Optimal Scheduling of Weak-Grid Green Ammonia Systems Based on ALK–PEM Electrolyzer Coordination

Abstract

Green ammonia systems provide an important pathway for converting fluctuating renewable electricity into transportable chemical products. To address the coupled challenges of renewable power variability, heterogeneous electrolyzer dynamics, hydrogen storage constraints, and continuous ammonia synthesis under weak-grid conditions, this paper develops a mixed-integer linear programming scheduling model considering the coordination and start–stop characteristics of ALK–PEM hybrid electrolyzers. The model uses a 15 min resolution over a two-day horizon and integrates renewable power supply, grid electricity purchase, electrolysis, hydrogen storage, and flexible ammonia synthesis in a unified framework. The off, hot-standby, and running states of ALK and PEM electrolyzers are explicitly represented. The case results show that, under the high-renewable-resource scenario, ammonia production reaches 494.93 t, with a curtailment ratio of 3.23% and a grid electricity share of 0.68%, indicating strong renewable-energy conversion capability. Under the low-renewable-resource scenario, ammonia production decreases to 180.09 t and the grid electricity share increases to 40%, showing that the operating priority shifts to maintaining continuous production and safe hydrogen inventory. The ALK hydrogen production share decreases from 93.96% in the high-resource scenario to 75.66% in the low-resource scenario, while the PEM share increases from 6.04% to 24.34%. This indicates that ALK mainly supports large-scale base-load hydrogen production under abundant renewable resources, whereas PEM provides fast compensation and marginal regulation when renewable resources are limited and more volatile. The results demonstrate that ALK base-load production, PEM fast regulation, hydrogen storage buffering, and platform-like flexible ammonia operation jointly provide the main flexibility sources in the studied weak-grid green ammonia system.

1. Introduction

The high penetration of renewable energy is strongly promoting the deep integration of renewable power, represented by wind and solar energy, into the traditional chemical industry [1,2]. Producing hydrogen through water electrolysis powered by renewable electricity, and then coupling it with the Haber–Bosch process to synthesize green ammonia, is widely regarded as a key pathway for connecting new power systems, hydrogen energy networks, and green chemical industry chains [3,4]. Compared with pure hydrogen, ammonia has more mature storage and transport infrastructure and a higher volumetric energy density. It also has broader industrial applications. Therefore, ammonia can serve both as a high-quality energy carrier and as an important chemical feedstock [5].

However, the optimal operation of green ammonia systems has long been challenged by strong coupling across multiple temporal and spatial scales [6]. On the supply side, wind and solar power output is highly random and fluctuating [7,8]. In addition to irradiance variability, PV output is also affected by module temperature and long-term degradation. Recent studies have shown that climate warming may increase high-temperature risks, accelerate PV degradation, and increase PV-related costs [9]. On the demand side, traditional ammonia synthesis plants are usually designed for steady-state operation and have very limited tolerance to load fluctuations. As a result, they are not suitable for frequent start–stop operations or large operating-condition adjustments [10,11,12]. Although hydrogen storage can provide a certain level of energy buffering, the overall flexibility of the system still depends heavily on the dispatchability of the front-end hydrogen production process. In this context, a heterogeneous hydrogen production cluster combining alkaline electrolyzers (ALK) and proton exchange membrane electrolyzers (PEM) has become an important technical route to improve the overall upward and downward flexibility of green ammonia systems [13,14]. ALK technology is mature, low-cost, and long-lasting, making it highly promising for large-scale grid-connected applications [15]. However, ALK electrolyzers have long cold-start times, slow dynamic responses, and serious safety risks caused by hydrogen–oxygen gas crossover under low-load conditions [16]. In contrast, PEM electrolyzers have a very wide load regulation range and millisecond-level power tracking capability [17]. Nevertheless, their high cost, mainly due to noble-metal catalysts such as iridium and platinum, limits full-capacity deployment [18]. Therefore, it is essential to accurately describe the differences between heterogeneous electrolyzers in terms of start–stop time and hot-standby energy consumption within a unified optimization framework. It is also important to reveal their dynamic coordination mechanisms under complex system constraints. These issues are key to improving the economic performance and operational robustness of green ammonia systems. In addition, weak-grid operation should not be evaluated only by renewable curtailment. A low curtailment rate may simply reflect insufficient renewable supply, while grid supplementation and low production output can still reduce economic performance. This trade-off provides an important motivation for the coordinated scheduling model developed in this study.

To address these challenges, many studies have investigated the planning and scheduling of green ammonia systems, hybrid capacity configuration, and the dynamic characteristics of key equipment [19,20,21]. Besides mathematical programming methods, reinforcement-learning-based scheduling approaches have also shown potential for fast online decision-making in virtual power plants and multi-energy systems with flexible resources [22]. At the system level, existing studies mainly focus on renewable-energy accommodation, energy storage sizing, and techno-economic assessment [23,24,25,26]. From a long-term economic perspective, green hydrogen production costs are also affected by future renewable resource conditions, system configuration, hydrogen storage requirements, and climate pathways [27]. At the equipment level, some studies have explored the complementary steady-state and dynamic characteristics of different types of electrolyzers. These studies aim to use the low cost and long lifetime of ALK electrolyzers together with the fast response and wide regulation range of PEM electrolyzers to improve hydrogen production flexibility [28,29,30,31]. In addition, the flexible operation of ammonia synthesis processes under uncertain front-end power supply has received increasing academic attention. Previous studies have shown that, if load switching is properly organized under load boundaries, ramping limits, and process stability constraints, the chemical process can better adapt to fluctuating renewable power [32,33]. Although these studies have made valuable contributions, several limitations remain. Existing work is still insufficient in the refined coordination of heterogeneous equipment, the physical coupling of the whole process, and especially the joint scheduling of front-end electrolyzer start–stop characteristics and back-end ammonia synthesis flexibility boundaries. In some models, the dynamic differences between ALK and PEM electrolyzers are simplified too much. In addition, the closed-loop process between hydrogen production and downstream chemical synthesis is often not described with rigorous mathematical constraints. This makes it difficult to ensure that the optimized strategies are executable in real physical systems.

To overcome these limitations, this paper develops a mixed-integer linear programming (MILP) optimal scheduling model for a weakly grid-connected green ammonia system. The proposed model describes system energy balance, dynamic hydrogen storage under variable operating conditions, and ammonia synthesis process constraints within a unified framework. It also provides a detailed representation of the three-state transition behavior of ALK–PEM hybrid electrolyzers, namely shutdown, hot standby, and operation. Furthermore, by introducing a chemical load fluctuation penalty, continuous load limits, and ramping constraints for ammonia synthesis, platform-like flexible operation is embedded into the system optimization. The main contributions and innovations of this paper are summarized as follows:

(1)

A refined physical model of heterogeneous equipment is established. An integrated MILP model is developed for the full chain of “wind–solar power, hybrid hydrogen production, hydrogen storage, and ammonia synthesis.” The shutdown, hot-standby, and operating states of electrolyzers are described through state-transition logic. Differentiated cold-start times and hot-standby power parameters are introduced to accurately represent the heterogeneous dynamic characteristics of ALK and PEM electrolyzers in practical operation.

(2)

A continuous-constraint-based platform-like flexible scheduling criterion for ammonia synthesis is designed. A flexible evaluation mechanism based on a chemical load fluctuation penalty is proposed for the ammonia synthesis section. This mechanism balances the conflict between maximizing ammonia production and maintaining process stability. The ammonia synthesis load is treated as a continuous decision variable, and strict mathematical constraints are imposed on its allowable load range and ramping rate.

(3)

The underlying coordination mechanism of the hybrid hydrogen production system is revealed. Based on real wind and solar meteorological data with a 15 min resolution over two consecutive days, the power allocation and state evolution of hydrogen storage, ALK electrolyzers, and PEM electrolyzers are compared under high- and low-renewable-resource scenarios. The results reveal a coordinated operating paradigm in which ALK electrolyzers provide stable base-load support, while PEM electrolyzers deliver fast and flexible regulation. This further clarifies the basic dispatch logic of the hybrid hydrogen production system.

The remainder of this paper is organized as follows. Section 2 describes the physical topology and research framework of the green ammonia system. Section 3 formulates the MILP optimization model for maximizing the comprehensive net benefit of the green ammonia system, together with the relevant constraints. Section 4 presents quantitative evaluations and detailed analyses of the proposed coordinated scheduling strategy based on specific meteorological scenarios and case studies. Section 5 summarizes the main conclusions and discusses future research directions.

2. System Structure and Research Framework

2.1. Composition of the Green Ammonia System

A renewable-energy-based hydrogen-to-ammonia system, also referred to as a green ammonia system, is a complex energy–chemical system that integrates wind and solar power generation, water electrolysis for hydrogen production, gaseous hydrogen storage, and ammonia synthesis [34,35]. Its process flow is shown in Figure 1. The core objective of the system is to maximize the utilization of renewable energy while ensuring the continuous and stable output of green ammonia. According to the physical energy and material flows of the “source–storage–load” structure, the overall system can be divided into three strongly coupled sections: source-side power supply, hybrid hydrogen production and storage, and ammonia synthesis. As the energy source of the system, renewable electricity generated by wind turbines and photovoltaic arrays is first supplied to the hydrogen production units and chemical loads in the plant. To maintain the minimum continuous operation of the chemical process under extreme conditions with little wind and solar power, the system is also connected to the external grid as backup power support. In the energy conversion and buffering section, the hydrogen production unit adopts a hybrid electrolyzer cluster composed of ALK and PEM electrolyzers. The produced hydrogen is divided into two streams. One stream is directly supplied to the downstream ammonia synthesis unit, while the other is injected into a high-pressure hydrogen storage tank. When the real-time hydrogen production from the electrolyzers is insufficient, the hydrogen storage tank releases hydrogen to make up the deficit. In this way, intermittent renewable-power generation is converted into a relatively stable hydrogen supply. Finally, in the ammonia synthesis section, high-purity nitrogen produced by cryogenic air separation is mixed with the steadily supplied hydrogen and then enters the ammonia synthesis reactor. Under high temperature, high pressure, and the action of catalysts, the Haber–Bosch reaction takes place. The generated gaseous ammonia is cooled and liquefied before being stored in a liquid ammonia tank. Through this process, hydrogen energy is converted into chemical energy and then delivered for external sale.

2.2. Synergistic Operation Mechanism of ALK–PEM

The hybrid hydrogen production unit consists of multiple ALK and PEM electrolyzers connected in parallel. A comparison of the technical parameters of the two types of electrolyzers is given in

Table 1. Comparison of electrolyzer parameters.

Parameter	Unit	ALK Electrolyzer	PEM Electrolyzer
Electrolysis efficiency	%	60~75	70~90
Load regulation range	%	30~110	20~110
Cold start-up time	min	45	15
Ramp rate	%/s	8	25
Hydrogen production energy consumption	kWh/Nm3	4.5~5.5	3.8~5.0

[36,37,38,39]. In terms of physical characteristics, these two electrolyzer technologies have clear complementary advantages. ALK electrolyzers have low investment cost and long service life, making them suitable for large-scale steady-state operation. However, they require a long cold-start time and have a relatively slow dynamic response. Frequent start–stop operations may accelerate equipment aging. In addition, under low-load conditions, ALK electrolyzers are more likely to face safety risks caused by hydrogen–oxygen crossover. By contrast, PEM electrolyzers have a wide load regulation range and excellent transient ramping capability. They can effectively follow the strong fluctuations of wind and solar power on a time scale of seconds to minutes. However, their high capital cost limits the feasibility of full-capacity deployment. Based on these physical differences, in the coordinated operation of the hybrid hydrogen production system, ALK electrolyzers are more suitable for serving as a “ballast” unit to undertake medium- and long-term stable base-load hydrogen production, while PEM electrolyzers should act as a “regulating valve” to smooth high-frequency power fluctuations and perform marginal dynamic tracking.

2.3. Optimal Scheduling Framework

To systematically solve the optimal scheduling problem of a green ammonia synthesis system considering the coordinated operation characteristics of ALK–PEM electrolyzers, this paper designs the research framework shown in Figure 2. The framework follows the logical chain of “data-driven input, physical modeling, mathematical optimization, and evaluation feedback.” Through a multi-dimensional coupled optimization method, the proposed scheduling framework coordinates the resources across the full process chain. It seeks a global optimum among system safety, renewable-energy utilization, and economic feasibility. The implementation of this framework not only improves the response flexibility of the system to renewable energy, but also significantly reduces the total electricity cost. More importantly, by accurately describing the coordinated characteristics of ALK and PEM electrolyzers, it provides a key technical approach for the transition of modern green energy–chemical systems from experience-based dispatch to scientific decision-making.

As shown in Figure 2, the proposed research framework first receives boundary conditions from three aspects in the input layer: meteorological data, market data, and process parameters. In the meteorological data module, typical wind and photovoltaic power output scenarios are introduced, including extreme cases with high and low renewable-power output. These scenarios are used to represent different renewable-resource levels and to compare the scheduling behavior under resource-rich and resource-limited conditions. In the market data module, time-of-use grid electricity prices and green ammonia selling prices are integrated to provide dynamic price signals for economic optimization. In the process parameter module, key physical benchmarks are defined, including the rated power of electrolyzers, the initial hydrogen storage state, and the rated load of the ammonia synthesis unit. These multi-source heterogeneous data jointly form the basic driving inputs for optimal scheduling.

Second, in the system modeling layer, this paper focuses on two main modeling challenges: the coordination of heterogeneous equipment and the coupling of hydrogen–ammonia mass flows. As a core innovation of this study, the model develops a detailed three-state transition logic for ALK and PEM electrolyzers, including off, hot standby, and operation states. To reflect the different dynamic response capabilities of the two types of electrolyzers, the model introduces differentiated constraints across multiple time scales. These mathematical formulations fully explore and utilize the complementary advantages of the slow start–stop behavior of ALK electrolyzers and the fast response of PEM electrolyzers. Meanwhile, in the hydrogen–ammonia mass flow module, the charging and discharging rate limits of the high-pressure hydrogen storage tank and the evolution of its storage state are strictly described. The dynamic ramping boundaries and continuous production constraints of the ammonia synthesis reactor are also deeply coupled. This ensures the conservation of energy and material flows, as well as process safety, throughout the whole scheduling horizon.

Finally, in the optimization and evaluation layers, the above complex physical system is rigorously transformed into a mixed-integer linear programming (MILP) model and solved by the high-performance commercial solver Gurobi to obtain the global optimum. In this stage, a comprehensive objective function with multiple indicators is designed. For the economic term, the system considers the net profit, which is calculated as the total revenue from ammonia production minus the grid electricity purchasing cost and the penalty for curtailed wind and solar power. For equipment lifetime and operational stability, power fluctuation management and joint start–stop penalty mechanisms are introduced to suppress the damage caused by frequent operating-condition switching. Based on this optimization framework, the system can automatically generate the optimal coordinated scheduling strategy. It outputs the best joint start–stop states and power allocation schemes for all units over the entire scheduling horizon. Finally, the proposed strategy is comprehensively verified by quantifying key performance indicators, including economic benefits, renewable-energy utilization rate, and coordinated operation flexibility. These results verify the effectiveness and engineering feasibility of the proposed scheduling strategy under the two renewable-resource scenarios considered in this study.

3. Green Ammonia System Optimal Scheduling Model

The green ammonia system optimal scheduling model developed in this paper is designed for weak-grid operation. Its objective is to maximize the comprehensive benefit of the system while satisfying power balance, hydrogen production equipment start–stop, hydrogen storage dynamics, air separation nitrogen production, and ammonia synthesis process constraints. The model uses the discrete time set $T$, with a scheduling step of $\Delta t$. In each period, renewable energy is first supplied to internal system loads. When wind and photovoltaic power is insufficient, the grid provides supplementary power; when renewable power exceeds the absorption capacity of the system, power curtailment occurs. To reflect the different dynamic characteristics of ALK and PEM electrolyzers, both types are modeled unit by unit, and the three states of shutdown, hot standby, and operation are explicitly described.

3.1. Power Balance Constraints

The power supply side of the system includes wind power, photovoltaic power, and grid electricity purchase. The system operates in a weak-grid mode. Renewable electricity is first supplied to internal hydrogen production and chemical loads, the remaining part is curtailed, and any deficit is purchased from the grid. The total renewable-energy output $P_t^{\mathrm{RES}}$ is defined as:

$$P_t^{\mathrm{RES}}=P_t^{\mathrm{Wind}}+P_t^{\mathrm{PV}}$$

(1)

where $P_t^{\mathrm{Wind}}$ and $P_t^{\mathrm{PV}}$ denote the wind power generation and photovoltaic power generation of the system at time t, respectively, in MW.

The real-time system power balance equation is:

$$P_t^{\mathrm{RES}}+P_t^{\mathrm{grid}}=P_t^{\mathrm{ele}}+P_t^{\mathrm{aux}}+P_t^{\mathrm{curt}},\forall t$$

(2)

where $P_t^{\mathrm{grid}}$ is the grid power purchased by the system at time t, in MW; $P_t^{\mathrm{ele}}$, $P_t^{\mathrm{aux}}$, and $P_t^{\mathrm{curt}}$ denote the water electrolysis hydrogen production power, plant auxiliary power consumption, including hydrogen production, hydrogen storage, air separation, and ammonia synthesis sections, and wind and photovoltaic curtailment power at time t, respectively, in MW. In this paper, the auxiliary power of electrolysis, hydrogen storage, air separation, and ammonia synthesis is aggregated, and the system auxiliary power is further expressed as:

$$P_t^{\mathrm{aux}}=\alpha P_t^{\mathrm{ele}},\forall t$$

(3)

where $\alpha$ is the auxiliary power coefficient, which is set to 0.1 in this paper. It is used to represent plant auxiliary electricity consumption other than the main electrolysis power. It is introduced for model simplification. In addition, to reflect the weak-grid characteristics, the model sets constraints on total purchased electricity and instantaneous capacity charge:

$${\displaystyle \sum _{t\in \mathcal{T}}{P}_t^{\mathrm{grid}}}\le {\eta }^{\mathrm{grid}}{\displaystyle \sum _{t\in \mathcal{T}}(P_t^{\mathrm{ele}}+P_t^{\mathrm{aux}})}$$

(4)

$$0\le P_t^{\mathrm{grid}}\le P_t^{\mathrm{grid},\max }$$

(5)

where ${\eta }^{\mathrm{grid}}$ is the grid power purchase constraint coefficient, which is set to 0.4 in this paper; $P_t^{\mathrm{grid},\max }$ is the maximum purchased power, in MW.

3.2. ALK–PEM Hybrid Hydrogen Production Cluster Model

The hydrogen production cluster consists of ALK and PEM electrolyzers. In this paper, both ALK and PEM electrolyzers are modeled unit by unit. Let $i\in {\mathcal{N}}^{\mathrm{A}}$ denote the i-th ALK electrolyzer and $j\in {\mathcal{N}}^{\mathrm{P}}$ denote the j-th PEM electrolyzer, with a scheduling step of $\Delta t$. The shutdown, hot-standby, and operation state variables of a single unit are defined as $x_{i,t}^{m,\mathrm{off}}$, $x_{i,t}^{m,\mathrm{hot}}$, and $x_{i,t}^{m,\mathrm{run}}$, respectively, where $m\in \{\mathrm{A},\mathrm{P}\}$. The hydrogen production amount and power of a single unit are denoted by $H_{i,t}^m$ and $P_{i,t}^m$, respectively.

As shown in Figure 3, in any time period, each unit can only be in one of three states: operation, shutdown, or standby:

$$x_{i,t}^{m,\mathrm{off}}+x_{i,t}^{m,\mathrm{hot}}+x_{i,t}^{m,\mathrm{run}}=1,\forall i,t,m$$

(6)

In the operating state, the electrolyzer must satisfy the upper and lower load limits. Taking ALK as an example:

$${\underset{\_}{\lambda }}_{\mathrm{A}}{R}_{\mathrm{A}}{x}_{i,t}^{\mathrm{A},\mathrm{run}}\le H_{i,t}^{\mathrm{A}}\le {\overline{\lambda }}_{\mathrm{A}}{R}_{\mathrm{A}}{x}_{i,t}^{\mathrm{A},\mathrm{run}},\forall i,t$$

(7)

PEM satisfies similar constraints:

$${\underset{\_}{\lambda }}_{\mathrm{P}}{R}_{\mathrm{P}}{x}_{j,t}^{\mathrm{P},\mathrm{run}}\le H_{j,t}^{\mathrm{P}}\le {\overline{\lambda }}_{\mathrm{P}}{R}_{\mathrm{P}}{x}_{j,t}^{\mathrm{P},\mathrm{run}},\forall j,t$$

(8)

where $R_{\mathrm{A}}$ and $R_{\mathrm{P}}$ are the rated hydrogen production capacities of a single ALK and PEM electrolyzer, respectively; ${\underset{\_}{\lambda }}_m$ and ${\overline{\lambda }}_m$ are the lower and upper load rate limits. In this paper, the load rate range is set to 0.3–1.1 for ALK and 0.2–1.1 for PEM.

Considering the maintenance power consumption in the hot-standby state, the power balance of a single unit is expressed as:

$$P_{i,t}^{\mathrm{A}}=c_{\mathrm{A}}^{\mathrm{P}2\mathrm{H}}{H}_{i,t}^{\mathrm{A}}+P_{\mathrm{A}}^{\mathrm{hot}}{x}_{i,t}^{\mathrm{A},\mathrm{hot}},\forall i,t$$

(9)

$$P_{j,t}^{\mathrm{P}}=c_{\mathrm{P}}^{\mathrm{P}2\mathrm{H}}{H}_{j,t}^{\mathrm{P}}+P_{\mathrm{P}}^{\mathrm{hot}}{x}_{j,t}^{\mathrm{P},\mathrm{hot}},\forall j,t$$

(10)

where $c_m^{\mathrm{P}2\mathrm{H}}$ is the unit electricity consumption coefficient for hydrogen production, and $P_m^{\mathrm{hot}}$ is the hot-standby power. In this paper, $c_{\mathrm{A}}^{\mathrm{P}2\mathrm{H}}$ = 0.0050 MWh/Nm³ and $c_{\mathrm{P}}^{\mathrm{P}2\mathrm{H}}$ = 0.0047 MWh/Nm³. The hot-standby power of ALK and PEM is set to 2% of the rated power, namely 0.10 MW/unit and 0.02 MW/unit, respectively.

At the system level, the total power and total hydrogen production are obtained by aggregating the two electrolyzer types:

$$P_t^{\mathrm{ele}}={\displaystyle \sum _{i\in {\mathcal{N}}^{\mathrm{A}}}{P}_{i,t}^{\mathrm{A}}}+{\displaystyle \sum _{j\in {\mathcal{N}}^{\mathrm{P}}}{P}_{j,t}^{\mathrm{P}}},\forall t$$

(11)

$$H_t^{\mathrm{pro}}={\displaystyle \sum _{i\in {\mathcal{N}}^{\mathrm{A}}}{H}_{i,t}^{\mathrm{A}}}+{\displaystyle \sum _{j\in {\mathcal{N}}^{\mathrm{P}}}{H}_{j,t}^{\mathrm{P}}},\forall t$$

(12)

where $P_t^{\mathrm{ele}}$ and $H_t^{\mathrm{pro}}$ denote the total electrolysis power and total hydrogen production, respectively. This aggregation directly maps the state of each unit to the system-level energy balance, thereby coupling equipment constraints with the system objective.

To describe the start–stop process, the start-up variable $s_{i,t}^m$ and shutdown variable $d_{i,t}^m$ are defined. The two electrolyzer types use different state transition logic. For ALK, the cold-start time from shutdown to hot standby is 45 min, corresponding to three 15 min periods. The transition from hot standby to operation requires 15 min. Therefore, a unit is allowed to enter the operating state in the current period only if it was in hot standby or operation in the previous period. First, to avoid repeated start-up triggering within the same cold-start window, the following constraint is set:

$${\displaystyle \sum _{\tau =\max (0,t-C_{\mathrm{A}}+1)}^t{s}_{i,\tau }^{\mathrm{A}}}\le 1,\forall i,t$$

(13)

ALK start-up can only be triggered from the shutdown state, and the unit enters hot standby in the period when start-up is triggered:

$$s_{i,t}^{\mathrm{A}}\le x_{i,t-1}^{\mathrm{A},\mathrm{off}},s_{i,t}^{\mathrm{A}}\le x_{i,t}^{\mathrm{A},\mathrm{hot}},\forall i,t\ge 1$$

(14)

$$x_{i,t}^{\mathrm{A},\mathrm{hot}}\ge s_{i,\tau }^{\mathrm{A}},\forall i,t,\tau \in [\max (0,t-C_{\mathrm{A}}+1),t]$$

(15)

The above equations indicate that once ALK start-up is triggered in period $\tau$, the unit must remain in the hot-standby state during the whole cold–start window from $\tau$ to $\tau +C_{\mathrm{A}}-1$. The available state of ALK consists of hot standby plus operation. Since the start-up process itself is counted as hot standby, the state balance satisfies:

$$\left(x_{i,t}^{\mathrm{A},\mathrm{hot}}+x_{i,t}^{\mathrm{A},\mathrm{run}}\right)-\left(x_{i,t-1}^{\mathrm{A},\mathrm{hot}}+x_{i,t-1}^{\mathrm{A},\mathrm{run}}\right)=s_{i,t}^{\mathrm{A}}-d_{i,t}^{\mathrm{A}},\forall i,t\ge 1$$

(16)

where $s_{i,t-C_{\mathrm{A}}}^{\mathrm{A}}$ denotes the ALK start-up signal in period $C_{\mathrm{A}}$. Furthermore, the source constraints for ALK operation and hot standby are written as:

$$x_{i,t}^{\mathrm{A},\mathrm{run}}\le x_{i,t-1}^{\mathrm{A},\mathrm{run}}+x_{i,t-1}^{\mathrm{A},\mathrm{hot}},\forall i,t\ge 1$$

(17)

$$x_{i,t}^{\mathrm{A},\mathrm{hot}}\le x_{i,t-1}^{\mathrm{A},\mathrm{hot}}+x_{i,t-1}^{\mathrm{A},\mathrm{run}}+s_{i,t}^{\mathrm{A}},\forall i,t\ge 1$$

(18)

For PEM, the transition from shutdown to hot standby requires only 15 min, corresponding to one period, and this start-up process is counted as hot standby. The times from hot standby to operation and from operation to hot standby are both ignored. Therefore, PEM start-up must satisfy:

$$s_{j,t}^{\mathrm{P}}\le x_{j,t-1}^{\mathrm{P},\mathrm{off}},s_{j,t}^{\mathrm{P}}\le x_{j,t}^{\mathrm{P},\mathrm{hot}},\forall j,t\ge 1$$

(19)

The available state of PEM increases in the period when start-up is triggered:

$$\left(x_{j,t}^{\mathrm{P},\mathrm{hot}}+x_{j,t}^{\mathrm{P},\mathrm{run}}\right)-\left(x_{j,t-1}^{\mathrm{P},\mathrm{hot}}+x_{j,t-1}^{\mathrm{P},\mathrm{run}}\right)=s_{j,t}^{\mathrm{P}}-d_{j,t}^{\mathrm{P}},\forall j,t\ge 1$$

(20)

Meanwhile, the following holds:

$$x_{j,t}^{\mathrm{P},\mathrm{run}}\le x_{j,t-1}^{\mathrm{P},\mathrm{run}}+x_{j,t-1}^{\mathrm{P},\mathrm{hot}},\forall j,t\ge 1$$

(21)

$$x_{j,t}^{\mathrm{P},\mathrm{hot}}\le x_{j,t-1}^{\mathrm{P},\mathrm{hot}}+x_{j,t-1}^{\mathrm{P},\mathrm{run}}+s_{j,t}^{\mathrm{P}},\forall j,t\ge 1$$

(22)

To reduce equivalent solutions caused by symmetric ordering of units of the same type, the model also includes symmetry-breaking constraints that give priority to units with smaller indices. Take ALK as an example:

$$x_{i,t}^{\mathrm{A},\mathrm{hot}}+x_{i,t}^{\mathrm{A},\mathrm{run}}\ge x_{i+1,t}^{\mathrm{A},\mathrm{hot}}+x_{i+1,t}^{\mathrm{A},\mathrm{run}},\forall i,t$$

(23)

$$P_{i,t}^{\mathrm{A}}\ge P_{i+1,t}^{\mathrm{A}},\forall i,t$$

(24)

PEM is the same. This constraint does not change the physical feasible region, but it helps improve MILP solution efficiency.

$$x_{i,t}^{\mathrm{P},\mathrm{hot}}+x_{i,t}^{\mathrm{P},\mathrm{run}}\ge x_{i+1,t}^{\mathrm{P},\mathrm{hot}}+x_{i+1,t}^{\mathrm{P},\mathrm{run}},\forall i,t$$

(25)

$$P_{i,t}^{\mathrm{P}}\ge P_{i+1,t}^{\mathrm{P}},\forall i,t$$

(26)

The above constraints reflect the different operating characteristics of ALK, which starts slowly and is suitable for continuous base-load operation, and PEM, which starts quickly and is suitable for marginal regulation.

3.3. Hydrogen Storage Section

The hydrogen storage unit buffers the temporal mismatch between the hydrogen production side and the ammonia synthesis side. Let $S_t$ be the hydrogen storage amount at period t, $H_t^{\mathrm{dir}}$ be the hydrogen flow directly sent to the ammonia synthesis section, $H_t^{\mathrm{ch}}$ and $H_t^{\mathrm{dis}}$ be the hydrogen charging and discharging amounts, respectively, and $H_t^{\mathrm{out}}$ be the total hydrogen consumption of the ammonia synthesis section. The relationship between hydrogen production and consumption satisfies:

$$H_t^{\mathrm{pro}}=H_t^{\mathrm{dir}}+H_t^{\mathrm{ch}},\forall t$$

(27)

$$H_t^{\mathrm{out}}=H_t^{\mathrm{dir}}+H_t^{\mathrm{dis}},\forall t$$

(28)

The hydrogen storage state transition satisfies:

$$S_t=S_{t-1}+\Delta t\left(H_{t-1}^{\mathrm{ch}}-H_{t-1}^{\mathrm{dis}}\right),\forall t\ge 1$$

(29)

The upper and lower limits of hydrogen storage are:

$$\underset{\_}{\beta }{S}^{\max }\le S_t\le \overline{\beta }{S}^{\max },\forall t$$

(30)

where $S^{\max }$ is the upper capacity limit of the hydrogen storage tank, and $\underset{\_}{\beta }$ and $\overline{\beta }$ are the minimum and maximum inventory ratios, respectively. In the case study, the hydrogen storage capacity is 80,000 Nm³, the operating lower and upper limits are 5% and 95%, and the initial hydrogen storage amount is 40,000 Nm³.

To avoid simultaneous hydrogen charging and discharging in the same period, three-state binary variables $b_t^{\mathrm{ch}}$, $b_t^{\mathrm{dis}}$, and $b_t^{\mathrm{idle}}$ are introduced and satisfy the following constraints:

$$b_t^{\mathrm{ch}}+b_t^{\mathrm{dis}}+b_t^{\mathrm{idle}}=1,\forall t$$

(31)

The hydrogen charging and discharging flow rates are constrained as follows:

$$0\le H_t^{\mathrm{ch}}\le H_t^{\mathrm{ch},\max },0\le H_t^{\mathrm{dis}}\le H_t^{\mathrm{dis},\max },\forall t$$

(32)

where $H_t^{\mathrm{ch},\max }$ and $H_t^{\mathrm{dis},\max }$ are the upper limits of the charging and discharging flows, respectively, both set to 10,000 Nm³.

3.4. Air Separation Nitrogen Production Section

The ammonia synthesis reaction requires a stable nitrogen supply. In this paper, the air separation nitrogen production process is simplified as a linear relationship with the total hydrogen consumption of ammonia synthesis:

$$N_t={\displaystyle \frac{H_t^{\mathrm{out}}}{r_{{\mathrm{H}}_2{/\mathrm{N}}_2}}},\forall t$$

(33)

where $N_t$ is the nitrogen demand and $r_{{\mathrm{H}}_2{/\mathrm{N}}_2}$ is the hydrogen–nitrogen ratio constant, which is set to 3 in this paper.

3.5. Ammonia Synthesis Section

Let $Q_t^{{\mathrm{NH}}_3}$ denote ammonia production. According to the hydrogen consumption per tonne of ammonia, ammonia production and total hydrogen consumption satisfy:

$$Q_t^{{\mathrm{NH}}_3}={\displaystyle \frac{H_t^{\mathrm{out}}}{c_{\mathrm{syn}}^{\mathrm{P}2\mathrm{H}}}},\forall t$$

(34)

here $c_{\mathrm{syn}}^{\mathrm{P}2\mathrm{H}}$ is the hydrogen consumption coefficient corresponding to unit ammonia production, which is set to 1960 Nm³/t in this paper. The ammonia synthesis plant must operate within the allowable load range:

$${\underset{\_}{Q}}^{{\mathrm{NH}}_3}\le Q_t^{{\mathrm{NH}}_3}\le {\overline{Q}}^{{\mathrm{NH}}_3},\forall t$$

(35)

where ${\underset{\_}{Q}}^{{\mathrm{NH}}_3}$ and ${\overline{Q}}^{{\mathrm{NH}}_3}$ are the minimum and maximum ammonia production amounts, respectively, corresponding to 30–110% of the rated ammonia load, approximately 3.75–13.75 t/h. The lower bound of 30% rated load is used to represent the minimum continuous operating load required for maintaining stable operation of the ammonia synthesis loop. Operation below this lower bound may require additional thermal management to maintain catalyst-bed temperature stability; therefore, such sub-minimum-load operation is not considered in the feasible scheduling region of the present model.

To reflect the continuous operation requirement of the ammonia synthesis plant, the model further sets ramping constraints:

$$r_{\min }^{{\mathrm{NH}}_3}\le {\displaystyle \frac{Q_t^{{\mathrm{NH}}_3}-Q_{t-1}^{{\mathrm{NH}}_3}}{\Delta t}}\le r_{\max }^{{\mathrm{NH}}_3},\forall t\ge 1$$

(36)

In this paper, $r_{\min }^{{\mathrm{NH}}_3}$ and $r_{\max }^{{\mathrm{NH}}_3}$ correspond to the upward and downward ramping rates of ammonia synthesis, respectively, set to ±20%/h of the rated load rate. It should be noted that this paper does not set an additional discrete steady-state set. Instead, the ammonia production rate is treated as a continuous decision variable within the allowable load range. The platform-like flexible operation discussed in this paper is jointly generated by the load limits, ramping constraints, and ammonia load fluctuation penalty in the objective function. This treatment enables the optimizer to determine more refined operating levels according to renewable-power availability, hydrogen storage inventory, electricity price, and process smoothness requirements. As a result, the ammonia synthesis load tends to remain near several relatively stable operating platforms and completes smooth platform switching at a limited rate when system resources change.

3.6. Objective Function and Decision Variables

Based on the above constraints, this paper constructs an optimization model with the objective of maximizing comprehensive benefit while considering both economy and operational smoothness. Let the ammonia selling price be ${\pi }^{{\mathrm{NH}}_3}$, the time-of-use electricity price be ${\pi }_t^{\mathrm{grid}}$, and the green electricity cost be ${\pi }^{\mathrm{RES}}$. The ammonia product revenue is:

$$R^{{\mathrm{NH}}_3}={\pi }^{{\mathrm{NH}}_3}\Delta t{\displaystyle \sum _{t\in \mathcal{T}}{Q}_t^{{\mathrm{NH}}_3}}$$

(37)

The electricity purchase cost and green electricity use cost are:

$$C^{\mathrm{grid}}=1000\Delta t{\displaystyle \sum _{t\in \mathcal{T}}{\pi }_t^{\mathrm{grid}}}{P}_t^{\mathrm{grid}}$$

(38)

$$C^{\mathrm{RES}}=1000\Delta t{\pi }^{\mathrm{RES}}{\displaystyle \sum _{t\in \mathcal{T}}\left(P_t^{\mathrm{ele}}+P_t^{\mathrm{aux}}-P_t^{\mathrm{grid}}\right)}$$

(39)

In this study, $C^{\mathrm{RES}}$ is interpreted as the internalized or contracted cost of renewable electricity consumed by the plant. The electrolyzer start–stop penalty is expressed as:

$$C^{\mathrm{ss}}={\displaystyle \sum _{i,t}\left(c_{\mathrm{A}}^{\mathrm{start}}{s}_{i,t}^{\mathrm{A}}+c_{\mathrm{A}}^{\mathrm{stop}}{d}_{i,t}^{\mathrm{A}}\right)}+{\displaystyle \sum _{j,t}\left(c_{\mathrm{P}}^{\mathrm{start}}{s}_{j,t}^{\mathrm{P}}+c_{\mathrm{P}}^{\mathrm{stop}}{d}_{j,t}^{\mathrm{P}}\right)}$$

(40)

where the start-up penalties of ALK and PEM are set to 200 CNY/start and 100 CNY/start, respectively, and the shutdown penalties are set to 50 CNY/shutdown and 0 CNY/shutdown, respectively.

To smooth the ammonia synthesis load, the total power of each same-type cluster, and the power variation of individual units, the model introduces absolute-value auxiliary variables. The ammonia synthesis fluctuation penalty is formulated as follows:

$$\left\{\begin{array}{l}{Z}_t^{{\mathrm{NH}}_3}\ge Q_t^{{\mathrm{NH}}_3}-Q_{t-1}^{{\mathrm{NH}}_3},Z_t^{{\mathrm{NH}}_3}\ge -(Q_t^{{\mathrm{NH}}_3}-Q_{t-1}^{{\mathrm{NH}}_3})\\ C^{{\mathrm{NH}}_3}=c^{{\mathrm{NH}}_3}{Z}_t^{{\mathrm{NH}}_3}\end{array}\right.$$

(41)

The fluctuation penalties of the ALK cluster, PEM cluster, and individual units can be expressed similarly, forming $C_{\mathrm{A}}^{\mathrm{grp}}$, $C_{\mathrm{P}}^{\mathrm{grp}}$, $C_{\mathrm{A}}^{\mathrm{unit}}$, and $C_{\mathrm{P}}^{\mathrm{unit}}$, respectively.

$$\left\{\begin{array}{l}{Z}_t^{\mathrm{A},\mathrm{total}}\ge {\displaystyle \sum _{i\in {\mathcal{N}}^{\mathrm{A}}}{P}_{i,t}^{\mathrm{A}}}-{\displaystyle \sum _{i\in {\mathcal{N}}^{\mathrm{A}}}{P}_{i,t-1}^{\mathrm{A}}},Z_t^{\mathrm{A},\mathrm{total}}\ge -({\displaystyle \sum _{i\in {\mathcal{N}}^{\mathrm{A}}}{P}_{i,t}^{\mathrm{A}}}-{\displaystyle \sum _{i\in {\mathcal{N}}^{\mathrm{A}}}{P}_{i,t-1}^{\mathrm{A}}})\\ C_{\mathrm{A}}^{\mathrm{grp}}=c_{\mathrm{A}}^{\mathrm{total}}{Z}_t^{\mathrm{A},\mathrm{total}}\end{array}\right.$$

(42)

$$\left\{\begin{array}{l}{Z}_t^{\mathrm{P},\mathrm{total}}\ge {\displaystyle \sum _{j\in {\mathcal{N}}^{\mathrm{P}}}{P}_{j,t}^{\mathrm{P}}}-{\displaystyle \sum _{j\in {\mathcal{N}}^{\mathrm{P}}}{P}_{j,t-1}^{\mathrm{P}}},Z_t^{\mathrm{P},\mathrm{total}}\ge -({\displaystyle \sum _{j\in {\mathcal{N}}^{\mathrm{P}}}{P}_{j,t}^{\mathrm{P}}}-{\displaystyle \sum _{j\in {\mathcal{N}}^{\mathrm{P}}}{P}_{j,t-1}^{\mathrm{P}}})\\ C_{\mathrm{P}}^{\mathrm{grp}}=c_{\mathrm{P}}^{\mathrm{total}}{Z}_t^{\mathrm{P},\mathrm{total}}\end{array}\right.$$

(43)

$$\left\{\begin{array}{l}{Z}_t^{\mathrm{A},\mathrm{unit}}\ge P_{i,t}^{\mathrm{A}}-P_{i,t-1}^{\mathrm{A}},Z_t^{\mathrm{A},\mathrm{unit}}\ge -(P_{i,t}^{\mathrm{A}}-P_{i,t-1}^{\mathrm{A}})\\ C_{\mathrm{A}}^{\mathrm{unit}}=c_{\mathrm{A}}^{\mathrm{unit}}{Z}_t^{\mathrm{A},\mathrm{unit}}\end{array}\right.$$

(44)

$$\left\{\begin{array}{l}{Z}_t^{\mathrm{P},\mathrm{unit}}\ge P_{j,t}^{\mathrm{P}}-P_{j,t-1}^{\mathrm{P}},Z_t^{\mathrm{P},\mathrm{unit}}\ge -(P_{j,t}^{\mathrm{P}}-P_{j,t-1}^{\mathrm{P}})\\ C_{\mathrm{P}}^{\mathrm{unit}}=c_{\mathrm{P}}^{\mathrm{unit}}{Z}_t^{\mathrm{P},\mathrm{unit}}\end{array}\right.$$

(45)

where the fluctuation penalty of the ammonia load is set to 200 CNY/(t/h) and the fluctuation penalties of the ALK cluster, PEM cluster are set to 50 CNY/MW and 1 CNY/MW, respectively, and the fluctuation penalties of individual units are set to 10 CNY/MW and 2 CNY/MW, respectively.

The curtailment penalty is written as:

$$C^{\mathrm{curt}}=1000\Delta t{\pi }^{\mathrm{RES}}{\displaystyle \sum _{t\in \mathcal{T}}{P}_t^{\mathrm{curt}}}$$

(46)

where $C^{\mathrm{curt}}$ represents the opportunity loss associated with unused renewable electricity. The penalty terms in the objective function have different operational meanings. The electrolyzer start–stop penalty ($C^{\mathrm{ss}}$) is used to discourage frequent switching of ALK and PEM units and to reflect the associated maintenance and lifetime effects. The group-level fluctuation penalties for ALK ($C_{\mathrm{A}}^{\mathrm{grp}}$) and PEM electrolyzer clusters ($C_{\mathrm{P}}^{\mathrm{grp}}$) smooth the total power variation of each technology group, thereby avoiding excessive aggregate power oscillations. The individual unit fluctuation penalties $C_{\mathrm{A}}^{\mathrm{unit}}$ and $C_{\mathrm{P}}^{\mathrm{unit}}$ further reduce unrealistic load chattering among parallel units and improve the engineering executability of the schedule. The ammonia synthesis fluctuation penalty ($C^{{\mathrm{NH}}_3}$) reflects the preference for process continuity and encourages the synthesis load to remain on relatively stable operating platforms when possible. The curtailment penalty ($C^{\mathrm{curt}}$) discourages unnecessary wind and PV curtailment and represents the lost value of unused renewable electricity. Together, these terms balance short-term economic profit with equipment smoothness, renewable-energy utilization, and downstream process stability.

Therefore, the objective function is considered to maximize the comprehensive benefit with penalty regularization. The revenue term encourages ammonia production, while the cost and penalty terms jointly reflect electricity expenditure, renewable-energy utilization, equipment switching, and operational smoothness. The total objective function is written as:

$$\max F=\left\{\begin{array}{l}{R}^{{\mathrm{NH}}_3}-\left(C^{\mathrm{grid}}+C^{\mathrm{RES}}\right)-C^{\mathrm{ss}}-\\ \left(C^{{\mathrm{NH}}_3}+C_{\mathrm{A}}^{\mathrm{grp}}+C_{\mathrm{P}}^{\mathrm{grp}}+C_{\mathrm{A}}^{\mathrm{unit}}+C_{\mathrm{P}}^{\mathrm{unit}}\right)-C^{\mathrm{curt}}\end{array}\right\}$$

(47)

The main decision variables of the model are summarized as:

$$x=\left\{\begin{array}{l}{P}_t^{\mathrm{grid}},P_t^{\mathrm{curt}},P_t^{\mathrm{ele}},H_t^{\mathrm{pro}},S_t,H_t^{\mathrm{dir}},H_t^{\mathrm{ch}},H_t^{\mathrm{dis}},\\ Q_t^{{\mathrm{NH}}_3},x_{i,t}^{m,\mathrm{off}},x_{i,t}^{m,\mathrm{hot}},x_{i,t}^{m,\mathrm{run}},s_{i,t}^m,d_{i,t}^m,P_{i,t}^m,H_{i,t}^m\end{array}\right\}$$

(48)

In summary, the scheduling problem in this paper can be uniformly described as a MILP problem that maximizes comprehensive benefit while satisfying the constraints of power balance, hydrogen production cluster operation, hydrogen storage, air separation, and ammonia synthesis. The load fluctuation penalty and equipment power fluctuation penalty in the objective function not only improve operational smoothness, but also guide the ammonia synthesis plant and electrolyzer clusters to form segmented and stable scheduling results that are more consistent with engineering operation.

4. Case Study

4.1. Case Scenarios and Parameter Settings

To verify the operation performance of the proposed optimal scheduling model under different renewable-energy conditions, this paper uses wind and photovoltaic power output profiles over two consecutive days for case analysis. The time resolution is 15 min, and the whole scheduling horizon contains 192 time steps. Two scenarios are considered: a high-renewable-resource scenario and a low-renewable-resource scenario. The two scenarios use the same system structure, equipment parameters, hydrogen storage boundaries, and economic parameters. Only the input levels of wind and photovoltaic resources are changed. This setting eliminates the influence of capacity configuration differences on the results. Therefore, the differences in scheduling behavior are mainly driven by changes in renewable-resource availability, which helps to more clearly analyze the coordination among the hybrid hydrogen production cluster, the hydrogen storage unit, and the ammonia synthesis section. The two scenarios are used as representative deterministic cases to examine the scheduling behavior under resource-rich and resource-limited conditions.

The renewable-energy part of the case system consists of a 150 MW wind farm and a 50 MW photovoltaic power station. The wind and PV output curves under the high- and low-renewable-resource scenarios are shown in Figure 4a and Figure 4b, respectively. The system operates in a weakly grid-connected mode. Renewable electricity is preferentially supplied to the internal hydrogen production and ammonia synthesis processes. Any power deficit is supplemented by the external grid, while surplus wind and solar power is curtailed when it cannot be absorbed by the system.

The hydrogen production cluster consists of 24 ALK electrolyzers and 8 PEM electrolyzers. The rated hydrogen production capacity and rated power of a single ALK electrolyzer are 1000 Nm³/h and 5 MW, respectively. The rated hydrogen production capacity and rated power of a single PEM electrolyzer are 200 Nm³/h and 1 MW, respectively. The allowable load ranges of ALK and PEM electrolyzers are 30–110% and 20–110%, respectively. The cold-start times of ALK and PEM electrolyzers are 45 min and 15 min, respectively. Their hot-standby powers are 0.10 MW/unit and 0.02 MW/unit, respectively.

The hydrogen storage tank has a capacity of 80,000 Nm³. The initial hydrogen inventory is 40,000 Nm³, and the safe operating range is 4000–76,000 Nm³. The allowable load range of the ammonia synthesis section is 3.75–13.75 t/h, and the ramping boundary is ±2.5 t/h. The model is solved using Gurobi 11.0.3, with the relative optimality gap set to 0.001. For the economic evaluation, the market price of green ammonia is set to 3000 CNY/t, the renewable-electricity cost is set to 0.12 CNY/kWh, and grid electricity is priced using a time-of-use tariff. The renewable-electricity cost and ammonia selling price are fixed in this case study to focus on short-term operational scheduling. The main model parameters are listed in

Table 2. Main model parameters.

Parameter	Value	Parameter	Value
Scheduling time step	0.25 h	ALK electricity-to-hydrogen coefficient	0.0050 MWh/Nm3
Total number of time steps	192	PEM electricity-to-hydrogen coefficient	0.0047 MWh/Nm3
Number of ALK electrolyzers	24 units	Hydrogen storage capacity	80,000 Nm3
Number of PEM electrolyzers	8 units	Initial hydrogen storage	40,000 Nm3
Rated hydrogen production of one ALK unit	1000 Nm3/h	Maximum hydrogen charging/discharging rate	10,000 Nm3/h
Rated hydrogen production of one PEM unit	200 Nm3/h	Load range	3.75–13.75 t/h
ALK load range	0.3–1.1	Load ramping range	−2.5–2.5 t/h
PEM load range	0.2–1.1	Grid electricity purchase constraint coefficient	0.4
ALK cold-start time	0.75 h	Grid electricity price, 09:00–21:00	980 CNY/MWh
PEM cold-start time	0.25 h	Grid electricity price, 06:00–09:00/21:00–23:00	680 CNY/MWh
ALK hot-standby power	0.10 MW/unit	Grid electricity price, 23:00–06:00	370 CNY/MWh
PEM hot-standby power	0.02 MW/unit

.

4.2. Renewable-Resource Characteristics and Overall Scheduling Results

Figure 4 shows that both scenarios are dominated by wind power and have clear day–night periodic characteristics for photovoltaic output. However, the total renewable-energy availability differs significantly between the two scenarios. In the high-renewable-resource scenario, the available wind and PV electricity during the scheduling horizon is 5438.23 MWh. In the low-renewable-resource scenario, the available wind and PV electricity is 1122.05 MWh. The available renewable electricity in the high-resource scenario is about 4.85 times that in the low-resource scenario. This provides a clear comparison for analyzing system operation under resource-rich and resource-limited conditions.

Table 3. Comparison of key scheduling results under two scenarios.

Indicator	High-Renewable-Resource Scenario	Low-Renewable-Resource Scenario
Available wind and PV electricity/MWh	5438.23	1122.05
Curtailed electricity/MWh	175.83	9.46
Curtailment rate/%	3.23	0.84
Grid electricity purchase/MWh	36.19	741.73
Grid electricity share/%	0.68	40
Electrolyzer electricity consumption/MWh	4816.90	1685.74
Process electricity consumption/MWh	5298.59	1854.32
Hydrogen production/Nm3	966,219.7	341,635.32
Hydrogen consumption for ammonia synthesis/Nm3	970,064.35	352,985
Ammonia production/t	494.93	180.09
Electricity cost/CNY	666,075.63	462,745.03
Unit ammonia production cost/CNY/t	1345.80	2569.46
Total profit/CNY	818,716.75	77,538.13
Share of hydrogen produced by ALK/%	93.96	75.66
Share of hydrogen produced by PEM/%	6.04	24.34
ALK operating time steps	4029	1473
ALK hot-standby time steps	86	99
PEM operating time steps	1286	1512
PEM hot-standby time steps	234	8
ALK start-up times	24	33
PEM start-up times	8	8
Minimum hydrogen storage/Nm3	4000	4000
Maximum hydrogen storage/Nm3	76,000	61,339.9
Solution time/s	50.50	120.89

compares the key scheduling indicators under the two scenarios. Figure 5 and Figure 6 show the integrated scheduling results under the two scenarios. In each figure, subfigure (a) presents the system power dispatch results, subfigure (b) presents the hydrogen–ammonia coupling results, subfigure (c) presents the change in hydrogen storage state, and subfigure (d) presents the hydrogen flow distribution.

As shown in Table 3 and Figure 5 and Figure 6, in the high-resource scenario, the electricity consumption of the electrolyzers is 4816.90 MWh, the process electricity consumption is 5298.59 MWh, the hydrogen production is 966,219.70 Nm³, and the ammonia production reaches 494.93 t. The grid electricity purchase is only 36.19 MWh, accounting for 0.68% of the total electricity consumption. This indicates that the system mainly relies on internal flexibility to absorb wind and PV fluctuations and match the hydrogen and ammonia loads. Although the curtailment rate is 3.23%, this curtailment mainly comes from local mismatch between instantaneous high renewable output and the absorption limits of the equipment. It does not change the overall operating feature of high renewable-energy conversion.

In the low-resource scenario, the electricity consumption of the electrolyzers decreases to 1685.74 MWh, the hydrogen production is 341,635.32 Nm³, and the ammonia production is 180.09 t. The curtailment rate is only 0.84%, but the grid electricity purchase reaches 741.73 MWh, and the grid electricity share increases to 40%. Therefore, a low curtailment rate does not necessarily mean better economic performance or higher system autonomy. Instead, it reflects the shortage of available wind and PV electricity, leaving little surplus power to be curtailed. In this case, the main scheduling challenge shifts from surplus renewable-energy accommodation to the coordination among the minimum ammonia synthesis load, hydrogen storage safety, and grid power supplementation.

The function of the hydrogen storage unit also differs significantly between the two scenarios. In the high-resource scenario, the hydrogen inventory reaches both the lower and upper safety boundaries of 4000–76,000 Nm³. This shows that the hydrogen storage tank is fully used to absorb surplus hydrogen and release it across different time periods, thereby expanding the renewable-energy accommodation boundary. In the low-resource scenario, the maximum hydrogen inventory is only 61,339.90 Nm³ and does not reach the upper limit. This indicates that the system lacks continuous surplus hydrogen for a long time. The main function of the hydrogen storage unit changes to maintaining a safe inventory and supporting continuous hydrogen supply. Therefore, the hydrogen storage unit is not simply a peak-shaving and valley-filling device. Under abundant resources, it expands the renewable-energy accommodation capacity. Under insufficient resources, it ensures hydrogen supply and maintains system resilience.

The ammonia synthesis load results further show the importance of platform-like flexible operation. In the high-resource scenario, the ammonia synthesis load varies between 3.75 and 12.04 t/h, with an average load of 10.31 t/h. It remains around several load platforms for certain periods. This indicates that the model does not force the ammonia synthesis unit to follow wind and PV fluctuations at every time step. Instead, it forms platform-based regulation within the ramping boundary. In the low-resource scenario, the ammonia synthesis load ranges only from 3.75 to 4.13 t/h, meaning that the unit almost maintains the minimum steady-state operation. This shows that when resources are insufficient, the system gives priority to the continuity of the chemical process rather than short-term production increase. The essence of platform-like flexibility is to allow the load to switch in an orderly way within an acceptable process range, rather than turning the downstream chemical process into a high-frequency fluctuating load.

From a break-even perspective, the unit ammonia production cost can be interpreted as the approximate break-even ammonia selling price under the current cost definition. Therefore, the break-even prices of the high- and low-renewable-resource scenarios are 1345.80 CNY/t and 2569.46 CNY/t, respectively. Under the assumed ammonia selling price of 3000 CNY/t, both scenarios are profitable. However, the profit margin decreases from 1654.20 CNY/t in the high-resource scenario to 430.54 CNY/t in the low-resource scenario. Thus, the low-resource scenario should be described as economically less favorable, rather than unprofitable, because it is much closer to the break-even boundary and more sensitive to ammonia price and electricity price variations.

The computational performance was also recorded. Under the same solver settings, the solution times of the high- and low-renewable-resource scenarios were 50.50 s and 120.89 s, respectively. This indicates that the proposed MILP model is computationally tractable for the 48 h deterministic scheduling horizon with a 15 min resolution.

4.3. Analysis of the Coordinated Operation Characteristics of ALK–PEM Electrolyzers

The coordination mechanism of the hybrid hydrogen production cluster is the key to improving the overall response capability of the system. Figure 7 shows the power sharing results of the two types of electrolyzers under different resource scenarios. In the high-resource scenario, ALK electrolyzers contribute 93.96% of the total hydrogen production and 94.28% of the total electrolyzer power consumption, while PEM electrolyzers contribute only 6.04% of the hydrogen production and 5.72% of the power consumption. In the low-resource scenario, the hydrogen production share of ALK electrolyzers decreases to 75.66%, while that of PEM electrolyzers increases to 24.34%. This change indicates that when resource conditions change, the system does not simply reduce the outputs of the two types of electrolyzers in the same proportion. Instead, it reconstructs their division of labor according to their dynamic characteristics. ALK electrolyzers are used to undertake stable and large-scale hydrogen production, while PEM electrolyzers are used for finer power matching and marginal compensation under low-resource conditions.

As shown in Figure 8 and Figure 9, in the high-resource scenario, the cumulative operating time steps of ALK electrolyzers reach 4029. On average, about 20.98 ALK units are in operation at each time step, and the maximum number of operating ALK units reaches 24. This indicates that the ALK cluster maintains a high online scale for a long time and provides the main support for high ammonia production. In this scenario, the cumulative operating time steps and hot-standby time steps of PEM electrolyzers are 1286 and 234, respectively. PEM electrolyzers mainly provide fast compensation during local fluctuation periods.

In the low-resource scenario, the cumulative operating time steps of ALK electrolyzers decrease to 1473, and the average number of operating ALK units is about 7.67. However, the number of start-ups increases to 33. This indicates that the system needs to select the online scale of large-capacity ALK units more carefully to avoid excessive power rigidity under low-resource conditions. In contrast, the cumulative operating time steps of PEM electrolyzers reach 1512, and the average number of operating PEM units is about 7.88, which is close to full-cluster online operation. This shows that PEM electrolyzers change from auxiliary regulation units to important flexible units for maintaining continuous system operation in the low-resource scenario.

Figure 10 and Figure 11 further reveal the above division of labor from the unit-level power perspective. In the high-resource scenario, ALK power shows large continuous high-load blocks, indicating that ALK electrolyzers mainly provide stable and sustained main power output. The PEM power distribution is more local and is mainly used to absorb marginal fluctuations. In the low-resource scenario, the high-load blocks of ALK electrolyzers shrink significantly, while the effective participation periods of PEM electrolyzers increase, and their power changes more frequently.

These results indicate that under low-resource conditions, the scheduling focus shifts from large-scale hydrogen production to more accurate supply–demand matching. If the system relies only on ALK electrolyzers, it will be easily limited by the minimum load ratio, slow start-up, and large unit capacity under low-resource conditions. If the system relies too much on PEM electrolyzers, the large-scale and low-cost hydrogen production capability under high-resource conditions will be weakened. Therefore, the value of the hybrid electrolyzer configuration lies in its ability to provide both large-scale conversion capability and fast regulation capability.

4.4. Comprehensive Economic Performance and Operational Adaptability

Figure 12 and Figure 13 summarize the economic performance and start–stop/hot-standby behaviors under the two scenarios. In the high-resource scenario, the electricity cost is 666,057.63 CNY, the unit ammonia production cost is 1345.80 CNY/t, and the total profit is 818,716.75 CNY. Since renewable resources are sufficient, the grid electricity share is low, and ALK electrolyzers remain online at a high level for a long time, the system can convert most renewable energy into hydrogen and ammonia products. In addition, the costs related to start–stop operations and hot standby are diluted by the larger production output. Therefore, the high-resource scenario not only achieves higher production, but also has a lower unit cost.

In the low-resource scenario, the electricity cost is 462,745.03 CNY, the unit ammonia production cost is 2569.46 CNY/t, and the total profit is 77,538.13 CNY. The economic pressure in this scenario does not come from power curtailment. Instead, it is caused by insufficient renewable energy, stronger dependence on grid electricity, and the dilution effect caused by low production. Since the ammonia synthesis unit must maintain a minimum continuous load, the system has to purchase electricity in many time periods to meet the demands of hydrogen production and process operation. When the unit ammonia production cost exceeds the ammonia selling price, the system can still maintain continuous operation from a technical perspective, but its economic performance becomes less favorable.

This result shows that the operation performance of a weakly grid-connected green ammonia system cannot be evaluated only by the curtailment rate. The low-resource scenario has the lowest curtailment rate, but the worst economic performance. The high-resource scenario has a certain amount of curtailment, but it achieves higher production, a lower unit cost, and higher profit. The reason is that the curtailment rate only reflects whether surplus renewable energy is absorbed. The economic performance of the system also depends on the total resource availability, grid electricity share, online equipment efficiency, and ammonia production scale. For engineering design, the key to improving the economic performance of a green ammonia system is not to pursue zero curtailment alone. Instead, it is necessary to optimize the matching among wind and PV resource scale, electrolyzer type ratio, hydrogen storage capacity, minimum ammonia synthesis load, and electricity price structure.

In summary, the high-resource scenario mainly tests the large-scale conversion capability of the system, while the low-resource scenario mainly tests its ability to ensure continuous operation. The former relies on a high online scale of ALK electrolyzers, sufficient hydrogen storage absorption capacity, and higher ammonia synthesis load platforms to increase production. The latter relies on the fast regulation of PEM electrolyzers, the safe inventory of hydrogen storage, and the minimum steady-state ammonia synthesis load to maintain system feasibility. Therefore, ALK–PEM coordination, hydrogen storage buffering, and platform-like flexible ammonia operation are not independent sources of flexibility. Instead, they jointly form a multi-level regulation structure that connects fluctuating renewable power with continuous chemical production in the studied weakly grid-connected green ammonia system.

5. Conclusions

This paper develops a mixed-integer linear programming optimal scheduling model for a weakly grid-connected green ammonia system with ALK–PEM hybrid hydrogen production. The model jointly considers wind and PV power output, grid power supplementation, three-state electrolyzer start–stop behavior, hydrogen storage dynamics, and flexible ammonia synthesis load. Comparative analyses are carried out under high- and low-renewable-resource scenarios. The results show that the proposed model can coordinate the operation of the electricity, hydrogen, and ammonia sections at a 15 min time scale. It enables the system to achieve a high level of renewable-energy conversion under abundant resources, while maintaining continuous production and safe hydrogen inventory under limited resources. The main conclusions are as follows.

(1)

The proposed model can effectively describe the multi-section coupled scheduling characteristics of a weakly grid-connected green ammonia system. In the high-resource scenario, the ammonia production is 494.93 t, the curtailment rate is 3.23%, and the grid electricity share is 0.68%. In the low-resource scenario, the ammonia production is 180.09 t, the curtailment rate is 0.84%, and the grid electricity share is 40%. These results show that feasible scheduling schemes can be obtained in both scenarios. The high-resource scenario reflects the renewable-energy conversion capability, while the low-resource scenario reflects the ability to ensure continuous production.

(2)

ALK and PEM electrolyzers form an adaptive division of labor under different resource conditions. In the high-resource scenario, ALK electrolyzers contribute 93.96% of the total hydrogen production and serve as the main units for large-scale hydrogen production. In the low-resource scenario, the hydrogen production share of PEM electrolyzers increases to 24.34%, and PEM units maintain a high online level. This indicates that PEM electrolyzers undertake more important marginal regulation tasks when renewable resources are insufficient and fluctuations become more significant. The advantage of the hybrid electrolyzer configuration is that it can provide both large-scale low-cost hydrogen production and fast power matching.

(3)

The hydrogen storage unit and the platform-like flexible ammonia synthesis load jointly reduce the impact of wind and PV fluctuations on the chemical process. In the high-resource scenario, the hydrogen inventory reaches the safety boundaries of 4000–76,000 Nm³, mainly to expand the renewable-energy absorption boundary. In the low-resource scenario, the maximum hydrogen inventory is 61,339.90 Nm³, and hydrogen storage is mainly used to maintain continuous hydrogen supply and inventory safety. The ammonia synthesis load shows multi-platform operation in the high-resource scenario and almost remains at the minimum steady state in the low-resource scenario. This indicates that the core role of flexible ammonia synthesis operation is to form orderly load regulation within the process-acceptable range.

(4)

System economic performance is highly sensitive to renewable-resource availability and the share of grid electricity. In the high-resource scenario, the unit ammonia production cost is 1345.80 CNY/t, and the total profit is 818,716.75 CNY. In the low-resource scenario, the unit ammonia production cost increases to 2569.46 CNY/t, and the total profit decreases to 77,538.13 CNY. A low curtailment rate does not necessarily correspond to better economic performance. When renewable energy is insufficient to support continuous chemical production, dependence on grid electricity and the low-output dilution effect can significantly increase the unit cost.

Overall, the key to optimal scheduling of a weakly grid-connected green ammonia system is not to maximize the efficiency of a single section, but to build a coordination mechanism among renewable-energy fluctuations, dynamic electrolyzer constraints, hydrogen storage inventory, and continuous ammonia synthesis operation. ALK electrolyzers provide large-scale conversion capability, PEM electrolyzers provide fast regulation capability, hydrogen storage provides cross-period material flow buffering, and platform-like flexible ammonia synthesis provides downstream process adaptability. Only when these sections are properly coordinated can the system achieve renewable-energy accommodation, production continuity, and economic feasibility at the same time.

The present validation is based on two deterministic two-day renewable-resource scenarios. Therefore, the conclusions mainly reflect the scheduling behavior under the selected high- and low-resource conditions. This study has several limitations that should be addressed in future work. Future research can be further extended in three directions. First, multi-seasonal, long-term, random and extreme weather scenarios can be further considered to more comprehensively evaluate the robustness and adaptability of the proposed scheduling strategy under more complex renewable-resource conditions. In addition, temperature-dependent PV efficiency loss, module degradation, and long-term climate impacts should be incorporated to obtain renewable-input scenarios with stronger physical grounding. Second, joint sensitivity analyses should be conducted for the ALK/PEM installed capacity ratio, hydrogen storage capacity, minimum ammonia synthesis load, grid connection capacity, electricity price structure, renewable-electricity cost, electrolyzer cost, hydrogen storage requirement, and ammonia market price, so as to identify the key boundaries where the system shifts from profit to loss under different techno-economic pathways. Finally, future work should incorporate electrolyzer lifetime degradation, start–stop fatigue, PEM stack replacement cost, dynamic ammonia catalyst performance, and renewable-energy forecasting errors into the scheduling framework. Meanwhile, although the current MILP model is tractable for the 48 h deterministic cases, its computational burden may increase under multi-day, seasonal, or stochastic scheduling horizons. Therefore, rolling-horizon optimization, decomposition methods, or hybrid MILP–learning-based frameworks can be further explored to improve scalability and engineering applicability.