Wind power plant layout and topological optimization method and system considering randomness of wind speed and wind direction

Abstract

The invention provides a wind power plant layout and topological optimization method and system considering wind speed and wind direction randomness, and relates to the technical field of wind power plant planning and optimization. Comprising the following steps: S1, selecting years of actually measured wind speed and wind direction sample data, and constructing a binary exponential polynomial wind speed and wind direction joint probability distribution model; s2, discretizing the wind speed and wind direction joint probability distribution model into a wind speed and wind direction discrete state probability matrix, calculating equivalent average power in combination with a Jensen wake flow model, and solving the optimal layout of the wind turbine generator by using an optimization algorithm; s3, on the basis of the optimal layout of the wind turbine generator, partitioning the position of the wind turbine generator by using a K-means clustering algorithm and solving a minimum spanning tree to determine cable connection in partitions, and performing global optimization on booster station site selection and partitioning by using an optimization algorithm to obtain an optimal topological structure; the double targets of maximizing the generating capacity of the wind power plant and minimizing the total length of the cable are achieved, the wind energy utilization efficiency and the project economic benefits are improved, and the model prediction accuracy is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of wind farm planning and optimization, in particular to a wind farm layout and topology optimization method and system considering the randomness of wind speed and direction. BACKGROUND

[0002] Under the trend of global energy structure transformation towards clean and low carbon, wind energy as an important part of renewable energy has key significance for alleviating energy crisis and reducing environmental pollution.

[0003] Currently, in the planning and construction of wind farms, the randomness of wind speed and direction, the significant influence of wake effect, and the fragmentation of layout and topology optimization have long restricted the improvement of wind farm power generation efficiency and economic benefits, which are specifically manifested in the following three aspects: first, traditional wind farm planning methods often ignore the random fluctuation characteristics of wind speed and direction, or only use single probability models such as Weibull distribution and Rayleigh distribution for simplified description. Such models cannot accurately capture the joint distribution law of wind speed and direction under complex wind conditions, resulting in a large deviation between wind resource assessment and actual situation, and thus making the subsequent layout optimization lose a reliable data basis and difficult to fully adapt to the actual wind conditions of the wind farm. Second, the wake effect of wind turbines in the wind farm can significantly reduce the power generation of downstream turbines, and in traditional layout optimization, the wake model is mostly based on the assumption of fixed wind conditions (such as constant wind speed and single wind direction), without fully considering the dynamic influence of wind speed and direction randomness on the wake field. This makes the wind turbine layout optimized unable to effectively avoid wake interference, resulting in the overall power generation of the wind farm being lower than expected and the wind energy utilization efficiency being low. Third, existing technologies often treat wind farm layout optimization (determination of wind turbine position) and topology optimization (cable routing and substation location selection) as two independent problems for separate processing: the layout optimization stage does not consider the engineering constraints of subsequent topology design (such as cable length and substation safety distance), and the topology optimization stage is limited by unreasonable previous layout, which requires additional cable usage or adjustment of substation location to meet engineering requirements, ultimately leading to increased investment cost of the power collection system and poor overall optimization effect. SUMMARY

[0004] The main purpose of the present application is to provide a wind farm layout and topology optimization method and system considering the randomness of wind speed and direction, which solves the technical problems of insufficient description accuracy of wind speed and direction randomness, poor coordination between wake effect and layout optimization, and independent layout and topology optimization.

[0005] To solve the above technical problems, the technical solution adopted by the present application is: a wind farm layout and topology optimization method considering the randomness of wind speed and direction, comprising the following steps: S1: select multi-year measured wind speed and wind direction sample data, and construct a bivariate exponential polynomial wind speed and wind direction joint probability distribution model; wherein the bivariate exponential polynomial is solved by least square method, and the optimal index is determined by means of root mean square error and determination coefficient; S2: discretize the wind speed and wind direction joint probability distribution model into wind speed and wind direction discrete state probability matrix, calculate the equivalent average power by combining Jensen wake model, and solve the optimal layout of wind turbine generator by using optimization algorithm; S3: on the basis of the optimal layout of wind turbine generator, the K-means clustering algorithm is used to partition the wind turbine generator position and solve the minimum spanning tree, so as to determine the cable connection in the partition, and the optimization algorithm is used to globally optimize the site selection of booster station and partition, and the optimal topological structure is obtained.

[0006] In the preferred scheme, in S1, the bivariate exponential polynomial wind speed and wind direction joint probability distribution model is constructed, including: The multi-year measured wind speed and wind direction sample data are pretreated, the synchronously measured wind speed and wind direction data are divided into multiple intervals, and the probability density of each interval is counted, so as to obtain a wind speed and wind direction frequency distribution histogram, and the formula is: ; In the formula, w v and w θ are wind speed and wind direction interval step, P is the total number of measured wind speed and wind direction samples, is the wind speed interval step change; The bivariate exponential polynomial parameters are calculated by using the probability density and least square method, and the expression of the bivariate exponential polynomial is: ; In the formula, v represents wind speed, θ represents wind direction, a(k, q) represents parameters, M 1 and M 2 represent the index, and C represents the normalization constant; The least square method objective function Q is: ; In the formula, Q is the sum of squares of errors of measured data and bivariate exponential polynomial values; Different combinations of M 1 and M 2 are traversed by means of root mean square error and determination coefficient to determine the optimal index of bivariate exponential polynomial, and the formulas are respectively: ; ; .

[0007] In the preferred embodiment, step S1, discretizing the joint probability distribution model of wind speed and direction into a discrete state probability matrix of wind speed and direction, includes: The formula for calculating the discrete state probability of wind speed and direction is: ; in v max This represents the maximum sample wind speed; i represents the discrete index of wind speed, and j represents the discrete index of wind direction. g (.) denotes a bivariate exponential polynomial; The downstream wind speed is calculated using the Jensen wake model, using the following formula: ; in, v 0 represents the upstream wind speed, and the radius of the wake cross-section is... pass Confirmed, among which r 0 represents the impeller radius, d represents the distance between wind turbine units, α represents the wake descent coefficient, and C T is the thrust coefficient; S represents the area of ​​the wake region; The discrete state probabilities of wind speed and direction for each group are calculated using the wind power conversion function and the Jensen wake model. p （i,j） Wind farm power generation P （i,j）， By performing a probability-weighted summation of the wind farm's power generation under all discrete wind speed and direction conditions, the equivalent average power of the wind farm under all wind conditions can be obtained. P eq .

[0008] In the preferred embodiment, the step of using an optimization algorithm to solve for the optimal layout of the wind turbine units includes: Construct an optimal layout optimization model for wind turbine units, with the objective function as follows: ; In the formula, x wi and y wi For the first i The coordinates of the typhoon turbine unit d ij For the first i Taiwan and the j The spacing between typhoon turbine units d min This is the minimum distance between two wind turbine units. U b This represents the upper limit of a wind farm in actual engineering.L b represents the lower bound of the wind farm in the actual project, and φ is a penalty factor; Initialize the coordinate position of the wind turbine, and update the coordinate position through global search and local development by optimization algorithm and cross operator disturbance iteration; If the current iteration coordinate satisfies the spacing constraint and the boundary constraint, the power generated by all wind speed and wind direction discrete states under the current layout is calculated and weighted to obtain Peq, otherwise the fitness value is adjusted by penalty and iteration is continued until convergence to obtain the optimal layout of the wind turbine with maximum power generation.

[0009] In the preferred embodiment, the K-means clustering algorithm is used to partition the wind turbine position, comprising: Initialize the position coordinates of the booster station, the number of partitions K and the cluster center, and according to the wind turbine coordinates in the optimal layout of the wind turbine, x s , y s , the K-means clustering algorithm is used to divide the wind turbine position into K partitions, and the number of wind turbines in each partition is controlled to be no more than the preset upper limit M; Solve the minimum spanning tree for each partition, the minimum spanning tree calculates the shortest cable connection mode in the partition by taking the cable length between wind turbine coordinates as the edge weight, and the cable length is the sum of the Euclidean distance between two wind turbine coordinates; Calculate the total cable length under the current configuration as the fitness value, the formula is: ; In the formula, K is the number of partitions, K min and K max represent the upper and lower limits of the number of partitions, the number of partitions is set by the upper and lower limits, x s , y s is the position coordinate of the booster station, U b represents the upper bound of the wind farm in the algorithm, L b represents the lower bound of the wind farm in the algorithm, i is the number of wind turbines, N w is the total number of units, D m is the minimum distance between the wind turbine and the booster station, and is also the size of the booster station exclusion zone, M is the number of units in each partition, and These are the penalty factors for the location constraints of the booster station and the number of wind turbine units in each zone, respectively.

[0010] In the preferred embodiment, step S3, which involves globally optimizing the location and zoning of the booster station using an optimization algorithm, includes: Initialization optimization variables include the location of the booster station, the number of partitions K, and the cluster centers. These optimization variables are iteratively updated using an optimization algorithm. If the location of the booster station ( x s , y s ) and each wind turbine in the optimal layout of the wind turbines ( x i , y i )distance D s satisfy D s Greater than or equal to D m If the total cable length is not found, K-means clustering and minimum spanning tree calculation are performed; otherwise, the fitness value is adjusted to increase the position constraint penalty. If the number of wind turbine units in each zone meets the requirements K min Less than or equal to K Less than or equal to K max If the total cable length does not exceed M, then retain the current total cable length as the fitness value; otherwise, increase the quantity constraint penalty and update the variables. Repeat the iterations until the maximum number of iterations is reached, and output the optimal booster station location that satisfies all constraints. x s , y s ), zoning scheme and cable connection method.

[0011] In the preferred embodiment, the thrust coefficient formula in the Jensen wake model is: ; In the formula, F f This represents the thrust acting on the wind turbine, where ρ represents the air density. v in It is the cut-in wind speed of the wind turbine. r 0 represents the impeller radius.

[0012] In the preferred embodiment, the optimization algorithm for the optimal layout of the wind turbine and the global optimization of the substation location and zoning includes particle swarm optimization or genetic algorithm, which iteratively solves the objective function through velocity update and location update or selection crossover and mutation operations.

[0013] In the preferred scheme, the formula for calculating the cable length is: ; In the formula, N w It refers to the number of wind turbine units; wind turbine units i Wind turbine j The coordinates are respectively ( x wi , y wi )and( x wj , y wj ).

[0014] The second aspect provides a wind farm layout and topology optimization system that takes into account the randomness of wind speed and direction, including: The data processing module is used to select measured wind speed and direction sample data over many years and construct a bivariate exponential polynomial joint probability distribution model of wind speed and direction; wherein the bivariate exponential polynomial is solved for parameters by the least squares method and the optimal exponent is determined by the root mean square error and the coefficient of determination. The joint probability distribution modeling module is used to discretize the joint probability distribution model of wind speed and wind direction into a discrete state probability matrix of wind speed and wind direction, calculate the equivalent average power in combination with the Jensen wake model, and use optimization algorithms to solve the optimal layout of wind turbine units. The global optimization module is used to partition the wind turbine locations based on the optimal layout of the wind turbines using the K-means clustering algorithm and solve the minimum spanning tree to determine the cable connections within the partitions. The optimization algorithm is then used to globally optimize the substation site selection and partitioning to obtain the optimal topology.

[0015] This invention provides a wind farm layout and topology optimization method that takes into account the randomness of wind speed and direction. By acquiring sample data and constructing a joint probability distribution model of wind speed and direction, and discretizing it into a discrete state probability matrix of wind speed and direction, the equivalent average power is calculated by combining the Jensen wake model. The optimal layout of wind turbine units is solved using an optimization algorithm. Then, the K-means clustering algorithm is used to partition the wind turbine unit locations and solve for the minimum spanning tree to determine the cable connections within the partition. The optimization algorithm is used to globally optimize the substation site selection and partitioning to obtain the optimal topology. This method solves the problems of traditional methods ignoring the randomness of wind speed and direction, insufficient consideration of wake effects, and the disconnect between layout and topology optimization. It achieves the dual objectives of maximizing wind farm power generation and minimizing the total cable length, improving wind energy utilization efficiency and project economic benefits, and enhancing the accuracy of model predictions. Attached Figure Description

[0016] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1This invention uses a histogram of frequency distribution of wind speed and direction from sample data. Figure 2 This is a joint probability distribution diagram of wind speed and wind direction obtained by the binary exponential polynomial fitting of this invention. Figure 3 This is a schematic diagram of the Jensen wake model of the present invention; Figure 4 This is the optimal layout diagram of the wind turbine unit of this invention; Figure 5 This is a flowchart of the wind turbine wiring optimization process of the present invention; Figure 6 This is a diagram showing the optimal location of the booster station and the cable connection method according to the present invention. Detailed Implementation

[0017] Example 1 like Figures 1-6 As shown, a wind farm layout and topology optimization method considering the randomness of wind speed and direction includes the following steps: S1: Select sample data of measured wind speed and direction over many years and construct a joint probability distribution model of wind speed and direction using a bivariate exponential polynomial. The parameters of the bivariate exponential polynomial are solved by the least squares method, and the optimal exponent is determined by the root mean square error and the coefficient of determination.

[0018] S2: Discretize the joint probability distribution model of wind speed and direction into a discrete state probability matrix of wind speed and direction, calculate the equivalent average power by combining the Jensen wake model, and use optimization algorithms to solve for the optimal layout of wind turbine units.

[0019] S3: Based on the optimal layout of wind turbine units, the K-means clustering algorithm is used to partition the wind turbine unit locations and solve the minimum spanning tree to determine the cable connections within the partitions. The optimization algorithm is then used to globally optimize the substation site selection and partitioning to obtain the optimal topology.

[0020] In this embodiment, considering the randomness of wind speed and direction, sample data is acquired, and a joint probability distribution model of wind speed and direction is constructed. This model is then discretized into a discrete state probability matrix of wind speed and direction. The equivalent average power is calculated using the Jensen wake model, and an optimization algorithm is used to solve for the optimal layout of wind turbine units. K-means clustering is then used to partition the locations of the wind turbine units and solve for the minimum spanning tree to determine the cable connections within each partition. Finally, an optimization algorithm is used to globally optimize the location of the booster station and the partitioning to obtain the optimal topology. This approach addresses the problems of traditional methods, such as neglecting the randomness of wind speed and direction, insufficient consideration of wake effects, and the disconnect between layout and topology optimization. It achieves the dual objectives of maximizing wind farm power generation and minimizing the total cable length, improving wind energy utilization efficiency and project economic benefits, and enhancing the accuracy of model predictions.

[0021] like Figure 1As shown, firstly, hourly wind speed and direction sample data from a certain location over many years are selected and preprocessed. The synchronously measured wind speed and direction data are first divided into multiple intervals, and the probability density of wind speed and direction samples in each interval is calculated. f m ( . Finally, a histogram of wind speed and direction frequency distributions was obtained.

[0022] In the preferred scheme, step S1 involves constructing a bivariate exponential multinomial joint probability distribution model for wind speed and direction, including: Preprocessing of multi-year measured wind speed and direction data involves dividing the synchronously measured data into multiple intervals and calculating the probability density of each interval to obtain a frequency distribution histogram of wind speed and direction. The formula is as follows: ; In the formula, w v and w θ These represent the interval steps for wind speed and wind direction, respectively. P This represents the total number of samples for measured wind speed and direction.

[0023] The parameters of a bivariate exponential polynomial are calculated using probability density and the least squares method. The expression for a bivariate exponential polynomial is: ; In the formula, v represents wind speed, θ represents wind direction, and a(k,q) represents parameters. M 1 and M 2 represents the exponent, and C represents the normalization constant.

[0024] The objective function Q of the least squares method is: ; In the formula, Q This is the sum of squared errors between the measured data and the values ​​of the bivariate exponential polynomial.

[0025] Using root mean square error and coefficient of determination to traverse different M 1 and M 2. Combinatorial determination of the optimal exponent of a bivariate exponential polynomial, the formulas are as follows: ; ; .

[0026] The root mean square error is the square root of the sum of squares of the differences between the measured probability density and the bivariate exponential polynomial value, divided by the number of sample points. The coefficient of determination is 1 minus the ratio of the sum of squares of the differences between the measured probability density and the bivariate exponential polynomial value to the sum of squares of the differences between the measured probability density and the mean.

[0027] likeFigure 2 As shown, for Figure 1 The measured data, through the visualization of the joint probability distribution obtained by fitting a binary exponential multinomial, accurately reflects the joint distribution pattern of wind speed and wind direction in the region. Compared with the traditional single distribution model, it is more in line with the actual characteristics of complex wind conditions and is the core model visualization presentation for describing the randomness of wind speed and wind direction.

[0028] In this embodiment, to address the randomness of wind speed and direction, a joint probability distribution model for wind speed and direction is constructed using a bivariate exponential polynomial fitting model. First, the bivariate exponential polynomial parameters are solved using the least squares method with years of measured wind speed and direction data. Then, the root mean square error (RMSE) and coefficient of determination (R²) are used to further refine the model. 2 Solving for the optimal exponent of the bivariate exponential polynomial and constructing the optimally fitted joint probability distribution model of wind speed and direction improves the accuracy of fitting the joint characteristics of wind speed and direction under complex wind conditions and reduces the error between measured data and model predictions.

[0029] In the preferred embodiment, step S1 discretizes the joint probability distribution model of wind speed and direction into a discrete state probability matrix of wind speed and direction, including: The formula for calculating the discrete state probability of wind speed and direction is: ; in v max This represents the maximum sample wind speed; i represents the discrete index of wind speed, and j represents the discrete index of wind direction. g (.) represents a bivariate exponential polynomial.

[0030] The downstream wind speed is calculated using the Jensen wake model, using the following formula: ; in, v 0 represents the upstream wind speed and the wake cross-sectional radius. pass Confirmed, among which r 0 represents the impeller radius, d represents the distance between wind turbine units, α represents the wake descent coefficient, and C T denoted as thrust coefficient; S represents the area of ​​the wake region.

[0031] The discrete state probabilities of wind speed and direction for each group are calculated using the wind power conversion function and the Jensen wake model. p （i,j） Wind farm power generation P （i,j）， By performing a probability-weighted summation of the wind farm's power generation under all discrete wind speed and direction conditions, the equivalent average power of the wind farm under all wind conditions can be obtained. P eq .

[0032] In the preferred scheme, the thrust coefficient formula in the Jensen wake model is: ; In the formula, F f This represents the thrust acting on the wind turbine, where ρ represents the air density. v in It is the cut-in wind speed of the wind turbine. r 0 represents the impeller radius.

[0033] like Figure 3 As shown, the core physical relationships of the Jensen wake model are presented, intuitively demonstrating the propagation law of the wake effect and providing a theoretical and visual basis for the calculation of wake impact in wind turbine layout optimization.

[0034] This embodiment obtains the discrete state probability matrix of wind speed and direction through discretization processing, and accurately calculates the actual wind speed of downstream wind turbines affected by the wake by combining the Jensen wake model. Then, the equivalent average power is obtained by probability weighted summation, making the wind farm power generation calculation more in line with actual wind condition fluctuations. This avoids the power prediction deviation caused by simplifying the wake calculation and provides an accurate objective function basis for layout optimization. The Jensen wake model combines key parameters such as rotor swept area, air density, and upstream wind speed to accurately quantify the impact of wind turbine forces on the wake effect, making the wake area and downstream wind speed calculations more physically meaningful and improving the accuracy of wake effect simulation.

[0035] In the preferred scheme, the optimal layout of the wind turbine units is solved using optimization algorithms, including: Construct an optimal layout optimization model for wind turbine units, with the objective function as follows: ; In the formula, x wi and y wi For the first i The coordinates of the typhoon turbine unit d ij For the first i Taiwan and the j The spacing between typhoon turbine units d min This is the minimum distance between two wind turbine units. U b This represents the upper limit of a wind farm in actual engineering. L b This represents the lower bound of a wind farm in actual engineering, and φ is the penalty factor.

[0036] Initialize the coordinate position of the wind turbine, perform global search and local development through optimization algorithm, and apply cross operator perturbation to iteratively update the coordinate position.

[0037] If the current iteration coordinates satisfy the spacing and boundary constraints, then calculate the discrete state power generation of all wind speeds and directions under the current layout and sum them by weight to obtain the Peq. Otherwise, continue iterating by adjusting the fitness value through penalty until convergence is obtained to obtain the optimal layout of wind turbine units with the maximum power generation.

[0038] like Figure 4 As shown, based on Figure 2 The joint probability distribution model and Figure 3 The Jensen wake model, solved by intelligent algorithms, yields the optimal layout scheme for wind farms in the Bowbells area. This layout maximizes the total power generation of the wind farm, effectively avoids power loss caused by the wake effect, and clarifies the optimal coordinate distribution of the wind turbine units.

[0039] This embodiment constructs an optimization objective function based on wind turbine spacing constraints and boundary constraints. Through global search, local exploitation, and cross operator perturbation mechanisms of the optimization algorithm, it effectively avoids local optima and ensures that a wind turbine layout scheme that maximizes power generation is found. At the same time, a penalty factor is used to ensure that the layout meets the actual engineering requirements (such as minimum safety spacing and site boundary restrictions).

[0040] In the preferred scheme, the K-means clustering algorithm is used to partition the locations of wind turbine units, including: Initialize the substation location coordinates, the number of zones K, and the cluster centers. Based on the wind turbine coordinates in the optimal wind turbine layout, for the current ( x s , y s The K-means clustering algorithm is used to divide the location of wind turbine units into K partitions, and the number of wind turbine units in each partition is controlled to not exceed the preset upper limit M.

[0041] For each partition, the minimum spanning tree is solved. The minimum spanning tree is calculated by using the cable length between the wind turbine coordinates as the edge weight to calculate the shortest cable connection method within the partition. The cable length is the sum of the Euclidean distances between the coordinates of the two wind turbines.

[0042] The fitness value is calculated by using the total cable length under the current configuration as the formula: ; In the formula, K For the number of partitions, K min and K max These represent the upper and lower limits of the number of partitions, respectively. The number of partitions is set by these upper and lower limits. xs , y s ( ) represents the location coordinates of the booster station. U b This represents the upper bound of the wind farm in the algorithm. L b This represents the lower bound of the wind farm in the algorithm. i The number of the wind turbine unit. N w This represents the total number of generating units. D m This represents the minimum distance between the wind turbine and the substation, and also the size of the restricted area around the substation. M The number of units in each partition. and These are the penalty factors for the location constraints of the booster station and the number of wind turbine units in each zone, respectively.

[0043] If the distance between the booster station and any wind turbine is less than the minimum distance D m If the number of wind turbines in any zone violates the location constraint penalty factor, a penalty factor will be applied. K min and K max If so, then a quantity constraint penalty factor is applied.

[0044] In the preferred scheme, based on the optimal layout of the wind farm and a tree topology, the shortest cable connection between wind turbines within the wind farm is studied. The formula for calculating the cable length is as follows: ; In the formula, N w It refers to the number of wind turbine units; wind turbine units i Wind turbine j The coordinates are respectively ( x wi , y wi )and( x wj , y wj ).

[0045] like Figure 5As shown, the impact of substation location selection on the topology optimization of wind farm power collection systems is further considered. Wind turbine wiring optimization based on K-means and minimum spanning tree is adopted. The shortest cable connection method for a given substation location is calculated. The topology optimization process based on K-means clustering and minimum spanning tree is presented, including reading wind farm coordinates, initializing substation and clustering parameters, determining the topology connection method through K-means clustering and minimum spanning tree, calculating the fitness value (cable length), and iteratively updating parameters through an intelligent algorithm until the maximum number of iterations is reached, at which point the optimal result is output.

[0046] In this embodiment, the K-means clustering algorithm is used to achieve reasonable zoning of wind turbine units, control the number of units connected by a single cable, and combine the minimum spanning tree algorithm to calculate the shortest cable connection method within the zoning, thereby reducing the cable laying cost of the power collection system. By setting constraints and penalty factors, the safety of the substation site selection (meeting the minimum safe distance from the units) and the rationality of the zoning are improved, avoiding cable overload or chaotic layout problems.

[0047] In the preferred scheme, step S3 involves using an optimization algorithm to globally optimize the location and zoning of the booster station, including: The initialization optimization variables include the location of the booster station, the number of partitions K, and the cluster centers. The optimization variables are updated iteratively through the optimization algorithm.

[0048] Set site selection constraints for the booster station, designating a shaded area around the booster station as a restricted zone. Considering the typical footprint of a booster station and the safe distance between the booster station and wind turbines, if the booster station's location ( x s , y s ) and each wind turbine in the optimal layout of wind turbine units ( x i , y i )distance D s Satisfying the inequality relationship: ; In the formula, D s The distance between the substation and each wind turbine. x s and y s Here are the coordinates of the booster station, ( x wi , y wi ) is the first i The coordinates of each wind turbine.

[0049] If so, perform K-means clustering and minimum spanning tree calculation to determine the total cable length; otherwise, adjust the fitness value to increase the position constraint penalty.

[0050] If the number of wind turbine units in each zone meets the requirements K min Less than or equal to K Less than or equal to K max If the total cable length does not exceed M, then the current total cable length is retained as the fitness value; otherwise, a quantity constraint penalty is added and the variables are updated.

[0051] Repeat the iterations until the maximum number of iterations is reached, and output the optimal booster station location that satisfies all constraints. x s , y s The zoning scheme and cable connection method maximize the power generation of the wind farm and minimize the total cable length.

[0052] This embodiment employs an optimization algorithm to perform global iterative optimization of the substation site selection, number of zones, and cluster centers. This breaks the limitations of the traditional approach of optimizing the layout and substation site selection independently, fully considering the mutual influence between the two, and ultimately outputting the optimal topology scheme that satisfies all engineering constraints. This further shortens the total cable length, reduces investment costs, and further ensures optimal power generation.

[0053] In the preferred scheme, the optimization algorithm for the optimal layout of wind turbine units and the global optimization of substation location and partitioning includes particle swarm optimization or genetic algorithm, which iteratively solves the objective function through velocity update and location update or selection crossover and mutation operations.

[0054] like Figure 6 As shown, in Figure 4 Based on the optimal layout, Figure 5 The final topology result obtained after process optimization clearly marks the optimal location of the booster station, the zoning of wind turbine units, and the shortest cable connection path based on minimum spanning tree within each zone, achieving the dual objectives of maximizing wind farm power generation and minimizing total cable length. By combining intelligent algorithms, the global optimization of booster station location and wind turbine unit zoning is performed. Through multiple iterations, the globally optimal cable routing method for the wind farm is solved, achieving both maximizing wind farm power generation and minimizing total cable length.

[0055] This embodiment selects particle swarm optimization or genetic algorithm as the core optimization tool. Through operations such as speed and position updates or selection, crossover, and mutation, it achieves efficient iterative solution of wind turbine layout, substation site selection, and zoning parameters. The algorithm has fast convergence speed and strong global search capability, and can quickly find the global optimal solution under complex constraints, thereby improving optimization efficiency and result reliability.

[0056] Example 2 To further illustrate with reference to Example 1, a wind farm layout and topology optimization system that takes into account the randomness of wind speed and direction includes: The data processing module is used to select measured wind speed and direction sample data over many years and construct a bivariate exponential polynomial joint probability distribution model of wind speed and direction. The bivariate exponential polynomial is solved for parameters by the least squares method, and the optimal exponent is determined by the root mean square error and the coefficient of determination.

[0057] The joint probability distribution modeling module is used to discretize the joint probability distribution model of wind speed and direction into a discrete state probability matrix of wind speed and direction, calculate the equivalent average power by combining the Jensen wake model, and use optimization algorithms to solve for the optimal layout of wind turbine units.

[0058] The global optimization module is used to partition the wind turbine locations based on the optimal layout of the wind turbines using the K-means clustering algorithm and solve the minimum spanning tree to determine the cable connections within the partitions. The optimization algorithm is then used to globally optimize the substation site selection and partitioning to obtain the optimal topology.

[0059] This embodiment provides a method for optimizing wind farm layout and topology that takes into account the randomness of wind speed and direction. The working process, working details and technical effects can be found in Embodiment 1, and will not be repeated here.

[0060] The above embodiments are merely preferred technical solutions of the present invention and should not be considered as limitations on the present invention. The scope of protection of the present invention should be limited to the technical solutions described in the claims, including equivalent substitutions of the technical features described in the claims. That is, equivalent substitutions and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A method for wind farm layout and topology optimization considering the randomness of wind speed and direction, characterized in that, Includes the following steps: S1: Select sample data of measured wind speed and direction over many years and construct a joint probability distribution model of wind speed and direction using a bivariate exponential polynomial; wherein the bivariate exponential polynomial is solved for parameters by the least squares method and the optimal exponent is determined by the root mean square error and the coefficient of determination. S2: Discretize the joint probability distribution model of wind speed and direction into a discrete state probability matrix of wind speed and direction, calculate the equivalent average power by combining the Jensen wake model, and use the optimization algorithm to solve the optimal layout of wind turbine units. S3: Based on the optimal layout of the wind turbine units, the K-means clustering algorithm is used to partition the wind turbine unit locations and solve the minimum spanning tree to determine the cable connections within the partitions. The optimization algorithm is then used to globally optimize the substation location and partitioning to obtain the optimal topology.

2. The wind farm layout and topology optimization method considering the randomness of wind speed and direction according to claim 1, characterized in that, In S1, a joint probability distribution model of wind speed and direction using a binary exponential multinomial is constructed, including: The measured wind speed and direction data from previous years are preprocessed by dividing the synchronously measured data into multiple intervals and calculating the probability density of each interval to obtain a frequency distribution histogram of wind speed and direction. The formula is as follows: ； In the formula, w v and w θ These represent the interval steps for wind speed and wind direction, respectively. P This represents the total number of measured wind speed and direction samples. This represents the change in wind speed interval step size; The parameters of the bivariate exponential polynomial are calculated using the probability density and least squares method. The expression for the bivariate exponential polynomial is: ； In the formula, v represents wind speed, θ represents wind direction, and a(k,q) represents parameters. M 1 and M 2 represents the exponent, and C represents the normalization constant; The objective function Q of the least squares method is: ； In the formula, Q This represents the sum of squared errors between the measured data and the values ​​of the bivariate exponential polynomial. Using root mean square error and coefficient of determination to traverse different M 1 and M 2. Combinatorial determination of the optimal exponent of a bivariate exponential polynomial, the formulas are as follows: ； ； 。 3. The wind farm layout and topology optimization method considering the randomness of wind speed and direction according to claim 1, characterized in that, In step S1, discretizing the joint probability distribution model of wind speed and direction into a discrete state probability matrix of wind speed and direction includes: The formula for calculating the discrete state probability of wind speed and direction is: ； in v max This represents the maximum sample wind speed; i represents the discrete index of wind speed, and j represents the discrete index of wind direction. g (.) denotes a bivariate exponential polynomial; The downstream wind speed is calculated using the Jensen wake model, using the following formula: ； in, v 0 represents the upstream wind speed, and the radius of the wake cross-section is... pass Confirmed, among which r 0 represents the impeller radius, d represents the distance between wind turbine units, α represents the wake descent coefficient, and C T is the thrust coefficient; S represents the area of ​​the wake region; The discrete state probabilities of wind speed and direction for each group are calculated using the wind power conversion function and the Jensen wake model. p （i,j） Wind farm power generation P （i,j）， By performing a probability-weighted summation of the wind farm's power generation under all discrete wind speed and direction conditions, the equivalent average power of the wind farm under all wind conditions can be obtained. P eq .

4. The wind farm layout and topology optimization method considering the randomness of wind speed and direction according to claim 1, characterized in that, The method of using optimization algorithms to solve for the optimal layout of wind turbine units includes: Construct an optimal layout optimization model for wind turbine units, with the objective function as follows: ； In the formula, x wi and y wi For the first i The coordinates of the typhoon turbine unit d ij For the first i Taiwan and the j The spacing between typhoon turbine units d min This is the minimum distance between two wind turbine units. U b This represents the upper limit of a wind farm in actual engineering. L b This represents the lower bound of a wind farm in actual engineering, where φ is the penalty factor; Initialize the coordinate position of the wind turbine, and iteratively update the coordinate position by performing a global search and local development through an optimization algorithm and applying a cross operator perturbation. If the current iteration coordinates satisfy the spacing and boundary constraints, then calculate the discrete state power generation of all wind speeds and directions under the current layout and sum them by weight to obtain the Peq. Otherwise, continue iterating by adjusting the fitness value through penalty until convergence is obtained to obtain the optimal layout of wind turbine units with the maximum power generation.

5. The wind farm layout and topology optimization method considering the randomness of wind speed and direction according to claim 1, characterized in that, The step of partitioning the wind turbine locations using the K-means clustering algorithm includes: Initialize the substation location coordinates, the number of zones K, and the cluster center. Based on the wind turbine coordinates in the optimal wind turbine layout, for the current ( x s , y s The K-means clustering algorithm is used to divide the location of wind turbine units into K partitions, and the number of wind turbine units in each partition is controlled to not exceed the preset upper limit M. For each partition, a minimum spanning tree is solved. The minimum spanning tree is calculated by using the cable length between the coordinates of the wind turbine units as the edge weight to calculate the shortest cable connection method within the partition. The cable length is the sum of the Euclidean distances between the coordinates of the two wind turbine units. The fitness value is calculated by using the total cable length under the current configuration as the formula: ； In the formula, K For the number of partitions, K min and K max These represent the upper and lower limits of the number of partitions, respectively. The number of partitions is set by these upper and lower limits. x s , y s ( ) represents the location coordinates of the booster station. U b This represents the upper bound of the wind farm in the algorithm. L b This represents the lower bound of the wind farm in the algorithm. i The number of the wind turbine unit. N w This represents the total number of generating units. D m This represents the minimum distance between the wind turbine and the substation, and also the size of the restricted area around the substation. M The number of units in each partition. and These are the penalty factors for the location constraints of the booster station and the number of wind turbine units in each zone, respectively.

6. The wind farm layout and topology optimization method considering the randomness of wind speed and direction according to claim 5, characterized in that, In step S3, the global optimization of the substation location and zoning using an optimization algorithm includes: Initialization optimization variables include the location of the booster station, the number of partitions K, and the cluster centers. These optimization variables are iteratively updated using an optimization algorithm. If the location of the booster station ( x s , y s ) and each wind turbine in the optimal layout of the wind turbines ( x i , y i )distance D s satisfy D s Greater than or equal to D m If the total cable length is not found, K-means clustering and minimum spanning tree calculation are performed; otherwise, the fitness value is adjusted to increase the position constraint penalty. If the number of wind turbine units in each zone meets the requirements K min Less than or equal to K Less than or equal to K max If the total cable length does not exceed M, then retain the current total cable length as the fitness value; otherwise, increase the quantity constraint penalty and update the variables. Repeat the iterations until the maximum number of iterations is reached, and output the optimal booster station location that satisfies all constraints. x s , y s ), zoning scheme and cable connection method.

7. The wind farm layout and topology optimization method considering the randomness of wind speed and direction according to claim 1, characterized in that, The thrust coefficient formula in the Jensen wake model is: ； In the formula, F f This represents the thrust acting on the wind turbine, where ρ represents the air density. v in It is the cut-in wind speed of the wind turbine. r 0 represents the impeller radius.

8. The wind farm layout and topology optimization method considering the randomness of wind speed and direction according to claim 6, characterized in that, The optimization algorithm for the optimal layout of the wind turbine and the global optimization of the location and partitioning of the booster station includes particle swarm optimization or genetic algorithm, and solves the objective function iteratively through velocity update and location update or selection crossover and mutation operations.

9. The wind farm layout and topology optimization method considering the randomness of wind speed and direction according to claim 6, characterized in that, The formula for calculating cable length is: ； In the formula, N w It refers to the number of wind turbine units; wind turbine units i Wind turbine j The coordinates are respectively ( x wi , y wi )and( x wj , y wj ).

10. A wind farm layout and topology optimization system considering the randomness of wind speed and direction, characterized in that, include: The data processing module is used to select sample data of measured wind speed and direction over many years and construct a joint probability distribution model of wind speed and direction using a binary exponential multinomial model. The parameters of the bivariate exponential polynomial are solved by the least squares method, and the optimal exponent is determined by the root mean square error and the coefficient of determination. The joint probability distribution modeling module is used to discretize the joint probability distribution model of wind speed and wind direction into a discrete state probability matrix of wind speed and wind direction, calculate the equivalent average power in combination with the Jensen wake model, and use optimization algorithms to solve the optimal layout of wind turbine units. The global optimization module is used to partition the wind turbine locations based on the optimal layout of the wind turbines using the K-means clustering algorithm and solve the minimum spanning tree to determine the cable connections within the partitions. The optimization algorithm is then used to globally optimize the substation site selection and partitioning to obtain the optimal topology.

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