Offshore wind plant current collection system loss pre-calculation and large-scale solution acceleration method

Abstract

An offshore wind power plant current collection system loss pre-calculation and large-scale solution acceleration method comprises the steps that an initial mathematical model considering cable construction cost and full life cycle loss cost is constructed, a nonlinear loss item is converted into a linear cost coefficient through a network loss pre-calculation sub-problem, and the linear cost coefficient is calculated; a mixed integer linear programming model easy to solve is obtained; based on the positions of a fan and a transformer substation, a hot start initial feasible solution meeting engineering constraints is constructed by adopting a clustering partition and an intra-sector routing strategy; screening potential connections based on a distance threshold, and supplementing the connections exceeding the threshold in the hot start solution to the candidate set to form a simplified final candidate cable set; and in combination with the candidate set and the hot start solution, efficiently solving the optimization model by using a solver, and outputting a planning scheme. According to the method, on the premise of accurately describing the network loss economy, the solving efficiency and the engineering practicability of the planning of the current collection system of the super-large-scale offshore wind power plant are remarkably improved through the model linearization and systematic solving acceleration design.

Description

Technical Field

[0001] This invention relates to the calculation of losses in offshore wind farm power collection systems, and in particular to a method for pre-calculating and accelerating large-scale solutions of losses in offshore wind farm power collection systems. Background Technology

[0002] With the rapid development of offshore wind power, the problem of power collection and transmission within offshore wind farms is becoming increasingly prominent. As a key engineering system connecting wind turbines and offshore substations, the power collection system accounts for 15% to 30% of the total project cost. It is not only an important part of the project investment and operating costs, but also a key link affecting the project feasibility and system operating efficiency.

[0003] From a systems planning perspective, the planning of offshore wind farm power collection systems not only needs to optimize construction costs but also must comprehensively consider power loss costs throughout the entire lifecycle, as well as operational reliability, construction feasibility, and other requirements. Essentially, this is a combinatorial optimization problem with numerous binary decision variables and nonlinear constraints: on the one hand, the choice of route and topology determines how different wind turbine powers are collected at the substation; on the other hand, cable selection and capacity allocation determine line loss levels and long-term operating costs. When the number of wind turbines reaches dozens or even hundreds, all possible turbine-turbine and turbine-substation connection combinations generate an extremely large set of candidate routes, causing the problem size to expand dramatically with the site size.

[0004] In existing research and engineering practice, there are generally two technical approaches for designing collector system topologies and cable configurations. One is the "quasi-empirical design" method, dominated by engineering experience and rule bases. This involves providing a feasible topology based on partitioning, branching structures, or empirical formulas, followed by local adjustments. This method is simple to implement and easy to integrate with engineering processes, but it often struggles to systematically balance line losses and life-cycle costs, and has limited ability to characterize complex constraints and multi-objective trade-offs. The other approach is the "optimization design" method, represented by mathematical programming and intelligent optimization algorithms, including various models based on mixed-integer linear programming (MILP), mixed-integer quadratic programming (MIQP), heuristics, and metaheuristic algorithms. Theoretically, these methods can simultaneously handle economy, losses, and constraints, but in practical applications, they generally face two structural challenges: One challenge is the nonlinearity introduced by loss modeling. Line losses in a power collection system are typically related to the line resistance and the square of the active power passing through it. Directly incorporating the quadratic loss term into the objective function or constraints leads to MIQP or more general nonlinear integer programming. Such models are difficult to solve and heavily reliant on solvers, making it challenging to guarantee high-quality solutions within an acceptable timeframe for large-scale wind farms. To address this, some studies simplify or even ignore losses, considering only the capacity limit in the constraints; others employ approximations such as coarse linearization and scenario equivalence. While these compromises improve solution efficiency, they inevitably sacrifice a detailed characterization of the lifecycle loss cost, resulting in discrepancies between the optimization results and actual operational economics.

[0005] Secondly, there is the uncontrolled growth of candidate routes and solution scale in large-scale scenarios. If all potential connections between wind turbines and between wind turbines and substations are included in the candidate set, the number of route variables and related constraints in the model will increase quadratically. Simultaneously, if engineering constraints such as non-intersecting routes, nodal degree ranges, and multi-loop parallelism are explicitly considered, the search space for the solver in branch and bound will expand dramatically. Existing research has attempted to reduce the scale by setting distance thresholds, pre-dividing regions, or using heuristic generation of candidate arcs, but these typically lack a systematic approach tightly coupled with the mathematical programming model, and lack a theoretically clear and reusable integrated technical path from candidate generation to solution acceleration. Without high-quality initial solutions and reasonable candidate set control, even maintaining the linear model form, the solution performance of mixed-integer programming on a scale of hundreds of wind turbines remains unsatisfactory.

[0006] For large-scale MILP / MIQP problems, hot-start techniques are widely considered an effective acceleration method. The basic idea is to construct a set of feasible initial solutions with good objective values ​​before optimization, allowing the solver to prioritize these solutions during branch and bound processes, thereby shortening the search path and improving solution efficiency. In the field of offshore wind farm collector system planning, common initial solution construction methods include radial layouts based on minimum spanning trees and partitioned connection schemes based on simple clustering. However, these methods are often designed around traditional radial or simple ring topologies and do not systematically adapt to the actual engineering constraints of the collector system (such as node degree requirements of "one in, one out" or "two in, one out", cable non-crossing constraints, parallel laying constraints, etc.); furthermore, they lack an overall acceleration framework linked to the construction of candidate cable sets.

[0007] Overall, existing technologies in the area of ​​"loss modeling + large-scale solution" have the following main shortcomings: First, there is a lack of a method to uniformly convert cable construction costs and discounted full-lifecycle network loss costs into a linear unit length cost coefficient, making it difficult to balance accurately accounting for network losses and maintaining model efficiency. Second, there is a lack of a systematic candidate cable set size control strategy for large-scale offshore wind farms, making it difficult to significantly reduce the number of candidate arcs while ensuring model optimality. Third, there is a lack of a hot-start construction method and solution acceleration framework tightly coupled with mathematical programming models, making it impossible to stably and efficiently obtain high-quality collection system optimization schemes in offshore wind farms with hundreds of turbines. Therefore, there is an urgent need for a new collection system planning technology that can accurately reflect the economics of line losses, maintain the linear or near-linear structure of the overall model, and achieve efficient optimization solutions for large-scale offshore wind farm collection systems through the reasonable construction of candidate line sets and high-quality initial solutions.

[0008] It should be noted that the information disclosed in the background section above is only for understanding the background of this application, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0009] The main objective of this invention is to overcome the deficiencies in the aforementioned background technology and provide a method for accelerating the pre-calculation and large-scale solution of losses in offshore wind farm power collection systems.

[0010] To achieve the above objectives, the present invention adopts the following technical solution: A method for accelerating the pre-calculation and large-scale solution of losses in offshore wind farm collector systems includes the following steps: S1. For the planning problem of power collection system in offshore wind farms, an initial mathematical model is constructed that considers cable construction costs and total life cycle loss costs. S2. By solving the network loss pre-calculation sub-problem, the nonlinear loss term in the initial mathematical model is transformed into a linear cost coefficient, resulting in a mixed integer linear programming model. S3. Based on the location information of wind turbines and substations, a strategy combining clustering partitioning and intra-sector routing is adopted to construct an initial feasible solution for hot start that satisfies engineering constraints. S4. Screen potential connections between wind turbines based on a preset distance threshold, and add connections that exceed the threshold in the initial feasible solution of the hot start to the candidate set to construct the final candidate cable set for solving the mixed integer linear programming model; S5. Based on the final candidate cable set and the initial feasible solution for hot start, the mixed integer linear programming model is optimized and solved using a solver to output the power collection system planning scheme.

[0011] A computer program product, which, when executed by a processor, implements a method for accelerating the pre-calculation and large-scale solution of losses in an offshore wind farm power collection system.

[0012] The present invention has the following beneficial effects: This invention provides a method for pre-calculating and accelerating large-scale solution of losses in offshore wind farm collection systems. It effectively solves the problem of solution efficiency caused by the introduction of model nonlinearity due to the quadratic term of power loss and the explosion of candidate arcs in large-scale wind farms in traditional mathematical optimization. This method transforms power loss into linear coefficients through pre-calculation and incorporates them into cost calculations. Thus, while accurately reflecting the economics of line losses, it maintains the linear or approximately linear structure of the overall model, significantly improving the solution efficiency of the optimization model.

[0013] Specifically, on the one hand, the proposed network loss pre-calculation method can accurately characterize network loss terms under the DC power flow assumption. By uniformly converting the total life-cycle network loss cost and the one-time construction cost into a linear unit length cost coefficient, it achieves a global optimization scheme that balances economic efficiency and engineering practicality while maintaining the model's efficient solution characteristics. On the other hand, for large-scale wind farm scenarios, by combining distance screening and hot-start layout, and designing a hot-start strategy that combines clustering partitioning and intra-fan routing, the number of candidate arcs can be systematically reduced and high-quality initial feasible solutions can be provided. This not only significantly improves the solution efficiency and convergence speed of the mathematical programming model when dealing with hundreds of wind turbines, but also enhances the scalability of the method in large-scale scenarios, thereby achieving efficient and stable solutions to the planning problem of ultra-large offshore wind farm power collection systems.

[0014] Other beneficial effects of the embodiments of the present invention will be further described below. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating the overall process of the proposed method for accelerating the pre-calculation and large-scale solution of losses in offshore wind farm power collection systems.

[0016] Figure 2 This is a schematic diagram showing the coordinates of the wind turbines and substations of a wind farm with 42 wind turbines, along with a list of candidate submarine cables.

[0017] Figure 3A This is a schematic diagram of the planning results of the power collection system for a 42-wind-turbine wind farm using the conventional MIQP model (Comparative Example 1).

[0018] Figure 3B This is a schematic diagram of the planning results of the power collection system of a 42-wind-turbine wind farm in the MILP model (Example 1) after pre-calculation of network losses.

[0019] Figure 4The coordinates of the wind turbines and substations for wind farms with 125 wind turbines and 300 wind turbines, as well as a schematic diagram of candidate submarine cables, are provided.

[0020] Figure 5 This is a schematic diagram of the solution gap-time curves for Comparative Example 2, Comparative Example 3, and Example 2 in a wind farm scenario with 125 wind turbines.

[0021] Figure 6 This is a schematic diagram of the solution gap-time curves for Comparative Example 3 and Example 2 in a wind farm scenario with 300 wind turbines. Detailed Implementation

[0022] The embodiments of the present invention will be described in detail below. It should be emphasized that the following description is merely exemplary and not intended to limit the scope and application of the present invention.

[0023] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of embodiments of the present invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0024] This invention aims to solve the problem of low solution efficiency caused by nonlinear power loss modeling and massive candidate connections in the planning of offshore wind farm collection systems. It proposes an integrated optimization method that combines pre-calculation linearization of network loss with clustering-based hot start acceleration. By pre-converting loss costs into linear coefficients to maintain model efficiency, and combining partitioning strategies and distance screening to construct high-quality initial solutions and a simplified candidate set, this method achieves efficient and stable solutions to ultra-large-scale wind farm planning problems while ensuring the economic efficiency and engineering feasibility of the scheme.

[0025] See Figure 1 This invention provides a method for accelerating the pre-calculation and large-scale solution of losses in offshore wind farm collection systems, comprising the following steps: Step S1: For the planning problem of offshore wind farm power collection system, construct an initial mathematical model that considers cable construction costs and total life cycle loss costs.

[0026] In some embodiments, the initial mathematical model constructed in step S1 is a mixed integer quadratic programming model or a mixed integer nonlinear programming model, whose objective function includes a network loss cost term that is proportional to the square of the line transmission power. This power square term is determined by the current-power relationship under the DC power flow assumption.

[0027] Step S2: By solving the network loss pre-calculation sub-problem, the nonlinear loss term in the initial mathematical model is transformed into a linear cost coefficient, resulting in a mixed integer linear programming model.

[0028] In some embodiments, solving the network loss pre-calculation subproblem in step S2 includes: for line segments carrying different numbers of wind turbines, pre-calculating and comparing the total cost per unit length corresponding to all optional cable models; the total cost per unit length consists of the sum of the construction cost per unit length and the linearized term of the full life-cycle network loss cost considering discount, wherein the linearized term of the network loss cost is calculated based on the DC power flow assumption and the square relationship between the cable transmission power; selecting the cable model with the minimum total cost per unit length and its cost value as the optimization cost coefficient under the corresponding number of wind turbines, integrating it into the objective function of the main optimization model, thereby transforming the nonlinear programming problem containing the power square term into a linear programming problem.

[0029] In some embodiments, the solution process of the network loss pre-computation sub-problem is independent of the iteration process of the main optimization model and is a preprocessing step that is completed in one go before the optimization solution.

[0030] Step S3: Based on the location information of the wind turbine and the substation, a strategy combining clustering partitioning and intra-sector routing is adopted to construct an initial feasible solution for hot start that satisfies engineering constraints.

[0031] In some embodiments, the construction of the initial feasible solution for hot start in step S3 includes: using the substation as a reference point, dividing the wind turbine nodes into several sector regions according to the preset line entry degree and sector capacity; within each sector region, generating an initial topology using a monotonic connection method based on a fixed direction, specifically: calculating the projected coordinates of each wind turbine node in the selected connection direction and its orthogonal direction, sorting the nodes according to the lexicographical order of the projected coordinates, and connecting the sorted nodes sequentially to form a monotonic path; matching the cable type that meets the capacity constraints and has the best cost according to the number of wind turbines carried downstream of each line segment in the initial topology, and calculating the total cost of the scheme; traversing the division methods with different wind turbine nodes as the starting point of sector scanning, and selecting the scheme with the lowest total cost as the initial feasible solution for hot start.

[0032] In some embodiments, the fixed-direction monotonic connection method specifically involves: selecting a connection direction and its unit orthogonal vector within a sector; calculating the signed projection of the position vector of each wind turbine node within the sector onto the connection direction and its orthogonal vector to obtain a set of two-dimensional projected coordinates; sorting all wind turbine nodes according to the lexicographical order of the projected coordinates; and connecting the sorted wind turbine node sequence sequentially to form a path whose coordinates monotonically do not decrease along the selected connection direction. This path naturally satisfies the degree constraints of no cable crossing and "one in, one out" nodes.

[0033] In some embodiments, the initial topology generated by the sector routing strategy satisfies the engineering constraints of the offshore wind farm collection system. The engineering constraints include at least the following: each line connection satisfies the node degree limit of "one in and one out" or "two in and one out", and the lines do not intersect in the spatial layout.

[0034] Step S4: Screen potential connections between wind turbines based on a preset distance threshold, and add connections that exceed the threshold in the initial feasible solution of the hot start to the candidate set to construct the final candidate cable set for solving the mixed integer linear programming model.

[0035] In some embodiments, the construction of the final candidate cable set in step S4 includes: first, setting a maximum candidate distance threshold, and only including connection arcs with Euclidean distances less than the threshold between wind turbines and between wind turbines and substations into the initial candidate set; then, adding all line arcs in the initial feasible solution for hot start generated in step S3 whose connection length exceeds the maximum candidate distance threshold to the initial candidate set; the initial candidate set and the added line arcs together constitute the final candidate cable set.

[0036] Step S5: Based on the final candidate cable set and the initial feasible solution for hot start, use the solver to optimize the mixed integer linear programming model and output the power collection system planning scheme.

[0037] In some embodiments, when performing optimization using the solver in step S5, the hot-start initial feasible solution is used as the initial input to the branch and bound process of the mixed-integer linear programming solver to accelerate convergence.

[0038] The proposed method for accelerating the pre-calculation and large-scale solution of losses in offshore wind farm collection systems cleverly transforms nonlinear loss terms into linear cost coefficients through network loss pre-calculation. This maintains the linear structure and efficient solution characteristics of the model while accurately considering the economic benefits of losses throughout the entire life cycle. Furthermore, by combining a hot-start construction method based on clustering partitioning and intra-sector routing, as well as a candidate set construction strategy that integrates distance screening and hot-start solution supplementation, the problem scale in large-scale scenarios is effectively controlled, and high-quality initial solutions are provided. Thus, in the planning of ultra-large offshore wind farms with hundreds of wind turbines, a globally optimized solution that is both economical and engineering feasible can be obtained stably and efficiently within an acceptable engineering timeframe.

[0039] The following further describes specific embodiments of the present invention, algorithm examples, and experimental verification.

[0040] A method for pre-calculating and accelerating large-scale solution of losses in offshore wind farm collection systems is proposed. The core of this method is to address the efficiency challenges in traditional mathematical optimization, such as the nonlinearity of the quadratic term in power loss leading to model nonlinearity and the explosion of candidate arcs in large-scale wind farms. Specifically, it includes pre-calculating power losses to convert them into linear coefficients that are integrated into cost calculations to maintain the linearity of the model; employing a combination of distance filtering and hot-start layout to reduce the number of candidate arcs; and designing a hot-start strategy that combines clustering partitioning and intra-sector routing to provide high-quality initial solutions. While ensuring planning feasibility, this method significantly improves the computational efficiency of large-scale wind farm collection system planning, enabling efficient optimization solutions for ultra-large wind farms.

[0041] Network loss pre-calculation subproblem Offshore wind power collection system planning is a large-scale, NP-hard planning problem. The line loss term in the objective function is the most complex, significantly impacting the model's solution efficiency. As the number of wind turbines in an offshore wind farm increases, the size of the solution model and the number of candidate submarine cables will grow significantly. Therefore, employing an efficient method for characterizing the network loss term can effectively improve the model's solution efficiency and scalability to large-scale scenarios. Considering the nodes in the power collection system... voltage amplitude , This indicates the per-unit value, therefore in cables Current flowing through , For the active power transmitted on cable (i,j), the active power loss can be calculated using the DC power flow assumption. By approximation, we have .in Select the resistance per unit length of submarine cable type t for this line. Denote the engineering length of the submarine cable (i,j) as... Under the assumption of DC power flow, the objective function expression of the model, which includes one-time construction costs and network loss costs, can be written as: (1) (2) in For the candidate submarine cable collection, For line selection, This is a collection of alternative cable models; Model Construction cost per unit length of submarine cable Let be a binary variable indicating whether to use the type t submarine cable on arc (i,j). A value of 1 indicates that type t is selected, and a value of 0 indicates otherwise. The discount factor for converting total lifecycle network losses into costs is as follows: This refers to the annual utilization hours of the wind farm. The annual discount rate is 10%. For the operating years of the wind farm, The above model represents the objective function under the assumption of DC power flow. However, the introduction of active power loss transforms the model into a MIQP problem, posing significant challenges to solution efficiency and scalability in large-scale wind farm scenarios.

[0042] In this invention, the power of the current collection system is considered to be cumulatively added in units of wind turbines as it is transmitted along the cable. Let the rated power of a single wind turbine be... At this time, the transmission power on a certain submarine cable carrying k wind turbines is Given the freedom in cable selection and the limitation of choosing from only a pre-defined range of cable types, the sub-problem of minimizing the sum of construction cost and discounted network loss cost under the condition of supporting k wind turbines can be solved first at the single-line scale. Specifically, the cable sub-problem for supporting k wind turbines takes the following form: (3) in This refers to the rated power of the fan. Let be the upper limit of the capacity of submarine cable of type t. Solve using constraint equation (3) to ensure the carrying capacity... Typhoon generator capacity constraints Under the premise of the specified model, the sum of the minimum construction cost and the total life-cycle network loss cost considering the discount rate. This is then integrated into the objective function. Therefore, the quadratic term of the loss no longer appears explicitly in the master programming model; instead, it is... The objective function is introduced as a constant parameter. Let... Let be a binary variable indicating whether candidate arc (i,j) carries k wind turbines; a value of 1 indicates that it carries k wind turbines, and a value of 0 indicates otherwise. Then the overall objective function of the collector system can be rewritten in linear MILP form: (4) Clustering hot-start and candidate cable assembly construction method Considering the increasing size of the candidate cable set in the model as the number of wind turbines increases. The sheer number of wind farms in large-scale offshore wind farms and other deep-sea scenarios will lead to high solution complexity for the model. This section proposes a cluster-based hot-start method and a candidate cable set construction method based on distance filtering and clustering results, aiming to accelerate the solution of planning problems for large-scale offshore wind farms.

[0043] Cluster-based hot-start construction Hot-start technology significantly accelerates convergence and improves solution efficiency by incorporating a superior initial solution provided in the optimization algorithm into the branch and bound process. This invention employs a "clustering and partitioning first, then connecting within each partition" hot-start approach. First, it pre-determines the number of sectors and the quota of wind turbines in each sector based on the substation's line access density and candidate cable capacity. Then, using the substation (booster station) as a reference point and a specific wind turbine as the scanning starting point, it scans and assigns wind turbines to sectors in ascending polar angle order. Once a sector's capacity quota is full, it is assigned to a new sector, continuing until all wind turbines are assigned. Next, feasible routes are constructed within each partition according to the partition situation, and cable types that meet current-carrying constraints are matched based on the number of downstream wind turbines for each cable. Finally, the total cost of the planned scheme is calculated, and the scheme with the lowest cost among all wind turbine nodes is selected as the hot-start scheme. This clustering and partitioning-based construction method efficiently provides initially feasible hot-start schemes.

[0044] In conventional methods for connecting areas in radial collector systems, this problem is often treated as a minimum spanning tree problem, seeking a topology with the minimum sum of weighted connected edges. This problem has mature algorithms that can solve it exactly in polynomial time, such as Kruskal's algorithm and Prim's algorithm, with time complexities of [missing information]. and However, practical radial collector system planning problems often impose restrictions on the degree of nodes, requiring the planning scheme to meet the engineering constraints of "two inputs and one output" or "one input and one output." In this case, the minimum spanning tree method may not be able to provide a solution that meets the engineering requirements. Furthermore, considering that the hot-start phase only provides an initial feasible solution to the planning problem, the emphasis is mainly on feasibility, and the quality of the solution is not particularly important. This invention proposes a monotonic connection method based on sector direction, which can efficiently provide a hot-start scheme for intra-sector connections that meets the most stringent "one input and one output" standard and does not intersect. A fixed connection direction is defined within each sector S. Let the unit vector orthogonal to it be... For each fan in the sector Calculate the signed projection and according to the first back lexicographical sorting Obtain the sorting results And connect them sequentially to obtain a monotonic path within the region. This path is in the direction The upper part is monotonically non-decreasing, therefore for any non-connected edge... , , its in Projection range of direction and They do not overlap; even for adjacent blocks Also because The increasing relationship of directions still satisfies the non-intersection rule. In summary, the sector direction monotonic connection method used in this invention naturally satisfies the cable non-crossing principle and the "one in, one out" engineering constraint. The complexity enables the efficient construction of a hot start scheme.

[0045] Construction of candidate cable sets based on distance filtering and clustering results Considering that the planning model aims to obtain the optimal power collection system planning scheme, and the objective function seeks to minimize the Euclidean distance of the connections between wind turbines in terms of construction and network loss costs, excessively long connections between wind turbines are unlikely to appear in the optimal layout and can be removed through targeted filtering. A maximum candidate distance (e.g., 5 times the wind turbine spacing) can be set first; cables exceeding this candidate distance are not included in the candidate cable set, thus effectively controlling the model size without affecting the optimality of the solution.

[0046] While using appropriate distances to filter candidate cable sets can effectively reduce model planning, the clustering hot-start method described in Section 1 often scans unevenly distributed fan-shaped areas when dealing with irregularly shaped or large-scale wind farm scenarios. In such cases, the heuristic connection method may construct some exceptionally long cables. Directly increasing the filtering distance to adopt this hot-start scheme would significantly increase the model size. This invention adopts a construction method that first filters the cable set using appropriate candidate distances, and then adds cables exceeding the maximum candidate distance from all hot-start schemes to the candidate cable set. This effectively utilizes the hot-start scheme without incurring excessive computational costs.

[0047] Experimental verification Experiment 1: Verify the effectiveness of network loss pre-calculation in a domestic wind farm with 42 wind turbines.

[0048] The coordinates of the wind turbines and substations of the wind farm, and a schematic diagram of the candidate submarine cables are shown below. Figure 2 As shown.

[0049] This experiment uses the conventional MIQP model (Comparative Example 1) and the MILP model after network loss pre-calculation (Example 1) to solve the problem. The comparison results are shown in Table 1 below.

[0050] Table 1

[0051] In this experiment, the model without network loss pre-computation had an optimal gap of 8.18% after 500 seconds of solution time, indicating room for cost optimization. However, the model with network loss pre-computation found the global optimal solution in just 2.8 seconds, showing a significant improvement in efficiency compared to the model without network loss pre-computation.

[0052] Experiment 2: The effectiveness of the proposed clustering hot-start and candidate cable assembly construction method was verified in two large-scale wind farms with 125 and 300 wind turbines respectively. The coordinates of the wind turbines and substations, and schematic diagrams of the candidate submarine cables are shown below. Figure 4 As shown: Figure 4 (a) in the image shows a scene with 125 wind turbines. Figure 4 (b) in the image shows a scene with 300 wind turbines. Figure 4 The purple line segment represents the candidate submarine cables obtained through distance screening, and the red line segment represents the expanded candidate submarine cables obtained through hot-start solution.

[0053] In a scenario with 125 wind turbines, the following three comparative examples are set up to verify the effectiveness of the method of the present invention: Comparative Example 2: Using an appropriate distance Filter, but do not use warm start.

[0054] Comparative Example 3: A hot start method based on clustering was used, but the screening distance was increased for this purpose. This will lead to an increase in model size.

[0055] Example 2: The construction method based on clustering for hot start and candidate cable expansion proposed in this invention is adopted.

[0056] In the scenario of 125 wind turbines, the solution results of Comparative Examples 2 and 3 and Example 2 are shown in Table 2 below.

[0057] Table 2

[0058] Accordingly, the gap-time curves of Comparative Examples 2 and 3 and Example 2 are as follows: Figure 5 As shown.

[0059] As can be seen, Comparative Example 2, due to the lack of a warm start, requires a certain amount of time to find a feasible solution in the solution space; Comparative Example 3, by providing an initial feasible solution, explores rapidly in the early stages of the solution process, but the expansion of the distance screening value leads to an increase in model size, affecting the efficiency of branch and bound exploration, resulting in no improvement in the efficiency of obtaining a high-quality solution compared to Comparative Example 2; while Example 2 (the method of this invention) implements a warm start with very low computational cost, and the solution effect is significantly improved compared to Comparative Example 2 and Comparative Example 3.

[0060] In the scenario of a 300 MW wind turbine, the solution gap-time curves for Comparative Example 3 and Example 2 are as follows: Figure 6 As shown.

[0061] In this ultra-large-scale scenario, Comparative Example 2, which did not employ a warm start, could not obtain a feasible solution within the given solution time limit (30,000 s). Comparative Example 3, although having an initial feasible solution, suffered from a gap that could hardly be reduced due to its excessive scale. Example 2 of this invention, however, was able to solve successfully, obtaining a high-quality feasible solution (Gap < 1%) within an engineering-acceptable timeframe in the ultra-large-scale scenario.

[0062] In summary, this invention proposes a method for pre-calculating and accelerating large-scale solutions of losses in offshore wind farm collection systems. Its key innovations and design features are: firstly, a precise and efficient method for pre-calculating network losses is designed. By transforming nonlinear loss terms into linear cost coefficients under the DC power flow assumption, it accurately characterizes the entire lifecycle network loss cost while maintaining efficient model solution. Secondly, a collaborative acceleration framework integrating clustering partitioning, intra-sector routing, and distance filtering is proposed. By constructing high-quality hot-start solutions that satisfy engineering constraints and dynamically optimizing the candidate cable set, the solution efficiency and scalability of the model in large-scale scenarios are significantly improved. Compared with existing technologies, the significant technical advantages of this invention are: it not only balances the economic accuracy and mathematical solution efficiency of the model, enabling the output of a global optimization scheme that considers construction and loss costs, but also effectively addresses the challenge of explosive solution scale in scenarios with hundreds of wind turbines through a systematic candidate set control and hot-start strategy, achieving efficient and stable optimization of ultra-large offshore wind farm collection systems within an acceptable engineering timeframe.

[0063] This invention also provides a storage medium for storing a computer program, which, when executed, performs at least the methods described above.

[0064] This invention also provides a control device, including a processor and a storage medium for storing a computer program; wherein the processor executes the computer program by performing at least the method described above.

[0065] This invention also provides a processor that executes a computer program, at least performing the methods described above.

[0066] The storage medium can be implemented by any type of non-volatile storage device, or a combination thereof. The non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), magnetic random access memory (FRAM), flash memory, magnetic surface memory, optical disc or CD-ROM; magnetic surface memory can be disk storage or magnetic tape storage. The storage media described in the embodiments of this invention are intended to include, but are not limited to, these and any other suitable types of memory.

[0067] In the several embodiments provided by this invention, it should be understood that the disclosed systems and methods can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods, such as: multiple units or components can be combined, or integrated into another system, or some features can be ignored or not executed. In addition, the coupling or direct coupling or communication connection between the various components shown or discussed can be through some interfaces, and the indirect coupling or communication connection between devices or units can be electrical, mechanical, or other forms.

[0068] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the units may be selected to achieve the purpose of this embodiment according to actual needs.

[0069] In addition, in the various embodiments of the present invention, each functional unit can be integrated into one processing unit, or each unit can be a separate unit, or two or more units can be integrated into one unit; the integrated unit can be implemented in hardware or in the form of hardware plus software functional units.

[0070] Those skilled in the art will understand that all or part of the steps of the above method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps of the above method embodiments. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0071] Alternatively, if the integrated units of this invention are implemented as software functional modules and sold or used as independent products, they can also be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of the embodiments of this invention, or the parts that contribute to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, ROM, RAM, magnetic disks, or optical disks.

[0072] The methods disclosed in the several method embodiments provided by this invention can be arbitrarily combined without conflict to obtain new method embodiments.

[0073] The features disclosed in the several product embodiments provided by this invention can be arbitrarily combined without conflict to obtain new product embodiments.

[0074] The features disclosed in the several method or device embodiments provided by the present invention can be arbitrarily combined without conflict to obtain new method or device embodiments.

[0075] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various equivalent substitutions or obvious modifications can be made without departing from the concept of the present invention, and all such modifications, achieving the same performance or application, should be considered within the scope of protection of the present invention.

Claims

1. A method for accelerated pre-calculation and large-scale solution of losses in offshore wind farm collection systems, characterized in that, Includes the following steps: S1. For the planning problem of power collection system in offshore wind farms, an initial mathematical model is constructed that considers cable construction costs and total life cycle loss costs. S2. By solving the network loss pre-calculation subproblem, the nonlinear loss term in the initial mathematical model is transformed into a linear cost coefficient, resulting in a mixed integer linear programming model. S3. Based on the location information of wind turbines and substations, a strategy combining clustering partitioning and intra-sector routing is adopted to construct an initial feasible solution for hot start that satisfies engineering constraints. S4. Screen potential connections between wind turbines based on a preset distance threshold, and add connections that exceed the threshold in the initial feasible solution of the hot start to the candidate set to construct the final candidate cable set for solving the mixed integer linear programming model; S5. Based on the final candidate cable set and the initial feasible solution for hot start, the mixed integer linear programming model is optimized and solved using a solver to output the power collection system planning scheme.

2. The method for accelerated pre-calculation and large-scale solution of losses in offshore wind farm collection systems according to claim 1, characterized in that, The initial mathematical model constructed in step S1 is a mixed integer quadratic programming model or a mixed integer nonlinear programming model. Its objective function includes a network loss cost term that is proportional to the square of the line transmission power. This power square term is determined by the current-power relationship under the DC power flow assumption.

3. The method for accelerated pre-calculation and large-scale solution of losses in offshore wind farm collection systems according to claim 1, characterized in that, The solution to the network loss pre-calculation sub-problem mentioned in step S2 includes: For line sections carrying different numbers of wind turbines, pre-calculate and compare the total cost per unit length for all available cable models; The total cost per unit length consists of the sum of the construction cost per unit length and the linearized term of the full life-cycle network loss cost considering discounting, wherein the linearized term of the network loss cost is calculated based on the DC power flow assumption and the square relationship between the cable transmission power. The cable model with the lowest total cost per unit length and its cost value are selected as the optimized cost coefficient for the corresponding number of wind turbines, and integrated into the objective function of the main optimization model, thereby transforming the nonlinear programming problem containing the power square term into a linear programming problem.

4. The method for accelerated pre-calculation and large-scale solution of losses in offshore wind farm collection systems according to claim 1, characterized in that, The solution process for the network loss pre-calculation subproblem is independent of the iteration process of the main optimization model and is a preprocessing step that is completed in one go before the optimization solution.

5. The method for accelerated pre-calculation and large-scale solution of losses in offshore wind farm collection systems according to claim 1, characterized in that, Step S3 involves constructing an initial feasible solution for a hot start, including: Using the substation as a reference point, the wind turbine nodes are divided into several sector areas according to the preset line entry degree and sector capacity; In each sector area, an initial topology is generated using a fixed-direction monotonic connection method. Specifically, the projected coordinates of each wind turbine node in the selected connection direction and its orthogonal direction are calculated, and the nodes are sorted according to the lexicographical order of the projected coordinates. The sorted nodes are then connected sequentially to form a monotonic path. Based on the number of wind turbines downstream of each line segment in the initial topology, match the cable model that meets the capacity constraints and has the best cost, and calculate the total cost of the scheme. The partitioning methods that use different wind turbine nodes as the starting point for sector scanning are traversed, and the scheme with the lowest total cost is selected as the initial feasible solution for the hot start.

6. The method for accelerated pre-calculation and large-scale solution of losses in offshore wind farm collection systems according to claim 5, characterized in that, The monotonic connection method based on a fixed direction is specifically as follows: Select a connecting direction and its unit orthogonal vector within the sector; For the position vector of each wind turbine node in the sector, calculate its signed projection on the connecting line direction and its orthogonal vector to obtain a set of two-dimensional projected coordinates; Sort all wind turbine nodes according to the lexicographical order of the projected coordinates; The sorted wind turbine node sequence is connected sequentially to form a path whose coordinates do not decrease monotonically in the selected connection direction. This path naturally satisfies the degree constraints of no cable crossing and "one in and one out" nodes.

7. The method for accelerated pre-calculation and large-scale solution of losses in offshore wind farm collection systems according to claim 5 or 6, characterized in that, The initial topology generated by the routing strategy within the sector satisfies the engineering constraints of the offshore wind farm collection system. These engineering constraints include at least the following: each line connection must satisfy the node degree limit of "one in and one out" or "two in and one out", and the lines must not intersect in the spatial layout.

8. The method for accelerated pre-calculation and large-scale solution of losses in offshore wind farm collection systems according to claim 1, characterized in that, Step S4, which involves constructing the final candidate cable set, includes: Set a maximum candidate distance threshold, and only include connection arcs with Euclidean distances between wind turbines and between wind turbines and substations that are less than the threshold into the initial candidate set; All line arcs whose connection length exceeds the maximum candidate distance threshold from the initial feasible solution for hot start generated in step S3 are added to the initial candidate set. The initial candidate set and the additional line arcs together constitute the final candidate cable set.

9. The method for accelerated pre-calculation and large-scale solution of losses in offshore wind farm collection systems according to claim 1, characterized in that, In step S5, when using the solver for optimization, the hot-start initial feasible solution is used as the initial input for the branch and bound process of the mixed-integer linear programming solver to accelerate convergence.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the method for accelerating the pre-calculation and large-scale solution of losses in the offshore wind farm collection system as described in any one of claims 1 to 9.

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