage thyristors-based and current are rectifiers required connected to supply to electrolyzers. alkaline electrolyzers In [8–10 have], 6-pulse been investigated and 12-pulse C 2020, 6, 29 8 of 20

C 2020, 6, x FOR PEER REVIEW 8 of 21 C 2020, 6, x FOR PEER REVIEW 8 of 21 thyristors-basedC 2020, 6, x FOR PEER rectifiers REVIEW connected to alkaline electrolyzers have been investigated from the point8 of 21 of from the point of view of power quality, gas quality, and output current ripple. It has been viewfrom of the power point quality, of view gas of quality, power and quality, output gas current quality, ripple. and It output has been current demonstrated ripple. It that has the been use demonstratedfrom the point that of the view use ofof apower 12-pulse quality, thyristor-based gas quality, rectifier and enablesoutput currentenhancing ripple. the powerIt has qualitybeen ofdemonstrated a 12-pulse thyristor-based that the use of rectifiera 12-pulse enables thyristor-based enhancing rectifier the power enables quality enhancing and the the gas power quality quality while anddemonstrated the gas quality that whilethe use reducing of a 12-pulse the output thyristor-based current ripple. rectifier enables enhancing the power quality reducingand the gas the outputquality currentwhile reducing ripple. the output current ripple. and the gas quality while reducing the output current ripple.

Figure 8. Hydrogen production systems supplied by wind energy with front-end based on multilevel FigureFigureFigure 8.8. Hydrogen HydrogenHydrogen production production production systems systems systems supplied supplied supplied by by wind wind by energy energy wind with energywith front-end front-end with based front-end based on on multilevel multilevel based on rectifier.multilevelrectifier.rectifier. rectifier.

FigureFigure 9. 9. Hydrogen Hydrogen production production systems systems with with DC DC micro micro grid grid system. system. FigureFigure 9. 9. HydrogenHydrogen production production systems systems with with DC DC micro micro grid grid system. system.

FigureFigure 10. 10. Hydrogen Hydrogen production production systems systems connected connected to to the the power power grid. grid. FigureFigure 10. 10. HydrogenHydrogen production production systems systems connected connected to to the the power power grid. grid.

TheThe fourfour typestypes ofof hydrogen hydrogen production production need need a a suitable suitable controller controller to to control control the the PEMEL PEMEL current current TheThe four four types types of of hydrogen hydrogen production production need need a a suitable suitable controller controller to to control control the the PEMEL PEMEL current current oror voltagevoltage toto managemanage its its hydrogen hydrogen flow flow rate rate and/or and/or its its energy energy efficiency. efficiency. Because Because of of the the intermittent intermittent oror voltage voltage to to manage manage its its hydrogen hydrogen flow flow rate rate and/or and/or its its energy energy efficiency. efficiency. Because Because of of the the intermittent intermittent behaviorbehavior ofof solarsolar andand windwind energyenergy systems, systems, the the input input voltage voltage of of the the DC-DC DC-DC converter converter may may change change behaviorbehavior of of solar solar and and wind wind energy energy systems, systems, the the input input voltage voltage of of the the DC-DC DC-DC converter converter may may change change quicklyquickly [23].[23]. AsAs aa result,result, withoutwithout aa suitable suitable and and dedicated dedicated controller, controller, output output hydrogen hydrogen production production quicklyquickly [23]. [23]. As a result,result, withoutwithout a a suitable suitable and and dedicated dedicated controller, controller, output output hydrogen hydrogen production production and andand energyenergy efficiencyefficiency as as well well can can be be impacted. impacted. andenergy energy efficiency efficiency as well as well can becan impacted. be impacted. DifferentDifferent controlcontrol techniquestechniques cancan bebe appliedapplied to to control control the the DC–DC DC–DC converter converter for for providing providing a a Different control techniques can be applied to control the DC–DC converter for providing a constantconstant currentcurrent oror voltagevoltage toto PEMELPEMEL suchsuch asas thethe maximummaximum powerpower point point tracking tracking (MPPT) (MPPT) to to constant current or voltage to PEMEL such as the maximum power point tracking (MPPT) to C 2020, 6, 29 9 of 20

Different control techniques can be applied to control the DC–DC converter for providing a constantC 2020, 6 current, x FOR PEER or voltage REVIEW to PEMEL such as the maximum power point tracking (MPPT) to overcome9 of 21 the intermittent issues in these systems. Besides, the modeling of the PEMEL is important for control overcome the intermittent issues in these systems. Besides, the modeling of the PEMEL is important purposes,for control since purposes, it might since have it anmight impact have on an the impact performance on the performance of the system of the [25 system]. [25]. 3. Proton Exchange Membrane Electrolyzer Modeling for Control Purpose 3. Proton Exchange Membrane Electrolyzer Modeling for Control Purpose TheThe proton proton exchange exchange membrane membrane electrolyzer electrolyzer modeling modeling is mandatory is mandatory for control for control purposes. purposes. Indeed, toIndeed, develop to e ffidevelopcient controllers, efficient controllers, the PEMEL the modelPEMEL has model to be has coupled to be coupled with the with model the model of the of DC–DC the converter.DC–DC converter. The objective The isobjective to get theis to overall get the model overall (i.e., model DC–DC (i.e., converterDC–DC converter and the and load) the under load) the formunder of athe transfer form of function a transfer or function a state–space or a state–space model. The model. developed The developed controllers controllers can be used can be to used supply theto PEMEL supply withthe PEMEL a constant with input a constant energy input (to optimize energy (to hydrogen optimize flow hydrogen rate and flow energy rate and effi ciency)energy or variableefficiency) input or energy variable to input manage energy the hydrogen to manage flow the ratehydrogen based flow on requirements rate based on (e.g., requirements state-of-charge (e.g., of hydrogenstate-of-charge tanks) [of25 hydrogen]. Based on tanks) the current[25]. Based literature, on the current three types literature, of modeling three types have of been modeling reported have and arebeen investigated reported and in the are following investigated section. in the following section.

3.1.3.1. Resistive Resistive Model Model FirstFirst of of all, all, the the PEMEL PEMEL can can bebe modeledmodeled as a resistor as as shown shown in in Figure Figure 11. 11 The. The resistor resistor is the is the simplestsimplest model model to to represent represent the the electric electric powerpower transferredtransferred to to the the PEMEL. PEMEL.

FigureFigure 11.11. EquivalentEquivalent electric model model by by using using a aresistor. resistor.

ThisThis simple simple model model has has been been used used to to study study the the power power quality quality ofof anan alkalinealkaline electrolyzerelectrolyzer [[10]10] and to developto develop controllers controllers applied applied to atosynchronous a synchronous [14 [14]] and and classicclassic buck converter converter [17], [17 ],full-bridge full-bridge multi multi resonantresonant converter converter [18 [18],], soft-switching soft-switching full-bridgefull-bridge converter converter [15,16], [15,16], and and three-level three-level interleaved interleaved buck buck converterconverter [23 [23].]. However, However, only only inin [[10,23],10,23], detailsdetails ar aree provided provided to to determine determine the the value value of ofthe the resistive resistive load. In [10], the authors have expressed the equivalent resistance of the electrolyzer based on the load. In [10], the authors have expressed the equivalent resistance of the electrolyzer based on the static voltage-current characteristic: static voltage-current characteristic: vel R1 == (4) (4) iel TheThe static static voltage-currentvoltage-current curve curve of of an an alkaline alkaline electrolyzer electrolyzer of 3 MW of 3 is MW shown is in shown Figure in 12. Figure Based 12. Basedon Equation on Equation (4) and (4) andFigure Figure 12, the 12 ,equivalent the equivalent resistive resistive load loadaccording according to the to current the current is provided is provided in inFigure Figure 13. 13 .It Ithas has to tobe benoted noted that that the theequivalent equivalent resistive resistive load decreases load decreases according according to the current to the since current sinceelectrolyzers electrolyzers are arehigh high current/low current/ lowvoltage voltage loads loads as shown as shown in Figure in Figure 9. 9To. To emphasize emphasize better better the the resistanceresistance decrease decrease for for a a current current range range includedincluded between 2000 2000 and and 20,000 20,000 A, A, an an additional additional curve curve has has beenbeen inserted inserted in in Figure Figure 13 13.. By comparison, in [23], the authors have expressed the value of the resistive load based on a dynamic electrical circuit model (presented in this section). The value of the resistance is determined as follows: v Rtot R = el (5) 1 v V el − int where -Rtot: sum of the resistances in the equivalent model, taking into account activation losses both at the anode and cathode and ohmic losses. The total resistance value is equal to 0.441 Ω. C 2020, 6, 29 10 of 20

-Vint: reversible voltage of the PEM EL, which is equal to 4.38 V. -Vel: PEMEL voltage (V), depending on the PEMEL current if the latter is controlled instead of the voltage. Based on Equation (5), the resistance value has been computed according to the PEMEL voltage range included between 5 and 8 V (rated stack power of 400 W), as shown in Figure 14. The higher the PEMELCC 2020 2020, voltage,,6 6, ,x x FOR FOR PEER PEER the REVIEW lowerREVIEW the resistive load. These results are similar to those introduced in10 [10 of of]. 21 21

FigureFigureFigure 12. 12. 12.Static Static Static voltage-current voltage-current voltage-current curvecurve curve of of anan alkaline alkaline electrolyzer electrolyzer (3 (3 (3 MW) MW) MW) [40]. [40]. [40 ].

C 2020, 6, x FOR PEER REVIEWFigureFigureFigure 13. 13. 13.Equivalent Equivalent Equivalent resistiveresistive resistive load load accordingaccording to to the the current current [40]. [40]. [40]. 11 of 21

ByBy comparison,comparison, inin [23],[23], thethe authorsauthors havehave expreexpressedssed thethe valuevalue ofof thethe resistiveresistive loadload basedbased onon aa dynamicdynamic electrical electrical circuit circuit model model (presented (presented in in this this section). section). The The value value of of the the resistance resistance is is determined determined asas follows: follows:

== (5)(5) −− wherewhere

--: : sumsum ofof thethe resistancesresistances inin thethe equivalentequivalent model,model, takingtaking intointo accountaccount activationactivation losseslosses bothboth atat the the anode anode and and cathode cathode and and ohmic ohmic losses. losses. Th Thee total total resistance resistance value value is is equal equal to to 0.441 0.441 Ω Ω. .

--: :reversible reversible voltage voltage of of the the PEM PEM EL, EL, which which is is equal equal to to 4.38 4.38 V. V. --: : PEMELPEMEL voltagevoltage (V),(V), dependingdepending onon thethe PEMELPEMEL currentcurrent ifif thethe latterlatter isis controlledcontrolled insteadinstead ofof thethe voltage. voltage.

BasedBased on on Equation Equation (5), (5), the the resistance resistance value value ha hass been been computed computed according according to to the the PEMEL PEMEL voltage voltage rangerange includedincluded betweenbetweenFigureFigure 514.14.5 andand Resistance 88 VV (rated(rated value stackstack variation powerpower according ofof 400400 W),W), toto as PEMELasPEMEL shownshown voltage.voltage. inin FigureFigure 14.14. TheThe higherhigher thethe PEMEL PEMEL voltage, voltage, the the lower lower the the resistive resistive load. load. Thes Thesee results results are are similar similar to to those those introduced introduced in in [10]. [10]. To summarize, based on these two previous works, the calculation of the resistance is based on the static behavior of the PEMEL.

C 2020, 6, 29 11 of 20

C 2020, 6, x FOR PEER REVIEW 12 of 21 To summarize, based on these two previous works, the calculation of the resistance is based on 3.2.the staticStatic behaviorModel of the PEMEL.

3.2. StaticThe static Model model of PEMELs is based on its current-voltage characteristic [19–22]. The parameters of the I-V characteristic curve are determined by using the measurements of a PEMEL singleThe cell. static model of PEMELs is based on its current-voltage characteristic [19–22]. The parameters of theAn I–V example characteristic of an I-V curve characteristic are determined curve by for using a PEMEL the measurements single cell is ofshown a PEMEL in Figure single 15. cell. This curveAn has example been obtained of an I–V for characteristic the following curve operating for a PEMEL conditions: single gas cell pressures is shown of in 1 Figure bar and 15 .an This ambient curve temperaturehas been obtained of 20 °C. for The the specifications following operating of the PE conditions:MEL used for gas the pressures experiments of 1 are bar provided and an ambientin Table 1.temperature of 20 ◦C. The specifications of the PEMEL used for the experiments are provided in Table1.

FigureFigure 15. 15. TheThe I-V I–V characteristic characteristic curve curve of a of PEMEL a PEMEL with with twotwo different different modeling modeling (i.e., (i.e.,nonlinear nonlinear and linear).and linear).

Table 1. Specifications of the PEMEL. Table 1. Specifications of the PEMEL.

ParametersParameters ValueValue Unit Unit RatedRated electrical electrical power power 400 400 W W StackStack operating operating voltage voltage 8 8 V V StackStack current current range range 0–50 0–50 A A DeliveryDelivery output output pressure pressure 0.1–10.5 0.1–10.5 bar bar CellsCells number, number, N N 3 3 - - Active area Section 50 2 Active area Section 50 cm cm2 Hydrogen flow rate at STP slpm (standard liter perslpm minute) (standard liter per Hydrogen flow(Standard rate at STP Temperature (Standard Temperature and 1 and Pressure, P = 11 bar, T = 20 ◦C minute) Pressure,20 20 °C◦C and and 1 1 bar) bar) P = 1 bar, T = 20 °C

FromFrom Figure 15,15, the PEMEL has a nonlinear behavior. It It can can be be mo modeleddeled by by using using either either a a linear linear oror a nonlinear model. First First of of all, all, a a simple simple static static modeling modeling approach approach can can be be developed based based on on the followingfollowing expression expression [20]: [20]:

∆y y == ∆ x + +c ∆∆x ∆vel 2.407 1.545 v = i + 1.545= − i + 1.545 (6) el ∆iel el 50 0 el ∆ ..− = vel =+0.0172 1.545i el =+ 1.545  R1iel + V1.545int (6) ∆ where: = 0.0172 + 1.545 ≅ + -R1 is an equivalent resistance [Ω]. where:-V int is a reversible voltage [V]. - is an equivalent resistance [Ω]. - is a reversible voltage [V]. C 2020, 6, x FOR PEER REVIEW 13 of 21

The reversible voltage Vint (electrochemical) is important for electrolysis process and hydrogen production, and can be calculated as follows [3]:

∆G V = = 1.233 V (7) C 2020, 6, 29 zF 12 of 20 where: -The∆ reversible is the Gibbs voltage energyV int(238(electrochemical) kJ.mol−1 for T = is20 important °C) allowing for electrolysissplitting the process deionized and water hydrogen into production,hydrogen and and oxygen. can be calculated as follows [3]: If the water is liquid, ∆ can be determined according to the temperature (°C): ∆G V = = 1.233 V (7) ∆ = 285,840int − 163.2(273zF + ) [J. mol] (8) where:-z is the number of electrons exchanged during the reaction. For H2, z = 2. 1 -F-∆ Gis isthe the Faraday’s Gibbs energy constant (238 (96 kJ 485 mol −C. molfor T =). 20 ◦C) allowing splitting the deionized water into hydrogenFrom andEquation oxygen. (6), an equivalent static electrical circuit for a single PEMEL cell can be deduced as shownIf the in water Figure is liquid, 16. It is∆ Gcomposedcan be determined of an electromotive according force to the representing temperature the (◦C): reversible voltage (Vint) in series-connected with an equivalent resistance (R1) [21]. h 1i The electrical power Pcell∆ forG =a single285, 840 cell 163.2is given(273 by:+ T) J mol− (8) − = = + (9) -z is the number of electrons exchanged during the reaction. For H2, z = 2. 1 Hence,-F is the the Faraday’s total electrical constant power (96 485 (Pel C) is mol obtained− ). by multiplying the power (Pcell) by the number of cellsFrom (N): Equation (6), an equivalent static electrical circuit for a single PEMEL cell can be deduced as shown in Figure 16. It is composed of an electromotive force representing the reversible voltage (Vint) = (10) in series-connected with an equivalent resistance (R1)[21].

FigureFigure 16. 16. EquivalentEquivalent staticstatic electrical model of a a prot protonon exchange exchange membrane membrane electrolyzer electrolyzer (PEMEL) (PEMEL) single cell. single cell.

FromThe electrical Figure power16, thePcell energyfor aefficiency single cell of is the given PEMEL by: is expressed as the ratio between the electrochemical hydrogen energy (PH2) and electrical power (Pel) as follows: 2 Pcell = vcelliel = iel R1 + ielVint (9) = = = (11) Hence, the total electrical power (Pel) is obtained by multiplying the power (Pcell) by the number of cellsFrom (N): Equation (11), the higher the cell voltage, the lower the energy efficiency. Besides, the cell voltage efficiency is definedPel = Nvas thecelli elratio between the thermoneutral cell voltage(10) VTN (given in Equation (13)) and the cell voltage, vcell [3]: From Figure 16, the energy efficiency of the PEMEL is expressed as the ratio between the electrochemical hydrogen energy (PH2) and electrical power (Pel) as follows: = (12) P i v V η = H2 = el∆int = int (11) el P =v i v (13) el cellel cell whereFrom Equation (11), the higher the cell voltage, the lower the energy efficiency. -Besides,∆ is the the change cell voltage of enthalpy efficiency (285.84 is defined kJ. mol as−1). the ratio between the thermoneutral cell voltage VTN (given in Equation (13)) and the cell voltage, vcell [3]:

VTN ηvcell = (12) vcell C 2020, 6, 29 13 of 20

∆H V = (13) TN zF where 1 -∆H is the change of enthalpy (285.84 kJ mol− ). Finally, the static model of the PEMEL can be modeled by an empirical current-voltage expression. The different parameter values can be found also by using a least-squares regression algorithm. The I–V relationship of the PEMEL is written as follows [41]:

vel = Vint + riel + slog(tiel + 1) (14)

where -r is the ohmic resistance of electrolyte (Ω). -s, t are the coefficients for overvoltage on electrodes It is well known that the overvoltages appearing in Equation (14) are dependent on the temperature. Therefore, the previous equation can be modified to take into consideration the effects of the temperature on the electrode and electrolyte overvoltage. The temperature-dependent I–V model can be expressed as follows [41]:

 2  2  vel = Vint + r1 + r2Tiel + s1 + s2T + s3T log t1 + t2/T + t3/T iel + 1 (15)

-ri is the parameters for ohmic resistance of electrolyte (i = 1...2). -si, ti are the parameters for overvoltage on electrodes (i = 1...3). -T is the temperature of electrolyte (◦C). The parameters ri, si, ti are provided in [41].

3.3. Dynamic Model The previously presented models are static and do not take into consideration the dynamics of the PEMEL in case of operating conditions change. These dynamics can be investigated in performing experimental tests by supplying the PEMEL with dynamic current profiles [24]. The realized experimentalC 2020, 6, x FOR testPEER bench REVIEW to analyze the dynamic behavior of PEMELs is shown in Figure 17. 15 of 21

FigureFigure 17.17. Investigation ofof dynamicdynamic operationoperation ofof aa PEMEL.PEMEL.

The DC power supply is controlled by using a virtual control panel with a laptop. The specifications of the used PEMEL are reported in Table1. A test has been carried out with a DC current (from 0 to

Figure 18. PEMEL stack response according to a current dynamic profile (time scale: 5 s.div−1).

The equivalent electrical circuit used to model the dynamic behavior of the PEMEL is shown in Figure 19. It consists of an electromotive force representing the reversible voltage (Vint), series- connected with a resistor (Rint) modeling the membrane, and an RC branch to emulate the losses in the anode and the dynamics [24]. In the literature, this dynamic model has been reported in other related works [9,42,43]. In [42], the authors have proposed this model based on previous works reported for fuel cells. Experimental results are provided to show the dynamics of a single-cell PEM electrolyzer, but the authors did not determine the parameters of the equivalent circuit. By comparison, in [43], the same model is presented based on [42], but only the static model is considered to be coupled with an interleaved DC–DC buck converter for control purposes. Finally, in [9], this model is presented for an alkaline electrolyzer to investigate the effects of rectifiers on the specific energy consumption and gas quality during dynamic operation. C 2020, 6, x FOR PEER REVIEW 15 of 21

C 2020, 6, 29 14 of 20

10 A) to supply the PEMEL. The PEMEL stack response is provided in Figure 18. A high time scale for this test has been chosen to see the dynamics of the PEMEL and the steady-state operation. Figure 17. Investigation of dynamic operation of a PEMEL.

1 Figure 18. PEMEL stack response according to a current dynamic profileprofile (time scale: 5 ss.div div−1).).

TheFrom equivalent Figure 18 electrical, the PEMEL circuit stack used voltage to model is the equal dynamic to the behavior open-circuit of the voltage PEMEL called is shown Nernst in V i Figurevoltage 19. or reversibleIt consists voltage of an (electromotiveint) at el = 0 A.force This representing voltage is approximately the reversible equal voltage to 4.33 (V V.int When), series- the connectedDC current with is supplied a resistor to (R theint) modeling PEMEL, an the immediate membrane, rise and in an PEMEL RC branch stack to voltage emulate can the be losses noticed, in thefollowed anode by and a slow the dynamics final rise before [24]. In reaching the literature, its steady-state this dynamic value. Themodel immediate has been rise reported in stack in voltage other relatedcan be modeledworks [9,42,43]. as a resistor, In [42], representing the authors the have ohmic proposed losses in this the membrane.model based Besides, on previous the slow works final reportedrise in stack for voltagefuel cells. represents Experimental the speed results of theare chemicalprovided reactionsto show the both dynamics at the anode of a andsingle-cell the cathode. PEM electrolyzer,In this test, this but final the rise authors lasts 13 did s and not can determine change according the parameters to the input of energythe equivalent supplying thecircuit. PEMEL. By comparison,Indeed, as highlighted in [43], the insame [24 ],model the duration is presented of the based final on rise [42], to reachbut only the the steady-state static model operation is considered due to tothe be move coupled of the with electrons an interleaved into the anode DC–DC and buck cathode converter lengthens for especially control purposes. as the input Finally, energy in increases. [9], this modelHowever, is presented when the for stack an voltagealkaline gets electrolyzer closer to theto investigate limit operating the effects voltage of (for rectifiers this PEMEL, on the thespecific limit energyvoltage consumption is equal to 8 V),and the gas dynamics quality during are faster, dynamic and theoperation. stack voltage in steady-state operation may drop [24]. To summarize, this slow rise represents the activation overvoltage both at the anode and cathode. Since this dynamic behavior is close to a first-order system, it can be modeled as RC branches. On one hand, the resistors result in activation losses both at the anode and cathode, while the capacitors represent the charge separation into the anode and cathode. Hence, the dynamic behavior of the PEMEL to the final duration required by the charge layers to move when a DC current is supplied can be replicated. On the other hand, in [24], it has been emphasized that the reaction speed at the anode is much slower than the reaction speed at the cathode. For this reason, the activation phenomena in PEMEL are mainly dominated by the anode reaction. The equivalent electrical circuit used to model the dynamic behavior of the PEMEL is shown in Figure 19. It consists of an electromotive force representing the reversible voltage (Vint), series-connected with a resistor (Rint) modeling the membrane, and an RC branch to emulate the losses in the anode and the dynamics [24]. In the literature, this dynamic model has been reported in other related works [9,42,43]. In [42], the authors have proposed this model based on previous works reported for fuel cells. Experimental results are provided to show the dynamics of a single-cell PEM electrolyzer, C 2020, 6, 29 15 of 20 but the authors did not determine the parameters of the equivalent circuit. By comparison, in [43], the same model is presented based on [42], but only the static model is considered to be coupled with an interleaved DC–DC buck converter for control purposes. Finally, in [9], this model is presented for an alkaline electrolyzer to investigate the effects of rectifiers on the specific energy consumption and gas quality during dynamic operation. C 2020, 6, x FOR PEER REVIEW 16 of 21

Figure 19. Equivalent electric model of the dynamic operation of a PEMEL.

From Figure 1919,, the PEMEL stack voltage cancan bebe expressedexpressed asas follows:follows:

= + + (16) vel = Vint + vACT + Rintiel (16) The dynamic activation overvoltage at the anode can be written as: The dynamic activation overvoltage at the anode can be written as: 1 = − (17) dvACT 1 vACT = iel (17) The couple R1C1 represents the time constantdt C in1 seconds− R1C1 of the dynamics. The equivalent resistor R1 at the anode can be determined based on the activation overvoltage vACT and the current flowing The couple R1C1 represents the time constant in seconds of the dynamics. The equivalent resistor through the electrolyzer iel. Hence, the constant time at the anode is expressed as follows: R1 at the anode can be determined based on the activation overvoltage vACT and the current flowing through the electrolyzer i . Hence, the constant time τ at the anode is expressed as follows: el = = (a ) (18) ! VACT By using the static model identificationτa = R1 C(see1 = Section 3.2),C1 the reversible voltage (Vint) and (18)the iel membrane resistor (Rint) can be determined. After that, to identify the parameters of the RC branch for theBy anode using thereaction, static a model dynamic identification model identificati (see Sectionon has 3.2 ),to thebe reversibleconsidered voltage by investigating (Vint) and the membranetransient operation resistor ( Rasint shown) can be in determined. Figure 18. AfterA leas that,t-squares to identify regression the parameters algorithm of has the RCbeen branch used forto thedetermine anode reaction,the time a dynamicconstant modelof the identification transient operation, has to be consideredthen the parameters by investigating of the the activation transient operationresistance asand shown double-layer in Figure capacitor18. A least-squares [24]. It has regression to be noted algorithm that the has equivalent been used todouble-layer determine thecapacitor time constantdetermined of thefor transientthis study operation, is equal roughl theny the to 37 parameters F, while the of thevalues activation reported resistance for PEM andfuel double-layercells and alkaline capacitor electrolyzers [24]. It has are to of be the noted order that of a the few equivalent Farad [44] double-layer and milli Farad capacitor [9], respectively. determined forThese this results study are is equalhigh in roughly terms of to capacitance 37 F, while va thelues values and are reported assimilated for PEM to supercapacitors. fuel cells and alkaline electrolyzers are of the order of a few Farad [44] and milli Farad [9], respectively. These results are high3.4. Comparison in terms of between capacitance Static values and Dynamic and are Model assimilated to supercapacitors. A comparison between the static model (Figure 16) and the dynamic model (Figure 19) 3.4. Comparison between Static and Dynamic Model providing the voltage response of the PEMEL according to a current profile is given in Figure 20 [24]. It canA be comparison noted that the between voltage the response static model obtained (Figure by 16the) anddynamic the dynamic model allows model replicating (Figure 19) accurately providing the voltagereal dynamic response behavior of the of PEMEL a PEMEL. according Based to on a currentprevious profile work is [24], given a dynamic in Figure model20[ 24]. features It can be a notedmaximum that theerror voltage of about response 4%, obtainedwhereas bya static the dynamic model presents model allows a maximum replicating error accurately of about the 15%. real dynamicUnfortunately, behavior the ofmaximum a PEMEL. error Based for on the previous static model work [occurs24], a dynamicjust after model the step features solicitation; a maximum it is a typical situation depicted by an abrupt variation of the available power when a RES is used. The equivalent model developed in Figure 19 has been used for the first time to design the controller of a suitable DC–DC converter to supply a PEMEL, namely a stacked interleaved buck converter (SIBC) as shown in Figure 21 [25]. Compared to a classic interleaved buck converter, the SIBC includes an additional capacitor Cs between the first and the second phase. The capacitor Cs allows blocking the DC component of the current flowing through the second phase. As a result, only the AC component of the current flows through the second phase. Besides, since a couple of power switches (i.e., S1 and S4, and S2 and S3) are controlled in an opposite way, only the DC current supplies C 2020, 6, x FOR PEER REVIEW 17 of 21

the PEMEL. A low current ripple is one of the most important features required for the DC–DC converter to supply the electrolyzer. Indeed, as demonstrated in the literature, the current ripple leads up to the decrease of the energy efficiency of the electrolyzer [45,46].

C 2020, 6, 29 16 of 20 C 2020, 6, x FOR PEER REVIEW 17 of 21 theerror PEMEL. of about A 4%,low whereascurrent aripple static is model one of presents the mo ast maximumimportant errorfeatures of about required 15%. for Unfortunately, the DC–DC converterthe maximum to supply error the for electrolyzer. the static model Indeed, occurs as demo just afternstrated the in step the solicitation; literature, the it iscurrent a typical ripple situation leads updepicted to the decrease by an abrupt of the variation energy effi of theciency available of the powerelectrolyzer when [45,46]. a RES is used.

Figure 20. Comparison of the voltage response between a static and a dynamic model [24].

Based on the static and dynamic models, the bode diagrams of the transfer function (to control the stack voltage of the PEMEL) of the SIBC (Figure 22), and accordingly, the step response of the system (Figure 23) changes by considering either a static or a dynamic load. Besides, it can be seen in Figure 24 that the step response of the SIBC with a dynamic model is slower due to the anode reaction. As a result, the design and the tuning of the controller require an accurate model, such as the dynamic model presented in Section 3.3. To control PEM electrolyzers efficiently, overshoot must be avoided that mayFigureFigure damage 20. 20. ComparisontheComparison electrolyzer of of the the and voltage voltage stability response response must betw between be eenensured a a static static without and and a a dynamic dynamic oscillation model model as [24].highlighted [24]. in [25]. Besides, since PEM electrolyzers present slow dynamics, the rapidity is not the most important criteriumBasedThe equivalent toon design the static controllers. model and dynamic developed models, in Figure the bode19 has diagrams been used of the for transfer the first function time to (to design control the thecontroller stackThe voltage different of a suitable of step the responses DC–DCPEMEL) converterof demonstrate the SIBC to (Figur supply that adope 22), a PEMEL,ting and a accordingly,simplified namely amodel stackedthe step such interleaved response as the static of buck the one systemconvertercould lead(Figure (SIBC) to a23) wrong as changes shown design in by Figure considering of the 21 [controller.25]. either Compared Ina staticdeed, to or athe classic a dynamicbode interleaved diagram load. Besides,of buck the converter,converter it can be the withseen SIBC thein Figureincludesstatic 24model anthat additional theshows step a response gain capacitor higher ofC the scomparedbetween SIBC withthe to a the firstdynamic dynamic and themodel secondmodel. is slower phase.This dueimplies The to capacitorthe the anode responseC reaction.s allows with Asblockingovershoot a result, the therequiring DC design component a and correction the of tuning the that current of would the flowing contro worsenller through threquiree dynamic. the an second accurate Contrarily, phase. model, As the such a real result, as response the only dynamic the of AC the modelcomponentsystem presented corresponds of the in current Section to the flows 3.3.dynamic To through control model the PEM in second which elec phase.trolyzers no overshoot Besides, efficiently, occurs. since overshoot a It couple means of must that power thebe switchesavoideddynamic that(i.e.,of the mayS1 PEMELand damageS4, enforces and theS electrolyzer2 and the Sstability3) are and controlled of stability the system; inmust an for oppositebe thisensured reason, way, without onlyit is crucial theoscillation DC to current take as highlightedit suppliesinto account. the in [25].PEMEL.Besides, Besides, Athis low sinceissue current PEMis strictly ripple electrolyzers tied is one to ofthe present the use most of slow RES important dynamics,since for features stationary the rapidity required grid-supplied is for not the the DC–DC most applications important converter no criteriumtoinput supply power to the design electrolyzer.variations controllers. occur Indeed, and as the demonstrated voltage or cu inrrent the literature, supplying the the current electr rippleolyzer leads can be up varied to the decreaseaccordingThe different of to the the energy quantitystep responses efficiency of hydrogen ofdemonstrate the electrolyzerto be produced. that adop [45,46 ting]. a simplified model such as the static one could lead to a wrong design of the controller. Indeed, the bode diagram of the converter with the static model shows a gain higher compared to the dynamic model. This implies the response with overshoot requiring a correction that would worsen the dynamic. Contrarily, the real response of the system corresponds to the dynamic model in which no overshoot occurs. It means that the dynamic of the PEMEL enforces the stability of the system; for this reason, it is crucial to take it into account. Besides, this issue is strictly tied to the use of RES since for stationary grid-supplied applications no input power variations occur and the voltage or current supplying the electrolyzer can be varied according to the quantity of hydrogen to be produced.

FigureFigure 21.21.Stacked Stacked interleavedinterleaved DC–DCDC–DC buckbuck converterconverter connectedconnected to to a a PEMEL. PEMEL.

Based on the static and dynamic models, the bode diagrams of the transfer function (to control the stack voltage of the PEMEL) of the SIBC (Figure 22), and accordingly, the step response of the system (Figure 23) changes by considering either a static or a dynamic load. Besides, it can be seen in Figure 24 that the step response of the SIBC with a dynamic model is slower due to the anode reaction. As a result, the design and the tuning of the controller require an accurate model, such as the dynamic

Figure 21. Stacked interleaved DC–DC buck converter connected to a PEMEL. C 2020, 6, 29 17 of 20

model presented in Section 3.3. To control PEM electrolyzers efficiently, overshoot must be avoided that may damage the electrolyzer and stability must be ensured without oscillation as highlighted in [25]. Besides, since PEM electrolyzers present slow dynamics, the rapidity is not the most important criterium to design controllers. The different step responses demonstrate that adopting a simplified model such as the static one could lead to a wrong design of the controller. Indeed, the bode diagram of the converter with the static model shows a gain higher compared to the dynamic model. This implies the response with overshoot requiring a correction that would worsen the dynamic. Contrarily, the real response of the system corresponds to the dynamic model in which no overshoot occurs. It means that the dynamic of the PEMEL enforces the stability of the system; for this reason, it is crucial to take it into account. Besides, this issue is strictly tied to the use of RES since for stationary grid-supplied applications no input power variations occur and the voltage or current supplying the electrolyzer can be varied according

Cto 2020C the 2020, 6 quantity, x, 6FOR, x FOR PEER of PEER hydrogenREVIEW REVIEW to be produced. 18 of18 21 of 21

FigureFigureFigure 22. 22.Bode 22.Bode Bode diagram diagram diagram of of the theof transfer the transfer transfer function function function of theof thof stackede thstackede stacked interleaved interleaved interleaved buck buck converter buck converter converter (SIBC) (SIBC) either(SIBC) with a static or a dynamic model.eithereither with with a static a static or aor dynamic a dynamic model. model.

Figure 23. Step response of the SIBC either by considering a static or dynamic model. FigureFigure 23. 23.Step Step response response of the of theSIBC SIBC either either by consideringby considering a static a static or dynamic or dynamic model. model.

FigureFigure 24. 24.Slow Slow response response of theof the system system with with the the dynamic dynamic model. model. C 2020, 6, x FOR PEER REVIEW 18 of 21

Figure 22. Bode diagram of the transfer function of the stacked interleaved buck converter (SIBC) either with a static or a dynamic model.

C 2020, 6, 29 18 of 20 Figure 23. Step response of the SIBC either by considering a static or dynamic model.

Figure 24. Slow response of the system with the dynamic model. 4. Conclusions The goal of this article was to underline the importance of using power converters, particularly DC–DC converters, to interface a high DC bus voltage to a low DC voltage required for PEM electrolyzers. With renewable energy sources as supply, green hydrogen can be produced and blended to natural gas or employed in other clean applications. Besides, the modeling of the PEM electrolyzer is mandatory to develop controllers such as energy efficiency or hydrogen flow rate-based controls. In this article, three types of modeling have been investigated (i.e., resistive, static, and dynamic load) showing that the use of RES implies different design constraints compared to stationary grid-supplied converters for electrolyzers. It has been demonstrated that the dynamics play an important role to understand the behavior of the PEM electrolyzer in case of dynamic operating conditions. Indeed, the PEM electrolyzers can be coupled with renewable energy sources and are submitted to dynamic operations due to the weather conditions change. As a result, if these dynamics were taken into account in designing the controller, the performance of the system could be enhanced greatly making hydrogen more attractive also in carbon-based fuels.

Author Contributions: Conceptualization, B.Y., D.G., M.P., W.K., and M.H.; methodology, B.Y., D.G., M.P., W.K., and M.H.; validation, B.Y., D.G., and G.V.; investigation, B.Y., D.G., and G.V.; writing—original draft preparation, D.G., and G.V.; writing—review and editing, B.Y., D.G., and G.V. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acknowledgments: The authors would like to thank sincerely the French Embassy in Bangkok (Thailand) and Campus France in supporting Burin Yodwong’s Ph.D. thesis within the framework of the Franco-Thai scholarship program. Besides, the authors are very thankful to the GREEN laboratory of the Université de Lorraine and Thai-French Innovation Institute of King Mongkut’s University of Technology North Bangkok for their constant support in developing research cooperation between France and Thailand. Conflicts of Interest: The authors declare no conflict of interest.

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