Optimizing Standalone Wind–Solar–Hydrogen Systems: Synergistic Integration of Hybrid Renewables and Multi-Electrolyzer Coordination for Enhanced Green Hydrogen Production

Abstract

To achieve optimal performance of renewable hydrogen production systems (RHPS), this study proposes a novel optimization framework for synergistically integrating wind–solar resources with diversified electrolyzers. A comprehensive techno-economic model is developed, incorporating both alkaline electrolyzers (AEL) and proton exchange membrane electrolyzers (PEMEL), and enabling the determination of the optimal wind–solar configuration ratio, electrolyzer types and capacities, and system-level economic performance. The results reveal that the nature of the renewable energy source predominantly influences the selection of electrolyzers. Specifically, pure photovoltaic (PV) systems tend to favor PEMEL, with an optimal PEMEL:AEL capacity ratio of 2:1, whereas pure wind turbine (WT) systems and PV–WT hybrid systems are more suited to AEL, with corresponding AEL:PEMEL ratios of 8:3 and 7:3, respectively. The combined operation of wind–solar complementarity and diversified electrolyzers reduces the levelized cost of hydrogen (LCOH) to USD 4.52/kg, representing a 41.1% reduction compared to standalone PV systems, with a renewable energy utilization rate of 92.26%. Case studies confirm that collaborative AEL–PEMEL operation enhances system stability and efficiency, with PEMEL mitigating power fluctuations and AEL supplying baseload hydrogen production. This synergy improves hydrogen production efficiency, extends equipment lifespan, and provides a viable and theoretically sound solution for RHPS optimization.

1. Introduction

The Paris Agreement has catalyzed global carbon neutrality commitments, transforming low-carbon development from a national initiative into an international imperative [1]. Hydrogen, owing to its carbon-free characteristics and cross-sectoral utility, is increasingly recognized as a strategic enabler of deep decarbonization in both energy and industry [2]. Notably, green hydrogen, generated through renewable-powered electrolysis, has been emphasized by the International Renewable Energy Agency (IRENA) as a key pathway for decarbonizing hard-to-abate industries such as steel and chemicals [3,4]. However, the inherent intermittency of renewable energy sources induces significant variations in electrolyzer operation, thereby diminishing efficiency, shortening equipment lifetime, and ultimately elevating the levelized cost of hydrogen (LCOH) [5]. Accordingly, comprehensive system-level simulations and optimization studies are crucial for assessing and mitigating the influence of renewable fluctuations on hydrogen generation systems.

Electrolyzers convert water into hydrogen with renewable electricity, and are central to PtH systems. Currently, there are three main types of electrolyzers, each with distinct advantages and challenges [6]. Alkaline electrolyzers (AELs) are the most mature and widely applied, renowned for their durability and cost-effectiveness. However, AELs suffer from lower operational efficiency and minimum power constraints, limiting their application in renewable energy systems with strong volatility [7]. Proton exchange membrane electrolyzers (PEMELs) exhibit higher efficiency and flexibility, enabling rapid response to input power fluctuations [8]. Nevertheless, PEMELs face challenges of high costs, complex systems, and strict requirements for water purity [9,10]. Solid oxide electrolyzers (SOELs) operate at high temperatures (700–1000 °C), achieving higher efficiency than other types, but their high cost due to high-temperature operation and complexity limits industrial-scale applicability, with feasibility yet to be validated. Thus, AEL and PEMEL dominate renewable hydrogen systems, with selection contingent on techno-economic trade-offs. PEMEL offers superior flexibility while AEL provides cost advantages.

Existing techno-economic models for the renewable hydrogen production systems (RHPS) frequently oversimplify electrolyzer efficiency as static [11], despite its dynamic correlation with operating power. While dynamic electrolyzer modeling [12] and storage-integrated optimization frameworks [13] have advanced, most studies neglect two critical dimensions: (1) electrolyzer synergy—particularly collaborative AEL/PEMEL operation leveraging complementary traits [14]; and (2) the multi-energy coupling -integrated optimization of wind–solar complementarity with multi-electrolyzer dynamics [15].

Recent studies have advanced optimal design strategies for AEL and PEMEL systems. Guo et al. [16] developed a design and operation framework for hydrogen production that accounts for the transitional states of multiple AEL units, enabling the minimization of LCOH under grid-connected photovoltaic (PV) and wind turbine (WT) power conditions. Ibáñez-Rioja et al. [17] analyzed how varying hydrogen supply rates influence LCOH in wind–solar–AEL systems. Fang et al. [18] sought to improve WT-AEL performance and reliability by introducing supercapacitor-based configurations to buffer power fluctuations. Ríos et al. [19] optimized system capacity and pricing strategies for offshore WT/PV-PEMEL setups. Zghaibeh et al. [20] explored hydro-PV grid systems, showing that turbines, PV modules, and PEMEL units dominate overall cost while maximizing hydrogen output. Mößle et al. [21] enhanced PEMEL performance by coupling electrolyzers with dynamic battery energy storage systems. Despite these advancements, most studies remain limited to single-electrolyzer designs, rarely extending to hybrid configurations that could leverage the techno-economic complementarities between AEL and PEMEL technologies.

Recent techno-economic analyses of AEL and PEMEL in renewable hydrogen production systems have emphasized the fundamental trade-offs between performance and cost, encouraging further investigation into hybrid electrolyzer configurations. Marocco et al. [22] identified AEL combined with lithium-ion batteries as the most cost-efficient choice for off-grid applications. In grid-connected solar hydrogen systems, Bhandari et al. [23] also verified the economic advantage of AEL, whereas Hurtubia et al. [24] noted that PEMEL, though better suited to fluctuating renewables, suffers from high capital costs that limit its competitiveness. Building on this, Xu et al. [25] introduced a hybrid AEL–PEMEL framework, showing 6.0–28.9% higher revenues by exploiting the complementary features of the two electrolyzers. However, their study excluded wind–solar integration, coordinated dual electrolyzer operations, and cost sensitivity assessments. As a result, comprehensive optimization strategies for hybrid AEL–PEMEL systems under renewable variability remain lacking, underscoring the need for robust techno-economic models to evaluate such configurations in realistic operating environments.

Therefore, current designs of RHPS encounter three fundamental constraints: (1) a predominant focus on single renewable sources or electrolyzer types, neglecting multi-energy complementarity and multi-electrolyzer techno-economic synergies; (2) the inadequate modeling of dynamic source-load matching; and (3) the oversimplification of electrolyzer efficiency as static rather than power-dependent. These constraints significantly undermine both the operational performance and economic feasibility of such systems. To address these shortcomings, this study contributes in the following ways: First, we propose a collaborative optimization framework for off-grid RHPS that incorporates spatio-temporal wind–solar complementarity alongside the techno-economic characteristics of AEL and PEMEL. Our model integrates the dynamic operational behavior of electrolyzers to harmonize the intermittency of renewable energy with the response profiles of AEL and PEMEL, thereby facilitating dynamic load distribution between the two technologies. Second, joint optimization is employed to ascertain optimal wind turbine-to-photovoltaic (WT-PV) ratios, types and capacities of electrolyzers, and the economic performance metrics of the system. Third, sensitivity analyses are conducted to quantify the effects of fluctuations in the capital costs of BESS and PEMEL on system configuration and revenue generation.

This paper is structured as follows: Section 2 elaborates on the system and corresponding model; Section 3 analyzes the research results and relevant application scenarios; and Section 4 summarizes the key findings of the study and puts forward prospective outlooks.

2. Methods

2.1. Description of the Renewable Hydrogen Production System

The configuration of RHPS is illustrated in Figure 1. Initially, WT and PV panels generate electricity for the overall system. This generated power drives AEL and PEM electrolyzers for hydrogen production, with excess electricity stored in battery systems. The produced hydrogen undergoes gas–liquid separation, purification, and compression before being dispatched for end use.

2.2. Mathematical Modeling of Electrolyzer

2.2.1. Mathematical Modeling of Alkaline Electrolyzer

The empirical expressions for the model’s I-U curve and Faraday efficiency are given by Equations (1) and (2) [26].

$$U_{\mathrm{el}}^{\mathrm{AEL}}=U_{\mathrm{rev}}^{\mathrm{AEL}}+{\displaystyle \frac{r_1+d_1+r_2{T}^{\mathrm{AEL}}+d_{2}p}{A^{\mathrm{AEL}}}}{I}_{\mathrm{el}}^{\mathrm{AEL}}+s\lg ({\displaystyle \frac{t_1+\frac{t_2}{T^{\mathrm{AEL}}}+\frac{t_3}{{(T^{\mathrm{AEL}})}^2}}{A^{\mathrm{AEL}}}}{I}_{\mathrm{el}}^{\mathrm{AEL}}+1)$$

(1)

$${\eta }_F=\left({\displaystyle \frac{{(I_{\mathrm{el}}^{\mathrm{AEL}})}^2}{f_{11}+f_{12}\cdot T^{\mathrm{AEL}}+{(I_{\mathrm{el}}^{\mathrm{AEL}})}^2}}\right)\cdot \left(f_{21}+f_{22}\cdot T^{\mathrm{AEL}}\right)$$

(2)

where $U_{\mathrm{el}}^{\mathrm{AEL}}$ is the voltage of a single alkaline electrolyzer (V); $I_{\mathrm{el}}^{\mathrm{AEL}}$ is the current of a single alkaline electrolyzer (A); $U_{\mathrm{rev}}^{\mathrm{AEL}}$ is the reversible voltage; $A^{\mathrm{AEL}}$ is the electrode area of the alkaline electrolyzer (m²); $T^{\mathrm{AEL}}$ is the electrode temperature (K); $p$ is the electrolyzer pressure (Pa); coefficients $s$, $r_1$, $r_2$, $t_1$, $t_2$, $t_3$, $d_1$ and $d_2$ are alkaline electrolyzer-specific parameters determined from the literature. $f_{11}$, $f_{12}$, $f_{21}$ and $f_{22}$ are the coefficients for Faraday efficiency.

The hydrogen production rate of the electrolyzer, determined by its electrochemical behavior, is calculated via Faraday efficiency and given by Equation (3) [27]:

$$v_{{\mathrm{H}}_2}={\displaystyle \frac{{\eta }_{\mathrm{F}}{n}_{\mathrm{c}}{I}_{\mathrm{el}}^{\mathrm{AEL}}}{zF}}$$

(3)

where $n_{\mathrm{c}}$ is the number of the electrolyzer cell.

The cell voltage efficiency is given as follows using the thermoneutral voltage and cell voltage, as shown in Equation (4):

$${\eta }_{\mathrm{v}}={\displaystyle \frac{U_{\mathrm{th}}}{U_{\mathrm{el}}^{\mathrm{AEL}}}}$$

(4)

where $U_{\mathrm{th}}$ represents the thermoneutral voltage.

The simulation of AEL was conducted using the parameters provided in Table S1.

2.2.2. Mathematical Modeling of Proton Exchange Membrane Electrolyzer

The cell voltage of PEMEL is the sum of the Nernst voltage, activation overpotential, ohmic overpotential, and concentration overpotential [28], as shown in Equation (5).

$$U_{\mathrm{el}}^{\mathrm{PEMEL}}=U_{\mathrm{N}}+U_{\mathrm{act}}+U_{\mathrm{ohm}}+U_{\mathrm{conc}}$$

(5)

The Nernst voltage is given by Equation (6) [29]:

$$U_N=U_{rev}^0+{\displaystyle \frac{\mathrm{R}{T}^{PEMEL}}{2\mathrm{F}}}\ln \left(\sqrt{{\displaystyle \frac{p_{O_2}^{an}}{p_0}}}{\displaystyle \frac{p_{H_2}^{cat}}{p_0}}\right)$$

(6)

The reversible cell voltage can be calculated using Equation (7).

$$U_{rev}^0=1.229\mathrm{V}-0.9\cdot {10}^{-3}\cdot (T^{\mathrm{PEMEL}}-298\mathrm{K}){\displaystyle \frac{\mathrm{V}}{\mathrm{K}}}$$

(7)

The activation overpotential, generated by electrode reaction kinetics, is given by Equations (8) and (9) [30].

$$U_{act}={\displaystyle \frac{R\cdot T^{\mathrm{PEMEL}}}{F}}{\sinh }^{-1}\left({\displaystyle \frac{I_{\mathrm{el}}^{\mathrm{PEMEL}}}{2\cdot i_0}}\right)$$

(8)

$$i_0=k_{i_0}\cdot \exp \left({\displaystyle \frac{-E_{act}}{R{T}^{\mathrm{PEMEL}}}}\right)$$

(9)

where $i_0$ is the exchange current density (A/m²); the anodic activation energy $E_{act}$ is 76,000 J/mol; and $k_{i_0}$ is the pre-exponential factor.

The cell’s ohmic overpotential is calculated via Ohm’s law and given by Equations (10)–(12) [6].

$$U_{ohm}=(R_{el,anode}+R_{el,cathode}+R_{mem})\cdot I_{\mathrm{el}}^{\mathrm{PEMEL}}\cdot A^{PEMEL}$$

(10)

$$R_{el,X}={\displaystyle \frac{t_{el,X}}{A^{PEMEL}}}{\rho }_{el,X}$$

(11)

$$R_{mem}={\displaystyle \frac{t_{mem}}{{\sigma }_{mem}\cdot A^{PEMEL}}}$$

(12)

where $R_{el,X}$ is the electrode resistance; $t_{el,X}$ is the electrode thickness; ${\rho }_{el,X}$ is the electrode resistivity. $R_{mem}$ is the membrane resistance; $t_{mem}$ is the membrane thickness; ${\sigma }_{mem}$ is the membrane conductivity, given by Equation (13).

$${\sigma }_{mem}=(0.005139\cdot \lambda -0.00326)\cdot \exp \left(1268\cdot \left({\displaystyle \frac{1}{303}}-{\displaystyle \frac{1}{{\mathrm{T}}_{\mathrm{cell}}}}\right)\right)$$

(13)

The concentration overpotential of the cell is considered only on the anode side and is given by Equation (14) [31]:

$$U_{conc}={\displaystyle \frac{\mathrm{R}\cdot T^{\mathrm{PEMEL}}}{{\mathsf{\alpha }}_{\mathrm{anode}}\cdot \mathrm{n}\cdot \mathrm{F}}}\cdot \ln \left({\displaystyle \frac{{\mathrm{i}}_{\mathrm{L}}}{{\mathrm{i}}_{\mathrm{L}}-I_{\mathrm{el}}^{\mathrm{PEMEL}}}}\right)$$

(14)

where ${\mathrm{i}}_{\mathrm{L}}$ is the limiting current density.

The Faraday efficiency of PEMEL remains essentially constant with changes in load ratio [10]. Therefore, this study sets its Faraday efficiency at a constant value of 99%.

The simulation of PEMEL was conducted using the parameters provided in Table S2.

2.3. Objective Function

A mixed-integer linear programming (MILP) model is employed to obtain the optimal configuration of the renewable energy hydrogen production system [2]. The objective is to maximize the system’s total annual revenue, defined as hydrogen production income minus investment and operation costs, as shown in Equation (15).

$$Revenue=R_{H_2}-C^{inv}-C^{ope}$$

(15)

where $R_{H_2}$, $C^{inv}$ and $C^{ope}$ indicate the hydrogen revenue, the investment cost, and the operation and maintenance cost, $Revenue$ indicates the system’s total annual revenue, respectively.

The RHPS investment cost is obtained by aggregating the annualized capital expenses of all system components across the project lifetime, as shown in Equation (16).

$$\begin{array}{l}{C}^{\mathrm{inv}}={\mathrm{C}}_{\mathrm{cap}}^{\mathrm{PV}}{P}^{\mathrm{PV},\mathrm{rated}}{\mathrm{CRF}}^{\mathrm{PV}}+{\displaystyle \sum _{m\in M}{\mathrm{C}}_{\mathrm{cap},\mathrm{m}}^{\mathrm{ELE}}{Q}_m^{\mathrm{ELE}}{\mathrm{CRF}}_{\mathrm{m}}^{\mathrm{ELE}}}+{\mathrm{C}}_{\mathrm{cap}}^{\mathrm{WT}}{P}^{\mathrm{WT},\mathrm{rated}}{\mathrm{CRF}}^{\mathrm{WT}}\\ +{\mathrm{C}}_{\mathrm{cap}}^{\mathrm{BESS}}{E}^{\mathrm{BESS},\mathrm{rated}}{\mathrm{CRF}}^{\mathrm{BESS}}+{\mathrm{C}}_{\mathrm{cap}}^{\mathrm{COMP}}{P}^{COMP,\mathrm{rated}}{\mathrm{CRF}}^{\mathrm{COMP}}\end{array}$$

(16)

where ${\mathrm{C}}_{\mathrm{cap}}^{\mathrm{PV}}$, ${\mathrm{C}}_{\mathrm{cap}}^{\mathrm{WT}}$, ${\mathrm{C}}_{\mathrm{cap}}^{\mathrm{BESS}}$ and ${\mathrm{C}}_{\mathrm{cap}}^{\mathrm{COMP}}$ are the unit capacity costs of the PV, WT, BESS and compressor (COMP), respectively; $P^{\mathrm{PV},\mathrm{rated}}$, $P^{\mathrm{WT},\mathrm{rated}}$, $E^{\mathrm{BESS},\mathrm{rated}}$ and $P^{COMP,\mathrm{rated}}$ are the rated capacities of PV, WT, BESS and COMP, respectively; M is the number of electrolyzer types; ${\mathrm{C}}_{\mathrm{cap},\mathrm{m}}^{\mathrm{ELE}}$ and $Q_m^{\mathrm{ELE}}$ are the unit cost and number of the m type electrolyzer.

The capital recovery factor (CRF) converts initial investments into annualized costs, as shown in Equation (17).

$$CRF={\displaystyle \frac{r{(1+r)}^{L^i}}{{(1+r)}^{L^i}-1}}$$

(17)

where $L^{\mathrm{i}}$ is the lifetime of the component; $r$ is the discount rate.

The operation and maintenance (O&M) $C^{\mathrm{ope}}$ can be derived as in Equation (18).

$$\begin{array}{l}{C}^{\mathrm{ope}}={\mathrm{C}}_{\mathrm{mai}}^{\mathrm{PV},\mathrm{unit}}{P}^{\mathrm{PV},\mathrm{rated}}+{\displaystyle \sum _{m\in M}\left({\mathrm{C}}_{\mathrm{mai},\mathrm{m}}^{\mathrm{ELE}}{Q}_m^{\mathrm{ELE}}\right)}+{\mathrm{C}}_{\mathrm{mai}}^{\mathrm{WT}}{P}^{\mathrm{WT},\mathrm{rated}}+{\mathrm{C}}_{\mathrm{mai}}^{\mathrm{BESS}}{E}^{\mathrm{BESS},\mathrm{rated}}\\ +{\mathrm{C}}_{\mathrm{mai}}^{\mathrm{COMP}}{P}^{\mathrm{COMP},\mathrm{rated}}\end{array}$$

(18)

where ${\mathrm{C}}_{\mathrm{mai}}^{\mathrm{PV},\mathrm{unit}}$, ${\mathrm{C}}_{\mathrm{mai},\mathrm{m}}^{\mathrm{ELE}}$, ${\mathrm{C}}_{\mathrm{mai}}^{\mathrm{WT}}$, ${\mathrm{C}}_{\mathrm{mai}}^{\mathrm{BESS}}$ and ${\mathrm{C}}_{\mathrm{mai}}^{\mathrm{COMP}}$ are the annual O&M costs per unit capacity for PV, electrolyzers (ELE), WT, BESS, and the compressor, respectively.

The levelized cost of hydrogen (LCOH) is used for system cost evaluation [17], calculated as annualized total cost divided by annualized hydrogen supply, as shown in Equation (19).

$$LCOH={\displaystyle \frac{COS{T}_{Initital}+{\displaystyle \sum _{t=1}^N\frac{{C^{\mathrm{ope}}}_t}{{\left(1+r\right)}^t}}}{{\displaystyle \sum _{t=1}^N\frac{Q_{ht}}{{\left(1+r\right)}^t}}}}$$

(19)

where $COS{T}_{Initital}$ represents the fixed capital investment of the hydrogen production project, $Q_{ht}$ denotes the hydrogen output in year t, ${C^{\mathrm{ope}}}_t$ refers to the project cost in year t (e.g., operation and maintenance costs), N is the project lifetime, and r is the discount rate.

2.4. Constraints

2.4.1. Power Generation System

The generated power may be directed to the BESS, consumed by the electrolyzer, or curtailed. The supply-side energy balance is therefore given by Equation (20).

$$P_k^S=P_k^{\mathrm{S},\mathrm{ELE}}+P_k^{\mathrm{S},\mathrm{BESS}}+P_k^{\mathrm{W}}$$

(20)

where $P_k^{\mathrm{S},\mathrm{ELE}}$ is the renewable power supplied to the electrolyzer, $P_k^{\mathrm{S},\mathrm{BESS}}$ is the renewable power supplied to the BESS, and $P_k^{\mathrm{W}}$ is the curtailed power. $P_k^S$ denotes the total power generation and can be expressed as in Equation (21).

$$P_k^{\mathrm{S}}=P^{\mathrm{PV},\mathrm{rated}}C{F}_k^{\mathrm{PV}}+P^{\mathrm{WT},\mathrm{rated}}C{F}_k^{\mathrm{WT}}$$

(21)

where $C{F}_k^{\mathrm{PV}}$ and $C{F}_k^{\mathrm{WT}}$ represent the capacity factors of the PV and WT systems, defined as the ratio of the actual electrical energy generated over a given period to the energy that would have been produced if the unit had operated at its rated power for the entire period [32].

2.4.2. Eelectrolyzers System

The electrolyzer receives input power from the power generation system and the BESS, which can be expressed as in Equation (22).

$$P_{k,\mathrm{total},\mathrm{in}}^{\mathrm{ELE}}=P_k^{\mathrm{S},\mathrm{ELE}}+P_k^{\mathrm{BESS},\mathrm{ELE}}$$

(22)

where $P_{k,\mathrm{total},\mathrm{in}}^{\mathrm{ELE}}$ is the total input power of the electrolyzer system, and $P_k^{\mathrm{BESS},\mathrm{ELE}}$ represents the power supplied from the BESS to the electrolyzer (ELE).

The total input power of the electrolyzer system is allocated to each electrolyzer. With M types of ELEs (I units per type), the power allocation is given by Equation (23).

$$P_{k,\mathrm{total},\mathrm{in}}^{\mathrm{ELE}}={\displaystyle \sum _{m\in M}{\displaystyle \sum _{i\in \mathrm{I}}{P}_{m,i,k,\mathrm{in}}^{\mathrm{ELE}}}}$$

(23)

In this study, two types of electrolyzers are employed, namely, AEL and PEMEL. Their operational performances vary notably. AEL exhibits restricted flexibility, with an operational range of 40–100% and limited start–stop capability, in contrast to PEMEL, which can cycle rapidly and function across 10–120% of rated power [10]. An electrolyzer operates only when input power exceeds its minimum threshold; otherwise, it shuts down.

Therefore, the working power limits of the electrolyzers are given by Equation (24).

$${\sigma }_{m,i,\mathrm{LB}}{P}_{m,i}^{\mathrm{ELE},\mathrm{rated}}{\delta }_{m,i}^{\mathrm{ELE}}\le P_{m,i,k,\mathrm{in}}^{\mathrm{ELE}}\le {\sigma }_{m,i,\mathrm{UB}}{P}_{m,i}^{\mathrm{ELE},\mathrm{rated}}{\delta }_{m,i}^{\mathrm{ELE}}$$

(24)

$$Q_m^{\mathrm{ELE}}={\displaystyle \sum _{i\in I}{\delta }_{m,i}^{\mathrm{ELE}}}$$

(25)

where ${\sigma }_{m,i,\mathrm{UB}}$ and ${\sigma }_{m,i,\mathrm{LB}}$ are the upper and lower bounds on the operation power of electrolyzers; $P_{m,i}^{\mathrm{ELE},\mathrm{rated}}$ is the rated power; ${\delta }_{m,i}^{\mathrm{ELE}}$ is a binary variable (1 if the electrolyzer is activated, 0 otherwise); $Q_m^{\mathrm{ELE}}$ is the total number of each type of electrolyzer during operation.

When PEMEL operates above 100% of its rated power, it is considered in overload state R. To avoid sustained overloading, the model restricts PEMEL from entering this state if it has already operated in overload during the two preceding time steps, as shown in Equation (26).

$${\displaystyle \sum _{\tau =t}^{t+T_{R\max }-1}{R}_n^{\tau }}⩽T_{R\max }$$

(26)

where $T_{R\max }$ is set to 2 time steps.

For each electrolyzer, ${\mathrm{ELE}}_{m,i}$, the relationship between the hydrogen production rate $f_{m,i,k}^{{\mathrm{H}}_2}$ and the operating load $P_{m,i,k,\mathrm{in}}^{\mathrm{ELE}}$ is given by Equation (27) [33].

$$f_{m,i,k}^{{\mathrm{H}}_2}=a_m^{\mathrm{ELE}}{P}_{m,i,k,\mathrm{in}}^{\mathrm{ELE}}+b_m^{\mathrm{ELE}}$$

(27)

where $a_m^{\mathrm{ELE}}$ and $b_m^{\mathrm{ELE}}$ represent the slope and intercept of the curve between the input power and the hydrogen output flow rate for the electrolyzer ${\mathrm{ELE}}_{m,i}$. PEMEL and AEL exhibit distinct values for these parameters. A detailed description is provided in Section 3.1.

2.4.3. Battery Energy Storage System

The charging and discharging power of the BESS are given by Equations (28) and (29).

$$P_{k,\mathrm{in}}^{\mathrm{BESS}}=P_k^{\mathrm{S},\mathrm{BESS}}{\eta }_{\mathrm{ch}}$$

(28)

$$P_{k,\mathrm{out}}^{\mathrm{BESS}}=P_k^{\mathrm{BESS},\mathrm{ELE}}{\eta }_{\mathrm{dis}}$$

(29)

where ${\eta }_{\mathrm{ch}}$ and ${\eta }_{\mathrm{dis}}$ are the charging and discharging efficiency of the BESS.

The energy balance of the BESS during the time interval t is given by Equation (30).

$$E_k^{\mathrm{BESS}}=E_{k-1}^{\mathrm{BESS}}+\left(P_{k,\mathrm{in}}^{\mathrm{BESS}}-P_{k,\mathrm{out}}^{\mathrm{BESS}}\right)\Delta t$$

(30)

where $E_k^{\mathrm{BESS}}$ represents the stored energy of the BESS at time t.

The battery capacity constraints are given by Equation (31).

$$SO{C}_{min}^{\mathrm{BESS}}\le E_k^{\mathrm{BESS}}/E^{\mathrm{BESS},\mathrm{rated}}\le SO{C}_{max}^{\mathrm{BESS}}$$

(31)

where $SO{C}_{max}^{\mathrm{BESS}}$ and $SO{C}_{min}^{\mathrm{BESS}}$ represent the upper and lower bounds of the battery state of charge.

The simultaneous charging and discharging of the battery are not allowed during any time interval, as shown in Equations (32)–(34).

$$0\le P_{k,\mathrm{in}}^{\mathrm{BESS}}\le {\delta }_{k,\mathrm{in}}^{\mathrm{BESS}}\cdot P_{\max }^{\mathrm{BESS}}$$

(32)

$$0\le P_{k,\mathrm{out}}^{\mathrm{BESS}}\le {\delta }_{k,\mathrm{out}}^{\mathrm{BESS}}\cdot P_{\max }^{\mathrm{BESS}}$$

(33)

$${\delta }_{k,\mathrm{in}}^{\mathrm{BESS}}+{\delta }_{k,\mathrm{out}}^{\mathrm{BESS}}\le 1$$

(34)

where ${\delta }_{k,\mathrm{in}}^{\mathrm{BESS}}$ and ${\delta }_{k,\mathrm{out}}^{\mathrm{BESS}}$ are binary variables ensuring that the battery cannot charge and discharge simultaneously.

2.4.4. Compressor Mathematical Modeling

The hydrogen compressor increases the electrolyzer outlet pressure (approximately 3 MPa) to about 20 MPa to meet the pressure requirements of tube–trailer vessels for downstream transportation [34].

The energy consumption of the hydrogen compressor is given by Equation (35).

$$P_{\mathrm{comp}}=z_{\mathrm{comp}}\cdot R\cdot n_{\mathrm{s}}\cdot {\displaystyle \frac{T_{\mathrm{in}}}{{\eta }_{\mathrm{it}}}}\cdot {\displaystyle \frac{r_{\mathrm{it}}}{r_{\mathrm{it}}-1}}\cdot \left[{\left({\displaystyle \frac{P_{\mathrm{out}}}{P_{\mathrm{in}}}}\right)}^{{\displaystyle \frac{r_{\mathrm{it}}-1}{n_{\mathrm{s}}{r}_{\mathrm{it}}}}}-1\right]\cdot m_{\mathrm{comp}}$$

(35)

$$z_{\mathrm{comp}}={\displaystyle \frac{z_2-z_1}{\ln (z_2-z_1)}}$$

(36)

where $T_{\mathrm{in}}$ is inlet temperature (K); $n_{\mathrm{s}}$ is stages; ${\eta }_{\mathrm{it}}$ is isentropic efficiency; $r_{\mathrm{it}}$ is hydrogen isentropic index; $P_{\mathrm{in}}$ and $P_{\mathrm{out}}$ are absolute pressures; $m_{\mathrm{comp}}$ is the compressor flow rate (kg/h); $z_{\mathrm{comp}}$ is the average hydrogen compression factor; $z_1$ and $z_2$ are inlet/outlet compression factors. The compressibility factor of hydrogen at each operating condition was obtained using the NIST REFPROP database, which is based on the high-accuracy equations of state for hydrogen [35]. Additional methodological details are provided in the Supplementary Materials [36,37].

3. Results

3.1. Fundamental Data

The specific energy consumption (SEC) of an electrolyzer represents the net electricity required to produce one cubic meter of hydrogen under standard conditions, expressed in kWh/Nm³. A lower SEC corresponds to higher electrolyzer efficiency. The SEC can be calculated using the established electrochemical models of AEL and PEMEL. Figure 2a shows how the SEC of AEL and PEMEL varies with part-load power input. At low part-loads, both electrolyzers show a marked rise in SEC, mainly due to auxiliary equipment consumption and efficiency losses. At high part-loads, SEC increases moderately as a result of electrochemical polarization at elevated current densities. Moreover, performance diverges under low load conditions. PEMEL records SEC values of 5.1–5.7 kWh/Nm³, slightly lower than AEL’s 5.3–5.8 kWh/Nm³. These energy consumption levels align with those in the literature [6]. Figure 2b depicts the hydrogen production rates of AEL and PEMEL as functions of operating power at a 1 MW rating. The dots represent simulation results (with models elaborated in the Supplementary Materials), while the lines denote the fitted curves. The differing slopes and intercepts of these curves highlight the distinct operational behaviors of the two electrolyzers.

This study selects renewable energy data from a wind farm and a photovoltaic power station in Zhangjiakou City, Hebei Province, as the core research object. This selection is based on the rich wind and solar energy resources in the Zhangjiakou region, where unique geographical and climatic conditions make the renewable energy output characteristics typical and representative, providing reliable sample support for relevant research. The data were obtained from the Renewable. ninja platform, with detailed descriptions of the data acquisition methods and the platform’s accuracy validation provided in references [38,39]. In this study, all calculations and optimization processes were performed using hourly temporal resolution, consistent with the time step of the Renewable. ninja dataset. Figure 3 specifically presents the hourly capacity factor changes of WT at this wind farm and PV throughout the year. As the ratio of actual to rated output, the capacity factor effectively characterizes the intermittency and variability of renewable resources. Examining the temporal distribution, peak offset, and complementary periods of wind and solar capacity factors provides a quantitative basis for assessing their complementarity, which is essential for evaluating its influence on the capacity configuration of integrated renewable energy systems.

To balance computational efficiency with research representativeness, the annual wind and solar generation data were clustered using the K-means algorithm. This partition-based unsupervised method groups similar daily generation profiles by minimizing intra-cluster variance. From the clustering analysis, six representative days were identified to characterize the yearly wind and solar output curves (Figure 4). These six representative days capture peak, trough, and intermediate power outputs of wind and solar generation, while also reflecting seasonal and weather-related variations. In this way, the data scale is greatly reduced without losing key statistical characteristics, offering an efficient and reliable input for subsequent system design and optimization. Figure 4 clearly reveals the significant dynamic changes in renewable energy generation during these six typical days. Among them, the power generation curves of the second, fourth, and fifth days exhibit particularly prominent time complementarity features. Through statistical analyses of the annual power generation data, as shown in

Table 1. Number of days and occurrence probabilities for different typical days.

Typical Day	1	2	3	4	5	6
days	28	104	66	40	75	52
probability	7.67%	28.49%	18.08%	10.96%	20.55%	14.25%

, the power generation patterns represented by the second, fourth, and fifth days account for 60% of the total number of days in a year. This relatively high probability of occurrence not only verifies that the above-mentioned time complementary characteristics are not accidental phenomena, but also indicates that there is significant complementary potential in the temporal distribution of wind and solar energy resources in the study area. This potential is crucial for enhancing the stability of comprehensive renewable energy utilization systems, reducing the curtailment of wind and solar energy, and optimizing energy storage configurations, providing key resource characteristic evidence for constructing efficient and coordinated energy utilization schemes.

3.2. Scenarios for the Case Study

To investigate the impact of wind–solar complementarity on system economics, three scenarios were designed and named as Scenario 1, Scenario 2, and Scenario 3. They represent the pure PV system, the PV–WT hybrid system, and the pure WT system, respectively. This setup enables a systematic comparison of capacity configurations of key components under varying renewable resource compositions and allows for quantifying the benefits derived from the temporal complementarity between wind and solar energy. All scenarios share the same assumptions: a total installed renewable energy capacity of 25 MW and a system lifetime of 20 years. The corresponding technical and economic parameters are summarized in

Table 2. Economic parameters used in the study [40,41].

Parameters	Unit	Value
Capital cost of PV	USD/kW	522
O&M cost of PV	USD/kW	2% Capital cost
Capital cost of WT	USD/kW	628
O&M cost of WT	USD/kW	2% Capital cost
Capital cost of battery	USD/kWh	400
O&M cost of battery	USD/kWh	1% Capital cost
Capital cost of AEL	Million USD/MW	1.25
Capital cost of PEMEL	Million USD/MW	1.74
O&M cost of electrolyzer	USD/MW	4% Capital cost
Cost of water	USD/m3	2.16
Capital cost of compressor	USD/Nm3·h	138
O&M cost of compressor	USD/Nm3·h	5% Capital cost
Lifetime of system	year	20
Lifetime of WT, PV	year	20
Lifetime of battery	year	10
Lifetime of electrolyzer	year	9
Interest rate	/	5%

and

Table 3. Technical parameters used in the study [16,23].

Equipment Parameters	Unit	Value
AEL
Capacity specification	MW	1
Water demand	L/Nm3	2
Output pressure	Bar	10
PEMEL
Capacity specification	MW	1
Water demand	L/Nm3	0.9
Output pressure	Bar	30
BESS
${\eta }_{\mathrm{ch}}$	-	90%
${\eta }_{\text{dis}}$	-	90%
Compressor
${\eta }_{\text{it}}$	-	75%

, including device service life and operating conditions, as well as capital and operation and maintenance costs. For optimization, the system is formulated as an MILP model and solved using the Gurobi solver, which enables the determination of the optimal configuration. Figure 5 illustrates the methodological framework adopted in this study.

3.3. Case Study

The optimal capacity configuration and economic performance of the RHPS under different scenarios can be derived from the established optimization model, and the results are shown in

Table 4. Energy consumption and cost of hydrogen production.

Scenarios	1	2	3
Electricity for hydrogen production (MWh)	29,741	49,403	52,782
Total hydrogen production (t)	537.24	880.41	942.17
Total hydrogen production cost (USD)	4,121,557	3,983,779	4,357,661
LCOH (USD/kg)	7.67	4.52	4.63

and Figure 6. Table 4 details the annual hydrogen production and LCOH for each scenario, providing a direct comparison of their techno-economic performance. The PV–WT hybrid system (scenario 2) achieves the LCOH at USD 4.52/kg, representing a 41.1% reduction compared to scenario 1. This result highlights the significant economic advantage conferred by wind–solar complementarity. In terms of hydrogen production, scenario 2 yields 880 tons per year, which is 64% higher than scenario 1 (537 tons) and only slightly lower than scenario 3 (897 tons). Despite this marginal difference in output, the total system cost in scenario 2 is substantially lower than in scenario 3, amounting to USD 3.984 million versus USD 4.358 million. This indicates that the hybrid configuration achieves a more favorable trade-off between cost and production, thereby enhancing the overall techno-economic performance of the system.

Figure 6a shows the cost breakdown of system components and hydrogen revenue across the three scenarios. Notably, the cost of electrolyzers accounts for approximately 60% of the total system cost in all cases, underscoring that reduction in electrolyzer capital expenditure is critical for lowering the LCOH. Figure 6b illustrates the optimal capacity configurations for each scenario. It is worth noting that the BESS capacity in scenario 1 is considerably higher than in scenarios 2 and 3. This difference arises from the explicit time-coupled dynamics modeled for the BESS, in which the state of charge evolves on an hourly basis depending on the instantaneous balance between renewable generation and electrolyzer demand. During periods of high PV generation, the BESS charges and stores excess electricity; this stored energy is subsequently discharged during low-generation hours to maintain the AEL minimum load requirement. Because the AEL must operate above 40% of its rated capacity and PV output is highly intermittent, the dynamic interaction between the BESS and the electrolyzer necessitates a larger storage capacity (11.09 MWh) in scenario 1 to ensure stable electrolyzer operation. In contrast, the relatively stable output of WT generation, together with the temporal complementarity between WT and PV, substantially reduces the reliance on BESS in scenarios 2 and 3. As shown in

Table 5. Optimal capacity configuration of renewable energy systems.

Scenario	1	2	3
PV (MW)	25	5.3	0
Wind (MW)	0	19.7	25
Battery (MW)	11.09	0.2	1
AEL (×1 MW)	3	7	8
PEMEL (×1 MW)	6	3	3
Compressor (Nm3/h)	2100	2200	2600

, scenario 2 utilizes a hybrid WT–PV configuration, with a capacity ratio of approximately 3.7:1. WT serves as the primary energy source, while PV acts as a complementary resource to smooth the overall generation profile.

Additionally, the utilization of renewable energy and the levelized cost of electricity are also analyzed, and the results are shown in Figure 7 and

Table 6. Generation and cost of renewable energy sources.

Scenario	1	2	3
Total renewable energy generation (MWh)	36,378	54,641	59,584
Total utilized renewable energy (MWh)	30,720	50,413	53,901
Renewable energy utilization rate	84.45%	92.26%	90.46%
LCOE (USD/kWh)	0.0301	0.0282	0.0277

. Figure 7 shows the power generation and consumption of the RHPS under different scenarios. Obviously, a significant proportion of the renewable electricity generated is utilized by electrolyzers, while a lesser amount is designated for auxiliary systems, compressors, and inherent electrical losses, and the residual energy is curtailed. Scenario 2 demonstrates the minimal level of curtailment, with just 4228 MWh of surplus power. The PV–WT hybrid system achieves the highest renewable energy utilization rate of 92.26%, considerably surpassing that of the exclusive PV (84.45%) and WT (90.46%) systems.

Table 6 presents the corresponding renewable energy utilization rates and LCOE for each scenario. The cost of the renewable energy power generation system is jointly determined by generation characteristics, capital investment, and operational expenses. Although WT systems require higher capital and maintenance outlays compared to PV systems, their superior energy yield results in the most competitive LCOE of USD 0.0277/kWh. In contrast, the pure PV system exhibits the highest LCOE of USD 0.0301/kWh. The hybrid PV–wind system has an LCOE of USD 0.0282/kWh, which is slightly higher than that of a pure WT system, yet it capitalizes on the synergistic benefits derived from the interplay of wind and solar resources, leading to enhanced economic efficacy.

Different scenarios have a significant impact on the capacity configuration of electrolyzers. Then, Figure 8 shows the capacity configuration of AEL and PEMEL across different scenarios. In scenario 1, the capacity ratio of PEMEL to AEL is 2:1, indicating that PEMEL is more suitable for the pure PV system. In scenarios 2 and 3, where WT serves as the primary power source, the capacity ratios of PEMEL to AEL are 7:3 and 8:3, respectively, reflecting a preference for AEL. This outcome reflects the broader load range (10–120%) and cycling flexibility of PEMEL, which matches well with PV’s volatility, while AEL, though more cost-effective in capital terms, is less tolerant of frequent cycling and requires steadier power input. Consequently, in systems predominantly influenced by WT or those exhibiting PV–WT complementarity, the relatively stable electricity provision facilitates the uninterrupted operation of AEL, thereby endorsing its extensive deployment and ultimately contributing to a reduction in overall system costs. In addition, the insights gained from the optimal electrolyzer configurations and cost distributions offer practical guidance for industrial stakeholders, helping them evaluate the trade-offs between AEL and PEMEL technologies and select the most suitable electrolyzer type under varying renewable resource conditions and system design requirements.

3.4. Comparative Analysis of Typical Daily Operation

This section conducts a comparative analysis of the operational profiles of the system across six representative days under varying scenarios. The patterns of the power generation and consumption associated with the RHPS for each typical day are illustrated in Figure 9. As depicted in Figure 9a, a notable level of power curtailment is observed in scenario 1 (pure PV), particularly on typical days 1, 2, 4, and 6. In contrast, the extent of the curtailment is substantially reduced in scenarios 2 and 3, as shown in Figure 9b and Figure 9c, respectively, with curtailment primarily confined to representative days 1 and 3. Furthermore, in scenario 1, BESS assumes a pivotal role in mitigating curtailment. When the PV generation surpasses the demand of the electrolyzer, the BESS engages in charging to accumulate the excess energy; conversely, during periods of insufficient PV output, it discharges to sustain AEL operation above its minimum load threshold, thereby averting shutdowns and ensuring both safety and stability in performance. This behavior underscores the essential role of storage in ensuring continuous and reliable operation within PV-dominated systems.

The operational results across typical days suggest that the high flexibility of PEMEL adeptly addresses the intermittency associated with renewable energy, while AEL predominantly fulfills the base load requirements, thereby enhancing the overall stability of the electrolysis system. Together, the two electrolyzer types provide complementary operational benefits that improve the reliability and efficiency of hydrogen production.

3.5. Sensitivity Analysis

As an integral component of the RHPS, BESS plays a crucial role in mitigating the fluctuations and intermittency inherent in renewable energy generation. This section analyzes the effects of variations in BESS capital expenditure on the optimal capacity configurations of BESS, AEL, and PEMEL, as well as on the total revenue, within the context of the PV–WT hybrid system (scenario 2). Figure 10 shows the total revenue and electrolyzer capacities of the RHPS under varying BESS capital costs. It can be observed that a reduction in BESS capital cost leads to increased capacities of both BESS and AEL, while the capacity of PEMEL decreases. Specifically, when the BESS cost is reduced by 30%, its capacity increases to 0.5 MW, enabling the utilization of surplus renewable energy to enhance hydrogen production and improve system revenue. With a 60% reduction in cost, the BESS capacity surges to 3.5 MW, AEL capacity increases to 8 MW, and PEMEL capacity declines to 2 MW, accompanied by a significant rise in total revenue. This phenomenon can be ascribed to the comparatively lower capital cost of AEL compared to PEMEL. Given AEL’s minimal operational power threshold and its constrained adaptability to frequent start-up and shutdown, supplementary BESS capacity is required to sustain continuous operational stability. Therefore, the optimization process necessitates a consideration of the trade-off between the combined cost of AEL and BESS and that of PEMEL. The findings demonstrate that with a 60% reduction in BESS capital cost, the augmentation of the capacities of AEL and BESS emerges as the more economically viable approach.

As discussed above, the electrolyzer is one of the core components of the RHPS, accounting for approximately 60% of the total system cost. Among the two types of electrolyzers considered in this study, PEMEL exhibits a higher capital cost than AEL. However, with ongoing technological advancements, the cost of PEMEL is expected to decline. In the photovoltaic–wind hybrid system, the impact of the reduction in the capital cost of PEMEL on the optimal capacity configuration of AEL and PEMEL and the resulting total system revenue was investigated. Figure 11 shows the influence of PEMEL capital cost on the electrolyzer capacity configuration and the overall profitability of the RHPS. The results reveal that a 20% reduction in PEMEL cost leads to a remarkable 60% increase in total system profit, highlighting the significant economic potential of PEMEL cost reductions. Moreover, declining PEMEL cost substantially alters the capacity allocation and selection of electrolyzers within the system. When the cost is reduced by 15%, the system configuration shifts to 6 MW of AEL capacity and 4 MW of PEMEL capacity. With a further reduction to 20%, PEMEL capacity rapidly increases to 9 MW, whereas AEL capacity is reduced to zero. These findings underscore that, as PEMEL investment costs continue to decline, it is expected to become the preferred electrolyzer type in RHPS, primarily due to its superior operational flexibility and short-term overload capability.

4. Conclusions

An integrated techno-economic optimization framework for RHPS has been developed in this study, explicitly accounting for the temporal variability of wind–solar resources and the dynamic behaviors of AEL and PEMEL, thereby facilitating the coordinated optimization of PV, WT, and BESS capacities alongside electrolyzer type and capacity in conjunction with the type and capacity of electrolyzers. Utilizing this model, multi-scenario analyses are conducted to assess system performance across diverse operational conditions. The results indicate that the characteristics of the renewable energy source predominantly influence the preferred electrolyzer configuration. In scenario 1, PEMEL shows clear advantages due to its fast dynamic response, yielding an optimal PEMEL:AEL ratio of 2:1. In contrast, scenarios 2 and 3 benefit from the cost-effectiveness of AEL, with optimal AEL:PEMEL ratios of 7:3 and 8:3, respectively. The PV–WT hybrid system achieves a LCOH of USD 4.52/kg, representing a 41.1% reduction compared to the pure PV system, with a renewable energy utilization rate as high as 92.26%. An analysis of typical daily operations reveals that the considerable flexibility of PEMEL effectively mitigates power fluctuations, whereas AEL provides the more stable management of the base load. This complementary behavior contributes to improved hydrogen production efficiency and overall economic performance.

Despite these contributions, several limitations remain. This study focuses solely on standalone hydrogen production and does not consider integration with downstream processes (e.g., ammonia or methanol synthesis), which could enhance system value. Only battery energy storage is included, while incorporating other storage options may further improve operational flexibility. In addition, electrolyzer degradation and long-term performance decline were not modeled. Future work should therefore examine (1) coupling RHPS with downstream chemical production, (2) integrating diversified storage technologies and multi-vector energy systems, and (3) incorporating long-term electrolyzer degradation and maintenance strategies to strengthen reliability and lifecycle performance.