A method for collaborative design of regular layout and mooring system of floating wind farm

Abstract

The application discloses a kind of floating wind farm regular layout and mooring system collaborative design method, comprising: obtaining wind farm basic data;Further construct the mixed integer linear programming model based on grid, by introducing depth proxy function approximation evaluation mooring cost and impose regular layout constraint, quickly solve to obtain the initial discrete position of wind turbine;Based on this, construct continuous coordinate optimization model, adopt meta-heuristic search algorithm to the continuous coordinate of wind turbine and mooring line parameter are cooperated and fine-tuned, and mooring line length is accurately calculated based on seabed topography.Therefore, solve the technical problems that mooring system design and wind turbine layout are disconnected in deep sea area due to complex seabed topography, optimization calculation complexity is high and it is difficult to meet the requirements of engineering regular layout.The method evaluates power generation by wake model, finally outputs the collaborative optimization scheme considering regular layout, wake loss and mooring economy, realizes the maximization of wind farm life cycle net present value.

Description

Technical Field

[0001] This invention relates to power system planning and offshore wind power technology, and in particular to a method for the coordinated design of regular layout and mooring system of floating wind farms. Background Technology

[0002] Research indicates that wake effects can lead to power losses of 10-20%. Therefore, micro-situation of wind turbines within a wind farm can effectively reduce wake effects and increase power generation. In deep-sea areas, floating offshore wind farms (FOWFs) demonstrate significant application potential. Unlike traditional near-shore fixed wind turbines, floating wind turbines (FWTs) are positioned using mooring systems, and their design is influenced by complex seabed topography and water depth variations. Furthermore, in practical engineering, offshore wind farms typically employ a regular layout to reduce infrastructure construction costs and facilitate operation and maintenance. However, existing research on the optimization of floating wind farm layouts still faces the following technical bottlenecks:

[0003] 1) Disconnect between mooring system and layout design: The impact of water depth on mooring line length and cost was ignored when optimizing the layout;

[0004] 2) Computational complexity and scale limitations: Accurate modeling of water depth variations would significantly increase computational complexity, resulting in slow optimization speed and limiting the planning capabilities of large-scale wind farms;

[0005] 3) Lack of regular layout constraints: Most heuristic addressing algorithms generate layouts that are too random and cannot meet the strict requirements of regular layouts in actual engineering.

[0006] 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

[0007] The main objective of this invention is to overcome the deficiencies in the aforementioned background technology and provide a method for the collaborative design of regular layout and mooring system of floating wind farms.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] A method for the coordinated design of regular layout and mooring system of floating wind farms includes the following steps:

[0010] S1. Obtain basic data of the wind farm, including wind resource data, seabed topography and water depth data, wind turbine parameters and economic parameters;

[0011] S2. Construct a grid-based mixed-integer linear programming model to maximize the net present value of the wind farm throughout its entire life cycle. By introducing a water depth surrogate function, the cost of the mooring system is approximated, and regular layout constraints are applied to solve for the initial discrete positions of the wind turbines that meet the requirements of the regularized layout of the project.

[0012] S3. Based on the initial discrete position, construct a continuous coordinate optimization model that allows the wind turbine to move continuously within the grid, and use the overall deflection angle and length of the mooring line as optimization variables. Use a metaheuristic search algorithm to fine-tune the continuous coordinates of the wind turbine and the parameters of the mooring system, accurately calculate the length of the mooring line and optimize its arrangement.

[0013] S4. During the optimization process, the wake model is used to calculate the wake effect between wind turbines to assess power generation. At the same time, the mooring line length is accurately calculated based on the seabed topography to assess the cost. Finally, a coordinated optimization layout scheme for wind turbines and mooring systems is output.

[0014] Furthermore, the construction and solution of the grid-based mixed-integer linear programming model in step S2 includes:

[0015] The planned sea area is discretized into a grid, with the grid center serving as the candidate wind turbine location;

[0016] An objective function is constructed to maximize the net present value, which is the difference between the discounted power generation revenue and the total construction and operation costs during the wind farm's operation period.

[0017] The cost calculation items are constructed, including using a water depth proxy function to express the platform cost, mooring line cost, electrical system cost and operation and maintenance cost as a first-order or proportional function of the water depth, wherein the mooring line cost is approximately evaluated by the water depth at the grid where the wind turbine is located;

[0018] Construct rule-based layout constraints by predefining a set of layout modes and introducing decision variables to control that each row of the wind farm can only select one layout mode, and the entire wind farm adopts a unified layout mode to ensure that the wind turbine positions are arranged in a regular manner.

[0019] In the model, the wind turbine installation decision is represented by 0 / 1 variables and includes constraints to ensure the total number of wind turbines installed, meet the minimum safety distance, and set logical upper and lower limits for the wind turbine output power.

[0020] The mixed-integer linear programming model was solved using a commercial solver to determine the initial installation location of the wind turbine on the discrete grid.

[0021] Furthermore, the process of constructing the rule layout constraints specifically includes:

[0022] Define a set of layout patterns, each pattern being defined by a starting column index and a fixed integer grid spacing, and ensure that the number of fans that can be installed in a specified row under this pattern does not exceed the grid column limit of that row;

[0023] A global pattern selection variable is introduced to constrain the entire wind farm to adopt only one dominant layout pattern.

[0024] Introduce row pattern activation variables to constrain each row of the wind farm to activate at most one layout pattern, and the activated pattern must be the globally selected dominant pattern.

[0025] By using a predefined binary mapping matrix, the selected layout pattern is combined with row activation variables and transformed into wind turbine installation decision variables at specific grid locations.

[0026] Furthermore, the water depth proxy function is specifically used for:

[0027] In the mixed-integer linear programming stage, the platform cost of a single floating wind turbine is modeled as a linear function of the water depth;

[0028] The proportion of operation and maintenance costs of a single floating wind turbine is also modeled as a linear function of water depth;

[0029] For the cost of the mooring system, the cost per unit length and the cost of the anchorage point are used as the basis, and the water depth value of the grid where the wind turbine is located is used to directly approximate the length of the mooring line for estimation, so as to calculate the total cost.

[0030] Furthermore, step S3, which involves constructing a continuous coordinate optimization model and using a metaheuristic search algorithm for collaborative fine-tuning, includes:

[0031] Using the discrete grid positions obtained in the first stage as the initial solution, the first wind turbine in each row is allowed to move freely within the continuous area corresponding to its original grid.

[0032] The positions of the remaining fans in the same row are determined by the coordinates of the first fan, the preset row direction vector, and the fixed row spacing, in order to maintain the regular arrangement characteristics.

[0033] A continuous optimization model is constructed with the continuous coordinates of the wind turbines, the spacing between rows, and the overall deflection angle of each wind turbine mooring system as decision variables, with the goal of maximizing net present value.

[0034] Apply minimum safe distance constraints between wind turbines and between mooring lines to the model;

[0035] The continuous optimization model is solved using a metaheuristic search algorithm to collaboratively optimize the wind turbine location and mooring line layout parameters.

[0036] Furthermore, the precise calculation of the mooring line length in step S3 includes:

[0037] Each wind turbine is equipped with multiple mooring lines, which are evenly distributed around the wind turbine on a horizontal plane;

[0038] Based on the plane coordinates of the wind turbine, the overall deflection angle of the mooring line, and the horizontal projection length of the mooring line on the sea level, calculate the plane coordinates of the anchoring point corresponding to each mooring line.

[0039] Based on the geometric relationship between the actual seabed depth at the anchoring point, the depth of the mooring guide hole, and the preset mooring line inclination angle, the necessary horizontal projection length of the mooring line is determined.

[0040] The actual length of the mooring line is accurately calculated using geometric relationships based on the horizontal projected length and the difference between the water depth at the anchor point and the depth of the guide hole.

[0041] Furthermore, the calculation of the wake model in step S4 includes:

[0042] The wake-induced velocity loss factor of the upstream wind turbine on the downstream wind turbine is calculated using a wake model based on the cosine function.

[0043] The calculation of the loss factor involves a core term related to the wind turbine thrust coefficient and rotor radius, multiplied by a cosine function term determined by the ratio of the radial distance from the downstream position to the wake centerline to the wake radius at a specific downstream position, where the wake radius increases linearly with the downstream distance.

[0044] For the multiple wake superposition effects on downstream wind turbines, a linear superposition model is used to calculate the actual output power under the combined effect. Specifically, under a given wind scenario, the actual output power of the downstream wind turbine is equal to the power without wake influence minus the sum of the power losses caused by all upstream wind turbines.

[0045] Furthermore, the wind turbine power output calculation is described using a piecewise function:

[0046] The power output of the wind turbine is expressed as a piecewise function of the incoming wind speed, including the zero-power region below the cut-in wind speed, the constant rated power region between the rated wind speed and the cut-out wind speed, and the power growth region between the cut-in wind speed and the rated wind speed, which is proportional to the cube of the wind speed.

[0047] Furthermore, the mooring system adopts a three-line mooring configuration, with each mooring line having a set angle evenly distributed on the horizontal plane, and the mooring line inclination angle is fixed.

[0048] A computer program product includes a computer program that, when executed by a processor, implements the method for co-designing the regular layout and mooring system of a floating wind farm.

[0049] The present invention has the following beneficial effects:

[0050] This invention provides a collaborative design method for the regular layout and mooring system of floating offshore wind farms. It effectively solves the technical challenges of high design difficulty and computational complexity of mooring systems in deep-sea areas due to complex seabed topography, as well as the difficulty of traditional site selection methods in balancing the requirements of regular engineering layout with maximizing economic benefits. Addressing bottlenecks in existing technologies such as the disconnect between mooring system and layout design, slow computation due to precise modeling, and lack of regular layout constraints, this invention proposes a two-stage optimization framework: In the initial site selection stage, a grid-based mixed-integer linear programming model is established, and a water depth surrogate function is used to approximate the platform, mooring, and operation and maintenance costs at different water depths. While integrating strict regular layout constraints, the initial position of the wind turbine can be quickly determined, effectively balancing computational efficiency and the engineering feasibility of the preliminary scheme. In the refined collaborative optimization stage, a continuous coordinate model is constructed based on the initial solution, and a metaheuristic search algorithm is used to jointly fine-tune the wind turbine coordinates, mooring line angles, and their precise lengths. This achieves the maximization of the net present value of the wind farm throughout its entire life cycle while accurately considering the influence of seabed topography.

[0051] Experimental results show that the wake loss of the wind farm is significantly reduced after applying the method of this invention, while the costs of the platform and mooring system, which are closely related to water depth, are also effectively controlled. Ultimately, the optimized layout, while meeting strict engineering rules, achieves increased power generation and a significant increase in the net present value over the entire life cycle, fully demonstrating the effectiveness and superiority of this collaborative design method in improving the economics of floating wind farms.

[0052] Other beneficial effects of the embodiments of the present invention will be further described below. Attached Figure Description

[0053] Figure 1 This is a flowchart illustrating the overall process of the collaborative design method for the regular layout and mooring system of a floating offshore wind farm according to the present invention.

[0054] Figure 2 This is a schematic diagram of a floating wind turbine and its mooring system in an embodiment of the present invention.

[0055] Figure 3 This is an initial layout diagram of the wind turbines and mooring lines of a floating offshore wind farm in an embodiment of the present invention.

[0056] Figure 4 This is the optimized layout diagram of the wind turbine and mooring line in the first stage obtained by solving the MILP model in an embodiment of the present invention.

[0057] Figure 5 This is the final optimized layout diagram of the wind turbine and mooring line in the second stage obtained by solving the continuous coordinate model in an embodiment of the present invention. Detailed Implementation

[0058] 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.

[0059] 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.

[0060] This invention aims to address the problems of disconnect between mooring system design and turbine layout, computational complexity, and difficulty in meeting the requirements of standardized engineering in the planning of deep-sea floating wind farms. It provides a joint configuration scheme for turbine location and mooring system in the early planning stage of offshore wind farms. While meeting the requirements for standardized layout in engineering design, it also considers the impact of seabed topography on mooring system design and cost, thereby reducing wake loss and maximizing net present value (NPV) over the entire life cycle.

[0061] See Figure 1 This invention provides a method for the collaborative design of regular layout and mooring system of floating offshore wind farms (FOWF), comprising the following steps:

[0062] Step S1: Obtain basic data for the wind farm, including wind resource data, seabed topography and water depth data, wind turbine parameters, and economic parameters.

[0063] In some embodiments, the acquired wind resource data may include, for example, annual average wind speed, prevailing wind direction and probability of different wind scenarios; seabed topography and water depth data may include, for example, specific water depth values ​​of various areas in the planned sea area; wind turbine parameters may include, for example, core performance indicators such as rated power, thrust coefficient, and rotor radius; and economic parameters may include, for example, electricity sales price per kilowatt-hour, discount rate, and unit mooring line cost.

[0064] Step S2: Construct a grid-based Mixed-Integer Linear Programming (MILP) model to maximize the net present value of the wind farm over its entire life cycle. By introducing a water depth surrogate function to approximate the cost of the mooring system and applying regular layout constraints, the initial discrete positions of the wind turbines that meet the requirements of the engineering regular layout are obtained.

[0065] In some embodiments, the construction and solution of the grid-based mixed-integer linear programming model in step S2 includes: discretizing the planned sea area into a grid, with the grid center as the candidate wind turbine location; constructing an objective function to maximize the net present value, wherein the net present value is the difference between the discounted power generation revenue and the total construction and operation and maintenance costs during the wind farm's operation period; constructing cost calculation items, including using a water depth proxy function to express platform cost, mooring line cost, electrical system cost, and operation and maintenance cost as a first-order or proportional function of water depth, wherein the mooring line cost is approximated by the water depth at the grid where the wind turbine is located; constructing regular layout constraints, by predefining a set of layout patterns and introducing decision variables to control that each row of the wind farm can only select one layout pattern, and the entire wind farm adopts a unified layout pattern to ensure that the wind turbine locations are arranged in a regular manner; in the model, the wind turbine installation decision is represented by 0 / 1 variables and includes constraints to ensure the total number of installed wind turbines, meet the minimum safety distance, and the logical upper and lower limits of the wind turbine output power; and using a commercial solver to solve the mixed-integer linear programming model to determine the initial installation location of the wind turbine on the discrete grid.

[0066] In some embodiments, the construction process of the rule layout constraints specifically includes: defining a set of layout patterns, each pattern being defined by a starting column index and a fixed integer grid spacing, and ensuring that the number of wind turbines that can be installed in a specified row under this pattern does not exceed the grid column limit of that row; introducing a global pattern selection variable to constrain the entire wind farm to adopt only one dominant layout pattern; introducing a row pattern activation variable to constrain each row of the wind farm to activate at most one layout pattern, and the activated pattern must be the globally selected dominant pattern; and using a predefined binary mapping matrix, combining the selected layout pattern with the row activation variable to transform it into wind turbine installation decision variables at specific grid locations.

[0067] In some embodiments, the water depth proxy function is specifically used to: model the platform cost of a single floating wind turbine as a linear function of water depth during the mixed-integer linear programming stage; model the operation and maintenance cost ratio of a single floating wind turbine as a linear function of water depth; and estimate the total cost based on the unit length cost and anchor point cost, using the water depth value of the grid where the wind turbine is located to directly approximate the mooring line length.

[0068] Step S3: Based on the initial discrete position, construct a continuous coordinate optimization model that allows the wind turbine to move continuously within the grid, and use the overall deflection angle and length of the mooring line as optimization variables. Use a metaheuristic search algorithm to fine-tune the continuous coordinates of the wind turbine and the parameters of the mooring system, accurately calculate the length of the mooring line and optimize its arrangement.

[0069] In some embodiments, the construction of the continuous coordinate optimization model and the collaborative fine-tuning using a metaheuristic search algorithm in step S3 includes: using the discrete grid positions obtained in the first stage as the initial solution, allowing the first wind turbine in each row to move freely within the continuous area corresponding to its original grid; stipulating that the positions of the remaining wind turbines in the same row are determined by the coordinates of the first wind turbine, the preset row direction vector, and the fixed row spacing to maintain the regular arrangement characteristics; using the continuous coordinates of the wind turbines, the row spacing, and the overall deflection angle of each wind turbine mooring system as decision variables, and constructing a continuous optimization model with the goal of maximizing the net present value; applying minimum safe distance constraints between wind turbines and minimum safe distance constraints between mooring lines to the model; and solving the continuous optimization model using a metaheuristic search algorithm to collaboratively optimize the wind turbine positions and mooring line layout parameters.

[0070] In some embodiments, the precise calculation of the mooring line length in step S3 includes: configuring multiple mooring lines for each wind turbine, with each mooring line evenly distributed around the wind turbine on a horizontal plane; calculating the plane coordinates of the anchoring point corresponding to each mooring line based on the wind turbine's plane coordinates, the overall deflection angle of the mooring line, and the horizontal projection length of the mooring line on the sea level; determining the necessary horizontal projection length of the mooring line based on the geometric relationship between the actual seabed depth at the anchoring point, the depth of the mooring guide hole, and the preset mooring line inclination angle; and precisely calculating the actual length of the mooring line based on the horizontal projection length and the difference between the anchoring point depth and the guide hole depth through geometric relationships.

[0071] Step S4: During the optimization process, the wake model is used to calculate the wake impact between wind turbines to assess power generation. At the same time, the mooring line length is accurately calculated based on the seabed topography to assess the cost. Finally, a coordinated optimization layout scheme for wind turbines and mooring systems is output.

[0072] In some embodiments, the calculation of the wake model in step S4 includes: calculating the wake-induced velocity loss factor of the upstream wind turbine on the downstream wind turbine using a wake model based on a cosine function; the core term of the loss factor calculation is related to the wind turbine thrust coefficient and rotor radius, and multiplied by a cosine function term determined by the ratio of the radial distance from the downstream position to the wake centerline to the wake radius at a specific downstream position, wherein the wake radius increases linearly with the downstream distance; for the multiple wake superposition effects on the downstream wind turbine, a linear superposition model is used to calculate the actual output power under its combined influence, specifically: under a given wind scenario, the actual output power of the downstream wind turbine is equal to the power without wake influence minus the sum of the power losses caused by all upstream wind turbines.

[0073] In some embodiments, the wind turbine power output calculation is described using a piecewise function: the wind turbine power output is expressed as a piecewise function with respect to the incoming wind speed, including a zero-power region below the cut-in wind speed, a constant rated power region between the rated wind speed and the cut-out wind speed, and a power growth region between the cut-in wind speed and the rated wind speed that is proportional to the cube of the wind speed.

[0074] In some embodiments, the mooring system employs a three-line mooring configuration, with each mooring line having a uniformly distributed angle on the horizontal plane at a predetermined angle, and the mooring line having a fixed inclination angle.

[0075] The proposed method for the collaborative design of regular layout and mooring system of floating offshore wind farms utilizes a two-stage collaborative optimization design. In the initial stage, a mixed-integer linear programming model combining a water depth surrogate function and regular layout constraints is introduced to quickly generate an initial scheme that meets engineering layout requirements and effectively approximates the cost of the mooring system, significantly improving optimization efficiency and feasibility in large-scale scenarios. Building upon this, a continuous coordinate model is further constructed and combined with a metaheuristic algorithm to perform collaborative fine optimization of turbine locations and mooring line parameters. This achieves overall control over wake loss and mooring costs while accurately considering the influence of seabed topography, thereby maximizing the economic benefits of the wind farm throughout its entire life cycle while ensuring regular layout and engineering feasibility.

[0076] The following further describes specific embodiments of the present invention, algorithm examples, and experimental verification.

[0077] A collaborative design method for the layout and mooring system of a floating offshore wind farm is proposed, which includes the following implementation methods.

[0078] (1) Two-stage optimization method

[0079] The first stage involves constructing a MILP model based on a water depth surrogate function to determine the initial locations of the wind turbines. Specifically, this includes: dividing the planned sea area into discrete grids, with the center of each grid serving as candidate wind turbine locations; introducing a water depth surrogate cost function: considering the impact of water depth on the cost of floating wind turbines, platform costs, electrical system costs, and operation and maintenance costs are expressed as linear functions of water depth, and the mooring line cost is estimated on the discrete grid using the surrogate function; defining regular layout constraints, ensuring that each row can only select one layout pattern to guarantee that the generated initial solution conforms to the regularized arrangement required by the engineering; using a Cosine wake model to characterize the wake effects between wind turbines, solving the MILP model using a commercial solver to determine the initial grid locations of the wind turbines, and using these as input for the second stage.

[0080] In the second stage, the wind turbines are allowed to move continuously within the grid, constructing a continuous coordinate model based on precise calculations. In this stage, the lengths of each mooring line are accurately calculated based on the actual seabed topography and wind turbine locations. The Grey Wolf algorithm is used to collaboratively optimize the wind turbine positions and mooring line layout angles to reduce mooring system costs and determine the final positions of the wind turbines and mooring lines.

[0081] (2) Wake model

[0082] The Cosine wake model was used to model the wind speed distribution within the FOWF (Front-of-Wave Stream). This model can accurately describe the wind speed deficit effect of the upstream FWT on the downstream FWT.

[0083] In FOWF, the upstream wind turbines It will create a wake region downstream, causing units located in that region to... Received wind speed Lower than upstream wind speed The relationship between the two is expressed as follows:

[0084]

[0085] in, Representative of the unit For the unit The formula for calculating the wake-induced loss factor is as follows:

[0086]

[0087] in, For thrust coefficient, The radius of the wind turbine rotor. The radial distance from the center of the downstream unit to the centerline of the wake. The wake radius at a specific downstream distance can be calculated using the following formula:

[0088]

[0089] in, is the wake attenuation constant.

[0090] (3) Fan power output

[0091] In FOWF, the power output curve of FWT can be approximated by the following formula:

[0092]

[0093] in, The cut-in wind speed of the fan. The rated wind speed of the fan. This refers to the cut-off velocity of the fan. This represents the output coefficient of the fan. This is the rated power.

[0094] In real-world large-scale wind farms, a single downstream wind turbine is affected by the wake effects of multiple upstream turbines. This invention considers the superposition effect of multiple wakes, specifically addressing the issue of downstream wind turbines... In wind speed scenario Actual output power The model is as follows:

[0095]

[0096] in, For wind scene The output power of the fan is not considered when the wake loss is not taken into account. Considering the wind turbine When the wake affects the fan . output power.

[0097] (4) Modeling of mooring lines

[0098] For the complex seabed environment of deep sea, this invention deeply couples the design of the mooring system with the layout of the wind turbine. The mooring system not only serves as a positioning guarantee for FWTs, but its length and cost are also directly constrained by the actual water depth at the anchoring point.

[0099] This invention preferentially employs a three-line mooring configuration to achieve a balance between the stability and economy of the wind turbine, such as... Figure 2 As shown. The angles between the mooring lines on the horizontal plane are uniformly distributed at 120°, therefore the... Taiwan FWT's The mooring line angle can be calculated as follows:

[0100]

[0101] in, Indicates the first The mooring line of FWT Taiwan is deflected at an overall angle.

[0102] Let the coordinate vector of the wind turbine at sea level be... The depth of the mooring guide hole is The mooring line has a downward inclination angle relative to the horizontal plane of _____. . No. Anchorage coordinates of the mooring line The relationship with the location of the fan is determined by the following formula.

[0103]

[0104] in, For the first Taiwan FWT's The horizontal projection length of the mooring line on the sea surface.

[0105] Due to the complex and varied seabed topography, the local water depth at each anchoring point is... There are differences. (Based on the specified mooring line inclination angle) The geometric constraint relationship between the cable guide hole and the seabed is as follows:

[0106]

[0107] Based on equations (7) and (8), the actual length of the mooring line can be calculated accurately. :

[0108]

[0109] (5) Optimization Model

[0110] 1) MILP model based on mooring line surrogate function

[0111] To quickly obtain a large number of initial site selection schemes in the early stages of planning, this invention constructs a grid-based MILP model. The core of this stage lies in using a mooring line surrogate function to approximate the mooring line cost and obtain a regular wind farm layout. The objective function used in this stage is to maximize NPV, expressed as follows:

[0112]

[0113] in, Let 0 / 1 be the decision variable, representing the first... Whether a fan is installed in each grid (1 for installed, 0 for not installed). This represents the discounted revenue generated during the wind farm's operating cycle. The fixed construction cost for a single wind turbine. Representing grids respectively The costs of the FWT platform, mooring system, electrical system, and operation and maintenance. The expressions for the revenue and various costs are shown below:

[0114]

[0115]

[0116]

[0117]

[0118]

[0119]

[0120] in, The price per kilowatt-hour of electricity sold. For wind scene The probability, The discount rate is... The percentage of power loss. , , These are the base cost of the FWT platform, the unit mooring line cost, and the anchoring cost. For FWT platform cost coefficient, Because of the water depth, and These represent the ratio of electrical system costs to operation and maintenance costs. and These are the basic coefficient and growth coefficient for the maintenance ratio, respectively.

[0121] During this phase, the overall deflection angle of the mooring line Fixed at 0°, its length Directly utilize the water depth at the location of the blower This is used as a surrogate value for approximate evaluation, thereby avoiding the nonlinear problem of unknown anchor point depth.

[0122] To ensure the regular arrangement of FWTs in practical engineering, this invention proposes a pattern-based layout optimization method. This method constrains the spatial position of FWTs through predefined geometric patterns, and the specific implementation scheme is as follows:

[0123] Define layout pattern set This is used to describe the distribution pattern of wind turbines in each row of a wind farm, as shown below:

[0124]

[0125] in, Representation pattern The starting column index in this row, Representation pattern Integer grid spacing between the wind turbines below Indicates the first In-line mode At that time, the final number of grid fans selected. Specifically, the mode Indicates every Each grid cell can be used to select a location to install the fan, and the selected column number cannot exceed the row number. Total number of columns limit .

[0126] The complete constraints of the MILP model are given below:

[0127]

[0128]

[0129]

[0130]

[0131]

[0132]

[0133]

[0134]

[0135] Equation (18) indicates that the total number of FWTs satisfies Equation (19) indicates that FOWF as a whole selects only one dominant pattern from the preset layout pattern set, where Representation pattern The 0 / 1 decision variables. Equations (20) and (21) ensure that each row in the wind farm... Only one specific layout mode can be activated, where Indicates line model The 0 / 1 decision variables. Equation (22) is obtained by using a binary matrix. Map the selected layout pattern to specific grid coordinates to ensure In-line wind turbine vector Strictly follow the pattern The spacing requirements. Equation (23) ensures that the minimum safe distance can be met between the fans. Equation (24) specifies the upper and lower limits of the output power of the fans.

[0136] 2) Continuous coordinate model based on accurate mooring line calculation

[0137] After obtaining the initial discrete grid solution provided by the Mixed Integer Linear Programming (MILP) model, this invention enters the fine-tuning optimization stage. By constructing a continuous coordinate model and employing a metaheuristic search algorithm, the aim is to break through grid limitations and jointly fine-tune the turbine position and mooring system parameters to achieve optimal economic benefits. Unlike the first stage, the overall deflection angle of the mooring line... In this stage, it is considered an optimization variable.

[0138] The complete mathematical model is as follows:

[0139]

[0140]

[0141]

[0142]

[0143]

[0144] The objective function (26) also aims to maximize the NPV of FOWF. Indicates the first Line number The coordinate vector of the typhoon. Equation (27) ensures that the first typhoon in each row can only be within its specified grid range. Inner movement. Equation (28) stipulates that the positions of the remaining fans in the row are determined by the first fan, and adjacent fans have the same vertical coordinates and a horizontal distance of . ,in It is the row direction vector. Formulas (29)–(30) impose constraints on the minimum safe distance between FWTs and between mooring lines. According to ISO 19901-7, mooring lines and anchorages must maintain a distance of at least 100 meters from other offshore installations, therefore the safe distance of mooring lines is... Set to 100 meters.

[0145] Experimental verification

[0146] (1) Basic Overview of the Implementation Location

[0147] The effectiveness of the proposed model was verified using a local FOWF (Free Wind Farm). This FOWF plans to install 30 13MW FWTs in water depths ranging from 320 to 480 meters, with an average annual wind speed of 8.83 m / s. Since the prevailing wind directions in this area are 40°, 60°, and 180°, a weighted calculation determined the prevailing wind direction to be 80°. To maximize wind energy capture, the overall layout of the wind farm was set perpendicular to the 80° prevailing wind direction. The initial layout of the FOWF turbines and mooring lines is shown below. Figure 3 As shown in Table 1, the wind turbine parameters used in the example are provided.

[0148] Table 1 Key parameters of the fan

[0149]

[0150] (2) Optimization Result Analysis

[0151] The optimized layout obtained by solving the first-stage layout of the MILP model is as follows: Figure 4As shown. Using this layout as the initial solution of the continuous coordinate model, a metaheuristic search algorithm (the Grey Wolf algorithm is used in this test case) is employed to further fine-tune the turbine coordinates, turbine spacing, and the overall deflection angle of the mooring lines for each turbine. The final layout result, obtained by solving the continuous coordinate model for the second-stage layout, is shown below. Figure 5 As shown.

[0152] Compared to the initial layout with a wake loss of 10.65%, the layout optimized using the MILP model and the continuous coordinate model reduced the wake loss by 1.61% and 4.16%, respectively. Furthermore, the dynamic yaw system cost and water depth-related costs in the final layout were significantly reduced, resulting in a net present value increase of approximately 33.3% compared to the initial layout. This fully demonstrates that the collaborative design method proposed in this paper can effectively improve the economic benefits of wind farms.

[0153] In summary, this invention proposes a collaborative design method for the regular layout and mooring system of floating offshore wind farms. Addressing the challenges of complex mooring system design and computational complexity in deep-sea areas due to the intricate seabed topography, and the difficulty of balancing regular engineering layout with maximizing economic benefits using traditional site selection methods, this invention provides a joint configuration scheme for turbine locations and mooring systems in the early planning stages of offshore wind power. Through a two-stage optimization framework, a grid-based mixed-integer linear programming model is established in the initial site selection stage. A water depth surrogate function is used to approximate the platform, mooring, and operation and maintenance costs, and the initial discrete locations of the turbines are quickly determined through regular layout constraints. In the refined collaborative optimization stage, a continuous coordinate model is constructed based on the initial solution. A metaheuristic search algorithm is used to jointly fine-tune the turbine coordinates, mooring line angles, and precise lengths. Ultimately, while meeting the requirements of regular engineering layout, the method comprehensively considers the impact of seabed topography on the mooring system, achieving the goals of reducing wake losses and maximizing the net present value of the wind farm throughout its entire life cycle.

[0154] This invention also provides a storage medium for storing a computer program, which, when executed, performs at least the methods described above.

[0155] 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.

[0156] This invention also provides a processor that executes a computer program, at least performing the methods described above.

[0157] 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.

[0158] 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.

[0159] 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.

[0160] 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.

[0161] 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.

[0162] 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.

[0163] The methods disclosed in the several method embodiments provided by this invention can be arbitrarily combined without conflict to obtain new method embodiments.

[0164] The features disclosed in the several product embodiments provided by this invention can be arbitrarily combined without conflict to obtain new product embodiments.

[0165] 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.

[0166] 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 the collaborative design of regular layout and mooring system of floating wind farms, characterized in that, Includes the following steps: S1. Obtain basic data of the wind farm, including wind resource data, seabed topography and water depth data, wind turbine parameters and economic parameters; S2. Construct a grid-based mixed-integer linear programming model to maximize the net present value of the wind farm throughout its entire life cycle. By introducing a water depth surrogate function to approximate the cost of the mooring system and applying regular layout constraints, the initial discrete positions of the wind turbines that meet the requirements of the regularized layout of the project are obtained. Specifically, the water depth surrogate function is used to estimate the total cost of the mooring system based on the unit length cost and the anchor point cost, and by directly approximating the mooring line length using the water depth values ​​of the grid where the wind turbine is located. S3. Based on the initial discrete positions, a continuous coordinate optimization model is constructed that allows the wind turbines to move continuously within the grid. The overall deflection angle and length of the mooring lines are used as optimization variables. A metaheuristic search algorithm is employed to fine-tune the continuous coordinates of the wind turbines and the parameters of the mooring system, accurately calculate the length of the mooring lines, and optimize their arrangement. The discrete grid positions obtained in the first stage are used as the initial solutions. The positions of the remaining wind turbines in the same row are determined by the coordinates of the first wind turbine, the preset row direction vector, and the fixed row spacing to maintain regular arrangement characteristics. The continuous coordinates of the wind turbines, the row spacing, and the overall deflection angle of each wind turbine's mooring system are used as decision variables to construct a continuous optimization model with the goal of maximizing net present value. Minimum safety distance constraints between wind turbines and between mooring lines are applied to the model. A metaheuristic search algorithm is used to solve the continuous optimization model, co-optimizing the wind turbine positions and mooring line arrangement parameters. S4. During the optimization process, the wake model is used to calculate the wake effect between wind turbines to assess power generation. At the same time, the mooring line length is accurately calculated based on the seabed topography to assess the cost. Finally, a coordinated optimization layout scheme for wind turbines and mooring systems is output.

2. The method for co-designing the regular layout and mooring system of a floating wind farm according to claim 1, characterized in that, Step S2, which involves constructing and solving a grid-based mixed-integer linear programming model, includes: The planned sea area is discretized into a grid, with the grid center serving as the candidate wind turbine location; An objective function is constructed to maximize the net present value, which is the difference between the discounted power generation revenue and the total construction and operation costs during the wind farm's operation period. The cost calculation items are constructed, including using a water depth proxy function to express the platform cost, mooring line cost, electrical system cost and operation and maintenance cost as a first-order or proportional function of the water depth, wherein the mooring line cost is approximately evaluated by the water depth at the grid where the wind turbine is located; Construct rule-based layout constraints by predefining a set of layout patterns and introducing decision variables to control that each row of the wind farm can only select one layout pattern, and the entire wind farm adopts a unified layout pattern to ensure that the wind turbine positions are arranged in a regular manner. In the model, the wind turbine installation decision is represented by 0 / 1 variables and includes constraints to ensure the total number of wind turbines installed, meet the minimum safety distance, and set logical upper and lower limits for the wind turbine output power. The mixed-integer linear programming model was solved using a commercial solver to determine the initial installation location of the wind turbine on the discrete grid.

3. The method for co-designing the regular layout and mooring system of a floating wind farm according to claim 1, characterized in that, The process of constructing the rule layout constraints specifically includes: Define a set of layout patterns, each pattern being defined by a starting column index and a fixed integer grid spacing, and ensure that the number of fans that can be installed in a specified row under this pattern does not exceed the grid column limit of that row; A global pattern selection variable is introduced to constrain the entire wind farm to adopt only one dominant layout pattern. Introduce row pattern activation variables to constrain each row of the wind farm to activate at most one layout pattern, and the activated pattern must be the globally selected dominant pattern. By using a predefined binary mapping matrix, the selected layout pattern is combined with row activation variables and transformed into wind turbine installation decision variables at specific grid locations.

4. The method for co-designing the regular layout and mooring system of a floating wind farm according to claim 1, characterized in that, The water depth proxy function is also specifically used for: In the mixed-integer linear programming stage, the platform cost of a single floating wind turbine is modeled as a linear function of the water depth; The maintenance cost ratio of a single floating wind turbine is also modeled as a linear function of water depth.

5. The method for co-designing the regular layout and mooring system of a floating wind farm according to claim 1, characterized in that, Step S3, which involves constructing a continuous coordinate optimization model and using a metaheuristic search algorithm for collaborative fine-tuning, also includes allowing the first wind turbine in each row to move freely within the continuous region corresponding to its original grid.

6. The method for co-designing the regular layout and mooring system of a floating wind farm according to claim 1, characterized in that, The precise calculation of the mooring line length in step S3 includes: Each wind turbine is equipped with multiple mooring lines, which are evenly distributed around the wind turbine on a horizontal plane; Based on the plane coordinates of the wind turbine, the overall deflection angle of the mooring line, and the horizontal projection length of the mooring line on the sea level, calculate the plane coordinates of the anchoring point corresponding to each mooring line. Based on the geometric relationship between the actual seabed depth at the anchoring point, the depth of the mooring guide hole, and the preset mooring line inclination angle, the necessary horizontal projection length of the mooring line is determined. The actual length of the mooring line is accurately calculated using geometric relationships based on the horizontal projected length and the difference between the water depth at the anchor point and the depth of the guide hole.

7. The method for co-designing the regular layout and mooring system of a floating wind farm according to claim 1, characterized in that, The calculation of the wake model in step S4 includes: The wake-induced velocity loss factor of the upstream wind turbine on the downstream wind turbine is calculated using a wake model based on the cosine function. The calculation of the loss factor involves a core term related to the wind turbine thrust coefficient and rotor radius, multiplied by a cosine function term determined by the ratio of the radial distance from the downstream position to the wake centerline to the wake radius at a specific downstream position, where the wake radius increases linearly with the downstream distance. For the multiple wake superposition effects on downstream wind turbines, a linear superposition model is used to calculate the actual output power under the combined effect. Specifically, under a given wind scenario, the actual output power of the downstream wind turbine is equal to the power without wake influence minus the sum of the power losses caused by all upstream wind turbines.

8. The method for co-designing the regular layout and mooring system of a floating wind farm according to claim 1, characterized in that, The power output calculation of the wind turbine is described using a piecewise function: The power output of the wind turbine is expressed as a piecewise function of the incoming wind speed, including the zero-power region below the cut-in wind speed, the constant rated power region between the rated wind speed and the cut-out wind speed, and the power growth region between the cut-in wind speed and the rated wind speed, which is proportional to the cube of the wind speed.

9. The method for co-designing the regular layout and mooring system of a floating wind farm according to claim 1, characterized in that, The mooring system adopts a three-line mooring configuration, with each mooring line having a set angle evenly distributed on the horizontal plane, and the mooring line inclination angle is fixed.

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 co-designing the regular layout and mooring system of a floating wind farm as described in any one of claims 1 to 9.

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