River water path hydrogen chain market bidding method based on double-layer decision model

Abstract

The invention belongs to the technical field of new energy scheduling models, and particularly relates to a river water path hydrogen chain market bidding method based on a double-layer decision model. Comprising the steps of designing a river water path hydrogen chain to participate in a double-layer decision-making architecture of a hydrogen energy market; a river water path hydrogen chain market bidding model based on a double-layer decision-making architecture is provided; and reconstructing the river water path hydrogen chain market bidding model based on a KKT condition, and converting the river water path hydrogen chain market bidding model into a classic mixed integer linear programming MILP problem by using a duality theory and a large M method so as to realize efficient solving of the river water path hydrogen chain market bidding model. According to the strategy provided by the invention, the operation economy of the system can be improved by not less than 6.9%.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of new energy dispatching model, and particularly relates to a river waterway hydrogen chain market bidding method based on a double-layer decision model. BACKGROUND

[0002] Green hydrogen, as a kind of green low-carbon secondary energy, has the advantages of high energy density, clean and environmental protection. With the development of electric hydrogen technology, green hydrogen has attracted widespread attention. It can not only be used in the transportation field as a fuel for hydrogen energy vehicles, but also as a long-period energy storage means to promote the energy supply and demand balance of the power system. Therefore, promoting the development and construction of the hydrogen energy market has important practical significance for improving the utilization rate of new energy and enhancing the flexibility of the power system.

[0003] There is little consideration of the potential for compressor power staging adjustment in the prior art, which cannot fully adapt to the flexible and variable hydrogen energy filling demand, resulting in serious waste of resources. In addition, the above work usually assumes that hydrogen energy demand and sales price are fixed, ignoring the supply and demand adjustment effect and price dynamic clearing mechanism of hydrogen energy market under the participation of other hydrogen energy operators. With further research, scholars have noticed the market trading mechanism of hydrogen energy and carried out a lot of exploratory work. For example, the existing literature [Sun C, Li Q, Qiu Y B, et al. Life cycle economic assessment of microgrid system under the mode of surplus electricity feeding into the grid or hydrogen production[J]. Power System Technology, 2021, 45(12): 4650-4660.] deeply analyzes the full life cycle economy of microgrid system under the two modes of surplus electricity feeding into the grid and surplus electricity hydrogen production, but it uses a fixed hydrogen sales price and does not design market participants' bidding strategies, which cannot reflect the market competition characteristics. The existing literature [Zhang Y, Li J, Ji X, et al. Optimal dispatching of electric-heat-hydrogen integrated energy system based on Stackelberg game[J]. Energy conversion and economics, 2023, 4(4): 267-275.] uses Stackelberg game theory to explore an optimal dispatching model for an electric-heat-hydrogen integrated energy system, but it only pursues the maximum profit of the leader, sacrificing the interests of the followers, resulting in a loss of overall social well-being. Similarly, the existing literature [Kumar A, Singh A, Maulik A, et al. Multi-market participation of electricity-hydrogen DC microgrid with correlated uncertainties[J]. Energy, 2025: 137095.] proposes a multi-market participation dispatching method for a DC microgrid based on the Stackelberg model, which achieves profit improvement for operators while reducing user costs, but the optimization model does not cover the hydrogen energy transportation link, resulting in limited practical application scenarios.The existing literature [Kountouris I, Forcellati M, Pantelidis I, et al. Renewable hydrogen and ammonia production: Location-specific considerations and competitive market dynamics in Europe [J]. Applied Energy, 2025, 397: 126168.] proposes a multi-region investment planning framework for port operators, quantifying the levelized cost of wind-to-hydrogen in four European ports, but hydrogen is sold at a fixed price, which does not reflect the impact of market competition on hydrogen pricing. The existing literature [Wang L, Jiao S, Xie Y, et al. Two-way dynamic pricing mechanism of hydrogen filling stations in electric-hydrogen coupling system enhanced by blockchain [J]. Energy, 2022, 239: 122194.] designs a two-way dynamic pricing mechanism for hydrogen filling stations based on blockchain, which realizes the linkage between electricity and hydrogen markets through cross-chain technology. However, this mechanism relies on pre-set inclination factors to adjust prices and does not consider the multi-agent market competition bidding factor, leading to biased price formation.The existing literatures [El-Taweel N A, Khani H, Farag H E Z. Hydrogen storage optimal scheduling for fuel supply and capacity-based demand response program under dynamic hydrogen pricing [J]. IEEE transactions on smart grid, 2018, 10 (4): 4531-4542] and [Gu Z, Pan G, Gu W, et al. Robust optimization of scale and revenue for integrated power-to-hydrogen systems within energy, ancillary services, and hydrogen markets [J]. IEEE Transactions on Power Systems, 2023, 39 (3): 5008-5023.] proposed dynamic hydrogen pricing strategy, in which the dynamic hydrogen pricing is only controlled by a linear adjustment factor, lacking the description of market game and supply and demand elasticity, resulting in limited flexibility of the pricing strategy. It can be seen that the existing researches rarely construct a multi-stakeholder game framework, and the benefit distribution is unbalanced. Secondly, few of them consider the spatio-temporal coordination relationship among hydrogen production, storage, transportation and trading links, resulting in limited practical application value. SUMMARY

[0004] The purpose of the present application is to provide a river and waterway hydrogen chain market bidding method based on a double-layer decision model, which can improve the economic efficiency of system operation by not less than 6.9%. The proposed strategy provides a new perspective for hydrogen chain operation and hydrogen market transaction.

[0005] To solve the above technical problems, the present application provides a river and waterway hydrogen chain market bidding method based on a double-layer decision model, which comprises:

[0006] A double-layer decision architecture for the river and waterway hydrogen chain participating in the hydrogen market is designed;

[0007] A river and waterway hydrogen chain market bidding model based on the double-layer decision architecture is proposed; the river and waterway hydrogen chain market bidding model comprises an upper-layer decision model for the river and waterway hydrogen chain and a lower-layer clearing model for the hydrogen market; wherein the upper-layer decision model takes the maximum daily operation income as the target and considers the fine power adjustment factor of the hydrogen compressor; the lower-layer clearing model takes the maximum social welfare as the target and considers the multi-stakeholder bidding factor;

[0008] The river and waterway hydrogen chain market bidding model is reconstructed based on a KKT condition, and the river and waterway hydrogen chain market bidding model is converted into a classic mixed integer linear programming MILP problem by using a dual theory and a large M method, so that efficient solution of the river and waterway hydrogen chain market bidding model is realized.

[0009] Preferably, the river and waterway hydrogen chain is composed of a new energy station and a hydrogen transport ship; the new energy station comprises a new energy unit, a hydrogen production device, a compressor and a hydrogen storage tank.

[0010] Preferably, the double-layer decision architecture comprises an architecture upper layer and an architecture lower layer; the architecture upper layer comprehensively considers new energy station power distribution and ship hydrogen carrying amount conservation factors, determines optimal on-grid power, bidding hydrogen amount and corresponding hydrogen price by evaluating a market clearing price; the architecture lower layer introduces an independent system operator ISO which matches transactions according to bidding information of the new energy station, other hydrogen selling parties and hydrogen buying parties, so as to realize market clearing.

[0011] Preferably, the river and waterway hydrogen chain upper-layer decision model comprises the following objective function:

[0012]

[0013] In the formula, formula (1) is an objective function for realizing maximization of a new energy station revenue composed of electricity selling revenue, hydrogen selling revenue and ship transportation cost; formulae (2)-(3) are transportation cost constraints.

[0014] In the formula, λ t is a hydrogen market clearing price MCP; is a winning hydrogen amount of the new energy station in the hydrogen market; is an on-grid electricity price; is total on-grid power; is a transportation cost of the ship k at time t, is a transportation cost of the hydrogen transport ship per kg of hydrogen per unit time at a constant driving power; is a real-time hydrogen carrying amount of the hydrogen transport ship; z i,k,t indicates a start-stop flag of the ship, z i,k,t =1 when the ship k is parked at the station i at time t, and z i,k,t =0 indicates that the ship is in a sailing state; M indicates a large enough positive number.

[0015] Preferably, the river and waterway hydrogen chain upper-layer decision model further comprises the following constraint conditions:

[0016] River and waterway hydrogen chain power balance constraint:

[0017]

[0018] wherein, formula (4) represents the power balance constraint; formula (5) is the on-grid power limit; formula (6) represents the non-negative abandoned power;

[0019] wherein, is the actual power generation of the wind turbine of the i-th new energy station at time t; is the actual power generation of the photovoltaic; is the hydrogen production power of the electrolyzer; is the compression power of the compressor of the new energy station; is the on-grid power of the new energy station i at time t; is the abandoned power that cannot be consumed; is the on-grid channel capacity limit;

[0020] Hydrogen production equipment operation constraint:

[0021]

[0022] wherein, formula (7) represents the equivalent relationship between hydrogen production and hydrogen production power; formula (8) represents the limit on hydrogen production power;

[0023] wherein, is the hydrogen production of the i-th new energy station at time t; η h is the electrolysis conversion rate; and are the minimum and maximum electrolysis power of the electrolyzer, respectively;

[0024] Hydrogen energy compressor fine operation constraint:

[0025]

[0026] wherein, represents the actual working power of the hydrogen compressor; is the rated working power of the compressor, which has n gears; is a Boolean variable, which represents that the compressor works in the n-th gear state.

[0027] Preferably, the upper-level decision model of the river waterway hydrogen chain further comprises the following constraint conditions:

[0028] Hydrogen storage constraint:

[0029]

[0030] wherein, formula (11) represents that the hydrogen amount compressed by the compressor does not exceed the hydrogen amount produced; formula (12) represents the hydrogen amount balance constraint of the hydrogen storage amount; formula (13) is the total hydrogen storage amount constraint of the container hydrogen storage tank;

[0031] wherein, E comto compress the power consumption per kg of hydrogen; is the winning hydrogen amount of new energy station i at t-1 time; is the actual hydrogen storage amount in the hydrogen storage tank of i station at t time; and are the minimum and maximum hydrogen storage amounts in the hydrogen storage tank of i station, respectively;

[0032] Ship space-time transfer constraints:

[0033]

[0034] wherein, formula (17)-(18) respectively represent the hydrogen loading and unloading rate constraints of the ship; formula (19) represents the real-time hydrogen loading amount balance constraint of the ship; formula (20) represents the hydrogen loading amount constraint of the ship; formula (21) represents the constant hydrogen loading amount at the start and end time of the ship;

[0035] wherein, are the hydrogen loading and unloading rates of ship k at station i at t time, respectively; are the maximum hydrogen loading and unloading rates of ship k at station i, respectively; are the real-time hydrogen loading amounts of the ship at t time and t-1 time, respectively; are the rated minimum and maximum hydrogen loading amounts of ship k, respectively; and are the hydrogen loading amounts at the start and end time of the ship, respectively.

[0036] Preferably, the hydrogen energy market lower layer dispatching model comprises the following objective function:

[0037]

[0038] wherein, respectively represent the hydrogen purchase party's bidding hydrogen price, the river and waterway hydrogen chain's bidding hydrogen price, and the remaining hydrogen selling party's bidding hydrogen price; are the winning hydrogen amounts of the hydrogen purchase party, the river and waterway hydrogen chain, and the remaining hydrogen selling party, respectively.

[0039] Preferably, the hydrogen energy market lower layer dispatching model further comprises the following constraint conditions:

[0040]

[0041] wherein, formula (23) represents the total winning hydrogen amount balance constraint of the hydrogen market; formulae (24)-(26) are winning hydrogen amount constraints; formula (27) is a bidding hydrogen amount constraint, representing that the bidding hydrogen amount does not exceed the existing hydrogen storage amount of the hydrogen storage station;

[0042] wherein, respectively represent the bidding hydrogen quantity of the hydrogen purchasing party, the bidding hydrogen quantity of the river and waterway hydrogen chain and the bidding hydrogen quantity of the remaining hydrogen selling party, the dual variables of each formula are defined respectively after the colon, and the physical meaning is the shadow price of the corresponding constraint; represent the shadow price of the highest winning amount of the hydrogen purchasing party i at time t; represent the shadow price of the lowest winning amount of the hydrogen purchasing party i at time t; represent the shadow price of the highest winning amount of the new energy station i at time t; represent the shadow price of the lowest winning amount of the new energy station i at time t; represent the shadow price of the highest winning amount of the traditional hydrogen production station i at time t; represent the shadow price of the lowest winning amount of the traditional hydrogen production station i at time t.

[0043] Compared with the prior art, the present application has the following beneficial effects:

[0044] The multi-agent game bidding mechanism based on the double-layer decision model of the present application guarantees the balance of benefit distribution, injects vitality into the hydrogen market, maximizes the income of the new energy plant and station, and improves the economic benefit by 6.9%. The river and waterway hydrogen chain based on the double-layer optimization model of the present application can increase the transportation efficiency and reduce the transportation cost, and the transportation cost is reduced by 27.8%. The power scheduling of the compressor of the present application will affect the cost of the hydrogen production link, and reasonable real-time scheduling can save unnecessary power consumption, so that the income of the power station is increased by 0.57%. BRIEF DESCRIPTION OF DRAWINGS

[0045] Figure 1 is the benefit logic diagram of each subject of the new energy plant and station provided by the present application.

[0046] Figure 2 is the double-layer decision architecture diagram of the river and waterway hydrogen chain participating in the hydrogen market provided by the present application.

[0047] Figure 3 is the hydrogen production flow chart provided by the present application.

[0048] Figure 4 is the river and waterway hydrogen chain schematic diagram provided by the present application.

[0049] Figure 5 is the clearing result diagram of the selling and buying parties of scheme one provided by the present application, (a) is the clearing result of the hydrogen selling party, and (b) is the clearing result of the hydrogen purchasing party.

[0050] Figure 6 is the clearing result diagram of the selling and buying parties of scheme two provided by the present application, (a) is the clearing result of the hydrogen selling party, and (b) is the clearing result of the hydrogen purchasing party.

[0051] Figure 7is a result of the third scheme provided by the present application, which is a result of the sale of hydrogen; (a) is a result of the sale of hydrogen; (b) is a result of the purchase of hydrogen.

[0052] Figure 8 is a result of the fourth scheme provided by the present application, which is a result of the sale of hydrogen; (a) is a result of the sale of hydrogen; (b) is a result of the purchase of hydrogen.

[0053] Figure 9 is a result of the fourth scheme provided by the present application, which is a result of the sale of hydrogen; (a) is a result of the sale of hydrogen; (b) is a result of the purchase of hydrogen.

[0054] Figure 10 is a result of the fourth scheme provided by the present application, which is a result of the sale of hydrogen; (a) is a result of the sale of hydrogen; (b) is a result of the purchase of hydrogen.

[0055] Figure 11 is a result of the fourth scheme provided by the present application, which is a result of the sale of hydrogen; (a) is a result of the sale of hydrogen; (b) is a result of the purchase of hydrogen.

[0056] Figure 12 is a result of the fourth scheme provided by the present application, which is a result of the sale of hydrogen; (a) is a result of the sale of hydrogen; (b) is a result of the purchase of hydrogen.

[0057] Figure 13 is a result of the fourth scheme provided by the present application, which is a result of the sale of hydrogen; (a) is a result of the sale of hydrogen; (b) is a result of the purchase of hydrogen.

[0058] Figure 14 is a result of the fourth scheme provided by the present application, which is a result of the sale of hydrogen; (a) is a result of the sale of hydrogen; (b) is a result of the purchase of hydrogen.

[0059] Figure 15 is a result of the fourth scheme provided by the present application, which is a result of the sale of hydrogen; (a) is a result of the sale of hydrogen; (b) is a result of the purchase of hydrogen. DETAILED DESCRIPTION

[0060] The present application will be further described in conjunction with the accompanying drawings and specific embodiments. The advantages and features of the present application will be more apparent according to the following description. It should be noted that the drawings are very simplified and use non-precise proportions, only to facilitate and clarify the purpose of assisting the description of the embodiments of the present application.

[0061] As Figure 1As shown, the embodiment of the present application specifically provides a river waterway hydrogen chain market bidding method based on a double-layer decision model. First, by constructing a double-layer decision framework of new energy stations participating in the hydrogen market, the advantages of waterway transportation are integrated with the depth of the hydrogen market. On this basis, a multi-agent game bidding mechanism is proposed, which can depict the characteristics of river waterway hydrogen chain decision and market clearing. Finally, the lower model is transformed using KKT technology, and the upper model is combined to form a classic mixed integer linear programming, which realizes efficient solution of the scheduling model.

[0062] As shown in Figure 1 is the interest logical relationship diagram of each market participant. As can be seen from Figure 1 , the river waterway hydrogen chain is composed of new energy hydrogen production stations (including new energy units, hydrogen production equipment, compressors, and hydrogen storage tanks, collectively referred to as new energy stations) and hydrogen carrier ships. New energy power generation can be directly connected to the grid to earn revenue, or it can be used to produce green hydrogen, which is then stored in hydrogen storage tanks. Subsequently, hydrogen carrier ships transport hydrogen to various hydrogen refueling stations and compete with traditional hydrogen energy suppliers in the market to meet the demand of hydrogen energy users.

[0063] The on-grid power of new energy stations, hydrogen production, hydrogen price, and the transportation route of the ship can be adjusted, and the operation economy of the river waterway hydrogen chain needs to be optimized. Therefore, the present application designs a double-layer decision framework of river waterway hydrogen chain suppliers participating in the hydrogen market, as shown in Figure 2 . The upper layer of the framework considers factors such as new energy station power distribution and ship hydrogen carrying capacity conservation, determines the optimal on-grid power, bidding hydrogen quantity, and corresponding hydrogen price by evaluating the market clearing price. The lower layer of the framework introduces an independent system operator (ISO) that matches transactions based on bidding information from new energy stations, other hydrogen sellers, and hydrogen buyers to achieve market clearing. The double-layer decision framework fully considers the transaction needs of market participants, effectively promoting the efficient use of hydrogen market resources.

[0064] As a further elaboration of the embodiments of the present application, the embodiments of the present application design a river waterway hydrogen chain market bidding model, specifically including a river waterway hydrogen chain upper decision model and a day-ahead market lower clearing model. The river waterway hydrogen chain upper decision model includes:

[0065] (1) Objective function: The upper model aims to maximize the revenue of new energy stations, which is composed of electricity sales revenue, hydrogen sales revenue, and ship transportation cost. In the following formulas, formula (1) is the objective function; formulas (2)-(3) are transportation cost constraints.

[0066]

[0067] In the formula, λ tMCP is the market clearing price of hydrogen; MCP is the market clearing price of hydrogen; MCP is the market clearing price of hydrogen; MCP is the market clearing price of hydrogen; MCP is the market clearing price of hydrogen; MCP is the market clearing price of hydrogen; MCP is the market clearing price of hydrogen; i,k,t MCP is the market clearing price of hydrogen; i,k,t MCP is the market clearing price of hydrogen; i,k,t MCP is the market clearing price of hydrogen;

[0068] (2) Constraints: The power of new energy stations mainly has four destinations, including flat price, electrolytic hydrogen production, compressor energy consumption and abandoned electricity. The power balance constraint of river and road hydrogen chain is shown in equations (4)-(6), wherein equation (4) represents the power balance constraint; equation (5) is the power limit; and equation (6) represents the non-negative abandoned power.

[0069]

[0070]

[0071] In the formula, MCP is the market clearing price of hydrogen; MCP is the market clearing price of hydrogen; MCP is the market clearing price of hydrogen; MCP is the market clearing price of hydrogen; MCP is the market clearing price of hydrogen; MCP is the market clearing price of hydrogen; MCP is the market clearing price of hydrogen;

[0072] The hydrogen production equipment operation constraint is shown in equations (7)-(8), wherein equation (7) represents the equivalent relationship between hydrogen production and hydrogen production power; and equation (8) represents the limitation on hydrogen production power.

[0073]

[0074] In the formula, MCP is the market clearing price of hydrogen; h MCP is the market clearing price of hydrogen; and are the minimum and maximum electrolysis power of the electrolyzer, respectively.

[0075] To achieve the fine operation of hydrogen energy compressor, define the Boolean variable to represent the operating power level of the hydrogen compressor, and its operating constraints are shown in equations (9)-(10):

[0076]

[0077] In the formula, represents the actual working power of the hydrogen compressor; is the rated working power of the compressor, which has n levels in total; is a Boolean variable, which indicates that the compressor is working in the nth level state.

[0078] When the ship cannot arrive at the site in time, the hydrogen produced can be stored in the hydrogen buffer tank, and then compressed by the compressor and filled into the pipe bundle type container hydrogen storage tank. The ship can directly load the container hydrogen storage tank for transportation after arriving at the site, as shown in Figure 3 The specific model is shown in equations (11)-(13). Among them, equation (11) represents that the amount of hydrogen compressed by the compressor does not exceed the amount of hydrogen produced; equation (12) represents the hydrogen balance constraint of the storage amount; and equation (13) is the total hydrogen storage amount constraint of the container hydrogen storage tank.

[0079]

[0080] In the formula, E com is the power consumption per kg of hydrogen; is the winning hydrogen amount of the new energy station i at t-1; is the actual hydrogen storage amount in the hydrogen storage tank of station i at t.

[0081] Since the start-stop and turning time of the ship accounts for a small proportion in the entire transportation process, for the sake of simplicity, the above-mentioned time-occupying time is not considered in this paper. In addition, this paper assumes that the port berth is sufficient, and the climate and hydrological conditions are relatively good, so as to ignore the influence of environmental factors uncertainty. The space-time transfer constraint of the ship can be expressed as

[29] :

[0082]

[0083] z i,k,0 = z i,k,T (15)

[0084]

[0085] wherein, formula (14) is a real-time position constraint of the ship, indicating that the kth ship can only be located at one station at most at t time; formula (15) makes the ship return to the initial position at T time, so as to participate in the next round of day-ahead scheduling; formula (16) indicates that the time of the ship at the jth station is not more than the time required for the ship to arrive at the jth station from the ith station, wherein ξ ij,t represents the time required for the ship to arrive at the jth station from the ith station.

[0086] The ship can flexibly transport the hydrogen tank, and the specific constraints are shown in formulas (17)-(21). Wherein, formulas (17)-(18) respectively represent the hydrogen loading and hydrogen unloading rate constraints of the ship; formula (19) represents the real-time hydrogen loading balance constraint of the ship; formula (20) represents the hydrogen loading constraint of the ship; and formula (21) represents that the hydrogen loading of the ship at the start and end time is constant.

[0087]

[0088]

[0089] In the formula, r t and r d respectively represent the hydrogen loading rate and the hydrogen unloading rate; is the real-time hydrogen loading of the ship at t time; are the rated minimum hydrogen loading and the maximum hydrogen loading of the hydrogen transport ship.

[0090] As a further elaboration of the embodiments of the present application, the hydrogen energy market lower layer clearing model includes:

[0091] (1) Objective function: the lower layer model aims to maximize social welfare, and the specific objective function is as follows:

[0092]

[0093] In the formula, p b, p r and p s respectively represent the hydrogen price bid by the hydrogen purchasing party, the hydrogen price bid by the river and waterway hydrogen chain, and the hydrogen price bid by the remaining hydrogen selling party; are the winning hydrogen quantity of the hydrogen purchasing party, the winning hydrogen quantity of the river and waterway hydrogen chain, and the winning hydrogen quantity of the remaining hydrogen selling party.

[0094] (2) Constraint condition: the bid quantity and the winning quantity of each market participant are constrained, and the specific formula is as follows:

[0095]

[0096] Formula (23) represents the total winning hydrogen quantity balance constraint of the hydrogen market; formulas (24)-(26) are winning hydrogen quantity constraints; and formula (27) is a bid hydrogen quantity constraint, indicating that the bid hydrogen quantity is not more than the existing hydrogen storage quantity of the hydrogen storage station, wherein ​​respectively represent the bidding hydrogen quantity of the hydrogen purchasing party, the bidding hydrogen quantity of the river waterway hydrogen chain, and the bidding hydrogen quantity of the remaining hydrogen selling party. The dual variables of each formula are defined respectively after the colon, and the physical meaning is the shadow price of the corresponding constraint.

[0097] As a further elaboration of the embodiments of the application, the following algorithm solving process is also included:

[0098] For the structure of the double-layer decision model, the lower model is equivalent to the upper model by using the duality theory, and is converted into a classic mixed integer linear programming (MILP) problem by using the big M method and other techniques, and finally solved by gurobi.

[0099] (1) Lower model reconstruction: based on the KKT condition, the constraint (23) is converted into formula (28)-(30):

[0100]

[0101] In the formula, respectively represent the bidding hydrogen quantity of the hydrogen purchasing party, the bidding hydrogen quantity of the river waterway hydrogen chain, and the bidding hydrogen quantity of the remaining hydrogen selling party.

[0102] Similarly, based on the KKT condition, the constraints (24)-(26) are converted into formula (31)-(36):

[0103]

[0104] It is worth noting that since formula (31)-(36) has variable product items, it is a non-convex problem and needs to be linearized.

[0105] (2) Model linearization: for the variable product items in the objective function (1) Combined with formula (28)-(30), the strong duality theory method is used to convert it into a variable and constant product item to achieve the purpose of linearization:

[0106]

[0107] For the nonlinear constraints (31)-(36), the big M method can be used for linearization:

[0108]

[0109] In the formula, ω i,t Both are Boolean variables; M Q , M μQis a sufficiently large positive number. Through the above processing, the model has been converted into a classic MILP model, which can be solved using the commercial solver Gurobi.

[0110] As a further elaboration of the embodiments of the application, the following example analysis process is also included:

[0111] (1) Example basic data: The embodiments of the application take two hydrogen refueling stations, two new energy stations, and three traditional hydrogen energy suppliers (hereinafter collectively referred to as hydrogen production station A, hydrogen production station B, and hydrogen production station C) as the main market participants. Among them, the customer facing hydrogen refueling station 1 is a large user such as a new energy logistics company, and its hydrogen demand is relatively fixed; the hydrogen load data of hydrogen refueling station 2 uses the 24-hour hydrogen load of a port in the existing literature [Li L, Shi Q, Wang Y, et al. Optimization scheduling of port electric-hydrogen integrated energy system considering high-order equation piecewise linearization [J]. Power automation equipment, 2023, 43(12): 21-28.], and its hydrogen demand fluctuates with the workload of the port. In addition, among the three traditional hydrogen production stations, hydrogen production station A is petroleum hydrogen production, hydrogen production station B is electricity-purchased water electrolysis hydrogen production, and hydrogen production station C is natural gas hydrogen production, and all traditional hydrogen production stations use land transportation to transport hydrogen to hydrogen refueling stations. The device parameters are shown in Tables 1-3, and the hydrogen transportation route is shown in Figure 4 , where the blue dashed line represents the water transportation route, and the black solid line represents the land transportation route.

[0112] Table 1 Hydrogen production and transportation configuration table of hydrogen selling party

[0113]

[0114] Table 2 Specific configuration of hydrogen purchasing party

[0115]

[0116] Table 3 Hydrogen transportation tool configuration

[0117]

[0118] The hydrogen production cost of the three hydrogen production stations is referenced from the existing literature [Guo, Xu Yongjie, Shi Ruijing. Economic analysis of three hydrogen production technology routes [J]. Electrical technology, 2024, (07): 40-43.], and 40% profit space is added on this basis. The new energy station adopts the method of electrolyzing water to produce hydrogen. The hydrogen purchasing station 1 takes its own marginal benefit as the bidding hydrogen price, and the bidding hydrogen price of the hydrogen refueling station 2 fluctuates around the marginal benefit with the change of hydrogen sales volume. In order to verify the advantages of the strategy, four schemes are designed for comparison in the embodiment of the application: scheme one: the new energy station does not participate in the hydrogen market; scheme two: the new energy station participates in the hydrogen market with a fixed bidding price in combination with the hydrogen carrier; scheme three: the new energy station participates in the hydrogen market with a double-layer decision model, but the transportation mode is changed to land transportation, and the transportation route is changed to land transportation route; scheme four: the new energy station participates in the hydrogen market with a double-layer decision model in combination with the hydrogen carrier.

[0119] (2) Result analysis: Figure 5 The clearing results of the hydrogen selling party and the hydrogen purchasing party in scheme one are shown. From the perspective of the hydrogen selling party, the bidding prices provided by hydrogen production stations B and C are lower than that of hydrogen production station A, so in the transaction process, the hydrogen purchasing party is more inclined to choose the hydrogen production stations B and C with lower cost to meet its hydrogen demand. For the hydrogen purchasing party, the hydrogen refueling station 1 becomes the preferred object of the hydrogen selling party in the transaction because of its stable demand and higher bid. In contrast, the bidding amount of the hydrogen refueling station 2 is more flexible, and its bid also fluctuates to a certain extent, especially outside the period from 8:00 to 19:00, when its demand decreases significantly. Due to the relatively high bidding price of hydrogen production station A and the instability of the demand of hydrogen refueling station 2, hydrogen production station A fails to successfully participate in the transaction at most times, which affects the winning amount of hydrogen refueling station 2 and makes the overall winning amount of hydrogen refueling station 2 less.

[0120] Figure 6 The clearing results of the new energy station after joining the hydrogen market in scheme two are shown. Figure 6 It can be seen that after the new energy station joins the hydrogen market, the transaction volume of hydrogen production station A is completely replaced by the new energy station, and the market share of hydrogen production station B also greatly decreases. At times such as 8:00 and 21:00-23:00, hydrogen production station B is completely replaced, and the market share of hydrogen production station C is also squeezed, resulting in a low market MCP in these periods. The reason is that the bidding prices of the traditional hydrogen production stations are all higher than that of the new energy station, and the electricity of the new energy station comes from wind and solar energy, without considering the cost of electricity, so the new energy station is more competitive in price, and is more popular in the market transaction with a bidding price of 33.8 yuan / kg. However, due to the limited hydrogen production capacity of the new energy station and the influence of the hydrogen production strategy and the bidding strategy, the new energy station cannot completely replace hydrogen production station B. From the clearing results of the hydrogen purchasing party, the winning amounts of the two hydrogen refueling stations are Figure 5Compared to almost the same, it shows that the addition of new energy stations will not disrupt the original market order while bringing more cheap hydrogen energy to the hydrogen market.

[0121] Figure 7 The new energy station is shown to participate in the clearing results of the hydrogen market by land transportation and using a double-layer decision model. From the clearing results of the hydrogen sellers, it can be seen that the market share of hydrogen production station A has been completely replaced by the new energy station. And in the time period of 4:00, 6:00 and 20:00-24:00, hydrogen production station B is also completely replaced by new energy. It can be seen that the strategic hydrogen production-bidding after using the double-layer optimization model makes the winning amount of new energy station slightly increase, and the winning amount is more stable compared to scheme two. It shows that the double-layer decision model effectively regulates the hydrogen production amount, bidding amount and bidding price of the new energy station. However, due to the low efficiency of traditional pipe bundle hydrogen transport vehicles, the bidding price of new energy stations is high, and the price advantage of 35 yuan / kg of hydrogen production station C is not obvious, resulting in a low overall winning amount of new energy stations.

[0122] Scheme four greatly improves the transportation efficiency by introducing hydrogen transport ships, solving the problem of high transportation cost and low efficiency in scheme three. Because the carrying capacity of hydrogen transport ships is much higher than that of traditional pipe bundle hydrogen transport vehicles, the transportation efficiency is greatly improved. From Figure 8 It can be seen that the new energy station can successfully bid at each time point, greatly increasing the total hydrogen transaction volume of the new energy station, from Figure 8 It can also be seen that the total winning amount of new energy stations in scheme four is significantly higher than that in scheme two and scheme three, and except at 24:00, the new energy station does not encroach on the market share of hydrogen production station C, making the overall market transaction price higher than that in scheme two. Obviously, the double-layer optimization model combined with the river waterway hydrogen chain effectively regulates the hydrogen production strategy, bidding strategy and bidding price of the new energy station, maximizing its economic benefits. It is worth noting that in scheme four, hydrogen production station A with the highest bidding price has been completely replaced, and the winning amount of hydrogen production station B has also been greatly reduced. Unlike scheme two and scheme three, the winning amount of new energy stations at each time point in scheme four is relatively more stable, which not only ensures the winning amount of new energy stations, but also does not lower the market clearing price due to a large number of concentrated bidding. Therefore, the revenue of scheme four is the highest among the four schemes. Compared to Figure 9The market clearing price (MCP) under the four schemes. It can be seen that scheme one has a relatively high MCP due to the lack of river waterway hydrogen chain competition, and the traditional hydrogen energy supplier is the main hydrogen supplier, resulting in a total market transaction hydrogen volume less than that of the other schemes. The bidding price of scheme two is low, especially during the periods of 8:00, 13:00-19:00, and 21:00-23:00, the clearing price is lower than that of the other three schemes, making the overall MCP of scheme two lower. The addition of new energy stations brings more cheap hydrogen to the hydrogen market. However, the one-sided low-price strategy results in lower overall profits than scheme four. The MCP curve of scheme three is basically the same as that of scheme one, but the lower transportation efficiency and higher transportation cost result in lower overall profits than scheme four. Scheme four combines the upper and lower layers of the double-layer decision model to dynamically balance the allocation of hydrogen production and on-grid power, avoiding the loss of profits caused by low-price dumping in scheme two. For example, in scheme four, the new energy station adjusts the bidding hydrogen price in real time to respond to market fluctuations, achieving 24-hour continuous bidding, while scheme two has a fixed low-price strategy, resulting in an excessively low market clearing price (MCP) and sacrificing part of the potential profits. The new energy station increases market competitiveness after introducing the river waterway hydrogen chain bidding mechanism based on the double-layer optimization model, maximizing its own profits while also increasing social welfare.

[0123] Table 4 Comparison of economic performance under the four schemes

[0124]

[0125] Table 4 shows the comparison of economic performance under the four schemes. As shown in Table 4, the total profit of scheme four is 1228553 yuan, which is 31.2%, 6.9%, and 11% higher than that of schemes one, two, and three, respectively. Although the total market transaction hydrogen volume of the four schemes is not significantly different, the proportion of green hydrogen increases from 26.4% in scheme three to 39.5%, promoting the transformation of energy structure towards low carbonization. This growth is due to the dynamic optimization of the double-layer decision model for hydrogen production strategy and bidding price, combined with the efficient transportation capacity of the river waterway hydrogen chain, significantly improving the market penetration rate of green hydrogen and highlighting the superiority of the river waterway hydrogen chain.

[0126] (3) The influence of compressor power scheduling on hydrogen production revenue: Table 5 shows the total profit of the compressor working under four modes, where mode one, two, and three are fixed power of 200kW, 320kW, and 400kW, respectively, and mode four is power staging scheduling, i.e., the above-mentioned scheme four.

[0127] Table 5 Total profit of the compressor working under different power

[0128]

[0129] The significant advantages of mode four (scheme four) under the real-time optimization scheduling strategy are disclosed. The data shows that the total profits of mode one, mode two and mode three using fixed gear power are 1200090 yuan, 1221494 yuan and 1219649 yuan respectively, while the total profit of scheme four is increased to 1228553 yuan through real-time optimization scheduling of compressor power, which is increased by 2.3%, 0.57% and 0.72% respectively compared with the fixed gear mode. At the same time, the hydrogen sales profit is increased by 11.3%, 2% and 2.1% respectively. Although the percentage increase seems limited, it has considerable economic gain in large-scale commercial application. This increase is due to the dynamic adjustment of compressor power in scheme four to respond to market clearing price fluctuations, reducing the power consumption of the compressor at high MCP time to save more electricity for hydrogen production, and increasing the compressor power at low MCP time to enrich the hydrogen amount in the hydrogen storage tank to achieve the optimal balance of energy consumption and income.

[0130] (4) Sensitivity analysis of influencing factors: ① Influence of wind and light output on market transaction: Considering the uncertainty of wind and light output, taking the total daily power generation of new energy Pn=230 million kW in the example of the application as the reference value, the sensitivity of the influence of different wind and light output on market transaction is explored below. Figure 10 Figures (a) and (b) respectively show the changes in economic efficiency and site income of each scheme under different power generation of new energy stations. From Figure 10 It can be seen from (a) that with the increase of daily power generation, the economic efficiency of each scheme shows an increasing trend. Under 100% Pn power generation, the capacity limit of the grid access channel makes the income of scheme one no longer increase, while scheme four always maintains economic efficiency advantage. From Figure 10 It can be seen from (b) that the total income of new energy stations shows an increasing trend. On the contrary, due to the occupation of hydrogen energy market share by new energy stations with increasing hydrogen production, with the increase of new energy station power generation, the income of hydrogen production station B shows a decreasing trend, while the income of hydrogen production stations A and C changes little, because hydrogen production station A has the lowest bidding price and is the preferred object of hydrogen purchase party, while hydrogen production station A has the highest bidding price, resulting in no clearing. ② Influence of hydrogen market demand on market transaction: Considering the uncertainty of market demand, the sensitivity of market transaction under different hydrogen market demand is explored below. Figure 11 Figures (a) and (b) respectively show the changes in economic efficiency and site income of each scheme under different hydrogen demand, wherein Qn=36150 kg. From Figure 11 It can be seen from (a) that with the increase of market demand, scheme four always maintains economic efficiency advantage. When 85% Qn, due to the saturation of hydrogen production equipment power, the income growth rate becomes slow. Figure 11 The income of each site in (b) also increases with the increase of demand. From Figure 11It can be seen that there is an obvious sequence of increase in revenue, which shows that the hydrogen purchasing party will prefer to trade with the hydrogen selling party with competitive bidding advantage. ③ The influence of water and land transportation hydrogen volume ratio on market transactions: To explore the income of new energy stations under the combination of water and land transportation, the influence of water and land transportation hydrogen volume ratio on market transactions will be shown below. Figure 12 The change of each station's income under different water and land transportation hydrogen volume ratios of new energy stations is shown. Figure 12 It can be seen that with the increase of water transportation ratio, the income of new energy stations shows an increasing trend. Secondly, the income of hydrogen production station B shows a downward trend, while the income of hydrogen production stations A and C changes little, because the selling price of hydrogen production station A is the highest, and its market share has been completely occupied by new energy stations, while the price of hydrogen production station C is relatively low, which is still the preferred object of the hydrogen purchasing party. ④ The influence of bidding hydrogen price on market transactions: To explore the adaptability of the model to different hydrogen pricing, the market transactions under different hydrogen pricing will be shown below. Figure 13-14 The influence of different hydrogen bidding prices on market transactions is shown. Sn represents the hydrogen benchmark price of each station, and the bidding price of each station in Table 1 is taken as the benchmark price, i.e. the benchmark price of station A is 48.9 yuan / kg, the benchmark price of station B is 46 yuan / kg, the benchmark price of station C is 35 yuan / kg, and the hydrogen purchasing party takes the price in Table 2 as the benchmark price. Figure 13 Figures (a)-(c) show the influence of bidding price changes of hydrogen production stations A, B and C on the income of other stations. As can be seen from the figure, Figure 13 the total income of station A in (a), Figure 13 station B in (b) and Figure 13 station C in (c) all increase, while the total income of new energy stations does not show obvious fluctuations, because the double-layer optimization model dynamically optimizes the bidding hydrogen volume and hydrogen price of new energy stations to maximize their income. Figure 14 The influence of hydrogen station bidding on economic benefits of each scheme and income of each station is shown, and Figure 14 it can be seen that except for scheme one, the economic benefits of each scheme decrease with the decrease of bidding price of the hydrogen purchasing party. In 0.9Sn, 0.7Sn, hydrogen production stations B and C successively exit the market, because of the lack of high bidding to increase the market unified clearing price, the winning hydrogen price of new energy stations decreases, resulting in the decrease of economic benefits. ⑤ The influence of fluctuation of on-grid price on market transactions: According to the new energy photovoltaic settlement price of Hubei Province from April to December 2024, the change of market transactions with the fluctuation of on-grid price is explored, as shown in Figure 15 Figures (a)-(d) show the change of market transactions with the fluctuation of on-grid price. Figure 15 As can be seen from (a), the fluctuation of on-grid price has a significant influence on the income of new energy stations, and with the change of on-grid price, the economic benefits of each scheme increase and decrease basically in the same trend, while scheme four always maintains economic advantage, verifying the applicability of the model proposed in the invention. Figure 15(b) is the change of each income of the new energy station with the fluctuation of the on-grid electricity price, wherein the traditional hydrogen production station takes the hydrogen production cost as the bidding hydrogen price. Figure 15 (b) It can be seen that the on-grid electricity price has little effect on the hydrogen sales revenue in the range of 355-435 yuan / MWh, because the electricity sales revenue is lower than the hydrogen sales revenue, and hydrogen production and sales are still the preferred profit way of the new energy station. When the electricity price reaches 450 yuan / MWh, the hydrogen sales revenue begins to decrease, because in some periods the electricity sales revenue begins to be higher than the hydrogen sales revenue, and hydrogen sales is no longer the preferred profit way. The influence of large M value on the solution: In order to explore the influence of large M value on the calculation results and calculation speed, the solution results and solution time corresponding to different large M values are listed in Table 6. It can be seen that as the value of M increases, the solution result remains the same, and the solution time increases. ⑦Comparison with similar researches: In order to verify the applicability of the model proposed in the invention, the hydrogen energy system scheduling method proposed in the literature [Sameti M, Mulcair E, Syron E. Green hydrogen production and storage at wind farms: An economic and environmental optimisation [J]. International Journal of Hydrogen Energy, 2025, 120: 572-583.] will be used for economic comparison. The literature proposes an optimization model for preparing green hydrogen using abandoned electricity, aiming to determine the optimal size of the abandoned electricity hydrogen production system to maximize profits. In the literature, land transportation is used for hydrogen transportation, and the compressor staging scheduling is not considered. The authors assume that the compressor runs at the maximum gear 400kW, and use the river waterway hydrogen chain model and the compressor staging scheduling model established in the invention for economic comparison. As shown in Table 7, the economic efficiency is improved by 11.5%.

[0131] Table 7 Economic comparison of two schemes

[0132]

[0133] The invention proposes a river waterway hydrogen chain market bidding mechanism based on a double-layer decision model, realizes hydrogen production, storage, transportation and transaction integration, maximizes the income of new energy plants and stations while improving social well-being. The invention quantitatively analyzes the dynamic energy consumption characteristics of hydrogen energy compressors, and establishes a hydrogen compressor power staging regulation model that can flexibly adapt to hydrogen refueling demand.

[0134] The above description is only a description of the preferred embodiments of the invention, and does not limit the scope of the invention in any way. Any changes and modifications made by those skilled in the art based on the above disclosure are within the scope of the claims.

Claims

1. A method for river waterway hydrogen chain market bidding based on a double-layer decision model, characterized in that, The application relates to a double-layer decision-making architecture for a river and sea hydrogen chain participating in a hydrogen energy market. The application discloses a river and sea hydrogen chain market bidding model based on the double-layer decision-making architecture; the river and sea hydrogen chain market bidding model comprises an upper-layer decision-making model of the river and sea hydrogen chain and a lower-layer clearing model of a hydrogen energy market; the upper-layer decision-making model takes the maximum daily operation income as a target and considers a fine power adjustment factor of a hydrogen compressor; and the lower-layer clearing model takes the maximum social welfare as a target and considers a multi-subject bidding factor. The river and sea hydrogen chain market bidding model is reconstructed based on KKT conditions, and the river and sea hydrogen chain market bidding model is converted into a classic mixed integer linear programming MILP problem by using a dual theory and a large M method, so that the river and sea hydrogen chain market bidding model is efficiently solved. The river and sea hydrogen chain is composed of a new energy station and a hydrogen transport ship; the new energy station comprises a new energy unit, a hydrogen production device, a compressor and a hydrogen storage tank.

2. The river waterway hydrogen chain market bidding method based on a double-layer decision model according to claim 1, characterized in that, The double-layer decision-making architecture comprises an architecture upper layer and an architecture lower layer; the architecture upper layer comprehensively considers a new energy station power distribution and a ship hydrogen carrying conservation factor, determines optimal on-grid power, bidding hydrogen and corresponding hydrogen price by evaluating a market unified clearing price; and the architecture lower layer introduces an independent system operation organization ISO which matches transactions according to bidding information of the new energy station, other hydrogen selling parties and hydrogen buying parties, and realizes market clearing.

3. The river waterway hydrogen chain market bidding method based on a double-layer decision model according to claim 1, characterized in that, The upper-layer decision-making model of the river and sea hydrogen chain comprises the following target function:

4. The river waterway hydrogen chain market bidding method based on a double-layer decision model according to claim 1, characterized in that, The target function (1) is used for realizing the maximum income of the new energy station, and the income is composed of electricity selling income, hydrogen selling income and ship transportation cost; the transportation cost constraints (2) and (3) are used for realizing the maximum income of the new energy station. The upper-layer decision-making model of the river and sea hydrogen chain further comprises the following constraint conditions: wherein, λ t is the unified clearing price MCP of the hydrogen market; is the winning hydrogen quantity of the new energy station in the hydrogen market; is the on-grid electricity price; is the total on-grid power; is the transportation cost of the ship k at time t, is the transportation cost of the hydrogen transportation ship per kg of hydrogen per unit time under a certain constant running power; is the real-time hydrogen carrying capacity of the hydrogen transportation ship; z i,k,t indicates the start-stop flag of the ship, when the ship k is docked at the station i at time t, then z i,k,t = 1, z i,k,t = 0 indicates that the ship is in a sailing state; M represents a large positive number.

5. The river waterway hydrogen chain market bidding method based on a double-layer decision model according to claim 4, characterized in that, The power balance constraint (4) is used for realizing the maximum income of the new energy station; the on-grid power limitation (5) is used for realizing the maximum income of the new energy station; and the abandoned power non-negative (6) is used for realizing the maximum income of the new energy station. The hydrogen production device operation constraint (7) is used for realizing the maximum income of the new energy station; and the hydrogen production power limitation (8) is used for realizing the maximum income of the new energy station. The hydrogen energy compressor fine operation constraint (9) is used for realizing the maximum income of the new energy station. wherein, is the actual power generation of the wind turbine of the i-th new energy station at time t; is the actual power generation of the photovoltaic; is the hydrogen production power of the electrolyzer; is the compression power of the compressor of the new energy station; is the on-grid power of the new energy station i at time t; is the electric power abandoned due to inability to be accommodated; is the on-grid channel capacity limit; The upper-layer decision-making model of the river and sea hydrogen chain further comprises the following constraint conditions: The hydrogen storage constraint (11) is used for realizing the maximum income of the new energy station; the hydrogen storage amount balance constraint (12) is used for realizing the maximum income of the new energy station; and the total hydrogen storage amount constraint (13) is used for realizing the maximum income of the new energy station. wherein, is the hydrogen production of the i-th new energy station at the t-th time interval; η h is the electricity-to-hydrogen conversion rate; and are the minimum and maximum electrolysis power of the electrolyzer, respectively. The ship space-time transfer constraint (17) is used for realizing the maximum income of the new energy station; the ship hydrogen loading and unloading rate constraint (18) is used for realizing the maximum income of the new energy station; the real-time hydrogen carrying amount balance constraint (19) is used for realizing the maximum income of the new energy station; the ship hydrogen carrying amount constraint (20) is used for realizing the maximum income of the new energy station; and the ship hydrogen carrying amount invariable constraint (21) is used for realizing the maximum income of the new energy station. wherein, represents the actual working power of the hydrogen compressor; is the rated working power of the compressor, and there are n gears in total; is a Boolean variable, indicating that the compressor is working in the nth gear state.

6. The river waterway hydrogen chain market bidding method based on a double-layer decision model according to claim 5, characterized in that, The lower-layer clearing model of the hydrogen energy market comprises the following target function: The lower-layer clearing model of the hydrogen energy market further comprises the following constraint conditions: The total winning hydrogen amount balance constraint (23) of the hydrogen market is used for realizing the maximum social welfare; the winning hydrogen amount constraints (24)-(26) are used for realizing the maximum social welfare; and the bidding hydrogen amount constraint (27) is used for realizing the maximum social welfare. wherein E com is the power consumption per kg of hydrogen gas; is the winning hydrogen amount of the new energy station i at t-1; is the actual hydrogen storage amount in the hydrogen storage tank of the i station at t; and are the minimum and maximum hydrogen storage amounts in the hydrogen storage tank of the i station, respectively. ​ ​ wherein, respectively the hydrogen loading and unloading rate of ship k at site i at time t; respectively the maximum hydrogen loading and unloading rate of ship k at site i at time t; respectively the real-time hydrogen load of ship at time t and t-1; respectively the minimum and maximum hydrogen load of ship k; and respectively the hydrogen load of ship at start and end time.

7. The river waterway hydrogen chain market bidding method based on a double-layer decision model according to claim 1, characterized in that, ​ wherein, respectively represent the hydrogen price bid by the hydrogen purchasing party, the hydrogen price bid by the river waterway hydrogen chain, and the hydrogen price bid by the remaining hydrogen selling party; respectively represent the hydrogen quantity bid by the hydrogen purchasing party, the hydrogen quantity bid by the river waterway hydrogen chain, and the hydrogen quantity bid by the remaining hydrogen selling party.

8. The river waterway hydrogen chain market bidding method based on a double-layer decision model according to claim 7, characterized in that, ​ ​ wherein, respectively represent the bidding hydrogen quantity of the hydrogen buying party, the bidding hydrogen quantity of the river waterway hydrogen chain, and the bidding hydrogen quantity of the remaining hydrogen selling party, and the dual variables of each formula are defined after the colon, and the physical meaning is the shadow price of the corresponding constraint.

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