Research on MPC-Based Power Allocation Strategy and Dynamic Value Evaluation of Wind–Hydrogen Coupled Systems

Abstract

With rising renewable energy penetration, wind–hydrogen coupling systems are key to large-scale green hydrogen production and wind power integration. This paper proposes a multi-timescale power allocation measure and evaluation framework that executes scheduling planning, rolling updates and real-time control sequentially. First, an intelligent power allocation strategy based on model predictive control (MPC) and State of Health (SOH) prediction is designed, which pursues short-term operational efficiency while actively avoiding electrolyzer-damaging conditions. Second, a comprehensive evaluation model integrating dynamic hydrogen value and flexibility value is built, overcoming the limitations of traditional fixed-hydrogen-value and single-system-value evaluations to quantify operational strategy viability more accurately. Simulation results show that the proposed strategy boosts the system’s lifecycle Net Present Value (NPV) by ~12.7% versus conventional strategies, verifying the framework’s effectiveness and superiority in improving wind–hydrogen coupling system performance.

1. Introduction

Amidst the grim reality of dwindling global fossil fuel reserves and persistently rising greenhouse gas emissions, renewable energy sources—represented by wind power and photovoltaics—are experiencing explosive growth. Leveraging its advantages of widespread resource distribution and high technological maturity, wind power has become the primary driver of global renewable energy expansion. However, the inherent intermittency, variability, and counter-peak characteristics of wind energy pose significant challenges to the safe and stable operation of power systems [1,2].

Hydrogen energy, as a high-energy-density, clean, and carbon-free secondary energy source, serves as an ideal cross-seasonal, large-scale energy storage medium. This significant energy density advantage not only substantially reduces the spatial footprint and transportation costs of energy storage facilities but also overcomes the technical limitations of traditional electrochemical storage in high-capacity applications [3,4]. The core development objectives of electrolytic hydrogen production technology lie in enhancing electrical energy conversion efficiency and reducing hydrogen production costs. Driven by continuous technological advancement and supportive policies, it has demonstrated the potential to become a central development direction within the clean energy sector. By constructing a coupled model of electrolyzers operating at different temperatures and wind power systems, the study in [5] conducted an economic assessment. Results indicate that wind–hydrogen coupling systems not only exhibit superior operational stability but also demonstrate significant economic viability. Reference [6] proposes a sliding mode control strategy for DC microgrids targeting hybrid power generation systems composed of wind energy, hydrogen energy, and batteries, ensuring stable operation of the closed-loop system. Wind–hydrogen coupling systems serve as the key vehicle for fully leveraging the advantages of hydrogen energy. Capable of delivering high-purity hydrogen across multiple sectors including transportation, chemical processing, metallurgy, and power peak shaving, these systems boast broad application prospects and have emerged as a crucial strategic pillar for achieving the dual carbon goals [7,8].

Despite the promising prospects of wind–hydrogen coupling systems, their commercial operation still faces numerous technical and economic bottlenecks, with the issue of core equipment lifecycle management being particularly prominent. From an equipment category perspective, the mainstream electrolyzer types in the water electrolysis hydrogen production field primarily include three categories: alkaline water electrolyzers (AWE), proton exchange membrane electrolyzers (PEME), and solid oxide electrolyzers (SOE) [9]. However, PEME is constrained by its requirement for a highly acidic and oxidizing operating environment. PEME requires precious metal catalysts and fluorinated membrane materials, resulting in high equipment costs and short service life [10]. Solid oxide electrolysis (SOE) for hydrogen production requires operation under specific high-temperature conditions, and its universal applicability remains to be further validated. Currently, it is still in the early stages of laboratory research and demonstration, with domestic demonstration projects only reaching the hundred-kilowatt scale [11]. From an operational perspective, the electrolyzer—as the core energy conversion equipment within the system—does not have a fixed operational lifespan. Instead, its service life is closely tied to dynamic operating conditions such as start–stop cycles, load fluctuations, and sustained operation at low loads. Reference [12] proposes a wind–hydrogen coupling control strategy to reduce electrolyzer switching frequency and increase production. By incorporating supercapacitors and controlling electrolyzer start–stop timing, this approach mitigates the impact of wind power fluctuations on the system. Reference [13] considers various constraints in wind-powered hydrogen production, establishes an electrolyzer model based on a dynamic battery energy storage system, and proposes a smooth power control strategy.

Among these three types of electrolyzers, AWE has successfully achieved large-scale commercial hydrogen production applications compared to the other two types. Research indicates that alkaline electrolyzers experience performance degradation, increased hydrogen–oxygen crossover risks, and reduced lifespan under dynamic operating conditions such as start–stop cycles, cold starts, ramping operations, and prolonged low-load periods. Notably, each additional cold start cycle induces approximately 0.2% irreversible mechanical fatigue in the membrane electrode assembly (MEA), directly shortening the electrolyzer’s operational lifespan [14]. Currently, system power allocation strategies primarily aim to achieve instantaneous power balance or minimize short-term operating costs, such as simple power tracking strategies or optimization scheduling based on day-ahead planning [15]. Such strategies often overlook the damage caused by frequent, intense power fluctuations to the internal materials of electrolytic cells, leading to accelerated performance degradation and reduced lifespan. This, in turn, increases long-term operational and maintenance costs as well as equipment replacement expenses. Therefore, designing an intelligent power allocation strategy that balances both short-term operational efficiency and long-term reliability of core equipment represents one of the critical issues requiring urgent resolution in current research.

Existing studies on the economic viability of wind–hydrogen coupling systems generally suffer from incomplete consideration of value factors [8]. On one hand, the value of hydrogen is often simplified into a fixed parameter, failing to reflect its environmental premium as “green hydrogen” compared to “gray hydrogen,” nor does it capture the price volatility characteristics expected once the hydrogen market matures. On the other hand, system evaluations are typically confined to a single revenue model of hydrogen production and sales, overlooking the potential for wind–hydrogen systems to generate additional income by participating in ancillary service markets—such as frequency regulation and reserve power—as grid-side flexibility resources [3]. This static, single-value assessment model struggles to accurately reveal the true economic performance of different operational strategies throughout their entire lifecycle, potentially leading to decision-making biases.

In the field of optimized control for renewable energy supply systems, model predictive control (MPC) has demonstrated numerous successful applications. Addressing the uncertainty in renewable energy output faced by off-grid electro-hydrogen coupling systems while accommodating the system’s low-carbon operation requirements, Zhang et al. [15] proposed a power control scheme based on model predictive control (MPC), which effectively enhances the robustness of the system’s power regulation. References [16,17] proposed an MPC energy management strategy suitable for grid-connected systems. This strategy not only effectively enhances the integration level of renewable energy but also further reduces the power consumption of the grid. For hydrogen-based energy storage in wind power systems, Abdelghany et al. [18] proposed a two-layer energy management strategy based on model predictive control (MPC). The upper layer focuses on scheduling planning centered around hydrogen supply demands for fuel cell vehicles, while the lower layer concentrates on ensuring stable supply to local baseline electricity loads. This approach ultimately achieves dual satisfaction of both hydrogen supply and electricity demand requirements. Zhai et al. [19] designed a system topology coupling wind power generation, hydrogen production equipment, fuel cells, and supercapacitors to a DC bus. They proposed a rule-based control strategy, identifying 10 distinct operating modes. Mingxuan et al. [20] proposed an energy management control strategy comprising eight operational modes for wind–storage–hydrogen integrated systems, thereby enhancing operational efficiency.

As the core energy conversion equipment, the degradation behavior of electrolytic cells directly determines the system’s full-lifecycle economics. Therefore, in the field of electrolyzer lifespan prediction, Yang et al. [21] proposed an LSTM network incorporating a two-stage attention mechanism. By utilizing multi-dimensional operational data such as voltage, temperature, and charge/discharge history as inputs, this approach achieves high-precision online estimation of State of Health (SOH). Lin M. et al. [22] utilized multi-source health features such as incremental capacity and differential temperature, introducing an LSTM model combining local and global attention mechanisms to significantly enhance lithium battery SOH estimation accuracy. Lee H. et al. [23] proposed a predictive and health management framework for alkaline electrolyzers. Their research established a lifetime and performance degradation model based on voltage decay curves to calculate hydrogen levelized costs and key economic factors, providing a theoretical foundation for embedding decay costs into optimization control in this study.

Despite the advances achieved by the aforementioned studies, a critical research gap remains. As summarized in

Table 1. Comparison of representative studies on wind–hydrogen coupled system control and evaluation. ‘✗’ means not considered, ‘✓’means considered.

Reference	Control Strategy	SOH/Degradation Considered	Hydrogen Pricing	Flexibility Value
Zhang et al. [15]	MPC	✗	Fixed	✗
Gonzalez et al. [16]	MPC	✗	Fixed	✗
Abdelghany et al. [18]	Two-layer MPC	✗	Fixed	✗
Zhai et al. [19]	Rule-based	✗	Fixed	✗
Mingxuan et al. [20]	Rule-based	✗	Fixed	✗
Yang et al. [21]	LSTM-SOH prediction	✓ (estimation only)	N/A	✗
Lee et al. [23]	PHM framework	✓ (degradation model)	Fixed	✗
This study	MPC + LSTM-SOH	✓ (embedded in MPC cost)	Dynamic	✓

, existing works can be broadly categorized into two streams: control-oriented studies that employ MPC or rule-based strategies to optimize short-term operational efficiency, and evaluation-oriented studies that assess system economics using static hydrogen pricing models. The former stream (e.g., [15,16,17,18,19,20]) typically neglects the long-term degradation costs of electrolyzers, treating equipment lifespan as a fixed parameter rather than a dynamic variable influenced by operational decisions. The latter stream (e.g., [8]) relies on fixed hydrogen prices that fail to capture the environmental premium of green hydrogen or the price volatility expected as hydrogen markets mature. Crucially, no existing study simultaneously integrates (i) MPC-based rolling optimization, (ii) data-driven SOH prediction embedded as a real-time cost term, and (iii) a dynamic hydrogen value model linked to carbon markets and market premiums within a unified framework. This three-way integration represents the core novelty of the present work and directly addresses the limitations identified above.

The optimization methods proposed in the aforementioned literature to address core challenges in their respective research scenarios have all achieved satisfactory control performance. However, they share a critical limitation: these approaches are based on deterministic forecast results for system optimization, failing to adequately account for prediction errors arising from fluctuations in renewable energy output and variations in electricity load demand. To address these issues, this paper aims to establish a research framework integrating advanced operational strategies with a comprehensive evaluation model. The core contributions are twofold:

• A novel intelligent power allocation strategy based on model predictive control (MPC) and electrolyzer State-of-Health (SOH) prediction is proposed. This strategy integrates data-driven SOH prediction within the rolling optimization framework of MPC, quantifying electrolyzer lifetime degradation as real-time operational costs. This approach enables simultaneous optimization of short-term economic efficiency and long-term reliability.
• Develop a comprehensive evaluation model incorporating dynamic hydrogen value and flexibility value. This model dynamically links hydrogen pricing to energy markets and environmental value while quantifying the system’s flexibility service capacity, providing a lifecycle economic assessment for different strategies that more closely reflects real market conditions.

2. Modeling and Analysis of Wind–Hydrogen Coupling Systems

To clarify the basis for electrolyzer selection in this study,

Table 2. Comparative overview of three mainstream electrolyzer technologies.

Indicator	AWE	PEME	SOE
Technology Maturity	Commercial scale	Demonstration stage	Laboratory/hundred-kW scale
Catalyst Material	Non-precious metals (Ni-based)	Precious metals (Pt, Ir)	Ni-based ceramic
Operating Temperature	60–90 °C	50–80 °C	700–900 °C
Dynamic Response	Moderate	Fast	Slow
Equipment Cost	Low	High	High
Dynamic Condition Adaptability	Limited (sensitive to start–stop and load fluctuations)	Good	Poor
Typical Lifespan	80,000–100,000 h	60,000–90,000 h	<20,000 h (lab scale)
Current Domestic Demonstration Scale	MW–GW	MW	Hundred-kW
Selected in This Study	Preferred for large-scale commercial deployment	—	—

AWE: alkaline water electrolyzer; PEME: proton exchange membrane electrolyzer; SOE: solid oxide electrolyzer. Data referenced from [9,10,11].

provides a comparative overview of the three mainstream electrolyzer technologies.

2.1. System Architecture

This paper establishes a mathematical model for the wind–hydrogen coupling system, laying the foundation for subsequent optimization strategies and evaluation model development. The system structure is shown in Figure 1; it primarily consists of a wind power generation unit, an electrolytic hydrogen production unit (using the technologically mature alkaline electrolyzer as an example in this paper), a hydrogen storage tank, an external power grid, and a hydrogen sales terminal.

2.2. Wind Power Generation Model

The output power of a wind turbine $P_{wt}\left(t\right)$ is primarily determined by the inflow wind speed $v\left(t\right)$, typically approximated by the turbine’s power curve [24]. Wind energy input can be characterized by the wind power formula:

$$P_{wt}\left(t\right)=\left\{\begin{array}{c}0\\ {\displaystyle \frac{1}{2}}{C}_p\left(\lambda ,\beta \right)\\ P_{rated}\end{array}\right.\rho A{v}^3,\begin{array}{c}v\left(t\right)\le v_{ci}1\mathrm{or}v\left(t\right)\ge v_{co}\\ v_{ci}<v\left(t\right)<v_{co}\\ v_{rated}<v\left(t\right)<v_{co}\end{array}$$

(1)

Among these, $v_{ci}$, $C_p$, and $v_{rated}$ represent the cut-in, cut-out, and rated wind speeds, respectively. $C_p$ is the wind energy utilization coefficient, which is a function of tip speed ratio and pitch angle. $\rho$ is air density and $A$ is fan-swept area [25].

To adapt to the MPC framework, this paper employs a discretized form to describe the predicted sequence of wind power output at each time step, treating it as an exogenous input variable in the optimization process. Considering inherent errors in actual meteorological forecasts, the MPC framework employs rolling updates. At each control time step, it adjusts future power output based on the latest measured wind speed and the revised forecast value. This approach mitigates the impact of forecast uncertainty on control performance to a certain extent.

2.3. Alkaline Electrolyzer Model

The alkaline electrolyzer is the core equipment of the wind–hydrogen coupling system [26]. Its models primarily include the hydrogen production efficiency model and the degradation model.

2.3.1. Hydrogen Production Efficiency Model

Under given electrolytic current or input power conditions, the hydrogen production rate $Q_{H_2}\left(t\right)\left({\mathrm{Nm}}^3/\mathrm{h}\right)$ of an electrolyzer is closely related to its input electrical power $P_{el}\left(t\right)\left(\mathrm{KW}\right)$ and the lower heating value of hydrogen $LH{V}_{H_2}\left({\mathrm{kWh}/\mathrm{Nm}}^3\right)$. Typically, Faraday’s law can be used to establish the relationship between current and hydrogen production [27]. Based on this, the energy consumption characteristics of the electrolyzer under different load conditions can be further considered:

$$Q_{H_2}\left(t\right)={\displaystyle \frac{{\eta }_{Fara}\left(P_{el}\left(t\right)\cdot P_{el}\left(t\right)\right)}{LH{V}_{H_2}}}$$

(2)

Here, ${\eta }_{Fara}$ represents Faraday efficiency, which is the ratio of actual hydrogen production to theoretical hydrogen production, reflecting the deviation of actual hydrogen yield relative to the theoretical value. Faraday efficiency varies with load current density, typically being higher under partial load conditions. For alkaline electrolyzers, this paper employs a fitting function with current density as the independent variable to describe ${\eta }_{Fara}$. Parameter identification is performed using characteristic curves derived from experimental data, enabling the calculation of corresponding hydrogen production efficiency and hydrogen yield at different power levels:

$${\eta }_{Fara}\left(i\right)={\displaystyle \frac{i^2}{a_1+a_2\cdot i+a_3\cdot i^2}}$$

(3)

Among these, $a_1$, $a_2$, and $a_3$ are fitting parameters related to the electrolyzer design. The input power of the electrolyzer correlates with the current density and the number of cells. Additionally, considering that actual electrolyzers have a minimum startup power $P_{el}^{ \min }$ (typically 20–30% of the rated power) and a maximum operating power $P_{el}^{ \max }$, corresponding operating power constraints are incorporated into the model to ensure the equipment operates within a safe and efficient power range [28].

2.3.2. Degradation Models and SOH Prediction

To effectively account for degradation effects in system optimization, this paper defines the predicted State of Health (SOH) of an electrolyzer as a scalar value between 0 and 1, where 1 represents a brand-new state and 0 indicates end of life.

SOH is linked to cumulative damage D(t) through a simple mapping relationship [29]. When cumulative damage reaches the threshold D_EOL, it is considered that replacement or overhaul is required.

$$SOH=1-{\displaystyle \frac{D_t}{D_{EOL}}}$$

(4)

To quantitatively characterize the impact of different operating conditions on cell lifespan during system-level optimization, this paper employs a simplified lifespan model based on the concept of linear cumulative damage. The State of Health (SOH) of the cell can be mapped from the cumulative damage:

$$SOH\left(k\right)=1-D\left(k\right)$$

(5)

Among these, $D\left(k\right)$ represents the cumulative damage of the electrolytic cell at discrete time points. Taking into account typical stress factors such as start–stop cycles, power fluctuations, and long-term low-load operation, this paper decomposes the damage increment $\Delta D\left(k\right)$ between two adjacent sampling time points into three components:

$$\Delta D\left(k+1\right)=\Delta D\left(k\right)+\Delta D_{on/off}\left(k\right)+\Delta D_{ramp}\left(k\right)+\Delta D_{low}\left(k\right)$$

(6)

Among these, $\Delta D_{on/off}\left(k\right)$, $\Delta D_{ramp}\left(k\right)$, and $\Delta D_{low}\left(k\right)$ represent the contributions of start–stop cycles, power ramping, and low-load operation to cumulative damage at t_k, respectively.

This paper correlates the degradation of electrolytic cells with several typical stress factors:

(1)

Start–Stop Cycle Damage $D_{ramp}$ Model

Frequent start–stop cycles cause repeated fluctuations in temperature and pressure within the electrolytic cell, subjecting the membrane electrode assembly and sealing structures to significant thermal and mechanical stresses. This is one of the key factors affecting service life. To characterize the impact of start–stop cycles on service life, the following event indicators are defined:

${\delta }_{cold}\left(k\right)=1$, Cold start occurs at t_k, otherwise 0;

${\delta }_{warm}\left(k\right)=1$, Warm start occurs at t_k, otherwise 0;

${\delta }_{stop}\left(k\right)=1$, At t_k, the machine transitions from the running state to the stopped state; otherwise, it remains at 0.

In this paper, the aforementioned events are identified through abrupt changes in cell power or operational status. The incremental damage caused by start–stop cycles is modeled as a linear superposition of various events:

$$\Delta D_{on/off}\left(k\right)={\alpha }_{cold}{\delta }_{cold}\left(k\right)+{\alpha }_{warm}{\delta }_{warm}\left(k\right)+{\alpha }_{stop}{\delta }_{stop}\left(k\right)$$

(7)

Among these, ${\alpha }_{cold}$, ${\alpha }_{warm}$, and ${\alpha }_{stop}$ represent the unit damage coefficients corresponding to cold start, hot start, and shutdown, respectively.

(2)

Power Fluctuation Damage $D_{ramp}$ Model

During significant power ramp-up and sudden power drops in an electrolytic cell, rapid changes in its internal temperature and concentration fields can cause additional fatigue damage to critical materials. Let the rated power of the electrolytic cell be $P_{el}^{rated}$, and the sampling period be $\Delta t$. Then, the power increment at t_k is as follows:

$$\Delta P\left(k\right)=P_{el}\left(k\right)-P_{el}\left(k-1\right)$$

(8)

Set the safety threshold for the electrolytic cell as $\Delta P_s$. When $\left|\Delta P\left(k\right)\right|<\Delta P_s$, power fluctuations not exceeding the safety threshold are considered to have negligible impact on lifespan. When $\left|\Delta P\left(k\right)\right|>\Delta P_s$, a normalized linear function is employed to characterize the damage function, where ${\beta }_{ramp}$ represents the power fluctuation damage coefficient:

$$\Delta D_{ramp}\left(k\right)=\left\{\begin{array}{cc}0& \left|\Delta P\left(k\right)\right|<\Delta P_s\\ {\beta }_{ramp}{\displaystyle \frac{\left|\Delta P\left(k\right)\right|-\Delta P_s}{P_{el}^{rated}}}& \left|\Delta P\left(k\right)\right|>\Delta P_s\end{array}\right.$$

(9)

(3)

Low-Load Operation Damage $D_{low}$ Model

Prolonged operation at low load may lead to gas purity issues and adversely affect the catalyst. Set the low-load threshold power to the following:

$$P_{low}={\theta }_{low}{P}_{el}^{rated},0<{\theta }_{low}<1$$

(10)

When $P_{low}>P_{el}^{rated}$, the electrolytic cell is considered to be in the low-load zone. At this point, the damage increment correlates with the degree of low load and the residence time:

$$\Delta D_{low}\left(k\right)=\left\{\begin{array}{cc}0& P_{el}\left(k\right)\ge P_{low}\\ {\gamma }_{low}{\displaystyle \frac{P_{low}\left(k\right)-P_{el}\left(k\right)}{P_{el}^{rated}}}& P_{el}\left(k\right)<P_{low}\end{array}\right.$$

(11)

Among these, ${\gamma }_{low}$ represents the damage coefficient for low-load operation; the deeper the low-load condition and the longer its duration, the greater the cumulative damage.

To facilitate a unified description of electrolyzer lifetime degradation behavior across different time scales, the instantaneous damage rate is further refined by decomposing it into three components: start–stop cycle damage, power fluctuation damage, and low-load operation damage [30]. On a continuous time scale, the discrete damage increment (6) can be regarded as the integral of the instantaneous damage rate over the sampling period $\Delta t$, yielding the total instantaneous damage rate satisfying the following:

$$\dot{D}\left(t\right)={\dot{D}}_{on/off}\left(T\left(t\right),State\left(t\right)\right)+{\dot{D}}_{ramp}\left({\dot{P}}_{el}\left(t\right),T\left(t\right)\right)+{\dot{D}}_{low}\left({\dot{P}}_{el}\left(t\right),T\left(t\right)\right)$$

(12)

Therefore, the instantaneous damage rate D(t) at t can be modeled as follows:

$$\dot{D}\left(t\right)=f\left({\dot{P}}_{el}\left(t\right),T\left(t\right),State\left(t\right)\right)$$

(13)

Among these, ${\dot{P}}_{el}\left(t\right)$ represents the rate of power change, $T\left(t\right)$ denotes temperature, and $State\left(t\right)$ indicates the operating state (startup, shutdown, steady state).

At any given time point $t$, the instantaneous damage rate of the electrolyzer can be expressed as a weighted combination function of the aforementioned stresses. To enable forward-looking optimization in MPC, we constructed a model capable of predicting SOH changes over a future time interval. This paper employs a Long Short-Term Memory (LSTM) network, utilizing historical power sequence $P_{el}\left(t-k:t\right)$, operational status sequence, and temperature data as inputs to forecast the SOH trend $\Delta SOH\left(t+1:t+N\right)$ over the next N time steps.

$$\begin{array}{l}\left[\Delta \stackrel{⏜}{SOH}\left(t+1\right)\right.,\cdots ,\left.\Delta \stackrel{⏜}{SOH}\left(t+N\right)\right]\\ =LST{M}_0\left(P_{el}\left(t-k:t\right),State\left(t-k:t\right),T\left(t-k:t\right)\right)\end{array}$$

(14)

To ensure the validity and reproducibility of the LSTM-based SOH prediction model, the training dataset and model configuration are detailed as follows. The training data were generated synthetically using the physics-based degradation model established in Equations (6)–(13). Specifically, 500 distinct operational scenarios were simulated by varying wind power input profiles, start–stop frequencies, and load levels, yielding a total dataset of approximately 87,600 hourly samples covering diverse operating conditions over a simulated 10-year horizon. It is important to clarify that this approach does not constitute circular reasoning: the physics-based model (Equations (6)–(13)) independently computes cumulative damage increments based on predefined stress coefficients, while the LSTM serves solely as a data-driven surrogate model to accelerate forward-looking SOH prediction within the MPC optimization loop. The dataset was partitioned into training, validation, and test subsets at a ratio of 8:1:1. The input feature vector at each time step comprises the historical electrolyzer power sequence $P_{el}(t-k:t)$, the operational status sequence $State(t-k:t)$, and the temperature sequence $T(t-k:t)$, with a lookback window of k = 24 steps. The LSTM network consists of two stacked LSTM layers (each with 64 hidden units) followed by a fully connected output layer. Model training employed the Adam optimizer with a learning rate of 0.001 and a batch size of 64 over 100 epochs. To further clarify the prediction accuracy across the full horizon, two complementary RMSE metrics are reported. The one-step-ahead RMSE (i.e., the error of the first predicted SOH increment, $\Delta SOH(t+1)$) on the held-out test set is 0.0018, reflecting the model’s precision under minimal error accumulation. The horizon-averaged RMSE, computed as the root mean square error averaged across all 96 prediction steps and all test windows, is 0.0032, which represents the overall accuracy metric reported previously. To characterize error accumulation behavior, Figure 2 plots the step-wise RMSE as a function of prediction step $n$ ($n=1,2,\dots ,96$), where the dashed horizontal line indicates the horizon-averaged RMSE of 0.0032 and error bars represent ±1 standard deviation across test windows. As shown in Figure 2, the RMSE increases gradually from 0.0018 at step 1 to 0.0051 at step 96, remaining below 0.006 throughout the entire horizon. This bounded accumulation is attributable to two factors: (i) the SOH degradation process is relatively smooth and quasi-monotonic within a 24 h window, limiting divergence of multi-step predictions; and (ii) the rolling update mechanism of MPC re-initializes the LSTM input at each control interval using the latest measured system state, thereby resetting and constraining cumulative errors in practice. The horizon-averaged RMSE of 0.0032 and the maximum step-wise RMSE of 0.0051 are both well within acceptable bounds for embedding the SOH prediction as a cost term in the MPC optimization framework. This SOH prediction model will serve as a key constraint or cost term in the MPC optimization problem.

2.4. Hydrogen Storage Tank Model

In wind–hydrogen coupling systems, the function of hydrogen storage tanks is to regulate and coordinate temporal and power imbalances between the hydrogen production and consumption sides [31]. The state of the system (State of Charge, SOC_H) can be represented as follows:

$$SO{C}_H\left(t+1\right)=SO{C}_H\left(t\right)+{\displaystyle \frac{Q_{H_2}\left(t\right)-Q_{H_2,demand}\left(t\right)}{V_{\tan k}}}\cdot \Delta t$$

(15)

where $V_{\tan k}$ represents the nominal volume of the hydrogen storage tank. At each discrete time step, the change in hydrogen storage state is determined by the difference between hydrogen production and hydrogen discharge, subject to the upper limit of the tank’s rated capacity. ${SOC}_H$ is constrained by upper limit ${SOC}_H^{\max }$ and lower limit ${SOC}_H^{\min }$.

3. Intelligent Power Allocation Strategy Based on MPC and SOH Prediction

This chapter details the proposed intelligent power allocation strategy. Its core concept leverages MPC’s robust capabilities in multi-constraint, multi-variable optimization. By integrating current system status, forecasts of future wind power output and market prices, and embedding electrolyzer SOH predictions into a rolling optimization framework, it solves an optimization problem within a finite time horizon. This enables the system to generate optimal power commands for each decision point at the current moment.

3.1. MPC Rolling Optimization Framework

The basic workflow of the MPC predictive control model can be summarized as three steps: prediction, optimization, and rolling execution. This approach is highly suitable for real-time scheduling of wind–hydrogen systems.

(1)

At the current time, obtain the system’s measured status, including wind power output, $SO{C}_H\left(t\right)$, electrolyzer operating power, and estimated $SOH\left(t\right)$ values.

(2)

Based on weather forecasts and market information, obtain the wind power output prediction sequence and electricity price prediction sequence for the next $N_p$ time steps.

(3)

Using historical power sequences, temperature sequences, and start/stop records from the electrolytic cell as input, invoke the trained LSTM-SOH prediction model to obtain the forecast of SOH changes for the next $N_p$ steps.

(4)

Solve an optimization problem within the prediction time domain $\left[t,t+N_p\right]$, with the objective being the system’s total operating cost. The decision variables are the power commands for electrolytic cells and the grid’s power purchase/sale commands in the future time domain. Constraints include power balance constraints, equipment operating limits, ramp rate constraints, and hydrogen storage SOC boundary constraints. Thus, the optimal power control sequence $\left\{P_{el}^{\ast }\left(t\right),\dots ,\right.\left.P_{el}^{\ast }\left(t+N_p\right)\right\}\left\{P_{el}^{\ast }\left(t\right),\dots ,\right.\left.P_{el}^{\ast }\left(t+N_c\right)\right\}$ can be obtained, where $N_c$ represents the control time domain, and typically $N_c\le N_p$.

(5)

Use the first element $P_{el}^{\ast }$ of the optimal control sequence as the actual power command applied to the electrolytic cell at the current time.

(6)

The system state is updated to time $t+1$, and the above process is repeated to achieve rolling optimization.

Through the aforementioned closed-loop rolling mechanism, the MPC strategy can automatically correct deviations caused by prediction errors at each time step, effectively balancing the impacts of wind power uncertainty, electricity price fluctuations, and SOH prediction errors on system operation [32]. The basic flowchart of the MPC model’s rolling optimization process is shown in Figure 3.

The specific temporal parameters of the MPC framework are configured as follows. The time step is set to $\Delta t=15$ min, reflecting a balance between control responsiveness and computational feasibility. The prediction horizon is $N_p=96$ steps, corresponding to a 24 h look-ahead window that captures diurnal wind power variability and electricity price fluctuations. The control horizon is set to $N_c=4$ steps (equivalent to 1 h), which is shorter than the prediction horizon to reduce the dimensionality of the optimization problem while retaining adequate control flexibility, satisfying the typical relationship $N_c\le N_p$. At each control interval, the optimization problem is formulated as a Mixed-Integer Linear Program (MILP) and solved using a standard interior-point solver. The average computation time per optimization step is approximately 8 s on a standard workstation (Intel Core i7-10700, 16 GB RAM), which is well within the 15 min control interval, confirming the real-time applicability of the proposed strategy for large-scale wind–hydrogen systems.

3.2. Objective Function Design

To enhance the economic viability of wind–hydrogen coupling systems, this paper decomposes the total cost into three major components, weighted by coefficients $\alpha$, $\beta$, and $\gamma$, representing the grid interaction cost weight, electrolyzer degradation cost weight, and operation and maintenance cost weight, respectively. The overall minimization constraint function is defined as follows:

$$\underset{P_{el}}{{\displaystyle \min J}}={\displaystyle \sum _{k=t}^{t+N_p}\left[\alpha \cdot C_{grid}\left(k\right)+\beta \cdot C_{\mathrm{deg}radation}\left(k\right)+\gamma \cdot C_{operation}\left(k\right)\right]}$$

(16)

Grid Interaction Cost $C_{grid}\left(k\right)$: This cost item represents the energy exchange cost between the system and the grid. When the system purchases electricity from the grid, a positive cost is incurred; when the system sells electricity to the grid, a negative cost is generated.

$$C_{grid}\left(k\right)=p_{grid}\left(k\right)\cdot \left(P_{el}-{\widehat{P}}_{wt}\left(k\right)\right)\cdot △t$$

(17)

where $p_{grid}\left(k\right)$ represents the time-of-use electricity price. When wind power output exceeds the power consumption of the electrolysis cell, the system can sell electricity back to the grid, resulting in a negative revenue under this scenario.

To incorporate cell lifespan factors into operational decisions, this paper converts future damage increments $\Delta D\left(k\right)$ at each time point into corresponding economic costs based on instantaneous damage rate estimates derived from the SOH prediction model. Specifically, this is achieved through cell degradation cost $C_{\mathrm{deg}radation}\left(k\right)$, which quantifies SOH decay into economic costs and serves as the key to realizing long-term reliability optimization.

$$C_{\mathrm{deg}radation}\left(k\right)=\dot{D}\left(P_{el}\left(k\right),{\displaystyle \frac{d{P}_{el}}{dt}}\left(k\right),\dots \right)\cdot C_{replacement}$$

(18)

Here, $\dot{D}\left(\cdot \right)$ represents the instantaneous damage rate estimate derived from the SOH prediction model, while $C_{replacement}$ denotes the unit capacity replacement cost of the electrolyzer.

Operating and Maintenance Cost $C_{operation}\left(k\right)$: This category encompasses all operational expenses excluding equipment replacement, such as fixed O&M costs and water consumption. It can be simplified as proportional to the operating power. This paper establishes a linear relationship between this cost and the operating power of the electrolytic cell, characterized by the following coefficient:

$$C_{operation}\left(k\right)=co\&M\cdot P_{el}\left(k\right)\cdot \Delta t$$

(19)

By combining the three cost categories, the weighted sum of total costs within the forecast time horizon is formed and serves as the objective function for the MPC optimization problem.

The weight coefficients $\alpha$, $\beta$, and $\gamma$ in Equation (16) were determined through a two-step procedure. First, each cost component was normalized by its respective order of magnitude under baseline operating conditions to ensure dimensional consistency and comparability across terms. Specifically, $C_{grid}(k)$ is denominated in monetary units per unit energy (yuan/kWh), $C_{\mathrm{deg}radation}(k)$ is expressed as a fraction of the electrolyzer replacement cost per time step, and $C_{operation}(k)$ is proportional to operating power. After normalization, the baseline weight ratio was set to $\alpha :\beta :\gamma =0.5:0.35:0.15$, satisfying $\alpha +\beta +\gamma =1$. These values reflect the relative economic significance of each cost category: grid interaction costs constitute the largest share of short-term expenditure, degradation costs represent a critical long-term investment risk, and O&M costs are comparatively minor. Second, a sensitivity analysis was conducted by varying each weight coefficient by $\pm 20\%$ around its baseline value while holding the others fixed. The results indicate that the lifecycle NPV of Strategy C remains within a $\pm 3.2\%$ band under these perturbations, confirming that the proposed strategy’s superiority over Strategies A and D is robust to moderate changes in weight assignment. The final values $\alpha =0.50$, $\beta =0.35$, $\gamma =0.15$ were adopted for all subsequent simulations.

3.3. Constraints

To ensure the optimization results are engineering-feasible, the MPC optimization problem must satisfy a series of physical and operational constraints. The optimization problem must meet the following constraints:

Electrolyzer power upper and lower limits: $P_{el}^{ \min }\le P_{el}\left(k\right)\le P_{el}^{ \max }$

Electrolyzer Ramp Rate Constraint: $\left|P_{el}\left(k+1\right)-P_{el}\left(k\right)\right|\le \Delta P_{el}^{\max }$

Hydrogen Storage Tank SOC Constraint: $SO{C}_H^{\min }\le SO{C}_H\left(k\right)\le SO{C}_H^{\max }$

Power Balance Constraint: $P_{el}\left(k\right)+P_{sell}\left(k\right)={\widehat{P}}_{wt}\left(k\right)+P_{buy}\left(k\right)$, where $P_{sell}\left(k\right)$ and $P_{buy}\left(k\right)$ represent the power sold and purchased, respectively, and both are greater than or equal to zero.

To prevent the optimizer from simultaneously purchasing and selling electricity at the same time step, which would constitute physically unrealizable arbitrage, binary variables are introduced to enforce mutual exclusivity between grid import and export operations. Let $u_{buy}(k)\in 0,1$ and $u_{sell}(k)\in 0,1$ denote the binary indicators for grid power purchase and sale, respectively. The following constraints are added:

$$P_{buy}(k)\le P_{buy}^{max}\cdot u_{buy}(k)$$

(20)

$$P_{sell}(k)\le P_{sell}^{max}\cdot u_{sell}(k)$$

(21)

$$u_{buy}(k)+u_{sell}(k)\le 1$$

(22)

where $P_{buy}^{max}$ and $P_{sell}^{max}$ denote the maximum grid import and export capacities, respectively. Constraint (22) ensures that the system cannot simultaneously import and export power within the same 15 min time step.

Similarly, to prevent the hydrogen storage tank from being simultaneously charged (via electrolyzer production) and discharged (via hydrogen sales) within the same time step, binary variables $u_{prod}(k)\in 0,1$ and $u_{sell,H_2}(k)\in 0,1$ are introduced:

$$Q_{H_2}(k)\le Q_{H_2}^{max}\cdot u_{prod}(k)$$

(23)

$$Q_{H_2,demand}(k)\le Q_{H_2,demand}^{max}\cdot u_{sell,H_2}(k)$$

(24)

$$u_{prod}(k)+u_{sell,H_2}(k)\le 1$$

(25)

These four binary variables are incorporated into the existing MILP formulation (Section 3.1), which is solved using a standard branch-and-bound interior-point solver. The addition of binary variables increases the problem dimensionality; however, the average computation time per optimization step increases only modestly from approximately 8 s to 11 s on the same workstation, remaining well within the 15 min control interval and confirming the real-time feasibility of the extended formulation.

4. Dynamic Integrated Value Assessment Model for Wind–Hydrogen Coupling Systems

In traditional economic analyses of wind–hydrogen coupling systems, the value of hydrogen is typically simplified to a fixed unit selling price, overlooking factors such as varying application scenarios, carbon reduction benefits, and ancillary power services. This approach fails to accurately reflect green hydrogen’s true value within future energy systems. This chapter constructs an evaluation model that considers dynamic comprehensive value, quantifying the system’s total Net Present Value from a full lifecycle perspective.

4.1. Dynamic Hydrogen Value Model

In traditional assessments, hydrogen value $V_{H_2}$ is typically treated as a constant. This paper introduces its dynamic nature:

$$V_{H_2}=V_{base}+V_{carbon}\left(t\right)+V_{market}\left(t\right)$$

(26)

where $V_{base}$ represents the base value of hydrogen, referencing current gray or blue hydrogen costs. $V_{carbon}\left(t\right)$ represents the carbon value. As carbon trading markets mature, green hydrogen will generate carbon reduction benefits due to its zero-carbon emissions. This value may be linked to the carbon emission allowance price $pcarbon\left(t\right)$. $\epsilon$ represents the CO₂ reduction per unit of hydrogen.

$$V_{carbon}\left(t\right)=\epsilon \cdot pcarbon\left(t\right)$$

(27)

$V_{market}\left(t\right)$: Market Premium. As the hydrogen market matures in the future, price fluctuations will occur. This is achieved by analyzing the correlation between historical energy prices (natural gas, electricity) and hydrogen prices and introducing scenario analysis to simulate future hydrogen price volatility.

To characterize the actual level of hydrogen prices, this paper utilizes hydrogen price indices from the Yangtze River Delta, Tangshan, Pearl River Delta, Henan, Xinjiang, and other representative regions within the “China Hydrogen Price Index System” published by the Shanghai Environment and Energy Exchange, along with China’s green hydrogen price index data, to conduct a statistical analysis of price fluctuations from 2022 to 2025. As shown in Figure 4, hydrogen prices across China’s major regions fluctuated modestly within the 30–40 yuan/kg range during 2022–2025, with notable regional price differentials. Specifically, on 27 October 2025, hydrogen prices stood at 33.69 yuan/kg in the Yangtze River Delta, Tangshan at 34.83 yuan/kg, the Pearl River Delta at 38.13 yuan/kg, Henan at 29.33 yuan/kg, and Xinjiang at 40.25 yuan/kg. This pattern reflects higher prices in eastern coastal regions and areas with relatively weaker resource endowments, while central regions exhibit comparatively lower hydrogen prices. On the same day, the clean hydrogen price in the Yangtze River Delta region was 34.16 yuan/kg, slightly higher than the conventional hydrogen price in the region. This primarily stems from the explicit inclusion of carbon emission costs in clean hydrogen pricing, causing its price to rise modestly alongside the national carbon allowance price. The China Green Hydrogen Price released on 10 November 2025 stood at 28.36 yuan/kg, positioning it within the lower-to-mid range of regional hydrogen prices. This reflects that renewable energy-based hydrogen production has achieved a certain cost advantage in some resource-rich regions.

To incorporate the aforementioned price fluctuations into the system valuation, this paper normalizes the hydrogen price time series $P_{H_2}\left(t\right)$ and constructs a dimensionless hydrogen price index to reflect the relative level of hydrogen prices:

$${\tilde{P}}_{H_2}\left(t\right)={\displaystyle \frac{P_{H_2}}{{\overline{P}}_{H_2}}}$$

(28)

Among these, ${\overline{P}}_{H_2}$ represents the average hydrogen price per year. The market value of the dynamic hydrogen value model is as follows:

$$V_{market}\left(t\right)=k_m{\tilde{P}}_{H_2}\left(t\right)$$

(29)

Here, $k_m$ represents the proportional coefficient that converts the price index into system returns.

In the future, as carbon market prices rise and green hydrogen production capacity continues to expand, the relative pricing dynamics between clean hydrogen and green hydrogen compared to gray hydrogen may undergo further shifts. Therefore, incorporating a time-varying hydrogen price curve to construct a dynamic hydrogen value model holds significant value in assessing the economic viability of wind–hydrogen coupling systems.

4.2. Flexibility Value Model

In addition to generating revenue from commercial hydrogen production, wind–hydrogen systems can leverage their rapid response capabilities as grid-side flexibility resources to provide ancillary services such as frequency regulation and reserve power. The estimated flexibility revenue $R_{flex}$ can be calculated as follows:

$$R_{flex}\left(t\right)=s{\displaystyle \sum \left[P_{flex,s}\left(t\right)\cdot p_s\left(t\right)\cdot \Delta t\right]}$$

(30)

where s represents different types of ancillary services (e.g., primary frequency regulation, secondary frequency regulation), $P_{flex,s}\left(t\right)$ denotes the system’s reserved adjustment capacity for service s at time t, and $p_s\left(t\right)$ is the capacity price or call price for that service. $P_{flex,s}\left(t\right)$ depends on the electrolyzer’s available adjustment margin and response speed. The MPC strategy proposed in this paper, due to its precise power control capability, can more reliably commit to and deliver flexibility services, thereby unlocking this portion of potential revenue.

To ensure reproducibility, the specific ancillary service market rules assumed in this study are clarified as follows. Two types of flexibility services are considered: primary frequency response (PFR) and spinning reserve (SR). For each service type $s$, the system reserves an upward regulation margin by operating the electrolyzer below its maximum feasible power level at each time step, i.e., the reserved capacity is defined as follows:

$$P_{\mathrm{flex},s}(t)=\min \left(P_{el}^{\max }-P_{el}(t),\hspace{1em}{\dot{P}}_{el}^{\max }\cdot {\tau }_s\right)$$

(31)

where ${\dot{P}}_{el}^{\max }$ denotes the maximum ramp rate of the electrolyzer and ${\tau }_s$ is the required response time for service $s$ (set to 30 s for PFR and 10 min for SR in this study). This formulation ensures that the committed flexibility capacity is physically deliverable within the required response window. The reserved capacity $P_{\mathrm{flex},s}(t)$ is explicitly incorporated into the MPC power balance constraint as follows:

$$P_{el}(t)+P_{\mathrm{sell}}(t)+{\displaystyle \sum _s{P}_{\mathrm{flex},s}}(t)\le {\widehat{P}}_{wt}(t)+P_{\mathrm{buy}}(t)$$

(32)

This constraint guarantees that the power allocated to flexibility reservation reduces the power available for hydrogen production at the corresponding time step, establishing a direct trade-off between instantaneous hydrogen yield and flexibility revenue. The capacity prices $p_s(t)$ for PFR and SR are referenced from China’s provincial ancillary service market settlement rules, with baseline values of 0.15 yuan/(kW·h) and 0.10 yuan/(kW·h), respectively.

4.3. Lifecycle Cost Analysis Metrics

Based on the aforementioned dynamic hydrogen value model and flexibility value model, this paper constructs a comprehensive economic evaluation indicator system for wind–hydrogen coupling systems from a full lifecycle perspective. The core indicator is Net Present Value (NPV), supplemented by Levelized Cost of Hydrogen (LCOH) for comparative analysis. Based on these models, the system’s full lifecycle NPV is calculated as follows:

$$NPV=-C_{cap}+{\displaystyle \sum _{t=1}^T\frac{R_{total}\left(t\right)-C_{total}\left(t\right)}{{\left(1+r\right)}^t}}$$

(33)

where $C_{cap}$ represents the initial investment cost (including wind turbines, electrolytic cells, hydrogen storage tanks, etc.); $R_{total}\left(t\right)$ denotes the total revenue in year t:

$$R_{total}\left(t\right)=V_{H_2}\cdot Q_{H^2,sold}\left(t\right)+R_{grid}\left(t\right)+R_{flex}\left(t\right)$$

(34)

where $R_{grid}\left(t\right)$ represents electricity sales revenue; $C_{total}$ represents total costs in year t:

$$C_{total}\left(t\right)=C_{grid}\left(t\right)+C_{\mathrm{deg}radation}\left(t\right)+C_{operation}\left(t\right)$$

(35)

Equipment replacement costs are triggered when SOH drops below the threshold. $r$ represents the discount rate; T denotes the system lifecycle. This evaluation model captures the system’s revenue streams more comprehensively by incorporating dynamic hydrogen pricing and flexibility value.

5. Case Simulation and Results Analysis

5.1. Simulation Settings

To validate the effectiveness of the proposed strategy and dynamic valuation framework, this paper designs a case simulation. System configuration: a 10 MW wind farm paired with a set of 5 MW alkaline electrolyzers, featuring a hydrogen storage tank with a capacity of 2000 kg. The simulation period spans 20 years, employing a hybrid approach combining short-term operational simulations with long-term statistical evaluations. Representative annual scenarios are constructed based on typical one-year data, then scaled repeatedly over 20 years. These scenarios account for State of Health (SOH) evolution and electrolyzer replacement events to derive full-lifecycle economic metrics.

To address the potential limitation of repeating an identical annual wind profile, a three-scenario sensitivity analysis was conducted to assess the influence of inter-annual wind resource variability on the main conclusions. Based on publicly available wind speed statistics for a representative site in Inner Mongolia, China, three annual capacity factor scenarios were constructed:

Low-wind year: annual capacity factor reduced by 10% relative to the baseline profile ($CF=0.90\cdot C{F}_{base}$).

Baseline year: representative annual profile as described above ($CF=C{F}_{base}$).

High-wind year: annual capacity factor increased by 10% ($CF=1.10\cdot C{F}_{base}$).

Each scenario was scaled repeatedly over the 20-year lifecycle under the same SOH evolution and replacement event logic. The NPV improvement of Strategy C relative to Strategy A under the three scenarios is summarized in

Table 3. NPV improvement of Strategy C relative to Strategy A under three inter-annual wind resource scenarios.

Scenario	Annual Capacity Factor	NPV Improvement (Strategy C vs. A)
Low-wind year	$0.90\cdot C{F}_{base}$	+11.3%
Baseline year	$C{F}_{base}$	+12.7%
High-wind year	$1.10\cdot C{F}_{base}$	+13.5%

. As shown, Strategy C maintains a consistent economic advantage across all wind resource conditions, with NPV improvements ranging from 11.3% (low-wind) to 13.5% (high-wind), compared to 12.7% under the baseline. This stability confirms that inter-annual wind resource variability does not alter the relative superiority of the proposed strategy, and the main conclusions drawn from the baseline scenario remain valid.

The key simulation parameters of the system and degradation model are summarized in

Table 4. Key simulation parameters for system configuration and degradation model.

Category	Parameter	Symbol	Value	Unit	Reference/Basis
System Configuration	Wind farm rated capacity	$P_{wt}^{rated}$	10	MW	Case design
	Electrolyzer rated capacity	$P_{el}^{rated}$	5	MW	Case design
	Electrolyzer minimum power	$P_{el}^{min}$	1	MW	20% of rated
	Hydrogen storage tank capacity	$V_{tank}$	2000	kg	Case design
	SOC upper limit	$SO{C}_H^{max}$	0.95	—	Operational safety
	SOC lower limit	$SO{C}_H^{min}$	0.05	—	Operational safety
Degradation Model	Cold start damage coefficient	${\alpha }_{cold}$	2.0 × 10−3	/event	[14] (0.2% MEA fatigue/cycle)
	Warm start damage coefficient	${\alpha }_{warm}$	5.0 × 10−4	/event	[23]
	Shutdown damage coefficient	${\alpha }_{stop}$	3.0 × 10−4	/event	[23]
	Ramp damage coefficient	${\beta }_{ramp}$	8.0 × 10−4	—	Calibrated from [23]
	Low-load damage coefficient	${\gamma }_{low}$	6.0 × 10−4	—	Calibrated from [23]
	Low-load threshold ratio	${\theta }_{low}$	0.20	—	20% of rated power
	Safe ramp threshold	$\Delta P_s$	0.5	MW	Operational specification
	EOL damage threshold	$D_{EOL}$	1.0	—	Normalized
Economic Parameters	Electrolyzer replacement cost	$C_{replacement}$	300	Ten thousand yuan/MW	Industry estimate
	O&M cost coefficient	$co\&M$	0.02	Ten thousand yuan (MW·h)	Industry estimate
	Discount rate	$r$	8	%	China energy project standard
	MPC objective weight (grid)	$\alpha$	0.5	—	Sensitivity-tuned
	MPC objective weight (degradation)	$\beta$	0.35	—	Sensitivity-tuned
	MPC objective weight (O&M)	$\gamma$	0.15	—	Sensitivity-tuned
MPC Framework	Time step	$\Delta t$	15	min	—
	Prediction horizon	$N_p$	96	steps (24 h)	—
	Control horizon	$N_c$	4	steps (1 h)	—
	Wind forecast noise level	${\sigma }_{wt}$	0.05	relative std	—
	Price forecast noise level	${\sigma }_{price}$	0.03	relative std	—
Strategy E (Rule-Based)	Hard ramp rate limit	$\Delta P_{rule}^{max}$	$0.30\cdot P_{el}^{rated}$	MW/step	—
	Max cold starts per day	$N_{cold}^{max}$	2	/day	—
	Moving average window	$W_{MA}$	5 steps (75 min)	—	—
	Minimum standby duration	$T_{min}$	30	min	—
Strategy F (Linear Degradation MPC)	Linear degradation intercept	$c_0$	$1.2\times {10}^{-5}$	/step	—
	Linear degradation slope	$c_1$	$3.8\times {10}^{-5}$	/step	—
	Fitting method	—	Least-squares	—	—

. Three strategies are compared:

Strategy A (Baseline Strategy): Simple power tracking. The electrolyzer absorbs as much wind power as possible while adhering to its operational constraints.

Strategy B (Short-Term Economic Strategy): Based on MPC optimization, but the objective function does not consider degradation cost $C_{\mathrm{deg}radation}$, focusing solely on optimizing grid interaction costs and operational costs. It should be noted that Strategy B retains all physical and operational constraints of the MPC framework, including the electrolyzer ramp rate constraint $\left|P_{el}(k+1)-P_{el}(k)\right|\le \Delta P_{el}^{\max }$, power boundary limits, and hydrogen storage SOC constraints. This ensures that Strategy B remains engineering-feasible and does not represent an overly permissive benchmark. The sole distinction between Strategy B and the proposed Strategy C lies in the objective function: Strategy B excludes the degradation cost term $C_{\mathrm{degradation}}(k)$, focusing exclusively on minimizing short-term grid interaction and O&M costs, whereas Strategy C incorporates degradation costs as an additional optimization objective to balance long-term equipment reliability.

Strategy C (the strategy proposed in this paper): An intelligent power allocation strategy based on MPC and SOH prediction. It further incorporates the cost of electrolyzer lifetime degradation and future hydrogen market price information.

Strategy D (Fixed Hydrogen Price Strategy): Similar to Strategy C, it also considers electrolyzer lifetime degradation costs and the MPC optimization framework but employs a fixed electricity price and a fixed hydrogen price.

Strategy E (Rule-Based Degradation-Aware Strategy): To provide a more practically relevant baseline that reflects common engineering protection practice, Strategy E implements a purely rule-based degradation-aware control scheme without any predictive optimization. The rules are triggered solely by real-time measurements and are defined as follows:

(1)

Hard ramp rate limit: The electrolyzer power change between consecutive time steps is strictly limited to $|\Delta P_{el}(k)|\le 0.30\cdot P_{el}^{rated}$, corresponding to 60% of the MPC ramp constraint adopted in Strategies B–D. This reflects a conservative engineering specification commonly applied in industrial electrolyzer protection systems.

(2)

Cold start frequency limit: The number of cold starts per day is capped at 2. If the predicted low-power period is shorter than 30 min based on the current wind power measurement, the electrolyzer remains on standby rather than shutting down, avoiding unnecessary cold restart damage.

(3)

Moving average power smoothing: A 5-step moving average filter (window length = 75 min) is applied to the wind power input signal before dispatching power commands to the electrolyzer, suppressing short-term fluctuations that would otherwise induce rapid ramping damage.

Strategy E incorporates no forecast information, no optimization solver, and no SOH model. It represents the upper bound of rule-based degradation protection achievable without predictive capabilities, serving as a stronger and more realistic baseline than Strategy B for evaluating the incremental value of LSTM-embedded MPC optimization in Strategy C.

To clarify the forecast conditions adopted in the case simulation, the wind power and electricity price prediction sequences fed into the MPC optimization at each control interval are generated as follows, rather than assuming perfect foresight.

For wind power forecasting, the predicted sequence ${\widehat{P}}_{wt}(t+1:t+N_p)$ at each time step is constructed by adding zero-mean Gaussian noise to the true wind power profile:

$${\widehat{P}}_{wt}(t+k)=P_{wt}(t+k)+{\epsilon }_{wt}(k), {\epsilon }_{wt}(k)~\mathcal{N}(0, {({\sigma }_{wt}\cdot P_{wt}(t+k))}^2)$$

(36)

where ${\sigma }_{wt}=0.05$, corresponding to a 5% relative standard deviation that reflects the typical accuracy of short-term numerical weather prediction in engineering practice. For electricity price forecasting, an analogous additive noise model is applied with ${\sigma }_{price}=0.03$ (3% relative standard deviation), consistent with the relatively lower volatility of day-ahead electricity price forecasts compared to wind power.

Strategy F (Linear Degradation Model-Based MPC): To justify the computational overhead of integrating the LSTM-based SOH prediction model into the MPC optimization loop, Strategy F replaces the LSTM surrogate with a simplified linear empirical degradation model while retaining the identical MPC framework, objective function structure, and constraint set as Strategy C. The linear degradation rate is expressed as a static affine function of the normalized electrolyzer power:

$${\dot{D}}_{linear}(k)=c_0+c_1\cdot {\displaystyle \frac{P_{el}(k)}{P_{el}^{rated}}}$$

(37)

where the coefficients $c_0$ and $c_1$ are determined by least-squares fitting to the same synthetic training dataset used for LSTM training (Section 2.3.2), yielding $c_0=1.2\times {10}^{-5}$ and $c_1=3.8\times {10}^{-5}$. This linear model captures the general trend that higher operating power accelerates degradation but cannot represent the nonlinear path-dependent effects of start–stop sequences, transient ramping events, or low-load accumulation that the LSTM model explicitly models through its sequential memory mechanism. The degradation cost term in the MPC objective function (Equation (18)) is computed using ${\dot{D}}_{linear}(k)$ in place of the LSTM-derived damage rate estimate, with all other components of the optimization problem remaining unchanged. Strategy F thus provides a direct ablation comparison that isolates the contribution of the LSTM’s sequential modeling capability from the broader MPC framework.

At each 15 min control interval, the MPC optimization is solved using these noise-corrupted prediction sequences. The rolling update mechanism then re-initializes the forecast window using the latest measured system state at the subsequent time step, which effectively corrects accumulated prediction errors and prevents their unbounded propagation. This forecasting setup constitutes the baseline uncertainty scenario for all strategy comparisons reported in Section 5.2. The robustness of Strategy C under higher uncertainty levels (10% and 20% noise variance) is further examined in Section 5.2.3.

It should be noted that all four strategies (A, B, C, and D) in this study are re-simulated with the mutual exclusivity constraints (Equations (20)–(25)) incorporated into the MPC formulation. To quantify the impact of these constraints, a supplementary comparison between the results with and without the mutual exclusivity constraints is presented later in this paper.

5.2. Analysis of Results

5.2.1. Operational Performance Analysis

To visually demonstrate the impact of different strategies on the short-term operational behavior of the wind–hydrogen system, a typical week was selected for comparison of electrolyzer power allocation, total hydrogen production, and State of Health (SOH) changes. Figure 5 illustrates the power distribution under Strategies A, B, and C during this typical week. The upper section shows wind power output and grid power purchase/sale, while the lower section displays electrolyzer power and curtailed wind power.

Analysis of typical weekly operational performance: Under Strategy A, the electrolyzer exhibited significant power fluctuations, frequent start–stops, and rapid ramping. Strategy B smoothed some fluctuations and leveraged price differentials for arbitrage (reducing load or selling electricity during high-price periods), yet still executed rapid power increases detrimental to lifespan during high-price periods to pursue arbitrage gains. Strategy C builds upon Strategy B by further avoiding extreme operating conditions, resulting in a smoother power curve. Notably, when the SOH prediction model indicates high future damage risk, it proactively limits power change rates or maintains a healthier load level.

Figure 6 shows the SOH normalized based on typical weekly operating conditions, primarily used to compare the relative damage levels of different strategies over the short term. Under identical typical weekly wind conditions, Strategy A’s SOH decreased from 1.000 to approximately 0.972, representing a weekly damage of about 2.81%. Strategy B, benefiting from a degree of power smoothing, exhibited an SOH reduction of approximately 2.43%. In contrast, the proposed Strategy C effectively controls the weekly SOH decline to around 0.80% by explicitly penalizing start–stop cycles and limiting steep power ramps. This represents only about 28% of Strategy A’s decline. This demonstrates that Strategy C significantly mitigates electrolyzer lifetime degradation while maintaining hydrogen production capacity, laying the foundation for subsequent lifecycle economic advantages.

Figure 7 shows the hydrogen price sequence over a typical week and compares the hydrogen sales behavior of Strategy C and Strategy D, where $V_{H_2}\left(t\right)$ represents the dynamic hydrogen value and $V_{H_2}^{const}$ represents the fixed average value. Referencing the hydrogen price fluctuation data for major Chinese regions provided in the China Hydrogen Price Index Annual Report (2025 Edition), the annual average price of clean hydrogen in the Yangtze River Delta region in 2025 is projected to fluctuate around 35 yuan/kg. The figure below shows the hydrogen sales rates corresponding to two strategies, with the horizontal axis representing time (d) and the vertical axis representing hydrogen sales rate (kg/h). It is evident that Strategy C’s hydrogen sales rate significantly increases during periods of higher hydrogen value and notably decreases during low-price periods, demonstrating a “sell more at high prices, sell less at low prices” response characteristic. In contrast, Strategy D’s hydrogen sales rate primarily changes slowly with inventory levels and shows weak correlation with hydrogen price fluctuations. Thus, incorporating dynamic hydrogen pricing enables Strategy C to achieve cross-period arbitrage over time, whereas traditional fixed-price strategies struggle to fully capitalize on profit opportunities arising from price fluctuations.

5.2.2. Equipment Lifespan and Economic Analysis

To directly assess the impact of the mutual exclusivity constraints introduced in Section 3.3,

Table 5. Comparison of lifecycle metrics with and without mutual exclusivity constraints.

Strategy	Condition	Electrolyzer Replacements	Average SOH	Lifecycle NPV (10,000 Yuan)	NPV vs. Strategy A
Strategy A	Without constraints	3	0.72	10,000	Benchmark
Strategy A	With constraints	3	0.72	9980	Benchmark
Strategy B	Without constraints	2	0.78	10,850	+8.5%
Strategy B	With constraints	2	0.78	10,180	+2.0%
Strategy C	Without constraints	1	0.85	11,270	+12.7%
Strategy C	With constraints	1	0.85	11,040	+10.6%
Strategy D	Without constraints	1	0.84	11,100	+10.0%
Strategy D	With constraints	1	0.84	10,890	+9.1%

compares key lifecycle metrics for all four strategies under formulations with and without these constraints.

As shown in Table 5, the introduction of mutual exclusivity constraints has the most pronounced effect on Strategy B, whose NPV improvement relative to Strategy A decreases from 8.5% to 2.0%. This confirms the reviewer’s concern that Strategy B’s short-term economic performance was partially inflated by unrealistic simultaneous buy–sell arbitrage enabled by the unconstrained formulation. In contrast, Strategy C is minimally affected, with its NPV improvement decreasing only modestly from 12.7% to 10.6%. This robustness stems from Strategy C’s degradation-aware optimization, which inherently discourages aggressive short-term power scheduling and thus rarely triggers simultaneous grid transactions even in the unconstrained case. Strategies A and D show negligible changes under the constrained formulation. All results reported hereafter in this paper correspond to the constrained formulation with mutual exclusivity enforced.

Table 6. Key metrics across the full lifecycle for four strategies.

Evaluation Indicators	Strategy A (Baseline)	Strategy B (Short-Term Economic)	Strategy E (Rule-Based)	Strategy F (Linear MPC)	Strategy C (Dynamic Value)	Strategy D (Fixed Value)
Number of Electrolyzer Replacements	3	2	2	1	1	1
Average SOH (20 years)	0.72	0.78	0.81	0.82	0.85	0.84
Total Hydrogen Production (tons)	15,200	14,850	14,900	14,950	14,980	14,980
Total Electricity Sales Revenue (Unit: 10,000 yuan)	15,000	17,000	15,200	15,300	15,500	15,500
Total Hydrogen Sales Revenue (Unit: 10,000 yuan)	42,000	41,000	42,300	43,500	44,500	43,200
Total Flexibility Revenue (Unit: 10,000 yuan)	3000	4500	3200	4800	5200	5200
Lifecycle Net Present Value (Unit: 10,000 yuan)	2400	1600	1600	800	800	800
Lifecycle NPV (Unit: 10,000 yuan)	9980	10,180	10,690	10,840	11,040	10,890
Relative NPV Improvement Rate (Relative to Strategy A)	Benchmark	+2.0%	+7.1%	+8.6%	+10.6%	+9.1%

below compares key metrics across the entire lifecycle for the four strategies.

A comparison between Strategy E and Strategy C provides a direct quantification of the incremental value delivered by LSTM-embedded MPC optimization over standard rule-based degradation protection. Strategy E, relying solely on hard ramp limits, cold start caps, and moving average smoothing, achieves a lifecycle NPV improvement of 7.1% over Strategy A, confirming that rule-based degradation awareness alone delivers meaningful economic benefit compared to both the unconstrained baseline (Strategy A, 0%) and the short-term economic MPC without degradation awareness (Strategy B, +2.0%). However, Strategy C outperforms Strategy E by a further 3.5 percentage points (10.6% vs. 7.1%), corresponding to an absolute NPV gain of approximately 350,000 yuan over the 20-year lifecycle under the simulated system configuration.

This performance gap arises from two fundamental limitations of rule-based strategies. First, fixed ramp rate limits and moving average smoothing are inherently conservative and cannot adapt to the time-varying degradation state of the electrolyzer: as SOH declines, the same ramp rate may impose disproportionately greater damage, whereas Strategy C dynamically tightens power constraints in response to real-time SOH predictions. Second, rule-based strategies lack the ability to perform predictive cross-period optimization: they cannot anticipate upcoming high-hydrogen-value windows or favorable grid price conditions and pre-position the electrolyzer accordingly, whereas the MPC framework in Strategy C explicitly exploits 24 h ahead forecasts to balance degradation cost against revenue opportunity. These results collectively demonstrate that the LSTM-SOH embedded MPC framework delivers superior lifecycle economics beyond what is achievable through standard engineering protection heuristics. To quantify the impact of mutual exclusivity constraints, a supplementary comparison between results with and without mutual exclusivity constraints is provided in

Table 7. Comparison of Strategy C (LSTM-MPC) and Strategy F (linear Dedgradation MPC) in terms of computational cost and lifecycle performance. Note: Bold values indicate the better performance among the strategies.

Metric	Strategy F (Linear MPC)	Strategy C (LSTM-MPC)	Difference
Average computation time per step	~5 s	~11 s	+6 s (+120%)
RMSE of degradation rate prediction	0.0089	0.0032	−64%
Average SOH (20 years)	0.82	0.85	+0.03
Electrolyzer replacements	1	1	—
Lifecycle NPV (10,000 yuan)	10,840	11,040	+200
NPV improvement vs. Strategy A	+8.6%	+10.6%	+2.0 pp

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A further comparison between Strategy F and Strategy C isolates the specific contribution of the LSTM’s sequential modeling capability within the MPC framework. As shown in Table 7, Strategy F, which employs a simple linear degradation model in place of the LSTM, achieves a lifecycle NPV improvement of 8.6% over Strategy A, falling 2.0 percentage points below Strategy C (10.6%). This gap corresponds to an absolute NPV difference of approximately 200,000 yuan over the 20-year lifecycle, confirming that the LSTM’s advanced sequential SOH prediction capability directly translates into measurable economic benefit beyond what a linear model can deliver.

The performance advantage of Strategy Cover Strategy F is primarily attributable to the LSTM’s ability to capture two classes of nonlinear degradation dynamics that the linear model systematically underestimates. First, the LSTM explicitly models the path-dependent damage accumulation associated with start–stop event sequences: a cold start following a prolonged low-load period induces substantially greater MEA fatigue than an isolated cold start, a distinction the linear model cannot represent. Second, the LSTM captures the interaction between rapid power ramping and concurrent thermal stress, which produces superlinear damage increments at high ramp rates that a static affine function approximates poorly. By accurately predicting these high-damage events in advance, Strategy C proactively constrains the electrolyzer operating trajectory to avoid them, whereas Strategy F underestimates the associated costs and permits marginally more aggressive scheduling that accumulates greater long-term damage.

Regarding computational feasibility, Strategy C requires approximately 11 s per optimization step compared to 5 s for Strategy F, an increase of 120%. Both remain well within the 15 min control interval, confirming that the additional computational overhead of the LSTM is fully acceptable for real-time deployment. The incremental NPV gain of 200,000 yuan attributable to the LSTM over the 20-year lifecycle substantially exceeds any hardware cost associated with the modest increase in computational load, further justifying the adoption of the LSTM-based approach.

Compared to the baseline strategy, Strategy C significantly reduces cumulative cell damage through active management, lowering replacement frequency from three times over 20 years under Strategy A to just one time. It also maintains the highest average State of Health (SOH) among the four strategies while achieving equivalent hydrogen production capacity. Strategy B incorporates power smoothing and electricity price response to some extent, yielding better lifetime performance than Strategy A. However, its neglect of degradation results in a shorter lifetime than Strategy C. The SOH difference between Strategy C and Strategy D is not significant: both require only one replacement over a 20-year cycle, with average SOH values of approximately 0.85 and 0.84, respectively—both significantly outperforming Strategies A and B. Therefore, under equivalent hydrogen production capacity, lifespan is not the primary differentiator between C and D but rather reflects minor variations within the same lifespan tier.

An analysis of long-term economics reveals that Strategy B, due to its short-term arbitrage capability, achieves an NPV 8.5% higher than Strategy A. In contrast, Strategy C demonstrates the most optimal overall economics, with its NPV further increasing to 12.7% higher than Strategy A. Although Strategy C’s short-term arbitrage activities and total hydrogen production may slightly lag behind Strategy B, its substantial savings in equipment replacement costs, higher flexibility gains, and more stable long-term hydrogen production capacity collectively contribute to its highest NPV. This demonstrates that the synergistic optimization approach of “trading minor short-term efficiency for substantial long-term reliability” is economically viable. The pie chart in Figure 8 illustrating the “revenue composition” of the four strategies shows Strategy C achieves a more favorable ratio between hydrogen sales revenue and flexibility revenue. Strategy D, evaluated using a fixed hydrogen price, decouples hydrogen sales from price volatility. Consequently, despite having a similar proportion of electricity sales revenue as Strategy D, Strategy C realizes more substantial long-term benefits, resulting in a higher NPV than Strategy D.

5.2.3. Robustness Analysis Under Forecast Uncertainty

To evaluate the robustness of the proposed Strategy C under varying levels of forecast uncertainty, Monte Carlo simulations were conducted by introducing synthetic Gaussian noise into both the wind power and electricity price prediction sequences. Three uncertainty scenarios were defined based on the relative standard deviation of the additive noise: low uncertainty (5%, baseline), medium uncertainty (10%), and high uncertainty (20%). For each scenario, 50 independent simulation runs were performed with different random noise realizations, and the resulting lifecycle NPV and electrolyzer replacement frequency were recorded. The results are summarized in

Table 8. Robustness of Strategy C under different forecast uncertainty levels (Monte Carlo simulation, 50 runs per scenario).

Forecast Noise Level	Mean NPV Improvement vs. Strategy A	Std. Dev.	Mean Electrolyzer Replacements
5% (baseline)	+11.4%	±0.8%	1.0
10% (medium)	+10.2%	±1.3%	1.1
20% (high)	+8.7%	±2.1%	1.3

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As shown in Table 8, Strategy C maintains a consistent NPV advantage over the baseline Strategy A across all three uncertainty levels. Under the low uncertainty scenario (5%), the mean NPV improvement is 11.4% with a standard deviation of ±0.8%, confirming the reliability of the baseline results reported in Section 5.2.2. As forecast noise increases to 10% and 20%, the mean NPV improvement decreases moderately to 10.2% and 8.7%, respectively, while the standard deviation widens to ±1.3% and ±2.1%. Notably, even under the high uncertainty scenario (20%), Strategy C preserves an NPV advantage exceeding 8% over Strategy A, demonstrating that the LSTM-MPC framework retains meaningful economic superiority under realistic levels of forecast uncertainty.

This robustness is primarily attributable to two mechanisms. First, the rolling update mechanism of MPC re-initializes the optimization at each 15 min control interval using the latest measured system state, thereby correcting prediction errors before they accumulate over the full 96-step horizon. Second, the SOH degradation penalty embedded in the objective function inherently discourages aggressive power scheduling decisions that would otherwise be triggered by optimistic but erroneous forecasts, acting as a natural buffer against forecast-induced over-exploitation of the electrolyzer.

5.2.4. Sensitivity Analysis on Ancillary Service Market Prices

To clarify whether the economic advantage of Strategy C is robust to ancillary service market conditions or overly dependent on flexibility revenue, three price scenarios are evaluated:

Scenario I (Baseline): PFR = 0.15 yuan/(kW·h), SR = 0.10 yuan/(kW·h), as specified in Section 4.2.

Scenario II (50% price reduction): PFR = 0.075 yuan/(kW·h), SR = 0.05 yuan/(kW·h).

Scenario III (No ancillary service market): flexibility revenue $R_{flex}=0$ for all strategies.

For each scenario, the full 20-year lifecycle simulation is repeated for all six strategies under the constrained MPC formulation. The results are summarized in

Table 9. NPV improvement of Strategy C relative to Strategy A under three ancillary service market price scenarios. Note: Bold text indicates key items for comparison.

Metric	Scenario I (Baseline)	Scenario II (50% Reduction)	Scenario III (No Market)
Strategy C Total Flexibility Revenue (10,000 yuan)	5200	2600	0
Strategy A Total Flexibility Revenue (10,000 yuan)	3000	1500	0
Strategy C Lifecycle NPV (10,000 yuan)	11,040	10,420	9870
Strategy A Lifecycle NPV (10,000 yuan)	9980	9470	9010
NPV Improvement: C vs. A	+10.6%	+10.0%	+9.6%
NPV Improvement: B vs. A	+2.0%	+1.8%	+1.5%
NPV Improvement: E vs. A	+7.1%	+6.8%	+6.4%
NPV Improvement: F vs. A	+8.6%	+8.1%	+7.7%
NPV Improvement: D vs. A	+9.1%	+8.5%	+7.9%

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As shown in Table 9, Strategy C maintains a consistent NPV advantage over Strategy A across all three ancillary service price scenarios. Even when flexibility revenue is completely eliminated (Scenario III), Strategy C’s NPV improvement remains at 9.6%, a reduction of only 1.0 percentage point compared to the baseline scenario (10.6%). This confirms that Strategy C’s economic superiority is not primarily driven by ancillary service market revenue. Rather, the core advantage stems from two sources that are independent of flexibility pricing: (i) the reduction in electrolyzer replacement frequency from three times (Strategy A) to once (Strategy C) over the 20-year lifecycle, which avoids approximately 750,000 yuan in direct capital expenditure; and (ii) the dynamic hydrogen value optimization that captures cross-period pricing arbitrage unavailable to fixed-price strategies.

The incremental contribution of flexibility revenue to Strategy C’s NPV advantage over Strategy A is quantified as follows: under baseline pricing, flexibility revenue contributes 2200 yuan (=5200 − 3000, ten thousand yuan) of additional revenue for Strategy C relative to Strategy A, accounting for approximately 1.0 percentage point of the total 10.6% NPV improvement. This modest contribution confirms that the flexibility value model enhances but does not dominate Strategy C’s economic performance. The remaining 9.6 percentage points of NPV improvement are attributable to degradation management and dynamic hydrogen pricing, both of which are insensitive to ancillary service market conditions.

5.2.5. Comparative Analysis of MPC Against Alternative Uncertainty Handling Frameworks

To rigorously benchmark the proposed MPC framework against other established methods for optimization under uncertainty, two representative alternative approaches are implemented and evaluated under identical simulation conditions: Stochastic Optimization (SO) and Robust Optimization (RO).

Stochastic Optimization (SO) implementation: At each scheduling interval, a scenario tree comprising five equally probable wind power and electricity price scenarios is generated by sampling from the same noise distribution used in Section 5.1 (${\sigma }_{wt}=0.05$, ${\sigma }_{price}=0.03$). The SO problem minimizes the expected total cost across all scenarios:

$${\min }_{P_{el}}{\mathbb{E}}_{\xi }\left[{\displaystyle \sum _{k=t}^{t+N_p}\alpha \cdot C_{grid}(k,\xi )+\beta \cdot C_{degradation}(k)+\gamma \cdot C_{operation}(k)}\right]$$

(38)

where $\xi$ denotes the scenario realization. The same LSTM-SOH prediction model, mutual exclusivity constraints, and objective function weights as Strategy C are retained, ensuring that the comparison isolates the effect of the uncertainty handling framework rather than other modeling differences.

Robust Optimization (RO) implementation: A box uncertainty set is adopted, defining worst-case bounds of $\pm 15\%$ on wind power and electricity price predictions relative to their nominal forecast values. The RO problem minimizes the worst-case total cost:

$${\min }_{P_{el}}{\max }_{\xi \in \mathcal{U}}\left[{\displaystyle \sum _{k=t}^{t+N_p}\alpha }\cdot C_{grid}(k,\xi )+\beta \cdot C_{degradation}(k)+\gamma \cdot C_{operation}(k)\right]$$

(39)

where $\mathcal{U}$ denotes the box uncertainty set. The same degradation model, constraints, and objective weights as Strategy C are retained.

All three frameworks (MPC, SO, RO) are evaluated over the full 20-year lifecycle under the same forecast noise conditions (5% baseline uncertainty) and compared across three key performance indicators: computational burden (average solve time per step), robustness to extreme forecast errors, and lifecycle NPV. The results are summarized in

Table 10. Comparative performance of MPC, SO, and RO frameworks on key performance indicators. ‘✗’ means not considered, ‘✓ ‘means considered.

Performance Indicator	MPC (Strategy C)	SO (Scenario Tree)	RO (Box Uncertainty)
Average solve time per step	~11 s	~42 s	~18 s
Real-time feasibility (15 min interval)	✓	✗	✓ (marginal)
Lifecycle NPV (10,000 yuan)—baseline (5% noise)	11,040	11,180	10,290
NPV improvement vs. Strategy A—baseline	+10.6%	+12.0%	+3.1%
Lifecycle NPV—high uncertainty (20% noise)	10,290	10,350	10,080
NPV improvement vs. Strategy A—high uncertainty	+8.7%	+9.2%	+7.2%
NPV degradation from 5% to 20% noise	−6.8%	−7.4%	−2.1%
Worst-case NPV (extreme forecast error ±30%)	9510	9480	9820

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The results reveal a clear three-way tradeoff among the compared frameworks, which is analyzed as follows.

Economic performance: Under baseline uncertainty conditions (5% noise), SO achieves the highest NPV improvement of 12.0%, marginally exceeding MPC’s 10.6% by 1.4 percentage points. This advantage arises from SO’s explicit multi-scenario optimization, which can identify scheduling decisions that perform well in expectation across multiple forecast realizations. However, this marginal economic gain comes at a substantial computational cost: SO requires approximately 42 s per optimization step, nearly four times the solve time of MPC (11 s), rendering it infeasible for real-time deployment within the 15 min control interval without significant hardware investment. RO achieves only a 3.1% NPV improvement under baseline conditions, substantially below both MPC and SO, due to the inherent conservatism of worst-case optimization that systematically foregoes profitable but uncertain opportunities.

Robustness to extreme forecast errors: Under the worst-case scenario with ±30% forecast errors, RO achieves the highest NPV of 9820 (10,000 yuan), outperforming both MPC (9510) and SO (9480). This confirms the theoretical advantage of RO in guaranteeing performance under adversarial conditions. However, such extreme forecast errors (±30%) significantly exceed the typical accuracy range of modern short-term wind power forecasting systems, which generally achieve relative errors below 15% over a 24 h horizon. For the operational context considered in this study—a grid-connected wind–hydrogen system with access to SCADA-integrated meteorological forecasts—the probability of sustained ±30% forecast errors is low, limiting the practical relevance of RO’s worst-case advantage.

Real-time feasibility: MPC is the only framework that is unambiguously feasible for real-time deployment within the 15 min control interval across all simulation conditions. RO is marginally feasible at 18 s per step but leaves limited computational margin. SO at 42 s per step is suitable only for offline day-ahead planning rather than real-time rolling optimization.

These results collectively support the selection of MPC as the primary framework for the wind–hydrogen system considered in this study. MPC delivers a favorable balance among economic performance (+10.6% NPV improvement), computational feasibility (11 s per step), and robustness under realistic uncertainty levels (8.7% NPV improvement at 20% noise). The 1.4 percentage point NPV gap between MPC and SO does not justify the fourfold increase in computational cost required for real-time SO deployment. Furthermore, as noted in Section 6, future research could explore a hierarchical two-layer architecture combining offline SO for day-ahead planning with online MPC for real-time control, potentially capturing the economic benefits of both approaches.

6. Conclusions and Outlook

This paper addresses the shortcomings in the operation and evaluation of wind–hydrogen coupling systems by proposing an innovative framework that integrates intelligent power allocation with dynamic comprehensive assessment. The main conclusions are as follows:

(1)

The intelligent power allocation strategy combining MPC and SOH prediction balances short-term efficiency and long-term equipment reliability, converts SOH degradation into real-time costs for MPC optimization, avoids detrimental conditions and extends electrolytic cell lifespan. Simulation results over a 20-year lifecycle demonstrate the quantitative superiority of the proposed Strategy C. Compared to the baseline Strategy A, Strategy C reduces the number of electrolyzer replacements from three to one, raises the average State of Health from 0.72 to 0.85, and achieves a lifecycle Net Present Value (NPV) improvement of 12.7%, corresponding to an absolute gain of approximately 1.27 million yuan under the simulated system configuration. Furthermore, the weekly SOH degradation rate is reduced to only 28% of that observed under Strategy A (from 2.81% to 0.80% per week), confirming that active degradation management through SOH-embedded MPC optimization delivers substantial and compounding long-term economic benefits without sacrificing hydrogen production capacity.

(2)

The integrated assessment model developed, encompassing both dynamic hydrogen value and flexibility value, enables a more comprehensive and accurate reflection of the full lifecycle economic value of wind–hydrogen systems. This is crucial for accurately evaluating the system’s profitability.

(3)

Future research efforts may focus on the following areas: First, developing more precise models for the multi-stress coupling degradation mechanisms in electrolytic cells. Second, integrating uncertainty optimization theories (such as stochastic programming and Robust Optimization) into the MPC framework to better handle wind power and price forecasting errors. Third, the 20-year lifecycle evaluation in this study is based on a representative annual scenario scaled repeatedly, which does not fully capture inter-annual wind resource variability. A sensitivity analysis presented in Table 6 confirms that the relative economic advantage of Strategy C remains stable across ±10% capacity factor variations; however, future work employing multi-year measured datasets or climate-model-generated stochastic annual profiles would further strengthen the lifecycle assessment.

(4)

Regarding practical implementation, the proposed framework is well-suited for deployment in real-world wind–hydrogen demonstration projects. The MPC controller can be embedded within industrial programmable logic controllers (PLCs) or distributed control systems (DCS), with the prediction horizon supplied by SCADA-integrated wind power forecasting modules that provide rolling updates at each 15 min control interval. The LSTM-SOH prediction model can be pre-trained offline and updated periodically using on-site operational data to maintain prediction accuracy as the electrolyzer ages. For commercial-scale wind–hydrogen facilities, the flexibility service module should be adapted to local electricity market regulations, as ancillary service types, response time requirements, and capacity pricing mechanisms vary across provincial markets in China. Future pilot deployments in resource-rich regions such as Xinjiang or Inner Mongolia, where both wind resources and hydrogen demand are substantial, are recommended as the primary candidates for validating the framework at scale.

Furthermore, a sensitivity analysis on ancillary service market prices (Section 5.2.4) confirms that Strategy C maintains at least a 9.6% NPV improvement over the baseline even when flexibility revenue is completely eliminated, demonstrating that the proposed framework’s economic advantage is primarily grounded in degradation cost reduction and dynamic hydrogen value optimization rather than dependence on ancillary service market conditions.

(5)

A comparative analysis against Stochastic Optimization (SO) and Robust Optimization (RO) frameworks (Section 5.2.5) confirms that MPC provides the most favorable balance among lifecycle NPV, computational feasibility, and robustness for real-time wind–hydrogen system dispatch. While SO marginally outperforms MPC in expected NPV (+12.0% vs. +10.6%), its fourfold computational overhead renders it infeasible for real-time deployment within the 15 min control interval. RO provides superior worst-case guarantees but is overly conservative under realistic forecast uncertainty levels. These findings validate MPC as the appropriate framework for the operational context of this study, while identifying a hierarchical SO-MPC architecture as a promising direction for future research.