Quantifying Grid-Forming Requirement for Electrolyzer-Based Hydrogen Production in Off-Grid Systems

Abstract

Off-grid renewable power-to-hydrogen (ReP2H) systems face stability and economic constraints driven by the variability of renewable resources. This paper presents a comparative analysis of grid-forming (GFM) service requirements under three approaches, i.e., centralized GFM battery energy storage system (BESS), GFM electrolyzers and coordinated multi-source GFM strategies. We first establish detailed GFM models for off-grid ReP2H systems under each approach and then conduct hardware-in-the-loop (HIL) real-time simulations. By evaluating both dynamic performance and cost, we identify the strengths and limitations of the three strategies and quantify the GFM capacity needed to ensure stable off-grid hydrogen production.

1. Introduction

In the green energy transition, renewable power-to-hydrogen (ReP2H) is regarded as a key pathway to achieving decarbonization across the electricity, energy and chemical industries [1,2], pointing towards critical applications in hard-to-abate sectors such as heavy transportation and industrial heating [3]. Driven by techno-economic concerns and policy incentives, ReP2H systems are required to integrate local renewable resources while limiting impacts on grid stability [4].

Despite advancements in solar-driven photocatalysis [5,6] and formic acid decomposition [7], water electrolysis remains the primary technology for green hydrogen. Its established maturity, zero carbon emissions and high product purity make it ideal for large-scale integration [8].

Off-grid ReP2H systems are particularly suitable for remote regions, islands and areas with weak grid connections, where they can use local low-cost wind and solar resources. Their independence from the grid, however, makes real-time power balance a central challenge. As a result, their design and operation must carefully reconcile economic efficiency with stable and reliable performance.

Most practical off-grid ReP2H projects use AC configurations [9], in which electrolyzers are directly coupled to wind and photovoltaic (PV) plants to form isolated 100% renewable networks [10]. These islanded systems must internally maintain voltage and frequency stability and continuously balance supply and demand [11,12,13]. Achieving these technical requirements while maximizing renewable utilization is critical to the economic viability of green hydrogen [14,15]. Recent studies mitigate renewable variability through advanced optimization and forecasting. Notably, Babay et al. [16] assessed green hydrogen production across diverse photovoltaic technologies.

In engineering practice, AC off-grid ReP2H systems commonly adopt a hybrid control architecture in which a battery energy storage system (BESS) operates in grid-forming (GFM) mode using a virtual synchronous machine (VSM) or voltage-frequency control. Other components, including wind turbines, PV inverters and electrolyzer rectifiers, typically operate in grid-following (GFL) mode and synchronize through phase-locked loops. This single-source GFM with multi-source GFL configuration remains the standard method for ensuring system stability.

BESS units are widely used in large-scale off-grid electrolyzer systems to improve renewable energy utilization [16,17]. Proper sizing and dispatch reduce curtailment and enhance energy-use efficiency. In practice, BESS can be deployed in centralized or distributed forms, but centralized configurations on the generation side are more common for smoothing renewable fluctuations and providing stable power delivery. Moreover, BESS units also frequently supply GFM support. For example, Sun et al. [18] proposed an enhanced VSM strategy that improves stability in low-inertia systems with storage constraints.

Recent research has also explored the GFM potential of electrolyzers. Tuinema et al. [19,20] developed a large-scale PEM electrolyzer model capable of contributing to frequency control. Wang et al. [21] analyzed the dynamic frequency response of alkaline electrolyzers, while Torres et al. [22] proposed a distributed power-sharing strategy for hybrid electrolyzer systems providing frequency regulation.

Beyond single-source GFM, multi-source coordinated strategies are gaining attention. Torres et al. [23] introduced a hybrid system integrating alkaline electrolyzers and supercapacitors, where supercapacitors address fast fluctuations and electrolyzers handle slower dynamics. Saha et al. [24] examined the use of multiple storage technologies to help electrolyzers meet grid requirements.

The recent literature addresses diverse hydrogen production challenges, beginning with reliability studies on fault diagnosis [25] and grid-forming services [26]. System planning advancements include optimal cost designs, dynamic balancing [27,28] and refined energy management strategies [29,30]. At the control level, research has improved capacitance modeling [31] while developing advanced DC/DC interfaces and rotational strategies [32,33]. Furthermore, studies have optimized efficiency, analyzed stability in weak grids and suppressed current ripples [34,35,36].

A broader set of related studies is summarized in

Table 1. Comparison of this work with previous studies on GFM services in hydrogen production.

Reference	System Configuration						Energy Support Provision	Real-Time Energy Balance Control
	Wind	PV	Off-Grid	On-Grid	ES	HE
2024 [9]	●	●	●	-	●	●	●	●
2023 [10]	-	●	●	-	-	●	-	●
2023 [11]	-	●	●	-	-	●	-	●
2022 [15]	-	●	●	-	-	●	-	-
2019 [18]	●	-	●	-	●	-	●	●
2023 [19]	-	-	-	●	-	●	●	-
2020 [20]	-	-	-	●	-	●	●	-
2025 [21]	●	-	●	●	●	●	●	●
2024 [22]	-	-	-	●	-	●	-	●
2025 [23]	-	●		●	●	●	-	●
2025 [25]	-	-	●	-	●-	●	-	●
2023 [26]	●	●	●	-	●	●	●	-
2023 [27]	-	●	●	●	●	●	●	●
2024 [28]	●	●	●	-	●	-	●	●
2023 [29]	-	-	-	●	-	●	-	●
2024 [30]	-	●	●	-	-	●	-	●
2023 [31]	-	-	-	●	-	●	●	-
2025 [32]	●	●	●	●	-	●	●	●
2025 [33]	●	-	●	-	-	●	●	●
2024 [35]	●	●	-	●	●	●	●	●
2025 [36]	-	●	●	-	-	●	●	●
2023 [37]	-	-	-	●	-	●	●	-
2024 [38]	-	●	●	-	-	●	-	●

“●” indicates included; “-” indicates not included.

. Overall, despite growing interest, the literature remains fragmented and does not fully address the system-level operation and design needs of large off-grid ReP2H facilities.

Building on these gaps, this paper focuses on analyzing the GFM capabilities of off-grid ReP2H systems. Section 2 introduces key principles and control schemes for GFM operation. Section 3 develops the modeling and optimization framework. Section 4 compares different GFM strategies through simulation and performance evaluation. The final section summarizes the main findings and outlines future research directions.

2. Analysis of GFM Control Principles and Strategies for Off-Grid ReP2H Systems

The stability of an off-grid ReP2H system requires establishing and maintaining internal voltage and frequency references. Unlike grid-connected configurations that rely on the external grid, off-grid systems must generate these references internally. This section outlines the fundamental principles of frequency and voltage control in off-grid electrolyzer systems and examines three GFM strategies.

2.1. Principles of Frequency and Voltage Control in Off-Grid ReP2H Systems

In an islanded system, frequency and voltage directly reflect the instantaneous balance of active and reactive power, as shown in Figure 1. Any mismatch between renewable generation and electrolyzer consumption causes deviations in these variables [37]. Surplus generation raises frequency and voltage, whereas a deficit lowers both. Maintaining stability, therefore, hinges on continuously matching power supply and demand.

Wind and PV output fluctuate rapidly, while electrolyzers, whose load changes are limited by electrochemical dynamics and controller response, cannot fully track fast variations. This mismatch creates a need for a dedicated GFM unit capable of supplying instantaneous power support [38]. The GFM units can be a single centralized BESS, electrolyzer with GFM control loops, or a combination of multiple GFM sources, which are introduced in Section 2.2, Section 2.3 and Section 2.4.

2.2. Solution Based on a Centralized Grid-Forming BESS

A common solution is to configure BESS as the system’s GFM unit. Rather than operating in the conventional GFL mode, the BESS runs in GFM mode using V/F droop control, acting similarly to a synchronous generator [9,15].

The BESS adjusts its voltage magnitude and frequency at the point of common coupling (PCC) based on deviations in its active and reactive power. During power imbalances, it rapidly absorbs or supplies power within its limits, providing the reference signals required for system-wide stability. The system structure is shown in Figure 2.

Despite its effectiveness, this centralized strategy has several limitations: (1) a single-point failure in the BESS can destabilize the entire system; (2) bidirectional energy transfer through the AC/DC converter increases losses; and (3) dedicated infrastructure adds engineering complexity, making deployment difficult in remote or constrained environments such as islands or high-altitude regions.

2.3. Solution Based on Grid-Forming Electrolyzers

Given the electrolyzer stack’s electrical double layer (EDL) effect, which enables fast energy buffers and load adjustments, recent work has investigated its potential to contribute to GFM services. Based on this idea, Dozein et al. [19] introduced the concept of a grid-forming electrolyzer by applying VSM control to the rectifier’s AC/DC converter.

Under this approach, the electrolyzer transitions from a passive GFL load to an active GFM unit. Through VSM control, the rectifier emulates synchronous machine dynamics to generate internal voltage and frequency references, enabling the electrolyzer to support system stability.

The VSM provides virtual inertia and damping. When a frequency deviation Δf occurs, the VSM provides a virtual inertia response by adjusting the active power consumption ΔP_stack of the electrolysis stack. Detailed modeling analysis can be found in Section 3.2.

However, the support duration is inherently limited by the small energy stored in the EDL capacitance, restricting effective operation to only a few seconds. In addition, electrochemical constraints, including gas–liquid separation, liquid level control and lye/water circulation, limit both the regulation range and ramp rate, making fast, large-scale power modulation impractical [19].

2.4. Composite Multi-Source Coordinated Grid-Forming Strategy

A third strategy places distributed batteries or supercapacitors on the DC bus of the electrolyzer rectifier to provide long-duration GFM support. This configuration includes three coordinated components inside the hydrogen electrolyzer: (1) an AC/DC control stage uses a VSM control framework, (2) an energy storage branch serves as the energy buffer, and (3) an electrolyzer branch that produces hydrogen. Through frequency-based power sharing, these elements coordinate across multiple timescales, enhancing both dynamic response and long-term stability. Detailed modeling appears in Section 3.

This approach enables sustained, stable hydrogen production, but practical deployment remains challenging. Key issues include selecting appropriate energy-storage technologies, sizing them relative to electrolyzer capacity and managing the added control complexity [39].

Each of the three GFM strategies offers distinct strengths and limitations. The following sections develop detailed models for each approach, followed by comparative analysis and verification.

3. Modeling and Optimization of GFM Capability in Off-Grid ReP2H Systems

3.1. Modeling of Centralized BESS Grid-Forming Control

In off-grid ReP2H systems, GFM control provides voltage support and virtual inertia by emulating the behavior of a synchronous generator. Among available methods, VSM control is widely adopted and is particularly suitable for BESS-based GFM operation.

VSM control reproduces the rotor motion and excitation mechanisms of a synchronous generator. Active power-frequency control is governed by the virtual inertia J and damping coefficient D, while reactive power-voltage control regulates the output voltage through reactive power deviations. If the DC-side voltage is assumed to be constant, the VSM model is derived from the power balance relationship.

The active power loop simulates primary frequency regulation:

$$J{\displaystyle \frac{d\Delta \omega }{dt}}=P_{\mathrm{ref}}-P-D\Delta \omega ,$$

(1)

where Δω is the angular frequency deviation, and P_ref and P are the reference active power and the measured active power, respectively.

Equation (1) reflects the inertial response of the VSM. The virtual inertia J mitigates the frequency change by momentarily storing or releasing kinetic energy, while the damping coefficient D suppresses oscillations. The state-space form follows:

$${\displaystyle \frac{d}{dt}}\left[\begin{array}{c}\Delta \omega \\ \theta \end{array}\right]=\left[\begin{array}{cc}-{\displaystyle \frac{D}{J}}& 0\\ 0& -{\displaystyle \frac{1}{J}}\end{array}\right]\left[\begin{array}{c}\Delta \omega \\ \theta \end{array}\right]+\left[\begin{array}{c}0\\ 1\end{array}\right](P_{\mathrm{ref}}-P),$$

(2)

where θ is the voltage phase angle, which is generated by integration and used for converter modulation.

Voltage support is achieved through reactive power droop control:

$$V=V_{\mathrm{ref}}+K_{\mathrm{q}}(Q_{\mathrm{ref}}-Q),$$

(3)

where V and V_ref are the output voltage and reference voltage, respectively; K_q is the reactive power droop coefficient; and Q_ref and Q are the reference reactive power and the measured value. This strategy enables the VSM to automatically adjust the voltage in response to load changes, mimicking the excitation control of a synchronous machine.

The overall architecture of the VSM control is shown in Figure 3, where the active power-frequency control simulates the mechanical equation and the reactive power-voltage control simulates the electromagnetic equation.

Centralized BESS-based GFM can be implemented on the grid-side converter and significantly improves system stability. Next, we model the ES-side power electronics. The ES branch uses a bidirectional DC/DC converter operating in Buck or Boost mode, as shown in Figure 4.

For charging (Buck mode):

$$V_{\mathrm{buck}}=D_{\mathrm{buck}}\cdot V_{\mathrm{dc}}\hspace{1em} (0<D_{\mathrm{buck}}<1),$$

(4)

where D_buck is the duty cycle of the Buch switch S₂. The charging power is as follows:

$$P_{\mathrm{charge}}=V_{\mathrm{buck}}\cdot I_{\mathrm{buck}}={\displaystyle \frac{V_{\mathrm{dc}}^2\cdot D_{\mathrm{buck}}^2}{R_{\mathrm{charge}}}},$$

(5)

where I_buck is the charging current, and R_charge represents the equivalent resistance of the charging path.

For discharging (Boost mode):

$$V_{\mathrm{dc}}={\displaystyle \frac{V_{\mathrm{boost}}}{1-D_{\mathrm{boost}}}},\hspace{1em}(0<D_{\mathrm{boost}}<1),$$

(6)

where D_boost is the duty cycle of the Boost switch S₁. The discharge power is as follows:

$$P_{\mathrm{discharge}}=V_{\mathrm{boost}}\cdot I_{\mathrm{boost}}={\displaystyle \frac{V_{\mathrm{dc}}^2\cdot (1-D_{\mathrm{boost}})\cdot D_{\mathrm{boost}}}{R_{\mathrm{discharge}}}},$$

(7)

where I_boost is the discharge current, and R_discharge represents the equivalent resistance of the discharge path. R_charge and R_discharge primarily consist of the parasitic resistance of the inductor (R_b, corresponding to R_edg in

Table 2. System and control parameters in the simulation.

Stack	Value	Unit	Circuit	Value	Unit
Cdl	0.02	F/cm2	Vdc	1000	V
Urev	1.228	V	Cdc	50	mF
Rohm	1.1918	Ω/cm2	fref	50	Hz
Iexchange	0.0015	A/cm2	Lbuck	25	mH
Ncell	445	-	Vacref	35/1	kV
area	15,000	cm2	Vdroop	0.9697	V
Kact	0.1521	-	Redge	0.0009	Ω
			Eon	40	mJ
			Eoff	100	mJ
			Ileak	5	mA

) and the internal resistance of the battery pack.

The ES-side circuit dynamics are as follows:

$$\left\{\begin{array}{l}{L}_{\mathrm{b}}{\displaystyle \frac{d{i}_{\mathrm{b}}}{dt}}=D_{\mathrm{b}}{V}_{\mathrm{bat}}-V_{\mathrm{dc}}-i_{\mathrm{b}}{R}_{\mathrm{b}}\hfill \\ C_{\mathrm{dc}}{\displaystyle \frac{d{V}_{\mathrm{dc}}}{dt}}=i_{\mathrm{s}}-i_{\mathrm{L}\_\mathrm{b}}-i_{\mathrm{b}}-{\displaystyle \frac{V_{\mathrm{dc}}}{R_{\mathrm{load}}}}\hfill \end{array}\right.,$$

(8)

where L_b, R_b, i_b, V_bat, i_s, I_{L_b} and R_load denote the inductance, resistance, ES current, terminal voltage, bus current, inductor current and load resistance of the ES-side circuit, respectively.

The external voltage loop stabilizes the DC bus voltage V_dc and sets the BESS reference current I_{bat_ref}:

$$I_{\mathrm{bat}\_\mathrm{ref}}=K_{\mathrm{p}1}\left(V_{\mathrm{dc}\_\mathrm{ref}}-V_{\mathrm{dc}}\right)+K_{i1}{\displaystyle \int \left(V_{\mathrm{dc}\_\mathrm{ref}}-V_{\mathrm{dc}}\right)}dt,$$

(9)

where V_{dc_ref} is the voltage reference; K_p1 and K_i1 are PI gains of the voltage loop of the ES-side circuit.

The internal current loop tracks the I_bat through duty cycle modulation as follows:

$$D_{\mathrm{b}}=K_{\mathrm{p}2}\left(I_{\mathrm{bat}\_\mathrm{ref}}-V_{\mathrm{dc}}\right)+K_{i2}{\displaystyle \int \left(I_{\mathrm{bat}\_\mathrm{ref}}-i_{\mathrm{b}}\right)}dt,$$

(10)

where D_b is the duty cycle of the ES-side circuit; K_p2 and K_i2 are the current loop gains of the ES-side circuit, which are tuned to achieve a fast response while limiting the rate of transient change.

3.2. Modeling of Electrolyzer Grid-Forming Control

Electrolyzers can also provide GFM support by introducing virtual inertia at their power-electronic interface. The unified dynamic model proposed by Dozein et al. [19] applies to both AEL and PEMEL systems, accounting for nonlinear stack behavior and thermal dynamics, as shown in Figure 5.

The virtual inertia response is described by a second-order transfer function:

$$G_{\mathrm{v}i}(s)={\displaystyle \frac{\Delta {\theta }_{\mathrm{m}}}{\Delta P_{\mathrm{stack}}}}={\displaystyle \frac{2H_{\mathrm{v}i}}{s^2}},$$

(11)

where H_vi is the virtual inertia coefficient. This component simulates rotor motion of the synchronous generator, but since its inherent damping is zero, it may lead to frequency oscillations.

To suppress these oscillations, a proportional damping term k_vd, is introduced. The output of the damping loop is proportional to the frequency deviation Δω:

$$\Delta {\theta }_d=k_{\mathrm{vd}}\cdot \Delta \omega ,$$

(12)

$$\Delta \omega =2\pi \cdot \Delta f,$$

(13)

where Δf is the frequency deviation.

Combining the virtual inertia loop and the damping loop yields the phase reference:

$${\theta }_m={\displaystyle \int \left(\frac{2H_{vi}}{s}\cdot \Delta P_{\mathrm{stack}}+k_{vd}\cdot \Delta \omega \right)}dt,$$

(14)

where the internal voltage magnitude V_m is adjusted according to the reactive power control loop.

The grid-side converter employs cascaded dq-axis current control to ensure terminal voltage tracking. The current controller parameters are designed based on the closed-loop transfer function to satisfy response time requirements.

In response to DC-link energy imbalance caused by AC/DC adjustments, the DC-DC converter of the electrolyzer utilizes cascaded voltage-current control, where the PI controller is tuned based on the electrolyzer’s parameters.

The electrolysis stack is modeled by the equivalent circuit in Figure 6. The total voltage of the stack is the sum of three components: the activation overpotential, the ohmic overpotential and the foundational reversible overvoltage U_rev [32]. U_rev is determined by the Gibbs free energy change associated with the water-splitting reaction:

$$U_{\mathrm{rev}}={\displaystyle \frac{\Delta G}{2F}}+{\displaystyle \frac{RT}{2F}}\ln \left({\displaystyle \frac{p_{{\mathrm{H}}_2}\sqrt{p_{{\mathrm{O}}_2}}}{a_{{\mathrm{H}}_2\mathrm{O}}}}\right),$$

(15)

where p_H2 and p_O2 are the partial pressures of hydrogen and oxygen; R is the gas constant; a_H2O is the activity of water; T is the stack temperature; and F is the Faraday constant.

The activation overpotential U_act models the voltage loss associated with the electrochemical reaction’s potential barrier and is commonly approximated by the following modified Tafel equation:

$$U_{\mathrm{act}}={\nu }_1\ln \left({\displaystyle \frac{I}{S{\nu }_2}}+1\right),$$

(16)

where v₁ and v₂ are temperature-dependent parameters; S is the effective electrode area; and I is the electrolysis current.

The ohmic overvoltage U_ohm represents the voltage drop across the internal resistance, and it is expressed as follows:

$$U_{\mathrm{ohm}}=I·R_{\mathrm{ohm}},$$

(17)

Summing up the above, the total electrolysis voltage U_stack is given by:

$$U_{\mathrm{stack}}=U_{\mathrm{rev}}+U_{\mathrm{act}}+U_{\mathrm{ohm}}.$$

(18)

Beyond the steady-state voltage components, the dynamic behavior is dominated by the EDL effect, which arises from charge accumulation at the electrode–electrolyte interface [19,32]. The resulting capacitance C_dl exhibits the following dynamic characteristics:

$$C_{\mathrm{dl}}{\displaystyle \frac{d{U}_{\mathrm{dl}}}{dt}}=I-I_{\mathrm{act}},$$

(19)

$$I_{\mathrm{act}}={\displaystyle \frac{U_{\mathrm{act}}}{R_{\mathrm{act}}}},$$

(20)

$$R_{\mathrm{act}}={\displaystyle \frac{d{U}_{\mathrm{act}}}{dI}},$$

(21)

where I_act is the current flowing through the activation resistance, and R_act represents its dynamically linearized value.

The circuit of the electrolyzer branch is composed of a buck circuit and an electrolysis stack, as shown in Figure 7.

The electrolysis power is regulated by the duty cycle D_stack of the DC/DC converter, as follows:

$$\left\{\begin{array}{l}L{\displaystyle \frac{d{i}_{\mathrm{L}\_\mathrm{stack}}}{dt}}=D_{\mathrm{stack}}{V}_{\mathrm{dc}}-V_{\mathrm{stack}}-i_{\mathrm{L}\_\mathrm{stack}}{R}_{\mathrm{L}\_\mathrm{stack}}\hfill \\ C{\displaystyle \frac{d{V}_{\mathrm{stack}}}{dt}}=i_{\mathrm{L}\_\mathrm{stack}}-I_{\mathrm{stack}}=i_{\mathrm{L}\_\mathrm{stack}}-{\displaystyle \frac{V_{\mathrm{stack}}}{R_{\mathrm{act}}}}\hfill \end{array}\right.,$$

(22)

where i_{L_stack} and I_stack are the inductor current and stack current, respectively; L_stack is the inductor; R_{L_stack} is the parasitic resistance of the inductor; and C is the output capacitance.

To compensate for the significant response latency introduced by the EDL effect, which can be as long as tens of seconds [19], a dual-loop control is implemented. The outer loop calculates stack current reference I_ref based on the power reference P_{ref_stack} as follows:

$$I_{\mathrm{ref}\text{\_}\mathrm{stack}}=P_{\mathrm{ref}\text{\_}\mathrm{stack}}/U_{\mathrm{stack}},$$

(23)

Following (23), the converter in the electrolyzer branch regulates the outer power loop and the inner current loop. The power loop tracks the power demand P_L:

$$\begin{array}{l}{I}_{\mathrm{ref}\text{\_}\mathrm{stack}}={\displaystyle \frac{P_{\mathrm{L}}}{V_{\mathrm{stack}}}}+\hspace{0.17em}{K}_{\mathrm{p}}\left(P_{\mathrm{L}}-V_{\mathrm{stack}}{i}_{\mathrm{L}\text{\_}\mathrm{stack}}\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+K_i{\displaystyle \int \left(P_{\mathrm{L}}-V_{\mathrm{stack}}{i}_{\mathrm{L}\text{\_}\mathrm{stack}}\right)}dt\end{array},$$

(24)

where K_p and K_i are the PI gains of the power loop.

The inner loop uses PI control to track I_{ref_stack}, generating the duty cycle D_ref:

$$D_{\mathrm{ref}}=K_{\mathrm{p}3}\left(I_{\mathrm{ref}\_\mathrm{stack}}-I_{\mathrm{stack}}\right)+K_{i3}{\displaystyle \int \left(I_{\mathrm{ref}\_\mathrm{stack}}-I_{\mathrm{stack}}\right)}dt,$$

(25)

where K_p3 and K_i3 are the PI gains of the inner current loop, respectively.

To actively release the EDL energy for fast active power support, the duty cycle D_ref can be rapidly increased to boost the stack inductor current i_{L_stack}, thereby discharging the EDL capacitance and providing a quick power boost.

To suppress high-frequency disturbances in the EDL voltage V_dl and reduce electrode stress, a feedforward term is added through the linearization of the inductor equation:

$$L{\displaystyle \frac{d{i}_{\mathrm{L}\_\mathrm{stack}}}{dt}}\approx V_{\mathrm{dc}}\Delta D-\Delta V_{\mathrm{stack}},$$

(26)

$$\Delta D=K_{\mathrm{ff}}\cdot {\displaystyle \frac{d{V}_{\mathrm{dl}}}{dt}},$$

(27)

Combining this with (26), we observe that V_stack ≈ V_dl at high frequencies. Therefore, the feedforward gain is as follows:

$$K_{\mathrm{ff}}=-{\displaystyle \frac{L_{\mathrm{stack}}}{V_{\mathrm{dc}}}}.$$

(28)

Therefore, the corrected duty cycle output is expressed as follows:

$$D^{\prime }=D_{\mathrm{ref}}+\Delta D.$$

(29)

However, electrolyzer-based GFM is inherently energy limited due to finite EDL storage and slow electrochemical response, especially in AEL systems. This limitation leads to the idea of a mixed configuration, as presented in Section 3.3.

3.3. Modeling of Composite Multi-Source Coordinated Grid-Forming Control

In the composite strategy, the BESS, electrolyzer and AC/DC converter jointly form the grid as shown in Figure 8. The BESS is connected directly to the electrolyzer DC bus and a modified VSM control framework enables self-synchronization through DC bus capacitance.

The ES and stack models follow Section 3.1 and Section 3.2. Here, we focus on the AC/DC link. Following [40], DC bus voltage dynamics provide virtual inertia:

$$C_{\mathrm{dc}}{\displaystyle \frac{d{V}_{\mathrm{dc}}}{dt}}=I_{\mathrm{dc}}-I_{\mathrm{bat}},$$

(30)

where C_dc is the DC bus capacitance; V_dc is the DC bus voltage; I_dc is the current injected by the AC/DC converter; and I_bat is the ES current. By controlling I_dc, the following rotor dynamics can be simulated:

$$J{\displaystyle \frac{d\omega }{dt}}=T_{\mathrm{m}}-T_{\mathrm{e}}-D\omega .$$

(31)

When the system frequency undergoes a sudden change, the DC bus capacitance C_dc instantaneously regulates the DC bus voltage V_dc according to (30). The VSM converts the DC voltage deviation $\mathsf{\Delta }$V_dc into a frequency regulation signal ω* by simulating the generator rotor dynamics, as follows:

$${\omega }^{*}={\omega }_0+K_J{\displaystyle \int \Delta }{V}_{\mathrm{dc}}dt+K_{\mathrm{D}}\Delta V_{\mathrm{dc}},$$

(32)

where K_J is the virtual inertia coefficient; K_D is the virtual damping coefficient; and ω₀ is the rated angular frequency.

The AC/DC control based on DC bus capacitance dynamics is realized within the GFM control strategy module shown in Figure 9.

In this module, the active power reference is adjusted according to the DC voltage deviation, thereby implementing the power–voltage droop characteristic:

$$P_{\mathrm{ref}}=P_0+K_{\mathrm{droop}}\left(V_{\mathrm{dc}}^{*}-V_{\mathrm{dc}}\right),$$

(33)

where P₀ is the initial set point, specified by the higher-level Energy Management System (EMS); K_droop is the droop coefficient; and V_dc* and V_dc are the rated and actual DC bus voltages of the composite multi-source coordinated GFM circuit.

Subsequently, the frequency regulation signal is derived via dynamic capacitance feedback:

$$\Delta \omega ={\displaystyle \frac{1}{K_{J}s+K_{\mathrm{D}}}}(P_{\mathrm{ref}}-P_{\mathrm{e}}),$$

(34)

where P_e is the rated power.

The phase angle θ is obtained by integration. This, combined with the voltage reference from the reactive power loop, enables precise AC/DC converter modulation for autonomous GFM control.

While this strategy enables longer-term support by coordinating multiple sources, practical deployment requires further refinement of the coordination controller design and capacity allocation.

3.4. Optimal Sizing Principles and Feasibility Constraints

Capacity optimization aims to balance economy, stability and operational continuity while maintaining voltage and frequency within limits at all times. These principles serve as a theoretical basis for the capacity ratio analysis in Section 4.3.

The levelized cost of hydrogen (LCOH) serves as the main economic objective:

$$\mathrm{LCOH}={\displaystyle \frac{C_{\mathrm{init}}+C_{O\&M}^{\mathrm{fixed}}+C_{O\&M}^{\mathrm{var}\mathrm{i}}}{M^{{\mathrm{H}}_2}}},$$

(35)

where C_init is the annualized investment cost; C_O&M is the operation and maintenance cost; and M^H2 is the annual hydrogen yield.

The annualized investment cost C_init is calculated using the Capital Recovery Factor (CRF) [9]:

$$C_{\mathrm{init}}={\displaystyle \sum _{\mathrm{j}\in \Omega }C}RF(r,T_{\mathrm{j}})\cdot S_{\mathrm{j}}\cdot c_{\mathrm{j}}^{\mathrm{unit}},$$

(36)

$$CRF(r,T_{\mathrm{j}})={\displaystyle \frac{r{(1+r)}^{T_{\mathrm{j}}}}{{(1+r)}^{T_{\mathrm{j}}}-1}}$$

(37)

where Ω = {PV, electrolyzer, BESS}, j is the capacity; $c_{\mathrm{j}}^{\mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}}$ is the unit capital cost; T_j is the lifetime (set to 20 years for the project); and r is the discount rate, set at 8%.

The O&M costs consist of fixed and variable components. The fixed annual O&M cost is estimated as a percentage of the initial investment:

$$C_{O\&M}^{\mathrm{fixed}}={\displaystyle \sum _{\mathrm{j}\in \Omega }{\lambda }_{\mathrm{j}}}\cdot S_{\mathrm{j}}\cdot c_{\mathrm{j}}^{\mathrm{unit}}$$

(38)

where ${\lambda }_{\mathrm{j}}$ is the O&M ratio (set at 2%). The variable cost primarily accounts for BESS replacement due to degradation:

$$C_{O\&M}^{\mathrm{vari}}={\displaystyle \sum _{k=1}^{K_{\mathrm{rep}}}{S}_{\mathrm{BESS}}}\cdot c_{\mathrm{BESS}}^{\mathrm{rep}}\cdot {(1+r)}^{-k\cdot T_{\mathrm{life}}/(K_{\mathrm{rep}}+1)}$$

(39)

where $c_{\mathrm{B}\mathrm{E}\mathrm{S}\mathrm{S}}^{\mathrm{r}\mathrm{e}\mathrm{p}}$ is the replacement cost, and K_rep is the number of replacements derived from the battery degradation model.

Finally, according to the empirical data, the unit prices of PV, electrolyzer and BESS are set as 4000 CNY/kW, 3500 CNY/kW and 1500 CNY/kWh.

The optimal ES size is primarily evaluated via the ES capacity ratio, defined as the ratio of the rated capacity of the ES to the total system power capacity. Minimizing this ratio while maintaining stability is the immediate goal of the optimization:

$${\rho }_{\mathrm{BESS}}={\displaystyle \frac{S_{\mathrm{BESS}}}{P_{\mathrm{total}}}}\times 100\%,$$

(40)

where S_BESS is the ES capacity, and P_total is the total system power.

In addition, three constraints must be satisfied: (1) GFM ability; (2) continuous operation capability under emergency; and (3) long-term energy balance. Verification of these three constraints is based on maintaining voltage and frequency stability at the PCC. Instantaneous stability is enforced by voltage and frequency limits at the PCC:

$$\left\{\begin{array}{l}{f}_{\min }^{\mathrm{PCC}}\le f_{\Delta t_{\mathrm{sim}}}^{\mathrm{PCC}}\le f_{\max }^{\mathrm{PCC}}\\ V_{\min }^{\mathrm{PCC}}\le V_{\Delta t_{\mathrm{sim}}}^{\mathrm{PCC}}\le V_{\max }^{\mathrm{PCC}}\end{array}\right.,$$

(41)

where $f_{\mathrm{m}\mathrm{i}\mathrm{n}}^{\mathrm{P}\mathrm{C}\mathrm{C}}$ and $f_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{P}\mathrm{C}\mathrm{C}}$ are minimum and maximum frequency deviation at the PCC, and $V_{\mathrm{m}\mathrm{i}\mathrm{n}}^{\mathrm{P}\mathrm{C}\mathrm{C}}$ and $V_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{P}\mathrm{C}\mathrm{C}}$ are minimum and maximum voltage deviation at the PCC.

A simulation-based iterative sizing algorithm determined the optimal capacity ratios in

Table 3. Comparison of optimal ES capacity ratio and economic metrics for three grid-forming strategies.

Type	Voltage Range (p.u.)	Frequency Deviation (Hz)	ES Proportion (%)	LCOH (CNY/kg)
GFM BESS strategy	±6–±12%	±0.6–±1.1	36	33.212
GFM electrolyzer strategy	±9.5–±15%	±1.1–±1.9	20	29.750
Composite multi-source coordinated GFM strategy	±3–±5%	±0.3–±0.5	16	25.458

. Unlike weighted multi-objective optimization, this approach treats system stability as a hard constraint. The process minimizes ES capacity subject to the voltage and frequency limits in Equation (41), as illustrated in Figure 10.

Figure 10 illustrates the descent search logic, which initializes with a large ES capacity to ensure stability. Capacity is iteratively reduced by 0.2 MW and 0.2 MWh while simulations monitor for voltage or frequency collapse under worst-case fluctuations. The process terminates when constraints are violated, selecting the previous iteration as the minimum viable size. This approach identifies the most economical solution that strictly satisfies safety margins.

The resulting capacity ratios offer a feasible baseline but may not be globally optimal. Further refinement of optimization algorithms remains an important direction for future work. Capacity results for the three GFM strategies are analyzed in Section 4.3.

4. Comparative Verification Analysis and Optimized Sizing of GFM Strategies

This section compares the three GFM strategies introduced earlier using simulation experiments and evaluates the optimal capacity ratio between the ES unit and the hydrogen electrolyzers. The case study setup is described below.

4.1. Simulation Setup and Verification Platform

To assess system performance under each GFM strategy, a 5 MW off-grid HE unit is directly coupled with a 5 MW grid-following PV unit. The 5 MW capacity represents a standard industrial electrolysis block. Large-scale systems typically aggregate these units in parallel through a modular design. As the proposed GFM strategies rely on local terminal measurements rather than high-speed central communication, they inherently support such modular scalability. The component models are obtained from [9]. Key parameters are listed in Table 2.

Verification is carried out on the HIL testbed shown in Figure 11. The plant model runs on an MT8020 real-time simulator (StarSim platform, manufactured by Shanghai Modeling Tech Energy Technology Co., Ltd., Shanghai, China) with a 1 μs time step. Control algorithms are executed on a TMS320C28346 DSP at 10 kHz, and a Xilinx XC6SLX16 FPGA (both supplied by Nanjing Ruidu Youte Information Technology Co., Ltd., Nanjing, China) performs PWM generation and IGBT gating. Dynamic responses of the three strategies are evaluated under multiple scenarios, including different levels of power fluctuation and emergencies such as ES branch disconnection, with focus on V/F stability, response speed and reliability.

Electrolyzer Materials and Specifications

To ensure reproducibility, simulation parameters derive from a standard commercial atmospheric AEL. The anodes employ nickel-plated steel or nickel-cobalt spinel coatings to withstand the oxygen evolution reaction, while the cathodes utilize Raney nickel or activated nickel-molybdenum alloys to enhance hydrogen evolution reaction kinetics. A Zirfon composite or polyphenylene sulfide fabric models the separator, preventing gas crossover while enabling hydroxide ion conductivity.

The system operates with a 30 wt% potassium hydroxide solution at 70 to 80 °C. These material characteristics directly determine the activation and ohmic overpotential parameters listed in Table 2.

4.2. Comparative Performance of the GFM Strategies

To comprehensively test the dynamic performance of the three GFM strategies under realistic conditions, a representative renewable energy output scenario, shown in Figure 12, is used as the primary output of the PV unit, which operates in GFL control. Babay et al. [16] analyzed nine years of meteorological data to highlight the impact of seasonal fluctuations. Since the upper-level energy management system typically manages these long-term variations via power setpoints, this study focuses on millisecond to second dynamic stability. The scenarios include periods of high fluctuation, rapid power decline and high power scenarios, allowing for a thorough assessment of each strategy’s ability to maintain system stability.

4.2.1. Centralized BESS-Based GFM Solution

The BESS-based VSM control is evaluated. Figure 13a,b shows that under fluctuating and rapidly declining PV output, the centralized BESS can quickly adjust its power to maintain the DC bus voltage within a narrow range. The stack voltage also remains stable, ensuring uninterrupted electrolysis. These results confirm that the BESS provides effective virtual inertia and damping against power imbalance.

However, Figure 13c reveals a key drawback. When the ES branch is lost, the system immediately loses its only V/F support source, causing large DC bus oscillations and eventual system collapse. This validates the single-point failure risk of centralized BESS-only GFM control noted in Section 2.2.

4.2.2. GFM Electrolyzer-Based Solution

Figure 14 shows the response of the ReP2H system when the electrolyzer provides GFM support. The VSM-controlled stack delivers a fast virtual inertia response by adjusting its power consumption ΔP_HE during the initial disturbance, helping suppress the rate of frequency change.

However, both the stack voltage V_stack and DC bus voltage V_dc exhibit persistent and considerable fluctuations. The limited energy stored in the EDL capacitors allows support only for a few seconds, after which the system becomes unable to handle sustained disturbances. In addition, the stack’s chemical nature restricts the speed and range of power regulation. As a result, the electrolyzer alone cannot reliably provide full GFM capability.

4.2.3. Composite Multi-Source Coordinated GFM Solution

Figure 15a,b demonstrates that the composite strategy maintains stable DC bus and stack voltages across both fluctuating and rapidly declining PV scenarios. Oscillations remain small because the BESS, electrolyzer and DC bus capacitor jointly participate in regulation.

To ensure stability with 16% BESS capacity, the control response time must satisfy the theoretical limit dictated by DC link dynamics. The critical time τ_limit for preventing voltage collapse during a maximum power step ΔP_max is determined by the DC capacitance C_dc and the minimum allowable DC voltage V_min:

$${\tau }_{\mathrm{limit}}\approx {\displaystyle \frac{C_{\mathrm{dc}}(V_{\mathrm{nom}}^2-V_{\min }^2)}{2\cdot \Delta P_{\max }}}.$$

(42)

Assuming a worst-case 5 MW power step, a 10% voltage drop tolerance and system parameters of C_dc = 50 mF and V_nom = 1000 V, the calculated limit τ_limit is approximately 1.9 ms. Since the proposed control system operates at 10 kHz (0.1 ms time step), significantly faster than this physical limit (0.1 ms $\ll$ 1.9 ms), it theoretically guarantees stability against rapid fluctuations.

This coordinated response also reduces the frequency of large electrolyzer adjustments, benefiting the lifetime.

Moreover, in the ES branch disconnection scenario shown in Figure 15c, the system remains operational. Although some voltage oscillations occur, the DC bus quickly settles to a new stable point. The converter’s self-synchronization mechanism and the electrolyzer branch provide additional V/F support, eliminating single points of failure and improving overall system reliability.

Furthermore, system stability relies on the DC bus capacitance C_dc to provide virtual inertia, as modeled in Equations (30)–(32). Sensitivity analysis indicates that C_dc is critical for limiting the initial rate of change in frequency during transients; values below 20 mF risk voltage collapse before control loops engage, whereas 50 mF offers a sufficient inertial buffer. Notably, while increasing C_dc enhances transient support and reduces dynamic stress on the BESS, it cannot replace the BESS capacity S_BESS, which is dictated by the long-term energy balance required for frequency stability.

4.3. Optimal ES–HE Capacity Ratio

The ES-to-HE capacity ratio strongly affects economic performance and operational stability. Using the criteria in Section 3.4, the LCOH and life-cycle cost (LCC) for each strategy are summarized in Table 3.

Table 4. Sensitivity analysis of stability metrics of different ES capacity ratios under high fluctuation scenario.

Strategy	Es Capacity Ratio (%)	Max Frequency Deviation (Hz)	Max Voltage Deviation (V)	Stability Check
GFM BESS strategy	30%	±1.53	±14%	Fail
	34%	±1.15	±12.5%	Fail
	36%	±1.08	±12%	Pass
	40%	±0.92	±10%	Pass
GFM electrolyzer strategy	16%	±2.15	±18%	Fail
	18%	±1.35	±16.5%	Fail
	20%	±1.10	±15%	Pass
	22%	±0.85	±12.5%	Pass
Composite multi-source coordinated GFM strategy	12%	±0.85	±8%	Fail
	14%	±0.62	±6%	Fail
	16%	±0.48	±5%	Pass
	18%	±0.40	±4.7%	Pass

presents the sensitivity analysis of the stability metrics across the three strategies near their critical thresholds.

4.3.1. ES Capacity Requirements

According to Figure 13, Table 3 and Table 4, the ES capacity must cover extreme power fluctuations and N-1 emergency scenarios. Simulation results show that the centralized BESS strategy requires a minimum 36% capacity ratio to maintain frequency stability. For the GFM electrolyzer, limited electrical double layer energy necessitates 20% supplemental capacity to prevent voltage collapse, despite the virtual inertia provided by VSM control. In contrast, the composite strategy maintains frequency limits with only 16% capacity. Since exceeding these thresholds increases costs without strict necessity, the values in Table 3 represent the optimal minimum required to satisfy hard stability constraints.

For the GFM electrolyzer strategy, the short support duration of the EDL leads to relatively large V/F deviations, as shown in Table 3. Maintaining stable operation, therefore, requires additional ES support, commonly from supercapacitors or other fast-response devices [8,29]. The required ES proportion is estimated at 20%.

Table 3 shows that the composite strategy achieves tighter V/F control and, because of coordinated energy sharing, requires the smallest ES proportion at 16%. However, the composite strategy involves multiple conversion stages and requires higher ratings for the grid-forming interface. Specifically, the main converter must handle the full electrolyzer power flow to provide support, necessitating a 100% peak rating of 5 MW. In contrast, the centralized BESS approach limits grid-forming operation to the battery converter (rated at 36% or 1.8 MW) and utilizes a standard grid-following rectifier for the electrolyzer. This requirement for higher capacity converters increases hardware investment for the composite strategy.

4.3.2. LCOH and Life-Cycle Cost Analysis

For the centralized GFM BESS strategy, the LCOH is 33.212 CNY/kg. The ES degradation is evaluated using a semi-empirical model that integrates calendar and cycle aging, with the latter being significantly influenced by depth of discharge and discharge rates. Based on the simulation, the ES degradation rate is about 4.87% annually [9]. Considering an end-of-life criterion of 20% capacity fade, the effective battery lifespan is approximately 4.1 years. Therefore, with five replacement cycles over the 20-year line span of the ReP2H project, total LCC increases by roughly 0.6 million CNY.

The GFM electrolyzer strategy lowers LCOH because it does not rely on a dedicated BESS. In practice, however, supplemental ES, such as supercapacitors, is typically added to enhance stability and compensate for limited EDL capacitance and its energy buffering ability [22]. The resulting LCOH is 29.750 CNY/kg.

The composite coordinated strategy yields the lowest LCOH at 25.458 CNY/kg by optimizing ES-HE capacity allocation [9,33], as shown in Table 3. Nonetheless, variations in ES device selection across studies make long-term replacement rates uncertain, and the more complex control requires higher inverter capacity, raising equipment costs.

Reliability improvements provide significant economic value as quantified by the expected energy not supplied (EENS) metric. A BESS converter fault in the centralized strategy causes a complete shutdown and incurs additional costs, as shown in Figure 13c. Conversely, the composite strategy maintains operation during such faults (Figure 15c), effectively reducing the EENS to zero. Since Table 3 demonstrates that the composite strategy yields the lowest LCOH at 25.458 CNY/kg, the avoided EENS costs further solidify its economic superiority over the centralized approach despite the higher converter power rating.

Overall, each strategy presents specific benefits and limitations. The selection and optimization of the ES-HE capacity ratio remain open research challenges, particularly for achieving balanced performance across stability, reliability and economic metrics.

Furthermore, practical deployment must account for component degradation, such as increased internal ohmic resistance in electrolyzers. The proposed PI controllers within the current and voltage loops provide robustness against these uncertainties, ensuring stability as components age.

5. Conclusions

This study examined three GFM strategies for off-grid renewable ReP2H systems, including the following: (1) centralized GFM BESS-based GFM control, (2) GFM electrolyzer-based approach, and (3) a composite multi-source coordinated GFM approach. Detailed models and hardware-in-the-loop simulations were used to quantify their stability performance, required ES capacity and economic impacts. The key findings are as follows:

• The centralized GFM BESS-based approach is straightforward to deploy and commonly used in practice but is vulnerable to single-point failures. Simulations show that it maintains voltage-frequency stability as summarized in Table 3 but requires the largest ES capacity among the three strategies, resulting in an LCOH of 33.212 CNY/kg.
• The GFM electrolyzer-based approach, i.e., using the electrolyzer and VSM dynamics alone for V/F control, simplifies system architecture and reduces ES needs. However, its stability margin is insufficient for sustained hydrogen production and maintaining production efficiency under long-term fluctuations remains an open challenge.
• The composite multi-source coordinated GFM solution provides strong V/F support and robustness while reducing ES capacity and lowering the LCOH to 25.458 CNY/kg. Its drawback lies in the higher complexity of coordinated control and the increased converter capacity required, which partially offsets its economic advantage.

Overall, the results indicate that composite-coordinated GFM offers the most balanced path for stable and economical off-grid hydrogen production. Future work should focus on optimizing the capacity allocation between ES and electrolyzer units and further improving coordinated multi-source GFM control to reduce converter requirements and overall system cost.