Method for constructing a wind farm with alignment constraints

Abstract

The invention relates to a method for constructing a wind farm in a predetermined space, in which at least the following successive steps are carried out: a) forming different grids (GR) in the predetermined space; b) for each grid, determining the average annual energy production of a mini-farm (AEP-mf) composed of wind turbines on the points of intersection of a mesh; c) selecting (Ch) a few grids that make it possible to maximize the energy production; d) for each grid c in step c), determining (Alg1) a first arrangement of the predefined number of wind turbines on the grid; e) modifying (Alg2) the position of the wind turbines on the grid; f) determining a definitive arrangement (Disp_F) of the wind turbines in the predetermined space, and constructing (Const) the wind farm.

Description

[0001] METHOD OF CONSTRUCTING A WIND FARM WITH ALIGNMENT CONSTRAINTS

[0002] Technical field

[0003] The present invention relates to a method of constructing a wind farm in a predetermined space.

[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 speed downstream of the turbine and therefore the energy recovered by other wind turbines, particularly those located downstream of those 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 in order 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").

[0009] 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.

[0010] 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.

[0011] 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. 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", in order 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.

[0012] 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.

[0013] Of course, the annual energy produced also depends on the wind turbines chosen.

[0014] Prior art

[0015] To determine the correct positioning of wind turbines in the planned location of the farm, several methods have been developed.

[0016] Patent application CN1051 19320 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.

[0017] Patent applications CN102142103A, CN105139269 and US2016171401 relate to wind turbine positioning methods based on genetic algorithms. Genetic algorithms are a class 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 computer memory.

[0018] The methods described in the following documents are also known:

[0019] - 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. - 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. 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 time and significant computer memory.

[0020] - 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.

[0021] - 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.

[0022] - Quan N., and Kim HM, 2018. Greedy robust wind farm layout optimization with feasibility guarantee. Engineering Optimization, September 6, 2018, pages 1 152-1 167. This method is based on a greedy algorithm that takes into account 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.

[0023] Also known is the applicant's patent application WO 2022 / 028 847, 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 the navigation of boats, the alignment of the wind turbines is part of the design constraints of the farms.

[0024] Thus, the technical problem that the invention proposes to solve consists of developing a method for constructing a wind farm that allows the 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 computer memory and by respecting constraints of alignment of the wind turbines in two directions forming a non-zero angle between them (two non-parallel directions).

[0025] Summary of the invention

[0026] To address the technical problem, the invention relates to a method for constructing a wind farm in a predetermined space, the wind farm being composed of a predefined number of wind turbines, the construction method comprising 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 said first and second discrete distributions, for which at least the following successive steps are carried out: a) For different pairs of first and second predefined spacings, and for different pairs of first and second predefined directions, grids are formed in the predetermined space,each grid being 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 being spaced apart from said second predefined spacing along the second predefined direction and the second lines being spaced apart from said first predefined spacing along the first predefined direction, each grid comprising at least one mesh delimited by said intersection points; b) For each 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 grid is determined, from said first discrete wind speed distribution,of said second discrete distribution of wind direction and said probability of occurrence; c) For each pair of first and second predefined spacings, at least one pair of first and second predefined directions is associated which maximizes the annual energy production of said mini-farm, d) For each grid corresponding to a pair of first and second predefined spacings and to a pair of first and second predefined directions associated with step c), a first arrangement of the predefined number of wind turbines is determined, each wind turbine being positioned on one of said points of intersection of the grid by a first positioning algorithm, e) then, for each grid used in step d),the position of the wind turbines is modified in order to improve the annual energy production 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. f) a final arrangement of the wind turbines in the predetermined space is determined, said final arrangement corresponding to the final arrangement obtained in step e) of the grid which maximizes the annual energy production, and 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.,

[0027] Preferably, in step e) of modifying the position of the wind turbines for each grid used in step d), 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 point of intersection 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.

[0028] Advantageously, said sequential order is obtained randomly. Preferably, the sequential order is modified at each iteration of step e1).

[0029] According to a configuration of the invention, before step a), 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.

[0030] According to an advantageous implementation of the invention, said predetermined space comprises non-connected and / or non-convex zones.

[0031] According to a variant of the invention, for each grid considered, said first positioning algorithm carries out at least the following steps:

[0032] - we arbitrarily define the position of the first wind turbine (P_E1) on one of the intersection points of the grid;

[0033] - 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 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);

[0034] We choose the position (PosJ) of the wind turbine to be positioned corresponding to the maximum calculated value of annual energy production:

[0035] - said first arrangement (Disp_Ej) is determined corresponding to the position of the predefined number of wind turbines among the intersection points of the grid considered in said predetermined space (Esp).

[0036] Preferably, 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.

[0037] The invention also relates to a wind farm obtained from the method of constructing a wind farm as described above.

[0038] List of figures

[0039] Other characteristics and advantages of the method and 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.

[0040] Figure 1 shows an example of a construction method according to the invention.

[0041] Figure 2 represents an example of the steps of repositioning the wind turbines of the construction method according to the invention.

[0042] Figure 3 shows an example of a complex location for positioning wind turbines according to the invention.

[0043] Figure 4 illustrates a variant of a first positioning algorithm according to the invention.

[0044] Figure 5 illustrates the definition of wind turbine alignment constraints for the method according to the invention.

[0045] Figure 6 illustrates the discontinuity of the intersection points as a function of the spacings between the lines of the grid of the method according to the invention. Figure 7 illustrates the definition of a grid in a predetermined space and the intersection points of the grid of the method according to the invention.

[0046] Figure 8 illustrates an arrangement of the wind turbines on a grid in the predetermined space, the arrangement resulting from one of the steps of the method according to the invention and this arrangement not being the final arrangement.

[0047] Figure 9 illustrates the final arrangement of the wind turbines on the same grid as Figures 7 and 8, in the predetermined space obtained by the method according to the invention.

[0048] Figure 10 illustrates an example of a search for optimal positioning of twelve wind turbines in a predetermined non-convex space, with alignment constraints, in order to construct the wind turbines while maximizing the annual energy produced, according to the invention.

[0049] Description of the embodiments

[0050] To facilitate the reading of this description, some definitions are explained below.

[0051] 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.

[0052] 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.

[0053] 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.

[0054] "Unconnected areas" are areas where 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 where each pair of points is connected by a continuous path entirely contained within the area.

[0055] A "convex area" is an area in which the segments connecting any two points in that area are all entirely contained within the area. For example, a circle, a square, or a rectangle all delimit convex areas. Conversely, a "non-convex area" 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 delimited by a concentric outer circle and an inner circle is not convex. In this description, "grid" means a plurality of intersection points located in the predetermined space (or at the boundary of that 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 special conditions). The first lines are spaced at a second predefined spacing along the second lines. In other words, the first lines are evenly spaced (they are all equidistant) at a pitch corresponding to the second spacing along the second lines. The second lines are spaced at a first predefined spacing along the first lines. In other words, the second lines are evenly spaced (they are all equidistant) at a pitch corresponding to the first spacing along the first lines.Thus, each grid comprises at least one mesh, in the shape of a parallelogram, delimited by points of intersection between the first and second lines (the first and second lines being intersecting with each other).

[0056] The invention relates to a method for constructing (or installing) a wind farm in a predetermined space which may be a land area or an offshore area at sea. The farm is composed 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. Advantageously, the predetermined space may include non-connected areas. Therefore, the predetermined space may correspond to actual locations planned for the installation of the 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. Preferably, the predetermined space may include non-convex areas in addition to or alternatively to the non-connected areas.Thus, the predetermined space may correspond to real 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 in particular be determined by taking into account the bathymetry, the nature of the soil, borders with other countries, navigation channels, cable or pipeline passages for example.

[0057] Figure 3 illustrates, in a schematic and non-limiting manner, an example of a predetermined space suitable for implementing the positioning method of the invention (or for constructing a wind farm of the invention).

[0058] The predetermined space may in particular include a first zone Z1 and a second zone Z2, zones represented by the vertical hatching. These zones Z1 and Z2 are not 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 is of complex, non-convex shape. Indeed, if we consider the two points A and B, we observe that a part of the segment Seg which connects the points A and B is located outside zone Z2.

[0059] To identify the zones Z1 and Z2 of the predetermined space in a third, larger zone ZE, encompassing these two zones Z1 and Z2, a Boolean matrix can be used. The third zone ZE is rectangular in shape, which is easier to process computationally 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, the boundary(s) of the predetermined space can be determined. Indeed, a point will be considered as part of the boundary 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.

[0060] The construction method comprises 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 said first and second discrete distributions. These 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 construction 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 of the site, and, thus, the statistical data of the wind 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 the wind data may be carried out over the predetermined duration, for the collection of the measurements, which may 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.

[0061] The measuring (collection) means can advantageously be a LIDAR sensor.

[0062] In this method, at least the following successive steps are carried out: a) For different (first) pairs of first and second predefined spacings, and for different (second) pairs of first and second predefined directions, grids are formed in the predetermined space, each grid being 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 being spaced apart from said second predefined spacing along the second predefined direction and the second lines being spaced apart from said first predefined spacing along the first predefined direction, the grid comprising at least one mesh delimited by said intersection points (each mesh is delimited by four intersection points and some intersection points may not be attached to a mesh). Thus,the intersection points of the grid form a discrete mesh. Discrete mesh means that the intersection points of the mesh that constitutes the grid are discrete values ​​(as opposed to continuous values). b) For each 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 grid is determined from said first discrete wind speed distribution, said second discrete wind direction distribution 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 associated which maximizes the annual energy production of said mini-farm,d) For each grid corresponding to a (first) pair of first and second predefined spacings and to a (second) pair of first and second predefined directions associated with step c), 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 grid by a first positioning algorithm, e) Then, for each grid used in step d), the position of the wind turbines is modified in order to improve the annual energy production and a final arrangement of the predefined number of wind turbines is obtained on each grid considered and an annual energy production for each final arrangement f) A final arrangement of the wind turbines in the predetermined space is determined, said final arrangement corresponding to the final arrangement obtained in step e) of the grid which maximizes the annual energy production,and constructing the wind farm by erecting the wind turbines at the positions of said final arrangement in the predetermined space so as to generate energy from the wind.,

[0063] The use of discrete values ​​for wind speed, wind direction and discrete intersection points of the different grids in the predetermined space simplifies the method, speeds up calculation times and limits the computer memory required, 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.

[0064] 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 80m and 120m 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 the variations in wind characteristics depending on the seasons. According to one embodiment, the annual energy production can be estimated by the following formula:.

[0065] [Math] aep = 8760 ■ E WsiWp [p(f, w s , w p ')}

[0066] 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 w p, for example by a Weibull distribution.

[0067] 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:

[0068] [Math2]

[0069] 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 .

[0070] 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 in particular come from CFD simulations (from the English "Computational Fluid Dynamics" meaning "Computational fluid dynamics calculations").

[0071] The instantaneous power Pf of each wind turbine f in the farm can be written:

[0072] [Math3] / [iy(w s )]

[0073] 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.

[0074] Indeed, the wake effects of wind turbines located upstream 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. The impacts of the wake effects taken into account in equation [Math3] can notably be based on wake models. These wake models can notably translate:

[0075] - 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),

[0076] - an increase in the turbulent intensity of the wind,

[0077] - 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 publication cited above and / or turbulent wind intensity from several wakes.

[0078] Wake patterns 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 consisting of the predefined number of wind turbines, by the mini-farm or by a farm consisting of a single wind turbine.

[0079] Preferably, in step e) of modifying the position of the wind turbines for each grid used in step d), 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 point of intersection 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 are obtained.

[0080] Figure 1 illustrates, in a schematic and non-limiting manner, the method of constructing the wind farm in a predetermined space Esp, in a global manner. From the predetermined space Esp chosen (an offshore or onshore geographical area) which may be a space comprising non-convex and / or non-connected zones (for example with a road or a river crossing 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.

[0081] Each of these grids (GR) is established from a multitude of first lines parallel to each other and regularly spaced and second lines parallel to each other 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).

[0082] The different GR grids are distinguished from each other by the combination of the first pairs C1 and second pairs C2.

[0083] For each GR grid, the first lines are oriented at an angle corresponding to the first 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 direction relative to the same direction of the predefined fixed reference point (the north direction for example).

[0084] 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.

[0085] 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.

[0086] 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.

[0087] The grid may 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 points of intersection.

[0088] 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. 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 intersection points of this grid portion, a wind turbine is positioned.Thus, if the grid portion has a single cell, the mini-farm will consist 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 on the grid to be assessed simply and quickly and without requiring a lot of memory or computing time when this step is carried out by computer.

[0089] 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.

[0090] By comparing the annual energy production values ​​of different grids comprising the same first C1 pair and different second C2 pairs, one or more of the most promising C2 pairs (giving the highest annual energy production(s)) can be associated. Thus, for each first C1 pair with predefined first and second spacings, one or more second C2 pairs are associated. This makes it possible to limit the number of combinations of first C1 pair and second C2 pair for the rest of the method.

[0091] 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.

[0092] Thus, we can choose Ch, from the annual energy production of the mini-farms, at least a second couple C2 for each first couple C1. Thus, we select a certain number of grids from those which have been established previously.

[0093] Then, for each selected grid, we establish a first arrangement of wind turbines Alg1 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.

[0094] 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 the 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.

[0095] Once the wind turbines have been repositioned and no better solution is found (we can no longer change the position of a wind turbine on the grid without degrading the annual energy produced), we have a final arrangement of the wind turbines on each selected grid and we compare the annual energy produced from each grid AEP g. We can then determine the final arrangement Disp_F of the wind turbines in the predetermined space Esp as being the final arrangement of the wind turbines on the grid which allows us to obtain the maximum annual energy produced.

[0096] The wind turbines are then built in the planned locations corresponding to the final arrangement determined in the predetermined space.

[0097] Step a) of defining the grids

[0098] 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 comprises 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. The cells 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 within 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.Using multiple grids, one can test different alignment constraints (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 second lines are intersecting.

[0099] By using different discrete values, the number of possible combinations is limited and therefore the computer's usable memory. In addition, these discrete values ​​are sufficient to ensure accuracy compatible with the construction of wind turbines on site (taking into account the possible construction accuracies).

[0100] 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.

[0101] 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.

[0102] Preferably, the minimum distance may be greater than twice the diameter of the rotor of the wind turbines, and more 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.

[0103] 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.

[0104] And preferably, the second predefined direction can be between -90° and the first direction. Therefore, with the symmetry effects, we scan all possible space while limiting the number of combinations.

[0105] The discrete values ​​of the first and second predefined spacings can be defined in steps of 0.5 times the rotor diameter and discrete values ​​of the first and second predefined directions can be defined in steps of 1°, these steps being sufficient to obtain sufficient accuracies at the locations of the wind turbines.

[0106] 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 arbitrarily fixed on a point of intersection between a first line Lig1 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 Lig1 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.

[0107] Figure 6 illustrates, in a schematic and non-limiting manner, the discontinuity of positions which can result from different grids, due to the different mesh.

[0108] In this figure, Q represents the predetermined space. Only one line is shown on the grid for ease of understanding.

[0109] In diagram a), the intersection points on the line are separated by a length L. We can therefore position the wind turbines, represented by the black dots, at each end of the predetermined space Q: they are therefore spaced by a distance corresponding to 2L.

[0110] In diagram b), the intersection points on the line are separated by a length L+E. Therefore, the wind turbines, represented by the black dots, can only be positioned on the intersection points shown: they are therefore spaced by a distance corresponding to L+E. Indeed, the point located at 2(L+E) is outside the domain of the predetermined space Q.

[0111] Thus, even if the value E is low, there will be a strong discontinuity of the solutions between a grid with lines spaced by a space L and those spaced by a space L+E, because of the limit of the space predetermined for the determination of the grid and the intersection points taken into account for the choice of the possible positions of the wind turbines.

[0112] Step b) determining the annual energy production of a mini wind farm on each grid

[0113] 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 wind turbine. Of course, in order to verify the alignment constraints of the wind turbines, it is not possible, in the present construction 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.

[0114] 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.

[0115] To do this, for each grid formed in step a), we consider a mini-farm made up 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 the sorting. Thanks to all the wind turbines installed on the grid portion (for example, four wind turbines if the grid portion comprises a single cell, 9 wind turbines if the grid portion is homothetic by a factor of 2 compared to a grid of a single cell), we can determine the annual energy production of the mini-farm, in particular using the formulas presented previously.

[0116] Thus, for each type of grid, we can associate an annual energy production of the mini-farm.

[0117] Step c) of choosing the (second) pairs of first and second predefined directions as a function of the first and second predefined spacings.

[0118] This step serves to limit the number of combinations to be used for the arrangement of the predefined number of wind turbines in the farm based on the results obtained in step b). Indeed, thanks to the mini-wind farm, it is possible to 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 directions and the first and second discrete distribution 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.

[0119] At least one (preferably only one) (second) pair of first and second predefined directions can then be chosen for each (first) pair of first and second predefined spacings, so as to limit the number of combinations for the following. Indeed, for the (first) pair of first and second predefined spacings, the (second) pair of first and second predefined directions makes it possible to maximize the annual energy produced and / or to limit the wake effects.

[0120] To determine the (second) first and second direction pair(s) associated with each (first) pair of first and second predefined spacings, one can either directly compare the annual production produced and retain the direction pairs which maximize this annual production of the mini-farm, or compare the loss of recovered energy due to wake effects.

[0121] 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: [Math 4]

[0122] Pioss =n*aep(f1, ws, wp)- aep(f2, ws, wp) 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 predefined 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 predefined space, ws and wp being the statistical distributions of wind speeds and wind direction, taking into account the probabilities of occurrence previously mentioned.

[0123] 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 the solutions for which the losses are too significant and retain only the relevant solution or solutions (with the lowest energy losses).

[0124] Step d) determining a first arrangement of wind turbines for the farm

[0125] During this step, a first arrangement of the wind turbines is determined on each grid defined by each (first) pair of first and second predefined spacings and for each (second) pair of first and second associated predefined directions obtained in the previous step c), 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 may 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 which 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 point of intersection 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 point of intersection 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), in particular by the local optimization search method of the following step e1).

[0126] According to one embodiment, for each grid considered (each grid defined by a first pair of first and second predefined spacings and by a second pair of first and second predefined directions associated with the first pair of first and second predefined spacings), said first positioning algorithm carries out at least the following steps:

[0127] - the position of the first wind turbine is arbitrarily defined on one of the intersection points of the grid considered;

[0128] - 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 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.

[0129] The position of the wind turbine to be positioned is chosen to correspond to the maximum calculated value of annual energy production. This maximizes the annual energy produced by the wind turbines whose position is defined in the predetermined space. These defined positions will 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.

[0130] - the first arrangement corresponding to the position of the predefined number of wind turbines among the intersection points of the grid considered in the predetermined space is determined.

[0131] Therefore, the first positioning algorithm is a greedy algorithm which includes a step of arbitrary positioning of the first wind turbine, then iteratively positions an additional wind turbine on intersection points of the grid considered until all the wind turbines of the predefined number are positioned on the grid. This greedy algorithm makes it possible, thanks to the step of selecting the potential positions, to accelerate the calculation time, 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. 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. For this, it is possible, for example, to use a greedy algorithm.

[0132] 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.

[0133] Then for each wind turbine j, we look for a position in order to maximize the annual energy produced.

[0134] Thus, iteratively according to F3, we define, for each wind turbine, 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.

[0135] 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.

[0136] 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.

[0137] 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 will be used in the next iteration to determine the potential positions PE Ej of the new wind turbine to be positioned and for the evaluation of the annual energy produced Eval_AEP.

[0138] 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 the fact that the first wind turbine is positioned in a step manner at step P_E1.

[0139] 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.

[0140] Step e) improving the position of wind turbines on each grid

[0141] 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. Step e1) of local search optimization

[0142] 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).

[0143] 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.

[0144] Preferably, this sequential order is 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, as these paths can bias the optimization results.

[0145] 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.

[0146] To determine the annual energy produced, we obviously take into account the first and second discrete distributions of wind speed and wind direction and the probability of occurrence, 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],

[0147] Step e2) of reproduction of step e1)

[0148] 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.

[0149] At the output of step e2), on each grid considered (corresponding to a first pair of first and second predefined spacings and to a second pair of first and second predefined directions associated with the first pair of first and second predefined spacings), we obtain a final arrangement of the wind turbines on each grid considered and an annual energy production associated with each of these final arrangements (one for each grid considered).

[0150] Preferably, in step e2), the sequential order is modified at each iteration of step e1) so as to limit the optimization paths based on pre-established orders.

[0151] Figure 2 illustrates, in a schematic and non-limiting manner, an example of search for optimization of the method according to the invention.

[0152] For each selected grid, a first arrangement Displ of the wind turbines on each of these grids is determined Alg1, 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 .

[0153] 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.

[0154] 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.

[0155] 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.

[0156] In more detail, this Alg2 optimization step includes the following steps:

[0157] - 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.

[0158] - 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:

[0159] * 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).

[0160] * 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.

[0161] * 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 step EvalJ.

[0162] * This gives a new arrangement DispJXI 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.

[0163] 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.

[0164] Once all the wind turbines have been repositioned by loop B1, we repeat several times, for each selected grid, 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 DispJXI.

[0165] 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.

[0166] 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).

[0167] Once loop B2 is complete, the last resulting DispJXI layout becomes the final DispM layout for the selected grid.

[0168] To choose the final arrangement of the wind turbines, we can then compare all the final arrangements of the different grids, and choose which arrangement maximizes the annual energy produced. It is this final arrangement that maximizes the energy produced that we retain and which becomes the final arrangement. We can then build the wind turbines in the planned positions according to the final arrangement in the physical site of the predetermined space to obtain a wind farm. Step f) of determining the final arrangement of the wind turbines in the predetermined space and building the farm

[0169] From each final arrangement of wind turbines obtained on each grid, 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 efficiency. The final arrangement of the wind turbines on the farm is then determined to correspond to this optimal final arrangement.

[0170] 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.

[0171] In the previous method, steps a) to f) (except for the part of step f) concerning the construction of the wind farm) can be implemented by a computer, a server or a supercomputer. Steps a) to f) then constitute a method for positioning the wind turbines in a predetermined space.

[0172] The invention may also relate to a computer program product implementing the method for positioning wind turbines in a predetermined space, consisting of steps a) to f) (apart from the part of step f) relating to the construction of the wind farm) 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 positioning method according to one of the preceding characteristics, when the program is executed on a computer or on a mobile phone. Indeed, the positioning method described above is particularly suitable for being implemented on computer means.It can therefore be implemented simply and results can be obtained quickly.

[0173] The invention also relates to a wind farm obtained from the method of constructing a wind farm as described above. This farm allows good energy efficiency by taking into account the statistical data of the wind on the site considered and by taking into account alignment constraints for the construction of the farm. Figure 7 illustrates in a schematic and non-limiting manner an example of creating a grid in a predetermined space.

[0174] The predetermined space Esp comprises two non-connected and non-convex zones Z1 and Z2. In order to obtain a grid defined by the first pair of first and second spacings R1 and R2 and by the second pair of first and second directions 01 and 02, the space is divided by first lines L1 and by second lines L2. The first lines L1 are parallel to each other and regularly spaced apart from said second spacing R2 along the second lines L2 and the second lines L2 are parallel to each other and regularly spaced apart from said first spacing R1 along the first lines L1. In addition, the first lines L1 are oriented along a first direction forming an angle 01 with the direction E of the reference frame (01, N, E) which is an arbitrarily defined reference frame, for example, 01 is a chosen geographical point, N is the North direction and E the East direction.The second lines L2 are oriented in a second direction forming an angle 02 with the direction E of the same reference frame (01, N, E). The angles 01 and 02 are chosen such that the first lines L1 intersect the second lines L2.

[0175] One of the first lines L1 and one of the second lines L2 can be positioned arbitrarily in space and then serve as a reference for the positions of the other first lines L1 and second lines L2.

[0176] The intersection points, represented by crosses, located in the predetermined space Esp (or on the border of this space) constitute the grid. Meshes such as represented by the hatched mesh M1, can be formed between the intersection points. It can be noted that the only intersection point located in the zone Z2 is part of the grid, even if it is not linked to a mesh since it is not connected to another intersection point to which it could be connected by a mesh.

[0177] The grid intersection points are points where wind turbines can potentially be positioned within the predetermined space Esp.

[0178] Figure 8 illustrates, in a schematic and non-limiting manner, a first arrangement obtained by the method according to the invention for positioning sixteen wind turbines in the predetermined space Esp, the same space as that of Figure 7, and on the grid obtained in Figure 7.

[0179] In this figure, the references identical to those in figure 7 correspond to the same elements and will not be detailed again. The crosses representing the intersection points in figure 7 have not been shown in figure 8 to facilitate reading. The black dots represent the positions of the sixteen wind turbines of the first arrangement in the predetermined space, each wind turbine being positioned on an intersection point of the grid in figure 7. This first arrangement corresponds to that obtained for the grid in figure 7 following step d) of the method according to the invention.

[0180] Figure 9 illustrates, in a schematic and non-limiting manner, a final arrangement obtained by the method according to the invention for repositioning the sixteen wind turbines following the first arrangement obtained in Figure 8 in the predetermined space Esp, the same space as that of Figure 7, and on the grid obtained in Figure 7.

[0181] In this figure, the references identical to those in figures 7 or 8 correspond to the same elements and will not be detailed again. The crosses representing the intersection points in figure 7 have not been shown in figure 9 to facilitate reading. The black dots represent the positions of the sixteen wind turbines in the final arrangement at the end of steps e1) and e2) in the predetermined space, each wind turbine being positioned at an intersection point in the grid in figure 7.

[0182] Examples

[0183] Figure 10 illustrates an example of searching for wind turbine positions in a predetermined space Z2 which is a non-convex space.

[0184] In this example, we seek to position twelve wind turbines in the predetermined space Z2, taking into account constraints of alignment of the wind turbines in two non-collinear directions.

[0185] The 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 turbines in the predetermined space Z2 is greater than 4 times the rotor diameter of the turbines.

[0186] 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

[0187] Diagrams a) to h) represent different positions of the wind turbines in this predetermined space Z2, from different grids in this predetermined space Z2. For this example, different grids were tested with the following characteristics:

[0188] - The angle of the direction of the first lines L1 relative to the reference R varies from 1° to 359° in steps of 1°,

[0189] - The angle of the direction of the second lines L2 relative to the reference R varies from 0° to the angle of the direction of the first lines L1 -1° in steps of 1°, The first spacing R1 of the first lines L1 along the second lines L2 varies from 4 times the diameter of the rotors to 8 times the diameter of the rotors in steps of 0.25 times the diameter of the rotors and;

[0190] The second spacing R2 of the second lines L2 along the first lines L1 varies from 4 times the rotor diameter to 8 times the rotor diameter in steps of 0.25 times the rotor diameter.

[0191] Diagrams a) to h) represent only a few of the grids tested.

[0192] For the different diagrams in figure 10:

[0193] The "round" points represent possible positions where wind turbines can be placed on the grid. They are therefore at the intersections of the first lines L1 and the second lines L2 of the grid in the predetermined space Z2;

[0194] The crosses represent the positions of the wind turbines allowing to maximize the recovery of energy on the grid considered;

[0195] The dotted lines represent the direction of the first L1 lines or the second L2 lines;

[0196] - The dashed lines represent a reference R which is used for the position of the first lines. For example, R can be a line representing the West-East direction.

[0197] - R1 spacings represent the spacing of the first L1 lines along the second L2 lines;

[0198] - The R2 spacings represent the spacing of the second L2 lines along the first L1 lines.

[0199] The first directions 01 1 , 012, and 013 represent the directions of the first lines L1 relative to the reference R.

[0200] Thus, in each of the diagrams shown in Figure 10, a different grid is used in the same predetermined space Z2.

[0201] For diagrams b), c), d) and e), the first lines L1 are parallel to the lines L1 shown in diagram b).

[0202] For diagrams f), g) and h), the first lines L1 are parallel to the lines L1 shown in diagram f).

[0203] Depending on the different grids used, the optimal positions of the wind turbines on each grid are different. The average annual energy recovered for each positioning scheme a) to h) varies between 486611 MWh and 487467.6 MWh, i.e. a gain of 856.6 MWh for the optimal configuration according to the invention.

Claims

Claims 1. Method for constructing a wind farm in a predetermined space (Esp), the wind farm being composed of a predefined number of wind turbines, the construction method comprising 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), for which at least the following successive steps are carried out: a) For different pairs (C1) of first and second predefined spacings (R1, R2), and for different pairs (C2) of first and second predefined directions (01, 02), grids (GR) are formed in the predetermined space (Esp),each 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 apart from said second predefined spacing (R2) along the second predefined direction (02) and the second lines (L2) being spaced apart from said first predefined spacing (R1) along the first predefined direction (01), the grid comprising at least one mesh (M1) delimited by intersection points. b) For each 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 grid is determined, from said first discrete wind speed distribution (RD1),of said second discrete wind direction distribution (RD2) and of said probability of occurrence (Prob); c) For each pair (C1) of first and second predefined spacings (R1, R2), at least one pair (C2) of first and second predefined directions (01, 02) is associated which maximizes the annual energy production of said mini-farm, d) For each grid corresponding to a pair (C1) of first and second predefined spacings (R1, R2) and to a pair (C2) of first and second predefined directions (01, 02) associated with step c), a first arrangement (Alg1) of the predefined number of wind turbines is determined, each wind turbine being positioned on one of said points of intersection of the grid by a first positioning algorithm;, e) then, for each grid used in step d), the position of the wind turbines is modified in order to improve the annual energy production 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; f) a final arrangement (Disp_F) of the wind turbines in the predetermined space (Esp) is determined, said final arrangement (Disp_F) corresponding to the final arrangement obtained in step e) of the grid which maximizes the annual energy production, and the wind farm is constructed (Const) by erecting the wind turbines at the positions of said final arrangement (Disp_F) in the predetermined space (Esp) so as to generate energy from the wind. Method for constructing a wind farm according to claim 1, for which, in step e) of modifying the position of the wind turbines for each grid used in step d),at least the following steps are carried out: e1) for each grid used in step d), a sequential order (OS) for modifying 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 point of intersection of the 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 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. method of constructing a wind farm according to claim 2,for which said sequential order (OS) is obtained randomly. Method for constructing a wind farm according to claim 2 or 3, for which the sequential order (OS) is modified at each iteration of step e1). Method for constructing a wind farm according to one of the preceding claims, for which, before step a), 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, Method for constructing a wind farm according to one of the preceding claims, for which said predetermined space (Esp) comprises non-connected (Z1, Z2) and / or non-convex (Z2) zones. Method for constructing a wind farm according to one of the preceding claims, for which, for each grid considered, said first positioning algorithm 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 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 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 grid considered in said predetermined space (Esp). method of constructing a wind farm according to one of the preceding claims, for 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 of the mini-farm. e wind turbine obtained from the method of constructing a wind farm according to one of the preceding claims 1 to 8.

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