A Multi-Time-Scale Energy Allocation Strategy Considering Start–Stop Characteristics of Electrolyzers for Electricity–Hydrogen Coupling Systems

Abstract

In electricity–hydrogen coupling systems (EHCSs), the uncertainty of renewable energy generation (REG) tends to impact electrolyzers (ELs) in the following ways: (1) input powers of ELs are prone to fluctuations; (2) ELs are forced to operate under variable load states. Consequently, both impacts will reduce the service life of ELs. In this paper, considering the start–stop characteristics and combined operation modes of multiple ELs, a two-stage multi-time-scale energy allocation strategy (MSEAS) is proposed to mitigate the impacts of REG uncertainty and optimize the energy allocation for EHCSs. First, five refined operating states of ELs, such as shutdown, cold standby, low-load, variable-load and overload, are formulated as mixed-integer constraints and embedded into the system-level energy optimization model. Second, to mitigate power fluctuations caused by REG, a day-ahead optimization is employed to plan the power allocations of ELs, lithium batteries, fuel cells, and the grid with a 1 h time step; and then an intra-day rolling optimization is employed to adjust the operating states and power outputs of the above units with a 4 h window and 15 min step. Third, by enabling multiple ELs to flexibly operate in a combined mode, power-sharing mode and switching mode, the proposed MSEAS can refine the operation powers of ELs and reduce their start-up frequency. Comparative case studies are conducted in the off-grid and grid-connected operation tests, and the relevant results verify that the proposed MSEAS can effectively prevent the frequent start–stop of ELs, which contributes to extending the service life of ELs and reducing the system operating cost.

1. Introduction

As a clean, low-carbon, and storable energy source, hydrogen has emerged as a cornerstone of the global energy transition and a strategic pillar for ensuring energy security [1,2]. Hydrogen production via water electrolysis can convert the surplus of renewable energy generation (REG) into storable hydrogen, while fuel cells can release the electricity from the stored hydrogen. Therefore, this bidirectional electricity–hydrogen coupling plays a positive role in accommodating renewable energy sources (RESs) and maintains the stable operation of the power systems.

Against this backdrop, electricity–hydrogen coupling systems (EHCSs) have attracted extensive research attention. A recent review study [3] has systematically summarized the dynamic operating behaviors of proton exchange membrane electrolyzers (PEMEs) with the intermittent power supply, while [4] has reviewed the potential of electrolyzer-based systems in providing grid ancillary services. More broadly, ref. [5] has provided a comprehensive overview of several integration schemes of hydrogen and batteries within the REG systems. These reviews collectively highlight three tightly coupled research frontiers that determine the economy, reliability, and service life of EHCSs: (i) the dynamic operation and start–stop characteristics of electrolyzers (ELs); (ii) the multi-time-scale coordination of EHCSs under the REG uncertainty; and (iii) the coordinated scheduling of hydrogen and battery storage. The following literature is organized along these three threads.

For the first thread, extensive work has been carried out on the operating state and mathematical model of ELs. In [6], a multi-objective algorithm is proposed for a wind-turbine/battery/EL energy management strategy adapted to low wind speed conditions. In [7], a cyclic energy storage system for hydrogen production and regeneration is constructed to improve the utilization efficiency of RES. In [8], a wind–hydrogen system is constructed, and then a related control method is proposed for ELs based on switching time constraints, while [9] further defines switching variables of ELs and employs an interaction strategy to coordinate their switching time limits. In [10], a dynamic frequency regulation method is developed for megawatt-scale alkaline ELs in wind-dominated EHCSs. In [11], a control strategy for a multi-EL system is proposed to enhance the renewable energy utilization and prolong the EL lifespan. In [12], a multi-time-scale scheduling strategy is developed for EHCS, where the operational characteristics of each equipment type are matched to the corresponding scheduling time scale. In [13], an optimization architecture for the hybrid EL system is developed, which incorporates the physical properties of alkaline ELs and PEMEs. Summarizing these studies [6,7,8,9,10,11,12,13], they either focus on the dynamic characteristics of a single EL or address the switching among multiple ELs in a simple manner. More importantly, the five refined operating states—shutdown, cold standby, low-load, variable-load, and overload—have rarely been jointly embedded as mixed-integer constraints within a system-level energy management model, which limits the accuracy of the resulting scheduling decisions.

For the second thread, multi-time-scale scheduling of EHCS has been investigated from various angles. In [14], a sustainable economic energy dispatch method is studied for a power-to-gas and gas-to-power system to ensure system economy. In [15], an electricity–hydrogen–heat multi-energy storage system is constructed, and then a coordinated optimization model is established to enhance the flexibility and economy of grids. In [16], a time-discrete approach is adopted for multi-time-scale modeling of EHCS to reduce operating costs. In [17], a multi-time-scale model predictive control (MPC) is proposed to smooth the power output for hybrid microgrids with hydrogen energy storage. In [18], under off-grid conditions, a POA-based multiple ELs switching scheduling strategy is proposed for wind–hydrogen systems, and this strategy can increase the hydrogen production revenue and reduce EL’s start–stop cycles. In [19], for electricity–hydrogen systems, an online operation optimization is proposed to optimize the operation cost considering the uncertainty of multiple factors. In [20], a rule-based method is employed to implement the energy management for multi-energy systems. However, it needs to be carefully designed heuristic logic and pre-set thresholds for ELs state transitions, which may be unable to embed the refined multiple operating states and start–stop loss of ELs. In [21], considering price-matching factors, a trading market model is developed for the integrated electricity-gas-heat system, which contributes to improving the utilization of various energy sources. In [22], with the high penetration of RES as the background, a probabilistic forecasting and robust optimization method is proposed to achieve the optimal power flow, in which uncertainties of RES are explicitly characterized to support reliable scheduling decisions. In [23], to accurately simulate the diverse operating states of PEMEs, a generic circuit model is established for PEMEs, in which the degradation behavior under variable-power operations is explicitly characterized. In summary, these studies [14,15,16,17,18,19,20,21,22,23] typically concentrate either on power fluctuation smoothing, economic performance, or AI-based intelligent scheduling. However, the operating-state transitions of multiple ELs have rarely been treated as optimization decision variables, and the degradation behavior of ELs under variable-power operations has rarely been incorporated as a constraint into multi-time-scale energy management models.

For the third thread, coordinated scheduling of hydrogen and battery storage has also received growing attention. In [24], a coordinated operation optimization method is proposed for power to hydrogen and heat in active distribution networks integrated with district heating systems. In [25,26], the hydrogen and thermal energy are jointly studied with heat recovery to improve device efficiency and reduce waste heat. In [27], considering the hydrogen energy trading, an energy-sharing architecture is proposed to implement energy dispatch for multi-energy systems. In [28], the integrated hydrogen storage system with cooling–heating–electricity supply is analyzed, and PSO is employed to confirm that water electrolysis is the optimal pathway. In [29], an “OP-APF” optimization framework is constructed for the integrated wind–EL–supercapacitor system, which can optimize the component size design and energy management. In [30], an optimization model with multi-objective constraints is developed for the EHCS and is employed to optimize the operation of the system. In [31], a multi-time-scale planning framework is proposed for the EHCS, in which a time-period selection is incorporated to improve the computational burden of system optimization. Nevertheless, in most of these studies [24,25,26,27,28,29,30,31], ELs are still treated as simple controllable loads, thereby overlooking their participation in system energy management with consideration of start–stop characteristics.

To overcome the above gaps, a two-stage multi-time-scale energy allocation strategy (MSEAS) is proposed for EHCS. Under off-grid and grid-connected conditions, the proposed MSEAS explicitly considers the start–stop characteristics and combined operation modes of multiple ELs. Beyond reporting simulation results, the paper makes the following contributions:

• Refined state modeling of ELs: Five operating states (shutdown, cold standby, low-load, variable-load, and overload) are formulated as mixed-integer constraints and embedded into the system-level optimization model, which can improve the fidelity of EL behaviors compared with existing simplified or on/off models.
• Two-stage multi-time-scale framework: A day-ahead optimization plan with a 1 h step is coordinated with an intra-day rolling optimization with a 4 h window and 15 min step. This coordination can mitigate the REG uncertainty in the day-ahead stage, and re-optimize the operating states and power outputs of ELs, lithium batteries, fuel cells, and the grid in the intra-day stage.
• Flexible combined operation of multiple ELs: By enabling multiple ELs to flexibly operate in a combined mode, power-sharing mode, and switching mode, the proposed MSEAS can reduce the start–stop frequency of ELs and mitigate the adverse impacts of REG uncertainty. Comparative case studies verify that the proposed MSEAS contributes to extending the service life of ELs and reducing the system operating cost.

This paper is organized as follows. Section 2 describes the EHCS system structure and then establishes the mathematical model of each unit. Section 3 formulates the day-ahead and intra-day optimization models together with their coordination scheme. Section 4 presents comparative case studies under off-grid and grid-connected conditions. Section 5 concludes the paper.

2. System Structure and Mathematical Model

2.1. System Structure

Figure 1 shows the EHCS structure, including the grid, wind energy, solar energy, lithium batteries, proton exchange membrane electrolyzers (PEMEs), proton exchange membrane fuel cells (PEMFCs), loads, and corresponding power electronic converters. In Figure 1, the EHCS operates in a grid-connected scenario when switch SW is closed, while the EHCS operates in an off-grid scenario when SW is open.

2.2. System Model

2.2.1. Wind Turbine Model

The wind turbine (WT) uses a direct-drive permanent magnet generator, and its output power, P_wt, can be expressed as [32]

$$P_{\mathrm{wt}}={\displaystyle \frac{1}{2}}{\rho }_{\mathrm{air}}\mathsf{\pi }{R}^2{v}^3{C}_{\mathrm{p}}\left(\beta ,\lambda \right)$$

(1)

where ρ_air is the ambient air density; R is the radius of the WT blade; v is the external wind speed; C_p is the energy utilization coefficient; β is the initial pitch angle of the WT; λ is the tip-speed ratio.

2.2.2. Photovoltaic Model

The photovoltaic (PV) cell can be simplified into a model correlated with factors including the irradiance, conversion efficiency, temperature, and panel area, and its output power P_pv can be expressed as [33]

$$P_{\mathrm{pv}}=P_{\mathrm{STC}}{\displaystyle \frac{S_{\mathrm{pv}}}{S_{\mathrm{STC}}}}\left[1+k_{\mathrm{T}}\left(T_{\mathrm{pv}}-T_{\mathrm{STC}}\right)\right]A_{\mathrm{r}}{\eta }_{\mathrm{pv}}$$

(2)

where P_STC is the output powers of PV under standard conditions (such as the irradiance of 1000 W/m² and the temperature of 25 °C); S_pv is the actual solar irradiance; S_STC is the standard solar irradiance (1000 W/m²); k_T is the temperature coefficient; T_STC is the standard ambient temperature (25 °C); T_pv is the actual temperature; A_r is the area of the PV panel; and η_pv is photovoltaic conversion efficiency.

2.2.3. Lithium Battery Model

Lithium batteries can serve to smooth the power fluctuations of REG and supply energy to the system, and the charging and discharging characteristics of lithium batteries can be expressed as [32]

$$S_{\mathrm{bat}}\left(t\right)=\left\{\begin{array}{c}\left(1-{\sigma }_{\mathrm{bat}}\right)S_{\mathrm{bat}}\left(t-1\right)-P_{\mathrm{bat}}\left(t\right)\mathsf{\Delta }t/{\eta }_{\mathrm{dis}}\\ \left(1-{\sigma }_{\mathrm{bat}}\right)S_{\mathrm{bat}}\left(t-1\right)-P_{\mathrm{bat}}\left(t\right)\mathsf{\Delta }t\cdot {\eta }_{\mathrm{cha}}\end{array}\right.$$

(3)

where S_bat(t) and S_bat (t − 1) are the remaining capacity of lithium batteries at time t and t − 1, respectively; P_bat(t) is the charging or discharging power of lithium batteries at time t (P_bat(t) > 0 and P_bat(t) < 0 indicate discharging and charging, respectively); η_dis and η_cha are the discharging and charging efficiencies, respectively; σ_bat is the self-discharge rate; Δt is the time interval.

2.2.4. Start–Stop Model of PEME

The operating states of PEME are divided into five types, as follows: shutdown state, cold standby state, hot standby state and normal operating state. Moreover, the normal operating state can be further divided into the low-load state, variable-load state and overload state. The detailed descriptions of these operating states are as follows:

(1)

Shutdown state: During the shutdown process, the PEME needs to perform a series of operations such as reducing the current, cutting off the power, venting pressure and cooling down. So, PEMEs require an interval of 30 min~1 h to fully start up from the shutdown state.

(2)

Cold standby state: The PEME is shut down while its control unit and anti-freezing unit still need to be kept in operation. In this state, the PEME will consume 0%~10% of $P_{\mathrm{el}}^{\mathrm{rated}}$. The transition time from the cold standby state to the normal operating state takes approximately 5 min to 10 min.

(3)

Hot standby state: The PEME is shut down but still requires low power to keep the necessary temperature and pressure. Note that the hot standby state is not separately modeled in this paper. Since its transition time to normal operation is extremely short (from seconds to a few minutes) and power consumption is negligible, its impact is insignificant within the 1 h time step. For this reason, the hot standby state is merged into the cold standby state for modeling.

(4)

Normal operation state: If the PEME is operated at the low or high current density for a long time, it may be at risk of explosion or cause damage to the stack materials. Therefore, considering the safety, the PEME should operate within the power range of 30%~100% of $P_{\mathrm{el}}^{\mathrm{rated}}$ for a long time. Additionally, the PEME can also operate in the low-load state (10%~30% of $P_{\mathrm{el}}^{\mathrm{rated}}$) and the overload state (100%~150% of $P_{\mathrm{el}}^{\mathrm{rated}}$) for a short time.

It should be noted that the PEME does not produce hydrogen in the shutdown state, cold standby state and hot standby state. To accurately characterize the operating states of the PEME, the above five states are represented by binary variables, that is, I denotes the shutdown state, S denotes the cold standby state, V denotes the low-load state, L denotes the variable-load state, and R denotes the overload state. When the binary value is 1, the PEME operates in the corresponding operating state, but when the binary value is 0, the PEME exits the corresponding operating state. Figure 2 shows the operating state transition diagram for the PEME, where Y and Z denote the start-up interval and the shutdown interval, respectively.

In the day-ahead optimization model, the time scale is set to 1 h, so the complete start-up time of the PEME $(I_n^t\to S_n^t$ or $I_n^t\to L_n^t$ or $I_n^t\to V_n^t$ or $I_n^t\to R_n^t$) is also set to 1 h. Since the transition time from cold standby state to cold start is less than 1 h, it is necessary to consider the energy loss during the cold startup process of PEMEs. In this way, the hydrogen production power $P_{\mathrm{el},{\mathrm{H}}_2,n}^t$ of the nth PEME can be expressed as

$$P_{\mathrm{el},{\mathrm{H}}_2,n}^t={\lambda }_n^t\left(P_{\mathrm{el},\mathrm{E},n}^t-S_n^t{P}_{\mathrm{el}}^s\right)-{\mu }_{\mathrm{el}}{W}_n^t$$

(4)

$$P_{\mathrm{el}}^t={\displaystyle \sum _{n=1}^n}{P}_{\mathrm{el},{\mathrm{H}}_2,n}^t$$

(5)

where ${\lambda }_n^t$ is the electrical-to-hydrogen conversion efficiency; μ_el is the penalty coefficient of hydrogen production power, which is used to characterize the hydrogen energy loss during the cold start; $P_{\mathrm{el},\mathrm{E},n}^t$ is the power drawn by the nth PEME; $P_{\mathrm{el}}^{\mathrm{s}}$ is the power consumed by the PEME in the cold standby state; $P_{\mathrm{el}}^t$ is the total power consumed by all PEMEs; W is a binary variable indicating whether the PEME transitions from the cold standby state to the normal operation state. Specifically, W = 1 means the PEME has transitioned from the cold standby state to the normal operation state; W = 0 means the PEME is in the cold standby state.

Further, W should satisfy the following relationship:

$$\left\{\begin{array}{l}{W}_n^t\le S_n^{t-1}\hfill \\ W_n^t\le L_n^t+R_n^t+V_n^t\hfill \\ W_n^t\le S_n^{t-1}+L_n^t+R_n^t+V_n^t-1\hfill \end{array}\right.$$

(6)

The power consumption range of each PEME can be expressed by binary variables, and the power consumption relationship of PEMEs in different operating states is as follows:

$$\begin{array}{l}{S}_n^t{P}_{\mathrm{el}}^s+0.3L_n^t{P}_{\mathrm{el}}^{\mathrm{rated}}+R_n^t{P}_{\mathrm{el}}^{\mathrm{rated}}+0.1V_n^t{P}_{\mathrm{el}}^{\mathrm{rated}}\le P_{\mathrm{el},\mathrm{E},n}^t\le \\ S_n^t{P}_{\mathrm{el}}^{\mathrm{s}}+L_n^t{P}_{\mathrm{el}}^{\mathrm{rated}}+1.5R_n^t{P}_{\mathrm{el}}^{\mathrm{rated}}+0.3V_n^t{P}_{\mathrm{el}}^{\mathrm{rated}}\end{array}$$

(7)

where $P_{\mathrm{el}}^{\mathrm{rated}}$ is the rated operating power of the PEME.

2.2.5. PEMFC Model

The PEMFC is used to output electrical energy by utilizing the chemical reaction between hydrogen and oxygen, and its output power P_fc can be expressed as

$$P_{\mathrm{fc}}=P_{\mathrm{tank-fc}}{\eta }_{\mathrm{fc}}$$

(8)

where P_tank-fc is the power obtained from the hydrogen storage tank (HST); η_fc is the operating efficiency of the PEMFC.

It is worth noting that the PEMFC degradation is also a recognized concern in practice, which is primarily caused by frequent start–stop cycles, prolonged operation with low- or over-load conditions, and fluctuations in the hydrogen supply. However, in the constructed EHCS, the PEMFC primarily serves as a backup power source to compensate for power deficits, and its power is scheduled by the proposed optimization model in this paper, resulting in the PEMFC having a relatively stable power output. Therefore, the PEMFC degradation is not treated as a primary optimization objective in this paper, but it will be acknowledged as a direction for future research.

2.2.6. Hydrogen Storage Tank Model

The HST can store the hydrogen from PEMEs and also supply hydrogen for the PEMFC. Considering the energy conversion efficiency, the HST model is as follows [19]:

$$E_{\tan k}\left(t\right)=E_{\tan k}\left(t-1\right)+\left(P_{\mathrm{el}}\left(t-1\right)\times {\eta }_{\mathrm{el}}-{\displaystyle \frac{P_{\mathrm{fc}}\left(t-1\right)}{{\eta }_{\mathrm{fc}}\times {\eta }_{\tan k}}}\right)\times \mathsf{\Delta }t$$

(9)

where E_tank(t) is the equivalent energy of the HST at time t (kWh); P_el is the power consumption of the PEME; η_el is the power conversion efficiencies of the PEME.

2.2.7. Electricity Demand Response Model

Loads can generally be divided into fixed loads, curtailable loads, and shiftable loads. Curtailable and shiftable loads are allowed to transfer their power consumption in both temporal and spatial dimensions, which will increase the flexibility of loads in system energy regulation. The above load powers can be expressed as

$$P_{\mathrm{L}}^t=P_{\mathrm{LS}}^t+P_{\mathrm{CL}}^t+P_{\mathrm{SL}}^t$$

(10)

where $P_{\mathrm{L}}^t$, $P_{\mathrm{LS}}^t$, $P_{\mathrm{CL}}^t$ and $P_{\mathrm{SL}}^t$ are the total load power, fixed load power, curtailable load power and shiftable load power, respectively.

Further, $P_{\mathrm{CL}}^t$ and $P_{\mathrm{SL}}^t$ can be expressed as

$$P_{\mathrm{CL}}^t=P_{{\mathrm{CL}}_0}^t\left[{\displaystyle \sum _{n=1}^{24}}{E}_{\mathrm{CL}}\left(m,n\right){\displaystyle \frac{{\rho }_n-{\rho }_{n_{-}0}}{{\rho }_{n_{-}0}}}\right]$$

(11)

$$P_{\mathrm{SL}}^{\mathrm{t}}=P_{{\mathrm{SL}}_0}^{\mathrm{t}}\left[{\displaystyle \sum _{n=1}^{24}}{E}_{\mathrm{SL}}\left(m,n\right){\displaystyle \frac{{\rho }_{\mathrm{n}}-{\rho }_{{\mathrm{n}}_0}}{{\rho }_{{\mathrm{n}}_0}}}\right]$$

(12)

where $P_{\mathrm{CL}\_0}^t$ and $P_{\mathrm{SL}\_0}^t$ are the initial powers of curtailable loads and shiftable loads at time t, respectively; E_CL(m, n) and E_SL(m, n) are the price-demand elasticity matrices of curtailable and shiftable loads, respectively; ρ_n is the electricity price at time n after the response.

3. Multi-Time-Scale Optimization Model

3.1. Optimization Model Design Ideas

Due to the randomness of the wind, PV and loads, there may be a deviation in EHCS system powers between the day-ahead and intra-day stages. To reduce power fluctuations caused by this deviation, a two-stage optimization model is established based on the day-ahead and intra-day stages, which can ensure the reliability and flexibility of the energy allocation plan for EHCS, as shown in Figure 3. For the day-ahead stage, a 24 h power allocation plan for each unit of EHCS is formulated to guide the operation power for each unit of EHCS in the intra-day stage. For the intra-day stage, the energy allocation plan formulated in the day-ahead stage is revised with a 4 h scheduling cycle, and is optimized in a rolling manner with a 15 min time interval. For further explanation, the 1 h time step for the day-ahead stage not only complies with the standard grid dispatch practices, but also is compatible with the start–stop characteristics of PEMEs. Additionally, the 15 min time step for the intra-day stage balances the short-term forecast accuracy and computational efficiency, and also is consistent with standard intra-day dispatch intervals in power systems.

Figure 4 shows the flowchart of the proposed MSEAS for EHCS in this paper, and the idea and process for energy optimization allocation are elaborated as follows:

Step 1: Utilizing the K-means clustering algorithm [34], the data from the hydrogen storage tank and the lithium batteries are preprocessed for initialization.

Step 2: The parameters from PEMEs and PEMFCs, as well as the predicted values from the WT, PV, and loads at a 1 h time scale, are used as input data for the day-ahead stage optimization model.

Step 3: Considering the hydrogen energy cost as well as the operation costs of WT and PV, the day-ahead energy scheduling objective function and the constraint of each unit are established.

Step 4: Utilizing the YALMIP toolbox in Matlab 2023b, the mixed-integer programming problem of the optimal scheduling can be solved in the day-ahead stage, thereby obtaining the hourly power allocation plan for each unit in EHCS.

Step 5: In the day-ahead stage, the data from the WT, PV and loads are predicted at a 1 h time scale, which inevitably leads to deviations between predicted values and actual values. Therefore, in the intra-day stage, these data are updated every 15 min, then the predicted data is generated for the subsequent 4 h. In this way, the power allocation results can be optimized based on more accurate data.

Step 6: During the intra-day stage, based on the updated data, objective functions and constraint conditions, the power allocation plan formulated in the day-ahead stage is revised with a 4 h scheduling cycle, and is optimized in a rolling manner with a 15 min time interval, as illustrated in Figure 3.

3.2. Day-Ahead Optimization Model

3.2.1. Objective Function

The power allocation priority for different sources (including WT, PV, lithium batteries, PEMFCs and PEMEs) is determined as follows: to minimize the waste of wind and PV powers, the priority coefficients of WT and PV are set to the highest, while those of PEMEs, PEMFCs and lithium batteries decrease in turn.

On this basis, an objective function with the primary consideration of reducing the system’s operational cost can be established as follows:

$$\min C_{\mathrm{T}}={\gamma }_1{C}_{\mathrm{Y}}+{\gamma }_{2}T\left(X\right)$$

(13)

$$C_{\mathrm{Y}}=C_{\mathrm{BS}}+C_{\mathrm{DR}}+C_{\mathrm{PE}}+C_{\mathrm{ELEN}}$$

(14)

$$\begin{array}{l}\begin{array}{l}{C}_{\mathrm{BS}}={\displaystyle \sum _{t=1}^T}\left(c_{\mathrm{buy}}{P}_{\mathrm{buy}}-c_{\mathrm{sell}}{P}_{\mathrm{sell}}\right)\mathsf{\Delta }t\\ C_{\mathrm{DR}}={\displaystyle \sum _{t=1}^T}\left(c_{\mathrm{CL}}{P}_{\mathrm{CL}}^{\mathrm{t}}+c_{\mathrm{SL}}{P}_{\mathrm{SL}}^{\mathrm{t}}\right)\mathsf{\Delta }t\end{array}\hfill \\ C_{\mathrm{PE}}={\displaystyle \sum _{t=1}^T}\left(c_{\mathrm{wt}}{P}_{\mathrm{cut},\mathrm{wt}}+c_{\mathrm{pv}}{P}_{\mathrm{cut},\mathrm{pv}}\right)\mathsf{\Delta }t\hfill \\ C_{\mathrm{ELEN}}={\displaystyle \sum _{t=1}^T}{\displaystyle \sum _{n=1}^N}{c}_{\mathrm{ELE}}{P}_{\mathrm{ELEN},\mathrm{t}}^{\mathrm{n}}+{\displaystyle \sum _{t=1}^T}{\displaystyle \sum _{n=1}^N}\left(Y_{\mathrm{n}}^{\mathrm{t}}{C}_{\mathrm{at}}+Z_{\mathrm{n}}^{\mathrm{t}}{C}_{\mathrm{op}}\right)\hfill \end{array}$$

(15)

$$\begin{array}{ll}T\left(X\right)& =\sum T_{nx}{X}_n\left(t\right)\\ & =T_{\mathrm{wt}}{X}_{\mathrm{wt}}\left(t\right)+T_{\mathrm{pv}}{X}_{\mathrm{pv}}\left(t\right)+T_{\mathrm{fc}}{X}_{\mathrm{fc}}\left(t\right)+T_{\mathrm{bat}}{X}_{\mathrm{bat}}\left(t\right)+T_{\mathrm{el}}{X}_{\mathrm{el}}\left(t\right)\end{array}$$

(16)

where γ₁ and γ₂ are weighting coefficients (γ₁ + γ₂ = 1); c_buy is the price of purchasing electricity from the grid; c_sell is the price of selling electricity to the grid; P_buy and P_sell are the power for purchasing from and selling to the grid at time t, respectively; C_DR is the demand response cost; c_CL and c_SL are the compensation prices for curtailable and shiftable loads, respectively; C_PE is the penalty cost for curtailed wind and photovoltaic powers; c_wt and c_pv are the unit penalty costs for curtailed wind and photovoltaic powers, respectively; P_cut,wt and P_cut,pv are the curtailed wind and photovoltaic powers, respectively; C_ELEN is the daily operating cost of PEMEs; c_ELE is the use cost of PEMEs; $P_{\mathrm{ELEN},t}^n$ is the power of the nth PEME at time t; C_at and C_op are the start-up cost and shutdown cost of PEME, respectively; C_T is the total system operating cost; T(X) is the penalty cost; T_nx is the priority coefficient of each unit; and X_n(t) is the operating state of different units. Note that, based on practical engineering experience, γ₁ = 0.9 and γ₂ = 0.1 are set in this paper, which indicates that C_Y has a higher priority than T(X) during the optimization process.

3.2.2. Constraints

(1)

System Power Balance Constraint:

$$P_{\mathrm{wt}}^t+P_{\mathrm{pv}}^t+P_{\mathrm{bat}}^t-P_{\mathrm{el}}^t+P_{\mathrm{grid}}^t+P_{\mathrm{fc}}^t=P_{\mathrm{load}}^t$$

(17)

where $P_{\mathrm{wt}}^t$ is the output powers of the WT; $P_{\mathrm{pv}}^t$ is the output power of the PV; $P_{\mathrm{bat}}^t$ is the power of lithium batteries; $P_{\mathrm{el}}^t$ is the power consumed by PEMEs; $P_{\mathrm{grid}}^t$ is the interactive power between the system and the grid; $P_{\mathrm{buy}}^t$ is the power purchased from the grid; $P_{\mathrm{sell}}^t$ is the power sold to the grid; $P_{\mathrm{fc}}^t$ is the output power of the PEMFC; and $P_{\mathrm{load}}^t$ is the load power.

(2)

WT and PV power constraints:

$$\begin{array}{l}0\le P_{\mathrm{wt}}^t\le P_{\mathrm{wt}}^{\max }\\ 0\le P_{\mathrm{pv}}^t\le P_{\mathrm{pv}}^{\max }\end{array}$$

(18)

where $P_{\mathrm{wt}}^{\max }$ and $P_{\mathrm{pv}}^{\max }$ is the maximum output power of WT and PV, respectively.

(3)

PEMFC power constraint:

The PEMFC only has a discharge form, and its power constraint can be expressed as

$$0\le P_{\mathrm{fc}}\le P_{\text{fc-max}}$$

(19)

where $P_{\text{fc-max}}$ is the maximum output power of the PEMFC.

(4)

Lithium battery power constraints:

The constraints of lithium batteries include the state of charge (SOC), charging and discharging powers, as follows:

$$\left\{\begin{array}{l}SO{C}_{\min }\le SOC\le SO{C}_{\max }\hfill \\ P_{\mathrm{ch}-\max }\le P_{\mathrm{bat}-\mathrm{cha}}^{\mathrm{t}}\le 0\hfill \\ 0\le P_{\mathrm{bat}-\mathrm{dis}}^t\le P_{\mathrm{dch}-\max }\hfill \end{array}\right.$$

(20)

(5)

Hydrogen storage tank capacity constraints:

$$E_{\tan \mathrm{k},\min }\le E_{\tan \mathrm{k}}^t\le E_{\tan \mathrm{k},\max }$$

(21)

where E_tank,min and E_tank,max are the lower and upper capacity limits of the HST, respectively.

(6)

PEME operating state constraints:

When the PEME is shut down, a certain period of time is required for its restart. Considering the past and current values of the shutdown state variable, the constraint for the shutdown state I is formulated as

$$-I_n^{t-2}+I_n^{t-1}-I_n^t\le 0$$

(22)

where $I_n^t$ is the shutdown state of the nth PEME; time t − 1 is the moment preceding time t; time t − 2 is the moment preceding time t − 1.

The relationship between the startup time interval Y, the shutdown time interval Z, and the 5 operating states is constrained as follows:

$$V_n^t+R_n^t+L_n^t+S_n^t+I_n^{t-1}-1\le Y_n^t$$

(23)

$$V_n^t+R_n^t+L_n^t+S_n^t+I_n^t-1\le Z_n^t$$

(24)

Since the PEME can only operate in one state at any given moment, the mutual exclusion constraint among the 5 operating states can be expressed as

$$V_n^t+R_n^t+L_n^t+S_n^t+I_n^t=1$$

(25)

To enable the PEME to operate at its rated state for a longer period, it is necessary to impose constraints on the maximum allowable duration for overload and low-load states:

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

(26)

$${\displaystyle \sum _{\tau =t}^{t+T_{\mathrm{V},\max }-1}}{V}_n^t\le T_{\mathrm{V},\max }$$

(27)

where T_R,max and T_V,max are the specified maximum durations for the overload and low-load states, respectively.

To avoid the frequent start-up of the PEME over a short timeframe, the minimum durations for the shutdown and cold standby states are constrained as follows:

$${\displaystyle \sum _{\tau =t}^{\mathrm{t}+T_{I\min }-1}}{I}_n^t\le T_{I\min }\left(I_n^t-I_n^{t-1}\right)$$

(28)

$${\displaystyle \sum _{\tau =t}^{\mathrm{t}+T_{\mathrm{Smin}}-1}}{S}_n^t\le T_{\mathrm{Smin}}\left(S_n^t-S_n^{t-1}\right)$$

(29)

where T_Imin and T_Smin are the minimum durations for the shutdown and cold standby states, respectively.

3.3. Intra-Day Optimization Model

3.3.1. Objective Function

In the intra-day stage, the data of WT, PV, and loads are predicted on a 1 h time scale, which inevitably results in deviations between the predicted nd actual values. Therefore, in the intra-day stage, these data should be predicted on a shorter time scale, and the power allocation plan formulated in the day-ahead stage should be adjusted based on the newly predicted data. To minimize adjustments to the day-ahead power allocation plan, the objective function of the intra-day stage is designed as

$$F=\min \left(\mathsf{\Delta }{P}_{\mathrm{bat}}+\mathsf{\Delta }{P}_{\mathrm{el}}+\mathsf{\Delta }{P}_{\mathrm{fc}}+\mathsf{\Delta }{P}_{\mathrm{grid}}\right)$$

(30)

where ΔP_bat, ΔP_el, ΔP_fc and ΔP_grid are the adjusted powers of lithium batteries, PEME, PEMFC and grid between the day-ahead stage and the intra-day stage, respectively.

$$\begin{array}{l}\mathsf{\Delta }{P}_{\mathrm{bat}}={\displaystyle \sum _{t=1}^T}{P}_{\mathrm{bat}}\left(t\right)-P_{{\mathrm{bat}}_0}\left(t\right)\hfill \\ \mathsf{\Delta }{P}_{\mathrm{el}}={\displaystyle \sum _{t=1}^T}{P}_{\mathrm{el}}\left(t\right)-P_{{\mathrm{el}}_0}\left(t\right)\hfill \\ \mathsf{\Delta }{P}_{\mathrm{fc}}={\displaystyle \sum _{t=1}^T}{P}_{\mathrm{fc}}\left(t\right)-P_{{\mathrm{fc}}_0}\left(t\right)\hfill \\ \mathsf{\Delta }{P}_{\mathrm{grid}}={\displaystyle \sum _{t=1}^T}{P}_{\mathrm{grid}}\left(t\right)-P_{{\mathrm{grid}}_0}\left(t\right)\hfill \end{array}$$

(31)

where P_bat(t), P_el(t), P_fc(t) and P_grid(t) are the output powers of lithium batteries, PEMEs, PEMFCs and grid in the intra-day stage, respectively; P_{bat_0}(t), P_{el_0}(t), P_{fc_0}(t) and P_{grid_0}(t) are the output powers of lithium batteries, PEMEs, PEMFCs, and grid in the day-ahead stage, respectively.

3.3.2. Constraints

For the WT, PV, lithium batteries, PEMEs and PEMFCs, their constraints in the intraday stage are identical to those in the day-ahead stage (i.e., Equations (17)–(29)), which are not repeated herein.

4. Case Study

4.1. Data Preprocessing

Annual wind speed data, solar irradiance data, and load data from a certain area in Northwest China serve as the sample data, which contains a total of 8760 sets. With the simulation time step set to 1 h, the distribution diagrams of wind speed, solar irradiance, and load power demand across 365 scenarios are obtained, as shown in Figure 5. The K-means clustering algorithm is employed to classify the annual wind speed, solar irradiance intensity, and loads data, thereby extracting typical scenarios with temporal characteristics from the large dataset. Based on engineering experience, the number of clusters K is set to 5; this value can characterize the variability of wind speed, solar irradiance, and load demand, as evidenced by the diverse occurrence probabilities of the five typical scenarios in

Table 1. Five typical scenario probabilities.

	Scenario 1	Scenario 2	Scenario 3	Scenario 4	Scenario 5
Wind speed	25.75%	10.68%	20.55%	18.90%	24.11%
Irradiance	29.40%	27.47%	19.51%	17.03%	6.59%
Loads	14.25%	17.26%	15.62%	24.38%	28.49%

. Furthermore, the extracted data are adopted as the input of the optimal dispatch model.

The specific process of data extraction is as follows: (1) randomly select the wind speed, solar irradiance intensity and load data from historical records for K days as cluster centers; (2) calculate the Euclidean distances between the data from the 365 scenarios across the aforementioned categories and the K cluster centers; (3) assign the samples to the corresponding cluster categories according to the principle of minimizing Euclidean distance; (4) update the category attribution of each sample and determine the typical scenarios for each data category.

After the aforementioned data extraction operation, the clustering results of various types of data can be obtained, and then the typical scenarios of WT, PV and loads are plotted, as shown in Figure 6.

According to these clustering results, Table 1 presents the probability values of the typical scenarios for wind, PV, and loads. Each scenario can be flexibly combined according to the different occurrence probability values of the typical scenarios. To make the input data more consistent with actual operating states, the scenarios with the highest probability among various types of data are selected as the input data for the two-stage optimization model. Specifically, the wind speed in Scenario 1, solar irradiance in Scenario 1, and loads in Scenario 5 are selected as the input data.

4.2. Off-Grid and Grid-Connected Operation Study

Taking the system shown in Figure 1 as the research object, where the PEME array is composed of six PEMEs connected in parallel. Each individual PEME has a 40 kW rated power and a 2 kW cold standby power. To verify the effectiveness of combined operation with different state combinations among multiple PEMEs, three cases are designed under off-grid and grid-connected conditions, respectively, as detailed below:

Case I: The PEMEs operate in a combined mode, excluding the operating state switching and power sharing among the PEMEs.

Case II: The PEMEs operate in a power-sharing mode and are allowed to switch between different operating states, excluding operation in a combined mode.

Case III: The PEMEs are allowed to operate flexibly in a combined mode, a power-sharing mode, and a mode of switching between different operational states.

Noted that, in the combined operation mode, the operating state of each PEME may be different at any given moment, while in the power sharing mode, the operating state of each PEME is identical at any given moment.

4.2.1. Case Study Under Off-Grid Conditions

(1)

Scheduling cost analysis: After simulating the three described cases, the scheduling cost of the EHCS is presented in

Table 2. Scheduling cost in different scenarios under off-grid conditions (million USD).

	CELEN	CBS	CPE	CDR	CT
Case I	3.785	0	0.020	0	3.845
Case II	3.765	0	0.22	0	3.794
Case III	3.656	0	0	0	3.604

. Under off-grid conditions, there is no electricity purchasing or selling with the grid, and the demand response does not need to be considered; thus, both C_BS and C_DR are zero. Based on the results in Table 2, the combined operation mode and state switching among PEMEs exert an impact on the system’s scheduling cost. For these three cases, the C_T in Case III is the lowest, which indicates that the economy of the system is improved by flexibly adjusting the operating states and combined operation modes of the PEMEs.

(2)

Power allocation analysis: The output powers of WT and PV are first used to supply the loads; the surplus powers can be absorbed by lithium batteries and PEMEs, while the deficit powers can be supplemented by lithium batteries and PEMFCs. In this section, taking Case III with the lowest CT as an example, the power allocation of the EHCS under off-grid conditions is discussed, and the power allocation results are presented in Figure 7.

During the period from 0 to 13 h, the output powers of WT and PV exceed the load power demand, so the surplus power is utilized for hydrogen production by PEMEs and charging the lithium batteries. During the period from 14 h to 20 h, the output powers of WT decrease significantly due to the decrease in wind speed, resulting in an insufficient power supply for the loads. To this end, lithium batteries and PEMFCs work collaboratively to supply the deficient power required by the loads. Based on the results from Figure 7, it can be found that PEMEs and lithium batteries can enhance the accommodation capacity of the system for wind and solar energy.

(3)

PEME operating states analysis: The operating duration under variable load states is a critical factor determining the service life of PEMEs. To illustrate that the flexible combined operation mode can reduce the duration of PEMEs operating under variable load states, a comparative analysis of Case II and Case III is conducted based on the power allocation results in Figure 7. Figure 8 shows the PEME power curves for Case II and Case III, respectively, where 1#~6# represent the six PEMEs. Figure 9 shows the operating states of PEMEs during one scheduling cycle for Case II and Case III, respectively, where the correspondence between operational states and color symbols is depicted in

Table 3. Correspondence between operational states and color symbols.

Symbols	Operating States
	overload state
	rated state
	variable load state
	cold standby state

.

The operating duration under variable load conditions is one of the key factors determining the service life of PEME.

During the 0 h~12 h period: In Figure 9a, the operating states of 6 PEMEs remain consistent at any given moment because they operate in the power-sharing mode of Case II. In Case III, as the output power of the WT increases, the PEMEs are scheduled to absorb the surplus power. Therefore, the PEMEs operate in the overload state multiple times, as shown in Figure 9b. Moreover, constrained by the allowable duration of overload operation, the PEMEs are switched between the overload state and the rated state.

During the 14 h~20 h period, the output powers of WT and PV are unable to satisfy the load power demand, thus the WT and PV are prioritized to supply the loads, causing the PEMEs to operate in cold standby mode.

During the 21 h~24 h period, the output powers of WT exceed the load power demand, and the surplus power is consumed by the PEMEs.

From Figure 9b, the different PEMEs will operate in different operating states in Case III, which can mitigate the uncertainty of REG and enhance the system’s flexibility in power regulation.

The power fluctuations caused by the WT, PV and loads are the primary factors leading to PEMEs operating in a variable load state. Since frequent variable load operation is prone to impairing the service life of PEMEs, the variable-load state is regarded as an unhealthy operating state. For this purpose, the ratio of the variable-load duration to 24 h is defined as the proportion of unhealthy operating states. This metric is motivated by the degradation mechanisms documented in [3], wherein the load fluctuation is identified as a primary cause of PEME degradation. Unhealthy operating states serve as a proxy metric for comparing relative degradation risk across different scheduling strategies, rather than a direct quantification of absolute lifetime.

Table 4. Operation status statistics of ELs in Case II and Case III under off-grid conditions.

		Overload (h)	Rated (h)	Variable Load (h)	Cold Standby (h)	Proportion of Unhealthy Operating
Case II		6	1	9	8	37.50%
Case III	PEME1	10	6	1	7	4.17%
	PEME2	10	4	2	8	8.33%
	PEME3	10	5	1	8	4.17%
	PEME4	10	6	2	6	8.33%
	PEME5	10	4	1	8	4.17%
	PEME6	10	4	1	8	4.17%

presents the operating states of PEMEs under Case II and Case III. It can be seen that the proportion of unhealthy operating states of PEMEs in Case III ranges from a minimum of 4.17% to a maximum of 8.33%, while that in Case II is 37.5%. Therefore, the combined mode for PEMEs can effectively alleviate the issue of service life reduction caused by the variable load state.

4.2.2. Case Study Under Grid-Connected Conditions

(1)

Scheduling cost analysis: After simulating the three described cases, the scheduling cost of the EHCS is presented in

Table 5. Scheduling cost in different scenarios under grid-connected conditions (million USD).

	CELEN	CBS	CPE	CDR	CT
Case I	3.725	0.733	0	0.307	4.781
Case II	5.101	0	0	0.310	5.443
Case III	2.548	0.861	0	0.297	3.736

. Under grid-connected conditions, the surplus power will be delivered to the grid when the output powers of WT and PV exceed the load power demand, which can effectively reduce the waste of wind and PV power. Based on the costs from Table 5, the CT in Case III is the lowest, and that of Case II is the highest. This indicates that under grid-connected conditions, the economic performance of the system is improved by flexibly adjusting the operating states and combination modes of PEMEs.

(2)

Power allocation analysis: Figure 10 shows the power allocation of Case III under grid-connected conditions. When the output powers of the lithium batteries and PEMFCs are unable to satisfy the load power demand, or c_buy is low, the EHCS will be permitted to purchase electricity from the grid. When the output powers of the lithium batteries and PEMFCs exceed the load power demand, or c_sell is high, the EHCS will sell the electricity to the grid.

For the convenience of analysis, the power of WT, PV and loads under grid-connected conditions is the same as that under off-grid conditions. From Figure 10, when the output powers of WT and PV exceed the load power demand, the EHCS sells the surplus power to the grid, resulting in the reduction of C_T. During the 15 h~17 h period, since the SOC of the lithium batteries is low and c_sell is in the price parity period, the EHCS purchases the electricity from the grid to satisfy the load power demand and charge lithium batteries, thereby restoring it to a healthy SOC.

(3)

PEME operating states analysis: Under grid-connected conditions, Case I and Case III also adopt the combined operation mode, so a comparative analysis of Case II and Case III is conducted in the same manner. As shown in Figure 11a and Figure 12a, since the grid can exchange power with the EHCS under grid-connected conditions, the PEMEs in Case II operate in the power sharing mode with different state switching strategies. Compared with off-grid conditions, the number of variable load shifts in the PEMEs is reduced, and the operating states of the six PEMEs remain consistent.

Furthermore, Figure 11 and Figure 12 reveal that the PEMEs in Case II maintain the maximum power or rated power state for most of the time, which indicates that the proposed strategy can adapt to energy fluctuations and grid price fluctuations while keeping the operating states of the PEMEs as stable as possible.

During the 3 h~5 h period: Figure 11a, 2#, 5#, and 6# operate in the cold standby state for a short time to avoid exceeding the HST capacity limit.

During the 11 h~23 h period: Since the output powers of WT and PV are low, most PEMEs operate in the cold standby state.

During the 23 h~24 h period: The HST capacity is about to reach its lower limit, so 1#, 2#, 4#, and 6# have an increase in their hydrogen production power.

Under grid-connected conditions, 3# and 4# operate under variable load states for an extended period of time, so they primarily serve the function of power regulation.

Table 6. Operation status statistics of ELs in Case II and Case III under grid-connected conditions.

		Overload (h)	Rated (h)	Variable Load (h)	Cold Standby (h)	Proportion of Unhealthy Operating
Case II		9	0	3	12	12.50%
Case III	PEME1	5	6	0	13	0.00%
	PEME2	5	3	1	15	4.17%
	PEME3	4	5	2	13	8.33%
	PEME4	6	4	3	11	12.50%
	PEME5	4	3	1	16	4.17%
	PEME6	4	7	1	12	4.17%

presents the operating states of PEMEs for Case II and Case III. In Case III, the number of PEMEs operating under variable load states is significantly reduced, with the proportion of unhealthy operating states ranging from a minimum of 0.00% to a maximum of 12.50%. In Case II, each PEME operates under variable load states for 12.50% of the time, which will worsen the service life of PEMEs. Similarly, under grid-connected conditions, the combined mode of PEMEs can alleviate the power fluctuation issue caused by the variable load states, thus extending the service life of PEMEs.

In summary, by combining the day-ahead and the intra-day scheduling strategies, the economy of EHCS operation is improved. Meanwhile, the accuracy of system scheduling is enhanced through the method of stepwise correction under multi-time scales, thereby ensuring the reliability of system operation. Based on three case study results under off-grid and grid-connected conditions, the proposed MSEAS is verified to be effective in the typical operating scenarios of EHCS extracted by K-means clustering. Aside from that, when power fluctuations occur in WT, PV, and loads, the proposed MSEAS can minimize the power drawn from the grid as much as possible, which contributes to reducing carbon emissions to some extent.

5. Conclusions

In this paper, considering the start–stop characteristics and combined operation modes of 6 PEMEs, a two-stage multi-time-scale energy allocation strategy (MSEAS) for EHCS is proposed to mitigate the impact of the REG uncertainty, thereby achieving the system energy optimal allocation. Under off-grid and grid-connected conditions, case studies are implemented to verify the rationality and effectiveness of the proposed MSEAS in energy optimization for EHCS. Based on these, the conclusions of this paper are summarized as follows:

(1)

Refined state modeling of PEMEs improves the accuracy of the system optimization model. Five operating states (shutdown, cold standby, low-load, variable-load, and overload) are formulated as mixed-integer constraints and incorporated into the system-level model. This refined modeling enables the optimization results to more accurately reflect the actual operating behaviors of PEMEs.

(2)

The proposed two-stage multi-time-scale framework mitigates the REG uncertainty to a certain extent. Guided by the objectives of minimizing the system operating cost and the power adjustment from the day-ahead stage to the intra-day stage, the power allocation among lithium batteries, PEMEs, PEMFCs, and the grid is planned at a 1 h time step in the day-ahead stage and re-optimized through a 4 h/15 min rolling scheme in the intra-day stage. Under off-grid conditions, the total operating cost of Case III is 3.604 million USD, which is 6.25% and 5.00% lower than that of Case I (3.845 million USD) and Case II (3.794 million USD), respectively. Under grid-connected conditions, the total operating cost of Case III is 3.736 million USD, which is 21.86% and 31.39% lower than that of Case I (4.781 million USD) and Case II (5.443 million USD), respectively. These results confirm that the proposed MSEAS can improve the economic benefits in both off-grid and grid-connected conditions.

(3)

The flexible combined operation of multiple PEMEs reduces the start–stop frequency and prolongs the service life. Comparative analyses of three case studies demonstrate that, by enabling PEMEs to operate flexibly in a combined mode, a power sharing mode, and a mode of switching between different operational states, the start–stop frequency of PEMEs is effectively reduced, which in turn extends their service life and lowers the system operating cost. Specifically, the proportion of unhealthy operating states of PEMEs in Case III ranges from 4.17% to 8.33% under off-grid conditions, compared with 37.50% in Case II. Under grid-connected conditions, this proportion ranges from 0.00% to 12.50% in Case III, compared with 12.50% in Case II. These results verify that the combined operation mode can alleviate the adverse impact of REG uncertainty on the PEME service life.

Objectively, this paper has certain limitations, and the future research plans to address these limitations are as follows: (1) The case study is based on a single representative scenario from Northwest China, and further validation across multiple scenarios and regions will be needed. (2) The proposed MSEAS mitigates the REG uncertainty through rolling correction rather than explicit stochastic or robust optimization, as well as investigates how the effectiveness of MSEAS under extreme uncertainty conditions will be achieved.

From the perspective of sustainable development, this paper contributes in three aspects. First, it promotes the efficient utilization of renewable energy by minimizing wind and solar curtailment, thereby reducing carbon emissions and dependence on fossil fuels. Second, it extends the service life of PEMEs by reducing their start-up frequency, shut-down frequency, and variable-load operation duration, which contributes to the sustainable operation of hydrogen production infrastructure. Third, it supports the large-scale integration of renewable energy into electricity–hydrogen coupling systems, providing a technically viable pathway toward a low-carbon and sustainable energy future.