Decentralized Dynamic Power Sharing Control for Frequency Regulation Using Hybrid Hydrogen Electrolyzer Systems

Hydrogen electrolyzers are promising tools for frequency regulation of future power systems with high penetration of renewable energies and low inertia. This is due to both the increasing demand for hydrogen and their flexibility as controllable load. The two main electrolyzer technologies are Alkaline Electrolyzers (AELs) and Proton Exchange Membrane Electrolyzers (PEMELs). However, they have trade-offs: dynamic response speed for AELs, and cost for PEMELs. This paper proposes the combination of both technologies into a Hybrid Hydrogen Electrolyzer System (HHES) to obtain a fast response for frequency regulation with reduced costs. A decentralized dynamic power sharing control strategy is proposed where PEMELs respond to the fast component of the frequency deviation, and AELs respond to the slow component, without the requirement of communication. The proposed decentralized approach facilitates a high reliability and scalability of the system, what is essential for expansion of hydrogen production. The effectiveness of the proposed strategy is validated in simulations and experimental results.

Abstract-Hydrogen electrolyzers are promising tools for frequency regulation of future power systems with high penetration of renewable energies and low inertia.This is due to both the increasing demand for hydrogen and their flexibility as controllable load.The two main electrolyzer technologies are Alkaline Electrolyzers (AELs) and Proton Exchange Membrane Electrolyzers (PEMELs).However, they have trade-offs: dynamic response speed for AELs, and cost for PEMELs.This paper proposes the combination of both technologies into a Hybrid Hydrogen Electrolyzer System (HHES) to obtain a fast response for frequency regulation with reduced costs.A decentralized dynamic power sharing control strategy is proposed where PEMELs respond to the fast component of the frequency deviation, and AELs respond to the slow component, without the requirement of communication.The proposed decentralized approach facilitates a high reliability and scalability of the system, what is essential for expansion of hydrogen production.The effectiveness of the proposed strategy is validated in simulations and experimental results.
Index Terms-Decentralized control, dynamic power sharing, frequency control, hybrid systems, hydrogen, electrolyzer.Inductor of the connecting line to the grid (H).P b G Base power of the SG control (kW).

P max
Maximum consumed power by the system (kW).

P min
Minimum consumed power by the system (kW).

P ref
Reference active power of the system (kW).P ref G Reference active power of the SG (p.u.).

Q ref
Reference reactive power of the system (kvar).R a CT , R c CT Charge transfer resistance in anode and cathode (Ω).

R i Internal resistance (Ω). R G
Frequency control gain of the SG (p.u.).T R Time constant of the regulator (s).T T Time constant of the turbine (s).

V ref
Reference voltage of the DC link (V).

V rev
Reverse voltage (V).

Δf max
Frequency deviation when full support is delivered (Hz).

Variables C j Virtual capacitor of an electrolyzer (F). C P , C P m
Virtual capacitor of a PEMEL (F).

C P eq
Equivalent virtual capacitor of reduced system (F).

C P eq Updated equivalent virtual capacitor after expansion (F). C P m
Updated virtual capacitor of a PEMEL after expansion (F).

I. INTRODUCTION
G REEN hydrogen production from electrolyzers is a key technology for the energy transition [1], [2].One of its main applications is the decarbonization of industrial processes, such as steel industry.Just in Sweden, several industrial projects in this sector are currently under development [3], [4], [5].The Transmission System Operator (TSO) includes up to 85 TWh of electric consumption for hydrogen production in scenarios for 2045 [6], representing one third of future Swedish consumption.This large proportion of consumption is flexible, thanks to the possibility of hydrogen storage to decouple the electric consumption from hydrogen demand, and will provide a relevant tool for grid stability.
In future power systems, large part of traditional synchronous generators will be replaced by renewable energies with power electronic interfaces.This results in low inertia power systems, where tools, such as demand response, can increase the stability of the system.Demand response from flexible consumers to provide fast response for frequency regulation is being implemented by TSOs of several countries to facilitate integration of renewable energies [7], [8], [9].In these systems with low inertia, electrolyzers for hydrogen production can provide a fundamental help for frequency regulation.
The use of electrolyzers for frequency regulations has been studied in literature.There are two dominating commercial technologies, Alkaline Electrolyzer (AEL) and Proton Exchange Membrane Electrolyzer (PEMEL).PEMELs are proposed as the main technology able to provide a fast response for frequency regulation, such as in case of contingencies or to provide Fast Frequency Regulation (FFR) [10], [11], [12], [13], [14].For frequency regulation with slower response time, AELs have also been proposed as a solution [15], [16], with lower costs compare to PEMELs [17], [18].However, it was demonstrated in [16] that large-scale AELs are not suitable in cases where a fast frequency regulation is required.The combination of both technologies into a Hybrid Hydrogen Electrolyzer System (HHES) allows a fast response for frequency regulation by PEMELs and reduced cost thanks to AELs, making use of the benefits of both technologies.However, to the best knowledge of the authors, these hybrid electrolyzer systems have not been studied in literature.In our recent work [19], we have developed a centralized control strategy as a first approach to control a HHES, but it requires high level of communication, and may suffer from single point of failure.
Decentralized control strategies improve reliability, and facilitates expansion of electrolyzer systems to increase their hydrogen production.Some decentralized control works have been developed for DC microgrids applications.In [20], a decentralized dynamic current sharing control for a PEM fuel cell and battery is proposed to maintain a constant voltage in a DC microgrid.An extension of this method for a supercapacitor and battery system is presented in [21], and the control strategies are further improved in [22] and [23] by considering the state of charge of the supercapacitor, and including a composite model predictive control.However, these control strategies have only been applied to Energy Storage Systems (ESSs), and not to flexible loads, such as electrolyzers.In addition, they cannot deal with larger systems to provide frequency regulation to the main grid.
The main contribution of our work is a novel decentralized dynamic power sharing control for HHESs to provide fast response for frequency regulation as a grid service.The major novelties of the proposed technique are summarized as follows: 1) This paper proposes a decentralized dynamic power sharing control for HHESs to provide grid frequency regulation, with full utilization of PEMELs and AELs, i.e., fast response for frequency control by PEMELs and reduced cost thanks to AELs. 2) The proposed method is fully decentralized with only local communications, thus achieving enhanced reliability and scalability compared with existing centralized method.As electrolyzer systems in industrial plants normally have multiple stacks of PEMELs and AELs, due to the high hydrogen demand and limited capacity of each electrolyzer stack, the proposed method provides a reliable and scalable solution for real-world applications.3) Moreover, a guideline for system expansion under the proposed method is provided so that system expansion can be flexibly achieved without the modification of existing control architectures.4) Compared with existing decentralized dynamic control methods, which are used for hybrid ESSs in islanded DC microgrids [20], [21], [22], [23], the proposed approach is for decentralized dynamic control of flexible loads to provide power grid frequency regulation.This cannot be achieved by existing methods that do not consider AC grid connection.In short, the proposed method provides a novel, cost-effective and practical solution for HHESs to provide grid frequency regulation without the requirement of additional energy storage.For industrial decarbonization, many industries (e.g., HYBRIT project from SSAB, LKAB, and Vattenfall [3], and Ovako [4]) already have AELs in their plants, and they are planning to expand their existing plants with PEMELs, thus the proposed method provide a cost-effective solution for HHESs in industrial plants to maximize their profits with easy implementation and flexible system expansion.
The rest of this paper is organized as follows.In Section II, electrolyzer technologies and modelling are explained, highlighting the advantages of HHESs.The proposed control strategy is presented in Section III.Section IV shows the easy scalability of the system with the proposed strategy.Simulations are performed in Section V to show the effectiveness of the proposed strategy to provide fast response for frequency regulation in low inertia power systems.Section VI validates the control strategy with experimental testing, and conclusions are drawn in Section VII.

II. ELECTROLYZER TECHNOLOGIES AND HYBRID HYDROGEN ELECTROLYZER SYSTEMS
Electrolyzers are devices where a chemical reaction is achieved by supplying external energy in the form of electricity.In hydrogen electrolyzers, the overall reaction is the decomposition of water into oxygen and hydrogen.A conceptual design of the two dominating electrolyzer technologies, AELs and PEMELs, is shown in Fig. 1.They consist of electrodes, divided in anodes and cathodes, where an electrolyte is used to transfer charge between the electrodes in the form of ions [24].In the case of the AEL, the electrolyte consists of water with 30 wt% potassium hydroxide KOH.The KOH creates the alkaline conditions where OH − is the charge carrier.In the case of the PEMEL, a solid electrolyte in the form of membrane is used in acidic conditions.This conditions are employed so that the charge carried is H + .
The conceptual designs of AELs and PEMELs are translated into a generalized dynamic model, shown in Fig. 2.This model is a general model of an electrochemical cell.Each of the electrical components is related to electrochemical characteristics [25], [26].R i is the internal resistance, which include all the Ohmic resistances of the system, such as electrolyte resistance.For each electrode, C EDL , represents the capacitance effect of the electrons and ions accumulated close to the surface of the electrode, so called Electric Double Layer (EDL).The resistance R CT represents the charge transfer losses between the ions and the electrons and it is connected in parallel to C EDL .The reverse voltage V rev represents the minimum voltage required to start the chemical reactions, and obtain a current flowing through the electrolyzer.If the system can be considered in stationary conditions, the dynamic model can be simplified to a static one, where the capacitances are neglected, and all resistances are summed.
The use of each individual electrolyzer technology comes with trade-offs.Some economical and technical parameters of each technology are shown in Table I.AELs, especially large scale systems operating at atmospheric pressure, are a well-established technology with lower cost and high lifetime.
However, the operation at atmospheric conditions, together with lower current densities, make these systems larger in size.This also limits the flexibility and response times of AELs, even more notably when considering the supporting and auxiliary components of the balance of plant [26].PEMELs currently have higher cost, lower efficiency, and reduced lifetime.However, these limitations are expected to improve in the upcoming years, and they come with other advantages [17], [18].Their higher current densities make them more compact.Their smaller size and ability to operate at higher pressure favor a high dynamic operation with fast response times.In addition, their lower internal resistance and low risk of bubble overpotential allow a higher overload capability.This flexibility and fast response makes them more suitable for providing frequency regulation.AELs flexibility and response time can be enhanced by the combination with other technologies with fast response times, such as supercapacitors or other ESSs.However, this implies an extra investment cost, which only objective is a faster response in the grid side, without a enhancement of hydrogen production capabilities.Therefore, the combination of AELs with PEMELs into HHESs is an attractive solution for industries where their main income comes from the hydrogen production [27] in order to increase their fast response for grid services, as well as hydrogen capabilities.Furthermore, it is especially relevant for industries that invest in AELs nowadays, and expand their hydrogen production with PEMELs in the upcoming future, due the current trend of costs reduction in the latter technology.
Fig. 3 shows a HHES to provide grid frequency support.It consists of an AEL and a PEMEL connected to the main grid.The PEI of the system connects both devices to a common DC bus by DC/DC converters, and a DC/AC converter connects the DC bus to the main grid.HHES, if properly controlled, can make use of the advantages of this two technologies to provide a fast response solution for frequency regulation thanks to PEMELs, and reduced cost thanks to AELs.They can also improve response times and flexibility of AEL facilities where PEMELs are introduced to expand hydrogen production.
In real-world applications, HHESs consist of multiple AEL stacks and multiple PEMEL stacks, due to the capacity limitation of single stacks.Centralized control methods have single point of failure issues, and are not flexible for system expansion.Therefore, a decentralized dynamic power sharing for HHESs that considers the slow dynamic of AELs is urgently needed to provide fast frequency support and with high reliability and scalability.

III. PROPOSED DECENTRALIZED DYNAMIC POWER SHARING CONTROL FOR FREQUENCY REGULATION
The proposed decentralized dynamic power sharing control for frequency regulation using HHESs is shown in Fig. 4. By the adaptation of decentralized control methods in DC microgrids, the PEMEL converter is able to provide fast response thanks to the use of an extended droop controller combining virtual capacitor and resistor.A virtual resistance droop controller is employed for the AEL converter to provide slow response considering AEL dynamics.The frequency regulation is provided by frequency-droop in the grid-connected converter.It is highlighted that there is no communication between the control of each converter, facilitating a high reliability and scalability of the system.The proposed control strategy is explained in details in the following subsections.

A. Decentralized Dynamic Power Sharing
A resistance droop control for electrolyzers is employed to determine the current sharing at steady state, which is equivalent to adding a virtual resistor at the output of the DC/DC converters.If the current entering the converters is considered positive: where v j and i j are the input voltage and current to the DC/DC converter of the jth electrolyzer, V ref is the reference voltage of the DC link, and R j is the droop control gain, which is seen as a virtual resistor.This gain can be calculated as: where ΔV max is the maximum permissible voltage variation in the DC bus, while I j max is the maximum steady state current entering the DC/DC converter of the jth electrolyzer.
The resistance droop control is able to achieve the appropriate current sharing of electrolyzers in steady state based on their power capacity.However, in a HHES with devices with different response times, the transitory state also need to be optimized.The control can be adapted so the fast response of PEMELs compensates the slow response of AELs, and achieve an overall fast response for frequency regulation.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.To achieve dynamic power sharing considering the dynamics of different electrolyzer technologies, an extended droop control is implemented in the PEMEL, which is equivalent to connect a virtual capacitor C j in parallel with the virtual resistor R j at the output of the converter: The HHES system design can be represented by the equivalent circuit in Fig. 5.The AC/DC converter provides frequency support with a total current i t .The DC/DC converters of the AEL and PEMEL are described as a voltage source connected to the virtual resistors and capacitors previously described: where v iA , v iP , i iA and i iP are the input voltages and currents of the AEL and PEMEL respectively, R A is the virtual resistors of the AEL, and R P and C P are the virtual resistor and capacitor of the PEMEL.
The output voltages of AEL and PEMEL DC/DC converters are equalized at steady state.Therefore, the load current sharing of AEL and PEMEL are: where τ and k are equal to: The dynamics show that the response of the AEL is a low pass filter of the total current i t , while the PEMEL absorbs the high frequency of i t .τ represents the time constant of the low pass filter, and k is the proportional contribution of the PEMEL in steady state based on its power capacity.To respect AEL settling time, and time constant τ A , the capacitor C P is selected as: The dynamic of the system for a step response is shown in Fig. 6, for τ equal to 1.33 seconds, and k equal to 0.5.The value of τ is selected considering an AEL setting time of 4 s [16].With the proposed control, the slow response of the AEL is respected, while achieving an overall fast response thanks to the PEMEL.The inner loop controls of the DC/DC converters are as it was shown in Fig. 4. The first Proportional-Integral (PI) controller is in charge of the input voltage v iA and v iP , considering as Fig. 6.Dynamic of the equivalent circuit for a step in the total current with τ = 1.33 s and k = 0.5.
reference V iA and V iP from ( 4) and ( 5) respectively.The second PI controller is in charge of the current flowing through the inductors L fA and L fP .The sizing of these PI controllers is based on [28].Finally the duty cycles, d A and d P , are transformed to switching signal, S A and S P , by the Pulse Width Modulation (PWM) blocks.

B. Frequency Regulation
The frequency regulation is achieved by a droop control using only local measurements of the AC/DC converter.The droop control is in charge of modifying the consumed active power P ref with ΔP ref .This variation of the active power depends on the deviation of the frequency f from its nominal value f 0 , and the droop gain R f .This gain is calculated as: where P max and P min are the maximum and minimum power variations allowed for the system, and Δf max is the frequency deviation when the system is giving its maximum support.
The inner loop control of the AC/DC converter measures the voltage and current, i abc and v abc respectively, and transforms them into synchronous coordinates dq, i dq and v dq , by Clarke and Park transformations.The frequency angle θ required for Park transformation, is obtained from the Phase-Locked Loop (PLL) block.This block also calculates the grid frequency f , required for the frequency regulation droop control to obtain ΔP ref .The sum of P ref and ΔP ref , as well as the reference of reactive power Q ref , are used by the current control to obtain the reference AC voltage u dq .This reference is then transformed to stationary references u abc , and the switching signals S abc are obtained with the PWM block.
The overall control strategy of the system provides a fast response for frequency regulation, while respecting the slow dynamics of the AEL.It avoids any communication between converters, using only local measurements.This facilitates a high scalability and reliability of the system compared to centralized control methods.This scalability will be shown in the next section, where the procedure for the expansion of the system is explained.
IV. SYSTEM EXPANSION WITH PROPOSED STRATEGY Fig. 7 shows the equivalent circuit of an expanded HHES with N AELs and M PEMELs under the proposed strategy.The expanded system can be transformed to an equivalent reduced system with one AEL with virtual resistor R Aeq , and one PEMEL with virtual resistor R P eq and capacitor C P eq : In case of installing one new AEL N + 1, the virtual capacitors of the existing M PEMELs has to be updated to maintain the same time constant τ .The new equivalent virtual resistors R Aeq are calculated as (12) for N + 1 AELs.The new equivalent virtual capacitor C P eq is calculated as: The update of each of the M virtual capacitors C P m are obtained considering ( 14): The expansion of the system with PEMELs is a more relevant case for future applications.If one PEMEL M + 1 is installed, once again the virtual capacitors of all the M + 1 PEMELs have to be updated.The new equivalent virtual resistors R P eq is calculated as (13) for M + 1 PEMELs.The new equivalent capacitor is equal to: and the update of each of the M + 1 virtual capacitors C P m are calculated as: Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.The system can be easily expanded without affecting existing dynamics, by only modifying high-level control parameters, i.e., virtual capacitors C P m .

V. SIMULATION MODEL AND RESULTS
Simulations are performed in MATLAB Simulink to show the effectiveness of the method to provide fast response for frequency regulation, while respecting the dynamics of the AEL.Firstly, the proposed method is verified in a simplified power system with a detailed model of the HESS shown in Fig. 3, and the high scalability of the system is shown for the most relevant case of expanding with a new PEMEL.Secondly, a 120 MW HHES is tested in a modified IEEE 9 bus system to show its effectiveness in large-scale power systems.

A. Verification in Simplified Low Inertia Power System
A 500 kW HHES is connected to a low inertia power system modelled as a synchronous generator (SG) connected in parallel to a 500 kW load.This load is suddenly connected and disconnected at different times of the simulation to cause a frequency deviation.The model of the SG is shown in Fig. 8.The model parameters are in per unit with respect to the base P b G set to 1500 kW.The generator controls the frequency of the grid with a frequency-droop control with gain R G .When there is a frequency deviation Δf , the set point P ref G is modified by the droop control.The model considers the delays in the regulator and turbine of the generator, with the time constants T R and T T respectively.The balance between the mechanical and electrical powers is guaranteed by the swing equation.ΔP m is the variation of power of the generator with respect to the set point, ΔP l is the variation of consumed power by the loads of the system, Δf pu is the frequency deviation in per unit, H is the inertia of the generator, and D is the damping of the system.The time constants T R and T T are set to 0.2 s and 0.3 s respectively.The damping D is 10 p.u., and the gain of the frequency regulation R G is 20 p.u.The inertia is set to 5 s, representing a low inertia power system.
The electrolyzers modelled in the simulations have a maximum current of 1500 A, and power of 250 kW, considering the characteristics of industrial electrolyzer stacks [11], [29].The settling time of each technology has been selected considering the limitations of each technology [16], [18].The atmospheric operating conditions and bigger size of AEL facilities slow down the dynamics of the electrolyzer, increasing the settling time of the device when considering the supporting and auxiliary components of the balance of plant [26].The model parameters have been calculated from the ones of electrolytic cells integrated together in series and parallel connections [30], [31].Table II summarizes the characteristics of the electrolyzers.In the case of the PEMEL, the cathodic effects can be neglected due to the fast dynamics of the cathode compared to the anode [30].
A simulation with a 500 kW AEL system, consisting of two 250 kW AEL stacks, is performed to show the challenges of low inertia power systems without resources able to provide a fast response for frequency regulation, and as a comparison to cases with a HHESs.The system is in steady state until the 500 kW load is suddenly connected, provoking the upward frequency regulation of the AEL system, which has a frequency-droop control R f of 500 kW/Hz.After 10 s the load is disconnected, provoking now the downward frequency regulation of the AEL system.Fig. 9 shows how the voltage at the DC bus v dc of the 500 kW AEL system is kept close to the reference voltage V ref of the system, defined as 1000 V.Only during the first seconds after a frequency deviation, there is an oscillation in the DC voltage until a new steady state is reached.Furthermore, the dynamic of the AELs has been respected, as it is shown with the currents of each AEL i A1 and i A2 , and the consumed power P t .However, their slow response produces a significant overshoot in the frequency.In the case of the upward regulation, the maximum frequency deviation or nadir is 49.37 Hz, this is a 77% overshoot compare to the steady frequency of 49.64 Hz.For the downward regulation, the obtained nadir is 50.27Hz, and the overshoot is also 77%.
A 500 kW HHES, consisting of a 250 kW AEL and 250 kW PEMEL, is simulated to show its effective response for frequency regulation compared to the 500 kW AEL system.The simulation parameters are shown in Table III.Fig. 10 shows the HHES responding with upward and downward frequency regulation to the sudden connection and disconnection of the 500 kW load.The nadir in upward regulation is 49.56 Hz and the overshoot obtained is 23%.The same overshoot is obtained for downward regulation with a nadir of 50.08 Hz.In Fig. 10, this overshoot is compared with the 77% overshoot obtained in case of the 500 kW AEL system, represented by the grey curve.This overshoot reduction is accomplished as the response of the Fig. 9. Simulation results for a 500 kW AEL system providing upward and downward frequency regulation with a settling time of 4 s.

TABLE III
SIMULATION PARAMETERS FOR 500 KW HHES Fig. 10.Simulation results for a 500 kW HHES (blue curves).Comparison of the frequency evolution and consumed power with a 500 kW system based only on AELs (grey curves).Fig. 11.Simulation results for a 500 kW HHES with an AEL control settling time of 4 s (blue curves) and 8 s (red curves).Comparison of the DC voltage and electrolyzer currents when implementing the dynamic (solid lines) and static (dashed lines) electrolyzer models.
system is fast enough to follow the frequency deviation, as it is shown with the total consumed power P t .
Fig. 11 shows the DC response of the HHES for two cases with different AEL control settling times, and depending on the use of the static or dynamic electrolyzer models in the simulations.The fast dynamic of the overall system is due to the response of the PEMEL current i P to the fast component of the power variation, while the control settling time of 4 or 8 s of the AEL is respected.This is thanks to the proposed extended droop control with virtual resistors and capacitors, which also keeps the variation of DC bus voltage below its maximum limit ΔV max of 250 V.During the downward regulation, the PEMEL current surpasses its rated value.However, this overcurrent can be withstood due to the wide overloading range of these flexible devices [17].To achieve different AEL control settling times, the virtual capacitor C P of the PEMEL control can be varied to change the AEL control time constant τ .This is achieve by (8), without affecting the effectiveness of the control strategy.In addition, as the frequency dynamics of the grid are slower than PEMEL settling time, and the control strategy respects the settling time of the AEL, the differences between the use of static or dynamic electrolyzer models are negligible.This simplifies the modelling of electrolyzers for simulations, and experimental testing of the PEI of the system.
The use of HESSs for frequency regulation comes with some limitations in certain operating points.If the HESSs is working at full load, it is not possible to offer downward regulation.Similarly, when the system operates at minimum load, it cannot provide upward regulation.The use of ESSs, such as supercapacitors or batteries, could enhance the performance of the system in these scenarios.However, this implies an extra investment cost without increasing hydrogen production capabilities.Therefore, we focus on the combination of AEL with PEMEL as a more attractive solution for industries which main interest is hydrogen production for their industrial processes.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.The expansion of the system with PEMELs is the most relevant case, as the cost and reliability of this technology is expected to improve in the upcoming future.An expanded 1000 kW HHES with a new 500 kW PEMEL is presented.The new PEMEL is selected with double power and current.The parameters of this electrolyzer are obtained by considering it equal to two of the previous 250 kW electrolyzers connected in parallel.The virtual resistor R P 2 of this new PEMEL is half of the other ones, 0.5 Ω, by using (2).The virtual capacitors of all the PEMELs have to be calculated again by (18), obtaining 1.77 F for C P 1 and 3.55 F for C P 2 .The frequency regulation gain R f is doubled to 1000 kW/Hz following (11).
Fig. 12, shows the results for the expanded system.The frequency deviation is lower due to the increase of load providing frequency regulation, obtaining for the upward regulation a nadir of 49.69 Hz and steady frequency deviation of 49.734 Hz.The nadir for the downward regulation is 50.05Hz.However, in percentage, the overshoot in both situations is only slightly reduced to 19%.Therefore, the effectiveness of the system is the same.The response of each individual electrolyzer is equal to the one in the 500 kW HHES, but the new PEMEL has the double of current.
The simulations results show the effectiveness of the control strategy to provide fast response for frequency regulation, while reducing costs with the combination of PEMELs with AELs.Fig. 13.IEEE 9-bus power system, with two wind farms in bus 2 and 3, a HHES in bus 4, and a load suddenly connected in bus 6. Fig. 14.Simulation results for a 120 MW HHES system connected to a modified IEEE 9-bus system.Comparison of the frequency evolution and consumed power with a 120 MW system only based on AELs (grey curves).
The system has been tested for different AEL control settling times, obtaining the same effective results.As the control strategy respects the dynamics of the electrolyzers, the dynamic electrolyzer models can be simplified to the static ones for simulations, and for the experimental testing described in the following section.The high scalability of the system is also shown, maintaining the effective response when new devices are connected to the system, with the only modification of high-level control parameters.

B. Application to IEEE 9-Bus System
A modified IEEE 9-bus system is shown in Fig. 13 representing a large-scale low inertia power system.A SG is located in bus 1, while Wind Farms (WFs) without inertia are connected to bus 2 and 3. A 125 MW load is suddenly connected and disconnected to bus 6, causing a frequency deviation in the system.A 120 MW HHES is connected to bus 5 supporting the frequency regulation of the generators.This large-scale HHES is achieved by the easy scalability of the system, proven in the simulations with the simplified low inertia power system.In the previous simulations the time response of the HHES is fast enough to follow the frequency deviation of the system, and this is also considered to recreate its behaviour in the IEEE 9-bus system simulations, where only the AC side response of the HHES is modelled.
The simulation results are shown in Fig. 14, where they are compared to the connection of a 120 MW AEL system instead of the HHES.For the HHES, the nadir during the upward regulation is 49.35 Hz and the steady state deviation is 49.65 Hz, obtaining an overshoot of 28%.In the downward regulation the nadir is 50.32 Hz, with a slightly higher overshoot of 31%.This small increase in the overshoot is due to different dynamics of the IEEE 9-bus generator models for ramping up or down.In the case of the AEL system, the nadir during upward regulation is 49.35 Hz, and the steady state frequency deviation is 49.65 Hz, with an overshoot of 83%.During the downward regulation, the nadir is 50.11Hz and the overshoot is 90%.There is a similar reduction in the overshoot between the HHES and the AEL system that the one obtained with the simplified low inertia power system.Therefore, the conclusions about the effectiveness of fast response of HHESs for frequency regulation are also valid for large-scale power systems with low inertia and high penetration of renewable energies.

VI. EXPERIMENTAL RESULTS
A scale down experimental setup is built to validate the proposed control strategy of the HHES PEI.As shown in Fig. 15, the experimental set up consists of two DC/DC buck converters connected in the same bus to a DC/AC three-phase active rectifier.The buck converters are connected to bidirectional DC power supplies representing the electrolyzers, AEL and PEMEL, and the rectifier is connected to a grid simulator.The control strategy for the converters is implemented in the Imperix B-Box, which collects the measurements, and provides the switching signals to the converters.
In the previous section it was shown that with the proposed control strategy the dynamic electrolyzer models can be simplified to the static ones.Therefore, the bidirectional DC power supplies represent the electrolyzers by a voltage source and a total internal resistance.To enhance the dynamic representation of the AEL slower response, a limitation of the current slew rate is included in its DC power supply The parameters of the system are scaled down for the experimental set up, and are shown in Table IV.
The experimental results for the DC side of the system are shown in Fig. 16 for an AEL control settling time of 4 s.For the experiments, the grid is simplified to a strong grid where the system has no influence in the frequency.This frequency is modified with a step down and up of 5 Hz to show downward and upward frequency regulation.The results show how the PEMEL current i P is absorbing the fast component of the frequency step, while the slow response of the AEL current i A is respected.The voltage in the DC bus v dc is kept close to the voltage reference of 50 V considering the maximum voltage variation.Fig. 17 shows   the current in phase a of the AC side i a during the frequency step down.The amplitude of the current instantly changes with the step down in frequency, indicating that there is a step down in the power of the system.The decrease of frequency is also visible in the change of period of the signal.
The validation of the control strategy for a different AEL control settling time of 8 s is also performed.Figs.18 and 19 shows the respective results for the DC and AC side of the system.The PEMEL is still taking the fast component of the frequency step, but the AEL responds slower.The voltage in the DC bus is also kept close to the reference, and the phase current of the AC side shows the same behaviour as with the previous AEL control settling time.The expansion of the system is validated by including an extra PEMEL.The virtual capacitors of both PEMEL have to be updated considering (18) to 0.4 F. Fig. 20 shows the results of the DC side of the expanded system.The dynamics of the AEL are still respected with an AEL control settling time of 4 s, and the 2 PEMEL achieve the same response to compensate the slow dynamic of the AEL.
The experimental results validate the proposed decentralized power sharing control strategy for frequency regulation of HHES.The effectiveness of the method is not affect for different AEL control settling times, and allows an easy expansion of the system.The proposed control strategy is an effective solution to provide fast response for frequency regulation using HHESs, where the PEMELs absorbs the fast component of frequency deviations, and the costs are reduced with the combination with AELs.

VII. CONCLUSION
This paper proposes a decentralized dynamic power sharing control for frequency regulation using HHESs.The decentralized approach of the control strategy implies that, for each converter in the system, only local measurements are needed.This eliminates reliability problems of centralized systems such as single point of failure.The simulation results for a simplified low inertia power system shows a reduction of the frequency overshoot from 77% of an AEL system to 23% of a HHES.Similar results are obtained for a modified IEEE 9-bus system, with a reduction of the overshoot from 90% to 31%.This proves the effectiveness of the method in large-scale low inertia power systems with high penetration of renewable energies.Experiments shows how the PEMEL converters compensate the slow dynamics of the AEL converter when there is a sudden change of consumed power due to a frequency step in the grid.Therefore, the experimental testing of the HHES power electronics interface validates the control strategy and scalability of the system.The proposed control strategy makes use of the advantages of AELs and PEMELs to achieve fast response for frequency regulation with reduced costs, while respecting the slower dynamics of the AELs.Therefore, the proposed control strategy for HHESs facilitates the use of electrolyzers as flexible loads to support large-scale power systems with high penetration of renewable energies.

Fig. 8 .
Fig. 8. Per unit model of the synchronous generator with frequency regulation to model a low inertia power system.

Fig. 12 .
Fig.12.Simulation results for a 1000 kW HHES with an AEL control settling time of 4 s.The system is expanded from the 500 kW HHES, with a new PEMEL of 500 kW.

Fig. 16 .
Fig. 16.Experimental results of the DC side of the system with an AEL control settling time of 4 s.

Fig. 17 .
Fig. 17.Zoom in the experimental results of the AC side of the system with an AEL control settling time of 4 s.The step down of frequency occurs in the middle of the graph.

Fig. 18 .
Fig. 18.Experimental results of the DC side of the system with an AEL control settling time of 8 s.

Fig. 19 .
Fig. 19.Zoom in the experimental results of the AC side of the system with an AEL control settling time of 8 s.The step down of frequency occurs in the middle of the graph.

Fig. 20 .
Fig. 20.Experimental results of the DC side of the expanded system with an AEL control settling time of 4 s.
d A Duty cycle of the AEL DC/DC converter.d P Duty cycle of the PEMEL DC/DC converter.