An optimization method for regular layout of offshore wind farms considering seabed topography and turbulence intensity

Abstract

This invention discloses a method for optimizing the regular layout of offshore wind farms, considering seabed topography and turbulence intensity. The method includes: discretizing the target area into a grid and defining the layout rotation angle; constructing a mixed-integer linear fractional programming model with the objective of minimizing the levelized cost of electricity (LCOE), which integrates a wake model based on axisymmetric cosine functions and a turbulence model based on axisymmetric double Gaussian functions, and piecewise linearizing the turbulence nonlinear terms; using predefined layout patterns and regular layout constraints, along with engineering constraints such as the number of wind turbines, power output, and safety distance; and employing the bounded Dinkelbach algorithm to iteratively solve the angle-decomposed subproblems to obtain the globally optimal layout. This method can effectively optimize wake loss, turbulence fatigue, and topography-related costs in a coordinated manner, providing an economical and efficient layout scheme for offshore wind farm planning.

Description

Technical Field

[0001] This invention relates to power system planning and offshore wind power technology, and in particular to a method for optimizing the regular layout of offshore wind farms that takes into account seabed topography and turbulence intensity. Background Technology

[0002] Offshore wind power, with its advantages of high capacity factor, proximity to coastal load centers, and support for large-scale dispatch, has become an important pillar for ensuring energy security, reducing dependence on fossil fuels, and addressing climate change. In the early planning stage of offshore wind farms, micro-site selection is a crucial step in reducing energy costs. To minimize visual impact, reduce infrastructure costs, and improve operational convenience, actual offshore wind farms typically adopt a regular layout.

[0003] However, the layout of offshore wind farms faces complex physical and economic challenges. First, wake effects can lead to power losses of approximately 10%–20%, while additional fatigue loads caused by turbulence can increase operation and maintenance costs by 5%–15%. Second, the cost of the support structure accounts for about 20% of the total investment cost, and its cost is significantly affected by seabed topography, water depth, and soil type (such as silt and rock). Current layout optimization methods are mainly divided into heuristic algorithms and mathematical programming methods. Although heuristic algorithms are widely used, they lack global optimality guarantees and their performance is highly dependent on parameter settings; while existing mathematical programming methods do not consider regular layouts and often assume that the site is rectangular, making it difficult to handle real sites with irregular boundaries. Currently, few studies have been able to integrate seabed topography, turbulence intensity, and regular layout strategies into a unified optimization framework for Levelized Cost of Energy (LCOE).

[0004] 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

[0005] The main objective of this invention is to overcome the deficiencies in the aforementioned background technology and provide a method for optimizing the regular layout of offshore wind farms that takes into account seabed topography and turbulence intensity.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A method for optimizing the regular layout of offshore wind farms, taking into account seabed topography and turbulence intensity, includes the following steps:

[0008] S1. Discretize the target offshore wind farm area into a grid, acquire and initialize wind resource data, seabed topography and water depth data, and soil type data, and define the rotation angle variable of the wind farm layout to adapt to different layout directions.

[0009] S2. Construct a mixed integer linear fractional programming model with the objective of minimizing the levelized cost of electricity. In the model, capital expenditure includes the cost of the supporting structure and installation cost calculated in detail based on water depth and soil type, and operation and maintenance expenditure includes fatigue maintenance cost coupled with the influence of turbulence intensity.

[0010] S3. The wake model and the turbulence model are integrated in the model. The wake model adopts a two-dimensional velocity deficit characterization based on the axisymmetric cosine function, and the turbulence model adopts an additional turbulence intensity characterization based on the axisymmetric double Gaussian function. The nonlinear radical term in the turbulence intensity calculation is piecewise linearized to transform the physical constraints into a linear form.

[0011] S4. Construct regular layout constraints by fitting the wind farm boundary to a rotatable rectangular grid and predefining a set of layout patterns determined by the spacing between the starting column and fixed columns. This constrains the entire wind farm to adopt a uniform rotation angle and layout pattern to generate regularly arranged wind turbine positions.

[0012] S5. Construct engineering constraints including constraints on the number of wind turbines, upper and lower limits of power output, and minimum safe distance.

[0013] S6. The mixed integer linear fractional programming model is decomposed into multiple subproblems according to the rotation angle. The bounded Dinkelbach algorithm is used to iteratively solve each subproblem. By constructing an auxiliary function, the fractional objective is transformed into a linear problem, and the upper and lower bounds are updated until convergence. Finally, the optimal layout scheme with the lowest levelized electricity cost is selected from all the solutions to the subproblems.

[0014] Furthermore, the construction of the mixed-integer linear fractional programming model aimed at minimizing the levelized cost of electricity (LCOE) in step S2 includes:

[0015] The levelized cost of electricity (LCOE) is defined as the ratio of the annualized total cost of a wind farm to its annual power generation. The annualized total cost includes capital expenditure, operating expenditure, and maintenance expenditure. Among these, the cost of the supporting structure in the capital expenditure is dynamically calculated based on the water depth at the wind turbine installation location, determining its geometric dimensions and steel usage. The installation cost is calculated using sensitivity coefficients for muddy and rocky terrain, respectively, based on the water depth at the installation location and binary variables indicating soil type. Maintenance expenditure is quantified by the fatigue damage frequency calculated from the superposition of turbulence intensity.

[0016] Furthermore, the method for quantifying fatigue maintenance costs in step S2 includes:

[0017] Maintenance costs consist of preventative maintenance costs and corrective maintenance costs;

[0018] The frequency of corrective maintenance is determined by the ratio of total fatigue damage in the wind farm to a preset fatigue threshold.

[0019] The total fatigue damage includes the working fatigue component calculated from the cumulative power generation of the wind turbine, and the disturbance fatigue component calculated from the cumulative turbulence intensity at the location of the wind turbine. The two are obtained by weighted summation using a disturbance coefficient.

[0020] Furthermore, the integration of the wake model and the turbulence model and the linearization process described in step S3 include:

[0021] In the wake model, the wind speed at the downstream fan is calculated by subtracting the wake-induced velocity deficit factor caused by the upstream fan from the ambient wind speed. The deficit factor is related to the fan thrust coefficient, rotor radius, and the downstream and lateral distances between the upstream and downstream fans. It is corrected by a radial distribution based on a cosine function to characterize the non-uniform radial distribution of the wake velocity.

[0022] In the turbulence model, the additional turbulence intensity generated by the upstream wind turbine on the downstream wind turbine is represented as the product of the downstream attenuation function and the radial distribution function. The radial distribution function is a weighted sum of two Gaussian functions, and its weighting coefficient is adjusted according to the relationship between the downstream position and the rotor radius of the upstream wind turbine to characterize the peak turbulence intensity in the tip region of the wind turbine blades.

[0023] For the overall turbulence intensity experienced by downstream wind turbines, the arithmetic square of the sum of the squares of the environmental turbulence and the additional turbulence of all upstream wind turbines is first calculated. Then, by introducing intermediate auxiliary variables and piecewise linearization techniques, the nonlinear square root operation is transformed into a linear expression composed of multiple linear interval constraints.

[0024] Further, in step S3, the radial distribution correction based on the cosine function in the wake model is achieved in the following way: the wake-induced velocity deficit factor is multiplied by a cosine function term determined by the ratio of the radial distance from the downstream fan position to the wake centerline to the wake radius at a specific downstream position, wherein the wake radius increases linearly with the downstream distance between the upstream and downstream fans.

[0025] In the turbulence model, the weighting coefficient of the radial distribution function is adjusted according to the relationship between the downstream position and the rotor radius of the upstream wind turbine. Specifically, when the downstream position is within the rotor radius, the weighting coefficient is defined by the square cosine function of the ratio of radial distance to rotor diameter; when the downstream position exceeds the rotor radius, the weighting coefficient is a constant.

[0026] Furthermore, in step S3, when calculating the superimposed effect of the wakes of multiple wind turbines using the wake model, a linear superposition model is adopted:

[0027] In a given wind scenario, the actual output power of the downstream wind turbine is equal to its power when there is no wake effect, minus the sum of the power losses caused by all upstream wind turbines that have a wake effect on it; wherein, the power loss caused by each upstream wind turbine is calculated by the wake model to obtain the actual wind speed at the downstream wind turbine, and determined according to the wind turbine power characteristic curve.

[0028] Furthermore, the calculation of the wind turbine output power in step S3 is described using a piecewise function:

[0029] Based on the incoming wind speed, the fan power is divided into the zero-power zone below the cut-in wind speed, the power growth zone between the cut-in wind speed and the rated wind speed that is proportional to the cube of the wind speed, the rated power zone between the rated wind speed and the cut-out wind speed that is constant, and the zero-power zone above the cut-out wind speed.

[0030] Furthermore, the construction rule layout constraints described in step S4 specifically include:

[0031] Define a rectangular grid covering the boundary of the wind farm and introduce a grid feasibility index to ensure that wind turbines can only be installed in the center of the grid within the boundary;

[0032] A predefined set of layout patterns is used, each pattern being uniquely determined by the starting column number and a fixed integer column spacing;

[0033] By introducing a global mode and rotation angle selection variable, the entire wind farm is constrained to use only one combination.

[0034] A row pattern activation variable is introduced to map the selected global layout pattern to each row of the wind farm. The row activation variable is then transformed into wind turbine installation decision variables at specific grid locations through a predefined binary mapping matrix that is related to the selected pattern and angle.

[0035] Furthermore, the step S6, which involves using the bounded Dinkelbach algorithm to solve the problem, includes:

[0036] For each subproblem with a fixed rotation angle, an auxiliary linear objective function is constructed in each iteration. This objective function is the annualized total cost minus the product of the current levelized cost of electricity (LCOE) estimate and the annual power generation.

[0037] Solve the auxiliary linear problem and update the lower bound estimate of the levelized cost of electricity (LCOE) based on the objective function value of the optimal solution;

[0038] Meanwhile, the optimal solution of the auxiliary problem is used to calculate the actual levelized cost of electricity as the current upper bound;

[0039] Repeat the iteration until the difference between the current upper and lower bounds is less than the preset tolerance, then output the current upper bound as the optimal levelized cost of electricity and the corresponding layout scheme for this subproblem.

[0040] After traversing all subproblems involving rotation angles, the globally optimal layout scheme is selected from them.

[0041] A computer program product includes a computer program that, when executed by a processor, implements the offshore wind farm regular layout optimization method.

[0042] The present invention has the following beneficial effects:

[0043] This invention proposes a method for optimizing the regular layout of offshore wind farms, taking into account seabed topography and turbulence intensity, providing a scientific micro-site selection scheme for the early planning stage of offshore wind farms. Over the entire life cycle, this method comprehensively couples the impact of seabed topography on support structures and installation costs, fatigue maintenance expenses caused by turbulence intensity, and power losses due to wake effects between turbines. While meeting the requirements of regular engineering layout, it aims to minimize the levelized cost of electricity (LCOE), ultimately achieving a significant improvement in the overall economic benefits of offshore wind power development.

[0044] The core of this method lies in constructing an optimization framework based on mixed-integer linear fractional programming. For the first time, it integrates accurate wake and turbulence models into the planning model, enabling a more realistic reflection of the interactions between wind turbines and fatigue loads under high-turbulence environments. Simultaneously, the model fully considers complex seabed topography, allowing for refined calculation of wind turbine support structure costs and installation costs based on water depth and soil type (e.g., mud or rock) at different locations. To overcome the computational bottleneck of large-scale layout optimization, this invention utilizes the characteristics of regular layouts to reduce the dimensionality of decision variables and further proposes an improved power calculation algorithm based on the traveling wind turbine to replace the traditional time-consuming individual turbine calculation method. The model ultimately employs the bounded Dinkelbach algorithm for efficient solution, significantly improving solution efficiency and global search capability.

[0045] The method proposed in this invention has demonstrated significant comprehensive optimization effects in practical engineering cases. By applying this optimization method, the spatial arrangement of wind farms has been rationalized after adjusting the direction, effectively improving the uniformity of turbine spacing. The optimized scheme has achieved positive results in overall cost control; while some cost items have increased slightly, the total cost has been reduced through significant savings in the cost of supporting structures. Simultaneously, this layout effectively alleviates wake interference between turbines, significantly improving wake losses and thus enhancing the overall power generation performance of the wind farm. Ultimately, the optimized layout has resulted in a substantial reduction in the levelized cost of electricity (LCOE), significantly improving the economic benefits of the wind farm throughout its entire life cycle. Experimental verification shows that the method proposed in this invention can effectively coordinate power generation revenue with construction and operation and maintenance costs, providing strong technical support for the efficient and economical development of offshore wind power.

[0046] Other beneficial effects of the embodiments of the present invention will be further described below. Attached Figure Description

[0047] Figure 1 This is the overall flowchart of the offshore wind farm regular layout optimization method of the present invention.

[0048] Figure 2 This is a schematic diagram of the 2D Jensen wake model and the additional turbulence model in an embodiment of the present invention.

[0049] Figure 3 This is a schematic diagram of piecewise linearization of the turbulence curve in an embodiment of the present invention;

[0050] Figure 4 This is a schematic diagram of grid division for wind farms of arbitrary shapes in an embodiment of the present invention;

[0051] Figure 5 This is a schematic diagram of the layout mode in an embodiment of the present invention;

[0052] Figure 6 This is a wind direction frequency diagram of the target wind farm in an embodiment of the present invention;

[0053] Figure 7 This is an initial layout diagram of a wind farm in an embodiment of the present invention;

[0054] Figure 8 This is the final layout diagram obtained by optimizing the wind farm in an embodiment of the present invention. Detailed Implementation

[0055] 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.

[0056] 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.

[0057] This invention aims to solve the problem of synergistic optimization of wake loss, turbulence fatigue and complex seabed topography costs in the micro-site selection of offshore wind farms. It proposes a regular layout optimization method that couples wake-turbulence model and topography cost analysis, and constructs a MILFP integrated optimization framework with LCOE as the objective. Through regular layout constraints and efficient solution algorithms, it achieves the comprehensive optimization of power generation efficiency and total life cycle cost while ensuring engineering practicality.

[0058] See Figure 1 This invention provides a method for optimizing the regular layout of offshore wind farms, taking into account seabed topography and turbulence intensity, comprising the following steps:

[0059] Step S1: Discretize the target offshore wind farm area into a grid, acquire and initialize wind resource data, seabed topography and water depth data, and soil type data, and define the rotation angle variable of the wind farm layout to adapt to different arrangement directions.

[0060] In some embodiments, the gridding discretization can be to fit the target offshore wind farm area into a rectangle and discretize it into equal-sized grids, with the center of each grid as the candidate installation location for wind turbines; the initialized wind resource data includes wind speed, wind direction and environmental turbulence intensity under different wind scenarios, and the seabed topography data clarifies the water depth value and soil type (mud or rock) corresponding to each grid center; the defined rotation angle variable is used to adjust the arrangement direction of the rectangular grids, and together with the grid feasibility index (effective when the grid center is located within the boundary of the wind farm), it can achieve adaptation to irregular boundary sites.

[0061] Step S2: Construct a mixed integer linear fractional programming model with the objective of minimizing the levelized cost of electricity. In the model, capital expenditure includes the cost of the support structure and installation cost calculated in detail based on water depth and soil type, and operation and maintenance expenditure includes fatigue maintenance cost coupled with the influence of turbulence intensity.

[0062] In some embodiments, the construction of a mixed-integer linear fractional programming model aimed at minimizing the levelized cost of electricity (LCOE) in step S2 includes:

[0063] The levelized cost of electricity (LCOE) is defined as the ratio of the annualized total cost of a wind farm to its annual power generation. The annualized total cost includes capital expenditure, operating expenditure, and maintenance expenditure. Among these, the cost of the supporting structure in the capital expenditure is dynamically calculated based on the water depth at the wind turbine installation location, determining its geometric dimensions and steel usage. The installation cost is calculated using sensitivity coefficients for muddy and rocky terrain, respectively, based on the water depth at the installation location and binary variables indicating soil type. Maintenance expenditure is quantified by the fatigue damage frequency calculated from the superposition of turbulence intensity.

[0064] In some embodiments, the method for quantifying fatigue maintenance costs in step S2 includes: maintenance expenditures consisting of preventive maintenance costs and corrective maintenance costs; the frequency of corrective maintenance is determined by the ratio of the total fatigue damage of the wind farm to a preset fatigue threshold; the total fatigue damage includes the working fatigue portion calculated from the cumulative power generation of the wind turbine, and the disturbance fatigue portion calculated from the cumulative turbulence intensity at the location of the wind turbine, the two being obtained by weighted summation using a disturbance coefficient.

[0065] In some embodiments, the integration of the wake model and the turbulence model and the linearization process in step S3 includes: In the wake model, the windward velocity of the downstream wind turbine is calculated by subtracting the wake-induced velocity deficit factor caused by the upstream wind turbine from the ambient wind speed. The deficit factor is related to the wind turbine thrust coefficient, rotor radius, and the downstream and lateral distances between the upstream and downstream wind turbines. It is corrected using a radial distribution based on a cosine function to characterize the non-uniform radial distribution of the wake velocity. In the turbulence model, the additional turbulence intensity generated by the upstream wind turbine on the downstream wind turbine is expressed as the product of the downstream attenuation function and the radial distribution function. The radial distribution function is a weighted sum of two Gaussian functions, and its weight coefficient is adjusted according to the relationship between the downstream position and the rotor radius of the upstream wind turbine to characterize the peak turbulence intensity in the tip region of the wind turbine blades. For the overall turbulence intensity experienced by the downstream wind turbine, the arithmetic square of the sum of squares of the ambient turbulence and the additional turbulence of all upstream wind turbines is first calculated. Then, by introducing intermediate auxiliary variables and piecewise linearization techniques, the nonlinear square root operation is transformed into a linear expression composed of multiple linear interval constraints.

[0066] Step S3: Integrate the wake model and the turbulence model into the model. The wake model adopts a two-dimensional velocity deficit characterization based on the axisymmetric cosine function, and the turbulence model adopts an additional turbulence intensity characterization based on the axisymmetric double Gaussian function. The nonlinear square root term in the turbulence intensity calculation is piecewise linearized to transform the physical constraints into a linear form.

[0067] In some embodiments, in step S3, the radial distribution correction based on the cosine function in the wake model is implemented as follows: the wake-induced velocity deficit factor is multiplied by a cosine function term determined by the ratio of the radial distance from the downstream turbine location to the wake centerline to the wake radius at a specific downstream location, wherein the wake radius increases linearly with the downstream distance between the upstream and downstream turbines; in the turbulence model, the weighting coefficient of the radial distribution function is adjusted according to the relationship between the downstream location and the rotor radius of the upstream turbine, specifically: when the downstream location is within the rotor radius range, the weighting coefficient is defined by the square cosine function of the ratio of the radial distance to the rotor diameter; when the downstream location exceeds the rotor radius range, the weighting coefficient is a constant.

[0068] In some embodiments, when the wake model in step S3 calculates the superimposed wake effects of multiple wind turbines, a linear superposition model is adopted: under a given wind scenario, the actual output power of the downstream wind turbine is equal to its power when it has no wake effect, minus the sum of the power losses caused by all upstream wind turbines that have wake effects on it; wherein, the power loss caused by each upstream wind turbine is calculated by the wake model to obtain the actual wind speed at the downstream wind turbine, and determined according to the wind turbine power characteristic curve.

[0069] In some embodiments, the calculation of the fan output power in step S3 is described by a piecewise function: based on the incoming wind speed, the fan power is divided into a zero power region below the cut-in wind speed, 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, a constant rated power region between the rated wind speed and the cut-out wind speed, and a zero power region above the cut-out wind speed.

[0070] Step S4: Construct regular layout constraints. By fitting the wind farm boundary to a rotatable rectangular grid and predefining a set of layout patterns determined by the spacing between the starting column and fixed columns, the entire wind farm is constrained to adopt a uniform rotation angle and layout pattern to generate regularly arranged wind turbine positions.

[0071] In some embodiments, the construction of rule layout constraints in step S4 specifically includes: defining a rectangular grid covering the boundary of the wind farm and introducing a grid feasibility index to ensure that wind turbines can only be installed in the center of the grid within the boundary; predefining a set of layout patterns, each pattern being uniquely determined by the starting column number and a fixed integer column spacing; introducing global pattern and rotation angle selection variables to constrain the entire wind farm to use only one combination; introducing row pattern activation variables to map the selected global layout pattern to each row of the wind farm, and transforming the row activation variables into wind turbine installation decision variables at specific grid locations through a predefined binary mapping matrix related to the selected pattern and angle.

[0072] Step S5: Construct engineering constraints including constraints on the number of wind turbines, upper and lower limits of power output, and minimum safe distance.

[0073] In some embodiments, the wind turbine quantity constraint is that the total number of wind turbines to be installed in the wind farm is fixed; the upper and lower limit constraints of power output are that the actual output power of a single wind turbine in any wind scenario does not exceed its theoretical power when there is no wake effect, and is not less than zero; the minimum safe distance constraint is that the straight-line distance between the installation positions of any two wind turbines is not less than a preset safety threshold (determined based on the diameter of the wind turbine blades) to avoid mutual interference.

[0074] Step S6: Decompose the mixed integer linear fractional programming model into multiple subproblems according to the rotation angle, and use the bounded Dinkelbach algorithm to iteratively solve each subproblem. By constructing an auxiliary function, the fractional objective is transformed into a linear problem, and the upper and lower bounds are updated until convergence. Finally, the optimal layout scheme with the lowest levelized electricity cost is selected from all the solutions to the subproblems.

[0075] In some embodiments, the solution using the bounded Dinkelbach algorithm in step S6 includes: for each subproblem with a fixed rotation angle, constructing an auxiliary linear objective function in each iteration, the objective function being the annualized total cost minus the product of the current levelized cost of electricity (LCOE) and the annual power generation; solving the auxiliary linear problem, and updating the lower bound estimate of the LCOE based on the objective function value of its optimal solution; simultaneously, calculating the actual LCOE using the optimal solution of the auxiliary problem as the current upper bound; repeating the iteration until the difference between the current upper and lower bounds is less than a preset tolerance, then outputting the current upper bound as the optimal LCOE and the corresponding layout scheme for the subproblem; after traversing all subproblems with rotation angles, selecting the globally optimal layout scheme from them.

[0076] This invention proposes a method for optimizing the regular layout of offshore wind farms. Addressing the challenges of coordinating wake loss, turbulent fatigue load, and costs associated with complex seabed topography in the micro-site selection of offshore wind farms, and the difficulty of existing mathematical programming methods in balancing irregular sites with regular engineering layouts, this invention, for the first time, constructs a unified framework of mixed-integer linear fractional programming with the levelized cost of electricity (LCOE) as the direct objective. This framework innovatively integrates a precise wake and turbulence physical model, a refined topographic cost model based on water depth and soil type, and regular layout constraints adaptable to irregular boundaries. Through an efficient solution strategy based on angle decomposition and the bounded Dinkelbach algorithm, it achieves a comprehensive optimization of power generation improvement, fatigue loss control, and construction cost savings while ensuring engineering practicality and global optimization capabilities. Real-world case studies (which will be further detailed later) demonstrate that this method effectively optimizes turbine layout, significantly reduces wake loss and overall LCOE, and ultimately greatly improves the economic benefits of offshore wind power development.

[0077] The following further describes specific embodiments of the present invention, algorithm examples, and experimental verification.

[0078] A method for optimizing the regular layout of offshore wind farms that takes into account seabed topography and turbulence intensity, the method comprising the following steps.

[0079] (1) Optimization steps

[0080] 1) Site gridding and data initialization. The offshore wind farm is discretized using a grid method, a rotation angle variable is defined to accommodate arbitrary layout directions, and wind resources, seabed depth, and soil type data are initialized.

[0081] 2) Construct the LCOE objective function. A function is established to minimize the LCOE, where the cost term is refined to consider the foundation and installation costs of wind turbines under different terrains, and the operation and maintenance term is coupled with equipment fatigue losses caused by turbulence intensity.

[0082] 3) Physical field modeling and linearization. The wake model and turbulence model are integrated, and piecewise linearization techniques are used to handle the nonlinear terms in the turbulence calculation, transforming the physical constraints into a linear programming form.

[0083] 4) Constraint Construction. Imposing power output constraints, regular layout constraints, and minimum safe distance constraints on the wind farm.

[0084] 5) Model Solving. The main problem of the MILFP model is decomposed into subproblems according to the rotation angle. Iterative optimization using BDA is used to quickly solve for the optimal layout scheme that minimizes LCOE.

[0085] (2) Wake model and additional turbulence model

[0086] This invention employs a 2D Jensen wake model to accurately characterize the velocity loss between wind turbines. This model overcomes the shortcomings of traditional linear models that ignore the uneven velocity distribution across the wake cross-section. By using an axisymmetric cosine function to fit the wake profile, it can more realistically reflect the radial distribution of wind speed, such as... Figure 2 As shown in (a). In a given wind scenario Next, consider the fan. When the wake effect occurs, the fan Wind speed Represented as:

[0087]

[0088] in, For the inflow wind speed of the environment, It is a tailflow-induced loss factor. Depends on thrust coefficient wake attenuation constant and wind turbines Japanese-style fan lateral distance and radial distance Its expression is:

[0089]

[0090] in, The radius of the wind turbine blade.

[0091] To evaluate the fatigue load and maintenance costs of wind turbines in high-turbulence environments, this invention integrates an improved additional turbulence model. This model uses an axisymmetric double Gaussian function to characterize the radial distribution of the added turbulence. Compared to traditional models, this model can accurately capture the local peak turbulence intensity at the tips of the wind turbine blades, thus providing a more precise assessment of the wind turbine's fatigue life. Figure 2 As shown in (b) of the image. In the wind scene. Below, the fan For the fan Additional turbulence generated It can be expressed as the following formula:

[0092]

[0093] in, These are the downstream function and the runoff function, respectively, and their specific expressions are shown in equations (4) and (5).

[0094]

[0095]

[0096] Where D is the diameter of the wind turbine blade. For environmental turbulence, The Gaussian distribution parameters are calculated using the following formula:

[0097]

[0098] In equation (5), and The turbulence parameters are calculated according to equations (7) and (8):

[0099]

[0100]

[0101] (3) Power output and turbulence superposition

[0102] In the wind scene Below, the fan Affected by a single wind turbine When the wake effect is present, the wind turbine Output power It can be represented by a piecewise function:

[0103]

[0104] 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. Considering the combined effect of multiple turbine wakes, the fan... power It can be represented as:

[0105]

[0106] in, 0 / 1 decision variables represent the grid. Whether to install a fan (1 indicates installation, 0 indicates no installation). Indicates a wind scene Below, without considering the wake effect, the fan . output power.

[0107] In this invention, the turbulence intensity of wind turbines in a wind farm is calculated using a sum of squares method. Downdraft fan The turbulence intensity is expressed as:

[0108]

[0109] The presence of a square root in the above superposition formula disrupts the linearity of the model and increases computational complexity. This invention innovatively employs piecewise linearization to address this issue:

[0110] First, define intermediate variables. Then we have:

[0111]

[0112] Secondly, the turbulence intensity square root curve is divided into A range, such as Figure 3 The diagram illustrates piecewise linearization of the turbulence curve. This is achieved by introducing 0 / 1 variables. and continuous variables The definition is as follows:

[0113]

[0114]

[0115] in, and For interval The upper and lower boundaries.

[0116] Construct complete piecewise linearization constraints:

[0117]

[0118]

[0119]

[0120]

[0121] in, and They are intervals The slope and intercept, and These are the upper and lower bounds of the interval. The above constraints ensure that the turbulence intensity of each wind turbine falls precisely within the corresponding interval of the piecewise curve, thereby achieving the mapping from secondary turbulence to linear turbulence.

[0122] (4) Rule layout constraints

[0123] For offshore wind farms of arbitrary shapes, a rectangle covering its boundaries is first used for fitting. This rectangle is then discretized into a series of uniformly sized grids, with the center of each grid considered as a candidate turbine installation location. To control the orientation of the layout, the rectangle can be rotated around its center by an angle. ,like Figure 4As shown. To clarify the areas where wind turbines can be installed, wind farm feasibility indicators are defined. If located at the rotation angle Next line, number If the center of the grid in the column is within the boundary of the wind farm, then ;otherwise .

[0124] Based on this discretization scheme, the wind turbine installation decision variables are transformed from binary variables. It means that, among them Indicates in Grid at angle ( The fan will be installed in the center. To ensure that the fan is placed only within the feasible area, the following constraints must be met:

[0125]

[0126] Inside the wind farm, each row The arrangement of the wind turbines is abstracted into a layout pattern. Each pattern Characterized by two key parameters: the initial column of the first wind turbine. and the column spacing between adjacent wind turbines Layout patterns such as Figure 5 As shown.

[0127] Define binary parameters If the pattern rotation angle The next If the fans are placed in the row, then Otherwise, the value is 0. To ensure the regularity of the rules, the present invention imposes the following constraints:

[0128]

[0129]

[0130]

[0131]

[0132]

[0133] in, Select mode 0 / 1 variables, Indicates the first Line adopts mode The decision variables. Equation (20) constraint ensures that the entire wind farm is only allowed to choose one rotation angle and one overall layout pattern, while equations (21) and (22) ensure that each row A perspective and pattern consistent with the global context must be adopted. Equations (23) and (24) then depend on the selected pattern. and angle For grid variables Assignment. The final two-dimensional... Can be mapped to a one-dimensional variable .

[0134] (5) Mathematical model

[0135] The optimization objective of this invention is to minimize LCOE, which is defined as the ratio of annualized total cost (AC) of a wind farm to annual total power generation (AEP).

[0136]

[0137] Where CE represents capital expenditure, OE represents operating expenditure, ME represents maintenance expenditure, and CRF represents the capital recovery factor, calculated as follows:

[0138]

[0139] in, The discount rate is... The number of years of operation.

[0140] CE covers wind turbine purchase Support structure Electrical system Installation costs and other expenses Among them, the cost of the supporting structure and installation costs It is significantly influenced by seabed topography (water depth and soil type).

[0141] Considering the differences in engineering difficulty and equipment requirements due to different seabed geology, installation costs... Calculated using the following formula:

[0142]

[0143] in, and These are the basic installation cost and the additional installation cost. and q represents the installation cost sensitivity coefficient for muddy and rocky terrain; The topographic indicator variable is 1 for rocks and 0 for mud. For grid The water depth is in the center.

[0144] The cost of the supporting structure is determined by the amount and unit price of steel used, and its geometric parameters vary with the water depth at the installation location. Dynamic adjustment:

[0145]

[0146] in, , To support the diameter, thickness, and length of the structure, This refers to the unit price of steel.

[0147] Purchase cost Electrical system costs Other expenses All are assumed to be fixed assets and converted based on installed capacity or number of wind turbines.

[0148] Meanwhile, this invention divides the annual operation and maintenance cost into two parts: annual fixed operating expenses (OE) and annual maintenance expenses (ME). The fixed operating expenses (OE) are linearly related to the total installed capacity of the offshore wind farm.

[0149]

[0150] in, This is the annual operating cost coefficient per unit capacity. This refers to the rated power of a single fan.

[0151] Maintenance expenses consist of preventative maintenance costs and corrective maintenance costs, and are designed to quantify the additional operational and maintenance requirements caused by turbulent environments.

[0152]

[0153] Where T represents the number of operating hours per year. For preventative maintenance (once every six months). The corrective maintenance frequency is calculated as follows:

[0154]

[0155] in, This is the preset fatigue threshold. The total fatigue damage of a wind farm can be broken down into operational fatigue. and disturbance fatigue Two parts:

[0156]

[0157] in, The disturbance coefficient is... The repair coefficient is... For reference turbulence intensity.

[0158] The complete mathematical model is given below:

[0159]

[0160]

[0161]

[0162]

[0163]

[0164] Equation (33) is the constraint on the number of wind turbines, Equation (34) is the constraint on the upper and lower limits of power, and Equation (35) is the constraint on the minimum safe distance between wind turbines.

[0165] (6) Optimization algorithm

[0166] Considering the wind turbine coordinate variables and layout rotation angle Due to the existence of strong coupling, this invention decomposes the MILFP Master Problem (MP) into... Each subproblem (SP) is based on a specific rotation angle. At a fixed rotation angle Find the optimal layout pattern This decouples the complex nonlinear search space into discrete angular intervals. The MP and SP distributions are expressed as equations (36) and (37):

[0167]

[0168]

[0169] in, For MP feasible region, For the first The feasible region of each subproblem For the first The rotation angle of the wind farm. Due to Therefore:

[0170]

[0171] For each SP, this invention uses BDA for solving. The algorithm steps are as follows:

[0172] 1) in the In the next iteration, an auxiliary function is constructed. The fractional form is transformed into a linear form for solution.

[0173] 2) Update the upper bound of the subproblem using the currently obtained optimal solution. Based on the solution of the auxiliary function, the lower limit is updated using the difference iteration formula. .

[0174] 3) The gap between the upper and lower limits If the value is less than the preset tolerance, the subproblem is considered to have reached its optimal solution, and then... = Otherwise, repeat steps 1)-2).

[0175] 4) After solving all the subproblems, the optimal solution is obtained according to equation (38).

[0176] Experimental verification

[0177] The effectiveness of the optimization method of this invention was verified through micro-site planning of an offshore wind farm in China. The site of the wind farm is approximately 13 km long from east to west and 10 km wide from north to south, with a total area of ​​approximately 88.6 square kilometers. The site has a water depth ranging from 37m to 43m. A triangular rocky area exists in the western part of the site, while the rest of the area is mainly muddy seabed. The average annual wind speed at the wind farm is 8.67 m / s, with the prevailing wind directions being northeast and south, and the wind frequency being as follows: Figure 6 As shown in the diagram. The plan is to install 47 wind turbine generators, each with a rated power of 13 MW, for a total installed capacity of 611 MW. The turbine rotor radius is 263 m, the hub height is 155 m, the cut-in wind speed is 3 m / s, and the cut-out wind speed is 21 m / s. The initial layout of the wind farm is as follows. Figure 7 As shown.

[0178] The optimized layout is as follows Figure 8 As shown. Compared to the initial layout where the fans were arranged horizontally, the optimized layout rotated 10° clockwise, achieving a more uniform distribution and increasing the spacing between the fans. In the original layout, no fans were placed in the rocky area, while the optimized layout includes one fan in that area. Table 1 shows the comparison results before and after optimization. Although the optimized layout leads to lower installation costs ( The cost of maintenance (O&M) increased by RMB 9.18 million, while the cost of supporting structures increased by RMB 18.5 million. This reduced costs by RMB 33.16 million, resulting in a lower total cost compared to the initial layout. Furthermore, the optimized layout significantly increased annual power generation (AEP), and wake losses were reduced by 4.64% compared to the initial layout. Ultimately, the levelized cost of electricity (LCOE) for the optimized layout was RMB 0.302 / kWh, a 5.5% reduction compared to the initial layout's RMB 0.320 / kWh.

[0179] Furthermore, even with a fixed feed-in tariff of 0.4298 yuan / kWh, and considering the 20% power generation loss due to maintenance shutdowns and power outages caused by extreme weather, the optimized wind farm layout is still expected to generate 896 million yuan more in revenue over its 20-year operational lifespan compared to the original layout (= [(0.4298-0.302)×2.460×...). -(0.4298-0.320)×2.353× The profit is (20 × 0.8).

[0180] Table 1 Comparison of results before and after optimization

[0181]

[0182] In summary, this invention provides a method for optimizing the regular layout of offshore wind farms considering seabed topography and turbulence intensity. By constructing a mixed-integer linear fractional programming framework aimed at minimizing the levelized cost of electricity (LCOE) over the entire lifecycle, it provides an efficient micro-site selection scheme for early-stage offshore wind power planning. This framework is the first to comprehensively integrate wake and turbulence models into a mathematical programming model and finely couples the impact of seabed topography on support structures and installation costs. By designing regular layout constraints adaptable to irregular sites to reduce the dimensionality of decision variables, and combining an improved power calculation algorithm based on wind turbines with the bounded Dinkelbach algorithm for efficient solution, it effectively reduces wake losses and turbulence fatigue loads while significantly improving the engineering practicality and economy of the optimization process, ultimately optimizing the overall economic benefits of offshore wind power development.

[0183] This invention also provides a storage medium for storing a computer program, which, when executed, performs at least the methods described above.

[0184] 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.

[0185] This invention also provides a processor that executes a computer program, at least performing the methods described above.

[0186] 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.

[0187] 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.

[0188] 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.

[0189] 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.

[0190] 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.

[0191] 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.

[0192] The methods disclosed in the several method embodiments provided by this invention can be arbitrarily combined without conflict to obtain new method embodiments.

[0193] The features disclosed in the several product embodiments provided by this invention can be arbitrarily combined without conflict to obtain new product embodiments.

[0194] 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.

[0195] 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 optimizing the regular layout of offshore wind farms considering seabed topography and turbulence intensity, characterized in that, Includes the following steps: S1. Discretize the target offshore wind farm area into a grid, acquire and initialize wind resource data, seabed topography and water depth data, and soil type data, and define the rotation angle variable of the wind farm layout to adapt to different layout directions. S2. Construct a mixed integer linear fractional programming model with the objective of minimizing the levelized cost of electricity. In the model, capital expenditure includes the cost of the supporting structure and installation cost calculated in detail based on water depth and soil type, and operation and maintenance expenditure includes fatigue maintenance cost coupled with the influence of turbulence intensity. S3. The wake model and the turbulence model are integrated in the model. The wake model adopts a two-dimensional velocity deficit characterization based on the axisymmetric cosine function, and the turbulence model adopts an additional turbulence intensity characterization based on the axisymmetric double Gaussian function. The nonlinear radical term in the turbulence intensity calculation is piecewise linearized to transform the physical constraints into a linear form. S4. Construct regular layout constraints by fitting the wind farm boundary to a rotatable rectangular grid and predefining a set of layout patterns determined by the spacing between the starting column and fixed columns. This constrains the entire wind farm to adopt a uniform rotation angle and layout pattern to generate regularly arranged wind turbine positions. S5. Construct engineering constraints including constraints on the number of wind turbines, upper and lower limits of power output, and minimum safe distance. S6. The mixed integer linear fractional programming model is decomposed into multiple subproblems according to the rotation angle. The bounded Dinkelbach algorithm is used to iteratively solve each subproblem. By constructing an auxiliary function, the fractional objective is transformed into a linear problem, and the upper and lower bounds are updated until convergence. Finally, the optimal layout scheme with the lowest levelized electricity cost is selected from all the solutions to the subproblems.

2. The method for optimizing the regular layout of offshore wind farms according to claim 1, characterized in that, The construction of the mixed-integer linear fractional programming model with the objective of minimizing the levelized cost of electricity (LCOE) in step S2 includes: The levelized cost of electricity (LCOE) is defined as the ratio of the annualized total cost of a wind farm to its annual power generation. The annualized total cost includes capital expenditure, operating expenditure, and maintenance expenditure. Among these, the cost of the supporting structure in the capital expenditure is dynamically calculated based on the water depth at the wind turbine installation location, determining its geometric dimensions and steel usage. The installation cost is calculated using sensitivity coefficients for muddy and rocky terrain, respectively, based on the water depth at the installation location and binary variables indicating soil type. Maintenance expenditure is quantified by the fatigue damage frequency calculated from the superposition of turbulence intensity.

3. The method for optimizing the regular layout of offshore wind farms according to claim 1, characterized in that, The method for quantifying fatigue maintenance costs in step S2 includes: Maintenance costs consist of preventative maintenance costs and corrective maintenance costs; The frequency of corrective maintenance is determined by the ratio of total fatigue damage in the wind farm to a preset fatigue threshold. The total fatigue damage includes the working fatigue component calculated from the cumulative power generation of the wind turbine, and the disturbance fatigue component calculated from the cumulative turbulence intensity at the location of the wind turbine. The two are obtained by weighted summation using a disturbance coefficient.

4. The method for optimizing the regular layout of offshore wind farms according to claim 1, characterized in that, Step S3, which involves integrating the wake model and the turbulence model and performing linearization, includes: In the wake model, the wind speed at the downstream fan is calculated by subtracting the wake-induced velocity deficit factor caused by the upstream fan from the ambient wind speed. The deficit factor is related to the fan thrust coefficient, rotor radius, and the downstream and lateral distances between the upstream and downstream fans. It is corrected by a radial distribution based on a cosine function to characterize the non-uniform radial distribution of the wake velocity. In the turbulence model, the additional turbulence intensity generated by the upstream wind turbine on the downstream wind turbine is represented as the product of the downstream attenuation function and the radial distribution function. The radial distribution function is a weighted sum of two Gaussian functions, and its weighting coefficient is adjusted according to the relationship between the downstream position and the rotor radius of the upstream wind turbine to characterize the peak turbulence intensity in the tip region of the wind turbine blades. For the overall turbulence intensity experienced by downstream wind turbines, the arithmetic square of the sum of the squares of the environmental turbulence and the additional turbulence of all upstream wind turbines is first calculated. Then, by introducing intermediate auxiliary variables and piecewise linearization techniques, the nonlinear square root operation is transformed into a linear expression composed of multiple linear interval constraints.

5. The method according to claim 4, characterized in that, In step S3, the radial distribution correction based on the cosine function in the wake model is achieved in the following way: the wake-induced velocity deficit factor is multiplied by a cosine function term determined by the ratio of the radial distance from the downstream fan position to the wake centerline to the wake radius at a specific downstream position, wherein the wake radius increases linearly with the downstream distance between the upstream and downstream fans. In the turbulence model, the weighting coefficient of the radial distribution function is adjusted according to the relationship between the downstream position and the rotor radius of the upstream wind turbine. Specifically, when the downstream position is within the rotor radius, the weighting coefficient is defined by the square cosine function of the ratio of radial distance to rotor diameter; when the downstream position exceeds the rotor radius, the weighting coefficient is a constant.

6. The method for optimizing the regular layout of offshore wind farms according to claim 5, characterized in that, When calculating the superimposed effect of the wakes of multiple wind turbines in step S3, a linear superposition model is used: In a given wind scenario, the actual output power of the downstream wind turbine is equal to its power when there is no wake effect, minus the sum of the power losses caused by all upstream wind turbines that have a wake effect on it; wherein, the power loss caused by each upstream wind turbine is calculated by the wake model to obtain the actual wind speed at the downstream wind turbine, and determined according to the wind turbine power characteristic curve.

7. The method for optimizing the regular layout of offshore wind farms according to claim 6, characterized in that, The calculation of the wind turbine output power in step S3 is described using a piecewise function: Based on the incoming wind speed, the fan power is divided into the zero-power zone below the cut-in wind speed, the power growth zone between the cut-in wind speed and the rated wind speed that is proportional to the cube of the wind speed, the rated power zone between the rated wind speed and the cut-out wind speed that is constant, and the zero-power zone above the cut-out wind speed.

8. The method for optimizing the regular layout of offshore wind farms according to claim 1, characterized in that, The construction rule layout constraints mentioned in step S4 specifically include: Define a rectangular grid covering the boundary of the wind farm and introduce a grid feasibility index to ensure that wind turbines can only be installed in the center of the grid within the boundary; A predefined set of layout patterns is used, each pattern being uniquely determined by the starting column number and a fixed integer column spacing; By introducing a global mode and rotation angle selection variable, the entire wind farm is constrained to use only one combination. A row pattern activation variable is introduced to map the selected global layout pattern to each row of the wind farm. The row activation variable is then transformed into wind turbine installation decision variables at specific grid locations through a predefined binary mapping matrix that is related to the selected pattern and angle.

9. The method for optimizing the regular layout of offshore wind farms according to claim 1, characterized in that, Step S6, which involves using the bounded Dinkelbach algorithm to solve the problem, includes: For each subproblem with a fixed rotation angle, an auxiliary linear objective function is constructed in each iteration. This objective function is the annualized total cost minus the product of the current levelized cost of electricity (LCOE) estimate and the annual power generation. Solve the auxiliary linear problem and update the lower bound estimate of the levelized cost of electricity (LCOE) based on the objective function value of the optimal solution; Meanwhile, the optimal solution of the auxiliary problem is used to calculate the actual levelized cost of electricity as the current upper bound; Repeat the iteration until the difference between the current upper and lower bounds is less than the preset tolerance, then output the current upper bound as the optimal levelized cost of electricity and the corresponding layout scheme for this subproblem. After traversing all subproblems involving rotation angles, the globally optimal layout scheme is selected from them.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the offshore wind farm regular layout optimization method as described in any one of claims 1 to 9.

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