Distributed multi-objective optimization method and apparatus for electro-hydrogen coupling systems

Abstract

This application relates to the field of energy optimization technology, and discloses a distributed multi-objective optimization method and apparatus suitable for electric-hydrogen coupling systems. Specifically, it discloses: constructing a dual-objective optimization model between power suppliers and hydrogen suppliers to effectively solve the competition and conflict problems existing in the scheduling process of power suppliers and hydrogen suppliers in existing electric-hydrogen systems, realizing the economic interests of both suppliers, and ensuring a more efficient bidirectional energy coupling process between the electricity and hydrogen energy systems. A distributed ξ-constrained optimization algorithm based on the alternating direction multiplier method is designed to solve the dual-objective optimization model. This algorithm can capture the optimal Pareto front while protecting the privacy of each participant in the electric-hydrogen system, restricting the objective function of each participant within a reasonable range, ensuring the stability and efficiency of the distributed computing process for scheduling, and improving the coordination between energy suppliers while satisfying the optimization objectives of electricity and hydrogen energy suppliers, thereby minimizing the system operating cost.

Description

Technical Field

[0001] This application relates to the field of energy optimization technology, specifically to a distributed multi-objective optimization method and apparatus suitable for electro-hydrogen coupling systems. Background Technology

[0002] With the rapid development of hydrogen energy technology and the large-scale integration of renewable energy sources, the integration of power systems and hydrogen energy systems has gradually become an important direction in the energy sector. Electric-hydrogen coupling systems, through bidirectional energy conversion, not only improve energy flexibility and utilization efficiency but also offer the possibility of addressing the volatility issues arising from the high proportion of renewable energy integration in power systems. However, in such integrated systems, the economic interests of power suppliers and hydrogen energy suppliers often conflict, making it difficult to reach a unified dispatch scheme.

[0003] Furthermore, in an electro-hydrogen coupling system, not only the energy conversion between electricity and hydrogen needs to be considered, but also various physical constraints of the power grid and hydrogen pipeline network must be satisfied. These complex physical couplings increase the difficulty of scheduling, especially when electricity and hydrogen energy suppliers are operated by different entities. Achieving effective and optimized scheduling without compromising the privacy of all parties becomes a major challenge. Existing centralized scheduling methods, while able to uniformly consider the overall system optimization, face information security and privacy protection issues due to the need to access the private data of all participants, making them unsuitable for practical application needs.

[0004] Therefore, designing a distributed scheduling method that can coordinate the scheduling needs of electricity and hydrogen energy suppliers without compromising privacy, while minimizing the system's operating costs, has become a key challenge for the optimal scheduling of electric-hydrogen coupling systems. Especially in multi-objective optimization, balancing the conflicting interests of different stakeholders and efficiently capturing Pareto optimal solutions through distributed computing has become an important research direction in electric-hydrogen coupling systems. Summary of the Invention

[0005] This application provides a distributed multi-objective optimization method applicable to electro-hydrogen coupling systems to address the problems in the prior art where the economic interests of power suppliers and hydrogen energy suppliers often conflict, making it difficult to reach a unified scheduling scheme, as well as the issues of information security and privacy protection.

[0006] Accordingly, this application also provides a distributed multi-objective optimization device, an electronic device, and a computer-readable storage medium suitable for electro-hydrogen coupling systems, to ensure the implementation and application of the above methods.

[0007] To address the aforementioned technical problems, this application discloses a distributed multi-objective optimization method applicable to electro-hydrogen coupling systems, the method comprising:

[0008] Based on the bidirectional energy coupling relationship between the power system and the hydrogen energy system, and the competitive relationship between power suppliers and hydrogen suppliers, a dual-objective optimization model is constructed between power suppliers and hydrogen suppliers; the dual-objective optimization model aims to minimize the operating costs of both power suppliers and hydrogen suppliers.

[0009] The bi-objective optimization model is solved using a distributed ξ-constraint optimization algorithm based on the alternating direction multiplier method to obtain the operating costs of the power supplier and the hydrogen supplier, as well as the corresponding optimized values ​​of the decision variables.

[0010] Preferably, based on the bidirectional energy coupling relationship between the power system and the hydrogen energy system, and the competitive relationship between power suppliers and hydrogen suppliers, a dual-objective optimization model is constructed between power suppliers and hydrogen suppliers, including:

[0011] Determine the objective functions of the target optimization model, including the objective functions of the power supplier and the hydrogen supplier;

[0012] Determine the constraints of the target optimization model, including constraints on power suppliers, constraints on hydrogen suppliers, and coupling constraints between the power system and the hydrogen energy system;

[0013] Construct a dual-objective optimization model based on the objective function and constraints:

[0014]

[0015] Where obj1 and obj2 are the power supplier optimization model and the hydrogen supplier optimization model, respectively; f(x) and f(y) are the objective functions of the power supplier and the hydrogen supplier, respectively; x is the decision variable of the power system; y is the decision variable of the hydrogen energy system; and g... i For the coupling constraints between the power system and the hydrogen energy system, h j For and d k These are the inequalities and equality constraints for the safe operation of the power system and the hydrogen energy system, respectively, N. cq N represents the number of coupling constraints. eq N represents the number of equality constraints. ieq denoted as the number of inequality constraints.

[0016] Preferably, a distributed ξ-constrained optimization algorithm based on the alternating direction multiplier method is used to solve the bi-objective optimization model to obtain the operating costs of the power supplier and the hydrogen supplier, as well as the corresponding optimized values ​​of the decision variables, including:

[0017] Ignoring the objective function of the power supplier, we only optimize the objective function of the hydrogen supplier to obtain the maximum and minimum operating costs that the hydrogen supplier can accept.

[0018] The operating costs of hydrogen suppliers are limited to increase linearly from the minimum to the maximum operating costs, thus determining the operating costs that hydrogen suppliers can accept.

[0019] The acceptable operating costs for hydrogen suppliers are added as constraints to the power supplier optimization model.

[0020] By optimizing the power supplier model multiple times, the operating costs of the power supplier and the hydrogen supplier, as well as the corresponding optimized values ​​of decision variables, were obtained.

[0021] Preferably, the distributed ξ-constraint optimization algorithm in the bi-objective optimization model takes the following form:

[0022]

[0023] Among them, C Gaccept The operating cost of a hydrogen supplier is constrained to be the highest acceptable operating cost, not exceeding C. Gaccept .

[0024] Preferably, before optimizing only the hydrogen supplier's objective function and obtaining the maximum and minimum operating costs acceptable to the hydrogen supplier, the method further includes:

[0025] Add a replicated variable to the variable information exchanged between the power supplier and the hydrogen supplier, and obtain replicated variable constraints;

[0026] The replication variable constraint is relaxed into the original objective function through an augmented Lagrangian form, resulting in the augmented Lagrangian forms of the power supplier's objective function and the hydrogen supplier's objective function.

[0027] Preferably, determining the objective function of the bi-objective optimization model includes:

[0028] Construct the power supplier's objective function based on the power supplier's operating costs;

[0029] Construct the objective function for hydrogen suppliers based on their operating costs;

[0030] The operating costs of the power supplier include the cost of purchasing electricity from the upper-level power grid, the operation and maintenance costs of the electrolyzer, and the cost of purchasing electricity from the fuel cells of the hydrogen supplier.

[0031] The operating costs of hydrogen suppliers include the cost of purchasing hydrogen wholesale from hydrogen source plants, the cost of operating and maintaining hydrogen fuel cells, and the cost of purchasing hydrogen from the electrolyzers of power suppliers.

[0032] Preferably, the supplier's constraints include distribution network constraints, electricity purchase constraints, and electricity sales constraints;

[0033] The constraints on hydrogen suppliers include hydrogen network constraints, gas pressure constraints, and flow constraints.

[0034] This application also discloses a distributed multi-objective optimization device suitable for an electro-hydrogen coupling system, the device comprising:

[0035] The model building module is used to construct a dual-objective optimization model between power suppliers and hydrogen suppliers based on the bidirectional energy coupling relationship between the power system and the hydrogen energy system, as well as the competitive relationship between power suppliers and hydrogen suppliers. The dual-objective optimization model aims to minimize the operating costs of both power suppliers and hydrogen suppliers.

[0036] The optimization solution module is used to solve the bi-objective optimization model using a distributed ξ-constraint optimization algorithm based on the alternating direction multiplier method, and to obtain the operating costs of the power supplier and the hydrogen supplier and the corresponding optimized values ​​of the decision variables.

[0037] This application also discloses an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement one or more of the methods described in this application.

[0038] This application also discloses a computer-readable storage medium storing a computer program that, when executed by a processor, implements one or more of the methods described in this application.

[0039] This application constructs a dual-objective optimization model for power and hydrogen energy suppliers based on the bidirectional energy coupling relationship between the power system and the hydrogen energy system, and the competitive relationship between power and hydrogen suppliers. This model effectively addresses the competitive conflict between power and hydrogen suppliers during scheduling in existing power-hydrogen systems. The dual-objective optimization model aims to minimize the operating costs of both power and hydrogen suppliers, thereby maximizing their economic benefits and ensuring a more efficient bidirectional energy coupling process between the power and hydrogen energy systems. Furthermore, a distributed ξ-constrained optimization algorithm based on the alternating direction multiplier method is designed to solve the dual-objective optimization model. This algorithm captures the optimal Pareto front while protecting the privacy of all participants in the power-hydrogen system, limiting the objective function of each participant within a reasonable range. This ensures the stability and efficiency of the distributed scheduling process, satisfying the optimization objectives of both power and hydrogen suppliers while improving coordination among energy suppliers and minimizing system operating costs.

[0040] Additional aspects and advantages of this application will be set forth in the following description, and will become apparent from the description or may be learned by practice of this application. Attached Figure Description

[0041] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein:

[0042] Figure 1 A flowchart of a distributed multi-objective optimization method for an electro-hydrogen coupling system provided in this application embodiment;

[0043] Figure 2 This is a topology diagram of an electro-hydrogen coupling system provided in an embodiment of this application;

[0044] Figure 3 The Pareto front results obtained by the weighted summation method provided in the embodiments of this application;

[0045] Figure 4 Pareto front results obtained by mathematical programming in the embodiments of this application;

[0046] Figure 5 Pareto front results obtained by the NSGA-II method for embodiments of this application;

[0047] Figure 6 Pareto front results obtained by the distributed ξ-constraint method in the embodiments of this application;

[0048] Figure 7 The convergence process of the algorithm under different penalty factors is provided in the embodiments of this application;

[0049] Figure 8 A schematic diagram of the structure of a distributed multi-objective optimization device for an electro-hydrogen coupling system provided in the embodiments of this application;

[0050] Figure 9 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0051] The embodiments of this application are described in detail below. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain this application, and should not be construed as limiting this application.

[0052] Those skilled in the art will understand that, unless explicitly stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this application means the presence of features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or combinations thereof. It should be understood that when we say an element is “connected” or “coupled” to another element, it can be directly connected or coupled to the other element, or there may be intermediate elements. Furthermore, “connected” or “coupled” as used herein can include wireless connections or wireless coupling. The term “and / or” as used herein includes all or any units and all combinations of one or more associated listed items.

[0053] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art and should not be interpreted in an idealized or overly formal sense unless specifically defined as herein.

[0054] The solutions provided in this application can be executed by any electronic device, such as a terminal device or a server. The server can be an independent physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server providing cloud computing services. The terminal can be a smartphone, tablet, laptop, desktop computer, smart speaker, smartwatch, etc., but is not limited to these. The terminal and server can be directly or indirectly connected via wired or wireless communication, which is not limited herein. Regarding the technical problems existing in the prior art, the distributed multi-objective optimization method and apparatus for electro-hydrogen coupling systems provided in this application aim to solve at least one of the technical problems of the prior art.

[0055] The technical solution of this application and how the technical solution of this application solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will now be described with reference to the accompanying drawings.

[0056] This application provides a possible implementation method, such as... Figure 1As shown, a flowchart of a distributed multi-objective optimization method suitable for an electro-hydrogen coupling system is provided. This method can be executed by any electronic device, optionally on a server or a terminal device.

[0057] like Figure 1 As shown, the method may include the following steps:

[0058] Step 101: Based on the bidirectional energy coupling relationship between the power system and the hydrogen energy system, and the competitive relationship between power suppliers and hydrogen suppliers, construct a dual-objective optimization model between power suppliers and hydrogen suppliers.

[0059] Among them, the dual-objective optimization model aims to minimize the operating costs of both the power supplier and the hydrogen supplier.

[0060] Step 102: Use the distributed ξ-constraint optimization algorithm based on the alternating direction multiplier method to solve the bi-objective optimization model and obtain the operating costs of the power supplier and the hydrogen supplier and the corresponding optimized values ​​of the decision variables.

[0061] Among them, the distributed ξ-constraint optimization algorithm optimizes and solves the models of each participating agent in the bi-objective optimization model, and can effectively capture the optimal Pareto front.

[0062] In this embodiment, a dual-objective optimization model is constructed based on the bidirectional energy coupling relationship between the power system and the hydrogen energy system, and the competitive relationship between power suppliers and hydrogen suppliers. This model effectively solves the competitive conflict problem between power suppliers and hydrogen suppliers during the scheduling process in existing electric-hydrogen systems. The dual-objective optimization model aims to minimize the operating costs of both power suppliers and hydrogen suppliers, thus realizing their economic interests and ensuring a more efficient bidirectional energy coupling process between the power and hydrogen energy systems. Furthermore, a distributed ξ-constrained optimization algorithm based on the alternating direction multiplier method is designed to solve the dual-objective optimization model. This algorithm can capture the optimal Pareto front while protecting the privacy of all participants in the electric-hydrogen system, limiting the objective function of each participant to a reasonable range, ensuring the stability and efficiency of the distributed computing process for scheduling. While satisfying the optimization objectives of both power and hydrogen suppliers, it also improves the coordination among energy suppliers, minimizing system operating costs. This method is not only adaptable to complex electric-hydrogen coupling systems but also flexibly addresses conflicting interests in multi-objective optimization, possessing strong practical application value.

[0063] In an optional embodiment, based on the bidirectional energy coupling relationship between the power system and the hydrogen energy system, and the competitive relationship between the power supplier and the hydrogen supplier, a bi-objective optimization model is constructed between the power supplier and the hydrogen supplier, including:

[0064] Determine the objective functions of the target optimization model, including the objective functions of the power supplier and the hydrogen supplier;

[0065] Determine the constraints of the target optimization model, including constraints on power suppliers, constraints on hydrogen suppliers, and coupling constraints between the power system and the hydrogen energy system;

[0066] Construct a dual-objective optimization model based on the objective function and constraints:

[0067]

[0068] Where obj1 and obj2 are the power supplier optimization model and the hydrogen supplier optimization model, respectively; f(x) and f(y) are the objective functions of the power supplier and the hydrogen supplier, respectively; x is the decision variable of the power system; y is the decision variable of the hydrogen energy system; and g... i For the coupling constraints between the power system and the hydrogen energy system, h j For and d k These are the inequalities and equality constraints for the safe operation of the power system and the hydrogen energy system, respectively, N. cq N represents the number of coupling constraints. eq N represents the number of equality constraints. ieq denoted as the number of inequality constraints.

[0069] The bi-objective optimization model uses x and y as optimization variables, considers the internal constraints of each system and the coupling constraints between systems, and optimizes to obtain the minimum operating cost of each system under the premise of constraint safety, and obtains the optimal Pareto front.

[0070] In an optional embodiment, determining the objective function of the bi-objective optimization model includes:

[0071] Construct the power supplier's objective function based on the power supplier's operating costs;

[0072] Construct the objective function for hydrogen suppliers based on their operating costs;

[0073] The operating costs of the power supplier include the cost of purchasing electricity from the upper-level power grid, the operation and maintenance costs of the electrolyzer, and the cost of purchasing electricity from the fuel cells of the hydrogen supplier.

[0074] The operating costs of hydrogen suppliers include the cost of purchasing hydrogen wholesale from hydrogen source plants, the cost of operating and maintaining hydrogen fuel cells, and the cost of purchasing hydrogen from the electrolyzers of power suppliers.

[0075] Electricity suppliers profit by selling electricity to users, while hydrogen suppliers profit by selling hydrogen to users.

[0076] Based on the above, the objective functions of the electricity supplier and the hydrogen supplier can be expressed as follows:

[0077]

[0078]

[0079] Among them, C P and C G These represent the operating costs of the electricity supplier and the hydrogen supplier, respectively, p W,e,t and p W,g,t P represents the wholesale electricity price of the upstream power grid and the wholesale hydrogen price of the hydrogen source plant during time period t. grid,t and G grid,t These represent the wholesale electricity and wholesale hydrogen quantities for time period t, respectively. EG and ζ GE The unit maintenance costs of the electrolyzer and the hydrogen fuel cell, respectively, P j,EG,t and G j,GE,t These represent the input electricity to the electrolyzer and the input hydrogen to the hydrogen fuel cell during time period t, respectively. j,GE,t and p j,EG,t These represent the electricity purchase price from the hydrogen fuel cell and the hydrogen purchase price from the electrolyzer during time period t, respectively. e,t and p g,t These represent the electricity price paid by the power supplier to the user and the hydrogen price paid by the hydrogen supplier to the user during time period t, respectively. j,t and G j,t Let represent the electricity and hydrogen purchased by node j during time period t, respectively. Let B be the set of all nodes j in the system, and ΔT be the unit scheduling period.

[0080] In an optional embodiment, the supplier's constraints include distribution network constraints, electricity purchase constraints, and electricity sales constraints, which can be expressed as follows:

[0081]

[0082]

[0083]

[0084]

[0085]

[0086]

[0087] Where j, u, and v are system node indices, ju and vj represent the branch from node j to node u and the branch from node v to node j, respectively, P ju,t Q ju,t P represents the active power and reactive power flowing through branch ju during time period t, respectively. vj,t Q vj,t I vj,tRepresent the active power, reactive power, and current flowing through branch vj during time period t, respectively. vj x vj r ju x ju V represents the resistance and reactance of branch vj and branch ju, respectively. j,t and V u,t P represents the voltages at nodes j and u during time period t, respectively. j,load,t P j,EG,t P j,GE,t These represent the electrical load, electrolyzer output power, and hydrogen fuel cell consumption at node j during time period t, respectively. and These are the sets formed by all nodes and all branches in the distribution network, respectively. Equations (4)-(8) represent the distribution network constraints, where equations (4)-(5) represent the power balance constraints of the distribution network nodes, equation (6) represents the voltage drop constraints, equation (7) represents the branch power constraints after second-order cone relaxation, and equation (8) represents the power balance constraints of the coupled nodes. The first part of equation (9) represents the power purchase constraints, and the second part represents the power sales constraints.

[0088] Hydrogen supplier constraints include hydrogen network constraints, gas pressure constraints, and flow rate constraints, which can be expressed as follows:

[0089]

[0090]

[0091]

[0092]

[0093]

[0094]

[0095]

[0096] Among them, f p,t f p,min and f p,max Let π represent the flow rate, minimum allowable flow rate, and maximum allowable flow rate of pipe p during time period t, respectively. i,t and π j,t Let π represent the air pressure at node i and node j during time period t, respectively. n,min and π n,max Let sgn represent the minimum and maximum air pressures at node n, respectively, where sgn is the sign function and f is the maximum air pressure at node n. k,t G s,t and G l,tB represents the flow rates of pipeline k, hydrogen source node s, and hydrogen load node l during time period t, respectively. nk G ns and D nl These represent the corresponding coefficient matrices, Φ p Let n be the conversion factor for pipe p. i,t and n j,t Let i and j represent the squared air pressure at nodes i and j during time period t, respectively. and Let represent the pipeline set and the node set, respectively. Equations (10)-(16) are all hydrogen network constraints, of which equation (13) is a gas pressure constraint, and equations (10)-(12) and (14)-(16) are flow constraints.

[0097] Electricity suppliers and hydrogen suppliers are interconnected at the coupling node using energy conversion equipment such as electrolyzers and hydrogen fuel cells to perform energy conversion and trading. Therefore, the coupling constraint can be expressed as:

[0098]

[0099]

[0100]

[0101]

[0102] Where, η EG and η GE These are the conversion efficiencies of the electrolyzer and the hydrogen fuel cell, respectively. and These represent the maximum output power of the electrolyzer and the hydrogen fuel cell, respectively. Equations (17)-(18) represent the constraints of the electrolyzer equipment, and equations (19)-(20) represent the constraints of the hydrogen fuel cell.

[0103] In an optional embodiment, a distributed ξ-constrained optimization algorithm based on the alternating direction multiplier method is used to solve the bi-objective optimization model to obtain the operating costs of the power supplier and the hydrogen supplier, as well as the corresponding optimized values ​​of the decision variables, including:

[0104] Ignoring the objective function of the power supplier, we only optimize the objective function of the hydrogen supplier to obtain the maximum and minimum operating costs that the hydrogen supplier can accept.

[0105] The operating costs of hydrogen suppliers are limited to increase linearly from the minimum operating cost to the maximum operating cost in fixed steps to determine the operating costs that hydrogen suppliers can accept.

[0106] The acceptable operating costs for hydrogen suppliers are added as constraints to the power supplier optimization model.

[0107] By optimizing the power supplier model multiple times, the operating costs of the power supplier and the hydrogen supplier, as well as the corresponding optimized values ​​of decision variables, were obtained.

[0108] In an optional embodiment, the distributed ξ-constraint optimization algorithm in the bi-objective optimization model takes the form of:

[0109]

[0110] Among them, C Gaccept To determine the highest acceptable operating cost for hydrogen suppliers, this algorithm uses the supplier's operating cost as the primary objective function, constraining the supplier's operating cost to not exceed C. Gaccept This constraint is then added to the original power supplier optimization model, thereby transforming the bi-objective optimization model into a single-objective form.

[0111] In an optional embodiment, before optimizing only the hydrogen supplier's objective function and obtaining the maximum and minimum operating costs acceptable to the hydrogen supplier, the method further includes:

[0112] Add a replicated variable to the variable information exchanged between the power supplier and the hydrogen supplier, and obtain replicated variable constraints;

[0113] The replication variable constraint is relaxed to the original objective function using an augmented Lagrangian form, resulting in the augmented Lagrangian forms of the power supplier's objective function and the hydrogen supplier's objective function.

[0114] The augmented Lagrangian form of the supplier's objective function is as follows:

[0115]

[0116] Where L is the augmented Lagrange form of the power supplier, and C P Let be the objective function of the power supplier, λ be the Lagrange multiplier, ρ be the penalty factor, and T be the scheduling period, which is taken as 24h.

[0117] Before optimization, the objective function of the power supplier is transformed into its augmented Lagrangian form. The objective function is restricted by a penalty term. During each iteration of optimization, local variable information is exchanged to reach a consensus. Through multiple iterations, a consensus constraint between the power supplier and the hydrogen supplier is gradually achieved, and the optimized values ​​of the decision variables are obtained while effectively protecting the privacy of the participating entities.

[0118] Based on the above, the specific process of solving the dual-objective optimization model using the distributed ξ-constraint optimization algorithm is as follows:

[0119] First, to protect the privacy of users of both the power supplier and the hydrogen supplier, a replication variable for the interaction power between them is added, that is, replication variables are added to the four variables involved in equations (17) and (19):

[0120]

[0121] in, and These represent the replicated variables for the electricity consumed and hydrogen output of the electrolyzer, respectively. and These represent the replication variables for the hydrogen energy consumed and the electrical energy output of the hydrogen fuel cell, respectively.

[0122] Secondly, the equality constraints in equation (23) above are relaxed into the original objective function through an augmented Lagrangian form, resulting in the augmented Lagrangian forms of the objective functions for the power supplier and the hydrogen supplier:

[0123]

[0124]

[0125] Furthermore, without considering the power supplier, optimizing the objective function of the hydrogen supplier yields the corresponding maximum operating cost C. Gmax and minimum operating cost C Gmin And determine the number N of the desired non-dominated optimal solution set.

[0126] Then, based on the order of increasing operating costs for hydrogen suppliers from lowest to highest, the acceptable operating costs for the current steps of the hydrogen supplier are determined as follows:

[0127] C Gaccept =C Gmin +n·(C Gmax -C Gmin ) / N (26)

[0128] Here, n represents the nth set of non-dominated optimal solutions. The acceptable cost of the hydrogen supplier at this point is added as a constraint to the supplier optimization model. Thus, the original bi-objective optimization problem is transformed into a single-objective optimization problem with a simpler solution:

[0129]

[0130] Next, initialize the relevant parameters, the maximum number of iterations, and the acceptable original residual convergence threshold. Perform optimization iterations on equation (27), calculate the original residual after each iteration, and determine whether it is less than the convergence threshold.

[0131] ||r k+1 ||2=||X S,k+1 -X C,k+1 ||2<ξ (28)

[0132] If the value is less than the target value, stop the iteration and output the objective function value and the optimization variable value.

[0133] If it is not less than, update the Lagrange multipliers as follows:

[0134] λ k+1 =λ k +ρ(X S,k+1 -X C,k+1 (29)

[0135] Continue iterating until the residual is less than the convergence threshold or the maximum number of iterations is reached.

[0136] Finally, according to the desired number of non-dominated optimal solution sets, the objective function of the power supplier is optimized and calculated multiple times. The objective function values ​​of the power supplier and the hydrogen supplier after each optimization are obtained, as well as the corresponding decision variables. The residual convergence of each solution iteration process is recorded until N solutions are obtained.

[0137] The distributed ξ-constraint optimization algorithm based on the alternating direction multiplier method proposed in this application effectively solves the problem while protecting the privacy of the participating entities by exchanging local information and iterating multiple times. By restricting the objective function of each participating entity, the stability and efficiency of the scheduling process are ensured, avoiding the information security problems caused by traditional centralized scheduling methods.

[0138] In this embodiment, the multiple iterations address the privacy protection issue for both electricity and hydrogen suppliers. Utilizing its model characteristics and algorithm flow, a distributed ξ-constraint optimization algorithm based on the alternating direction multiplier method is modeled and solved using Matlab.

[0139] For example, after implementing the algorithm designed in the embodiments of this application using Matlab programming, the following computational scenario is set up: A 33-node power distribution system (power distribution network) and a 20-node hydrogen energy system (hydrogen energy network) are set up in the computational scenario. Nodes 17, 24, and 31 of the power distribution system and nodes 17, 19, and 16 of the hydrogen energy system are set as coupling nodes. Corresponding energy conversion devices (i.e., coupling devices) are set up in the two systems and connected to each other. The system topology is as follows: Figure 2 As shown. The maximum number of iterations per cycle is set to 50, the residual convergence threshold is 1e-8, the penalty factor is set to 100, and the expected number of non-dominated optimal solution sets is N=100. To demonstrate the advantages of the embodiments of this application, the uniformity of the Pareto front obtained by each method will be compared with that of the weighted summation method, mathematical programming method, and NSGA-II method.

[0140] (1) Pareto front homogeneity analysis

[0141] The 100 sets of non-dominated optimal solutions obtained by the weighted summation method, mathematical programming method, NSGA-II method, and the method proposed in this invention are respectively as follows: Figure 3 , Figure 4 , Figure 5 and Figure 6 As shown. Among them, Figure 3 The Pareto frontier result obtained by the weighted summation method, Figure 4 The Pareto front result obtained by mathematical programming. Figure 5 The Pareto front results are obtained by the NSGA-II method. Figure 6 The figure shows the Pareto front results obtained by the distributed ξ-constraint method in the embodiments of this application. The horizontal axis represents the cost of hydrogen suppliers (thousand yuan), the vertical axis represents the cost of electricity suppliers (thousand yuan), and a negative operating cost indicates that the electricity supplier or hydrogen supplier is profitable.

[0142] The results show that the Pareto front obtained using the method in this application is more uniform, while the uniformity of the Pareto fronts obtained by the weighted summation method and mathematical programming method is relatively poor. For the weighted summation method, this is due to its limitations. The weighted summation method merges multiple objectives into one. Although the weight distributions of the objective function values ​​are different, their performance is the same, and they are not necessarily different Pareto optimal solutions. In other words, the diversity of the Pareto front is insufficient. In reality, this means that the interaction intensity between the power supplier and the hydrogen supplier is inconsistent over time, but both can obtain the same benefits, which is undesirable. From the perspective of operating costs, the effect is consistent, but this increases the workload of scheduling planning. The non-uniformity of the mathematical programming method is caused by the limitations of the objective function. The mathematical programming method uses the square of the distance between two objective functions and their respective optimal values ​​as a new objective function. To make the new objective function as small as possible, the results always tend to be distributed in the region close to the optimal values ​​of both, which inevitably makes the region far from a single objective value more difficult to reach. The results also show that under the mathematical programming method, the maximum costs achieved by the power supplier and the hydrogen supplier are approximately -10 and -7 respectively, and can never be 0. In other words, mathematical programming methods struggle to capture solutions at the edge of the Pareto boundary. However, such extreme cases are possible in practical applications. Under certain conditions, only one power supplier or one hydrogen supplier might be responsible for the energy supply of both the power grid and the hydrogen grid simultaneously throughout the scheduling period. This leads to critical situations with high operating costs, making mathematical programming methods difficult to generalize and resulting in a relatively small feasible region. For the NSGA-II algorithm, the optimization process is a multi-stage evolutionary process. Due to different iteration numbers, the results are not entirely consistent and are significantly affected by crossover and mutation operators. Furthermore, to protect boundary diversity, the algorithm introduces the concept of crowding distance, which eliminates unqualified individuals during the evolutionary process. Therefore, the number of solutions obtained is not consistent with the population size, increasing the instability of the algorithm's results. In other words, to obtain a relatively stable solution, the NSGA-II algorithm requires more iterations and a larger population size, which undoubtedly increases computational resources.

[0143] On the contrary, such as Figure 6 As shown, the method proposed in this embodiment can obtain a relatively uniform Pareto front. From the perspective of density estimation, the solution set is uniformly distributed within the feasible region, avoiding situations where the density is very high in local areas. This is mainly because the method proposed in this embodiment fully considers the interests of both competing parties. Optimizing one party's cost while restricting the cost range of the other party ensures that both parties can achieve a relatively satisfactory competitive result as long as the cost range is reasonable. In practical optimization problems, the electricity supplier and the hydrogen supplier can exchange acceptable cost ranges. For example, the electricity supplier's operating cost can be used as the main objective function, meaning the hydrogen supplier is satisfied with the objective function of optimizing the electricity supplier. In this case, the objective function is a single objective, thus avoiding conflicts of interest caused by unequal weight allocation during the optimization process. Furthermore, different solutions can be obtained by restricting different ranges within the feasible region, and decision-makers can choose the step size and range of the restriction according to the actual situation. Theoretically, any set of Pareto solutions within the acceptable cost range of both parties can be obtained, which is very useful for maintaining the diversity of the Pareto front.

[0144] (2) Algorithm performance analysis

[0145] First, the convergence characteristics of the algorithm proposed in the embodiments of this application are analyzed. With varying penalty factor values, the system converges from the original residual as follows: Figure 7 As shown, with a fixed penalty factor ρ, the residual decreases faster as the penalty factor increases. With the same number of iterations, the final residual continuously decreases as the penalty factor increases. When the penalty factor reaches 100, only about 10 iterations are needed to achieve an accuracy of 1e-8, reflecting the high convergence speed and reliability of the algorithm in this embodiment. Furthermore, the computation time required by the distributed ξ-constraint method, weighted summation method, mathematical programming method, and NSGA-II in this embodiment was analyzed and compared under different sets of non-dominated optimal solution sets. The number of non-dominated optimal solution sets was set to 10, 20, 50, and 100, respectively, and the computation time of the four different methods was compared and analyzed. The results are shown in Table 1.

[0146] Table 1. Computation time (in seconds) for different methods on different solution sets.

[0147]

[0148] The results show that the computation time of the method proposed in this application is longer than that of the weighted summation method and the NSGA-II algorithm. This is mainly because the weighted summation method and NSGA-II do not generate iterative steps within each set of optimal solutions, and only have one outer loop when searching for the next set of optimal solutions, thus their time is relatively short. On the other hand, the computation time of mathematical programming and the proposed method is relatively long, and the computation time increases rapidly with the increase of the number of solution sets. When the number of solution sets is small, such as 10 and 20, the time taken by the proposed method is slightly longer than that of mathematical programming. This is mainly because the number of solution sets is small, the number of outer loop iterations is small, and the loop computation time of the residuals in the proposed method is similar to that of mathematical programming for optimizing quadratic functions. When the number of solution sets increases, such as 50 and 100, the time taken by the proposed method is shorter. This is because when the number of solution sets is large, the inner loop of the proposed method only needs to optimize one objective function, and as the iteration progresses, the residuals become smaller and smaller, and the optimization time also decreases. Mathematical programming methods require optimizing a squared objective function for each iteration, which is time-consuming and does not change with the number of solution sets. Therefore, when the number of solution sets is large, the computation time of the method proposed in this application is shorter than that of mathematical programming methods. Overall, due to the introduction of a distributed iterative process, the method proposed in this application is slower than centralized and heuristic multi-objective optimization algorithms in terms of solution time. However, since it can effectively protect the privacy of participants, sacrificing some solution time is acceptable to a certain extent.

[0149] The above examples demonstrate that the distributed ξ-constraint method proposed in this application has a simple mathematical principle, reliable theoretical foundation, and strong interpretability. By introducing the concept of a distributed algorithm and adding interactive weighted copy variables, it effectively protects the privacy of participants and achieves high convergence accuracy in a relatively small number of iterations. Compared with traditional centralized and heuristic algorithms, it can obtain a Pareto front with higher uniformity regardless of the number of solution sets, providing a better geometry for multi-objective optimization results. Furthermore, decision-makers can select appropriate penalty factors based on problem complexity and parameter size to achieve fast and high-precision convergence.

[0150] Based on the same principles as the methods provided in the embodiments of this application, the embodiments of this application also provide a distributed multi-objective optimization device suitable for electro-hydrogen coupling systems, such as... Figure 8 As shown, the device includes:

[0151] Model building module 801 is used to construct a dual-objective optimization model between power suppliers and hydrogen suppliers based on the bidirectional energy coupling relationship between the power system and the hydrogen energy system, as well as the competitive relationship between power suppliers and hydrogen suppliers; wherein, the dual-objective optimization model aims to minimize the operating costs of power suppliers and hydrogen suppliers.

[0152] The optimization solution module 802 is used to solve the bi-objective optimization model using a distributed ξ-constraint optimization algorithm based on the alternating direction multiplier method, and to obtain the operating costs of the power supplier and the hydrogen supplier and the corresponding optimized values ​​of the decision variables.

[0153] In this embodiment, a dual-objective optimization model is constructed based on the bidirectional energy coupling relationship between the power system and the hydrogen energy system, and the competitive relationship between power suppliers and hydrogen suppliers. This model effectively solves the competitive conflict problem between power suppliers and hydrogen suppliers during the scheduling process in existing electric-hydrogen systems. The dual-objective optimization model aims to minimize the operating costs of both power suppliers and hydrogen suppliers, thus realizing their economic interests and ensuring a more efficient bidirectional energy coupling process between the power and hydrogen energy systems. Furthermore, a distributed ξ-constrained optimization algorithm based on the alternating direction multiplier method is designed to solve the dual-objective optimization model. This algorithm can capture the optimal Pareto front while protecting the privacy of all participants in the electric-hydrogen system, limiting the objective function of each participant to a reasonable range, ensuring the stability and efficiency of the distributed computing process for scheduling. While satisfying the optimization objectives of both power and hydrogen suppliers, it also improves the coordination among energy suppliers, minimizing system operating costs. This method is not only adaptable to complex electric-hydrogen coupling systems but also flexibly addresses conflicting interests in multi-objective optimization, possessing strong practical application value.

[0154] The distributed multi-objective optimization device for electro-hydrogen coupling systems provided in this application embodiment can achieve… Figures 1 to 7 The various processes implemented in the method embodiments are not described in detail here to avoid repetition.

[0155] The distributed multi-objective optimization device for electro-hydrogen coupling systems in this application embodiment can execute the distributed multi-objective optimization method for electro-hydrogen coupling systems provided in this application embodiment. The implementation principle is similar. The actions performed by each module and unit in the distributed multi-objective optimization device for electro-hydrogen coupling systems in each embodiment of this application correspond to the steps in the distributed multi-objective optimization method for electro-hydrogen coupling systems in each embodiment of this application. For detailed functional descriptions of each module of the distributed multi-objective optimization device for electro-hydrogen coupling systems, please refer to the descriptions in the corresponding distributed multi-objective optimization methods for electro-hydrogen coupling systems shown above, which will not be repeated here.

[0156] Based on the same principles as the methods shown in the embodiments of this application, this application also provides an electronic device, which may include, but is not limited to: a processor and a memory; the memory for storing computer programs; and the processor for executing the distributed multi-objective optimization method for an electric-hydrogen coupling system shown in any optional embodiment of this application by calling the computer program. Compared with the prior art, the distributed multi-objective optimization method for an electric-hydrogen coupling system provided in this application constructs a dual-objective optimization model between power suppliers and hydrogen suppliers, which can effectively solve the competition and conflict problem between power suppliers and hydrogen suppliers in the scheduling process in existing electric-hydrogen systems. It can realize the economic interests between power suppliers and hydrogen suppliers and ensure that the bidirectional energy coupling process between the power and hydrogen energy systems is more efficient. The designed distributed ξ-constraint optimization algorithm can capture the optimal Pareto front while protecting the privacy of each participant in the electric-hydrogen system, and restrict the objective function of each participant within a reasonable range, ensuring that the distributed computing process of scheduling is stable and efficient. While satisfying the objective optimization of power and hydrogen energy suppliers, it improves the coordination between energy suppliers and minimizes the system operating cost.

[0157] In an alternative embodiment, an electronic device, such as Figure 9 As shown, Figure 9 The illustrated electronic device 900 can be a server, including a processor 901 and a memory 903. The processor 901 and the memory 903 are connected, for example, via a bus 902. Optionally, the electronic device 900 may also include a transceiver 904. It should be noted that in practical applications, the transceiver 904 is not limited to one type, and the structure of this electronic device 900 does not constitute a limitation on the embodiments of this application.

[0158] Processor 901 may be a CPU (Central Processing Unit), a general-purpose processor, a DSP (Digital Signal Processor), an ASIC (Application Specific Integrated Circuit), an FPGA (Field Programmable Gate Array), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. It can implement or execute the various exemplary logic blocks, modules, and circuits described in conjunction with the disclosure of this application. Processor 901 may also be a combination that implements computational functions, such as including one or more microprocessor combinations, a combination of a DSP and a microprocessor, etc.

[0159] Bus 902 may include a pathway for transmitting information between the aforementioned components. Bus 902 may be a PCI (Peripheral Component Interconnect) bus or an EISA (Extended Industry Standard Architecture) bus, etc. Bus 902 can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 9 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0160] The memory 903 may be a ROM (Read Only Memory) or other type of static storage device capable of storing static information and instructions, RAM (Random Access Memory) or other type of dynamic storage device capable of storing information and instructions, or an EEPROM (Electrically Erasable Programmable Read Only Memory), CD-ROM (Compact Disc Read Only Memory) or other optical disc storage, optical disc storage (including compressed optical discs, laser discs, optical discs, digital universal optical discs, Blu-ray discs, etc.), magnetic disk storage media or other magnetic storage devices, or any other medium capable of carrying or storing desired program code in the form of instructions or data structures and accessible by a computer, but not limited thereto.

[0161] The memory 903 stores application code that executes the scheme of this application, and its execution is controlled by the processor 901. The processor 901 executes the application code stored in the memory 903 to implement the content shown in the foregoing method embodiments.

[0162] Among them, electronic devices include, but are not limited to: mobile terminals such as mobile phones, laptops, digital radio receivers, PDAs (personal digital assistants), PADs (tablet computers), PMPs (portable multimedia players), and in-vehicle terminals (such as in-vehicle navigation terminals), as well as fixed terminals such as digital TVs and desktop computers. Figure 9 The electronic device shown is merely an example and should not impose any limitation on the functionality and scope of use of the embodiments of this application.

[0163] The server provided in this application can be a standalone physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server providing basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, CDN, and big data and artificial intelligence platforms. The terminal can be a smartphone, tablet, laptop, desktop computer, smart speaker, smartwatch, etc., but is not limited to these. The terminal and server can be directly or indirectly connected via wired or wireless communication, which is not limited herein.

[0164] This application provides a computer-readable storage medium storing a computer program that, when run on a computer, enables the computer to execute the corresponding content in the aforementioned method embodiments.

[0165] It should be understood that although the steps in the flowcharts of the accompanying figures are shown sequentially as indicated by the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the accompanying figures may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times, and their execution order is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the sub-steps or stages of other steps.

[0166] It should be noted that the computer-readable storage medium described above in this application can also be a computer-readable signal medium or a combination of computer-readable storage media and computer-readable storage media. Computer-readable storage media can be, for example,—but not limited to—electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatuses, or devices, or any combination thereof. More specific examples of computer-readable storage media may include, but are not limited to: electrical connections having one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this application, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. In this application, a computer-readable signal medium can include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium can be any computer-readable medium other than a computer-readable storage medium, which can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the computer-readable medium can be transmitted using any suitable medium, including but not limited to: wires, optical fibers, RF (radio frequency), etc., or any suitable combination thereof.

[0167] The aforementioned computer-readable medium may be included in the aforementioned electronic device; or it may exist independently and not assembled into the electronic device.

[0168] The aforementioned computer-readable medium carries one or more programs, which, when executed by the electronic device, cause the electronic device to perform the methods shown in the above embodiments.

[0169] According to one aspect of this application, a computer program product or computer program is provided, comprising computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the computer device to perform the distributed multi-objective optimization method and apparatus for electro-hydrogen coupling systems provided in the various alternative implementations described above.

[0170] Computer program code for performing the operations of this application can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0171] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0172] The modules described in the embodiments of this application can be implemented in software or hardware. The names of the modules do not necessarily limit the module itself; for example, the model building module can also be described as "a model building module for constructing a dual-objective optimization model between power suppliers and hydrogen suppliers based on the bidirectional energy coupling relationship between the power system and the hydrogen energy system, and the competitive relationship between power suppliers and hydrogen suppliers."

[0173] The above description is merely a preferred embodiment of this application and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of disclosure in this application is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the above-described concept. For example, technical solutions formed by substituting the above features with (but not limited to) technical features with similar functions disclosed in this application.

Claims

1. A distributed multi-objective optimization method suitable for electro-hydrogen coupling systems, characterized in that, The method includes: Based on the bidirectional energy coupling relationship between the power system and the hydrogen energy system, and the competitive relationship between power suppliers and hydrogen suppliers, a dual-objective optimization model is constructed. The dual-objective optimization model aims to minimize the operating costs of both the power supplier and the hydrogen supplier. The objective functions for the power supplier and the hydrogen supplier can be expressed as follows: In the formula: and These are the operating costs of the electricity supplier and the operating costs of the hydrogen supplier, respectively. and They are respectively t The wholesale electricity price of the upstream power grid and the wholesale hydrogen price of the hydrogen source plant during the same period. and They are respectively t Wholesale electricity and wholesale hydrogen volume during the period and The unit maintenance costs are for the electrolyzer and the hydrogen fuel cell, respectively. and They are respectively t The input electricity to the electrolyzer and the input hydrogen to the hydrogen fuel cell during the time period. and They are respectively t The time period for purchasing electricity from hydrogen fuel cells and purchasing hydrogen from electrolyzers. and These represent the output power of the hydrogen fuel cell and the output hydrogen quantity of the electrolyzer at node j during time period t, respectively. and They are respectively t The electricity price paid by the power supplier to the user during the time period and the hydrogen price paid by the hydrogen supplier to the user. and They are nodes j exist t Electricity and hydrogen purchases during different time periods B For all nodes in the system j The formed set The scheduling period is per unit. The constraints include: (4) (5) (6) (7) (8) (9) in, j , u , v All are system node indexes. and They represent respectively by j Node to u Branches of a node and branches of a node v To the node j The side road, , They represent t Time-of-day branch The active and reactive power flowing through, , , They represent t Time-of-day branch The active power, reactive power, and current flowing through the system. , , , Representing branch roads Resistance, reactance and branches resistance, reactance and They represent t Time period nodes j and u voltage, express t Time period nodes j electrical load, and These are the sets formed by all nodes and the sets formed by all branches in the distribution network, respectively. (10) (11) (12) (13) (14) (15) (16) in, , and They represent pipes p exist t Traffic flow during a given time period, minimum allowed flow rate, and maximum allowed flow rate. and They represent t Time period i Nodes and j The air pressure at the node and Representing nodes respectively n The minimum and maximum air pressure, sgn For symbolic functions, , and They represent t Time-of-use pipeline k Hydrogen source node s and hydrogen load nodes l Traffic, , and These represent the corresponding coefficient matrices. The pipeline corresponding to time period t p The conversion factor, and They represent t Time period nodes i and j The square of the air pressure; and Represent the pipe set and the node set, respectively; (17) (18) (19) (20) in, and These are the conversion efficiencies of the electrolyzer and the hydrogen fuel cell, respectively. and These are the maximum output power of the electrolyzer and the hydrogen fuel cell, respectively. Distributed method based on alternating direction multipliers ξ - The constrained optimization algorithm solves the bi-objective optimization model to obtain the operating costs of the power supplier and the hydrogen supplier, as well as the corresponding optimized values ​​of the decision variables. The steps include: For each of the four variables involved in equations (17) and (19), add its replication variable: (23) in, and These represent the replicated variables for the electricity consumed and hydrogen output of the electrolyzer, respectively. and These represent the replicated variables for hydrogen energy consumption and electrical energy output of the hydrogen fuel cell, respectively. By relaxing the equality constraints of equation (23) into the original objective function using an augmented Lagrangian form, we obtain the augmented Lagrangian forms of the objective functions for the electricity supplier and the hydrogen supplier: （24） （25） in, It is the Lagrange penalty factor; Optimize the objective function of the hydrogen supplier to obtain the corresponding maximum operating cost. and minimum operating cost And determine the number of sets of non-dominated optimal solutions to be obtained. N ; Based on the principle of increasing operating costs from lowest to highest among hydrogen suppliers, the acceptable operating costs for the current steps of hydrogen supply are determined as follows: (26) in, n Indicates the first n Non-dominated optimal solution set; By adding the acceptable cost of the hydrogen supplier as a constraint to the supplier optimization model, the bi-objective optimization problem is transformed into a single-objective optimization problem that is easier to solve: (27) Initialize the relevant parameters, the maximum number of iterations and the acceptable original residual convergence threshold, optimize and iterate Equation (27), calculate the original residual after each iteration, and determine whether it is less than the convergence threshold: if it is less, stop the iteration and output the objective function value and the optimization variable value; if it is not less, update the Lagrange multiplier and continue iterating until the residual is less than the convergence threshold or the maximum number of iterations is reached. Finally, based on the desired number of non-dominated optimal solution sets, the objective function of the power supplier is optimized multiple times. The objective function values ​​of the power supplier and hydrogen supplier, along with the corresponding decision variables, are obtained after each optimization. The residual convergence of each solution iteration is recorded until a result is obtained. N Solution to the problem.

2. A distributed multi-objective optimization device suitable for electro-hydrogen coupling systems, characterized in that, The device includes: The model building module is used to construct a dual-objective optimization model between power suppliers and hydrogen suppliers based on the bidirectional energy coupling relationship between the power system and the hydrogen energy system, and the competitive relationship between power suppliers and hydrogen suppliers. The dual-objective optimization model aims to minimize the operating costs of both power suppliers and hydrogen suppliers. The objective functions for power suppliers and hydrogen suppliers can be expressed as follows: In the formula: and These are the operating costs of the electricity supplier and the operating costs of the hydrogen supplier, respectively. and They are respectively t The wholesale electricity price of the upstream power grid and the wholesale hydrogen price of the hydrogen source plant during the same period. and They are respectively t Wholesale electricity and wholesale hydrogen volume during the period and The unit maintenance costs are for the electrolyzer and the hydrogen fuel cell, respectively. and They are respectively t The input electricity to the electrolyzer and the input hydrogen to the hydrogen fuel cell during the time period. and They are respectively t The time period for purchasing electricity from hydrogen fuel cells and purchasing hydrogen from electrolyzers. and These represent the output power of the hydrogen fuel cell and the output hydrogen quantity of the electrolyzer at node j during time period t, respectively. and They are respectively t The electricity price paid by the power supplier to the user during the time period and the hydrogen price paid by the hydrogen supplier to the user. and They are nodes j exist t Electricity and hydrogen purchases during different time periods B For all nodes in the system j The formed set The scheduling period is per unit. The constraints include: (4) (5) (6) (7) (8) (9) in, j , u , v All are system node indexes. and They represent respectively by j Node to u Branches of a node and branches of a node v To the node j The side road, , They represent t Time-of-day branch The active and reactive power flowing through, , , They represent t Time-of-day branch The active power, reactive power, and current flowing through the system. , , , Representing branch roads Resistance, reactance and branches resistance, reactance and They represent t Time period nodes j and u voltage, ,express t Time period nodes j electrical load, and These are the sets formed by all nodes and the sets formed by all branches in the distribution network, respectively. (10) (11) (12) (13) (14) (15) (16) in, , and They represent pipes p exist t Traffic flow during a given time period, minimum allowed flow rate, and maximum allowed flow rate. and They represent t Time period i Nodes and j The air pressure at the node and Representing nodes respectively n The minimum and maximum air pressure, sgn For symbolic functions, , and They represent t Time-of-use pipeline k Hydrogen source node s and hydrogen load nodes l Traffic, , and These represent the corresponding coefficient matrices. The pipeline corresponding to time period t p The conversion factor, and They represent t Time period nodes i and j The square of the air pressure; and Represent the pipe set and the node set, respectively; (17) (18) (19) (20) in, and These are the conversion efficiencies of the electrolyzer and the hydrogen fuel cell, respectively. and These are the maximum output power of the electrolyzer and the hydrogen fuel cell, respectively. The optimization solution module is used for distributed solutions based on the alternating direction multiplier method. ξ - The constrained optimization algorithm solves the bi-objective optimization model to obtain the operating costs of the power supplier and the hydrogen supplier, as well as the corresponding optimized values ​​of the decision variables. The steps include: For each of the four variables involved in equations (17) and (19), add its replication variable: (23) in, and These represent the replicated variables for the electricity consumed and hydrogen output of the electrolyzer, respectively. and These represent the replicated variables for hydrogen energy consumption and electrical energy output of the hydrogen fuel cell, respectively. By relaxing the equality constraints of equation (23) into the original objective function using an augmented Lagrangian form, we obtain the augmented Lagrangian forms of the objective functions for the electricity supplier and the hydrogen supplier: （24） （25） in, It is the Lagrange penalty factor; Optimize the objective function of the hydrogen supplier to obtain the corresponding maximum operating cost. and minimum operating cost And determine the number of sets of non-dominated optimal solutions to be obtained. N ; Based on the principle of increasing operating costs from lowest to highest among hydrogen suppliers, the acceptable operating costs for the current steps of hydrogen supply are determined as follows: (26) in, n Indicates the first n Non-dominated optimal solution set; By adding the acceptable cost of the hydrogen supplier as a constraint to the supplier optimization model, the bi-objective optimization problem is transformed into a single-objective optimization problem that is easier to solve: (27) Initialize the relevant parameters, the maximum number of iterations and the acceptable original residual convergence threshold, optimize and iterate Equation (27), calculate the original residual after each iteration, and determine whether it is less than the convergence threshold: if it is less, stop the iteration and output the objective function value and the optimization variable value; if it is not less, update the Lagrange multiplier and continue iterating until the residual is less than the convergence threshold or the maximum number of iterations is reached. Finally, based on the desired number of non-dominated optimal solution sets, the objective function of the power supplier is optimized multiple times. The objective function values ​​of the power supplier and hydrogen supplier, along with the corresponding decision variables, are obtained after each optimization. The residual convergence of each solution iteration is recorded until a result is obtained. N Solution to the problem.

3. An electronic device, characterized in that, It includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the method of claim 1.

4. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the method of claim 1.

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