An Effective Optimisation Method for Coupled Wind–Hydrogen Power Generation Systems Considering Scalability

: A wind–hydrogen coupled power generation system can effectively reduce the power loss caused by wind power curtailment and further improve the ability of the energy system to accommo‑ date renewable energy. However, the feasibility and economy of deploying such a power generation system have not been validated through large‑scale practical applications, and the economic compar‑ ison between regions and recommendations on construction are still lacking. In order to solve the aforementioned problems, this paper establishes an economic analysis model for the wind–hydrogen coupled power generation system and proposes a linear optimisation‑based priority analysis method focusing on the major net present value for regional energy system as well as a cost priority analy‑ sis method for hydrogen production within sample power plants. The case study proves the effec‑ tiveness of the proposed analysis methods, and the potential to develop wind–hydrogen coupled power generation systems in various provinces is compared based on the national wind power data in recent years. This provides recommendations for the future pilot construction and promotion of wind–hydrogen coupled power generation systems in China.


Introduction
In order to gain an edge over the competition in the renewable energy era, address global climate change and move away from dependence on traditional fossil fuels, more than 140 economies across the country have set carbon neutrality targets of varying degrees.China set the goal of reaching the peak of carbon dioxide emissions before 2030 and expect to achieve carbon neutrality by 2060, which is called the "3060" carbon goal.Following the establishment of this goal, the state has imposed higher requirements for the consumption level of renewable energy, such as wind and solar energy.
China currently sees the largest amount of carbon emissions in the world, and there is relatively higher pressure to reduce the carbon emissions.To transit to clean and lowcarbon energy, other countries are also endeavouring to develop renewable energy at large scale.However, due to the shortcomings, such as random fluctuation and strong intermittency of the wind energy, the application of wind power generation is restricted to isolated grid systems or areas with high penetration of wind power.
The wind-hydrogen coupled system can maximise the consumption of curtailed wind energy by using the control system to adjust the ratio between the amount of wind power injected to the grid and the mount of hydrogen produced.Moreover, when the water is electrolysed to produce hydrogen and secondary oxygen, compressors can be deployed to increase the storage density so that the hydrogen can be stored in long term and in large scale.As multipurpose and high-density clean energy, hydrogen is not only used to supply the power grid during peak time, but also as an energy carrier in industrial and commercial sectors via vehicles or pipelines.Such a technology will also significantly stimulate the rapid development of the hydrogen fuel cell vehicle industry.For non-renewable energy, the generation capacity is not restricted by the demand on the user side, and the generation can always match the load.In contrast, it is difficult for the renewable generation to follow the demand because of the intermittency, and thus, making the demand follow the generation has become an focus for the development of renewable energy consumption.
China has operated several pilot projects where the hydrogen is produced from renewable energy sources, such as wind power, but it is far from the stage of large-scale application.The wind-hydrogen coupled power generation technology has potential in terms of application and environmental benefits, although it is still in the experimental stage [1].In order to increase the proportion of renewable sources in the energy mix, countries around the world have developed a variety of renewable energy consumption technologies [2].Accurate modelling of profit analysis for hydrogen and methane is also implemented in the energy market sector [3], and authors in [4] comprehensively summarise the current progress of renewable energy consumption electro-chemical (P2X) technology in China and compare the corresponding level of energy consumption.In addition to the energy consumption technology, the application and development of electrolysis hydrogen production equipment and fuel cells in existing power industry are shown in [5] whilst researchers in [6] list the progress and technical characteristics of energy transition in China.The long-term hydrogen storage technology in China is also continuously developing and has become competitive in the current energy storage market [7].
The wind-hydrogen coupled power generation is a technology aimed at solving the limitation where the wind energy (as non-synchronous generation) cannot be sufficiently consumed due its randomness, intermittency and irregularity, and it consists of wind turbines, control/conversion systems, hydrogen production systems, hydrogen/oxygen storage systems, fuel cell power generation systems and transportation systems.Among these systems, the control/conversion section is the most important part for the entire system because it will determine the amount of power being injected to the grid, the hydrogen production power, and the fuel cell generating power based on the collected real-time data, which lays the foundation for the safe, reliable and stable operation of the system.When the demand for electricity is low, excess electricity is used to produce hydrogen being stored whilst during periods of peak electricity consumption, fuel cells or hydrogen turbines can be used to generate electricity to increase the wind power output.The structure of the wind-hydrogen coupled power generation system is shown in Figure 1, and the flow sequence is indicated by serial numbers in it.It is important to note that the nature of this energy source from wind power does not change compared to conventional thermal power, which means that this kind of power generation still cannot follow the power demand response as synchronous generation; at the same time, the power imbalance problem caused by the wind power supply to the grid can only be weakened by this system, but it cannot be completely eliminated.Despite these shortcomings, it does not prevent this technology from being a powerful tool to improve the capacity of wind power consumption and promote low-carbon development.
Embedding the hydrogen energy storage in wind generation can effectively increase the capability to consume wind power and the flexibility to connect wind energy to the grid [8].Authors of [9] analyse the optimal scale of wind-hydrogen coupled power generation system under different application modes in fixed scenarios using a linear programming based optimisation algorithm.A comprehensive index evaluation system is established in [10] to evaluate the feasibility of adding a hydrogen production module to an existing wind farm to achieve the transition to a wind-power-coupled system, which provides a strong reference for evaluating the retrofit benefits.The economics of a gridconnected-coupled hydrogen production system is analysed in [11,12] but such a system is not as competitive as traditional power generation yet.For the off-grid wind power hydrogen production system, several research studies have been conducted, and practical applications have been deployed in certain developed countries [13][14][15][16].The researchers in [17] proposed commercial plans for producing hydrogen from curtailed wind power in the northern region of China with a comparison and analysis of the economics of each plan.
Authors of [18] present the optimal dispatch strategy and benefit analysis method for the wind-hydrogen coupled power generation system whilst [19] establishes the full life cycle economic mathematics of the wind-hydrogen hybrid energy storage system, which can compute the system investment payback period and net profit in the whole life cycle.Furthermore, the wind power hydrogen production system coupled with fuel cells is simulated in [20] with economic analysis of the energy value.The research results show that such a system is not economically feasible from the perspective of existing hydrogen market and hydrogen production technology.Jiarong Li et al. studied the optimal combination and optimisation planning of the electrical hydrogen production module employed in the active distribution network [21], which also indicates the technical feasibility of using excessive electricity to generate hydrogen.
To solve the above optimisation problems, refs.[22,23] used the traditional mathematical solution method to solve the optimisation problem analytically, while in refs.[24,25], the optimal design problem is transformed into a linear programming problem by linearising the constraints, etc., so that it can be solved by using a commercial solver, which speeds up the solution efficiency but loses accuracy to some extent.
At the same time, mechanical learning algorithms and artificial intelligence algorithms are being developed to solve optimal design problems.Reinforcement learning algorithms have been applied in the optimisation decision making of power systems [26].A bidirectional artificial neuro-fuzzy inference system (ANFIS) is used to solve the problem of system resilience in synchronized and islanded grid mode/operation [27].A poly-algorithm, including the Grey-Taguchi method, fuzzy logic system, and adaptive neuro-fuzzy inference system (ANFIS) algorithm, can be used to attain multi-objective optimisation [28].The method of grey relational analysis (GRA), which is based on the Taguchi method (TM), and finite element analysis (FEA), has also been developed to address the optimisation of design problems [29].
Most of the existing research focuses on the evaluation of wind power coupled hydrogen production systems in existing wind farms or analysis of practical projects, but there is neither macro analysis on the profitability of wind power coupled power generation systems in large-scale energy systems nor the comparison of profitability in different regions.
According to the review of the existing research, the modelling of the wind-hydrogen coupled power generation system is only implemented when evaluating existing wind farm or analysing practical projects, and only the feasibility and development of the windhydrogen coupled power generation project are assessed and highlighted.There is neither an optimisation method to analyse and compare the overall economy of the project in regions with large-scale energy nor guidance for the future construction of a wind-powerbased hydrogen production system.
Since the wind-hydrogen coupled power generation system is promising in the aspect of renewable energy consumption, this paper proposes two optimisation evaluation and analysis schemes, which can effectively assess the economic efficiency of the windhydrogen coupled power generation system.The economy of wind-hydrogen coupled power generation at different development stages is compared among various regions, which will provide certain recommendations for the development of this technology.The main innovations of this paper are summarised below:

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The wind-hydrogen coupled power generation system can be established by upgrading the existing wind power system, where the production capacity limit is configured, and the proportion of the wind energy being injected to the grid is determined by the grid's capability to accommodate asynchronous sources.The corresponding economic analysis methods is subsequently built.

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Considering the regional differences and the estimated profits after the roll-out of the wind-hydrogen coupled power generation system, the net present value priority analysis method focusing on the major net present value for regional energy system is established to compare the development potential and profitability of the windhydrogen coupled power generation system in various regions.

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To compare the economy of the pilot construction of a wind-hydrogen coupled power generation system, this paper establishes an analysis method aiming to minimise the LCOH for sample power plants with a fixed amount of generated hydrogen.This paper also compares the profitability of using electric-hydrogen coupling module within a hydrogen-coupled power generation system in different areas.

•
Using the aforementioned two schemes, the wind power data of each province in China in the past five years are collected to compare the development potential of the wind-hydrogen coupled power generation system, which can give recommendations for future pilot construction and the promotion of the wind-hydrogen coupled power generation system.
The research flow of this paper is shown in Figure 2.This paper is organised in a way where Section 2 presents the economic evaluate method of the wind-hydrogen coupled power generation technology.The economic analysis method under two preferences is established in Section 3. Section 4 presents the case study of economic analysis methods under two preferences and compares the results of optimisation simulation for each province with the summary given in Section 5.At the same time, the source data for this study can be found in the refs.[30,31].

Materials and Methods
To analyse the economics of a wind-hydrogen coupled power generation system, this chapter investigates the production capacity, cost and benefit of the system and formulates the core indicators that can measure the effectiveness of the system.

Production Capacity
In order to compare the economics of the wind power coupled hydrogen production system in various districts, the production capacity of the system will be set at various limits subject to indicators, including the development status of wind generation, hydrogen consumption capability and the amount of wind power that can be connected to the grid in different provinces.
Because the wind energy is an asynchronous source, restrictions will apply when it is integrated into the grid so that the proportion of the asynchronous source does not exceed a certain threshold at any time.This constraint on asynchronous power generation is called the system asynchronous penetration rate (SNSP) limit [22]: where P ein is the real-time wind power integrated into the grid, P ene indicates the real-time system demand, P vin represents the real-time HVDC input power and P vou denotes the real-time HVDC output power.
The SNSP is mainly affected by the current technology and the capability to connect the wind generation to the grid, and its value was estimated between 60% and 75% in 2020 [22].Considering that more asynchronous sources, such as wind generation, will be further accommodated following the development of the power grid, the upper limit of SNSP is specified as 75%.Since the total demand of the power network differs in various regions, this constraint is equivalent to the upper limit of the total amount of grid-connected wind power provided by the wind power coupling system.
When establishing the benefit analysis model, it is essential to specify the life cycle of the system to analyse and calculate the total profitability of the wind power coupling system.According to the service contract of most existing wind farms in China, this paper proposes that the life cycle of the wind power coupled hydrogen production system is 20 years.Because the capacity of the wind farm is determined by the installed capacity of wind generators and electrolyser simultaneously, there will be various constraints for different analysis methods, which will be introduced in the next section.

Cost
The costs in this model are mainly divided as variable costs and constant costs where the former involves maintenance and operating costs of various equipment, hydrogen transportation and compression costs, and these costs will change as the wind power output, amount of hydrogen generated and hydrogen price vary.Whilst the constant costs consist of the construction cost of wind farms, electrolysers, compressors, etc., and such costs will not change after the establishment of the entire wind and hydrogen plant.

Initial Cost
The initial cost refers to the construction cost of the wind-hydrogen power generation plant, including the construction cost of various devices, such as electrolyser, compressor and hydrogen storage equipment and the land-purchase cost.Specific cost values are described in the following section.
(1) According to the estimated data given by the Bloomberg New Energy Finance in 2020, the unit construction cost of a wind farm is 6400 (RMB/kW) across the nation, and the annual unit maintenance cost is approximately 166 (RMB/kWh-year) [18] where the Vestas V150 4000 wind turbine that is suitable for large-capacity development is used because it is designed for areas with low wind speed, such as China.
(2) This research uses the proton exchange membrane electrolysis of water technology for hydrogen production, and the system parameters of the electrolysis hydrogen production equipment are listed in Table 1.Because the domestic hydrogen market is not sufficiently mature and the hydrogen produced by the proton exchange membrane electrolysis is of high quality, this paper assumes that the price of the domestic hydrogen is 5 (RMB/kg) which is equivalent to 55.62 (RMB/kg).Five hydrogen price tiers (i.e., 20, 30, 40, 50, and 60 RMB/kg) are used when analysing the case studies in various provinces.
The total initial cost can be expressed as: where C FD is the unit construction cost of the wind farm, f F represents the wind farm capacity, C DJ denotes the unit construction cost of the electrolytic cell equipment, f D is the electrolytic cell capacity and C YS is the construction cost of the compressor.

Operating Cost (1) Equipment Operation Cost
The equipment operating costs refer to the total costs for 20 years of operation under normal operating conditions, and the net present value of the operating cost is described in Equation ( 3): where C YP is the total annual operating cost of all equipment, g indicates the inflation rate, I represents the discount rate and Y denotes the life cycle of the equipment. (

2) Electricity Cost
The electricity cost involves the cost to purchase the electricity from the grid to produce hydrogen and operate all equipment.Equation ( 4) shows the net present value of the electricity cost: In Equation ( 4), C RE is the unit price of abandoned electricity.Because all abandoned electricity in this model comes from the wind farm,C RE is set as 0. C IE represents the unit price of industrial electricity, and the compressor is driven by electricity from the grid by default.E E denotes the amount of electricity consumed per unit hydrogen produced from the alkaline electrolyser, whilst E C is the amount of electricity consumed per unit hydrogen compressed by the compressor.g E is the inflation rate for the electricity price, and Q H is the amount of hydrogen produced in unit time.

Benefit
Benefit analysis focuses on the profit of the wind power coupled hydrogen production system from selling the electricity to the grid and selling the produced hydrogen during the life cycle of the project.This paper uses the net present value analysis method to evaluate the annual profitability of the project.

Sale Revenue
The direct sale revenue of the wind power coupled hydrogen production system mainly consists of two parts: the sales of electricity to the grid and the sales of hydrogen.
The net present value of the benefit by selling electricity to the grid is indicated by Equation ( 5): where P E is the price for selling electricity to the grid, whilst Q E is the real-time supply power.
The net present value of the benefit from the sale of hydrogen is expressed in Equation ( 6): where P H is the real-time market price for the hydrogen.

Environmental Benefit
The coal power generation and its associated coal hydrogen production account for the highest market share in China.There are many pollution sources when operating the coal-to-hydrogen power plants, and the cost is inevitable to implement the corresponding remedy to mitigate the exhaust gas and pollution waste.Compared with the coal hydrogen production system, the wind power coupled hydrogen production has an environmental benefit.
To calculate the environmental benefit of the wind power coupled hydrogen production system, the method of environmental benefit monetisation is adopted in this paper to convert the annual power consumption of the wind farm into coal consumption, which can be represented by Equation (7): In Equation ( 7), Q M is the calorific value of coal, equalling 21.2 MJ/kg [16].
The annual emission of each pollutant is calculated by multiplying the annual amount of consumed coal with the emission rate of each pollutant.Subsequently, the environmental cost of conventional coal-fired power plants can be obtained by multiplying the annual emission with the environmental value of each pollutant.
The equation to calculate the net present value of the environmental benefits of coalfired power plants can be written as where NPV EN is the environmental value of each pollutant and R i is the emission rate of the pollutant.The pollutant emission rate and environmental value of a conventional coal-fired power plant are summarized in Table 2.

Economic Optimisation Analysis Method
To explore the long-term development potential and prospects of the wind power coupled hydrogen production system in various regions, this paper proposes an economic analysis method that considers the differences in provinces, limits the maximum wind power capacity according to the wind power development status and prioritizes the net present value.Because the wind-hydrogen coupled power generation is an emerging technology, pilot construction and feasibility tests have to be carried out before largescale roll-out.There will be differences in the economic profitability of pilot construction in various regions, and this paper adopts an economic analysis method that focuses on wind-hydrogen coupled power plants, fixes the hydrogen output value and prioritizes the LCOH.The flow diagram of the above two optimisation methods is shown in Figure 3, and the specific method is introduced in the following sections.

Optimisation Analysis Methods in Large Scale Application Preferences
In this analysis method, various wind-hydrogen-coupled energy areas will be analysed.More specifically, multiple groups of areas with different scales, geographical locations and equipment parameters can be selected for comparison, and the time interval of this method is one hour.
This method aims to maximize the profitability of the system by changing the proportion of wind and hydrogen and the price of selling hydrogen based on the estimated capacity of wind power development in a specific region.
In the method, equipment capacities and hourly energy flows are constrained, cost data and environmental data are entered, and then the commercial linear programming solver CPLEX is used to solve for the optimal configuration, i.e., maximising the net present value of a given area for a given environmental condition.Moreover, the influence of hydrogen price and wind hydrogen proportion on the benefit of wind power coupled hydrogen production system in the region is analysed as well as the benefit potential in various regions under the same constraint.
This research specifies the regions as the provinces in China so that the long-term development potential and prospects of the wind power coupled hydrogen production system in each province in China can be compared.

Parameter Setting
Due to the differences in the wind power capacity that can be utilized in various regions, the development status of wind power technology and the hydrogen consumption capability also differ.In order to show the gap between the wind power construction capability and the level of received support in different regions, the current installed wind power capacity in the province is used as the benchmark.The estimated growth rate of wind power installation is denoted as the regional wind power capacity expansion factor n w .The product of a province's installed wind power capacity and the corresponding wind power capacity factor will set the upper limit for the estimated wind power capacity within the province.
Since the hydrogen market is not sufficiently mature, it is impossible to obtain accurate hydrogen purchase price for each province.Therefore, a segmented analysis method is used to assess the performance of the project with different hydrogen prices.When the price of hydrogen is too high, purchasing the electricity from the power grid for hydrogen production will lead to a positive benefit.In order to pursue the maximum NPV, the optimisation method will indefinitely expand the electrolytic hydrogen production equipment, which will result in an unbounded solution for the optimisation algorithm, leading to run error.Hence, the maximum capacity of the hydrogen production system is constrained by different preset proportions of wind and hydrogen.This constraint will take effect when there is positive benefit to purchase electricity from the grid for hydrogen production.In actual analysis, the reasonable value can be selected from multiple wind and hydrogen proportions.The cost and benefit parameters of other equipment use the data provided in Section 3.1.2.
The maximum wind power capacity and the maximum electrolysis equipment capacity are shown in the following equation: where L wmax is the upper limit of the capacity of the electrolytic hydrogen production equipment, C wmax denotes the existing wind power capacity of the province, L wmax shows the upper limit of the wind power capacity and n w represents the regional wind power capacity expansion factor.

Constraints
According to the upper limit of wind power capacity and electrolytic hydrogen production capacity discussed in the previous section, the wind power and electrolyser capacity are optimized to avoid the endless expansion of capacity in the net present value optimisation analysis.More specifically, the real-time input power of the electrolyser is configured as less than or equal to the upper limit of the electrolysis equipment capacity.The unit wind output data are derived from the average value of the unit wind power output per hour of the commonly used 80 m Vestas V150 4000 wind turbines deployed between 2015 and 2019 in specific provinces.Multiplying the unit wind power output with the optimized wind power capacity, the real-time wind power output can be obtained.Furthermore, there are certain restrictions for the power grid on the consumption of asynchronous sources, and SNSP is used to constrain the power grid's capability to accommo-date the wind power, which is equivalent to adding additional constraints on the amount of wind-based electricity being injected to the grid.The associated constraints are shown in expression (10):  (10) where C H is the optimal electrolyser capacity, C w denotes the optimal wind power capacity, P I H represents the real-time input power of the electrolyser, P I Hb is the real-time power purchased by the system from the power grid, P Own and P OwH are the power delivered by the wind turbines to the grid and to the electrolyser for hydrogen production, respectively.P pw is the unit wind power output, E in is the annual total input electrical energy of HVDC in the province, and E ne is the annual total produced electrical energy of the province.Because the generation power needs to balance the HVDC output and the grid demand, the SNSP can be calculated using Equation (10).

Net Present Value Analysis
The net present value (NPV) is the difference between the present value of future capital inflow and the present value of future capital outflow and is the basic indicator of the net present value method used in project assessment.The NPV method comprehensively considers the cash inflow and outflow of each period in the project investment stage, the project opportunity cost, additional benefits and negative effects, and the value of NPV can measure the level of net benefit of the project during the operation life cycle.A larger NPV value suggests higher feasibility for the investment plan.
The net present value of the economic model for the wind power coupled hydrogen production system can be expressed as Equation (11): (11) For this analysis method, the optimisation objective is to maximise the NPV and identify the associated optimal configuration of other parameters under the aforementioned constraints.The optimal NPV and LCOH data are treated as the main indication of the economic benefit.
NPV is the overall benefit indication of the project during the operation years, which reflects the profitability of the wind power coupled hydrogen production system in the province under the existing development pace of wind power facilities in the province.Since this model focuses on the macro analysis of the province, larger NPV suggests higher feasibility for the project and greater potential to develop a wind power coupled hydrogen production system in the province.LCOH refers to the levelised cost of hydrogen production, which is the unit production cost of hydrogen in the project.Because the wind power coupled hydrogen production technology discussed in this paper can also inject electricity to the grid, selling hydrogen is not the only way to generate revenue.This indicator is mainly used to reflect the development potential of the wind-power-coupled hydrogen production system when the hydrogen price is at a specific value.Lower LCOH means that there will be a bigger deviation from the preset hydrogen price, which indicates greater development potential.

Optimisation Analysis Methods in Pilot Application Preferences
Aiming to compare the economics of the pilot constructions of wind-hydrogen coupling system, this paper establishes the analysis method focusing on the sample power plants with the LCOH as the optimisation objective.
In this analysis method, sample power plants with a considerable amount of capacity are analysed and the unit time interval is specified as one hour.This model uses 50 MW wind farms for the wind power generation and assumes that the amount of produced hydrogen is fixed.By optimising the electrolyser capacity, wind power distribution, purchase of grid electricity, etc., the optimal levelised hydrogen production cost of the sample power plants in each region is obtained.
Due to differences in wind resource density in various region, there will be significant gap between data.Moreover, when the cost of selling electricity is deducted from the cost, the levelised hydrogen production cost in certain regions will be negative.This represents the cost of producing hydrogen in a conventional wind farm with a given amount of hydrogen being produced.Because the hydrogen output is fixed, the data reflect the profitability brought by the electro-hydrogen coupling module installed in the wind-hydrogen coupled power plant.A smaller value suggests higher profit and the profitability of a pilot wind power coupled hydrogen production system in various regions is compared.

Parameter Setting
The parameters of this analytical model are configured below.For the sample power plants, the wind power capacity is specified as 50 MW considering the sale of an existing wind-hydrogen coupled power generation system.There is no need to use SNSP to limit the amount of wind power that can be integrated into the grid for the sample plants.This analysis method is to assess the profitability brought by the added hydrogen production module after upgrading the conventional wind farm to wind power coupled hydrogen production system, where the daily hydrogen production of the power plant is fixed and the levelised hydrogen production cost during the working years of the project is used as an analysis index.
The parameters, such as unit cost for hydrogen production and conversion rate of the remaining equipment are identical to those in the previous model.
Different from the previous optimisation analysis solution, the maximum wind power capacity and the maximum electrolysis equipment capacity are shown in the following equation: where L ′ Hmax is the upper limit of the capacity of the electrolytic hydrogen production equipment, and L ′ wmax denotes the capacity of the wind farm.

Constraints
The constraints of this analytical model are as defined below.Fewer optimisation variables (i.e., electrolyser capacity and real-time power flow) exist due to the fixed wind power capacity (50 MW) and daily hydrogen production amount.The asynchronous energy output of the sample power plant is negligible compared to the power flow of the entire province.In addition, the penetration rate of wind power in China is relatively low, and the wind-hydrogen coupled power generation technology is still in the experimental stage without large-scale construction and application.Therefore, there will be no constraint on the amount of electricity being injected from the plant to the grid.
The specific constraints are presented in Equation (13).
where C ′ H is the optimal electrolyser capacity, C ′ w represents the fixed wind power capacity, P ′ I H denotes the real-time input power of the electrolyser, P ′ I Hb is the real-time power purchased by the system from the power grid, and P ′ Own and P ′ OwH are the power delivered by the wind power equipment to the grid and electrolyser, respectively.

Optimisation Objectives
The levelised cost of hydrogen (LCOH) is the unit cost of producing hydrogen and is derived by levelising the total cost and total amount of hydrogen produced in the entire project life cycle.More specifically, it is the present value of the cost over the present value of hydrogen production in the life cycle.The levelised cost analysis can reflect the actual rate of return on investment for the project to a certain extent, where a lower levelised cost of hydrogen production indicates higher actual rate of return on investment and shorter payback period for the project if the unit price of hydrogen is unchanged.This indicator can effectively measure the benefit of hydrogen production for the project.
The levelised unit cost for hydrogen production is shown in Equation ( 14): where H n is the amount of hydrogen being produced in a year.
LCOH is the levelised unit hydrogen production cost.In this optimisation algorithm, it is possible that LCOH is less than zero when there is only a small amount of hydrogen being produced because the revenue of selling electricity to the grid will be deducted from the hydrogen production cost.It can be derived that LCOH will be less than 0 due to the positive income of pure wind farm, when there is relatively small volume of hydrogen produced.As the preset amount of daily produced hydrogen continues to increase, the LCOH will rise to the price at which the hydrogen is produced using the electricity purchased from the grid.

Case Study
This paper presents the process of establishing various indicators in the model as well as the optimisation algorithm and implementation method to analyse the wind power coupled hydrogen production system in previous sections.The aforementioned modelling will be used to assess and analyse the economics of the wind power coupled hydrogen production system in various regions across China.To achieve the analysis target, this paper will apply the two economics analysis methods formulated in Section 3 and replace data of Anhui Province with the data of other provinces.In this way, various economic indicators of each province under different parameter settings can be obtained.By comparing and analysing the indicators, recommendations for the development and construction of the wind power coupled hydrogen production system in each province are provided.
In the following section, the two analysis methods will be run, and the reasons for certain phenomena occurring during the model operation will be analysed with an initial conclusion of economic analysis.

Case Study of Optimisation Analysis Methods in Large Scale Application Preferences
In order to ensure the accuracy of the analysis method, verify its practical significance and determine the value of certain parameters, the data of a province are firstly used for analysis.The analysis results can suggest whether this method satisfies the design purpose and expectations.This section uses the power data in Anhui province to run the case study focusing on NPV and provinces with various wind-hydrogen ratios and hydrogen prices.The operation parameters of wind power coupling hydrogen production system are listed in the Table A1 in Appendix A. The analysis results are presented in Figure 4.It can be seen from the figure that when the hydrogen price is below 30 (RMB/kg), the revenue from selling hydrogen is less than the hydrogen production cost.To achieve the highest profitability, the optimisation algorithm will set the capacity of the hydrogen production equipment to zero.This means there are no economic benefits to producing hydrogen using the wind power coupled hydrogen production system without subsidies.When the hydrogen price is 40 (RMB/kg), the NPV and LOCH increase following the decrease in the wind-hydrogen ratio and the upper limit of the capacity.The value of NPV and LOCH remain unchanged when the wind-hydrogen ratio is 2.This indicates that the income from the hydrogen sale cannot offset the cost of purchasing electricity from the grid fir hydrogen production.If the wind-hydrogen ratio is less than 2, the upper limit of the electrolyser capacity will no longer constrain the objective to achieve the highest NPV.The electrolyser capacity will reach the optimal value for the specific hydrogen price.The corresponding data can subsequently be used to measure the profitability of the wind-power coupled hydrogen production system.In this paper, the air-hydrogen ratio and hydrogen price are in the feasible range when the electrolyser capacity reaches the optimal value.When the hydrogen price is higher than 50 (RMB/kg), both NPV and LCOH continue to rise whilst the wind-hydrogen ratio drops, which means that the hydrogen production merely relying on the grid electricity has profits.Using the optimisation method that aims to achieve maximum allowed NPV, the electrolyser capacity will expand indefinitely if there is no upper limit for the capacity and wind-hydrogen ratio.
In summary, the analysis model works as expected.This research needs to compare the project profitability in various provinces, and the feasible range is affected by the level of wind power development, amount of wind resources and the relationship between grid supply and demand within each province.In order to achieve the purpose of this analysis method, this paper selects a relatively small wind-hydrogen ratio (0.5) and analyses the profitability of each province's wind power coupled hydrogen production system.The corresponding data and conclusion are shown in the next section.

Case Study of Optimisation Analysis Methods under Pilot Application Preferences
The purpose of this analysis method is to compare the benefits of the small-scale construction of a wind power coupled hydrogen production system in various provinces so that it can provide certain recommendations for the pilot construction and development of this new technology.To achieve that, it is necessary to select an appropriate amount for the fixed daily hydrogen production.By comparing the optimal LCOH of each province with an identical installed wind power capacity and daily hydrogen production amount, the area with the lower index indicates that this area is more suitable for adopting the wind power coupled hydrogen production system, and such a system can generate more profit than a conventional wind farm.
In order to assess whether the established model works as expected and to select an appropriate amount for the fixed daily hydrogen production for comparison between various provinces, this paper first selects Anhui province as an example and uses the amount of daily hydrogen production as a variable.The optimisation analysis results are shown below.
From Figure 5, the LCOH increases as the amount of daily hydrogen production of the sample power plant grows.When the volume of daily hydrogen production is between 2000 and 3000 kg, the LCOH becomes 0 and subsequently rises to approximately 48 (RMB/kg).The results roughly align with the analysis, and the model runs as expected.
To facilitate the comparative analysis between regions and reduce the impact of a large amount of hydrogen produced using electricity from the grid on the wind-hydrogen coupling, the amount of daily hydrogen production is set at 3000 kg.The analysis results of each province are presented in the next section.

Overall Benefit Analysis and Conclusion
This section shows the conclusion from the analysis method focusing on regions with NPV as the optimisation objective.In this method, the analysis subject is the province, and the unit of time interval is one hour.On top of the current estimated capacity of wind power development in the province, the upper limit of the wind hydrogen ratio is set as 0.5, and five groups of price data ranging between 20 and 60 are used.The net present value and levelised hydrogen production cost of each province when the NPV is optimal under different constraints are identified.Using such data, the influence of the hydrogen price and wind hydrogen ratio on the benefit of the wind power coupled hydrogen production system in the province as well as the profitable potential under specific constraints can be analysed.The amount of electricity generation and demand of each province are listed in Table A2 in Appendix A. The analysis is described in the Figure 6 with detailed results presented in Tables A3 and A4 in Appendix B. It is worth noting that the hydrogen production modules within the wind power coupled hydrogen production system in each province only generate negative returns when the local hydrogen market price is 20 RMB/kg and there is no need to plot the data.Furthermore, due to the lack of wind resources and weak development of the wind power industry in Tibet (i.e., tiny installed capacity), it is found that the hydrogen production module cannot bring positive income under all hydrogen prices.Therefore, the LCOH of each province under this circumstance is 0. In terms of the total profitability, the NPV values of Inner Mongolia, Liaoning, Hebei, Shandong and Ningxia stay in the top five position in the Table A4 in Appendix B. Since the hydrogen production is not as competitive as directly selling the electricity to the grid at this hydrogen price, the total profitability data are merely attributed to the pure wind generation, which match the current status of the wind power market in China.
When the hydrogen market price reaches 30 RMB/kg, the hydrogen module in most provinces still has no positive profitability.Only four provinces, including Inner Mongolia, Ningxia, Qinghai and Yunnan, gain a positive income.To guarantee the highest net present value of earnings, models in other provinces have removed the hydrogen production module.In terms of the LCOH, Yunnan province has the lowest value, followed by Inner Mongolia.From the perspective of overall profitability, the top five regions are still Inner Mongolia, Liaoning, Hebei, Shandong and Ningxia.It should be noted that it is still not able to show the improvement in the absorption capability brought by the hydrogen production module, and the traditional wind power characteristics are dominant.Inner Mongolia has a much higher profit than other provinces because of its wide area, abundant wind resources and rapid development of wind generation.From these two analyses for hydrogen price, it can be discovered that each province has a different acceptable minimum hydrogen market price in order to gain positive return.
If the hydrogen market price increases to 40 RMB/kg, the ranking of the top five provinces with the lowest NPV will change with Inner Mongolia still at the top place followed by Ningxia, Xinjiang, Yunnan and Hebei.Provinces with abundant wind resources, such as Shandong and Liaoning, do not stay on the top of the league.More specifically, Shandong and Liaoning currently have relatively high wind power generation capacity due to their relatively strong capability to consume renewable energy.However, the wind power coupling system can improve the wind power absorption capability for each province, which lowers the level of advantage of this feature in the algorithm.Therefore, provinces with relatively rich wind power capacity and moderate consumption capability would see better profits.
At the price of 50 RMB/kg for hydrogen, provinces with relatively high levels of wind resources including Inner Mongolia, Ningxia and Qinghai have shown advantages in LCOH.In order to maximise the profitability, an appropriate amount of electricity will be purchased to produce hydrogen, and an increasing amount of electricity will be used for hydrogen production as the hydrogen price increases.When the hydrogen price is low, a low LCOH has to be maintained to achieve a positive profit.In case the hydrogen price is too low, the hydrogen production module could be removed.Following the increase in hydrogen price, the amount of hydrogen production will gradually grow with higher LCOH.In terms of the total profitability of the province under this hydrogen price, Xinjiang becomes the runner-up province, just behind Inner Mongolia.The top five provinces from the perspective of NPV are Inner Mongolia, Xinjiang, Hebei, Yunnan and Ningxia.It is worth noting that with the rise in hydrogen prices, the overall profitability of Gansu also climbs to the forefront, shown in Table A2.
The price of hydrogen at 60 RMB/kg will exceed the cost of using electricity purchased from the grid to produce hydrogen in most provinces.If the upper limit of the electrolyser capacity is not constrained, the algorithm will indefinitely expand the electrolyser capacity to maximise the net present value of benefit, which cannot provide effective analysis and conclusion.Therefore, this paper involves an upper limit on the wind hydrogen proportion to avoid such a phenomenon leading to reduced differences in LCOH for certain provinces when the hydrogen price is 50 RMB/kg and 60 RMB/kg.Moreover, the maximum benefit at this hydrogen price cannot be achieved because the upper limit of the electrolyser capacity is constrained in the previous hydrogen price stage (50 RMB/kg).
In summary, the results of the analysis show the following:

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The wind hydrogen coupling power generation system can improve a province's capability to absorb wind power, but it is affected by the price of hydrogen.Higher hydrogen price will result in stronger capability for wind power consumption.

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When the hydrogen price is higher than 40 RMB/kg, the overall income of the wind power coupled hydrogen production system outweighs that of ordinary wind farms in most provinces.The acceptable minimum hydrogen market price for each province can be calculated, and the profitability can be estimated based on the price using the model.

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Provinces with higher NPV of benefits, such as Inner Mongolia, Ningxia, Xinjiang, Hebei, and Yunnan, are more suitable to roll-out and develop the wind power coupled hydrogen production system.

Benefit Analysis and Recommendation for Pilot Construction
This section compares the profitability and economic benefits of the wind power coupled hydrogen production system if it is to be deployed in small scale in a short period as an emerging renewable energy consumption technology based on the results from the analysis method focusing on plant with LCOH as an optimisation objective.The optimisation results from the model are shown in Figure 7. Since the daily hydrogen production and wind power capacity are fixed in this analysis method, the obtained LCOH values can clearly indicate the differences in profit for hydrogen production at the sample power plants in various provinces.Lower LCOH means that the hydrogen production module in the wind power coupled hydrogen production system is more profitable than ordinary wind farms.This suggests there is higher feasibility to deploy pilot wind hydrogen coupled power plant project in the corresponding province.
From the analysis data and the optimisation results, the provinces with the lowest LCOH are Liaoning, Jilin, Shanghai, Qinghai, Ningxia and Inner Mongolia.Affected by the distribution of wind resources, LCOH is generally lower in the Three North Regions and areas with abundant wind resources whilst it is higher in districts with scarce wind resources, such as Sichuan and Chongqing.It is worth noting that Shanghai has very high profitability for the wind power coupled hydrogen production, whilst the profitability of the neighbouring Zhejiang Province and Fujian Province that are further south in the country rank in the bottom tier of the league.Furthermore, the profitability of hydrogen module in Xinjiang is not as advantageous as in the previous analysis because the overall profitability of the province is limited by the associated wind energy consumption capability and progress of wind power construction.Based on the aforementioned analysis, the wind power coupled hydrogen production modules in provinces with rich wind resources, such as Jilin, Liaoning, Qinghai and Inner Mongolia, can achieve more profits.Considering the trend where there will be more wind generation construction in the southern part of China, the recommended locations for pilot constructions of wind power coupled hydrogen generation system can be Shanghai, Shandong, Guangdong, Guangxi, Tianjin and Jiangsu.

Conclusions
With the enforcement of the "30 • 60" carbon goal, the state has imposed higher requirements for the consumption level of renewable energy, such as wind and solar energy.Following the increase in the installed capacity of various renewable energy, the capacity being allowed to connect to the grid will become a critical factor restricting the development of renewables.There is limited capability in the power grid to accommodate asynchronous sources such as renewable energy.In order to solve this problem, a wind power coupled hydrogen production technology using the hydrogen as the energy carrier to effectively consume the curtailed wind power that cannot be absorbed by the power grid is proposed.
In this paper, two economic evaluation methods for wind power coupled hydrogen production are proposed with the associated mathematical model established.Two optimisation algorithms are designed based on the economic evaluation methods, and the corresponding computational models are built.Finally, the data of each province are inserted, and the economic analysis indicators of each province are obtained and compared providing the recommendations on the development of the wind power coupling system in China.The primary achievement and conclusion of this paper are summarised below.
(1) Economic Evaluation Methods of Wind-Hydrogen Power Coupling System Due to the uneven development of wind power in various parts of China, there are significant regional differences in the construction of the wind power industry.Therefore, it is crucial to establish appropriate evaluation methods to assess the economics of the wind power coupled hydrogen production system.
(2) Optimisation Algorithm and Economic Analysis Method Under Two Preferences From the perspectives of rolling out and constructing a wind coupled hydrogen production system at the scale of a province or sample plant, analysis methods focusing on regions with NPV as an optimisation objective and a plant with LCOH as an optimisation objective are established.The former method aims to achieve the maximum profit whilst the latter seeks to minimise the levelised hydrogen production cost.The power distribution inside the wind power coupled hydrogen production system is optimised, and the corresponding economic indicators are calculated.The proposed methods compare the profitability of a wind hydrogen coupled power generation system in various regions.
(3) Economic Analysis of Wind-Hydrogen Power Coupling System for Each Province in China Under different hydrogen prices, the overall profitability of each province will vary.In general, the profitability of Inner Mongolia, Xinjiang, Hebei, Ningxia and Qinghai is more advantageous.Comparing the benefits of a wind power coupling hydrogen production system and conventional power plant, the hydrogen production modules in provinces with abundant wind resources, such as Jilin, Liaoning, Qinghai and Inner Mongolia, can generate higher income.Considering the trend where there will be more wind generation construction in the southern part of China, the recommended locations for pilot constructions of a wind power coupled hydrogen generation system can be Shanghai, Shandong, Guangdong, Guangxi, Tianjin and Jiangsu.The conclusion can provide certain recommendations for the construction and development of wind hydrogen coupled power generation systems in China.

Figure 1 .
Figure 1.Structure of wind-hydrogen coupled power generation system.

Figure 2 .
Figure 2. Flowchart of the proposed study process.

Figure 3 .
Figure 3. Flowchart of the optimisation process.

Figure 4 .
Figure 4. Case study for Anhui province (analysis method focusing on regions with NPV as optimisation objective).

Figure 5 .
Figure 5. Case study for Anhui province (analysis method focusing on plant with LCOH as optimisation objective).

Figure 7 .
Figure 7. LCOH heat map of 50 MW sample wind hydrogen coupled power plants in each province with 3000 kg daily hydrogen production.

Table 1 .
Parameters of electrolysis hydrogen production equipment.

Table 2 .
Emission rate and environmental value of pollutant in coal-fired power plant.
Hb 0 ≤ P Own 0 ≤ P OwH P OwH + P Own ≤ P pw × C w P OwH + P I Hb = P I H SNSP = ΣP Own +E in