Offshore wind plant current collection line economic arrangement method based on dynamic partition optimization

Abstract

According to the economic arrangement method for the current collection line of the offshore wind plant based on dynamic partition optimization, the topological optimization problem of a current collection system is converted into the minimum spanning tree problem, a dynamic edge weight minimum spanning tree algorithm is introduced, and on the basis of an existing minimum spanning tree, edge addition and deletion operation is dynamically processed so as to keep updating of the minimum spanning tree. According to the method, the algorithm is applied, and submarine cable type selection and submarine cable cross avoidance functions are added, so that a radial topological structure is formed. And dynamic partition design: for the condition of multiple fans or multiple booster stations, performing dynamic partition by utilizing fan grouping based on a scanning method and fan grouping based on adjacent position variation, and improving the optimization speed. Compared with a traditional algorithm, the economic arrangement method for the current collection lines of the offshore wind power plant based on dynamic partition optimization can converge to a better current collection system design scheme more quickly, and the full life cycle cost of the current collection system is remarkably reduced.

Description

Technical Field

[0001] The present invention relates to the offshore wind power field, and in particular to an economical arrangement method of offshore wind farm collector lines based on dynamic zoning optimization. Background Art

[0002] Compared with onshore wind power, the offshore wind power collection system has the following characteristics: (1) The submarine cables in the offshore wind power collection system are mainly laid on the seabed, which has fewer constraints than the onshore wiring. At the same time, since the laying of submarine cables does not require the protective infrastructure of the laying of land cables, the wiring of the offshore wind farm collection system is more flexible than that of the onshore wind farm. (2) The main cost of onshore wind power is the cost of the wind turbine, and the cost of the collection system accounts for about 10%. Offshore wind power uses more expensive submarine cables to collect electricity, and the distance between wind turbines is greater. Therefore, the cost of the offshore wind power collection system is higher, accounting for 20%-30% of the total cost of the offshore wind farm.

[0003] With the rapid development of renewable energy, especially offshore wind power technology, how to effectively reduce the construction and operation costs of offshore wind farms has become a research hotspot. As an important component connecting wind farms and power grids, the optimal design of the power collection system is directly related to the economy and reliability of the entire wind farm.

[0004] However, traditional power collection system design methods often rely on experience or relatively simple optimization algorithms, which makes it difficult to fully consider the complex constraints of the power collection system, such as the non-crossing of submarine cables and current carrying capacity restrictions, resulting in suboptimal system design and excessively high costs. The present invention proposes an economic layout method for offshore wind farm power collection lines based on dynamic partition optimization, which can provide a better wiring scheme for different wind farm layouts and optimize its economy and reliability.

[0005] The present application is different from the prior art as follows:

[0006] Technical comparison with patent CN112909981A_A method for economic optimization of electrical collection system design for large offshore wind farms

[0007] 1. The algorithm used in CN112909981A;

[0008] Patent CN112909981A proposes an optimization scheme for the electrical collection system of a large offshore wind farm. The method mainly uses a regional radial fuzzy clustering algorithm to segment wind turbines and uses the Prim algorithm to find the optimal cable topology path. The specific steps include:

[0009] The wind turbines are divided into regions using a fuzzy clustering algorithm to reduce the complexity of cable connections between wind turbines.

[0010] The shortest path spanning tree is generated using the Prim algorithm to optimize the cable connection path between the wind turbine and the offshore substation.

[0011] Under different slicing methods, the investment cost, maintenance cost and loss cost of the collection system are calculated, and the solution with the best total cost is selected.

[0012] This method uses classic clustering and shortest path algorithms in cable topology optimization, which can solve the optimization problem of wind turbine cable connection paths to a certain extent. However, its optimization process mainly focuses on finding the optimal path in fixed partitions and static networks, and fails to fully consider the situation where cable costs change with the dynamic changes of the system. In addition, in the case of large and complex wind farms, the optimization efficiency is limited.

[0013] 2. The method of the present invention;

[0014] This paper proposes an economic layout method for offshore wind farm collection lines based on dynamic partition optimization, which uses a dynamic edge weighted minimum spanning tree (DMST) algorithm combined with a graph genetic algorithm to achieve full life cycle cost optimization of the wind farm collection system. The core innovations of the method include:

[0015] Dynamic partition design: When the distribution of wind turbines and booster stations is more complex, the scanning method and adjacent mutation algorithm are used to group wind turbines. The partition scheme can be dynamically adjusted according to the actual system to improve the optimization speed.

[0016] DMST algorithm: The DMST algorithm is an improvement on the Prim algorithm, taking into account the relationship between the current carrying capacity of submarine cables and dynamic edge weights. It is not only based on distance, but also combines cable selection, cost changes and other factors to dynamically optimize the spanning tree. Compared with the static Prim algorithm in CN112909981A, the DMST algorithm can handle system changes and improves adaptability to complex topologies.

[0017] Graph Genetic Algorithm: Combining the elite selection method, crossover operator and mutation operator design in the genetic algorithm, the global search capability is enhanced, and the computational efficiency and solution quality of the algorithm are improved by improving the encoding method.

[0018] 3. Comparison of technical advantages

[0019] Algorithm flexibility: The DMST algorithm in the present invention can handle complex constraints such as cable current carrying capacity and submarine cable selection, dynamically adjust edge weights, and optimize results that are more in line with actual conditions. In contrast, the Prim algorithm in CN112909981A is a static algorithm that fails to dynamically adapt to cost changes caused by cable selection.

[0020] Global optimization capability: The present invention introduces a graph genetic algorithm, generates an initial population through the DMST algorithm in the initial stage, and further optimizes the topological structure through elite selection and crossover mutation mechanisms, which can jump out of the local optimum and find a better global solution. However, CN112909981A mainly relies on exhaustive methods and local optimization, and has a large dimensionality curse problem.

[0021] Cost optimization effect: The method of the present invention takes into account the full life cycle cost of the collector line (including equipment procurement costs, construction costs, maintenance costs, loss costs, etc.), and the optimization result is more economical and reliable. Examples show that the system cost after optimization by this method is lower than that of the method of CN112909981A.

[0022] In summary, the economical layout method of offshore wind farm collection lines based on dynamic partition optimization of the present invention is superior to CN112909981A in terms of algorithm flexibility, global optimization capability and cost optimization effect, and can provide a more economical and reliable collection system design solution for offshore wind farms. Summary of the invention

[0023] In order to solve the above technical problems, the present invention proposes an economical layout method for offshore wind farm collection lines based on dynamic partition optimization. By introducing a dynamic variable weight strategy and a special encoding mechanism, coupled with carefully designed crossover and mutation operations, and supplemented by dynamic partitioning, the search efficiency and solution quality of the graph genetic algorithm in the topology optimization of offshore wind farm collection systems are significantly improved. In addition, the present invention also takes into account constraints such as submarine cable length, cable capacity, and total system cost, thereby ensuring that the obtained optimization solution is superior to traditional methods in terms of economy and reliability.

[0024] To achieve the above object, the technical solution adopted by the present invention is:

[0025] The economical layout method of offshore wind farm collector lines based on dynamic partition optimization has the following specific steps:

[0026] (1) A mathematical model is established to transform the topology optimization problem of the power collection system into an MST problem, where vertices represent wind turbines or booster stations, edges represent submarine cables, and edge weights are the costs of submarine cables. Considering the changes in edge weights, the DMST algorithm is introduced to dynamically process the addition and deletion of edges to keep the minimum spanning tree updated. The functions of submarine cable selection and submarine cable crossing avoidance are also added to form a radial topology structure.

[0027] (2) Dynamic zoning design of wind farms. For situations with multiple wind turbines or multiple substations, dynamic zoning is performed using wind turbine grouping based on scanning methods and wind turbine grouping based on adjacent position variation to improve the optimization speed.

[0028] (3) Design of graph genetic algorithm, including DMST algorithm design, encoding method design, fitness function and selection operator design, crossover operator design, and mutation operator design;

[0029] (4) Perform case analysis and optimization.

[0030] Further, in the step (1), the specific steps are as follows:

[0031] The economic indicators of the power collection system include the procurement and construction costs of submarine cable equipment, submarine cable operation loss and sea area use fees. The dielectric loss of the submarine cable operation loss is relatively small and is not considered for the time being. The submarine cable operation loss and sea area use fee are the net present value of the total cost for 25 years. The objective function is to minimize the total present value of the full life cycle cost of the power collection line C, which is expressed as:

[0032] min(C)=min(C 1 +(C 2 +C 3 )D)

[0033]

[0034] In the formula, C 1 The cost of purchasing and constructing submarine cable equipment; 2 C is the submarine cable operation loss cost, which refers to the economic loss caused by the power loss of the submarine cable conductor during operation each year; 3 is the sea area use fee; D is the discount factor; r is the discount rate; T is the life of the wind farm;

[0035] The calculation formula of the economic index of the power collection system is:

[0036]

[0037] Where K is the number of types of submarine cables; n is the type of segmented submarine cables of different lengths of the i-th submarine cable; N ij is the number of the i-th submarine cable with the j-th length; l ij is the length of the i-th type of submarine cable of the j-th length; p i1 is the unit cost of the i-th submarine cable equipment; p i2 is the unit cost of the i-th submarine cable construction; p 3 I is the on-grid electricity price; i is the working current of the submarine cable; R i is the resistance per unit length of the submarine cable; S is the sea area used by the wind farm; p 4 The annual usage fee for the unit sea area;

[0038] The total present value of the life cycle cost of the collector line C is taken as the objective function. The constraints for the topology optimization of the collector system mainly include the current carrying capacity constraint of the submarine cable, the cross avoidance constraint of the submarine cable and the number of outgoing lines of the booster station.

[0039] Due to the limitation of the current carrying capacity of submarine cables, the number of wind turbines connected to a single submarine cable is limited. When selecting a submarine cable, it should be ensured that the number of wind turbines mounted on the submarine cable does not exceed the maximum number of wind turbines that can be mounted on the submarine cable, expressed as:

[0040]

[0041] Where: M is the number of wind turbines connected to a single submarine cable; M max is the maximum number of wind turbines that can be mounted on a single submarine cable; floor is the rounding function; S cmax is the maximum wind turbine capacity that the collector cable can bear; P is the rated capacity of the wind turbine;

[0042] The node coordinate information is used to determine whether the submarine cable crosses. The collector line is regarded as a line segment. The anti-crossing method is as follows:

[0043] 1) Rapid rejection test;

[0044] According to the line segments forming rectangles as diagonal lines, determine whether there are intersections between different rectangles. If the rectangles do not intersect, then the two line segments must not intersect; if the rectangles intersect, proceed to step 2. Because the rapid exclusion test in step 1 only shows that the two rectangles intersect, and the line segments do not necessarily intersect, if the exclusion test does not pass, it is directly determined that the two line segments do not intersect. The logic of the rapid exclusion test is as follows:

[0045]

[0046] Set line segment P 1 P 2 Form a dotted rectangle 1, line segment P 3 P 4 Form a dotted rectangle 2, max(P 3 .x,P 4 .x) indicates that P is selected 3 , P 4 The maximum x coordinate, min(P 1 .x,P 2 .x) indicates that P is selected 1 , P 2 The smallest x-coordinate in the first logical judgment means: the maximum x-coordinate of rectangle 1 is greater than or equal to the minimum x-coordinate of rectangle 2, and the subsequent logic is the same;

[0047] If the result is that the rapid repulsion test is passed, it is necessary to proceed to step 2 and perform the straddle test to finally determine whether the two line segments intersect;

[0048] 2) straddling experiment;

[0049] The judgment principle of the straddling experiment is: if two line segments intersect, the two ends of one of the line segments must be on both sides of the other line segment.

[0050]

[0051] If F<0 in the formula, the two line segments must intersect; if one of the endpoints of one of the two line segments is on the other line segment, then F=0. Therefore, the entire basis for the straddling judgment must be F<0. When these two conditions are met at the same time, it proves that the two line segments must intersect.

[0052] Furthermore, in step (2), the specific steps are as follows:

[0053] The minimum spanning tree algorithm uses relevant theories in graph theory. It selects the edge with the smallest weight each time it connects to obtain the shortest collection system topology. However, it cannot control the depth of the tree, that is, the number of wind turbines connected to a single submarine cable. Therefore, a scanning method is introduced to group the wind turbines, and then they are connected using the minimum spanning tree algorithm. In order to optimize the wind turbine grouping information, neighbor mutation is used to obtain a variety of different grouping schemes.

[0054] Furthermore, in step (3), the graph genetic algorithm is specifically as follows:

[0055] 1) DMST algorithm design:

[0056] The initial population is generated by using the dynamic edge weight minimum spanning tree algorithm, taking into account the impact of the price coefficient brought by the current carrying capacity of the submarine cable;

[0057] In the process of selecting points, the DMST algorithm will delete the points that have been added to the tree topology from the set U of points to be selected. Therefore, the collector topology obtained by the algorithm must satisfy the tree structure constraint.

[0058] In order to meet the crossover constraint, a crossover determination process is added to the tree generation process of the DMST algorithm. When DMST performs an edge selection, all optional edges are prioritized according to the size of the cost change. Then, starting from the optimal edge, the anti-crossover method is used to cross-check it with all the selected edges. If no crossover occurs, the edge can be added to the tree; if a crossover occurs, the suboptimal edge is checked in order of priority until the selected edge does not cross.

[0059] 2) Coding method design:

[0060] Using an n×n matrix A n×nrepresents a spanning tree with n nodes, A(i,j)=1 means nodes i and j are connected. Since the offshore wind power collection system under consideration adopts a tree structure, there is no loop phenomenon. The linked list encoding method is complete and corresponds one-to-one with the spanning tree structure.

[0061] 3) Design of fitness function and selection operator;

[0062] The inverse of the cost of the power collection system is used as the fitness function in the genetic algorithm to ensure that individuals with lower costs are "excellent" and individuals with higher costs are "inferior". The fitness function is expressed as:

[0063]

[0064] The elite selection method plus roulette method is used as the selection operator. The elite selection selects the best individuals in the current population into the next generation population, verifies the optimization of the genetic process, and improves the convergence of the algorithm.

[0065] 4) Crossover operator design:

[0066] The crossover operator crosses the codes of two individuals between populations to generate new individuals. The crossover operator simulates the process of chromosome recombination in nature. The offspring generated by the crossover operator contains the information of two parents, so the characteristics of both parents are retained in the offspring. A new crossover operator, the superposition tree crossover operator, is redesigned based on the relevant characteristics and limitations of the collector system topology problem.

[0067] 5) Mutation operator design

[0068] Simulating the process of gene mutation in nature, gene mutation adds new heritable traits to the population and promotes species evolution. The mutation operator in the genetic algorithm adds uncertainty to the optimization process, allowing the genetic algorithm to jump out of the local optimal solution and increase the probability of finding the global optimal solution.

[0069] The present invention discloses an economical layout method of offshore wind farm collector lines based on dynamic partition optimization. The method comprises:

[0070] The method includes: converting the topology optimization problem of the power collection system into a minimum spanning tree (MST) problem, in which the vertices represent wind turbines or booster stations, the edges represent submarine cables, and the edge weights are the costs of the submarine cables. Taking into account the changes in edge weights, a dynamic edge weight minimum spanning tree (DMST) algorithm is introduced, which is an algorithm for solving the minimum spanning tree problem in the dynamic changes of the graph. On the basis of the existing minimum spanning tree, it dynamically handles the addition and deletion operations of edges to keep the minimum spanning tree updated. The present invention applies the algorithm and adds the functions of submarine cable selection and submarine cable crossing avoidance to form a radial topological structure. Dynamic partition design: For the case of multiple wind turbines or multiple booster stations, dynamic partitioning is performed using wind turbine grouping based on scanning method and wind turbine grouping based on adjacent variation to improve the optimization speed. Graph genetic algorithm, including the optimization of initial population: using DMST algorithm to generate initial population, providing a high-quality starting point for the algorithm; linked list coding: using linked list coding to efficiently represent the spanning tree structure while ensuring the completeness of the coding; elite selection operator: using elite selection method to ensure that excellent individuals are inherited to the next generation, accelerating the convergence of the algorithm. The effectiveness of the method of the present invention is demonstrated through specific offshore wind farm case analysis. Compared with traditional algorithms, the economic layout method of offshore wind farm collector lines based on dynamic partition optimization can converge to a more optimal collector system design more quickly, significantly reducing the full life cycle cost of the collector system. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 This is a flow chart of the economical arrangement method of offshore wind farm collector lines based on dynamic partition optimization of the present invention;

[0072] Figure 2 This is a schematic diagram of MST connection;

[0073] Figure 3 It is a schematic diagram of the scanning method;

[0074] Figure 4 Schematic diagram of adjacent position variation;

[0075] Figure 5 This is the manual layout diagram of the power collection system of the Shanwei Yuedong 1-2 offshore wind farm;

[0076] Figure 6 This is an intelligent layout diagram of the Shanwei Yuedong 1-2 offshore wind farm power collection system based on the present invention. DETAILED DESCRIPTION

[0077] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments:

[0078] The present invention provides an economical layout method of offshore wind farm collector lines based on dynamic partition optimization, such as Figure 1 As shown, the following steps are included:

[0079] (1) A mathematical model is established to transform the topology optimization problem of the power collection system into an MST problem, where vertices represent wind turbines or booster stations, edges represent submarine cables, and edge weights are the costs of submarine cables. Considering the changes in edge weights, the DMST algorithm is introduced to dynamically process the addition and deletion of edges to keep the minimum spanning tree updated. The functions of submarine cable selection and submarine cable crossing avoidance are also added to form a radial topology structure.

[0080] (2) Dynamic zoning design of wind farms. For situations with multiple wind turbines or multiple substations, dynamic zoning is performed using wind turbine grouping based on scanning methods and wind turbine grouping based on adjacent position variation to improve the optimization speed.

[0081] (3) Design of graph genetic algorithm, including DMST algorithm design, encoding method design, fitness function and selection operator design, crossover operator design, and mutation operator design;

[0082] (4) Perform case analysis and optimization.

[0083] In the step (1), the topology optimization problem of the offshore wind power collection system is transformed into an MST problem.

[0084] The economic indicators of the power collection system include the procurement and construction costs of submarine cable equipment, submarine cable operation loss, sea area use fees, etc. The dielectric loss of the submarine cable operation loss is relatively small and is not considered for the time being. The submarine cable operation loss and sea area use fees are the net present value of the total cost for 25 years. The life of an offshore wind farm is generally 25 years, and the operation cycle is relatively long, so its time value needs to be considered. Taking the minimum sum of the present value of the full life cycle cost of the power collection line C as the objective function, it can be expressed as:

[0085] min(C)=min(C 1 +(C 2 +C 3 )D)

[0086]

[0087] In the formula, C 1 The cost of purchasing and constructing submarine cable equipment; 2 C is the submarine cable operation loss cost, which refers to the economic loss caused by the power loss of the submarine cable conductor during operation each year; 3 is the sea area use fee; D is the discount factor; r is the discount rate; T is the life of the wind farm.

[0088] The calculation formula of the economic index of the power collection system is:

[0089]

[0090] Where K is the number of types of submarine cables; n is the type of segmented submarine cables of different lengths of the i-th submarine cable; N ij is the number of the i-th submarine cable with the j-th length; l ij is the length of the i-th type of submarine cable of the j-th length; p i1 is the unit cost of the i-th submarine cable equipment; p i2 is the unit cost of the i-th submarine cable construction; p 3 I is the on-grid electricity price; i is the working current of the submarine cable; R i is the resistance per unit length of the submarine cable; S is the sea area used by the wind farm; p 4 The annual usage fee for the unit sea area.

[0091] The total present value of the full life cycle cost C of the collector line is taken as the objective function. The constraints for the topology optimization of the collector system mainly include the current carrying capacity constraint of the submarine cable, the crossing avoidance constraint of the submarine cable and the number of outgoing lines from the substation.

[0092] Due to the limitation of the current carrying capacity of submarine cables, the number of wind turbines connected to a single submarine cable is limited. When selecting a submarine cable, it should be ensured that the number of wind turbines mounted on the submarine cable does not exceed the maximum number of wind turbines that can be mounted on the submarine cable, which can be expressed as

[0093]

[0094] Where: M is the number of wind turbines connected to a single submarine cable; M max is the maximum number of wind turbines that can be mounted on a single submarine cable; floor is the rounding function; S cmax is the maximum wind turbine capacity that the collector submarine cable can withstand; P is the rated capacity of the wind turbine.

[0095] The offshore wind power collection cables are usually installed by blowing and burying. Considering the actual engineering requirements, the collection cables are not allowed to cross each other. The input information of the model is the wind turbine location coordinates, so it is necessary to use the node coordinate information to determine whether the cables cross each other. Figure 2 An MST connection diagram is shown. Considering the collector line as a line segment, the anti-crossing method is as follows:

[0096] 1) Rapid rejection test

[0097] According to the line segments forming rectangles with diagonal lines, determine whether there are intersections between different rectangles. If the rectangles do not intersect, then the two line segments must not intersect; if the rectangles intersect, proceed to step 2; because the rapid exclusion test in step 1 only shows that the two rectangles intersect, and the line segments do not necessarily intersect. If the exclusion test does not pass, it can be directly determined that the two line segments do not intersect. The logic of the rapid exclusion test is as follows:

[0098]

[0099] Set line segment P 1 P 2 Form a dotted rectangle 1, line segment P 3 P 4 Form a dotted rectangle 2, max(P 3 .x,P 4 .x) indicates that P is selected 3 , P 4 The maximum x coordinate, min(P 1 .x,P 2 .x) indicates that P is selected 1 , P 2 The first logical judgment means: the maximum x-coordinate of rectangle 1 is greater than or equal to the minimum x-coordinate of rectangle 2, and the subsequent logic is the same.

[0100] If the result is that the rapid repulsion test is passed, it is necessary to proceed to step 2 and perform a straddle test to finally determine whether the two line segments intersect.

[0101] 2) Straddle experiment

[0102] The judgment principle of the straddling experiment is: if two line segments intersect, the two ends of one of the line segments must be on both sides of the other line segment.

[0103]

[0104] If F<0 in the formula, the two line segments must intersect; if one of the endpoints of one of the two line segments is on the other line segment, then F = 0. Therefore, the entire basis for the straddling judgment must be F<0. When these two conditions are met at the same time, it is proved that the two line segments must intersect.

[0105] In the step (2), a dynamic zoning design of wind turbines is performed. For the case of multiple wind turbines or multiple booster stations, dynamic zoning is performed using wind turbine grouping based on scanning method and wind turbine grouping based on adjacent position variation to improve the optimization speed.

[0106] The minimum spanning tree algorithm uses the relevant theories in graph theory. Each time it connects, it selects the edge with the smallest weight, which can obtain the shortest collection system topology. However, it cannot control the depth of the tree, that is, the number of wind turbines connected by a single submarine cable. Therefore, the scanning method is introduced to group the wind turbines and then connect them using the minimum spanning tree algorithm.

[0107] The scanning method steps are as follows:

[0108] 1) Determine the position of the baseline. Figure 3As shown, one end of the baseline is connected to the booster station, and the angle θ (0°≤θ<360°) between the baseline and the vertical upward direction can be used to determine the position of the baseline. The baseline is generally selected at a location where wind turbines are sparsely distributed, because the scattered distribution of wind turbines in the same group will lead to an excessively long submarine cable connection length, increasing investment costs.

[0109] 2) Determine the number of wind turbines in each group. Use the neighbor mutation algorithm described later to obtain the grouping information of the wind turbines. Scan the baseline in a clockwise direction and add the specified number of wind turbines scanned to the corresponding group. To optimize the wind turbine grouping information, use neighbor mutation to obtain a variety of different grouping schemes.

[0110] The number of wind turbines in each group. The adjacent mutation algorithm described later is used to obtain the grouping information of the wind turbines. The baseline is scanned in a clockwise direction, and the specified number of wind turbines scanned are added to the corresponding group.

[0111] To optimize the wind turbine grouping information, adjacent mutations were used to obtain a variety of different grouping schemes, such as Figure 4 shown.

[0112] The steps of adjacent mutation operation are as follows:

[0113] 1) Randomly generate a group of qualified group information: (n 1 ,n 2 ,n 3 ,n 4 ,…,n m-1 ,n m ). 1 is the number of wind turbines in group 1; m is the number of groups (i.e. the number of submarine cable loops). min ≤n i ≤n max (i∈[1,m]). min and n max The minimum and maximum number of wind turbines allowed to be connected to the submarine cable are

[0114] 2) Two adjacent elements in the same grouping information are subtracted by one and added by one respectively. This operation changes the grouping information while keeping the total number of wind turbines unchanged.

[0115] 3) Check the generated new grouping information to see if it satisfies n min ≤n i ≤n max (i∈[1,m]). Delete the grouping information that does not meet the requirements.

[0116] 4) To ensure that the algorithm does not fall into local optimality, after the neighbor mutation is completed, a set of random numbers is generated to satisfy n min ≤n i≤n max (i∈[1,m]) conditional grouping information to increase the diversity of grouping information.

[0117] In the step (3), the graph genetic algorithm mainly includes DMST algorithm design, encoding method design, fitness function and selection operator design, crossover operator design, and mutation operator design.

[0118] 1) DMST algorithm design

[0119] This method uses the dynamic edge weight minimum spanning tree algorithm (DMST) to generate the initial population. The DMST algorithm makes some improvements on the dynamic edge weight problem based on the Prim algorithm. The edge weights of the edges in the graph of the Prim algorithm are given, and there is no weight coefficient related to the current carrying capacity. Therefore, it is impossible to solve the coupling problem between the topological structure and the submarine cable selection in the topological optimization problem of the power collection system. The improvement of the DMST algorithm is that it takes into account the impact of the price coefficient brought by the current carrying capacity of the submarine cable.

[0120] First, three sets are established: the point set S that has been selected to be connected to the tree topology, the point set U that has not been connected to the tree topology, and the edge set H that has been added to the tree topology. The process of the DMST algorithm is as follows: (1) Input the point set V and edge set E of the complete graph G corresponding to the offshore wind farm, and initialize the matrix S = {1}, which only includes the nodes of the offshore substation. Collector topology adjacency matrix A T All elements of U are 0; (2) arbitrarily select a point i in U and a point j in S to connect, and use the submarine cable purchase cost calculation formula to calculate the cost change ΔC before and after the connection. ij ; (3) Select the edges corresponding to i and j with the smallest cost change and add them to set H, delete node j from U, and add it to set S to obtain the adjacency matrix of the tree with the new edges added; (4) Continue to select new edges according to (2) and (3), update S, U and H until S = V, all nodes are added to the topology, and the complete collector topology is obtained; (5) Output the final adjacency matrix and total cost.

[0121] In the process of point selection, the DMST algorithm will delete the points that have been added to the tree topology from the set U of points to be selected. Therefore, the collector topology obtained by the algorithm must satisfy the tree structure constraint.

[0122] The main difference between the DMST algorithm and the Prim algorithm lies in the way they select newly added edges. The Prim algorithm only considers the edge weights of the newly added edges, but does not consider the impact of the newly added edges on the original tree topology cost. The DMST edge adding process calculates the overall cost changes before and after adding edges, taking into account the impact of adding edges on the original topology cost, thereby making the optimized topology cost tend to be better.

[0123] In order to meet the crossover constraint, a crossover determination process can be added to the tree generation process of the DMST algorithm. When DMST performs an edge selection, all optional edges are prioritized according to the size of the cost change. Then, starting from the optimal edge, the anti-crossover method is used to cross-check it with all selected edges. If no crossover occurs, the edge can be added to the tree; if a crossover occurs, the suboptimal edge is checked in order of priority until the selected edge does not cross.

[0124] Although the DMST algorithm can optimize the collector topology, its optimality cannot be guaranteed. Therefore, the DMST algorithm can be combined with the genetic algorithm for further optimization.

[0125] 2) Coding method design

[0126] The encoding method is a method of mapping the solution space to the encoding space, corresponding to the solution of the optimization problem to the "individual" in the genetic process. The encoding method needs to meet the requirements of completeness, soundness and non-redundancy.

[0127] Using an n×n matrix A n×n Represents a spanning tree with n nodes. A(i,j)=1 means that nodes i and j are connected. Since the offshore wind power collection system under consideration adopts a tree structure, there is no loop phenomenon. The linked list encoding method is complete and can correspond one-to-one with the spanning tree structure.

[0128] 3) Fitness function and selection operator design

[0129] The fitness function in the genetic algorithm is used to scale the individuals in the population, so as to judge the "goodness" of the individuals in the population, which is related to the objective function in the optimization problem. The topology optimization of the offshore wind power collection system focuses on the cost of the collection system. Therefore, the inverse of the collection system cost can be directly used as the fitness function in the genetic algorithm to ensure that individuals with lower costs are more "excellent" and individuals with higher costs are more "inferior". The fitness function can be expressed as

[0130]

[0131] The function of the selection operator of the genetic algorithm is to select the best individuals in the existing population and make them the next generation population, which reflects the survival of the fittest in the genetic process of nature. Common selection operators include roulette selection, expected value method, sorting selection, tournament selection and elite selection. This paper adopts elite selection method plus roulette method as the selection operator. Elite selection selects the best individuals in the current population into the next generation population, which can ensure the optimization of the genetic process and improve the convergence of the algorithm.

[0132] 4) Crossover operator design

[0133] The crossover operator crosses the codes of two individuals in the population to generate new individuals. The crossover operator simulates the process of chromosome recombination in nature. The offspring generated by the crossover operator contains the information of the two parents, so the characteristics of both parents are retained in the offspring. This method redesigns a new crossover operator - the superposition tree crossover operator based on the relevant characteristics and limitations of the collector system topology problem. The crossover process can be divided into two steps. (1) Take two individuals A in the population 1 and A 2 , respectively get the adjacency matrix description of the two parents and Superimposing the two spanning trees of the parent generation can be achieved by superimposing the adjacency matrix. (2) Using the result of superposition of the parent generation as the feasible space, the DMST algorithm is used to generate a subtree to obtain the offspring.

[0134] This superposition tree crossover operator can not only retain the relevant characteristics of the parent generation, allowing the inheritance process to proceed smoothly, but also the problem of submarine cable selection and the limitation of submarine cable current carrying capacity have been considered in the implementation process of the DMST algorithm. Therefore, the feasibility of the offspring can be guaranteed without adding additional judgment processes, thereby improving the efficiency of generating effective offspring.

[0135] 5) Mutation operator design

[0136] The mutation operator simulates the process of gene mutation in nature. Gene mutation can add new heritable traits to the population and promote species evolution. The mutation operator in the genetic algorithm can add uncertainty to the optimization process, allowing the genetic algorithm to jump out of the local optimal solution and increase the probability of finding the global optimal solution.

[0137] In order to improve the mutation efficiency, the mutation operator is implemented in a similar way to the crossover operator. The mutation operator is also divided into two steps. (1) Take the parent individual A 1 , and convert it into an adjacency matrix expression to obtain the parent adjacency matrix Add k edges randomly to the adjacency matrix to get (2) Based on this, the DMST algorithm is used to regenerate offspring. This mutation method takes into account the characteristics of the topological structure of the spanning tree, introduces a certain degree of uncertainty in the process of random edge addition, can realize the mutation process, and at the same time ensures the feasibility of generating offspring and improves the efficiency of generating effective offspring.

[0138] By comprehensively utilizing the above improved methods, a graph genetic algorithm based on DMST can be obtained.

[0139] In step (4), optimization verification is performed on the Shanwei Yuedong 1-2 wind farm. The project has a planned total installed capacity of about 1000MW, and plans to deploy 54 wind turbines with a single unit capacity of 18.8MW, and build two 500MW / 220kV offshore substations. Each offshore substation is equipped with two main transformers, which are sent out through four 220kV submarine cables after boosting. The manual layout plan is shown in Figure 5 The relevant parameters of the power collection submarine cable are shown in the following table.

[0140]

[0141] right Figure 5 The topology optimization of the Zhongshanwei Yuedong 1-2 wind farm. The economic layout method of the offshore wind farm collector line based on dynamic partition optimization of the present invention was used to solve the problem, and 20 iterations were performed. The final topology optimization result is as follows: Figure 6 The total life cycle cost of the power collection system converges to 340.0446 million yuan, compared with Figure 3 The cost of manually planning the power collection system was 342.1696 million yuan, and the cost of the power collection system was significantly reduced by 2.125 million yuan. Since the encoding method and genetic operators were improved according to the characteristics of topology optimization problems, the calculation efficiency was greatly improved.

[0142] In the model solution, Figure 5 The Shanwei Yuedong 1-2 offshore wind farm was tested. Figure 6 The optimized layout diagram of the collection line of the Shanwei Yuedong 1-2 offshore wind farm based on the present invention. It can be seen that the invention not only improves the optimization efficiency, but also ensures the economy and reliability of the optimization results. The method provides a new tool for the design and construction of offshore wind farms and has broad application prospects.

[0143] The above description is only a preferred embodiment of the present invention and does not constitute any other form of limitation to the present invention. Any modification or equivalent change made based on the technical essence of the present invention still falls within the scope of protection required by the present invention.

Claims

1. An economical layout method for offshore wind farm collector lines based on dynamic zoning optimization, characterized in that: The specific steps are: (1) A mathematical model is established to transform the topology optimization problem of the power collection system into an MST problem, where vertices represent wind turbines or booster stations, edges represent submarine cables, and edge weights are the costs of submarine cables. Considering the changes in edge weights, the DMST algorithm is introduced to dynamically process the addition and deletion of edges to keep the minimum spanning tree updated. The functions of submarine cable selection and submarine cable crossing avoidance are also added to form a radial topology structure. (2) Dynamic zoning design of wind farms. For situations with multiple wind turbines or multiple substations, dynamic zoning is performed using wind turbine grouping based on scanning methods and wind turbine grouping based on adjacent position variation to improve the optimization speed. (3) Design of graph genetic algorithm, including DMST algorithm design, encoding method design, fitness function and selection operator design, crossover operator design, and mutation operator design; (4) Perform case analysis and optimization.

2. The economical layout method of offshore wind farm collector lines based on dynamic partition optimization according to claim 1 is characterized in that: In the step (1), the specific steps are as follows: The economic indicators of the power collection system include the procurement and construction costs of submarine cable equipment, submarine cable operation loss and sea area use fees. The dielectric loss of the submarine cable operation loss is relatively small and is not considered for the time being. The submarine cable operation loss and sea area use fee are the net present value of the total cost for 25 years. The objective function is to minimize the total present value of the full life cycle cost of the power collection line C, which is expressed as: min(C)=min(C1+(C2+C3)D) In the formula, C1 is the procurement and construction cost of submarine cable equipment; C2 is the submarine cable operation loss cost, which refers to the economic loss caused by the power loss of submarine cable conductors every year during operation; C3 is the sea area use fee; D is the discount coefficient; r is the discount rate; T is the life of the wind farm; The calculation formula of the economic index of the power collection system is: Where K is the number of types of submarine cables; n is the type of segmented submarine cables of different lengths of the i-th submarine cable; N ij is the number of the i-th submarine cable of the j-th length; l ij is the length of the i-th submarine cable of the j-th length; p i1 is the unit cost of the i-th submarine cable equipment; p i2 is the unit construction cost of the i-th submarine cable; p3 is the on-grid electricity price; I i is the working current of the submarine cable; R i is the resistance per unit length of the submarine cable; S is the sea area used by the wind farm; p4 is the annual sea area usage fee; The total present value of the life cycle cost of the collector line C is taken as the objective function. The constraints for the topology optimization of the collector system mainly include the current carrying capacity constraint of the submarine cable, the cross avoidance constraint of the submarine cable and the number of outgoing lines of the booster station. Due to the limitation of the current carrying capacity of submarine cables, the number of wind turbines connected to a single submarine cable is limited. When selecting a submarine cable, it should be ensured that the number of wind turbines mounted on the submarine cable does not exceed the maximum number of wind turbines that can be mounted on the submarine cable, expressed as: Where: M is the number of wind turbines connected to a single submarine cable; M max is the maximum number of wind turbines that can be mounted on a single submarine cable; floor is the rounding function; S cmax is the maximum wind turbine capacity that the power collection cable can bear; P is the rated capacity of the wind turbine; The node coordinate information is used to determine whether the submarine cable crosses. The collector line is regarded as a line segment. The anti-crossing method is as follows: 1) Rapid rejection test; According to the line segments forming rectangles as diagonal lines, determine whether there are intersections between different rectangles. If the rectangles do not intersect, then the two line segments must not intersect; if the rectangles intersect, proceed to step 2. Because the rapid exclusion test in step 1 only shows that the two rectangles intersect, and the line segments do not necessarily intersect, if the exclusion test does not pass, it is directly determined that the two line segments do not intersect. The logic of the rapid exclusion test is as follows: Set line segments P1P2 to form dotted rectangle 1, and line segments P3P4 to form dotted rectangle 2. max(P3.x,P4.x) means selecting the one with the largest x coordinate between P3 and P4, and min(P1.x,P2.x) means selecting the one with the smallest x coordinate between P1 and P2. The first logical judgment means: the maximum x coordinate of rectangle 1 is greater than or equal to the minimum x coordinate of rectangle 2, and the subsequent logic is the same. If the result is that the rapid repulsion test is passed, it is necessary to proceed to step 2 and perform the straddle test to finally determine whether the two line segments intersect; 2) straddling experiment; The judgment principle of the straddling experiment is: if two line segments intersect, the two ends of one of the line segments must be on both sides of the other line segment. If F<0 in the formula, the two line segments must intersect; if one of the endpoints of one of the two line segments is on the other line segment, then F=0. Therefore, the entire basis for the straddling judgment must be F<0. When these two conditions are met at the same time, it proves that the two line segments must intersect.

3. The economical layout method of offshore wind farm collector lines based on dynamic partition optimization according to claim 1 is characterized in that: In the step (2), the specific steps are as follows: The minimum spanning tree algorithm uses relevant theories in graph theory. It selects the edge with the smallest weight each time it connects to obtain the shortest collection system topology. However, it cannot control the depth of the tree, that is, the number of wind turbines connected to a single submarine cable. Therefore, a scanning method is introduced to group the wind turbines, and then they are connected using the minimum spanning tree algorithm. In order to optimize the wind turbine grouping information, neighbor mutation is used to obtain a variety of different grouping schemes.

4. The economical layout method of offshore wind farm collector lines based on dynamic partition optimization according to claim 1 is characterized in that: In the step (3), the graph genetic algorithm is specifically as follows: 1) DMST algorithm design: The initial population is generated by using the dynamic edge weight minimum spanning tree algorithm, taking into account the impact of the price coefficient brought by the current carrying capacity of the submarine cable; In the process of selecting points, the DMST algorithm will delete the points that have been added to the tree topology from the set U of points to be selected. Therefore, the collector topology obtained by the algorithm must satisfy the tree structure constraint. In order to meet the crossover constraint, a crossover determination process is added to the tree generation process of the DMST algorithm. When DMST performs an edge selection, all optional edges are prioritized according to the size of the cost change. Then, starting from the optimal edge, the anti-crossover method is used to cross-check it with all the selected edges. If no crossover occurs, the edge can be added to the tree; if a crossover occurs, the suboptimal edge is checked in order of priority until the selected edge does not cross. 2) Coding method design: Using an n×n matrix A n×n represents a spanning tree with n nodes, A(i,j)=1 means nodes i and j are connected. Since the offshore wind power collection system under consideration adopts a tree structure, there is no loop phenomenon. The linked list encoding method is complete and corresponds one-to-one with the spanning tree structure. 3) Design of fitness function and selection operator; The inverse of the cost of the power collection system is used as the fitness function in the genetic algorithm to ensure that individuals with lower costs are "excellent" and individuals with higher costs are "inferior". The fitness function is expressed as: The elite selection method plus roulette method is used as the selection operator. The elite selection selects the best individuals in the current population into the next generation population, verifies the optimization of the genetic process, and improves the convergence of the algorithm. 4) Crossover operator design: The crossover operator crosses the codes of two individuals between populations to generate new individuals. The crossover operator simulates the process of chromosome recombination in nature. The offspring generated by the crossover operator contains the information of two parents, so the characteristics of both parents are retained in the offspring. A new crossover operator, the superposition tree crossover operator, is redesigned based on the relevant characteristics and limitations of the collector system topology problem. 5) Mutation operator design Simulating the process of gene mutation in nature, gene mutation adds new heritable traits to the population and promotes species evolution. The mutation operator in the genetic algorithm adds uncertainty to the optimization process, allowing the genetic algorithm to jump out of the local optimal solution and increase the probability of finding the global optimal solution.

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