Improved method for positioning wind turbines with alignment constraints

Abstract

The invention relates to a method for simulating a wind farm in a predetermined space, for which at least the following consecutive steps are carried out: a) different grids are formed (GR) in the predetermined space; b) for each grid, the average annual energy production of a mini-farm (AEP-mf) is determined; c) a few grids are selected (Ch) that allow energy production to be maximised; d) for each grid, a first arrangement (Alg1) of the predefined number of wind turbines is determined on the grid; e) the position (Alg2) of the wind turbines on the grid is modified; f) second grids (Gr2) are formed with modified spacings, and steps d) and e) are repeated; g) third grids (Gr3) are formed with modified directions, and steps d) and e) are repeated; h) a final layout (Disp_F) of the wind turbines in the predetermined space is determined for the construction (Const) of the wind farm according to this layout.

Description

[0001] IMPROVED METHOD FOR POSITIONING WIND TURBINES WITH ALIGNMENT CONSTRAINTS

[0002] Technical field

[0003] The present invention relates to a method for simulating a wind farm in a predetermined space, a method for positioning wind turbines of a farm in a predetermined space, a method for constructing a wind farm in a predetermined space and a wind farm.

[0004] To address environmental issues, wind farms have emerged. These wind farms consist of several wind turbines spaced apart within a defined area. This defined area can be on land or at sea. A distinction is made between onshore wind farms (also called "onshore" wind farms) and offshore wind farms, i.e., those located at sea.

[0005] The wind turbines in these farms are usually horizontal axis wind turbines that have a system to orient the horizontal axis of rotation in the direction of the wind, in order to maximize the energy recovered by the wind turbine. Sometimes, the wind turbine is designed to automatically orient itself in the direction of the wind.

[0006] We also know of wind turbines with a vertical axis of rotation, which have the advantage of not requiring orientation in the direction of the wind.

[0007] In wind farms, wakes generated by wind turbines can reduce wind speeds downstream of the turbine and therefore reduce the energy recovered by other wind turbines, particularly those located downstream, downwind, of the turbines generating these wakes. The positioning of wind turbines within the farm is therefore important in order to maximize the energy recovered by the farm.

[0008] Furthermore, in a location chosen to install a wind farm, the local characteristics of the wind may vary. Indeed, the direction and speed of the wind are parameters that can vary over time at the location considered. These characteristics can be obtained by sensors positioned at the defined location and maintained at this position for several months or years, so as to obtain sufficient statistical data to characterize the wind resource at the chosen location. These sensors may in particular be anemometers positioned at a sufficient altitude (of the order of 100m above the ground) to characterize the wind that will be seen by the wind turbines (i.e. the wind that is substantially at the level of the rotor axis for example). Wind data can also be obtained by laser remote sensing, also called LiDAR (from the English "Light Detection And Ranging").Statistical knowledge of the wind at the considered location of the farm makes it possible in particular to obtain the distribution of the wind speed (also called subsequently "wind speed distribution"), the distribution of the wind direction (also called subsequently "wind direction distribution") and the joint probability of occurrence of a wind speed in a given direction.

[0009] In order to maximize the annual energy produced by the farm, it is therefore necessary to position the wind turbines optimally in the location planned for the farm. The term "annual energy produced" or "annual energy production" refers to the total average energy produced by the farm, i.e. by all the wind turbines on the farm, over a year. This average energy, estimated by taking into account statistical wind data (distributions of wind speeds, wind direction and probability of occurrence), is based on a period of one year, hence the term "annual", so as to avoid a seasonal influence that could distort the results. Indeed, the wind, whether its speed or direction, can vary greatly depending on the seasons.

[0010] Average energy is obtained by knowing the distribution of wind direction, the distribution of wind speeds and the probability of occurrence of a wind speed in a given direction.

[0011] Of course, the annual energy produced also depends on the wind turbines chosen and their positioning.

[0012] Prior art

[0013] To determine the correct positioning of wind turbines in the planned location of the farm, several methods have been developed.

[0014] Patent application CN105119320 relates to a method based on an evolutionary algorithm. This type of algorithm is stochastic, using random processes. This type of algorithm requires a large number of tests to obtain a result, which generates significant computing time and requires significant computer memory. Patent applications CN102142103A, CN105139269 and US2016171401 relate to wind turbine positioning methods based on genetic algorithms. Genetic algorithms are a category of evolutionary algorithms. They require a multitude of evaluations and cross-referencing of these evaluations from possible real (continuous) data. As a result, genetic algorithms are complex and therefore require significant computing time and significant computer memory.

[0015] The methods described in the following documents are also known:

[0016] - Tao S., Xu Q., Feijoo A., Zheng G., Zhou J., 2020. Wind farm layout optimization with a three-dimensional Gaussian Wake model. Renewable Energy, Volume 159, October 2020, Pages 553-569: This method requires that the planned farm location be bounded by a rectangle. In other words, this method is not suitable for farms comprising non-convex or even non-connected spaces.

[0017] - Antonini EGA, Romerp DA, Amon, CH, 2018. Continuous adjoint formulation for wind farm layout optimization. Applied Energy, Volume 228, 15 October 2018, Pages 2333-2345: This method is based on an analytical method for evaluating wake effects.

[0018] This method is therefore a continuous optimization method, based on CFD calculations (from the English "Computational Fluid Dynamics" meaning "Fluid dynamics calculations"), which requires significant computing times and significant computer memory.

[0019] - Wagner M., Day J., Neuman F., 2012. A fast and effective local search algorithm for optimizing the placement of wind turbines. Renewable Energy, Volume 51, March 2013, pages 64-70: The application of this method requires locations delimited by a rectangle. Therefore, it is not suitable for locations with non-convex or non-connected shapes.

[0020] - Feng J., Shen WZ, 2015. Solving the wind farm layout optimization problem using random search algorithm. Renewable Energy, Volume 78, June 2015, Pages 182-192: This method requires locations bounded by polyhedra. Therefore, it is not suitable for locations of unconnected shapes.

[0021] - Quan N., and Kim HM, 2018. Greedy robust wind farm layout optimization with feasibility guarantee. Engineering Optimization, September 6, 2018, pages 1152-1167. This method is based on a greedy algorithm that considers all positions located at a minimum distance from the wind turbines already positioned in the location to determine the location of the next wind turbine. It therefore requires significant computing time and computer memory, especially if the discretization of the planned location for the farm is fine, if the space in which the wind turbines are to be placed is large and / or if the number of wind turbines to be positioned is large.

[0022] Also known is the applicant's patent application WO 2022 / 028847, which relates to a method for constructing a wind farm. In this method, the wind turbine locations are discrete positions in the predetermined space. Although satisfactory, this method does not implement alignment constraints for the wind turbines, which does not facilitate the installation and maintenance of the wind turbines. In addition, for offshore wind turbines and in order to facilitate boat navigation, the alignment of the wind turbines is one of the design constraints for the farms. The applicant's patent application FR 22 / 09.630 relates to a method for constructing a wind farm taking into account alignment constraints. However, this method requires significant computing time and significant computing resources (memory and processors).

[0023] Thus, the technical problem of the invention consists in finding an optimal positioning of wind turbines in locations of complex shape, such as non-convex and / or non-connected areas, so as to maximize the total energy produced by the wind farm, by minimizing the necessary calculation time and computing resources, and by respecting constraints of alignment of the wind turbines in two directions forming a non-zero angle between them (two non-parallel directions).

[0024] Summary of the invention

[0025] To address the technical problem, the invention relates to a method for simulating a wind farm in a predetermined space for the construction of said wind farm in said predetermined space so as to maximize the annual energy produced, the wind farm being composed of a predefined number of wind turbines, from a first discrete wind speed distribution, a second discrete wind direction distribution and a probability of occurrence of each discrete wind speed value in each discrete wind direction value of the first and second discrete distributions, in which at least the following successive steps are carried out by computer means, such as a computer: a) For different first predefined spacings separated by a first spacing step, different second predefined spacings separated by said first spacing step,different first predefined directions separated by a second direction pitch, and different second predefined directions separated from said second direction pitch, different first pairs of first and second predefined spacings are formed, and different second pairs of first and second predefined directions, then for the different first pairs and for the different second pairs, first grids are formed in the predetermined space, each first grid being defined by a plurality of points of intersection between first lines oriented in the first predefined direction and second lines oriented in the second predefined direction, the first lines being spaced from said second predefined spacing along the second predefined direction and the second lines being spaced from said first predefined spacing along the first predefined direction,each first grid comprising at least one mesh delimited by intersection points. b) For each first grid of said predetermined space, the average annual energy production of a mini-farm composed of wind turbines positioned at all the intersection points of one or more connected meshes of the first grid is determined, from said first discrete distribution of wind speed, said second discrete distribution of wind direction and said probability of occurrence; c) For each first pair of first and second predefined spacings, at least one second pair of first and second predefined directions is identified which maximizes the annual energy production of said mini-farm,then a set of second pairs is formed grouping the identified second pairs; d) For each first grid defined by a first pair of first and second predefined spacings and by a second pair of first and second predefined directions among said set of second pairs, a first arrangement of the predefined number of wind turbines is determined, each wind turbine being positioned on one of said intersection points of the first grid by a first positioning algorithm; e) then, for each first grid used in step d), the position of the wind turbines is modified among the intersection points of the first grid on which no wind turbine is positioned,in order to improve the annual energy production so as to obtain an arrangement of the predefined number of wind turbines on each first grid considered and an annual energy production for each arrangement and a predetermined quantity of arrangements corresponding to the arrangements maximizing the annual energy production is retained and each first grid associated with each arrangement retained; f) For each first grid retained in step e), the first spacing step is reduced, preferably by half, and second grids are formed from the first reduced spacing step, then steps d) and e) are repeated using the second grids as replacements for the first grids; g) For each second grid retained in step f), the second direction step is reduced, preferably by half, and third grids are formed from the second direction step,then steps d) and e) are repeated using the third grids to replace the first grids; h) A final arrangement of the wind turbines in the predetermined space is determined, said final arrangement corresponding to the final arrangement obtained in step g) of the third grid which maximizes the annual energy production, for the construction of the wind turbines according to the final arrangement in the predetermined space.,

[0026] Preferably, steps f) and / or g) are repeated until the first spacing step reaches a first threshold and / or until the second direction step reaches a second threshold.

[0027] Advantageously, the first threshold is between one fiftieth of the diameter of the wind turbines and one fifth of the diameter of the wind turbines or less than 1 m and / or the second threshold is less than 2°, preferably less than 1°.

[0028] Advantageously, in step f), a predetermined number of second grids is formed, each second grid being defined by lines of the same orientation as the first grid retained in step e), the first spacing of each second grid corresponding to the sum of the first spacing of the first grid retained in step e) and a first integer of reduced first spacing pitch, the second spacing of each second grid corresponding to the sum of the second spacing of the first grid retained in step e) and said first integer of reduced first spacing pitch, preferably, said first integer being 1 or -1.According to a variant of the invention, in step g), a predetermined number of third grids is formed, each third grid being defined by lines of the same spacing as the second grid retained in step f), the first direction of each third grid corresponding to the sum of the first direction of the second grid retained in step f) and a second integer of the second reduced direction pitch, the second direction of each third grid corresponding to the sum of the second direction of the second grid retained in step f) and said second integer of the second reduced direction pitch, preferably, said second integer being 1 or -1.

[0029] According to a configuration of the invention, in step e) of modifying the position of the wind turbines for each first grid, at least the following steps are carried out: e1) for each grid used in step d), a sequential order of modification of the positions of the wind turbines determined by the first positioning algorithm is defined and each wind turbine of the defined sequential order is repositioned, one by one, by finding a free point of intersection of the first grid which maximizes the annual energy production from said first discrete distribution of wind speed, said second discrete distribution of wind direction and said probability of occurrence;e2) step e1) is repeated as many times as necessary until, at the end of a step e1), no wind turbine has been repositioned and an arrangement of the predefined number of wind turbines is obtained on each first grid considered and an annual energy production for each final arrangement; and a predetermined quantity of arrangements corresponding to the arrangements maximizing the annual energy production and each first grid associated with each arrangement retained is retained.;

[0030] Preferably, said sequential order is obtained randomly and / or the sequential order is modified at each iteration of step e1).

[0031] Advantageously, in step e1), a selection of intersections is chosen from among the intersection points on which no wind turbine is positioned, for each wind turbine to be repositioned.

[0032] Preferably, the selection of intersections corresponds to a predetermined value of intersection points on which no wind turbine is positioned, said selection of intersections being chosen randomly or being chosen as corresponding to said predetermined value of intersection points on which no wind turbine is positioned closest to the position of the wind turbine to be repositioned.

[0033] Advantageously, said predetermined space comprises non-connected and / or non-convex zones.

[0034] According to a variant of the invention, for each first grid considered, said first positioning algorithm carries out at least the following steps:

[0035] - we arbitrarily define the position of the first wind turbine on one of the intersection points of the first grid;

[0036] - then for each wind turbine to be positioned, successively: potential positions are defined for the wind turbine to be positioned, said potential positions being constituted by the intersection points of the first grid located between a minimum distance and a maximum distance from all the positioned wind turbines; the annual energy production of the positioned wind turbines and of the wind turbine to be positioned is calculated for the defined potential positions, from said first discrete distribution of wind speed, said second discrete distribution of wind direction and said probability of occurrence;

[0037] We choose the position of the wind turbine to be positioned corresponding to the maximum calculated value of annual energy production:

[0038] - said first arrangement is determined corresponding to the position of the predefined number of wind turbines among the intersection points of the first grid considered in said predetermined space.

[0039] According to one implementation of the invention, in step c), the difference is made between the annual energy production of the mini-farm obtained in step b) and the annual energy production of a single wind turbine multiplied by the number of wind turbines in the mini-farm. Advantageously, in step a), the first spacing step is between twice and ten times the diameter of the wind turbines, preferably between twice and six times the diameter of the wind turbines.

[0040] Preferably, in step a), the second steering step is between 1° and 20°, preferably between 5° and 10°.

[0041] Advantageously, in step e), the predetermined quantity of arrangements is between 1 and 20, preferably between 1 and 10.

[0042] Preferably, in step c), a predetermined number of second pairs of first and second predefined directions is identified for each first pair of first and second predefined spacings, preferably the predetermined number is between 1 and 20, preferably between 1 and 10.

[0043] The invention also relates to a method for positioning wind turbines of a wind farm in a predetermined space for the construction of said wind farm in said predetermined space, in which statistical wind data are measured, by measuring means, preferably a LIDAR sensor, in the predetermined space to determine the first and second discrete distributions and the probabilities of occurrence of each wind speed in each wind direction of the first and second discrete distributions, then the simulation method is implemented according to one of the preceding configurations to determine the positions of the wind turbines of said wind farm in the predetermined space, so as to position the wind turbines in the predetermined space for the construction of said wind farm in said predetermined space.The invention also relates to a method of constructing a wind farm in which the simulation method is implemented according to one of the variants or combinations of variants described above, or the method of positioning the wind turbines is implemented as described above, then the wind farm is constructed by erecting the wind turbines in the positions of said final arrangement in the predetermined space.

[0044] The invention also relates to a wind farm obtained from the method of constructing a wind farm as described above.

[0045] List of figures

[0046] Other characteristics and advantages of the methods and processes as well as of the farm according to the invention will appear on reading the following description of non-limiting examples of embodiments, with reference to the figures appended and described below.

[0047] Figure 1 represents an example of a simulation method according to the invention. Figure 2 represents an example of carrying out the steps of repositioning the wind turbines of the simulation method according to the invention.

[0048] Figure 3 shows an example of a complex location for positioning wind turbines according to the invention.

[0049] Figure 4 illustrates a variant of a first positioning algorithm according to the invention.

[0050] Figure 5 illustrates the definition of wind turbine alignment constraints for the simulation method according to the invention.

[0051] Figure 6 illustrates the positioning of wind turbines in a predetermined non-convex space using the simulation method according to the invention.

[0052] Description of the embodiments

[0053] To facilitate the reading of this description, some definitions are explained below.

[0054] A "greedy algorithm" is an algorithm that consists of establishing a local optimum step by step. In the case of a wind farm, it consists of positioning each wind turbine one after the other until all the wind turbines are positioned in the predetermined space.

[0055] An "Evolutionary Algorithm" is a bio-inspired algorithm whose idea is to evolve a set of solutions to obtain better results. They are therefore stochastic and iteratively use random processes.

[0056] A "genetic algorithm" is an evolutionary algorithm that uses the concept of natural selection. This type of algorithm can, in particular, cross-reference or modify certain parameters of previous solutions in order to improve results.

[0057] Unconnected areas are areas in which there are at least two points that cannot be connected by a continuous path entirely contained within the area in question. Conversely, a connected area is an area in which each pair of points is connected by a continuous path entirely contained within the area.

[0058] A convex zone is an area in which the segments connecting any two points in that area are all entirely contained within the area. A circle, a square, or a rectangle, for example, all delimit convex zones.

[0059] Conversely, a "non-convex region" is an area in which there are at least two points connected by a segment that is not entirely contained within the area. For example, an area bounded by a concentric outer circle and an inner circle is not convex.

[0060] In the present description, the term "grid" means a plurality of intersection points located in the predetermined space (or at the boundary of this space). The intersection points of the grid are points located at the intersection between first lines, all parallel to each other, and oriented in the first predefined direction and second lines, also all parallel to each other, and oriented in the second predefined direction. The first and second predefined directions are defined relative to a global reference frame; they are generally different from the wind direction (but may be collinear with it under particular conditions). The first lines are spaced apart by a second predefined spacing along the second lines. In other words, the first lines are regularly spaced (they are all equidistant) by a pitch corresponding to the second spacing along the second lines.The second lines are spaced at a predefined first spacing along the first lines. In other words, the second lines are regularly spaced (they are all equidistant) at a pitch corresponding to the first spacing along the first lines. Thus, each grid comprises at least one cell, of parallelogram shape, delimited by points of intersection between the first and second lines (the first and second lines being intersecting with each other).

[0061] The invention relates to a method for simulating a wind farm in a predetermined space for constructing the wind farm in the predetermined space, with the aim of maximizing the annual energy produced. In other words, the simulation method can be used to position (and construct at these positions) the wind turbines of the farm in the predetermined space so as to maximize the annual energy produced by the farm. By means of the method, the optimal locations of the wind turbines can thus be found, taking into account alignment constraints. Once constructed, the farm allows for the production of more electricity thanks to the optimal locations.

[0062] The predetermined space may be a land area or an offshore area at sea. Advantageously, the predetermined space may comprise non-connected areas. Therefore, the predetermined space may correspond to actual locations planned for the installation of wind turbines, for example a farm planned in a location comprising two areas separated by a road of significant width (several meters, or even several tens of meters), such as a highway, or by a river or stream. Preferably, the predetermined space may comprise non-convex areas in addition to or alternatively to the non-connected areas. Thus, the predetermined space may correspond to actual locations of complex shape such as a space delimited by a hill or a steep cliff, the coastline, the passage of a river, a stream or any other body of water.In offshore, the predetermined space may include non-convex zones which may be determined by taking into account bathymetry, the nature of the soil, borders with other countries, navigation channels, cable or pipeline passages, for example.

[0063] A wind farm consists of a predefined number of wind turbines. In other words, the (predefined) number of wind turbines that will be installed in the predetermined space has been previously defined.

[0064] Figure 3 illustrates, in a schematic and non-limiting manner, an example of a predetermined space suitable for implementing the simulation method, the positioning method and the construction method of the invention.

[0065] The predetermined space may include a first zone Z1 and a second zone Z2, zones represented by the vertical hatching. These zones Z1 and Z2 are non-connected. Indeed, a non-zero minimum distance D appears between the two zones Z1 and Z2. In addition, zone Z1 is rectangular. Therefore, it is convex. Zone Z2 has a complex, non-convex shape. Indeed, if we consider the two points A and B, we observe that part of the segment Seg which connects the points A and B is located outside zone Z2. To identify zones Z1 and Z2 of the predetermined space in a third, larger zone ZE, encompassing these two zones Z1 and Z2, we can use a Boolean matrix. The third zone ZE is rectangular in shape, which is easier to process by computer than non-connected and / or non-convex zones such as Z1 and Z2.The Boolean matrix associates with each discrete value (discrete position) of the zone ZE a value equal to 1 if the discrete position is located in the zone Z1 or Z2 and a value 0 if it is located outside Z1 and Z2. This Boolean matrix makes it possible to define the determined space used for the method. From this Boolean matrix, we can determine the border(s) of the predetermined space. Indeed, a point will be considered as part of the border if its value in the Boolean matrix is ​​1, and if it has among its direct neighbors, at least one point which has a value in the Boolean matrix of 0.

[0066] For the simulation method of the invention, a first discrete wind speed distribution, a second discrete wind direction distribution and a probability of occurrence of each discrete wind speed value in each discrete wind direction value of the first and second discrete distributions are used. These wind data are considered at the level of the corresponding predetermined space. These wind data can in particular be obtained by a wind data collection means, such as a LIDAR (Light Detection And Ranging) sensor, a measuring mast or an anemometer.To do this, the invention may relate to a positioning method, for which the simulation method is implemented and the positioning method may advantageously comprise a preliminary collection step, before step a), during which the measuring means (or collecting means) of the wind data are installed in the predetermined space for a predetermined duration on the physical site of the predetermined space (the planned land region of installation or the planned offshore zone) in order to collect the wind data from the site, and, thus, the statistical wind data are measured, by these measuring means, to determine the first and second discrete distributions of wind speed and wind direction, and the probabilities of occurrence of each wind speed in each wind direction of the first and second discrete distributions.The measurement of wind data can be carried out over the predetermined duration, for the collection of measurements, which can be at least one year, in order to have the data relating to the four seasons. Thus, a step of collecting statistical wind data in the predetermined space from at least one collection means can be provided.

[0067] The measuring (collection) means can advantageously be a LIDAR sensor.

[0068] For this method, at least the following successive steps are carried out by computer means, such as a computer or a server or a (super)computer: a) Formation of different grids b) Calculation of annual energy for a mini-farm on each grid c) Conservation of certain grids maximizing the annual energy production of the mini-farm d) For each grid, determination of a first arrangement of the wind turbines e) Modification of the positions of the wind turbines f) Creation of new grids, from the best grids obtained previously, with a new spacing and repetition of steps d) and e) g) Creation of new grids, from the best grids obtained previously, with new directions and repetition of steps d) and e) h) Determination of the final position of the wind turbines in the predetermined space.

[0069] The use of discrete values ​​for wind speed, wind direction and discrete intersection points of the different grids in the predetermined space simplifies the simulation process, speeds up calculation times and limits the necessary computing resources (memory and processor), compared to methods using continuous real data. Indeed, discrete values ​​limit the number of possible combinations (this is called a combinatorial method), while continuous real data (this is called a continuous method) provide an infinite number of solutions. The combination of the first and second discrete distributions and the grid intersection points thus makes it possible to obtain good accuracy in the positioning of the different wind turbines in the predetermined space, taking into account alignment constraints, while limiting the calculation time required to determine the positions.

[0070] The probability of occurrence of each wind speed, in each wind direction is used in particular for the calculation of the average annual energy production. This probability can in particular come from a wind rose corresponding to the predetermined space, this wind rose being well known to those skilled in the art. To establish this wind rose, it is possible in particular to use the collection means mentioned above, such as an anemometer positioned on a mast at a sufficient altitude (between 80 m and 120 m for example to be substantially at the level of the hub of the wind turbine for example), or by means of a LiDAR sensor (acronym from "Light Detection And Ranging"), positioned close to the ground and oriented vertically.This means of collection is kept in place for a long period, several months and ideally more than a year, so as to be able to take into account variations in wind characteristics depending on the seasons.

[0071] According to one embodiment, the annual energy production can be estimated by the following formula:

[0072] [Math] aep = 8760 ■ E Ws>Wp {P f,w s ,w p > )}

[0073] Where aep is the annual energy production of the wind farm and is the expectation of the total power produced by the wind farm (by the predefined number of wind turbines in the predetermined space) with respect to the joint probability distribution of wind speed w s and wind direction w p . Therefore, the total power produced by the farm takes into account a statistical distribution of each wind speed w s in each wind direction wp , for example by a Weibull distribution.

[0074] In the case where the rotors of the wind turbines are systematically aligned in a plane orthogonal to the wind direction w p , the total power produced by the farm can be written: [Math2]

[0075] Where N is the predefined number of wind turbines in the farm in the predetermined space, Pf is the instantaneous power supplied by each wind turbine f, in the farm, for each wind speed w s in each wind direction w p .

[0076] In the case where some rotors of the wind turbines are in a plane offset from the plane orthogonal to the direction of the wind w p(in other words, the wind turbine is not oriented towards the wind but is offset from it), a correction factor can be taken into account to take into account the effect of the offset. This correction factor can notably come from CFD simulations (from the English "Computational Fluid Dynamics" meaning "Computational fluid dynamics"). The instantaneous power Pf of each wind turbine f in the farm can be written: [Math3]

[0077] 1 Pf w s ,w p ) = - ■ p ■ S - v (w s ) ■ C p / [iy(w s )]

[0078] With p is the density of air, S is the surface swept by the rotor of the wind turbine f, Vf(w s ) the wind speed at the rotor of the wind turbine f and the power coefficient C P f of the wind turbine f depending on the speed v f (w s ) of the wind at the rotor of the wind turbine f, the power coefficient C P f being a characteristic of the wind turbine f.

[0079] Indeed, the wake effects of wind turbines located upwind (in the direction of the wind) and / or to the side of wind turbine f can impact the energy production of wind turbine f. This wake can generate a decrease in wind speed at wind turbine f and / or wind turbulence. These wake effects have the impact that the speed v f at the level of the wind turbine rotor no longer corresponds to the speed w s and that the power coefficient C P f is then also impacted.

[0080] The impacts of wake effects taken into account in equation [Math3] can notably be based on wake models. These wake models can notably translate:

[0081] - a reduction in wind speed upstream of the wind turbine f due to the wake from an upstream wind turbine. One such model, well known to those skilled in the art, is the Jensen wake model (described in the publication “A simple model for Cluster Efficiency”, Katie, Hojstrup and Jensen, EWEC 1986, in particular in paragraph 2.1 of this publication),

[0082] - an increase in the turbulent intensity of the wind,

[0083] - and / or a superposition of wakes from several wind turbines upstream on the same wind turbine f, as described in the publication "A note on wind generator interaction" Jensen, DTU, 1983. This wake superposition can combine the effects of speed reduction as in the previously cited publication and / or turbulent wind intensity from several wakes. Wake models can also be determined from CFD (Computational Fluid Dynamics) calculations. The above formulas can be used to calculate the annual energy produced by the farm composed of the predefined number of wind turbines, by the mini-farm or by a farm consisting of a single wind turbine.

[0084] Figure 1 illustrates, in a schematic and non-limiting manner, the method of simulating the wind farm in a predetermined space Esp, in a global manner, the simulation method being used in particular to determine the position of the wind turbines of the farm in the predetermined space, in an optimal manner to maximize the annual energy produced by the farm.

[0085] From the predetermined space Esp chosen (an offshore or onshore geographical area for example) which can be a space comprising non-convex and / or non-connected areas (for example with a road or a river which crosses this space), and different first pairs C1 of first and second predefined spacings and different second pairs C2 of first and second predefined directions, grids (GR) are established in the predetermined space.

[0086] Each of these GR grids is established from a multitude of first lines parallel to each other and regularly spaced and second lines parallel to each other, regularly spaced and intersecting with the first lines (in other words, the angle formed between the first lines and the second lines is non-zero and non-flat).

[0087] The different GR grids are distinguished from each other by the combination of the first pairs C1 and second pairs C2.

[0088] For each GR grid, the first lines are oriented at an angle corresponding to the first predefined direction relative to a direction of a predefined fixed reference point (for example a reference point with a north direction and an east direction) and the second lines are oriented at an angle corresponding to the second predefined direction relative to the same direction of the predefined fixed reference point (the North direction for example).

[0089] The first lines are spaced at the second predefined spacing along the second lines and the second lines are spaced at the first predefined spacing along the first lines.

[0090] A first line and a second line can be positioned arbitrarily in space, these lines then serving as a reference for the positions of the other lines.

[0091] The intersection points between the first lines and the second lines which are located in the predetermined space (within the predetermined space, the boundary of this predetermined space being advantageously included or on the contrary being able to be excluded) define the grid. The grid can thus comprise meshes, and the meshes of the grid form parallelograms taking into account the parallelism of the first and second lines, delimited by said lines and the intersection points.

[0092] For each defined GR grid, the annual energy production of a mini-farm AEP-mf is determined. The annual energy production is based on statistical wind data from, for example, a LIDAR sensor or any other means of measuring wind data, these statistical data comprising a first discrete distribution RD1 of wind speeds, a second discrete distribution RD2 of wind directions and a probability of occurrence Prob of each wind speed value of the first discrete distribution RD1 in each wind direction of the second discrete distribution RD2.

[0093] The mini-farm is a farm composed of a grid portion with at least one grid cell (or several connected cells) and where, at all the intersection points of this grid portion, a wind turbine is positioned. Thus, if the grid portion has a single cell, the mini-farm will be composed of four wind turbines, one at each intersection point of the cell. This situation with a mini-farm of four wind turbines is advantageous because it allows the impact of the wake of the wind turbines between them on the grid to be evaluated simply and quickly and without requiring a lot of memory or computing time when this step is carried out by computer.

[0094] For the purposes of this description, a mesh is understood to mean an elementary mesh: this means that a parallelogram delimited by four points of intersection is considered to be a mesh if this parallelogram does not include any other parallelogram defined by four points of intersection, inside itself.

[0095] By comparing the annual energy production values ​​of different grids comprising the same first C1 pair and different second C2 pairs, one or more most promising second C2 pairs can be identified (giving the highest annual energy production(s). A set of second pairs is formed, grouping together all the identified (most promising) second C2 pairs. In other words, this set groups together the most promising second pairs. Thus, for each first C1 pair with predefined first and second spacings, one or more second C2 pairs are identified and added to the set. Thus, the most promising direction pairs are retained for the future, which makes it possible to limit the number of configurations to be tested.

[0096] Comparisons of annual energy production values ​​can be made directly (by direct comparison of the different values, we then look for the second C2 pairs that maximize the annual energy produced), or indirectly. In the latter case, we compare the annual energy produced by the mini-farm to the annual energy produced by the same number of wind turbines as that of the mini-farm as if each wind turbine were independent (therefore without taking into account the wake effects): we will then estimate the loss linked to the wake effects of the mini-farm. In this case, of course, we retain the second C2 pair(s) that minimize the loss linked to the wake effects. Thus, we can choose Ch, from the annual energy production of the mini-farms, at least one second C2 pair. Thus, we select a certain number of grids among those that have been previously established.The selected grids corresponding to each first pair C1 and to a second pair of the set formed (i.e. the second pair is chosen from among the most promising direction pairs) are used subsequently. In other words, the use of the mini-farm makes it possible to preselect grids for the following (and to eliminate the other grids which are the least promising).

[0097] Then, for each selected grid, we establish a first arrangement of wind turbines Alg 1 on this grid (on intersection points of this grid). This first arrangement seeks to obtain a good energy yield and therefore takes into account the first and second discrete distributions RD1 and RD2 and the probability of occurrence Prob.

[0098] From this first arrangement of the wind turbines on each selected grid, we then seek to improve energy recovery. We then reposition the wind turbines Alg2 on each grid, seeking, each time a wind turbine is repositioned, to find the position on the grid that allows us to obtain the highest annual energy production. Of course, to do this, we take into account the first and second discrete distributions RD1 and RD2 and the probability of occurrence Prob.

[0099] Once all the wind turbines have been repositioned, a predetermined number of layouts maximizing annual energy production and each associated grid Grr of each of these retained layouts are retained. In other words, a certain number of layouts are retained (the number being fixed at the start) which are the most promising layouts for annual energy production and the associated grids (the other grids are eliminated, which further limits the most promising grids for the future).

[0100] From each grid Grr associated with the retained arrangements, the first spacing step MAr is reduced (for example, it is divided by two) and Gr2 is formed from the first reduced spacing step and from each of the grids Grr associated with the retained arrangements. Each second grid formed comprises the same second pair of first and second directions and a new first pair of first and second spacing is generated. The first spacing of each second grid is determined from the first spacing of the associated grid Grr and from the first reduced spacing step. For example, it may correspond to the sum of the first spacing of the associated grid Grr and a first integer (preferably equal to 1 or -1) of the first reduced spacing step.Similarly, the second spacing of each second grid is determined from the second spacing of the associated Grr grid and from the first decreased spacing step. For example, it may correspond to the sum of the second spacing of the associated Grr grid and a first integer (preferably equal to 1 or -1) of the first decreased spacing step. When the first integer can be equal to 1 or -1, four second grids can thus be formed for each Grr grid associated with a selected arrangement.

[0101] Then we repeat steps Alg 1 of establishing a first arrangement of wind turbines on each second grid and Alg2 of repositioning each wind turbine on each second grid and we retain AEP g a predetermined quantity of arrangements maximizing the annual energy production and each second grid associated with each of these retained arrangements, each second associated grid then in front of an associated grid Grr.

[0102] From each Grr grid associated with the retained arrangements (i.e., second grid retained after the step of repositioning the wind turbines on each second grid), the second direction step is reduced MAS (for example, it is divided by two) and Gr3 third grids are formed from the reduced second direction step and from each of the Grr grids associated with the retained arrangements (i.e., second retained grids). Each third grid formed has the same first pair of first and second spacings as each Grr grid and a new second pair of first and second directions is generated. The first direction of each third grid is determined from the first direction of the associated Grr grid (second retained grid) and from the reduced second direction step.For example, it may correspond to the sum of the first direction of the associated Grr grid (second retained grid) and a second integer (preferably equal to 1 or -1) of the second decreased direction pitch. In the same way, the second direction of each third grid is determined from the second direction of the associated Grr grid (second retained grid) and from the second decreased direction pitch. For example, it may correspond to the sum of the second direction of the associated Grr grid (second retained grid) and a second integer (preferably equal to 1 or -1) of the second decreased direction pitch. When the second integer can be equal to 1 or -1, four third grids can thus be formed for each Grr grid associated with a retained arrangement (second retained grid).

[0103] Of course, you can repeat the steps several times:

[0104] - Reduction MAr of the first spacing step and formation Gr2 of the second grids, then steps of establishing a first arrangement Alg 1 and repositioning the wind turbines Alg2 to retain AEP g of new grids from new second grids and / or;

[0105] - MAS reduction of the second first step of direction and formation Gr3 of the third grids, then steps of establishing a first arrangement Alg 1 and repositioning the wind turbines Alg2 to retain AEP g of new grids from new third grids;

[0106] For example, these steps can be repeated several times until the first spacing step reaches a first threshold and / or until the second direction step reaches a second threshold.

[0107] The final arrangement Disp_F of the wind turbines in the predetermined space Esp is then determined as the final arrangement of the wind turbines on the selected grid which makes it possible to obtain the maximum annual energy produced among the last selected grids AEP g (after the last step of repositioning the wind turbines Alg2 has been carried out).

[0108] The wind turbines can then be built Const at the planned locations corresponding to the final layout Disp_F determined in the predetermined space. This step is shown in dotted lines to indicate its optional nature. When this step is carried out, the invention then relates to a method for constructing the wind turbines of a wind farm in a predetermined space, so as to optimize the annual energy produced by the farm.

[0109] This step allows the definition of several possible grids within the predetermined space. Each grid therefore has a spatial limit and cannot extend beyond the predetermined space. This grid consists of one or more cells separated by intersection points. These cells are parallelogram-shaped, for example rectangular or square, and the intersection points are at the boundary between the cells. All cells and intersection points of each grid are located within the predetermined space.

[0110] The meshes of each grid are defined between the first and second lines. These grids each constitute a possible option for placing the wind turbines of the farm in the predetermined space, taking into account alignment constraints (according to the first and second lines). The intersection points of each grid constitute possible positions for installing a wind turbine (at each intersection point, only one wind turbine can be positioned). By using several grids, different alignment constraints can be tested (different values ​​of first and second predefined spacings and different values ​​of first and second predefined directions). The first and second directions are non-collinear and form a non-zero (and non-flat) angle so as to consider alignment constraints in two dimensions in space such that the first lines and the second lines are intersecting.By using different discrete values, the number of possible combinations and therefore the useful computer memory are limited. In addition, these discrete values ​​are sufficient to ensure an accuracy compatible with the construction of wind turbines on site (taking into account the possible construction accuracies).

[0111] The first and second predefined spacings are advantageously between a minimum distance and a maximum distance, these minimum and maximum distances depending for example on the diameter of the rotor of the wind turbine. The minimum distance corresponds to the minimum value by which two successive wind turbines must be separated in order to limit energy losses linked to wake effects and the maximum distance corresponds to the maximum value by which two wind turbines must be separated, a greater distance no longer resulting in a gain in energy recovery and limiting the possibility of installing enough wind turbines in the predetermined space, to ensure sufficient energy efficiency.

[0112] Indeed, first and / or second predefined spacings less than the minimum distance or greater than the maximum distance are not necessary since the wind turbines must respect a minimum distance between them to avoid excessive energy losses linked to wake effects and a maximum distance to install the predefined number of wind turbines and obtain an interesting energy yield from the farm in space.

[0113] Preferably, the minimum distance may be greater than or equal to twice the diameter of the rotor of the wind turbines, and preferably, greater than four times the diameter of the rotor of the wind turbines; the maximum distance may be at least four times the diameter of the wind turbines and preferably at least eight times the diameter of the wind turbines.

[0114] Preferably, the first predefined direction may be between -90° and 90°, taking into account the symmetry, relative to an orthonormal reference point, for example the terrestrial reference point with the north located at 90° and the south at -90°, this orthonormal reference point preferably being the one used to define the wind directions.

[0115] And preferably, the second predefined direction can be between -90° and the first direction. Therefore, with the symmetry effects, we scan the entire possible space while limiting the number of combinations.

[0116] For different first predefined spacings separated by a first spacing step, different second predefined spacings separated by the (same) first spacing step, different first predefined directions separated by a second direction step, and different second predefined directions separated by the (same) second direction step, different first pairs of first and second predefined spacings are formed, and different second pairs of first and second predefined directions.

[0117] Then, for the different first pairs and for the different second pairs, grids are formed in the predetermined space. Each grid is defined by a plurality of intersection points between first lines oriented in the first predefined direction and second lines oriented in the second predefined direction. The first lines are spaced (two by two) by the second predefined spacing along the second predefined direction and the second lines are spaced (two by two) by the first predefined spacing along the first predefined direction. The grid comprises at least one cell delimited by intersection points (each cell is delimited by four intersection points and some intersection points may not be attached to a cell). Thus, the intersection points of the grid form a discrete mesh.Discrete meshing means that the intersection points of the mesh that make up the grid are discrete values ​​(as opposed to continuous values).

[0118] In this step a), a first spacing step and / or a second coarse direction step can be chosen (for example, the first spacing step can correspond to at least the minimum distance, i.e. at least twice the diameter of the wind turbines and / or the second direction step can be between 5° and 10°). Indeed, the grids formed in this step a) are used in the following to select first pairs and second pairs offering the best compromises. Then new grids are developed in steps e) and f) in order to refine the mesh and thus increase the optimal precision of the positioning of the wind turbines and increase the annual energy produced.

[0119] For example, in step a), the first (coarse) spacing step may be between two and ten times the diameter of the wind turbines (i.e. the rotor diameter of the wind turbines), preferably between two and six times the diameter of the wind turbines. Advantageously, in step a), the second (coarse) steering step may be between 1° and 20°, preferably between 5° and 10°.

[0120] Figure 5 illustrates, in a schematic and non-limiting manner, the change of reference frame between the reference frame (01, N, E) which corresponds to the global reference frame, 01 being able to be based arbitrarily, N can correspond to the North direction and E to the East direction, and a reference frame linked to the grid with 02 a point fixed arbitrarily on a point of intersection between a first line Lig 1 and a second line of the grid Lig2, the first line Lig 1 and the second line Lig2 being intersecting with each other. The first line Lig 1 here forms an angle 01 with the direction E and the second line Lig2 forms an angle 02 with the direction E (alternatively, one could also have the first line Lig 1 forming an angle 01 with the direction N and the second line Lig2 forming an angle 02 with the direction N). The reference frame (01, N, E) can advantageously be the one used to determine the wind directions.

[0121] Step b): Calculation of annual energy for a mini-farm on each grid

[0122] Step a) made it possible to define a panel of grids where the intersection points of each grid are points likely to correspond to the location of a (single) wind turbine. Of course, in order to verify the alignment constraints of the wind turbines, it is not possible, in the present method, to use intersection points of one grid to locate some of the wind turbines with intersection points of another grid to locate other wind turbines.

[0123] In order to avoid searching for the optimal arrangement of wind turbines on each grid, calculating the annual energy production each time, it is preferable to sort to use only the grids likely to offer the best possibilities of finding the optimal arrangement. Step b) seeks to carry out this first sorting among the different grids.

[0124] To do this, for each grid formed in step a), we consider a mini-farm consisting of wind turbines at each intersection point of the grid portion considered. The grid portion corresponds to a few connected cells (a few cells all connected to each other), and preferably to a single grid, so as to further simplify sorting.

[0125] Using all the wind turbines installed on the grid portion (for example, four wind turbines if the grid portion comprises a single mesh, 9 wind turbines if the grid portion is homothetic by a factor of 2 compared to a grid with a single mesh), the annual energy production of the mini-farm can be determined, in particular using the formulas presented previously.

[0126] Thus, for each type of grid, we can associate an annual energy production of the mini-farm.

[0127] For each grid of the predetermined space defined in step a), the average annual energy production of the mini-farm (i.e. composed of wind turbines positioned at all the intersection points of one or more connected grid cells - preferably, the mini-farm is composed of four wind turbines, each positioned at a different intersection point of the same grid cell) is determined from the first discrete wind speed distribution, said second discrete wind direction distribution and said probability of occurrence.

[0128] :Preservation of certain lines maximizing the annual distribution of the mini-farm This step serves to limit the number of combinations to be used for the arrangement of the predefined number of wind turbines of the farm from the results obtained in step b). Indeed, thanks to the mini-wind farm, we can estimate for different (first) pairs of first and second predefined spacings, the annual energy production as a function of the (second) pair of first and second predefined direction and the first and second discrete distributions of wind speed and wind direction and the probability of occurrence of each discrete value of wind speed in each discrete value of wind direction.

[0129] We can then choose (identify) at least one (preferably only one) (second) pair of first and second predefined directions, so as to limit the number of combinations for the future. Indeed, the choice of the (second) pair of first and second predefined directions is determined so as to maximize the annual energy produced and / or limit the wake effects. Thus, the second pairs define the most promising pairs of first and second directions (for the annual energy produced). To determine the (second) pair of first and second directions identified, we can either directly compare the annual production produced and retain the pairs of directions which maximize this annual production of the mini-farm, or compare the loss of recovered energy due to the wake effects.

[0130] In this second case, the energy loss of the mini-farm considered is determined in relation to the ideal production of the same number of wind turbines as the mini-farm, without taking into account the wake effects of the wind turbines between them. Thus, in step c), we can for example make the difference between the annual energy production of the mini-farm obtained in step b) and the annual energy production of a single wind turbine multiplied by the number of wind turbines in the mini-farm. This energy loss Pl oss can be determined by the following formula:

[0131] [Math 4]

[0132] Pioss =n*aep(f1, ws, wp)- aep (f2, ws, wp)

[0133] Where aep(f1, ws, wp) is the annual energy produced according to the formula [Math 1] for a farm f1 consisting of a single wind turbine in the predetermined space, and where aep(f2, ws, wp) corresponds to the annual energy produced according to the formula [Math 1] for a farm f2 consisting of a number n of wind turbines in the mini-farm of the predetermined space, ws and wp being the statistical distributions of wind speeds and wind direction, taking into account the probabilities of occurrence previously mentioned.

[0134] The advantage of this formula [Math 4] is that it provides direct information on the impact of the wake effects of the mini-farm, an effect which depends directly on the alignment directions and the chosen spacings. We can then discard (eliminate) the solutions for which the losses are too significant to retain only the relevant solution or solutions (with the lowest energy losses).

[0135] For each first pair of first and second predefined spacings, at least one second pair of first and second predefined directions is thus identified (chosen) which maximizes the annual energy production of said mini-farm. In other words, one or more second pairs are selected to maximize the annual energy production produced. As a result, the following steps are limited to a selection of a few grids, instead of carrying out the following steps for all the grids of step a). A set can then be formed which groups together all the identified second pairs which will be used for the following: in other words, the second pairs which are not kept in said set will no longer be considered for the following: only the most promising second pairs of first and second directions are thus kept. This makes it possible to limit the combinations to be made for the following.

[0136] Advantageously, in step c), a predetermined number of pairs of first and second predefined directions can be identified for each pair of first and second predefined spacings. Thus, the number of grid configurations retained for the following can be limited.

[0137] Preferably, the predetermined number may be between 1 and 20, more preferably between 1 and 10. This provides a good compromise between calculation time, use of computing resources and accuracy of the optimization results.

[0138] Step d): For each grid, determination of a first arrangement of the wind turbines. During this step, a first arrangement of the wind turbines is determined on each grid (grids retained in step c) or second grids formed in step e) or third grids formed in step f) depending on the implementation of this step d) in the method), so as to limit the number of combinations. Each wind turbine is positioned on a point of intersection (a single wind turbine on the same point of intersection for obvious construction reasons) of the space predetermined by a first positioning algorithm. Preferably, this first positioning algorithm can be an optimization algorithm which makes it possible to obtain a first distribution making it possible to obtain a satisfactory annual energy produced.Advantageously, this first positioning algorithm can be a greedy algorithm that positions each wind turbine one after the other so as to maximize the annual energy produced by each wind turbine that is added. The first wind turbine can be positioned arbitrarily in the predetermined space (at a discrete value of the first discrete mesh). The second wind turbine will be positioned at the intersection point of the grid considered to maximize the annual energy produced by the two wind turbines, the chosen position of the n-th wind turbine at the intersection point of the grid to maximize the annual energy produced by the n wind turbines. The use of a greedy algorithm makes it possible to obtain, in a simple manner, a first arrangement of the wind turbines in the predetermined space, which makes it possible to initialize the optimization method of step e).

[0139] According to one embodiment, for each grid considered, said first positioning algorithm can carry out at least the following steps:

[0140] - the position of the first wind turbine is arbitrarily defined on one of the intersection points of the grid considered;

[0141] - then for each wind turbine to be positioned, successively: potential positions are defined for the wind turbine to be positioned, the potential positions being constituted by the (free) intersection points of the grid. In other words, intersection points of the grid are selected where the next wind turbine would be advantageously positioned. the annual energy production of the positioned wind turbines and of the wind turbine to be positioned is calculated for the defined potential positions. As a result, for each defined potential position, an annual energy production value is associated. In addition, the calculation of the annual energy production takes into account the first discrete distribution of wind speed, the second discrete distribution of wind direction and the probability of occurrence.This calculation also involves the known characteristics of wind turbines, namely the surface swept by the wind turbine rotor, the drag coefficient and / or the power coefficient.

[0142] The position of the wind turbine to be positioned is chosen to correspond to the calculated maximum annual energy production value. This maximizes the annual energy produced by the wind turbines whose position is defined in the predetermined space. These defined positions serve as a basis for determining the position of the next wind turbine, in particular to define the potential positions of the next wind turbine to be positioned.

[0143] - the first arrangement corresponding to the position of the predefined number of wind turbines among the (free) intersection points of the grid considered in the predetermined space is determined.

[0144] Therefore, the first positioning algorithm is a greedy algorithm that includes a step of arbitrary positioning of the first wind turbine, then iteratively positions an additional wind turbine on intersection points of the considered grid until all the wind turbines of the predefined number are positioned on the grid. This greedy algorithm allows, thanks to the step of selecting potential positions, to accelerate the calculation time and to limit the computing resources, while positioning the wind turbines judiciously. Such an algorithm makes it possible to obtain a first arrangement suitable for the following step of local optimization of positioning search for each wind turbine.

[0145] Figure 4 illustrates, in a schematic and non-limiting manner, an example of a step for obtaining a first arrangement of the wind turbines on each grid selected according to the invention.

[0146] For this, we can, for example, use a greedy algorithm.

[0147] For each grid G(C1, C2) selected from the predetermined space, the position of the first wind turbine P_E1 is defined, for example arbitrarily.

[0148] Then for each wind turbine j, we look for a position in order to maximize the annual energy produced.

[0149] Thus, iteratively according to F3, we define, for each wind turbine j, one by one, potential positions PE Ej for the wind turbine j to be positioned, the potential positions PE Ej being determined by the free intersection points (i.e. those on which no wind turbine is planned for the moment) of the grid of the predetermined space.

[0150] Once these potential positions PE Ej have been defined for the wind turbine j to be positioned, we evaluate Eval_AEP, for each of these potential positions PE Ej, the annual energy produced by the wind turbines already positioned and by the wind turbine j to be positioned in the predetermined space. For this Eval_AEP evaluation, we use in particular the first and second discrete distributions RD1 and RD2 of the wind speeds and directions as well as the probability of occurrence Prob of each wind speed in each wind direction. We can, in a known manner, use the characteristics of the wind turbines and the wake effects previously described in this description.

[0151] We can then choose the position PosJ of wind turbine j, position corresponding to the maximum value of the annual energy produced in the previous step.

[0152] We can then define a new arrangement Disp_Ej of the positioned wind turbines (including wind turbine j) in the predetermined space. This new arrangement Disp_Ej is used in the following iteration to determine the potential positions PE Ej of the new wind turbine j to be positioned and for the evaluation of the annual energy produced Eval_AEP.

[0153] Loop F3 is performed for, j ranging from 1 to N-1 , N being the predefined number of wind turbines in the predetermined space, taking into account that the first wind turbine is positioned in a stepwise manner at step P_E1 . Once all the wind turbines are positioned (i.e. when j=N- 1 ), the last arrangement found Disp_Ej for each grid then corresponds to the first arrangement Displ of the wind turbines for each grid.

[0154] Thus, for each defined grid (which may be the grids selected in step c), the second grids defined in step e) or the third grids defined in step f)), a first arrangement of the predefined number of wind turbines is determined, each wind turbine being positioned on one of the intersection points of the grid concerned by a first positioning algorithm.

[0155] Step e): Changing the positions of the wind turbines

[0156] Then, for each grid used in the previous step d), the position of the wind turbines among the free intersection points of the grid is modified (the “free” intersection points being the intersection points on which no wind turbine is positioned; indeed, it is not possible to position two wind turbines at the same position), in order to improve (preferably strictly - by this, it is meant that the wind turbine is repositioned only if the annual energy production is strictly greater than the annual energy production of the previous arrangement) the annual energy production so as to obtain an arrangement of the predefined number of wind turbines on each grid considered and to obtain an annual energy production for each arrangement. Then, a predetermined quantity of arrangements corresponding to the arrangements maximizing the annual energy production is retained and each grid associated with each retained arrangement is retained.

[0157] For each grid in step d), we seek to improve the annual energy by modifying the position of the wind turbines on the grid. This can be done in particular by steps e1) and e2) which are described below.Indeed, at least the following steps can be carried out: e1) for each grid used in step d), a sequential order of modification of the positions of the wind turbines determined by the first positioning algorithm is defined and each wind turbine of the defined sequential order is repositioned, one by one, by finding a free intersection point (i.e. an intersection point which is not occupied by another wind turbine) of the grid which maximizes the annual energy production from said first discrete distribution of wind speed, said second discrete distribution of wind direction and said probability of occurrence; e2) step e1) is repeated as many times as necessary until, at the end of a step e1), no wind turbine has been repositioned and a final arrangement of the predefined number of wind turbines on each grid considered and an annual energy production for each final arrangement is obtained.Step e1) of local search optimization.

[0158] In this step, we seek to improve annual energy production by modifying the position of the farm's wind turbines, one by one, on each grid from step d).

[0159] To do this, we define a sequential order of modification of the positions of the wind turbines determined by the first positioning algorithm: in other words, we do not necessarily reposition the wind turbines in the same order as that in which they were determined by the first algorithm and we preferentially use a different order to improve the chances of obtaining a better solution.

[0160] Preferably, this sequential order can be obtained randomly. Indeed, by using a random function for the sequential order, the quality of the optimization is improved by avoiding optimization paths based on pre-established orders, these paths being able to bias the optimization results.

[0161] Advantageously, the sequential order can be modified at each iteration of step e1), so as to further improve the quality of the optimization.

[0162] Once the sequential order is defined, each wind turbine is repositioned one by one, by this defined sequential order, by finding a free intersection point of the grid which maximizes the annual energy production: if no other intersection point of the grid allows to improve the annual energy production, the wind turbine considered is kept at its previously determined position. We can then try to modify the position of the next wind turbine in the defined sequential order.

[0163] To determine the annual energy produced, the first and second discrete distributions of wind speed and wind direction and the probability of occurrence are of course taken into account, which are directly dependent on the geographical position of the predetermined space and its local environment (presence of forests, mountains, geological features, buildings for example) and the characteristics of the wind turbines. The annual energy produced can in particular be determined from the formulas previously mentioned, in particular by the formula [Math 1],

[0164] According to an advantageous variant of the method of the invention, in step e1), a selection of free intersection points can be chosen (i.e. from among the intersection points on which no wind turbine is positioned), for each wind turbine to be repositioned. In other words, the number of intersection points to be considered for the wind turbine to be repositioned is limited so as to limit the computing resources.

[0165] For example, the selection of intersection points may correspond to a predetermined value of free intersection points (on which no wind turbine is positioned), said selection of intersection points being chosen randomly or being chosen as corresponding to said predetermined value of free intersection points (on which no wind turbine is positioned) closest to the position of the wind turbine to be repositioned. The random selection makes it possible to improve the quality of the optimization, by limiting the number of possible configurations in each iterative calculation. The selection of the free intersection points closest to the position of the wind turbine to be repositioned makes it possible to delimit an area in which it is desired to reposition the wind turbine. Thus, an increasingly restricted area is gradually delimited for repositioning the wind turbine.

[0166] Step e2) of reproduction of step e1)

[0167] At the end of step e1), we cannot a priori know whether the arrangement of the wind turbines in each grid is optimal or whether an improvement can still be made. To further optimize the arrangement of the wind turbines on each grid, we repeat step e1) as many times as necessary as long as, during this step, we reposition at least one wind turbine on an intersection point of the grid. We stop iterating when, at the last iteration of step e1), no wind turbine has been repositioned: we then consider that the optimal arrangement of the predefined number of wind turbines on the grid considered has been found.

[0168] At the output of step e2), on each grid considered (from step c) or second grid formed in step f) or third grid formed in step g)), we obtain a layout of the wind turbines on each grid considered and an annual energy production associated with each of these layouts (one for each grid considered).

[0169] We can then retain for the future a predetermined quantity of provisions corresponding to the provisions maximizing annual energy production and we can retain each grid associated with each retained provision.

[0170] Advantageously, in step e), and more particularly in step e2), the predetermined quantity of arrangements may be between 1 and 20, preferably between 1 and 10.

[0171] Preferably, in step e2), the sequential order can be modified at each iteration of step e1) so as to limit the optimization paths based on pre-established orders.

[0172] Figure 2 illustrates, in a schematic and non-limiting manner, an example of search for optimization of the method according to the invention.

[0173] For each selected grid, we determine Alg 1 a first arrangement Displ of the wind turbines on each of these grids, taking into account as input data at least a first discrete distribution RD1 of wind speeds, a second discrete distribution RD2 of wind directions, and the probability of occurrence Prob of each wind speed in each wind direction. The characteristics of the wind turbines and the wake models can also be used for the determination of the annual energy produced in order to establish this first arrangement Displ .

[0174] Wind data, speed, direction and probability of occurrence of each speed value in each direction may in particular be obtained from collection means during a preliminary step. These data may in particular be used to establish a wind rose known to those skilled in the art.

[0175] This first arrangement Displ is perfectible but of sufficient quality to allow local optimizations in subsequent steps. This step of determining Alg 1 the first arrangement Displ of the wind turbines on each selected grid can be a greedy algorithm.

[0176] This first Displ layout obtained quickly thanks to the greedy algorithm is used as input data for the following optimization step Alg2. This optimization step Alg2 modifies, one by one, the position of the different wind turbines of the first Displ layout, on other intersection points of the same grid, so as to increase the annual energy produced by the farm by testing other possible positions on the grid, thus respecting the alignment constraints.

[0177] In more detail, this Alg2 optimization step includes the following steps:

[0178] - we define a sequential order OS for modifying the positions of the wind turbines, one by one. This sequential order OS can in particular be obtained by a random function.

[0179] - Then iteratively, for each selected grid, we modify the position of at least one wind turbine i, preferably of each wind turbine i, by carrying out the following sub-steps:

[0180] * we determine possible positions PDPJ for wind turbine i, these possible positions being the current position of wind turbine i and the intersection points of the grid on which no wind turbine is planned (the other wind turbines remaining in their position, either the initial position from the first arrangement, or the position already repositioned).

[0181] * we then evaluate EvalJ the annual energy produced for each possible arrangement (for each possible position PDPJ of wind turbine i to be repositioned, the other wind turbines remaining at the last position fixed for them). The annual energy produced takes into account the first and second discrete distributions RD1 and RD2 of wind speeds and directions, as well as the probability of occurrence Prob of each wind speed in each wind direction. Thus, at the end of this evaluation step, an annual energy produced corresponds to each possible position PDPJ of wind turbine i to be repositioned.

[0182] * we retain as position PosJ of wind turbine i the possible position PDPJ which corresponds to the maximum value of the annual energy produced at the EvalJ step. * We thus obtain a new arrangement Disp_N of the wind turbines in the determined space. This new arrangement includes the last positions of the wind turbines already positioned as well as the new position PosJ of wind turbine i.

[0183] Loop B1 then allows F1 to select the next wind turbine in the sequential order (i becomes i+1) defined in order to carry out the same procedure for the following wind turbines.

[0184] Once all the wind turbines have been repositioned by loop B1, we repeat several times, for each selected grid, by a loop B2, the steps of determining the sequential order OS, and of loop B1 for each of the wind turbines, one by one, loop B1 comprising for each wind turbine i to be repositioned the determination of the possible positions PDPJ, the evaluation of the annual energy produced EvalJ for each possible position, the choice of the position PosJ of the wind turbine i to be repositioned and the definition of the new arrangement Disp_N.

[0185] By repeating these steps several times, the annual energy produced by the farm can be improved. Changing the sequential order each time (by randomly drawing each time, for example) further improves the annual energy produced.

[0186] Loop B2 ends when during the last loop B1 performed, no wind turbine has been repositioned (all wind turbines have been kept at the same position as obtained in the previous iteration).

[0187] Once loop B2 is complete, the last resulting Disp Xl layout becomes the (final) DispM layout for the selected grid.

[0188] Among the different grids, we can then retain the grids allowing us to maximize annual energy production (and we eliminate the other grids which are the least promising).

[0189] Step f): Creation of new arid areas and repetition of steps d) and e)

[0190] For each grid retained in step e), the first spacing step is reduced, preferably by half, and second grids are formed from the first reduced spacing step.

[0191] Each second grid is formed from a grid retained in step e). The second grid uses the same second pair of first and second directions as said retained grid, but each second grid is distinguished from the grid retained in step e) by the first and second spacings. Indeed, the first and second spacings of the second grids are varied from the first and second spacings of the grid retained in step e), as a function of the reduced first spacing step. In other words, these second grids are used to refine the discretization of the spacing step around the configuration retained in the previous step (i.e. the grid retained in step e) making it possible to maximize the annual energy production), with the aim of improving the accuracy of the method.

[0192] For example, the first spacings n' of the second grids can be defined by: r = ri ± il ■ Ar

[0193] With ri the first grid spacing retained in step e) concerned it is a first positive integer (which can be positive or negative)

[0194] Ar the first spacing step decreased (compared to the previous first spacing step).

[0195] Advantageously, in order to gradually refine the discretization, the product of the absolute value of the first integer and the first reduced spacing step can be less (in particular strictly less) than the first previous spacing step (i.e. the one used before the definition of the first reduced spacing step).

[0196] Similarly, the second spacings r2' of the second grids can be defined by: r2 = r2± il ■ Ar

[0197] With r2 the second grid spacing retained in step e) concerned it is the first positive integer (which can be positive or negative)

[0198] Ar the first spacing step decreased (compared to the previous first spacing step).

[0199] Using the second grids, the grid spacing is varied to refine the mesh spacing around the relevant configurations found in the previous step (i.e., grids that maximize annual energy production).

[0200] From the second grids thus formed, steps d) and e) are repeated in order to reposition the wind turbines optimally on each of the second grids (for these reiterations, the grids are replaced by second formed grids).

[0201] Preferably, in step f), a predetermined number of second grids can be formed. Each second grid can be defined by lines of the same orientation as the grid retained in step e), the first spacing of each second grid can correspond to the sum of the first spacing of the grid retained in step e) and an integer number of reduced first spacing pitch, and the second spacing of each second grid can correspond to the sum of the second spacing of the grid retained in step e) and said integer number of reduced first spacing pitch. Thus, for each grid retained, a predetermined number of second grids is formed, the predetermined number depending on the integer. The second grids make it possible to refine the spacings around the first and second spacings of the grids retained in step e).

[0202] Preferably, the integer can be 1 or -1. Considering these values ​​of 1 and -1, for each grid retained in step e), four second grids are formed, which makes it possible to limit the number of configurations to be tested, while refining the precision of the grids little by little around the most promising previous grids (those which make it possible to maximize annual energy production).

[0203] Step a): Creation of new arid areas and repetition of steps d) and e)

[0204] For each grid retained in step f) (i.e. at the end of the reiterations of steps d) and e)), the second direction step is reduced, preferably by half, and third grids are formed from the second direction step.

[0205] Each third grid is formed from a grid retained in step f) (at the end of step f), i.e. after the step of local repositioning of each wind turbine). The third grid uses the same first pair of first and second spacings as said retained grid but each third grid is distinguished from the grid retained in step f) by the first and second directions. Indeed, the first and second directions of the third grids of the first and second directions of the grid retained in step f) are varied as a function of the reduced second direction step. In other words, these third grids are used to refine the discretization of the second direction step around the configuration retained in the previous step (i.e. the grid retained in step f) making it possible to maximize the annual energy production), with the aim of improving the accuracy of the method.

[0206] For example, the first 0 / direction of the third grids can be defined by:

[0207] 9 = 9^ + 12 ■ A9

[0208] With 01 the first direction of the grid retained in step f) concerned i2 a second positive integer (which can be equal to the first integer) A0 the second direction step reduced (compared to the previous second direction step).

[0209] Advantageously, in order to gradually refine the discretization, the product of the absolute value of the second integer and the second reduced direction step can be less (in particular strictly less) than the previous second direction step (i.e. the one used before the definition of the second reduced direction step).

[0210] Similarly, the second directions 02' of the third grids can be defined by:

[0211] With 02 the second direction of the grid retained in step f) concerned i2 the second positive integer

[0212] A0 the second direction step decreased (compared to the previous second direction step).

[0213] Using the third grids, the direction of the grid lines is varied in order to refine the mesh direction variations around the relevant configurations found in the previous step (i.e., grids that maximize annual energy production).

[0214] From the third grids thus formed, steps d) and e) are repeated in order to reposition the wind turbines optimally on each of the second grids (for these reiterations, the grids are replaced by second formed grids).

[0215] Preferably, in step g), a predetermined number of third grids may be formed. Each third grid may be defined by lines of the same spacing as the grid retained in step f), the first direction of each third grid may correspond to the sum of the first direction of the grid retained in step f) and an integer of the second reduced direction pitch, and the second direction of each third grid may correspond to the sum of the second direction of the grid retained in step f) and said integer of the second reduced direction pitch. Thus, for each grid retained, a predetermined number of third grids is formed, the predetermined number depending on the integer. The third grids make it possible to refine the directions around the first and second directions of the grids retained in step f).

[0216] Preferably, the integer can be 1 or -1. Considering these values ​​of 1 and -1, for each grid retained in step f), we form four third grids, which makes it possible to limit the number of configurations to be tested, while refining the precision of the grids little by little around the most promising previous grids (those which make it possible to maximize annual energy production).

[0217] Thanks to steps f) and g), the mesh can be refined in two stages, in terms of spacing and directions. Thus, in step a), a coarse mesh is used to preselect certain grids in step c). Some grids are then re-selected in step e). The mesh can then be refined on the most promising grids selected in step e).

[0218] Thus, the process makes it possible to limit the necessary computing resources (memory and processor), to limit the calculation time, while refining the precision of the position of the different wind turbines by maximizing the annual energy produced. definitive of the wind turbines in the

[0219] A final arrangement of the wind turbines is determined in the predetermined space. The final arrangement corresponds to the (final) arrangement obtained in step g) of the grid that maximizes the annual energy production. This final arrangement can be used for the construction of the wind turbines according to the final arrangement in the predetermined space, this final arrangement making it possible to maximize the annual energy of the farm.

[0220] For each (final) arrangement obtained at the end of step g) of the wind turbines obtained on each grid (which are therefore third grids), the annual energy production of each of these (final) arrangements is compared and the (final) arrangement with the highest annual energy production is chosen to maximize the farm's yield. The final arrangement of the wind turbines on the farm is then determined as corresponding to this optimal (final) arrangement.

[0221] From the final layout obtained, the wind turbines of the farm can then be built in the positions corresponding to the final layout in the predetermined space. Thanks to the use of grids, the wind turbines will be aligned in two directions and along lines regularly distributed in space, so as to meet operational constraints and constraints specific to offshore.

[0222] In the present method, steps a) to h) are implemented by computer means, such as a computer, a server and / or a supercomputer. Steps a) to h) also constitute a method for positioning the wind turbines in a predetermined space which is intended to construct the wind turbines of the farm at the positions defined by the positioning method.

[0223] Advantageously, steps f) and / or g) can be repeated until the first spacing step reaches a first threshold and / or until the second direction step reaches a second threshold. By repeating steps f) and / or g), the positioning accuracy is increased and the annual energy produced can be increased by increasing the discretization of the grid spacings and directions.

[0224] According to one configuration of the invention, the first threshold may be between one fiftieth of the diameter of the wind turbines and one fifth of the diameter of the wind turbines. Thus, the discretization is sufficiently fine to obtain high annual energy production and precision on the positions of the wind turbines. Alternatively or additionally, the first threshold may be less than or equal to 1 m. Indeed, the precision of the construction of the wind turbines at the planned positions of one meter is sufficient.

[0225] According to a configuration of the invention, the second threshold may be less than 2°, preferably less than 1°. Indeed, this precision on the directions of the grid lines is sufficient.

[0226] The invention also relates to a method for positioning wind turbines of a wind farm in a predetermined space for the construction of the wind farm in the predetermined space. In this method, statistical wind data are measured, by measuring means, preferably a LIDAR sensor, in the predetermined space to determine the first and second discrete distributions and the probabilities of occurrence of each wind speed in each wind direction of the first and second discrete distributions, then the simulation method is implemented according to one of the variants or combinations of variants described above, to determine the optimal positions of the wind turbines of the wind farm in the predetermined space, so as to position the wind turbines in the predetermined space for the construction of the wind farm in the predetermined space.This method can increase the accuracy of the annual energy produced, based on statistical data measured at the location of the predetermined space. The optimal positions of the wind turbines in this space can then be determined, taking into account alignment constraints and maximizing the annual energy produced, from the measured wind data.

[0227] The invention may also relate to a computer program product implementing the simulation method (positioning method) of wind turbines in a predetermined space, consisting of steps a) to h) described above, using computer means, such as a computer, a mobile phone or a tablet. The computer program product may be downloadable from a communication network and / or recorded on a computer-readable medium and / or executable by a processor or a server, and it comprises program code instructions for implementing the simulation method (or positioning method) according to one of the variants or combinations of variants described above, when the program is executed on a computer or on a mobile phone. Indeed, the simulation (or positioning) method described above is particularly suitable for being implemented on computer means.It can thus be implemented in a simple manner and results can be obtained quickly. Furthermore, the invention also relates to a method for constructing a wind farm in which the simulation method is implemented according to one of the variants or combinations of variants described above or in which the method for positioning the wind turbines described above is implemented, and then the wind farm is constructed by erecting the wind turbines at the positions of said final arrangement in the predetermined space so as to generate energy from the wind. By constructing the wind turbines at the optimal positions determined by the simulation method or by the positioning method, the annual energy produced by the farm in the predetermined space can be increased.

[0228] Furthermore, the invention also relates to a wind farm obtained from the method of constructing a wind farm as described above.

[0229] Example

[0230] Figure 6 illustrates an example application of the wind farm simulation method used to find the optimal positions of the wind turbines of the farm in a predetermined space Z2 which is a non-convex space so as to use the optimal layout to construct the wind turbines at these optimal positions.

[0231] In this example, we seek to position twenty-nine wind turbines in the predetermined space Z2, taking into account constraints of alignment of the wind turbines in two non-collinear directions.

[0232] The wind turbines considered are turbines with a nominal power of 10 MW, whose nacelle height is positioned at 119.8 m from the ground and whose rotor diameter is 198 m. The distance between the wind turbines in the predetermined space Z2 is greater than 4 times the rotor diameter of the wind turbines.

[0233] The wind data used for this example correspond to those from: Baker, NF, Thomas, JJ, Stanley, APJ, and Ning, A. IEA Task 37 Wind Farm Layout Optimization Case Studies, https: / / doi.org / 10.5281 / zenodo.5809681 , 2021

[0234] For this example, we consider the following criteria:

[0235] - The minimum distance between wind turbines (two by two) is twice the diameter of the wind turbines (also called rotor diameter);

[0236] The maximum distance between wind turbines (two by two) is six times the diameter of the wind turbines (also called rotor diameter);

[0237] The predetermined quantity of arrangements retained at each step e) is 10; The predetermined number of second pairs of first and second directions associated with each first pair of first and second spacings at step c) is 10.

[0238] - The first spacing step used in step a) is twice the diameter of the wind turbines; then at each step f), it is divided by two;

[0239] The second steering step used in step a) is 5°; then at each step g), it is divided by two;

[0240] The first threshold is defined by one tenth of the diameter of the wind turbines;

[0241] The second threshold is defined by 0.5°;

[0242] - At each step f) and g), we form, for each grid retained, four second or other third grids respectively.

[0243] Figure 6 shows the result obtained, i.e. the optimal arrangement found using the simulation method according to the invention. In this figure:

[0244] The small light gray dots represent possible positions where wind turbines can be placed on the grid. They are therefore at the intersections of the first L1 lines and the second L2 lines of the grid in the predetermined space Z2;

[0245] The large black dots represent the positions of the wind turbines allowing to maximize the energy recovery on the grid considered;

[0246] The dotted lines represent the direction of the first L1 lines or the second L2 lines.

[0247] At the end of step c), if twenty second pairs are formed grouping the second identified pairs, to obtain the same precision in angle and position in space, the method according to the invention performs 380 optimizations while the method of the applicant's patent application FR 22 / 09.630 performs 33,620 optimizations under the same conditions. The use of the method makes it possible to constrain the positioning with alignments of the wind turbines, on the one hand by limiting the number of configurations to be tested (therefore limiting the computing resources and the calculation time) and on the other hand by improving the annual energy recovery by refining the discretization of the different grids little by little.

Claims

Claims 1. Method for simulating a wind farm in a predetermined space (Esp) for the construction of said wind farm in said predetermined space (Esp), the wind farm being composed of a predefined number of wind turbines, from a first discrete wind speed distribution (RD1), a second discrete wind direction distribution (RD2) and a probability of occurrence (Prob) of each discrete wind speed value in each discrete wind direction value of said first and second discrete distributions (RD1, RD2), in which at least the following successive steps are carried out by computer means, such as a computer: a) For different first predefined spacings separated by a first spacing step, different second predefined spacings separated by said first spacing step, different first predefined directions separated by a second direction step,and different second predefined directions separated from said second direction step, different first pairs (C1) of first and second predefined spacings are formed, and different second pairs (C2) of first and second predefined directions (01, 02), then for the different first pairs (C1) and for the different second pairs (C2), first grids (GR) are formed in the predetermined space (Esp), each first grid being defined by a plurality of intersection points between first lines (L1) oriented in the first predefined direction (01) and second lines (L2) oriented in the second predefined direction (02), the first lines (L1) being spaced from said second predefined spacing along the second predefined direction (02) and the second lines (L2) being spaced from said first predefined spacing along the first predefined direction (01),each first grid comprising at least one mesh delimited by intersection points. b) For each first grid of said predetermined space, the average annual energy production of a mini-farm (AEP-mf) composed of wind turbines positioned at all the intersection points of one or more connected meshes of the first grid is determined, from said first discrete wind speed distribution (RD1), said second discrete wind direction distribution (RD2) and said probability of occurrence (Prob); c) For each first pair (C1) of first and second predefined spacings, at least one second pair (C2) of first and second predefined directions (01, 02) is identified (Ch) which maximizes the annual energy production of said mini-farm, then a set of second pairs is formed grouping the identified second pairs; d) For each first grid defined by a first pair of first and second predefined spacings and by a second pair of first and second predefined directions among said set of second pairs, a first arrangement (Alg1) of the predefined number of wind turbines is determined, each wind turbine being positioned on one of said intersection points of the first grid by a first positioning algorithm;e) then, for each first grid used in step d), the position of the wind turbines (Alg2) is modified among the intersection points of the first grid on which no wind turbine is positioned, in order to improve the annual energy production so as to obtain an arrangement of the predefined number of wind turbines on each first grid considered and an annual energy production for each arrangement and a predetermined quantity of arrangements corresponding to the arrangements maximizing the annual energy production and each first using the second grids in replacement of the first grids e grid (Grr) associated with each arrangement retained; f) For each first grid retained in step e), the first spacing step (MAr) is reduced, preferably by half, and second grids (Gr2) are formed from the first reduced spacing step, then steps d) and e) are repeated;g) For each second grid retained in step f), the second direction step (MAS) is reduced, preferably by half, and third grids (Gr3) are formed from the second direction step, then steps d) and e) are repeated using the third grids to replace the first grids; h) A final arrangement (Disp_F) of the wind turbines in the predetermined space (Esp) is determined, said final arrangement (Disp_F) corresponding to the arrangement obtained in step g) of the third grid which maximizes the annual energy production, for the construction (Const) of the wind turbines according to the final arrangement (Disp_F) in the predetermined space (Esp).; 2. Simulation method according to claim 1, in which steps f) and / or g) are repeated until the first spacing step reaches a first threshold and / or until the second direction step reaches a second threshold.

3. Simulation method according to claim 2, wherein the first threshold is between one fiftieth of the diameter of the wind turbines and one fifth of the diameter of the wind turbines or less than 1 m and / or the second threshold is less than 2°, preferably less than 1°.

4. Simulation method according to one of the preceding claims, wherein, in step f), a predetermined number of second grids (Gr2) is formed, each second grid (Gr2) being defined by lines of the same orientation as the first grid retained in step e), the first spacing of each second grid (Gr2) corresponding to the sum of the first spacing of the first grid retained in step e) and a first integer number of reduced first spacing pitch, the second spacing of each second grid (Gr2) corresponding to the sum of the second spacing of the first grid retained in step e) and said first integer number of reduced first spacing pitch, preferably, said first integer number being 1 or -1.

5. Simulation method according to one of the preceding claims, in which, in step g), a predetermined number of third grids (Gr3) are formed, each third grid (Gr3) being defined by lines of the same spacing as the second grid retained in step f), the first direction of each third grid (Gr3) corresponding to the sum of the first direction of the second grid retained in step f) and a second integer of the second reduced direction pitch, the second direction of each third grid (Gr3) corresponding to the sum of the second direction of the second grid retained in step f) and said second integer of the second reduced direction pitch, preferably, said second integer being 1 or -1.

6. Simulation method according to one of the preceding claims, in which, in step e) of modifying the position of the wind turbines (Alg2) for each first grid, at least the following steps are carried out: e1) for each first grid used in step d), a sequential order (OS) of modification of the positions of the wind turbines determined by the first positioning algorithm (Alg1) is defined and each wind turbine of the defined sequential order is repositioned, one by one, by finding a free intersection point of the first grid which maximizes the annual energy production from said first discrete distribution of wind speed (RD1), said second discrete distribution of wind direction (RD2) and said probability of occurrence (Prob);e2) step e1) is repeated as many times as necessary until, at the end of a step e1), no wind turbine has been repositioned and an arrangement of the predefined number of wind turbines is obtained on each first grid considered and an annual energy production for each final arrangement; and a predetermined quantity of arrangements corresponding to the is retained (AEP g); provisions maximizing annual energy production and each first grid (Grr) associated with each provision retained.

7. Simulation method according to claim 6, for which said sequential order (OS) is obtained randomly and / or the sequential order (OS) is modified at each iteration of step e1).

8. Simulation method according to one of claims 6 to 7, in which, in step e1), a selection of intersections is chosen from among the intersection points on which no wind turbine is positioned, for each wind turbine to be repositioned.

9. Simulation method according to claim 8, wherein the selection of intersections corresponds to a predetermined value of intersection points on which no wind turbine is positioned, said selection of intersections being chosen randomly or being chosen as corresponding to said predetermined value of intersection points on which no wind turbine is positioned closest to the position of the wind turbine to be repositioned.

10. Simulation method according to one of the preceding claims, in which said predetermined space (Esp) comprises non-connected (Z1, Z2) and / or non-convex (Z2) zones.

11. Simulation method according to one of the preceding claims, in which for each first grid considered, said first positioning algorithm (Alg1) carries out at least the following steps: - we arbitrarily define the position of the first wind turbine (P_E1) on one of the intersection points of the first grid; - then for each wind turbine to be positioned, successively: potential positions (PE Ej) are defined for the wind turbine to be positioned, said potential positions (PE Ej) being constituted by the intersection points of the first grid located between a minimum distance and a maximum distance from all the positioned wind turbines; the annual energy production (Eval_AEP) of the positioned wind turbines and of the wind turbine to be positioned is calculated for the defined potential positions (PE Ej), from said first discrete distribution (RD1) of wind speed, from said second discrete distribution (RD2) of wind direction and from said probability of occurrence (Prob); We choose the position (PosJ) of the wind turbine to be positioned corresponding to the maximum calculated value of annual energy production: - said first arrangement (Disp_Ej) is determined corresponding to the position of the predefined number of wind turbines among the intersection points of the first grid considered in said predetermined space (Esp).

12. Simulation method according to one of the preceding claims, in which, in step c), the difference is taken between the annual energy production of the mini-farm obtained in step b) and the annual energy production of a single wind turbine multiplied by the number of wind turbines in the mini-farm.

13. Simulation method according to one of the preceding claims, in which, in step a), the first spacing step is between two times and ten times the diameter of the wind turbines, preferably between two times and six times the diameter of the wind turbines.

14. Simulation method according to one of the preceding claims, wherein in step a), the second direction step is between 1° and 20°, preferably between 5° and 10°.

15. Simulation method according to one of the preceding claims, in which, in step e), the predetermined quantity of arrangements is between 1 and 20, preferably between 1 and 10.

16. Simulation method according to one of the preceding claims, in which in step c), a predetermined number of second pairs of first and second predefined directions is identified for each first pair of first and second predefined spacings, preferably the predetermined number is between 1 and 20, preferably between 1 and 10.

17. A method of positioning wind turbines of a wind farm in a predetermined space for the construction (Const) of said wind farm in said predetermined space (Esp), in which statistical wind data are measured, by measuring means, preferably a LIDAR sensor, in the predetermined space (Esp) to determine the first and second discrete distributions (RD1, RD2) and the probabilities of occurrence (Prob) of each wind speed in each wind direction of the first and second discrete distributions (RD1, RD2), then the simulation method according to one of the preceding claims is implemented to determine the positions of the wind turbines of said wind farm in the predetermined space, so as to position the wind turbines in the predetermined space for the construction of said wind farm in said predetermined space.

18. Method for constructing a wind farm in which the simulation method according to one of claims 1 to 16 is implemented or in which the method for positioning the wind turbines according to claim 17 is implemented, then the wind farm is constructed (Const) by erecting the wind turbines in the positions of said final arrangement (Disp_F) in the predetermined space (Esp).

19. Wind farm obtained from the method of constructing a wind farm according to the preceding claim.

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