A topology optimization method and system for offshore wind power collection system

Abstract

The application discloses a kind of offshore wind power collection system topology optimization method and system, method includes: establishing offshore wind power collection system full life cycle cost objective function;Topological initialization generates initial topology and candidate edge set;Candidate edge in candidate list is screened, and active set is obtained;Candidate edge in active set is checked with constraint, candidate edge meeting all constraints enters to be verified set, otherwise, skip the candidate edge;Candidate edge in to-be-verified set is checked with anti-crossing constraint and capacity constraint, candidate edge passing through anti-crossing constraint and capacity constraint is added to merging set, each candidate edge in merging set is merged, form new topology, obtain the final optimized offshore wind power system topology, utilize the optimized offshore wind power system topology to connect each fan;The application has the advantages that: full life cycle cost optimization, anti-crossing engineering constraint and global search capability are considered.

Description

Technical Field

[0001] This invention relates to the field of new energy power system planning and optimization technology, specifically to a method and system for topology optimization of offshore wind power collection systems. Background Technology

[0002] As offshore wind farms develop towards large-scale and offshore deployment, the number of wind turbines is constantly increasing, and the submarine cable connections of the on-site power collection system are becoming increasingly complex. As a crucial power transmission network connecting various wind turbine nodes to offshore substations, the topology of the offshore wind power collection system directly impacts cable construction costs, cable procurement costs, operating losses, and system reliability, thus necessitating its optimization design. Topology optimization for offshore wind power collection systems faces challenges such as increased cable investment costs and the difficulty in meeting complex engineering constraints. While the classic Esau-Williams algorithm has certain advantages, it is prone to getting trapped in local optima under complex engineering constraints and struggles to meet practical engineering requirements such as preventing cross-connection.

[0003] In the area of ​​topology optimization solutions for offshore wind power collector systems, the Esau-Williams algorithm is a classic heuristic method for topology generation. Starting from an initial topology, it gradually reduces wiring costs by replacing node-to-root node connections with node-to-node connections, offering high computational efficiency. However, this algorithm inherently employs a greedy decision-making strategy, which can easily lead to local optima in medium- to large-scale wind farms and under complex engineering constraints, resulting in insufficient global economic efficiency in the final topology solution.

[0004] Furthermore, in practical offshore wind farm engineering, submarine cable crossings are typically not permitted. If submarine cables cross within the collector system, it not only increases the difficulty of laying and maintenance but may also cause faults due to mechanical stress or thermal effects, thus affecting the long-term operational reliability of the system. Therefore, anti-crossing constraints have become one of the important engineering constraints in collector system topology optimization. However, the classic Esau-Williams algorithm, in its basic form, does not effectively handle this constraint and is difficult to directly meet the needs of engineering applications. Summary of the Invention

[0005] The technical problem to be solved by this invention is how to provide a method and system for optimizing the topology of offshore wind power collection systems that can simultaneously take into account full life cycle cost optimization, anti-cross-engineering constraints, and global search capabilities.

[0006] This invention solves the above-mentioned technical problems through the following technical means: a topology optimization method for offshore wind power collection systems, comprising: S1. Establish the objective function for the full life cycle cost of offshore wind power collection systems; S2. Perform topology initialization to generate an initial topology and a candidate edge set, and sort all candidate edges in the candidate edge set to generate a candidate list; S3. Filter the candidate edges in the candidate list to obtain the active set; S4. Perform constraint checks on the candidate edges in the activation set. Candidate edges that satisfy all constraints are added to the set to be verified; otherwise, the candidate edge is skipped. S5. Apply anti-crossing constraints and capacity constraints to the candidate edges in the set to be verified. Add the candidate edges that pass the anti-crossing constraints and capacity constraints to the merge set. Merge the candidate edges in the merge set to form a new topology. Return the new topology as the initial topology to S2. Iterate continuously until the maximum number of iterations is reached or the value of the objective function no longer decreases. Stop the iteration to obtain the final optimized offshore wind power system topology. Use the optimized offshore wind power system topology to connect the various wind turbines.

[0007] Further, S1 includes: Establish the objective function for the entire lifecycle cost of offshore wind power collection systems:

[0008] in, This represents the total cost of an offshore wind farm. , , , These represent cable construction costs, cable procurement costs, energy loss costs, and opportunity costs for failures, respectively.

[0009] Further, S2 includes: Let the set of wind turbine nodes be V The root node set is r The root node is an offshore substation, wherein r ≥1, when the root node set contains only one root node, a single-root-node collector topology is formed; when the root node set contains two or more root nodes, a multi-root-node collector topology is formed. During topology initialization, for each wind turbine node i ∈ V Calculate the connection cost between the wind turbine node and each root node, and initially assign the wind turbine node to the root node with the lowest connection cost. Establish the root node affiliation mapping, and connect the wind turbine node to the corresponding root node through a submarine cable to form the initial topology. In the initial topology, any two nodes form a node pair as a candidate edge, and all candidate edges form a candidate edge set. The saving value is calculated for all candidate edges in the candidate edge set, and all candidate edges are sorted in descending order of saving value to generate a candidate list. The savings are calculated as follows:

[0010] in, For nodes and nodes The savings value of the formed candidate edges, It is a node The cost of connecting to the root node, It is a node and nodes The cost of the connection is calculated by multiplying the cable length by the unit price of the cable.

[0011] Furthermore, S3 includes: S31. Calculate the probability that a candidate edge in the candidate list is selected. ; S32. For each candidate edge Generate random numbers in the range of 0 to 1 If random number Less than or equal to Then candidate edge Selected, enter the active set Otherwise, it will not be included in the activation set. .

[0012] Further, S31 includes: Calculate the probability that a candidate edge in the candidate list is selected. ,in, Indicate candidate edges The probability of being selected. For quantum weights and , For quantum field strength, Candidate edge The corresponding weights It is a node and nodes The resulting candidate edges, Let be the set of candidate edges.

[0013] Furthermore, after S32, it also includes: S33, The quantum field strength is determined according to the formula Update Indicates the first iteration This represents the quantum field strength in the current iteration. This represents the quantum field strength in the next iteration. This represents the attenuation coefficient.

[0014] Further, S31 includes: Calculate the probability that a candidate edge in the candidate list is selected. ,in, Indicate candidate edges The quantum energy difference and , This represents the highest saving value among the saving values ​​of candidate edges in the candidate list. It is the quantum tunneling coefficient. It is the annealing time parameter.

[0015] Furthermore, after S32, it also includes: S33. Adjust the annealing time parameter according to the formula. To be updated, among which, This indicates the preset annealing parameters for the current iteration. This represents the annealing time parameter for the current iteration. This indicates the annealing time parameter for the next iteration.

[0016] Furthermore, the constraint check in S4 includes: Submarine cable current carrying capacity: for candidate edges Through formula Calculate the subtree current of its subtree, where, Represented by node subtree with root Total current, Subtree Any node in, Represents a node power, Indicates the reference voltage; if Then the current carrying capacity of the submarine cable is satisfied, if If the current-carrying capacity of the submarine cable is not met, a potential energy penalty is applied, and the candidate edge is... Probability of being selected Updated to , Indicates the rated current; Submarine cable voltage constraint: Each candidate edge is checked to see if the voltage difference is within the allowable range, and candidate edges that exceed the absolute value of the voltage difference are skipped.

[0017] Furthermore, the anti-crossing constraint and capacity constraint in S5 include: First, perform anti-crossing constraint verification on the line segments corresponding to the candidate edges and existing edges in the initial topology: if the two line segments do not overlap in the coordinate projection interval, they are directly determined not to cross and the subsequent cross product calculation is skipped; if the projection intervals overlap, the cross product judgment is continued. Let the two line segments be from endpoints... and Build, extract endpoint coordinates, calculate

[0018] in, , , , There are four intermediate parameters. This represents the two-dimensional cross product function, used to determine the directional relationship of a point relative to a line segment. Where A, B, and C are plane coordinate points. The X-axis coordinate represents the Mercator projection coordinates of point A. The y-coordinate represents the Mercator projection coordinates of point A. The X-axis coordinates represent the Mercator projection coordinates of point B. The y-coordinate represents the Mercator projection coordinates of point B. The X-axis coordinates represent the Mercator projection coordinates of point C. The y-coordinate represents the Mercator projection coordinates of point C. The cross product of vectors AB and AC is represented by a positive, negative, or zero value, which indicates that point C is located on one side, the other side, or collinear with the directed line segment AB, respectively. When the following conditions are met:

[0019] If the two line segments intersect, the current candidate edge is not accepted; otherwise, the candidate edge is retained and proceeded to the next capacity constraint check. The capacity constraint verification process is as follows: If a candidate edge, after being added to the current topology, causes the corresponding branch to no longer meet the constraint...

[0020] If the candidate edge is rejected, the next candidate edge is selected from the set to be verified, and the process returns to the steps of anti-crossing constraint verification and capacity constraint verification. If the capacity constraint is satisfied, the candidate edge is allowed to enter the merge set. Indicates the first The downstream section of the submarine cable connects to a collection of wind turbines. Indicates wind turbine 'output power' This is the model number of the submarine cable. Indicates the first The rated capacity of the selected submarine cable model for this section of the submarine cable. It represents the power factor angle, which corresponds to the uniform power factor angle of the fan's output power.

[0021] Furthermore, the merging of candidate edges in the merge set to form a new topology includes: For a candidate edge that enters the merge set, first determine whether the two subtrees connected by the candidate edge belong to the same root node. If the two subtrees belong to the same root node, then all wind turbine nodes in the two subtrees are connected to the root node to form a new topology. If two subtrees belong to different root nodes, two cross-root node merging schemes are constructed: The first scheme retains the connection between the first subtree and its original root node, deletes the connection between the second subtree and its original root node, and updates the root node of all wind turbine nodes in the second subtree to the root node of the first subtree; the second scheme retains the connection between the second subtree and its original root node, deletes the connection between the first subtree and its original root node, and updates the root node of all wind turbine nodes in the first subtree to the root node of the second subtree. If both cross-root node merging schemes satisfy the constraint check, anti-crossing constraint, and capacity constraint, the scheme with the smaller value of the life cycle cost objective function is selected for merging; if only one merging scheme satisfies the constraints, the merging scheme that satisfies the constraints is executed; if neither merging scheme satisfies the constraints, the current candidate edge is rejected, thereby updating and forming a new topology.

[0022] This invention also provides a topology optimization system for an offshore wind power collection system, which executes the aforementioned method for topology optimization of an offshore wind power collection system, including: The objective function construction module is used to establish the objective function for the full life cycle cost of offshore wind power collection systems; The initialization module is used to perform topology initialization, generate an initial topology and a candidate edge set, and sort all candidate edges in the candidate edge set to generate a candidate list; The candidate edge filtering module is used to filter the candidate edges in the candidate list and obtain the active set; The constraint checking module is used to perform constraint checks on candidate edges in the activation set. Candidate edges that satisfy all constraints are added to the set to be verified; otherwise, the candidate edge is skipped. The anti-crossing and capacity constraint module is used to apply anti-crossing constraints and capacity constraints to candidate edges in the set to be verified. Candidate edges that pass the anti-crossing and capacity constraints are added to the merge set. The candidate edges in the merge set are merged to form a new topology. The new topology is returned to the initialization module as the initial topology. The iteration continues until the maximum number of iterations is reached or the value of the objective function no longer decreases. The iteration stops, and the final optimized offshore wind power system topology is obtained. The optimized offshore wind power system topology is used to connect the various wind turbines.

[0023] The advantages of this invention are: (1) The present invention performs constraint checks on candidate edges in the activation set. Candidate edges that satisfy all constraints are entered into the set to be verified. Otherwise, the candidate edge is skipped. Anti-crossing constraints and capacity constraints are applied to candidate edges in the set to be verified. When the value of the objective function no longer decreases, the iteration stops, thereby taking into account the whole life cycle cost optimization, anti-crossing engineering constraints and global search capability.

[0024] (2) By introducing a simulated quantum annealing mechanism and drawing on the search idea of ​​quantum annealing in complex combinatorial optimization, this invention significantly enhances the algorithm's ability to escape local optima and improves global search performance. Through dynamic cooling mechanism and quantum field strength adjustment mechanism, it effectively suppresses the expansion of the number of candidate solutions while improving optimization quality and avoiding the dimensionality curse problem. The overall solution is applicable to complex scenarios such as multiple nodes, mixed submarine cable types and mixed equipment, and has strong engineering application value.

[0025] (3) This application has significant advantages over the prior art. Specifically, the core framework of the prior art document 1 (e.g., CN119129153A) is "dynamic partitioning + dynamic edge weight minimum spanning tree DMST + graph genetic algorithm", which first groups wind turbines through scanning method and neighbor mutation, and then searches the topology based on DMST and genetic algorithm; the core framework of the prior art document 2 (e.g., CN114896746A) is "fuzzy clustering partitioning + Voronoi neighbor topology search + improved Dijkstra feeder avoidance", which focuses on solving the problem of crossover between feeders and submarine cables and wind turbine supports after partitioning. This application is based on the improved Esau-Williams value merging framework, and introduces a simulated quantum annealing mechanism in the closed loop of "initial topology generation, candidate edge value sorting, candidate edge probability activation, constraint screening, anti-crossover and capacity verification, and candidate edge merging iteration". Its overall advantage lies in the fact that it does not rely on pre-fixed partitions or the MST / DMST spanning tree framework. Instead, it dynamically controls the probability of candidate edges entering the activation set through parameters such as quantum field strength, annealing time parameter, and quantum energy difference. This allows the algorithm to retain the high computational efficiency of the Esau-Williams method while enhancing its ability to escape local optima. Specific differences in algorithm details mainly include: First, this application... , , , First, this application establishes a candidate edge probability screening mechanism based on parameters such as edge weight, distance, or genetic operators, rather than simply searching by edge weight, distance, or genetic operators. Second, this application sets up an activation set, a verification set, and a merging set to perform hierarchical screening of candidate edges, avoiding an expansion of the number of candidate edges. Third, this application performs current carrying capacity, voltage, anti-crossing, and capacity constraint verification simultaneously before merging candidate edges, ensuring that candidate edges that do not meet engineering constraints cannot enter the merging process. Fourth, this application further adapts to complex engineering scenarios such as multiple nodes, mixed submarine cable models, and mixed wind turbine models, improving the applicability of the solution through dynamic redistribution of root node ownership and submarine cable selection based on downstream load.

[0026] Therefore, the essential difference between this application and the aforementioned prior art is that it does not simply repeat the "anti-crossing + cost reduction" approach, but proposes a topology optimization framework that combines "simulated quantum annealing probability screening mechanism with improved Esau-Williams merging strategy". It also embeds the entire lifecycle cost, engineering constraints and complex scenario expansion capabilities into the iteration process, thereby improving global search capability, engineering adaptability and optimization result quality. Attached Figure Description

[0027] Figure 1 This is a flowchart of a method for topology optimization of an offshore wind power collection system disclosed in an embodiment of the present invention; Figure 2 This is a basic layout diagram of the Walney1 offshore wind farm in a topology optimization method for an offshore wind power collection system disclosed in an embodiment of the present invention. Figure 3 This is a multi-node expansion analysis diagram in a topology optimization method for an offshore wind power collection system disclosed in an embodiment of the present invention; Figure 4 The diagram shows the performance of simulated quantum annealing and simulated annealing iteration in a topology optimization method for offshore wind power collection systems disclosed in this embodiment of the invention. Figure 5 This is a hybrid submarine cable topology diagram of the Walney 1 wind farm in a topology optimization method for an offshore wind power collection system disclosed in an embodiment of the present invention; Figure 6 This is a topology diagram of a 10MW wind turbine hybrid system in the Walney 1 wind farm, as disclosed in an embodiment of the present invention for a topology optimization method for an offshore wind power collection system. Figure 7 The diagram shows the power output of a 15MW wind turbine mixed with the Walney 1 wind farm in a topology optimization method for an offshore wind power collection system disclosed in an embodiment of the present invention. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0029] Example 1 Embodiment 1 of this invention provides a topology optimization method for offshore wind power collection systems. Taking the collection topology design between wind turbine nodes and the root node within an offshore wind farm as the object, and under the engineering constraints of submarine cable current carrying capacity, anti-crossing, and topology feasibility, the method optimizes the topology of the offshore wind power collection system with the goal of minimizing the total lifecycle cost. The specific steps include: S1. Establish the objective function for the full life cycle cost of offshore wind power collection systems. The specific process is as follows: First, establish the objective function for the full lifecycle cost of offshore wind power collection systems:

[0030] in, This represents the total cost of an offshore wind farm. , , , These represent cable construction costs, cable procurement costs, energy loss costs, and opportunity costs for failures, respectively. This objective function allows for the unification of the economics of different topology schemes during both the construction and operation phases within a single evaluation framework.

[0031] The formula for calculating cable construction costs is as follows:

[0032] In the formula, Indicates the first The length of the submarine cable Indicates the total number of submarine cable segments. This represents the cost per unit length of submarine cable laying. Therefore, it is evident that, while meeting engineering constraints, shortening the total length of the submarine cable helps reduce construction costs.

[0033]

[0034] in, It is a function related to the cable power capacity and ， , and It is a cost constant. This refers to the rated power of this type of cable.

[0035]

[0036] in, For grid connection electricity price, For the inflation rate, For the current moment, Where m is the length of the time window, and m is the cable model number. Let represent the power loss of the m-th type submarine cable.

[0037]

[0038] in, Indicates the first wind-like fans, This indicates the total number of wind turbines. The cost of submarine cable failure is calculated using the following formula:

[0039] In the formula, The hourly failure rate of the m-th type submarine cable. The estimated maintenance time for the m-th type submarine cable is... For the first After a fault occurs in section M of the submarine cable, the total output of the downstream wind turbines is reduced. This represents the total number of Class m submarine cables.

[0040] The formula for wind turbine failure cost is:

[0041] In the formula, For the first The hourly failure rate of wind turbines. For the first Estimated maintenance time for air purifiers. For wind turbine 'output power' For the first Total number of wind turbines.

[0042] In scenarios involving mixed submarine cable types, each branch also needs to meet capacity limitations, using the following constraints:

[0043] in, Indicates the first The downstream section of the submarine cable connects to a collection of wind turbines. Indicates the first The rated capacity of the selected submarine cable model for this section of the submarine cable. This represents the power factor angle. Subsequent candidate edge selection and submarine cable type allocation are based on this constraint.

[0044] S2. Perform topology initialization and generate a candidate edge set. Sort all candidate edges in the candidate edge set to generate a candidate list. The specific process is as follows: After establishing the objective function and constraint model, the topology initialization phase begins. Let the set of wind turbine nodes be... V The root node set is r The root node is an offshore substation, wherein r ≥1, when the root node set contains only one root node, a single-root-node collector topology is formed; when the root node set contains two or more root nodes, a multi-root-node collector topology is formed; during topology initialization, for each wind turbine node... i ∈ V The connection costs between each wind turbine node and each root node are calculated, and the node is initially assigned to the root node with the lowest connection cost, establishing a root node affiliation mapping. Simultaneously, the wind turbine node is connected to the corresponding root node via a submarine cable, thus forming the initial topology. At the same time, initial annealing time parameters, initial annealing parameters, maximum number of iterations, and initial quantum field strength are set. The annealing time parameter controls the temperature decrease during classical annealing, and the quantum field strength controls the search depth of candidate edge combinations; both together balance the global search and local convergence process.

[0045] During the candidate list initialization phase, any two nodes in the initial topology form a node pair as a candidate edge, and all candidate edges form a candidate edge set. The saving value is calculated for all candidate edges in the candidate edge set, and all candidate edges are sorted in descending order of saving value to generate the candidate list.

[0046] The savings are calculated as follows:

[0047] in, For nodes and nodes The savings value of the formed candidate edges, It is a node The cost of connecting to the root node, It is a node and nodes The cost of the connection is calculated by multiplying the cable length by the unit price of the cable.

[0048] S3. Filter the candidate edges in the candidate list. S31. Calculate the probability of a candidate edge being selected from the candidate list. There are two methods for calculation: The first type, ,in, Indicate candidate edges The probability of being selected. For quantum weights and , For quantum field strength, Candidate edge The corresponding weights It is a node and nodes The resulting candidate edges, For the candidate edge set; The second type, ,in, Indicate candidate edges The quantum energy difference and , This represents the highest saving value among the saving values ​​of candidate edges in the candidate list. It is the quantum tunneling coefficient (a preset constant that controls the decay rate of the tunneling probability). It is the annealing time parameter.

[0049] S32. For each candidate edge Generate random numbers in the range of 0 to 1 If random number Less than or equal to Then candidate edge Selected, enter the active set Otherwise, it will not be included in the activation set. .

[0050] S33, Parameter Update: When the probability of a candidate edge being selected from the candidate list in S31 is calculated using the first method, the quantum field strength is calculated according to the formula... Update Indicates the first iteration This represents the quantum field strength in the current iteration. This represents the quantum field strength in the next iteration. This represents the attenuation coefficient.

[0051] When the probability of a candidate edge being selected in the candidate list in S31 is calculated using the second method, the annealing time parameter is calculated according to the formula. To be updated, among which, This indicates the preset annealing parameters for the current iteration. This represents the annealing time parameter for the current iteration. This indicates the annealing time parameter for the next iteration; after each iteration, the annealing time parameter decreases exponentially according to the preset annealing parameter. Initially... Smaller, higher tunneling probability, allowing exploration of regions far from the current solution. Later stages. Increasing the value reduces the tunneling probability, focusing on candidate edges with low energy (high savings).

[0052] S4. Perform constraint checks on candidate edges in the activation set, including the following three constraints. Candidate edges that satisfy all constraints are added to the verification set; otherwise, the candidate edge is skipped. The three constraints are as follows: (1) Submarine cable current carrying capacity limitation: for candidate edges Through formula Calculate the subtree current of its subtree, where, Represented by node subtree with root Total current, Subtree Any node in, Represents a node power, Indicates the reference voltage; if Then the current carrying capacity of the submarine cable is satisfied, if If the current-carrying capacity of the submarine cable is not met, a potential energy penalty will be applied. Updated to , Indicates the rated current; (2) Coverage constraint and branch independence constraint: Ensure that each fan is connected to a unique branch and that all fans belong to a certain branch, thus guaranteeing the independence of the branch.

[0053] (3) Submarine cable voltage constraint: Each cable segment (i.e. each candidate edge) needs to check whether the voltage difference is within the allowable range. Candidate edges that exceed the absolute value of the voltage difference are skipped.

[0054] S5. Apply anti-crossing constraints and capacity constraints to the candidate edges in the verification set. Add the candidate edges that pass the anti-crossing constraints and capacity constraints to the merge set. For the candidate edges that enter the merge set, first determine whether the two subtrees connected by the candidate edge belong to the same root node. If the two subtrees belong to the same root node, then connect all the wind turbine nodes in the two subtrees to the root node to form a new topology. If two subtrees belong to different root nodes, two cross-root node merging schemes are constructed: The first scheme retains the connection between the first subtree and its original root node, deletes the connection between the second subtree and its original root node, and updates the root node of all wind turbine nodes in the second subtree to the root node corresponding to the first subtree; the second scheme retains the connection between the second subtree and its original root node, deletes the connection between the first subtree and its original root node, and updates the root node of all wind turbine nodes in the first subtree to the root node corresponding to the second subtree. If both cross-root node merging schemes satisfy the constraint check, anti-crossing constraint, and capacity constraint, the scheme with the smaller value of the life cycle cost objective function is selected for merging; if only one merging scheme satisfies the constraints, the merging scheme that satisfies the constraints is executed; if neither merging scheme satisfies the constraints, the current candidate edge is rejected, thereby updating and forming a new topology. The new topology is used as the initial topology and returned to step S2. The iteration continues until the maximum number of iterations is reached or the value of the objective function no longer decreases, at which point the iteration stops, and the final offshore wind power system topology is obtained. The specific process is as follows: To improve efficiency, we first perform anti-crossing constraint checks on candidate edges and existing edges (existing edges refer to edges in the initial topology). If the two line segments do not overlap within the coordinate projection interval, we directly determine that they do not intersect and skip the subsequent cross product calculation. If the projection intervals overlap, we continue with the cross product determination. Let the two line segments originate from endpoints... and To construct the system, first extract the endpoint coordinates and then calculate:

[0055] in, , , , There are four intermediate parameters. This represents the two-dimensional cross product function, used to determine the directional relationship of a point relative to a line segment. Where A, B, and C are plane coordinate points. The X-axis coordinate represents the Mercator projection coordinates of point A. The y-coordinate represents the Mercator projection coordinates of point A. The X-axis coordinates represent the Mercator projection coordinates of point B. The y-coordinate represents the Mercator projection coordinates of point B. The X-axis coordinates represent the Mercator projection coordinates of point C. The y-axis coordinate represents the Mercator projection coordinates of point C; This represents the two-dimensional cross product of vectors AB and AC. The result is positive, negative, or zero, indicating that point C is located on one side, the other side, or collinear with the directed line segment AB, respectively.

[0056] When the following conditions are met:

[0057] If the two line segments intersect, the current candidate edge is rejected; otherwise, the candidate edge is retained for the next capacity constraint check. This process ensures that the generated collector system topology meets the anti-intersection engineering requirements.

[0058] After determining the anti-crossing behavior, candidate edges are then validated based on capacity constraints. If a candidate edge, after being added to the current topology, causes the corresponding branch to no longer meet the requirements...

[0059] If the candidate edge is rejected, the next candidate edge is selected from the set to be verified, and the process returns to the steps of anti-cross-validation and capacity constraint verification. If the capacity constraint is satisfied, the candidate edge is allowed to enter the merge set.

[0060] Merge each candidate edge in the merge set to form a new topology, and return to step S2 as the initial topology; stop iterating until the maximum number of iterations is reached or the value of the objective function no longer decreases, and obtain the final optimized offshore wind power system topology, and use the optimized offshore wind power system topology to connect each wind turbine.

[0061] In multi-node scenarios, after each cross-node subtree merging, the root node affiliation, downstream power of branches, submarine cable capacity requirements, and candidate edge set are updated to ensure that any updated connected subtree connects to only one root node. This also extends the topology optimization from single-node to multi-node topology optimization within a unified algorithm framework. This approach makes the invention applicable to medium-to-large-scale offshore wind farms where multiple offshore booster stations participate in power collection.

[0062] In scenarios involving the expansion of mixed submarine cable models, determining the appropriate cable specification for a given branch requires calculating the number of downstream wind turbines and the downstream power aggregation result. Under a chain topology, determining upstream and downstream relationships is a directed tree traversal problem; therefore, a hierarchical load tracing method based on depth-first search can be used to resolve parent-child relationships and accumulate loads for the current topology. For a given branch, its downstream power can be aggregated according to the set of downstream nodes, and then, based on the aforementioned capacity constraints, a submarine cable model that meets current-carrying requirements and has a lower cost can be selected. This allows for the hierarchical configuration of multiple cable specifications in different branches, improving the economy and feasibility of mixed equipment scenarios.

[0063] In summary, this invention combines a full lifecycle cost model, an anti-crossing improved Esau-Williams algorithm, and a simulated quantum annealing mechanism. While maintaining strict adherence to engineering constraints, it enhances the global search capability, adaptability to complex scenarios, and engineering implementation capability of offshore wind power collection systems. This effectively reduces the full lifecycle cost of the system and improves the reliability and feasibility of the cabling scheme.

[0064] To verify the effectiveness of the proposed method for topology optimization of offshore wind power collection systems based on simulated quantum annealing and anti-cross-connection improved Esau-Williams algorithm, the following example is provided using the Walney1 offshore wind farm. This invention analyzes and verifies the method from the perspectives of multiple node expansion, mixed submarine cable types, and mixed wind turbine and submarine cable types, focusing on the Walney1 wind farm. Figure 2 This is a basic layout diagram of the Walney 1 offshore wind farm.

[0065] In each simulation case, the node layout of the Walney1 offshore wind farm is used as the basic input to optimize the topology of the power collection system. The total length of submarine cable, submarine cable procurement cost, submarine cable laying cost, comprehensive cost and opportunity cost of failure are analyzed to illustrate the feasibility and superiority of the method of the present invention under complex engineering constraints.

[0066] Simulation Case 1: Topology Optimization of Collector System in Multi-Node Extension Scenario In this embodiment, addressing the challenge of a single offshore booster station in a large-scale offshore wind farm simultaneously achieving both collection distance and load balancing, multiple root nodes are set up on the Walney1 offshore wind farm to construct a multi-root-node expansion scenario. This verifies the topology optimization capability of the method under the condition of coordinated operation of multiple booster stations. In the multi-root-node scenario, the root node set must first be input, and each wind turbine node is initially connected to the nearest root node to form an initial topology. Subsequently, the node affiliation is dynamically updated during the subtree merging process.

[0067] Figure 2 This diagram illustrates the basic node distribution of the Walney 1 offshore wind farm. It visually shows the spatial relationships of each turbine node in the sea area, as well as the geometric basis upon which subsequent multi-node partitioning, nearest-root node mapping, and branch connection optimization rely. When the turbine node distribution area is large, using a single-node aggregation method can easily lead to long gate edges and unbalanced branches; a multi-node scheme is more conducive to shortening local aggregation distances and creating conditions for subsequent subtree redistribution.

[0068] In the implementation process, the nearest root node mapping is first established based on the spatial distance relationship between wind turbine nodes and multiple root nodes, and each wind turbine node is assigned to a corresponding region. Then, within each root node's corresponding region, candidate edge saving value calculation, priority queue screening, anti-crossing discrimination, and simulated quantum annealing probability selection processes are performed, forming a subtree for each root node's corresponding region. When a subtree merges with another subtree across root nodes, the connection relationship between the merged subtree and each root node is recalculated, and two schemes for retaining connections between two different root nodes are evaluated. One scheme is selected based on cost and constraints to ensure that each subtree is ultimately connected to only one root node. This approach avoids problems such as long door edge retention, uneven branch division, and low local aggregation efficiency that occur in traditional single-root node models in large-scale scenarios.

[0069] Figure 3 This is used to demonstrate typical topology results after expanding with multiple root nodes. Figure 3 It can be seen that when multiple root nodes participate in the aggregation, the wind turbine nodes no longer form long-distance connections around a single root node, but instead form a more balanced chain or branch topology based on local spatial relationships. Figure 3 The invention demonstrates that its method can bypass unreasonable long chain structures caused by local constraints in multi-root node scenarios, allowing some nodes that were originally directly connected to the root node to converge through optimized branches, thereby reducing the overall wiring length and improving topology balance. Typical results show that, under a simulated quantum annealing capacity limit of 5, the method generates a total topology weight of 40.11 km, exhibiting a superior connection structure compared to the comparative scheme.

[0070] Furthermore, in the aforementioned topology optimization process, the method of this invention does not immediately complete the merging based solely on the maximum saving value in a single step. Instead, under the premise of satisfying anti-crossing and capacity constraints, it retains several candidate connection paths with competing relationships and performs probabilistic screening through a simulated quantum annealing mechanism. This not only expands the search range of feasible solutions but also avoids the premature solidification of local connection structures in the early iteration stages, thereby improving the overall optimization capability in multi-root node scenarios.

[0071] Figure 4This figure further illustrates the iterative search characteristics of the method in multi-root node scenarios. As shown in the figure, simulated quantum annealing can quickly reduce the target value in the early stages of iteration, and at several key iteration points, it escapes the local optimum by accepting suboptimal solutions, ultimately converging to a better overall cost result. This figure not only reflects the convergence process of the method but also demonstrates that under complex multi-root node conditions, the algorithm maintains good global search capability and relatively stable late-stage convergence performance. The results show that the EW algorithm improved with simulated quantum annealing ultimately converges to 207.6686 million yuan, while the EW algorithm improved with simulated annealing converges to 211.3987 million yuan, indicating that the method of this invention has advantages in overall cost optimization.

[0072] In summary, in multi-root node expansion scenarios, the method of this invention can effectively improve the problems of long gate edges, unbalanced branches, and local optima in traditional single-root node topologies through nearest-nearest-root node initialization, dynamic merging across subtrees, node ownership redistribution, and simulated quantum annealing global search mechanism. It is applicable to medium and large-scale offshore wind farm scenarios in which multiple offshore booster stations participate in the aggregation.

[0073] Simulation Case 2: Topology Optimization of the Power Collection System in a Scenario Involving Mixed Submarine Cable and Mixed Wind Turbine Models In this embodiment, the heterogeneous equipment configuration problem commonly found in offshore wind farms in actual engineering is further considered, namely, different branches use submarine cables of different specifications, and some areas are connected to large-capacity demonstration wind turbines, thereby verifying the adaptability of the method of the present invention in scenarios involving mixed submarine cable models and mixed wind turbine models. Next, the scenarios involving mixed submarine cable models and mixed 10MW and 15MW demonstration wind turbines combined with multiple specifications of submarine cables are analyzed.

[0074] During implementation, firstly, upstream and downstream identification is performed on each branch based on the generated topology, and a hierarchical load tracing method based on depth-first search is used to calculate the downstream aggregation power of each branch. Then, based on the matching relationship between branch capacity requirements and submarine cable rated capacity, submarine cables of appropriate specifications are allocated to different branches. Simultaneously, in the scenario of mixed wind turbines, different node weights are assigned to wind turbines with different rated capacities, so that they reflect differentiated load requirements during candidate edge selection, branch aggregation, and submarine cable configuration. Through the above methods, joint optimization of "wind turbine capacity differentiation—branch load differentiation—submarine cable model differentiation" can be achieved under heterogeneous equipment conditions.

[0075] The table below shows the parameter differences of three typical submarine cables in a mixed submarine cable configuration: Table 1. Parameters of Medium Voltage Submarine Cable Equipment

[0076] The maximum current carrying capacity of the 3×70 mm² submarine cable is 210 A, with a cable unit price of 816 yuan / m and a laying cost of 307 yuan / m; the maximum current carrying capacity of the 3×185 mm² submarine cable is 366 A, with a cable unit price of 1270 yuan / m and a laying cost of 381 yuan / m; and the maximum current carrying capacity of the 3×400 mm² submarine cable is 542 A, with a cable unit price of 1900 yuan / m and a laying cost of 430 yuan / m. Therefore, while using large-section submarine cables for all branches would provide a higher capacity safety margin, it would significantly increase procurement and laying costs. Thus, a tiered configuration based on the downstream load level of each branch is necessary.

[0077] Figure 5 This diagram illustrates representative topology results for scenarios involving mixed submarine cable types. Compared to topologies with more branch splits under low capacity constraints, this diagram shows that under medium to high capacity constraints, some branches can be further merged, the trunk and branches are more concentrated, and the topology structure tends to be stable. The diagram also visually demonstrates the configuration hierarchy after different branches use submarine cables of different specifications, making the hierarchical deployment logic of "using larger cross-section submarine cables for trunk branches and smaller cross-section submarine cables for terminal branches" clearer. The results show that, in the mixed submarine cable scenario, as the capacity limit increases from 9 to 14, the total length of the submarine cable decreases from 41.13 km to 39.25 km, the procurement cost of the submarine cable decreases from RMB 51,292,720 to RMB 47,097,020, the laying cost of the submarine cable decreases from RMB 14,888,440 to RMB 14,043,150, and the total cost of the submarine cable decreases from RMB 66,181,160 to RMB 61,140,170. This indicates that the method of the present invention can continuously optimize the topology under relaxed capacity constraints, while avoiding the local optimum phenomenon in the traditional EW algorithm where "the constraints are more relaxed but the results are worse".

[0078] Furthermore, in the mixed-model wind turbine scenario, this embodiment adds four demonstration wind turbines to the periphery of the original Walney1 wind turbine cluster, constructing two scenarios: 10MW and 15MW. The location coordinates of the four demonstration wind turbines are (470.8, 5988.4), (465.2, 5993.4), (466.15, 5984), and (463.35, 5986.5), respectively. In the 10MW scenario, the weight of the demonstration wind turbines is set to twice that of ordinary 5MW wind turbines; in the 15MW scenario, the overall power output limit of the wind farm is further increased, significantly enhancing the requirements for trunk and branch line loads and submarine cable specifications.

[0079] Figure 6This diagram illustrates the changes in topology after a 10MW demonstration wind turbine is connected. As can be seen, the introduction of large-capacity wind turbines in the periphery alters the convergence relationships of some main and branch paths. The algorithm needs to reallocate local connection paths while ensuring cross-connection prevention and capacity safety. This diagram primarily serves to demonstrate that the method of this invention can still produce a clear and highly implementable topology even in scenarios with mixed wind turbine capacities.

[0080] Based on the above, as the capacity of the demonstration wind turbines further increases to 15MW and the branch load level continues to increase, the algorithm needs to further optimize the configuration of the trunk path and the location of large-section submarine cables to ensure that the power collection system after the connection of higher capacity wind turbines still meets engineering constraints and maintains better overall performance.

[0081] Figure 7 This diagram illustrates the power or load distribution in a 15MW scenario. As shown in the figure, with the addition of higher-capacity wind turbines, the overall power output of the wind farm increases from 255 MW to 315 MW, and the branch load level increases accordingly. Results indicate that under typical conditions with a capacity limit of 7, the generated topology uses 15.07 km of 3×70 mm² submarine cable, 17.90 km of 3×185 mm² submarine cable, and 18.37 km of 3×400 mm² submarine cable, for a total length of 51.34 km. Although the total cable length and failure probability loss increase, the equivalent annual power loss is still slightly better than the original Walney 1 wind farm scenario, demonstrating that the method of this invention still has good adaptability and engineering feasibility in high-capacity demonstration wind turbine integration scenarios.

[0082] In summary, in the combined scenario of mixed submarine cable models and mixed wind turbine models, the method of this invention can achieve topology optimization of the power collection system under complex heterogeneous equipment conditions through branch upstream and downstream load tracking, hierarchical configuration of submarine cables, and differentiated processing of node weights, demonstrating strong scalability and engineering application value.

[0083] Example 2 Based on Embodiment 1, Embodiment 2 of the present invention provides a topology optimization system for an offshore wind power collection system, which executes the topology optimization method for an offshore wind power collection system described in Embodiment 1, including: The objective function construction module is used to establish the objective function for the full life cycle cost of offshore wind power collection systems; The initialization module is used to perform topology initialization, generating the initial topology and candidate edge set; The candidate edge filtering module is used to filter the candidate edges in the candidate list and obtain the active set; The constraint checking module is used to perform constraint checks on candidate edges in the activation set. Candidate edges that satisfy all constraints are added to the set to be verified; otherwise, the candidate edge is skipped. The anti-crossing and capacity constraint module is used to apply anti-crossing constraints and capacity constraints to candidate edges in the set to be verified. Candidate edges that pass the anti-crossing and capacity constraints are added to the merge set. The candidate edges in the merge set are merged to form a new topology. The new topology is returned to the initialization module as the initial topology. The iteration continues until the maximum number of iterations is reached or the value of the objective function no longer decreases. The iteration stops, and the final optimized offshore wind power system topology is obtained. The optimized offshore wind power system topology is used to connect the various wind turbines.

[0084] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A topology optimization method for an offshore wind power collection system, characterized in that, include: S1. Establish the objective function for the full life cycle cost of offshore wind power collection systems; S2. Perform topology initialization to generate an initial topology and a candidate edge set, and sort all candidate edges in the candidate edge set to generate a candidate list; S3. Filter the candidate edges in the candidate list to obtain the active set; S4. Perform constraint checks on the candidate edges in the activation set. Candidate edges that satisfy all constraints are added to the set to be verified; otherwise, the candidate edge is skipped. S5. Apply anti-crossing constraints and capacity constraints to the candidate edges in the set to be verified. Add the candidate edges that pass the anti-crossing constraints and capacity constraints to the merge set. Merge the candidate edges in the merge set to form a new topology. Return the new topology as the initial topology to S2. Iterate continuously until the maximum number of iterations is reached or the value of the objective function no longer decreases. Stop the iteration to obtain the final optimized offshore wind power system topology. Use the optimized offshore wind power system topology to connect the various wind turbines.

2. The method for topology optimization of an offshore wind power collection system according to claim 1, characterized in that, S1 includes: Establish the objective function for the entire lifecycle cost of offshore wind power collection systems: in, This represents the total cost of an offshore wind farm. , , , These represent cable construction costs, cable procurement costs, energy loss costs, and opportunity costs for failures, respectively.

3. The method for topology optimization of an offshore wind power collection system according to claim 1, characterized in that, S2 includes: Let the set of wind turbine nodes be V The root node set is r The root node is an offshore substation, wherein r ≥1, during topology initialization, for each wind turbine node i ∈ V Calculate the connection cost between the wind turbine node and each root node, and initially assign the wind turbine node to the root node with the lowest connection cost. Establish the root node affiliation mapping, and connect the wind turbine node to the corresponding root node through a submarine cable to form the initial topology. In the initial topology, any two nodes form a node pair as a candidate edge, and all candidate edges form a candidate edge set. The saving value is calculated for all candidate edges in the candidate edge set, and all candidate edges are sorted in descending order of saving value to generate a candidate list. The savings are calculated as follows: in, For nodes and nodes The savings value of the formed candidate edges, It is a node The cost of connecting to the root node, It is a node and nodes The cost of the connection is calculated by multiplying the cable length by the unit price of the cable.

4. The method for topology optimization of an offshore wind power collection system according to claim 3, characterized in that, S3 includes: S31. Calculate the probability that a candidate edge in the candidate list is selected. ; S32. For each candidate edge Generate random numbers in the range of 0 to 1 If random number Less than or equal to Then candidate edge Selected, enter the active set Otherwise, it will not be included in the activation set. .

5. The method for topology optimization of an offshore wind power collection system according to claim 4, characterized in that, S31 includes: Calculate the probability that a candidate edge in the candidate list is selected. ,in, Indicate candidate edges The probability of being selected. For quantum weights and , For quantum field strength, Candidate edge The corresponding weights It is a node and nodes The resulting candidate edges, Let be the set of candidate edges.

6. The method for topology optimization of an offshore wind power collection system according to claim 5, characterized in that, Following S32, the following is also included: S33, The quantum field strength is determined according to the formula Update Indicates the first iteration This represents the quantum field strength in the current iteration. This represents the quantum field strength in the next iteration. This represents the attenuation coefficient.

7. The method for topology optimization of an offshore wind power collection system according to claim 4, characterized in that, S31 includes: Calculate the probability that a candidate edge in the candidate list is selected. ,in, Indicate candidate edges The quantum energy difference and , This represents the highest saving value among the saving values ​​of candidate edges in the candidate list. It is the quantum tunneling coefficient. It is the annealing time parameter.

8. The method for topology optimization of an offshore wind power collection system according to claim 7, characterized in that, Following S32, the following is also included: S33. Adjust the annealing time parameter according to the formula. To be updated, among which, This indicates the preset annealing parameters for the current iteration. This represents the annealing time parameter for the current iteration. This indicates the annealing time parameter for the next iteration.

9. A method for topology optimization of an offshore wind power collection system according to claim 4, characterized in that, The constraint check in S4 includes: Submarine cable current carrying capacity: for candidate edges Through formula Calculate the subtree current of its subtree, where, Represented by node subtree with root Total current, Subtree Any node in, Represents a node power, Indicates the reference voltage; if Then the current carrying capacity of the submarine cable is satisfied, if If the current-carrying capacity of the submarine cable is not met, a potential energy penalty is applied, and the candidate edge is... Probability of being selected Updated to , Indicates the rated current; Submarine cable voltage constraint: Each candidate edge is checked to see if the voltage difference is within the allowable range, and candidate edges that exceed the absolute value of the voltage difference are skipped.

10. A method for topology optimization of an offshore wind power collection system according to claim 4, characterized in that, The anti-crossing constraints and capacity constraints in S5 include: First, perform anti-crossing constraint verification on the line segments corresponding to the candidate edges and existing edges in the initial topology: if the two line segments do not overlap in the coordinate projection interval, they are directly determined not to cross and the subsequent cross product calculation is skipped; if the projection intervals overlap, the cross product judgment is continued. Let the two line segments be from endpoints... and Build, extract endpoint coordinates, calculate in, , , , There are four intermediate parameters. This represents the two-dimensional cross product function, used to determine the directional relationship of a point relative to a line segment. Where A, B, and C are plane coordinate points. The X-axis coordinate represents the Mercator projection coordinates of point A. The y-coordinate represents the Mercator projection coordinates of point A. The X-axis coordinates represent the Mercator projection coordinates of point B. The y-coordinate represents the Mercator projection coordinates of point B. The X-axis coordinates represent the Mercator projection coordinates of point C. The y-coordinate represents the Mercator projection coordinates of point C. The cross product of vectors AB and AC is represented by a positive, negative, or zero value, which indicates that point C is located on one side, the other side, or collinear with the directed line segment AB, respectively. When the following conditions are met: If the two line segments intersect, the current candidate edge is not accepted; otherwise, the candidate edge is retained and proceeded to the next capacity constraint check. The capacity constraint verification process is as follows: If a candidate edge, after being added to the current topology, causes the corresponding branch to no longer meet the constraint... If the candidate edge is rejected, the next candidate edge is selected from the set to be verified, and the process returns to the steps of anti-crossing constraint verification and capacity constraint verification. If the capacity constraint is satisfied, the candidate edge is allowed to enter the merge set. Indicates the first The downstream section of the submarine cable connects to a collection of wind turbines. Indicates wind turbine 'output power' This is the model number of the submarine cable. Indicates the first The rated capacity of the selected submarine cable model for this section of the submarine cable. It represents the power factor angle.

11. The method for topology optimization of an offshore wind power collection system according to claim 1, characterized in that, The process of merging candidate edges in the merge set to form a new topology includes: For a candidate edge that enters the merge set, first determine whether the two subtrees connected by the candidate edge belong to the same root node. If the two subtrees belong to the same root node, then all wind turbine nodes in the two subtrees are connected to the root node to form a new topology. If two subtrees belong to different root nodes, two cross-root node merging schemes are constructed: The first scheme retains the connection between the first subtree and its original root node, deletes the connection between the second subtree and its original root node, and updates the root node of all wind turbine nodes in the second subtree to the root node of the first subtree; the second scheme retains the connection between the second subtree and its original root node, deletes the connection between the first subtree and its original root node, and updates the root node of all wind turbine nodes in the first subtree to the root node of the second subtree. If both cross-root node merging schemes satisfy the constraint check, anti-crossing constraint, and capacity constraint, the scheme with the smaller value of the life cycle cost objective function is selected for merging; if only one merging scheme satisfies the constraints, the merging scheme that satisfies the constraints is executed; if neither merging scheme satisfies the constraints, the current candidate edge is rejected, thereby updating and forming a new topology.

12. A topology optimization system for an offshore wind power collection system, comprising executing the topology optimization method for an offshore wind power collection system as described in any one of claims 1-11, characterized in that, include: The objective function construction module is used to establish the objective function for the full life cycle cost of offshore wind power collection systems; The initialization module is used to perform topology initialization, generate an initial topology and a candidate edge set, and sort all candidate edges in the candidate edge set to generate a candidate list; The candidate edge filtering module is used to filter the candidate edges in the candidate list and obtain the active set; The constraint checking module is used to perform constraint checks on candidate edges in the activation set. Candidate edges that satisfy all constraints are added to the set to be verified; otherwise, the candidate edge is skipped. The anti-crossing and capacity constraint module is used to apply anti-crossing constraints and capacity constraints to candidate edges in the set to be verified. Candidate edges that pass the anti-crossing and capacity constraints are added to the merge set. The candidate edges in the merge set are merged to form a new topology. The new topology is returned to the initialization module as the initial topology. The iteration continues until the maximum number of iterations is reached or the value of the objective function no longer decreases. The iteration stops, and the final optimized offshore wind power system topology is obtained. The optimized offshore wind power system topology is used to connect the various wind turbines.

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