Offshore wind turbine layout method based on three-dimensional staggered and PSO-MPA algorithm

Abstract

The application discloses a kind of offshore wind turbine layout method based on three-dimensional skew and PSO-MPA algorithm.Belongs to offshore wind farm design technical field.The application first identifies main wind direction and secondary main wind direction by wind energy rose diagram;Then establish three-dimensional skew transformation model, and the hub height is uniformly represented as spatial affine transformation with horizontal offset, so that the equivalent horizontal position of wind turbine changes adaptively with height;Introduce secondary main wind direction wake overlap area constraint in horizontal reference layout, realize double wind direction joint pre-adjustment;Finally, a hybrid particle swarm-ocean predator algorithm is used to optimize the binary coding of hub height, which includes non-uniform population initialization, double wind direction coordination penalty fitness function, stage switching mechanism and adaptive inertia weight and step adjustment.The application uses the coordinates after skew transformation for wake evaluation, forms a closed-loop optimization, and can improve the sum of power generation of main wind direction and secondary main wind direction and total annual power generation.

Description

Technical Field

[0001] This invention relates to the field of offshore wind farm design technology, specifically to an offshore wind turbine layout method based on three-dimensional shearing and PSO-MPA algorithm (hybrid particle swarm optimization-oceanic predator algorithm). Background Technology

[0002] Offshore wind farms are typically located in open sea areas with abundant but variable wind resources. The wake effect between wind turbines within the farm can reduce the input wind speed to downstream turbines, thus decreasing overall power generation. Traditional turbine layout methods primarily employ horizontal staggered arrangements along the prevailing wind direction to minimize wake obstruction. However, this approach only optimizes for a single prevailing wind direction. When significant secondary prevailing winds exist, a single-direction staggered layout struggles to effectively mitigate wake losses from multiple wind directions. Furthermore, existing layout strategies often fix the hub height of all turbines, failing to utilize the potential for vertical staggering to further reduce wake impact. Therefore, achieving the most economically viable turbine layout under multi-wind-direction conditions through coordinated horizontal and vertical optimization, while considering both construction costs and power generation revenue, remains a key technical challenge in the micro-site selection of offshore wind farms.

[0003] The existing offshore wind farm setup has the following problems.

[0004] 1. Limitations of traditional experience-based layout strategies for offshore wind farms.

[0005] (1) Single dimension of layout decision: Only focus on the row and column spacing and grid density of wind turbines, without taking into account factors such as offshore wind turbine investment costs, resulting in an inability to effectively balance the power generation and investment costs of wind farms, making it difficult to support the actual micro-site selection assessment of wind farms.

[0006] (2) Limited number of layout results: Traditional methods rely on fixed row and column spacing multiples and preset grid templates, which can only generate a limited number of regular layout schemes. They do not incorporate the attenuation effect of the wake model into the optimization loop and cannot search for the optimal micro-location in the continuous solution space.

[0007] 2. The limitations of considering only a single prevailing wind direction.

[0008] (1) Lack of adaptability to multiple wind directions: The core assumption of this method is based on a single dominant wind direction, without considering the wind direction change characteristics of other wind directions with greater wind energy or sea areas with two dominant wind directions. Its fixed row and column direction is difficult to adapt to two dominant wind conditions, and it does not consider the impact of wind energy direction changes on wake loss and power generation, resulting in the layout scheme deviating from the theoretical optimum in complex wind conditions.

[0009] 3. Disadvantages of using horizontal misalignment alone.

[0010] (1) Single planning dimension: It is assumed that the wind resources in the wind farm area are evenly distributed and the wind direction is constant. Only the wake effect is optimized by horizontal misalignment. Only the misalignment of wind turbines in the horizontal plane is considered. The wake effect is reduced by optimizing the horizontal spacing and misalignment angle. Even if a few studies consider vertical misalignment, horizontal misalignment and vertical misalignment are usually treated independently, lacking a unified spatial geometric description.

[0011] (2) Lack of three-dimensional spatial adaptability: The vertical wind speed shear of the atmospheric boundary layer under complex sea conditions, the difference in wind turbine hub height, and the diffusion and superposition effect of the wake in the vertical direction are not considered. When the wind turbine actually operates at different hub heights or there are complex wind shears, simple horizontal misalignment cannot fully tap the vertical arrangement potential, and it is also difficult to accurately consider the impact of the three-dimensional wind field on power generation.

[0012] 4. Limitations of the optimization algorithm.

[0013] (1) Genetic algorithms or particle swarm optimization algorithms are commonly used, but no substantial improvements have been made to the algorithm structure to address the characteristics of "continuous-discrete mixed variables" and "dual wind direction target conflict" in wind farm layout. These algorithms suffer from problems such as slow convergence, premature convergence, and poor dual wind direction balancing ability. Although the marine predator algorithm (MPA) has been attempted for wind farm layout in recent years, there have been no reports of mixing particle swarm optimization with MPA and making adaptive improvements to address vertical misalignment of dual wind directions. Summary of the Invention

[0014] To address the aforementioned problems, this invention proposes an offshore wind turbine layout method based on three-dimensional staggered transformation and the PSO-MPA algorithm, including the following key innovations: First, the horizontal and vertical positions are unified into a three-dimensional staggered transformation, establishing a geometric coupling relationship between the wind turbine's spatial position and the wind direction angle; simultaneously, dual-wind direction constraints are considered, ensuring that the horizontal layout scheme simultaneously meets the minimum spacing requirements between rows in the main wind direction and the secondary main wind direction, while the vertical optimization objective simultaneously considers the power generation of both wind directions; finally, an improved hybrid particle swarm optimization algorithm is adopted, combining the fast convergence of the particle swarm algorithm with the global exploration capability of the ocean predator algorithm, and introducing improvements such as non-uniform initialization of wind resources, dual-wind direction coordination penalties, and adaptive parameter adjustment to ensure that the offshore wind farm can improve overall power generation efficiency while adapting to the multi-wind direction wake effect.

[0015] The above objectives are achieved through the following technical solutions:

[0016] The offshore wind turbine layout method based on three-dimensional staggered shear and PSO-MPA algorithm of the present invention includes the following steps:

[0017] S1: Acquire and initialize site wind resource data, and set dual wind direction discrimination thresholds. ;

[0018] S2: Based on the initial wind resource data in S1, construct a wind energy rose diagram and calculate the wind energy contribution of each wind direction sector on the wind energy rose diagram, according to the dual wind direction discrimination threshold set in S1. The wind direction that contributes the most to wind energy is determined as the dominant wind direction, and the secondary dominant wind direction is determined in the same way. After that, a three-dimensional shear transformation model is established to uniformly describe the wind turbine layout space.

[0019] S3. Arrange the wind turbines in a horizontal staggered manner along the main wind direction in the horizontal dimension of the three-dimensional staggered transformation model described in S2 as the baseline layout, and verify whether the equivalent spacing between rows in the secondary main wind direction satisfies the requirement that the wake overlap area is less than a preset threshold.

[0020] S4. Based on the baseline layout described in S3, with the optimization objective of maximizing the unit cost power generation in the main wind direction and the secondary main wind direction, a vertical misalignment optimization model is constructed, and a dual wind direction coordination penalty term is introduced into the objective function.

[0021] S5: The hybrid particle swarm optimization-ocean predator algorithm is used to iteratively optimize the wind turbine hub height in the optimization model described in S4, and combined with three-dimensional shear transformation to achieve horizontal-vertical joint adjustment, so as to obtain the final wind turbine layout scheme of the offshore wind farm.

[0022] Compared with the prior art, the present invention has the following advantages:

[0023] 1. This invention adopts three-dimensional staggered unified modeling: This invention describes the difference between the horizontal layout and the vertical hub height in a unified manner through staggered transformation, so that the equivalent horizontal position of the wind turbine in the wake evaluation is adaptively offset with the hub height, avoiding the solution space fragmentation caused by the independent optimization of horizontal and vertical in the traditional method, and realizing true three-dimensional spatial collaborative layout.

[0024] 2. This invention employs a dual-wind-direction joint constraint: During the horizontal baseline layout stage, a wake overlap area constraint based on the secondary prevailing wind direction is introduced, ensuring that the final layout possesses good wake obstruction control capabilities in both the prevailing and secondary prevailing wind directions. Simulations show that, compared to methods that only optimize the prevailing wind direction, the power generation in the secondary prevailing wind direction increases by 8%–13%, and the total annual power generation increases by 6%–10%.

[0025] 3. This invention improves upon the PSO-MPA algorithm with adaptive enhancements, employing a hybrid strategy that switches between rapid exploration using the Particle Swarm Optimization (PSO) algorithm and fine-grained development using the Ocean Predator Algorithm (MPA). It also introduces non-uniform population initialization based on the prevailing wind direction coordinates (higher probability of upstream hub), a dual-wind-direction coordination penalty term, dynamic distance penalty, and adaptive inertia weight / step size adjustment. Compared to the standard genetic algorithm, it increases power generation per unit cost by 8.7% and reduces the number of convergence generations by approximately 40%.

[0026] 4. This invention adopts a shear-wake closed-loop transfer, directly substituting the equivalent coordinates after shear transformation into the calculation of wind direction rotation and overlap area in the Jensen wake model, so that every change in hub height can be accurately mapped to wake loss and power generation assessment, forming a complete closed loop of design variables → equivalent coordinates → wake overlap → fitness function, and the optimization results have clear physical interpretability.

[0027] 5. This invention achieves a balance between engineering cost and power generation: the objective function includes both the annual power generation and construction cost of the main and secondary wind directions, and suppresses the deviation in power generation through a dual-wind direction coordination penalty term, avoiding the blind increase of tower height in pursuit of power generation or the sacrifice of power generation efficiency in pursuit of cost reduction, thus achieving the best balance between economy and power generation efficiency. Attached Figure Description

[0028] Figure 1 This is a flowchart of the dual-wind-direction coordinated wind turbine layout method based on three-dimensional shear transformation and PSO-MPA algorithm of the present invention;

[0029] Figure 2 It is the iterative curve of power generation per unit cost of a wind farm;

[0030] Figure 3 This is the optimal layout for wind farms. Detailed Implementation

[0031] like Figure 1 As shown, the offshore wind turbine layout method based on three-dimensional staggered shear and PSO-MPA algorithm of the present invention includes the following steps:

[0032] S1: Acquire and initialize wind resource data for the selected site. The wind resource data includes statistical information on wind speed and wind direction. Set a dual wind direction discrimination threshold. ;

[0033] S2. Based on the initial wind resource data in S1, establish a wind energy rose diagram. Calculate the wind energy contribution of each wind direction sector based on the cumulative value of different wind speeds multiplied by the corresponding number of hours on the wind energy rose diagram, and apply the dual-wind-direction discrimination threshold set in S1. The wind direction that contributes the most to wind energy is determined as the main wind direction, and the secondary main wind direction is determined by analogy. After that, a three-dimensional shear transformation model is established to uniformly describe the wind turbine layout space, and the horizontal and vertical misalignment are uniformly represented as spatial affine transformation.

[0034] S3. Arrange the wind turbines in a horizontal staggered manner along the main wind direction in the horizontal dimension of the three-dimensional staggered transformation model described in S2 as the baseline layout, and verify whether the equivalent spacing between rows in the secondary main wind direction meets the requirement that the wake overlap area is less than the preset threshold. If it does not meet the requirement, adjust the stagger amount until both the main wind direction and the secondary main wind direction meet the requirements.

[0035] S4. Based on the baseline layout described in S3, with the optimization objective of maximizing the unit cost power generation in the main wind direction and the secondary main wind direction, a vertical misalignment optimization model is constructed, and a dual wind direction coordination penalty term is introduced into the objective function. Then, the wake model used for wake calculation is determined, and the effective wind speed of each wind turbine under each wind direction is calculated based on the model, including the actual wind speed at the height of the wind turbine hub and the wind speed after being affected by the wake effect. Finally, the effective wind speed is substituted into the power generation calculation function and accumulated to obtain the annual power generation, which is then substituted into the optimization objective.

[0036] S5: The PSO-MPA algorithm, namely the hybrid particle swarm optimization-ocean predator algorithm, is used to iteratively optimize the wind turbine hub height in the optimization model described in S4, and combined with three-dimensional shear transformation to achieve horizontal-vertical joint adjustment, so as to obtain the final wind turbine layout scheme of the offshore wind farm.

[0037] In this embodiment, the process of obtaining and initializing the site wind resource data in step S1 is as follows:

[0038] S1-1: Perform NCDC number lookup for the target weather station;

[0039] S1-2: Download data from the target weather station using the open FTP server provided by NCDC;

[0040] S1-3: After extracting and decompressing the file, the raw data obtained includes time, wind direction angle, temperature, dew point temperature, air pressure, wind speed, rainfall, etc. Python is used to process the data to obtain data containing only wind speed and wind direction angle, and the data is extracted into a table format for easy subsequent processing.

[0041] S1-4: Initialize calculation parameters and set the dual wind direction discrimination threshold. .

[0042] In this embodiment, step S2 specifically includes the following sub-steps:

[0043] S2-1: Use the wind speed and wind direction angle data obtained in step S1 to draw a scatter plot of wind resources. Based on the density of each point in the plot, set the wind speed interval of the wind rose diagram reasonably. Specifically, in wind speed areas with low density, a longer wind speed interval needs to be divided into one wind speed interval, while in wind speed areas with high density, a shorter wind speed interval needs to be divided into one wind speed interval. Finally, divide it into 5 to 6 wind speed intervals.

[0044] S2-2: From arrive The system was divided into 16 sectors, and the number of hours corresponding to each wind speed range in each sector was calculated. The corresponding wind rose diagram was then drawn.

[0045] S2-3: Determine the prevailing wind direction based on the wind energy contribution of each wind sector. The formula for calculating wind energy is as follows: , In the formula For wind energy; The area through which the free-flowing airflow passes; air density; The wind speed is obtained from S1.

[0046] This shows that wind energy is directly proportional to the cube of wind speed. Then, calculate the sum of the cubes of wind speeds for each wind direction sector, compare the sums of the cubes of wind speeds for each wind direction sector, and the wind direction of the sector with the maximum value is the prevailing wind direction. , In the formula This represents the number of wind speeds corresponding to each wind direction sector. For different wind speeds corresponding to different wind directions in each sector; This represents the total number of hours for each wind sector corresponding to different wind speeds.

[0047] S2-4: Repeat step S2-3 to determine the second prevailing wind direction, i.e., the secondary prevailing wind direction. The selection of the secondary prevailing wind direction must simultaneously satisfy: ① The proportion of wind energy is greater than or equal to... ② The angle between the wind direction and the prevailing wind direction is between 30° and 90°. If there is no secondary prevailing wind direction that meets the conditions, this method degenerates into a single wind direction optimization case, that is, the weight of the secondary prevailing wind direction related items in subsequent steps is set to zero. This invention uses a wind rose diagram to identify the above-mentioned primary and secondary wind directions, which has the following advantages:

[0048] (1) Clear directionality: Compared with the simple wind frequency rose diagram, which only reflects the probability of wind direction, the wind energy rose diagram takes into account the product of wind speed cube and wind direction frequency, and can more realistically reflect the energy potential that incoming winds from different directions can contribute, avoiding misleading situations such as "high wind speed but low frequency" or "high frequency but low wind speed".

[0049] (2) Reliable identification of primary and secondary wind directions: The wind rose diagram can accurately determine the primary wind direction (the direction corresponding to the maximum wind energy) and the secondary primary wind direction (the direction corresponding to the second largest wind energy), providing a quantitative basis for subsequent reasonable setting of wind turbine spacing and staggered strategies, so as to reduce mutual shading between wind turbines in the direction with greater wake loss, improve the total power generation, and maximize the overall power generation efficiency.

[0050] (3) Adapting to complex wind conditions: For offshore or onshore wind farms, the wind rose diagram can adapt to multiple wind directions and mixed wind characteristics, guiding the optimization algorithm to make layout decisions under the condition of considering both primary and secondary wind directions, and avoiding the wake loss problem caused by single wind direction layout.

[0051] (4) The graphics are intuitive and easy to apply in engineering: the wind rose diagram compresses a large amount of wind resource statistics into a polar coordinate graph, which is conducive to reasonable layout and scheme selection in the preliminary design stage.

[0052] S2-5: After determining the prevailing and secondary prevailing wind directions, this invention establishes a three-dimensional shear transformation model to uniformly describe the wind turbine layout space. A spatial rectangular coordinate system is defined: with sea level as the XY plane, the positive Y-axis pointing towards the prevailing wind direction, the X-axis perpendicular to the prevailing wind direction (horizontally to the right), and the Z-axis vertically upward (height direction). This coordinate system is used throughout the subsequent process, thus representing the spatial position of any wind turbine as follows: , where z is the hub height of the wind turbine.

[0053] In traditional layouts, horizontal misalignment is equivalent to applying a fixed translation in the X-axis direction. Vertical misalignment involves selecting different z values. This invention unifies both into a three-dimensional shear transformation: , In the formula coordinates Coordinates after 3D shear transformation Shear coefficient This refers to the horizontal position offset corresponding to a unit change in vertical height. Its physical meaning is: when the wind turbine hub height changes from the low hub... Turn into a high hub When this is the case, its equivalent horizontal coordinate in wake assessment should be increased. Among them, the shear coefficient The angle between the prevailing wind direction and the secondary prevailing wind direction and wake attenuation coefficient This shared determination serves as the link between vertical differences and horizontal layout. (Shear coefficient) The settings must meet the following engineering requirements:

[0054] (1) When the angle between the prevailing wind direction and the secondary prevailing wind direction is small, the vertical height change has a greater impact on the wake obstruction in the secondary wind direction, requiring a larger horizontal misalignment compensation. It should be relatively large;

[0055] (2) When the included angle is close to 90°, the two wind directions are approximately orthogonal, and the change in vertical height has little effect on the horizontal projection of the secondary wind direction. It can be smaller;

[0056] (3) The larger the wake attenuation coefficient, the faster the wake spreads, and the more obvious the shielding effect caused by vertical misalignment, the greater the coefficient should be.

[0057] To meet the above requirements, Represented as: , In the formula This is an engineering adjustment factor (value range 0.2~0.5). This is the wake attenuation coefficient.

[0058] Through this three-dimensional shear transformation, the improved hybrid particle swarm-ocean predator algorithm, when searching for combinations of hub heights, will automatically incorporate horizontal-vertical coupling effects in its wake overlap calculations for fitness evaluation, thus achieving true three-dimensional collaborative optimization. In the wake evaluation step, this invention replaces the actual coordinates with the transformed coordinates.

[0059] In this embodiment, step S3 is as follows:

[0060] S3-1: In the coordinate system established in step S2, with the prevailing wind direction determined in step S2 as the reference direction (i.e., the Y-axis), the wind turbines are arranged in a row-and-column pattern. Multiple rows of wind turbine units are defined along the Y-axis, and the wind turbines in each row are arranged sequentially along the X-axis. This row-and-column pattern arrangement has the advantages of simple structure, easy engineering implementation and management and maintenance, and is a common initial layout form for offshore wind farms.

[0061] Referring to traditional empirical layout methods and based on offshore wind farm engineering experience, to reduce the impact of wake effects, the longitudinal spacing is typically set at 5 to 9 times the rotor diameter, and the lateral spacing is typically set at 3 to 5 times the rotor diameter. The determination of these ranges is mainly based on the analysis conclusions of classical wake models (such as the Jensen model): when the longitudinal spacing is less than 5 times the rotor diameter, downstream turbines will fall into the strong wake region of upstream turbines, leading to significant power loss; when the lateral spacing is less than 3 times the rotor diameter, lateral wake interference between adjacent rows will also be exacerbated. Therefore, traditional empirical layouts usually choose larger spacing to weaken the wake superposition effect, but this results in low site utilization for offshore wind farms. Considering subsequent vertical offset optimization, the longitudinal spacing is set to 3 times the rotor diameter, and the lateral spacing is set to 2 times the rotor diameter.

[0062] To achieve a horizontally staggered arrangement, a preset lateral offset is applied to the wind turbines in the X-axis direction between adjacent rows, based on a fixed foundation spacing. The core purpose of this horizontally staggered arrangement is to ensure that the wake influence area of ​​the upstream wind turbine is no longer directly opposite the rotor center of the downstream wind turbine, thereby reducing the overlap ratio of wake shadows on the swept surface of the downstream wind turbine and further mitigating the wake accumulation effect within the same height layer.

[0063] Specifically, for the v-th and v+1-th rows of fans, the fans in the v+1-th row are offset relative to the fans in the v-th row by a preset distance in a positive or negative direction perpendicular to the main wind direction (i.e., the X-axis), thus creating a staggered arrangement. The offset direction can alternate; for example, the first and second rows are offset in the positive X-axis direction, while the second and third rows are offset in the negative direction, and so on, forming a staggered pattern. The preset distance can be a fixed value or adjusted according to the number of rows. For example, as the number of rows increases, the offset is appropriately increased to cope with the gradually expanding wake influence range. The lateral offset can be set to a fixed value, such as half the spacing within the row, or set to a variable range based on engineering experience.

[0064] S3-2: After determining the above horizontal offset scheme, it is also necessary to verify whether the equivalent row spacing in the secondary prevailing wind direction satisfies the requirement that the wake overlap area is less than a preset threshold, i.e., whether the overlap area is less than or equal to 20% of the rotor sweep area. If not, the offset is adjusted and recalculated until both wind directions meet the requirements. The resulting horizontal offset layout is a compromise optimal layout under the dual constraints of the prevailing and secondary prevailing wind directions. It should be noted that the horizontal offset adjustment here temporarily uses the same reference hub height for all turbines (e.g., low hub). The optimization of the "baseline layout" is carried out under the baseline layout. The subsequent steps will be based on the baseline layout, and introduce individual equivalent horizontal offsets related to the wheel hub height through three-dimensional shear transformation to achieve more refined dual wind direction coordination.

[0065] In this embodiment, step S4 specifically includes the following sub-steps:

[0066] S4-1: Objective function for optimizing the model in the vertical direction: , In the formula To maximize this objective function; This represents the total annual power generation of the wind farm in the prevailing wind direction. This represents the total annual power generation of the wind farm in the secondary prevailing wind direction. The construction cost of wind turbines in a wind farm consists of two parts: the cost of the turbine foundation and the cost per unit height of the tower. , In the formula The basic construction cost of a single wind turbine; Cost per unit height of wind turbine tower; This represents the total number of wind turbines in the wind farm.

[0067] In practical optimization, to further balance the contributions of the prevailing wind direction and the secondary prevailing wind direction, this invention introduces a dual-wind-direction coordination penalty term into the fitness function, resulting in the following final fitness function: , In the formula The final fitness function during the iteration process. This is a dynamic adjustment coefficient. As the number of iterations increases, the value increases linearly from 0.1 to 0.5. This will be used as the final fitness function in the subsequent step S5.

[0068] Constraints:

[0069] by To represent the coordinates of wind turbine i, the following should be satisfied: , In the formula and These represent the length and width of the wind farm, respectively. In addition, there are two wind turbines in each pair within the wind farm. The minimum distance between the fan and the fan should be guaranteed, that is: ,

[0070] S4-2: The optimization model in S4-1 above establishes a mathematical description of the problem, providing a basis for computation. and For the effective wind speeds of the wind turbines relied upon, this invention employs the Jensen wake model. This model is highly consistent with the environmental characteristics of stable wind conditions in the deep ocean, a near-neutral atmospheric boundary layer, and low sea surface roughness. Furthermore, a single calculation only requires microseconds, and embedding it into a large-scale optimization loop can significantly improve computational efficiency. The Jensen wake model is based on the following key assumptions:

[0071] (1) Uniform radial velocity distribution in the wake. This model assumes that within the wake region of the wind turbine, on any cross-section perpendicular to the incoming flow direction, the wind speed is uniformly distributed radially without gradient changes. That is, the velocity profile on the wake cross-section does not change with the radial position, and the overall distribution is characterized by a "pancake" or "cap" shape. This assumption simplifies the spatial description of the wake velocity field; only the average velocity of a single cross-section is needed to characterize the flow state of the entire wake region. (Jensen model, downstream) The velocity distribution at the wake section is as follows: , In the formula Wake radius Wind speed at the cross-section; The wind speed within the wake section is the wind speed affected by the wake effect of the upstream wind turbine. This refers to the actual wind speed of the upstream fan. This refers to the hub height of the upstream wind turbine.

[0072] (2) Linear expansion of the wake. The wake region generated during wind turbine operation gradually expands downstream, and its radius of influence has a linear relationship with the downstream distance. That is, the radius of influence of the wake increases linearly with the increase of the downstream wind turbine distance, and its expansion slope is determined by the wake attenuation coefficient. The formula for calculating the radius of influence of the wake is: , In the formula Let x be the radius of influence of the wake at a distance x from the wind turbine; The radius of the wind turbine blades; The wake attenuation coefficient is calculated using the following formula: , In the formula For the first The horizontal height of the center of the typhoon turbine hub; This refers to the surface roughness.

[0073] S4-3: Reference Height in Initial Wind Resource Data The wind speed at a given location is often not the same as the height of the wind turbine hub. Therefore, after confirming the wake model in S4-2, the actual wind speed at the hub height of all wind turbines must first be calculated before considering the wake effect between turbines. Wind speed conversion at different heights typically uses a power-law wind shear model, and the specific wind shear calculation formula is shown below: , In the formula For the first Typhoon hub height The actual wind speed at the location; For reference height Wind speed at the location; The wind shear index.

[0074] Based on the calculation formulas for wind shear and wake attenuation coefficient, the impact of hub height variation on wind turbine power generation efficiency is twofold: first, as the height increases or decreases, the change in wind speed directly leads to an increase or decrease in power; second, as the height increases, the wake attenuation coefficient decreases, indirectly affecting power through the wake effect.

[0075] S4-4: After calculating the actual wind speed at the hub height of all wind turbines in S4-3, it is necessary to further determine the upstream and downstream relationships between wind turbines and the degree of wake overlap under each wind direction in order to accurately calculate the effective wind speed of each wind turbine. However, wind direction in a wind farm usually has the characteristic of random variation, that is, the incoming flow direction exhibits an uncertain distribution over time. Under different wind directions, the upstream and downstream relative positions of each wind turbine will change, and the wind turbines affected by the wake effect will also be different. Therefore, it is necessary to determine the upstream and downstream relationships between all wind turbines in the wind farm under different wind directions in order to accurately quantify the wake superposition effect and power loss under each wind direction. Assume the wind direction angle is... , will be located in the original coordinate system By projecting the wind turbine at the location onto a new coordinate system where the y-axis is parallel to the wind direction, the corresponding new location coordinates can be obtained.

[0076] Before rotating the wind direction, the three-dimensional shear transformation model described in step S2-5 should be applied to the wind turbine coordinates to map the actual hub height to an equivalent horizontal offset. , In the formula The offset of the equivalent horizontal mapping; For the first The actual hub height of the typhoon turbine; For reference wheel height (lower wheel height can be used) Then, substitute the transformed equivalent coordinates into the wind direction rotation formula: , Subsequent determinations of upstream and downstream relationships and calculations of wake overlap area are all based on the rotated coordinates. conduct.

[0077] Based on this, it is necessary to accurately quantify the impact of the wake generated by the upstream wind turbine on the downstream wind turbine, specifically including two scenarios:

[0078] The impact of a single unit's wake effect:

[0079] Assume the distance between the centers of the upstream and downstream wind turbines is Considering the relative positions of upstream and downstream wind turbines, the degree to which downstream wind turbines are affected by upstream wake can be divided into three scenarios:

[0080] (1) Complete non-overlap, meaning the swept surface of the downstream wind turbine is completely outside the wake region of the upstream wind turbine. In this case, the upstream wake does not have a direct impact on the downstream wind turbine, and the following equation must be satisfied: ,

[0081] (2) Partial overlap, meaning that part of the downstream wind turbine sweep surface falls into the upstream wake region, while the other part is in the undisturbed free flow, which must satisfy the following equation: ,

[0082] (3) Complete overlap, meaning the entire swept surface of the downstream wind turbine is covered by the upstream wake region, must satisfy the following equation: ,

[0083] For both partial and complete overlap cases, it is necessary to further calculate the wake shadow area and wake region area to obtain the wake influence factor. The calculation formula is as follows: , In the formula The area of ​​the shaded region; The area of ​​the wake region; This is the wake influence factor.

[0084] The impact of the wake effect of upstream wind turbines on downstream wind turbines can be divided into two categories, considering the downstream wind turbine speed after taking the wake effect into account. The calculation needs to be discussed in two cases:

[0085] (1) The downstream fan is only affected by the wake effect of the upstream single fan:

[0086] Based on this, the downstream... The wind speed of a typhoon turbine affected only by the wake effect of a single upstream turbine can be expressed as: , In the formula For downstream The wind speed of a typhoon turbine is only affected by the wake effect of a single upstream turbine. This refers to the actual wind speed of the upstream fan. This is the inference coefficient; it is usually obtained from the thrust coefficient curve provided by the manufacturer.

[0087] (2) The downstream wind turbine is affected by the superposition effect of the wakes of multiple upstream wind turbines:

[0088] In actual wind farms, downstream turbines are often simultaneously affected by the wakes of multiple upstream turbines. This phenomenon of intertwined multi-source wakes is called the wake superposition effect. For the engineering treatment of this wake superposition effect, the current mainstream calculation method adopts a superposition strategy based on the square root of the sum of squares of energy deficits. This method assumes that the velocity deficit caused by the wakes generated by each upstream turbine at a certain downstream point is independent of each other; that is, the interaction between different wakes is ignored, and their respective velocity deficits can be considered linearly independent. Based on this, the total velocity deficit is calculated as follows:

[0089] The velocity loss caused by each upstream wind turbine at the downstream target location is determined individually. The sum of squares of each loss value is calculated, and the square root of this sum is taken to obtain the equivalent total loss after superposition. This method is physically equivalent to the linear superposition of energy losses from individual wakes. Due to its simple calculation and low parameter requirements, it is widely used in wind farm flow simulation and power prediction in engineering practice. Within the Jensen model framework, it exhibits good computational stability and engineering applicability. Based on this, the downstream... The wind speed of a typhoon turbine affected by the superposition of wakes from multiple upstream turbines can be expressed as: , In the formula For downstream The wind speed of the typhoon turbine is affected by the wake effect of multiple upstream wind turbines; For downstream The wind speed of the typhoon after being affected by the wake effect of the j-th upstream typhoon; This corresponds to the wake influence factor of the j-th upstream wind turbine. In summary, the downstream... Downwind speed after typhoon turbines are affected by the wake effect of upstream turbines It can be represented as: .

[0090] S4-5: By considering the wake effect mentioned above, the effective wind speed of each wind turbine under each wind direction can be obtained. Then, these wind speed values ​​are substituted into the power characteristic curve to calculate the single-unit power multiplied by the corresponding number of hours, and accumulated to obtain the theoretical annual power generation of the wind farm, thus providing specific values ​​for AEP_main and AEP_second in the optimization objective.

[0091] The actual wind speed is obtained by considering the influence of hub height and wake effect. Then, the actual power of the wind turbine at that location can be calculated by substituting the values ​​into the power characteristic curve. This power curve is typically defined by three characteristic wind speeds: the cut-in wind speed, the rated wind speed, and the cut-out wind speed. Its operating characteristics can be fitted using a cubic function model, as shown in the following expression: , In the formula The first [stage] after considering the influence of wheel hub height and wake effect The power output of the typhoon generator; To cut in wind speed; Rated wind speed; To cut off the wind speed; This refers to the rated power of the fan. Its operating characteristics are as follows: when the wind speed is lower than the cut-in wind speed, the fan does not start, and the output power is zero; when the wind speed reaches the cut-in wind speed but is lower than the rated wind speed, the output power increases with the wind speed; when the wind speed reaches the rated wind speed, the fan outputs the rated power; within the range of rated wind speed to cut-out wind speed, power control stabilizes the output at the rated power; and when the wind speed exceeds the cut-out wind speed, to ensure safety, the fan stops, and the output power drops to zero.

[0092] Finally, by summing up the calculated annual power generation results of all wind turbines, the theoretical annual power generation of the wind farm can be obtained, which can be expressed as: , In the formula This refers to the annual power generation of the wind farm. This represents the total number of wind turbines in the wind farm. The amount of annual wind resource observation data; For the first Typhoon machine in Power generation under wind resource data; For the first Typhoon machine in Power generation hours under wind resource data.

[0093] S5: Further, the hybrid particle swarm optimization-ocean predator algorithm is used to iteratively optimize the wind turbine hub height in the optimization model described in S4, and combined with three-dimensional shear transformation to achieve horizontal-vertical joint adjustment. The process of obtaining the final wind turbine layout scheme for the offshore wind farm is as follows:

[0094] S5-1: Perform non-uniform population initialization. Assume the wind farm has N wind turbines, and the horizontal coordinates are fixed by S3. The hub height of each turbine is encoded using binary codes, i.e., 0: lower hub. (This article uses 103.5m); 1: High hub (This paper uses 163.5m). The population size is K. During initialization, the probability that the code of the i-th wind turbine is 1 is... for: , In the formula The coordinates of the wind turbine in the prevailing wind direction; Let be the total length of the wind farm along the prevailing wind direction. This strategy makes upstream turbines more likely to have high hubs and downstream turbines more likely to have low hubs. The physical basis for this is that in the upstream region of the prevailing wind direction, using high hubs reduces the obstruction of the wake of downstream turbines, thus reducing the wake accumulation effect; while in the downstream region, using low hubs reduces tower costs, and since the upstream wake has already been weakened, the negative impact of low hubs on power generation is smaller. In this way, the initial population already contains a better hub height distribution trend, which helps to accelerate algorithm convergence and improve the quality of the final solution.

[0095] S5-2: Coordinated Fitness Function and Dynamic Penalty for Two Wind Directions. The final fitness function obtained in S4-1 needs to be referenced. : , In the formula With the number of iterations Linear growth. Its purpose is to allow for significant differences in power generation between the primary and secondary wind directions in the early stages of optimization, enabling the algorithm to quickly explore the wide-area solution space. As iterations progress, the penalty weight gradually increases, forcing the algorithm to find a more balanced solution in terms of power generation between the two wind directions. The distance penalty factor adopts a cubic function form, resulting in a weaker penalty in the early stages (allowing a small number of infeasible solutions to participate in evolution to maintain population diversity), and a sharp increase in the penalty in later stages to ensure that the final solution satisfies the safe distance constraint, as shown in the following formula: , In the formula The final fitness function taking into account the distance penalty factor; This represents the maximum number of iterations. The cumulative degree of violation of constraints; The number of individuals that violated the constraints.

[0096] S5-3: The hybrid evolutionary mechanism employs a phase switching between PSO and MPA, dividing the entire optimization process into two phases. This phase-switching design is based on the following considerations: In the early stages of optimization, the solution space is large, requiring the Particle Swarm Optimization (PSO) algorithm to quickly traverse different regions to avoid prematurely falling into local optima; in the later stages of optimization, the solution space has shrunk, requiring the Lévy flight and Brownian motion of the Ocean Predator algorithm for fine-grained searching to approximate the global optimum. Transferring the elite individuals selected by the PSO algorithm to the Ocean Predator algorithm fully utilizes the results of the earlier searches, avoiding a restart and thus maintaining population diversity while accelerating convergence.

[0097] Phase 1 (first 0.4) (Generation): A particle swarm optimization (PSO) algorithm is used for fast exploration. The position of each particle is encoded in binary, and the velocity update formula is: , In the formula Let $\frac{0}{ ...1}{\frac{t}{\ Let be the velocity of the o-th particle in generation t; w is the inertial weight, which adopts a linear decreasing strategy and considers the energy ratio of both wind directions; The individual learning factor (usually 2.0) represents the weight by which a particle learns from its own historical best position. The social learning factor (usually 2.0) represents the weight by which a particle learns to the global optimal position of the group; Given two independent random numbers, Uniform distribution within the interval is used to increase the randomness of the search; This represents the optimal position found in the history of the o-th particle; The optimal position found throughout the entire history of the population; Let be the position of the o-th particle in generation t.

[0098] The position update is then mapped to binary probabilities using the Sigmoid function: , In the formula Encode the probability that the o-th particle takes the value 1 at position t+1; Let be the velocity of the o-th particle in generation t+1.

[0099] Phase 2 (after 0.6) (Next): Switch to the Marine Predator Algorithm (MPA) for further refinement. The core update rule of MPA is:

[0100] (1) When hour( (This is the current iteration number), using Lévy flight for global search: , In the formula The step size vector controls the distance and direction of a predator's (or prey's) single movement; The algorithm generates a long-tailed redistribution of random number vectors based on the Lévy distribution, enabling the algorithm to make large jumps and enhance its global exploration capabilities. This is an elite matrix that stores the location information of several individuals with the highest fitness in the current population, representing the location of predators. This is the prey matrix, which stores the position information of all individuals in the current population, representing the positions of prey (potential solutions).

[0101] (2) When At that time, Brownian motion was used for local development: , In the formula It generates small, continuous shifts in a random number vector (Brownian motion) based on a normal distribution, which are used for fine-grained local searches.

[0102] Location update: ,in When switching phases, the top 30% of individuals with the highest fitness in the final population of phase 1 are used as the initial prey group for phase 2.

[0103] S5-4: Adaptive parameter adjustment is performed. In the PSO phase, the inertia weight w not only decreases linearly with iteration, but also adjusts according to the energy ratio of the main and secondary wind directions. Make corrections: , In the formula The inertia coefficient; The ratio of primary to secondary wind direction energy; Total wind energy in the prevailing wind direction; This represents the total wind energy from the secondary prevailing wind direction. Please refer to the wind energy calculation formula in step S2-3 for details.

[0104] During the MPA phase, the step scaling factor FADs (fish swarming effect parameter) is determined based on population diversity. Adaptive adjustment: , In the formula As an indicator of population diversity, it reflects the degree of difference between individuals in the current population; Let be the position vector of the o-th particle; It is the mean vector of all particle position vectors.

[0105] when hour, ,otherwise The correction term for the inertia weight w takes into account the energy ratio of the primary and secondary wind directions: when the energy of the secondary primary wind direction is large, the correction term approaches 0, and w decays normally; when the energy of the secondary primary wind direction is small, the correction term is positive, w decays more slowly, and more exploration ability is retained to avoid ignoring the secondary primary wind direction too early; while the population diversity Div reflects the degree of difference between individuals. If Div is too small, it indicates that the population tends to be homogeneous. In this case, increasing FADs can introduce random perturbations to help the algorithm escape local optima.

[0106] S5-5: Perform elite retention and determine the termination condition. In each generation, the current best individual is retained and directly enters the next generation (elite strategy). Repeat the above steps until the maximum number of iterations is reached. Or the relative change in optimal fitness over 20 consecutive generations is less than When the time is reached, the algorithm terminates. The hub height scheme corresponding to the individual with the highest fitness is output, which yields the final wind turbine layout.

[0107] The hub height scheme optimized by the improved PSO-MPA algorithm, combined with the baseline horizontal layout determined in S3, constitutes the complete turbine layout for an offshore wind farm. In the wake effect assessment, the equivalent horizontal coordinates of each turbine are calculated according to the shear transformation in S2-5, ensuring the consistency between the optimization process and the physical model.

[0108] Taking a rectangular offshore wind farm in a certain location as an example, measuring 4 kilometers long and 3 kilometers wide, a simulation study of the micro-site selection of the wind farm will be conducted using 6MW offshore wind turbines to verify the effectiveness of the proposed layout strategy combining horizontal and vertical offsetting. The relevant basic parameters and cost parameters of the wind turbines are shown in Tables 1 and 2, respectively.

[0109] Table 1. Basic parameters of the fan Rated power / kW 6000 Blade radius / m 77 Wheel hub height / m 103.5 / 163.5 Cut-in wind speed (m / s) 3 Rated wind speed (m / s) 12 Cut-off wind speed (m / s) 25

[0110] Table 2. Wind Turbine Cost Parameters Basic cost / 10,000 yuan 481 Tower cost (ten thousand yuan / m) 3.64

[0111] The initial population size was set to 80, and the number of iterations was set to 100. Iterative calculations were performed using the improved PSO-MPA algorithm of this invention, and the iteration curves and layout distributions are shown in the attached figures of the specification. Figure 2 , Figure 3 As shown.

Claims

1. A method for offshore wind turbine layout based on three-dimensional staggered shearing and PSO-MPA algorithm, characterized in that, The method includes the following steps: S1: Acquire and initialize site wind resource data, and set dual wind direction discrimination thresholds. ; S2: Based on the initial wind resource data in S1, construct a wind energy rose diagram and calculate the wind energy contribution of each wind direction sector on the wind energy rose diagram, according to the dual wind direction discrimination threshold set in S1. The wind direction that contributes the most to wind energy is determined as the dominant wind direction, and the secondary dominant wind direction is determined in the same way. After that, a three-dimensional shear transformation model is established to uniformly describe the wind turbine layout space. S3. Arrange the wind turbines in a horizontal staggered manner along the main wind direction in the horizontal dimension of the three-dimensional staggered transformation model described in S2 as the baseline layout, and verify whether the equivalent spacing between rows in the secondary main wind direction satisfies the requirement that the wake overlap area is less than a preset threshold. S4. Based on the baseline layout described in S3, with the optimization objective of maximizing the unit cost power generation in the main wind direction and the secondary main wind direction, a vertical misalignment optimization model is constructed, and a dual wind direction coordination penalty term is introduced into the objective function. S5: The hybrid particle swarm optimization-ocean predator algorithm is used to iteratively optimize the wind turbine hub height in the optimization model described in S4, and combined with three-dimensional shear transformation to achieve horizontal-vertical joint adjustment, so as to obtain the final wind turbine layout scheme of the offshore wind farm.

2. The offshore wind turbine layout method based on three-dimensional staggered shearing and PSO-MPA algorithm according to claim 1, characterized in that, The process of obtaining site wind resource data in step S1 is as follows: S1-1: Perform NCDC number lookup for the target weather station; S1-2: Download data from the target weather station using the open FTP server provided by NCDC; S1-3: After extracting and decompressing the file, the raw data obtained includes time, wind direction angle, temperature, dew point temperature, air pressure, wind speed, and rainfall. The data is processed using Python to obtain data containing only wind speed and wind direction angle, and then extracted into a table format. S1-4: Initialize calculation parameters and set the dual wind direction discrimination threshold. .

3. The offshore wind turbine layout method based on three-dimensional staggered shearing and PSO-MPA algorithm according to claim 1 or 2, characterized in that, The process of step S2 is as follows: S2-1: Use the wind speed and wind direction angle data obtained in step S1 to draw a scatter plot of wind resources, and divide it into 5 to 6 wind speed intervals according to the density of each point in the plot. S2-2: From arrive The system was divided into 16 sectors, and the number of hours corresponding to each wind speed range in each sector was calculated. The corresponding wind rose diagram was then drawn. S2-3: Determine the prevailing wind direction based on the wind energy contribution of each wind sector. The formula for calculating wind energy is as follows: ， In the formula For wind energy; The area through which the free-flowing airflow passes; air density; The wind speed obtained in step S1; This shows that wind energy is directly proportional to the cube of wind speed. Then, calculate the sum of the cubes of wind speeds for each wind direction sector, compare the sums of the cubes of wind speeds for each wind direction sector, and the wind direction of the sector with the maximum sum of the cubes of wind speeds is the prevailing wind direction. ， In the formula This represents the number of wind speeds corresponding to each wind direction sector. For different wind speeds corresponding to different wind directions in each sector; This represents the total number of hours corresponding to different wind speeds in each wind sector. S2-4: Repeat step S2-3 to determine the sector containing the wind speed cube and the second largest value as the second prevailing wind direction, i.e., the secondary prevailing wind direction. The selection of the secondary prevailing wind direction must simultaneously meet the following conditions: 1) Wind energy accounts for a greater than or equal to ; 2) The angle between the wind direction and the prevailing wind direction is to between; If there is no secondary prevailing wind direction that meets the conditions, the process degenerates into a single wind direction optimization case, in which case the weight of the secondary prevailing wind direction related items in subsequent steps is set to zero. S2-5: After determining the prevailing and secondary prevailing wind directions, a three-dimensional shear transformation model is established to uniformly describe the wind turbine layout space, as follows: Define a spatial rectangular coordinate system: with sea level as the XY plane, the positive Y-axis pointing in the prevailing wind direction, the X-axis perpendicular to the prevailing wind direction, and the Z-axis pointing vertically upwards. The spatial position of any wind turbine can then be represented as follows: , where z is the hub height of the wind turbine; Unify horizontal and vertical misalignment into a three-dimensional shear transformation: ， In the formula coordinates Coordinates after 3D shear transformation ; This represents the shear coefficient.

4. The offshore wind turbine layout method based on three-dimensional staggered shearing and PSO-MPA algorithm according to claim 3, characterized in that, Shear coefficient This represents the horizontal position offset corresponding to a unit change in vertical height. Represented as: ， In the formula This is an engineering adjustment factor, with a value range of 0.2 to 0.5; This is the wake attenuation coefficient.

5. The offshore wind turbine layout method based on three-dimensional staggered shearing and PSO-MPA algorithm according to claim 4, characterized in that, The specific process of arranging the fans in a horizontally staggered manner as the baseline layout in step S3 is as follows: S3-1: In the coordinate system established in step S2, the main wind direction determined in step S2 is used as the reference direction, i.e., the Y-axis. The fans are arranged in a row-column pattern. Multiple rows of fans are defined along the Y-axis. The fans in each row are arranged sequentially along the X-axis. The longitudinal spacing is set to 3 times the rotor diameter, and the lateral spacing is set to 2 times the rotor diameter. A preset lateral offset is applied to the fans between adjacent rows in the X-axis direction. Specifically, for the fans in the v-th row and the v+1-th row, the fans in the v+1-th row are offset relative to the fans in the v-th row by a preset distance in the positive or negative direction perpendicular to the main wind direction, i.e., the X-axis, to form a staggered arrangement. The offset direction is alternated. S3-2: After determining the row and column rule arrangement in step S3-1, it is also necessary to verify whether the equivalent row spacing in the secondary main wind direction meets the requirement that the wake overlap area is less than the preset threshold, that is, whether the overlap area is less than or equal to 20% of the wind turbine sweep area. If it does not meet the requirement, the offset is adjusted and recalculated until both the main wind direction and the secondary main wind direction meet the requirements. The resulting horizontal staggered layout is the optimal compromise layout under the dual constraints of the main wind direction and the secondary main wind direction.

6. The offshore wind turbine layout method based on three-dimensional staggered shearing and PSO-MPA algorithm according to claim 5, characterized in that, The construction of the vertical misalignment optimization model in step S4 includes: S4-1: Objective function for optimizing the model in the vertical direction: ， In the formula To maximize this objective function; This represents the total annual power generation of the wind farm in the prevailing wind direction. This represents the total annual power generation of the wind farm in the secondary prevailing wind direction. The construction cost of wind turbines in a wind farm consists of two parts: the cost of the turbine foundation and the cost per unit height of the tower. ， In the formula The basic construction cost of a single wind turbine; Cost per unit height of wind turbine tower; This represents the total number of wind turbines in the wind farm. By introducing a dual-wind-direction coordination penalty term into the fitness function, the final fitness function becomes: ， In the formula The final fitness function during the iteration process. This is a dynamic adjustment coefficient. As the number of iterations increases, it increases linearly from 0.1 to 0.5; Constraints: by To represent the coordinates of wind turbine i, the following should be satisfied: ， In the formula and Let i and j represent the length and width of the wind farm, respectively. In addition, the minimum distance between any two wind turbines i and j in the wind farm must be guaranteed, i.e.: ， S4-2: The optimization model in step S4-1 establishes a mathematical description of the problem, providing a basis for computation. and The effective wind speeds of each wind turbine on which it is based are determined using the Jensen wake model. S4-3: After confirming the wake model in S4-2, the actual wind speed at the height of all wind turbine hubs must first be calculated before considering the influence of wake effects between wind turbines. The wind speed conversion at different heights usually adopts the power-law wind shear model. The specific wind shear calculation formula is as follows: ， In the formula For the first Typhoon hub height The actual wind speed at the location; For reference height Wind speed at the location; Wind shear index; S4-4: After calculating the actual wind speed at the hub height of all wind turbines in S4-3, it is necessary to further determine the upstream and downstream relationship between wind turbines under each wind direction and the degree of wake overlap in order to accurately calculate the effective wind speed of each wind turbine. S4-5: By considering the influence of the wake effect mentioned above, the effective wind speed of each wind turbine under each wind direction can be obtained; then, these wind speed values ​​are substituted into the power characteristic curve to calculate the single unit power multiplied by the corresponding number of hours, and accumulated to obtain the annual theoretical power generation of the wind farm, thus providing specific values ​​for AEP_main and AEP_second in the optimization objective.

7. The offshore wind turbine layout method based on three-dimensional staggered shearing and PSO-MPA algorithm according to claim 6, characterized in that, The Jensen wake model described in step S4-2 is based on the following assumptions: (1) Uniform radial velocity distribution in the wake: The Jensen wake model assumes that in the wake region of the wind turbine, on any cross section perpendicular to the incoming flow direction, the wind speed is uniformly distributed radially without gradient changes. That is, the velocity profile on the wake cross section does not change with the radial position, and the overall distribution is "pancake" or "cap" shaped. In the downstream of the Jensen model The velocity distribution at the wake section is as follows: ， In the formula Wake radius Wind speed at the cross-section; The wind speed within the wake section is the wind speed affected by the wake effect of the upstream wind turbine. This refers to the actual wind speed of the upstream fan. This refers to the hub height of the upstream wind turbine; (2) Linear expansion of the wake: The Jensen wake model assumes that the wake region generated by the wind turbine gradually expands downstream, and its radius of influence is linearly related to the downstream distance. That is, the radius of influence of the wake increases linearly with the increase of the downstream wind turbine distance, and its expansion slope is determined by the wake attenuation coefficient. The formula for calculating the radius of influence of the wake is: ， In the formula Let x be the radius of influence of the wake at a distance x from the wind turbine; The radius of the wind turbine blades; The wake attenuation coefficient is calculated using the following formula: ， In the formula For the first The horizontal height of the center of the typhoon turbine hub; This refers to the surface roughness.

8. The offshore wind turbine layout method based on three-dimensional staggered shearing and PSO-MPA algorithm according to claim 7, characterized in that, The specific method for step S4-4 is as follows: Assuming the wind direction angle is , will be located in the original coordinate system By projecting the wind turbine at its current location onto a new coordinate system where the y-axis is parallel to the wind direction, the corresponding new position coordinates can be obtained. Before rotating the wind direction, the wind turbine coordinates should first be transformed using the three-dimensional shear transformation model described in steps S2-5, mapping the actual hub height to an equivalent horizontal offset. ， In the formula The offset of the equivalent horizontal mapping; For the first The actual hub height of the typhoon turbine; Using the hub height as a reference, the transformed equivalent coordinates are then substituted into the wind direction rotation formula to obtain the rotated coordinates. : ， Subsequent determinations of upstream and downstream relationships and calculations of wake overlap area are all based on the rotated coordinates. conduct; Based on this, it is necessary to accurately quantify the impact of the wake generated by the upstream wind turbine on the downstream wind turbine, specifically including two scenarios: The impact of a single unit's wake effect: Assume the distance between the centers of the upstream and downstream wind turbines is Considering the relative positions of upstream and downstream wind turbines, the degree to which downstream wind turbines are affected by upstream wake can be divided into three scenarios: (1) Complete non-overlap, meaning the swept surface of the downstream wind turbine is completely outside the wake region of the upstream wind turbine. In this case, the upstream wake does not have a direct impact on the downstream wind turbine, and the following equation must be satisfied: ， (2) Partial overlap, meaning that part of the downstream wind turbine sweep surface falls into the upstream wake region, while the other part is in the undisturbed free flow, which must satisfy the following equation: ， (3) Complete overlap, meaning the entire swept surface of the downstream wind turbine is covered by the upstream wake region, must satisfy the following equation: ， For both partial and complete overlap cases, it is necessary to further calculate the wake shadow area and wake region area to obtain the wake influence factor. The calculation formula is as follows: ， In the formula The area of ​​the shaded area; The area of ​​the wake region; Wake flow influencing factors; The impact of the wake effect of upstream wind turbines on downstream wind turbines can be divided into two categories, considering the downstream wind turbine speed after taking the wake effect into account. The calculation needs to be discussed in two cases: (1) The downstream fan is only affected by the wake effect of the upstream single fan: Based on this, the downstream... The wind speed of a typhoon turbine affected only by the wake effect of a single upstream turbine is expressed as: ， In the formula For downstream The wind speed of a typhoon turbine is only affected by the wake effect of a single upstream turbine. This refers to the actual wind speed of the upstream fan. The inference coefficient is obtained from the thrust coefficient curve provided by the manufacturer. (2) The downstream wind turbine is affected by the superposition effect of the wakes of multiple upstream wind turbines: the downstream first The wind speed of a typhoon turbine affected by the combined wakes of multiple upstream wind turbines is expressed as: ， In the formula For downstream The wind speed of the typhoon turbine is affected by the wake effect of multiple upstream wind turbines; For downstream The wind speed of the typhoon after being affected by the wake effect of the j-th upstream typhoon; This corresponds to the wake influence factor of the j-th upstream wind turbine; In summary, the downstream... Downwind speed after typhoon turbines are affected by the wake effect of upstream turbines Represented as: 。 9. The offshore wind turbine layout method based on three-dimensional staggered shearing and PSO-MPA algorithm according to claim 8, characterized in that, The specific methods for steps S4-5 are as follows: In step S4-4, the downstream first Downwind speed after typhoon turbines are affected by the wake effect of upstream turbines Then, the actual power of the wind turbine at that location is calculated by substituting the power characteristic curve into the curve. The power characteristic curve is defined by three characteristic wind speeds: cut-in wind speed, rated wind speed, and cut-out wind speed. A cubic function model is then used to fit the operating characteristics of the wind turbine. The specific expression is as follows: ， In the formula The first [stage] after considering the influence of wheel hub height and wake effect The power output of the typhoon generator; To cut in wind speed; Rated wind speed; To cut off the wind speed; This refers to the rated power of the fan. Finally, the annual power generation calculations of all wind turbines are summed to obtain the theoretical annual power generation of the wind farm, expressed as: ， In the formula This refers to the annual power generation of the wind farm. This represents the total number of wind turbines in the wind farm. The amount of annual wind resource observation data; For the first Typhoon machine in Power generation under wind resource data; For the first Typhoon machine in Power generation hours under wind resource data.

10. The offshore wind turbine layout method based on three-dimensional staggered shearing and PSO-MPA algorithm according to claim 9, characterized in that, The specific method for step S5 is as follows: S5-1: Perform non-uniform population initialization: Suppose there are N wind turbines in the wind farm, and the horizontal coordinates have been fixed in step S3. The hub height of each wind turbine is encoded in binary, i.e., 0: low hub. 1: High-profile wheels The population size is K. During initialization, the probability that the code of the i-th wind turbine is 1 is... for: ， In the formula The coordinates of the wind turbine in the prevailing wind direction; This represents the total length of the wind farm in the prevailing wind direction. S5-2: The fitness function and dynamic penalty for coordinated operation between two wind directions require referencing the final fitness function obtained in S4-1. : ， In the formula With the number of iterations Linear growth; To ensure the final solution satisfies the safety distance constraint, the following equation applies: ， In the formula The final fitness function taking into account the distance penalty factor; This represents the maximum number of iterations. The cumulative degree of violation of constraints; The number of individuals that violated the constraints; S5-3: The hybrid evolutionary mechanism employs a phase switching between PSO and MPA, dividing the entire optimization process into two phases: Phase 1 is the first 0.4 Generation: Particle Swarm Optimization (PSO) is used for fast exploration. The position of each particle is encoded in binary, and the velocity update formula is: ， In the formula Let $\frac{0}{\frac{0}{\frac{1}{\frac{t ... Let be the velocity of the o-th particle in generation t; w is the inertial weight, which adopts a linear decreasing strategy and considers the energy ratio of both wind directions; The individual learning factor represents the weight by which a particle learns to its own historical best position. The social learning factor represents the weight by which a particle learns to align with the global optimal position of the group. Given two independent random numbers, Uniform distribution within the interval is used to increase the randomness of the search; This represents the optimal position found in the history of the o-th particle; The optimal position found throughout the entire history of the population; Let be the position of the o-th particle in generation t; The position update is then mapped to binary probabilities using the Sigmoid function: ， In the formula Encode the probability that the o-th particle takes the value 1 at position t+1; Let be the velocity of the o-th particle in generation t+1; Phase 2 is the latter 0.6 Next: Switch to the Marine Predator Algorithm (MPA) for refined development. The core update rule of MPA is: (1) When the current iteration number At that time, Lévy flight was used for global search: ， In the formula The step size vector controls the distance and direction of a predator's or prey's single movement; The algorithm generates a long-tailed redistribution of random number vectors based on the Lévy distribution, enabling the algorithm to make large jumps and enhance its global exploration capabilities. This is an elite matrix that stores the location information of several individuals with the highest fitness in the current population, representing the location of predators. The prey matrix stores the position information of all individuals in the current population, representing the position of prey or potential solutions; (2) When At that time, Brownian motion was used for local development: ， In the formula A random number vector generated based on a normal distribution is used to produce small, continuous shifts for fine-grained local searches. Location update: ,in When switching phases, the top 30% of individuals with the highest fitness in the final population of phase 1 are used as the initial prey group for phase 2. S5-4: Adaptive parameter adjustment is performed. In the PSO phase, the inertia weight w not only decreases linearly with iteration, but also adjusts according to the energy ratio of the main and secondary wind directions. Make corrections: ， In the formula The inertia coefficient; The ratio of primary to secondary wind direction energy; Total wind energy in the prevailing wind direction; The total wind energy is for the secondary prevailing wind direction; refer to the wind energy calculation formula in step S2-3 for details. During the MPA phase, the step scaling factors FADs are based on population diversity. Adaptive adjustment: ， In the formula As an indicator of population diversity, it reflects the degree of difference between individuals in the current population; Let be the position vector of the o-th particle; It is the mean vector of all particle position vectors; when hour, ,otherwise ; Among them, the correction term of the inertia weight w takes into account the energy ratio of the primary and secondary wind directions: when the energy of the secondary primary wind direction is large, the correction term approaches 0 and w decays normally; when the energy of the secondary primary wind direction is small, the correction term is positive and w decays more slowly, retaining more exploration ability to avoid ignoring the secondary primary wind direction too early; while the population diversity Div reflects the degree of difference between individuals. If Div is too small, it indicates that the population tends to be homogeneous. At this time, increasing FADs introduces random perturbation to help the algorithm escape local optima; S5-5: Perform elite retention and determine termination conditions: retain the current best individual in each generation and directly enter the next generation; Repeat steps S5-1 through S5-5 until the maximum number of iterations is reached. Or the relative change in optimal fitness over 20 consecutive generations is less than When the algorithm terminates, it outputs the hub height scheme corresponding to the individual with the highest fitness, thus obtaining the final wind turbine layout.

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