METHOD FOR CONSTRUCTING A WIND PARK IN A PREDEFINED SPACE

Description

Domaine technique

[0001] The present invention relates to a method of constructing a wind farm in a predetermined space.

[0002] To address environmental challenges, 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. We thus distinguish between onshore wind farms and offshore wind farms, that is, those located at sea.

[0003] The wind turbines in these farms are generally horizontal axis turbines equipped with a system to orient the horizontal axis of rotation in the direction of the wind, in order to maximize the energy harvested by the turbine. Sometimes, the turbine is designed to automatically orient itself in the direction of the wind.

[0004] We also know of vertical axis wind turbines, which have the advantage of not requiring orientation in the direction of the wind.

[0005] In wind farms, the wakes generated by the turbines can reduce wind speeds downstream of the turbine, thus decreasing the energy captured by other turbines, particularly those located downstream of the turbines generating these wakes. The positioning of the turbines within the farm is therefore crucial to maximizing the energy harvested.

[0006] Furthermore, in a chosen location for a wind farm, local wind characteristics can vary. Indeed, wind direction and speed are parameters that can change over time at the given location. These characteristics can be obtained using sensors positioned at the defined location and maintained there for several months or years to obtain sufficient statistical data to characterize the wind resource at the chosen site. These sensors can include anemometers positioned at a sufficient altitude (approximately 100 meters above ground level) to characterize the wind that will be perceived by the wind turbines (i.e., the wind that is roughly at the level of the rotor axis, for example). Wind data can also be obtained through laser remote sensing, also known as LiDAR (Light Detection and Ranging).

[0007] Statistical knowledge of the wind at the location of the farm allows us to obtain the wind speed distribution (also referred to hereafter as "wind speed distribution"), the wind direction distribution (also referred to hereafter as "wind direction distribution") and the joint probability of occurrence of a wind speed in a given direction.

[0008] 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.

[0009] The term "annual energy produced" or "annual energy production" refers to the total average energy produced by the wind farm, meaning by all the wind turbines on the farm. This average energy, estimated using statistical wind data (wind speed distribution, wind direction, and probability of occurrence), is based on a one-year period, hence the term "annual," to avoid seasonal influences that could skew the results. Indeed, wind speed and direction can vary significantly depending on the season.

[0010] The average energy is obtained through knowledge of 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. Technique antérieure

[0012] To determine a good positioning of the wind turbines in the planned location for the farm, several methods have been developed.

[0013] Patent application CN105119320 relates to a method based on an evolution 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 computation time and necessitates substantial computer memory.

[0014] 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 numerous evaluations and cross-referencing of these evaluations using real-world (continuous) data. Consequently, genetic algorithms are complex and therefore require significant computation time and memory.

[0015] The methods described in the following documents are also known: “Wind farm layout optimization with a three-dimensional Gaussian Wake model,” Tao et al., Renewable Energy, June 9, 2020: This method requires that the planned location for the wind farm be bounded by a rectangle. In other words, this method is not suitable for wind farms containing non-convex or even non-connected spaces. “Continuous adjoint formulation for wind farm layout optimization,” Antonini et al., Applied Energy, July 25, 2018: This method is based on an analytical method for evaluating wake effects. This method is therefore a continuous optimization method, based on CFD (Computational Fluid Dynamics) calculations, which requires significant computation time and computer memory."A fast and effective local search algorithm for optimizing the placement of wind turbines," Wagner et al., Renewable Energy, October 10, 2012: Applying this method requires locations delimited by a rectangle. Therefore, it is not suitable for locations with non-connected or non-connected shapes. "Solving the wind farm layout optimization problem using random search," Feng & Shen, Renewable Energy, January 20, 2015: This method requires locations delimited by polyhedra. Therefore, it is not suitable for locations with non-connected shapes. "Greedy robust wind farm layout optimization with feasibility guarantee," Quan and Kim, Engineering Optimization, September 6, 2018: This method is based on a greedy algorithm that considers all positions located within a minimum distance of the wind turbines already positioned in the location to determine the location of the next wind turbine.It therefore requires significant computation 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.

[0016] Thus, the technical problem that the invention proposes to solve consists of developing a method of 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, and minimizing the computation time required and computer memory. Résumé de l'invention

[0017] To this end, the invention relates to a method for constructing a wind turbine farm (or simply a wind farm) from a predetermined number of wind turbines in a predetermined space. The construction method comprises a first discrete distribution of wind speed, a second discrete distribution of wind direction, and a probability of occurrence for each wind speed value and each wind direction value in said first and second discrete distributions. Furthermore, the predetermined space is divided into a first discrete mesh. The method comprises at least the following successive steps: a) A first arrangement of wind turbines is determined in the first discrete mesh of the space predetermined by a first positioning algorithm; b) A sequential order for modifying the positions of the wind turbines determined by the first positioning algorithm is defined, then at least the following steps are carried out iteratively, for at least one wind turbine to be repositioned, one by one, in the defined sequential order: b1) For each wind turbine to be repositioned, new possible discrete positions of the wind turbine are determined. b2) The average annual energy production of the predetermined number of wind turbines is calculated for each possible discrete position of the wind turbine to be repositioned, based on the first discrete distribution of wind speed, the second discrete distribution of wind direction, and the probability of occurrence.b3) The position of the wind turbine to be repositioned corresponding to the calculated maximum value of annual energy production is chosen and the wind turbine to be repositioned is placed there; b4) A new arrangement of the wind turbines is defined in the predetermined space corresponding to the arrangement where only the wind turbine to be repositioned has been moved according to state b3; c) A final arrangement corresponding to the last arrangement obtained is determined.

[0018] Then, the wind turbine farm is constructed by erecting (installing / building) the wind turbines (the predetermined number of wind turbines) at the predetermined positions of the final arrangement on the predetermined physical site in such a way as to produce energy, for example, electricity, from the wind. The invention also relates to a computer program product implementing the method defined above, as well as to a wind farm obtained using the method defined above.

[0019] The invention relates to a method for constructing a wind farm, the method of constructing a wind farm 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, said predetermined space being divided into a first discrete mesh. In this method, at least the following successive steps are performed: a) A first arrangement of said wind turbines is determined in the first discrete mesh of said space predetermined by a first positioning algorithm; b) A sequential order for modifying the positions of the wind turbines determined by the first positioning algorithm is defined, then at least the following steps are carried out iteratively, for at least one wind turbine to be repositioned, one by one, in the defined sequential order: b1) For each wind turbine to be repositioned, new possible discrete positions of the wind turbine to be repositioned are determined by establishing a grid of at least a first predefined length, the grid being centered on the position of the wind turbine to be repositioned, the grid being divided into a predetermined number of cells, said new possible discrete positions comprising the points of intersection of the cells,the intersection points of the grid cells being positioned within said predetermined space and at a minimum distance from the positions of the other wind turbines. b2) The average annual energy production of the predetermined number of wind turbines is calculated for each possible discrete position of the wind turbine to be repositioned, based on said first discrete wind speed distribution, said second discrete wind direction distribution, and said probability of occurrence. b3) The position of the wind turbine to be repositioned corresponding to the maximum calculated value of annual energy production calculated in step b2 is chosen. b4) A new arrangement of the wind turbines is defined within said predetermined space.(c) A final arrangement corresponding to the last arrangement obtained is determined, and said wind farm is constructed by erecting the predetermined number of wind turbines at the determined positions of the final arrangement in the predetermined physical site of space so as to produce electricity from the wind,

[0020] According to one implementation of the invention, prior to step a), statistical wind data is collected, by means of collection, 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.

[0021] According to a configuration, the said predetermined space is in two dimensions.

[0022] Preferably, said sequential order is obtained randomly.

[0023] Preferably, step b) is repeated several times, preferably changing the sequential order at each iteration.

[0024] Preferably, for each iteration of step b), we choose a first predefined length less than the first predefined length of the previous iteration, said pre-established number being the same from one iteration to the next and we stop the iteration of step b) when the first predefined length becomes less than a first threshold.

[0025] According to one implementation of the invention, said predetermined space comprises non-connected areas.

[0026] According to one variant of the invention, said predetermined space comprises non-convex areas.

[0027] Advantageously, said first positioning algorithm performs at least the following steps: The position of the first wind turbine is arbitrarily defined; then, for each wind turbine to be positioned, successively: potential positions are defined in the first discrete mesh for the wind turbine to be positioned, these potential positions comprising the discrete positions of the first discrete mesh located between a minimum distance and a maximum distance from all the positioned wind turbines and / or the discrete positions of the boundary of the predetermined space located at the said minimum distance from all the positioned wind turbines. The annual energy production of the positioned wind turbines and the wind turbine to be positioned is calculated for the defined potential positions, based on the first discrete wind speed distribution, the second discrete wind direction distribution, and the probability of occurrence.The position of the wind turbine to be positioned corresponding to the calculated maximum value of annual energy production is chosen; the first arrangement corresponding to the position of the predetermined number of wind turbines in the predetermined space is then determined.

[0028] According to one embodiment of the invention, the arbitrary position corresponds to the largest sum of the coordinates of the positions of said first discrete mesh.

[0029] The invention also relates to a computer program product implementing the method described above using computer means.

[0030] Furthermore, the invention also relates to a wind farm obtained from the method of constructing a wind farm as described above. Liste des figures

[0031] Other features and advantages of the method and systems according to the invention will become apparent from the following description of non-limiting examples of implementations, with reference to the figures attached and described below. There figure 1 represents an overview of the different stages of positioning methods according to the invention. figure 2 represents a detailed view of the various stages of a first method for constructing a wind farm according to the invention. figure 3 represents a detailed view of the various stages of a second method for constructing a wind farm according to the invention. figure 4 illustrates an example of a complex location for positioning wind turbines according to the invention. figure 5 illustrates a variant of a first positioning algorithm according to the invention. figure 6 illustrates a first example of the application of a first positioning algorithm according to the invention. figure 7 illustrates a second example of the application of a first positioning algorithm according to the invention. figure 8 illustrates an example of the local search process for repositioning a wind turbine on the farm according to the invention. figure 9 illustrates different stages of the local search process for repositioning a wind turbine on the farm according to the invention. figure 10 illustrates different stages of the method for constructing a wind farm in a complex location that includes non-connected areas and a non-convex area. figure 11 illustrates a variant of the method for constructing a wind farm for the same complex location as that of the figure 10 . Description des modes de réalisation

[0032] To make this description easier to read, some definitions are explained below.

[0033] A "greedy algorithm" is an algorithm that establishes a local optimum step by step. In the case of a wind farm, this involves positioning each turbine one after the other until all the turbines are positioned within the predetermined space.

[0034] 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.

[0035] A "genetic algorithm" is an evolutionary algorithm that uses the concept of natural selection. This type of algorithm can, in particular, combine or modify certain parameters of previous solutions in order to improve results.

[0036] Areas in which there are at least two points that cannot be connected by a continuous path entirely contained within the area are called "non-connected areas." Conversely, a connected area is one in which every pair of points is connected by a continuous path entirely contained within the area.

[0037] A "convex area" is an area in which the line segments connecting any two points within that area are all entirely contained within the area. A circle, a square, or a rectangle, for example, all define convex areas.

[0038] 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 bounded by a concentric outer circle and inner circle is not convex.

[0039] The invention relates to a method for positioning a predetermined number of wind turbines in a predetermined space, or alternatively, a method for constructing a wind turbine farm. The method for positioning or constructing a wind farm comprises a first discrete distribution of wind speed, a second discrete distribution of wind direction, and a probability of occurrence of each discrete wind speed value within each discrete wind direction value of said first and second discrete distributions. The predetermined space is divided into a first discrete mesh. By discrete mesh, it is understood that the predetermined space is divided into pieces, for example, rectangular or square, and the discrete mesh consists of the points defined by this mesh.For example, the first discrete mesh can be made up of the points delimiting the pieces (the four points of each rectangular or square piece for example), and / or of the points of intersection of the pieces, and / or of the centers of the meshes (for example the center of the square or rectangular pieces).

[0040] Using discrete values ​​for wind speed, wind direction, and the discrete points of the first discrete mesh of the predetermined space simplifies the method, accelerates computation time, and reduces the required computer memory compared to methods using continuous real-world data. Discrete values ​​limit the number of possible combinations (a combinatorial method), whereas continuous real-world data (a continuous method) provides an infinite number of solutions. Combining the first and second discrete distributions with the first discrete mesh thus allows for accurate positioning of the different wind turbines within the predetermined space while minimizing the computation time required to determine their positions.

[0041] The probability of occurrence of each wind speed, in each wind direction, is used, in particular, to calculate the average annual energy production. This probability can be derived from a wind rose corresponding to the predetermined area, a wind rose being well known to those skilled in the art. To establish this wind rose, one can use methods for collecting wind speed and direction data, such as an anemometer positioned on a mast at a sufficient altitude (between 80m and 120m, for example, to be roughly at the level of the wind turbine hub), or via a LiDAR sensor (an acronym for "Light Detection and Ranging"), positioned close to the ground and oriented vertically.This data collection method is maintained in place for an extended period, several months and ideally more than a year, to account for seasonal variations in wind characteristics. In other words, the method may include a step in which a data collection device, such as an aneometer, a measuring mast, or, more advantageously, a LiDAR (Light Detection and Ranging) sensor, or any similar device, is deployed for a predetermined duration at the predetermined physical location to collect wind data at that site. The predetermined data collection period can be at least one year to obtain data for all four seasons. Thus, a data collection step for statistical wind data in the predetermined area using at least one data collection device can be planned.

[0042] This method involves at least the following successive steps: a) A first arrangement of wind turbines is determined within the first discrete grid of the predetermined space by a first positioning algorithm. Preferably, this first positioning algorithm can be an optimization algorithm that yields a first distribution resulting in a high annual energy output. Advantageously,This first positioning algorithm can be a greedy algorithm that positions each wind turbine one after the other in order to maximize the annual energy produced. The first wind turbine can be positioned arbitrarily within the predetermined space (at a discrete value on the first discrete grid). The second wind turbine will be positioned at the discrete position on the first discrete grid that maximizes the annual energy produced by both turbines. The position chosen for the nth wind turbine corresponds to the discrete position on the first discrete grid that maximizes the annual energy produced by the n turbines. Using a greedy algorithm allows for a simple initial arrangement of the wind turbines within the predetermined space.This allows us to initialize the local optimization search process of step b) below. b) We define a sequential order for modifying the positions of the wind turbines determined by the first positioning algorithm, then we perform at least the following steps, iteratively, for at least one wind turbine to be repositioned (preferably, for all the wind turbines in the predefined number of wind turbines), one by one, in the defined sequential order: b1) we determine, for each wind turbine to be repositioned, new possible discrete positions of the wind turbine to be repositioned, by establishing a grid of at least a first predefined length (for example, the grid can be a first square whose first predefined length corresponds to the side of the first square), the grid being centered on the position of the wind turbine to be repositioned (the position of the wind turbine to be repositioned then corresponds to the center of the first square, for example),The grid is divided into a predetermined number of cells (the cells could be, for example, second squares). The new possible discrete positions include the intersection points of the cells (second squares, for example) positioned within the predetermined space and at a minimum distance from the positions of the other wind turbines. In other words, the goal here is to find positions in the vicinity of the wind turbine to be repositioned where it could be installed. Therefore, we eliminate from these positions those that are too close to the other wind turbines and those that are outside the predetermined space (outside the area planned for the installation of the wind turbines). Using the grid (the first square, for example) allows us to globally delimit the neighborhood of the wind turbine to be repositioned, and then dividing the grid (the first square, for example) into cells allows us to obtain discrete positions within this neighborhood.rather than using continuous real positions, which would unnecessarily increase computation time and computer memory. Furthermore, this method allows for more precise local accuracy in repositioning the wind turbines than the positioning obtained in the first arrangement based on the first discrete mesh, since the mesh discretization can advantageously be finer than that of the first discrete mesh. Preferably, the minimum distance is greater than twice the diameter of the wind turbine rotor, and preferably, greater than four times the diameter of the wind turbine rotor; b2) The average annual energy production of the predefined number of wind turbines is calculated for each possible discrete position of the turbine to be repositioned, based on the first discrete wind speed distribution, the second discrete wind direction distribution, and the probability of occurrence. Of course,To calculate the annual energy production, the wind turbine characteristics are needed, including the rotor sweep area and the power coefficient. This annual energy production also takes into account the wake effects produced by the wind turbines, which can induce power losses for downstream or adjacent turbines. b3) The (discrete) position of the wind turbine to be repositioned is chosen, corresponding to the maximum calculated value of annual energy production determined in step b2). b4) A new arrangement of the wind turbines is defined within the predetermined space. This new arrangement includes the modified positions of the turbines that have been repositioned and those of the turbines to be repositioned. c) A final position corresponding to the last arrangement obtained is determined, and once the final arrangement is determined,Wind turbines are constructed according to the final arrangement in the predetermined space (the physical site of the predetermined space) in order to obtain a wind farm to generate energy from the wind (in other words, a wind farm is constructed by installing the wind turbines in the positions of the final arrangement in the predetermined space, i.e., the physical site of the predetermined space, said wind farm being determined to generate energy, for example electricity, from the wind).

[0043] In other words, step b) constitutes a local search optimization method based on discrete values ​​around the original position of the wind turbine to be repositioned. Indeed, starting from the initial arrangement obtained in step b), the position of the wind turbines is modified one by one by locally searching around the original position for discrete positions where the turbine could be placed (i.e., excluding discrete positions located closer than another wind turbine and those located outside the predetermined boundary or area). The local search optimization then consists of evaluating the annual energy produced for each new possible arrangement, that is, keeping the positions of all the wind turbines other than the one to be repositioned and taking into account each possible discrete position of the turbine to be repositioned. The selected position is the one that maximizes the annual energy produced.Once a position is determined, this position is maintained for subsequent wind turbine repositioning. In other words, for each subsequent modification of the wind turbine positions, a new arrangement is used, based on the positions of the turbines that have already been modified.

[0044] Step c) enables the construction of a wind farm with optimization of the positioning of the wind turbines to maximize the total energy recovered by the wind turbines.

[0045] Thus, the method of positioning wind turbines or constructing a wind farm in a predetermined space of the invention uses an optimization based on a purely combinatorial approach.

[0046] Steps a) and b) are implemented by computer means, including a computer, a mobile phone or a tablet.

[0047] According to one embodiment, the annual energy production can be estimated using the following formula: aep = 8760 ⋅ E w s , w p P f w s w s

[0048] Where aep is the annual energy production of the wind farm and E ws,wp { P ( f, w s , w p )} is the expected total power produced by the wind farm (by the predetermined number of wind turbines in the predetermined space) for each wind speed ws and each wind direction wp. Therefore, the total power produced by the farm takes into account a statistical distribution of each wind speed ws in each wind direction wp, for example by a Weibull distribution.

[0049] In the case where the wind turbine rotors are systematically oriented in a plane orthogonal to the wind direction wp, the total power produced by the farm can be written as: P f w s w p = ∑ f = 1 N P f w s w p

[0050] Where N is the predetermined number of wind turbines in the farm within the predetermined space, Pf is the instantaneous power supplied by each wind turbine f, in the farm, for each wind speed ws in each wind direction wp.

[0051] In cases where some wind turbine rotors are located in a plane that is offset from the plane perpendicular to the wind direction wp (in other words, the turbine is not oriented directly into the wind but is offset from it), a correction factor can be applied to account for the effect of this offset. This correction factor can be derived from CFD (Computational Fluid Dynamics) simulations.

[0052] The instantaneous power Pf of each wind turbine f in the farm can be written as: P f w s w p = 1 2 ⋅ ρ ⋅ S ⋅ v f 3 w s ⋅ C pf v f w s

[0053] With ρ being the air density, S being the area swept by the rotor of the wind turbine f, vf (ws ) the wind speed at the rotor of the wind turbine f and the power coefficient C pf of the wind turbine f depending on the speed vf (ws ) of the wind at the rotor of the wind turbine f, the power coefficient C pf being a characteristic of the wind turbine f.

[0054] 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 mean that the wind speed vf at the turbine rotor no longer corresponds to the wind speed ws, and the power coefficient C pf is therefore also affected.

[0055] The impacts of wake effects considered in equation [Math3] can be based on wake models. These wake models can, in particular, represent: a reduction in wind speed upstream of wind turbine f due to the wake from an upstream wind turbine. Such a model, well known to those skilled in the art, is the Jensen wake model (described in the publication "A simple model for Cluster Efficiency", Katic, Hojstrup and Jensen, EWEC 1986, particularly in section 2.1 of this publication), an increase in wind turbulence intensity, and / or a superposition of wakes from several upstream wind turbines 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 wind speed reduction, as in the previously cited publication, and / or increased wind turbulence intensity from several wakes.

[0056] Wake patterns can also be determined from CFD calculations (from the English "Computational Fluid Dynamics" meaning "Fluid Dynamics Calculations").

[0057] Preferably, the defined sequential order differs from the order in which the wind turbines were positioned to obtain the initial arrangement, for example, using a greedy algorithm. This improves the optimization accuracy. Step b) involves a second algorithm to optimize the position of each wind turbine within the predetermined space.

[0058] c) A final arrangement is determined, corresponding to the last arrangement obtained. The final arrangement therefore corresponds to the positions of the wind turbines once they have all been repositioned in step b). It thus represents an optimization of the first arrangement in order to improve the annual energy produced by the predetermined number of wind turbines in the predetermined space.

[0059] Once the final layout is determined, the wind turbines can then be constructed according to this layout within the predetermined space to create a wind farm. The resulting wind farm maximizes the total energy produced and recovered from the wind within the physical space of the predetermined area.

[0060] Advantageously, the predetermined space can be two-dimensional. This eliminates the need to consider the ground's elevation relative to sea level. In other words, variations in ground level are disregarded when positioning wind turbines. This simplifies calculations while still ensuring sufficient accuracy.

[0061] Preferably, the sequential order can be obtained randomly. Indeed, using a random function for the sequential order improves the quality of the optimization by avoiding optimization paths based on pre-established orders, as these paths can bias the optimization results.

[0062] According to one embodiment of the invention, the predetermined number can be a multiple of the square of an integer (preferably, four times the multiple of the square of an integer). Therefore, the discrete position of the wind turbine to be repositioned lies on one of the possible discrete positions to be re-evaluated. Indeed, by using four times the multiple of the square of an integer, the grid can be discretized in two dimensions by having a first line (for example, vertical) of intersection of the cells corresponding to a first axis of symmetry of the grid (of the first square, for example) and a second line (for example, horizontal) of intersection of the cells corresponding to a second axis of symmetry of the grid.

[0063] Therefore, the pre-established number can take the following values: 4, 16, 25, 64, 100 etc.

[0064] According to a preferred configuration of the invention, step b) can be repeated several times. Thus, several local search optimization loops for repositioning wind turbines are performed, which further improves the annual energy produced.

[0065] Preferably, for each iteration of step b), the sequential order of changes to the wind turbine positions can be modified. This improves the local search for repositioning. When the sequential order is obtained randomly each time, the influence of multiple optimization paths (by optimization path, we mean the incremental optimization of the repositioning, which is influenced by the defined sequential order) on each other is avoided. Consequently, the annual energy production can be increased.

[0066] According to an advantageous embodiment of the invention, for each iteration of step b), a first predefined length can be chosen that is shorter than the first predefined length of the previous iteration, the predetermined number being the same from one iteration to the next. The iteration of step b) can be stopped when the first predefined length falls below a first threshold. Therefore, at each iteration of step b), the local neighborhood in which the position of the wind turbine to be repositioned is being improved is reduced compared to the preceding iteration. Furthermore, since the predetermined number is invariant from one iteration to the next, the discretization of the neighborhood becomes increasingly refined from one iteration to the next. Consequently, the accuracy of the wind turbine's position is gradually improved.Defining the first threshold allows the iterations to stop at a level of positional accuracy sufficient for implementation but which would no longer provide a significant gain in annual energy production (or a gain that would fall within the uncertainty range of the calculations). For example, the first threshold could be between 1m and 10m, preferably between 4m and 6m, in order to obtain a good compromise between computation time, computer memory used, positional accuracy, and the gain in annual energy production.

[0067] Advantageously, the predetermined space can include non-connected areas. Therefore, the predetermined space can 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.

[0068] Preferably, the predetermined area may include non-convex zones. Thus, the predetermined area may correspond to real locations of complex shapes, such as an area bounded by a hill or steep cliff, the coastline, a river crossing, a stream, or any other body of water. In offshore areas, the predetermined area may include non-convex zones, which can be determined by taking into account bathymetry, seabed characteristics, borders with other countries, shipping channels, cable or pipeline crossings, for example.

[0069] According to one embodiment of the invention, the first positioning algorithm can perform at least the following steps: The position of the first wind turbine is arbitrarily defined. Thus, the position of the first wind turbine is chosen within a discrete value of the first discrete mesh. Then, for each wind turbine to be positioned, successively (one by one): potential positions of the first discrete mesh are defined for the wind turbine to be positioned. These potential positions include the discrete positions of the first discrete mesh located between a minimum and a maximum distance (for example, the maximum distance is at least four times the diameter of the wind turbines and preferably at least eight times the diameter of the wind turbines) from all the positioned wind turbines and / or the discrete positions of the boundary of the predetermined space located at a minimum distance from all the positioned wind turbines. In other words, positions of the first discrete mesh are selected where the next wind turbine would be advantageously positioned.Therefore, the number of calculations and the computer memory required to define the chosen position are limited, thus accelerating the calculations. Furthermore, when discrete values ​​are chosen for positions between a minimum and maximum distance from the already positioned wind turbines, the chances of placing the maximum number of turbines within the predetermined space are improved. By placing the most turbines within the predetermined space, the annual energy production can be increased. Choosing to position the turbines evenly along the entire boundary located at a minimum distance from the already positioned turbines allows for the virtual use of a larger area than if the turbines were placed strictly within the boundary. By using a larger area, more energy can be produced.The annual energy production of the wind farm is calculated based on the existing wind turbine positions and the various potential positions defined for the turbine to be positioned. Therefore, an annual energy production value is associated with each defined potential position. Furthermore, the calculation of annual energy production takes into account the first discrete wind speed distribution, the second discrete wind direction distribution, and the probability of occurrence. This calculation also incorporates known characteristics of the wind turbines, namely the area swept by the turbine rotor, the drag coefficient, and / or the power coefficient. The position of the turbine to be positioned is chosen that corresponds to the maximum calculated annual energy production value from the previous step. Thus, the annual energy produced by the wind turbines whose positions are defined within the predetermined space is maximized.These defined positions will serve as a basis for determining the position of the next wind turbine, in particular for defining the potential positions of the first discrete grid. The first arrangement corresponding to the position of the predetermined number of wind turbines in the predetermined space is determined once all the wind turbines have been positioned.

[0070] Therefore, the first positioning algorithm is a greedy algorithm that includes an arbitrary positioning step for the first wind turbine, then iteratively positions an additional wind turbine in a chosen area of ​​the predetermined space until all the predetermined number of wind turbines are positioned within the predetermined space. This greedy algorithm, thanks to the potential position selection step, accelerates computation time while positioning the wind turbines judiciously. Such an algorithm allows for an initial layout suitable for step b) of local optimization of each wind turbine's positioning.

[0071] According to one embodiment of the invention, the arbitrary position can correspond to the largest sum of the coordinates of the positions in the first discrete mesh. Thus, the wind turbine is positioned at one end of the predetermined space. This choice allows for the placement of more wind turbines within the predetermined space, thereby offering more potential choices for the positions of the predefined number of turbines. Consequently, there is greater flexibility in optimizing the annual energy produced by the wind farm.

[0072] The invention also relates to a computer program product implementing the method as described above using computing resources, such as a computer, mobile phone, or tablet. The computer program product can be downloaded from a communication network and / or stored on a computer-readable medium and / or executable by a processor or server, comprising program code instructions for implementing the method according to one of the preceding characteristics, when the program is executed on a computer or mobile phone. Indeed, the method described above is particularly well-suited for implementation using computing resources. It can thus be implemented simply, and results can be obtained quickly.

[0073] Furthermore, the invention relates to a wind farm obtained using the method of positioning a predetermined number of wind turbines in a predetermined space (or constructing a wind farm) as described above. Indeed, once the positioning of the wind turbines is determined, the individual turbines can be physically constructed (or installed) at the positions determined by the method within the physical site of the predetermined space. This results in a wind farm with optimized total annual energy production.

[0074] There figure 1 illustrates, schematically and without limitation, an overall view of the method of positioning a predetermined number of wind turbines (or constructing a wind farm) in a predetermined space according to the invention.

[0075] This method includes, in particular, a first positioning algorithm, Alg1. This first positioning algorithm, Alg1, takes as input at least a first discrete distribution, RD1, of wind speeds, a second discrete distribution, RD2, of wind directions, and a first discrete mesh, RD3, of the predetermined space in which the predefined number of wind turbines and the probability of occurrence, Prob, of each wind speed in each wind direction can be placed. It can also use the characteristics of the wind turbines necessary to determine the annual energy produced. The wind data—speed, direction, and probability of occurrence of each speed value in each direction—can be obtained from data collection methods during a preliminary step. This data can be used, in particular, to establish a wind rose known to a person skilled in the art.

[0076] The first positioning algorithm, Alg1, determines an initial arrangement, Disp1, of the predefined number of wind turbines within the predetermined space. This initial arrangement, Disp1, can be improved but is of sufficient quality to allow for local optimizations in subsequent steps. This first positioning algorithm, Alg1, can be a greedy algorithm.

[0077] This first arrangement Disp1, obtained quickly using the greedy algorithm, is used as input data in a second algorithm Alg2. This second algorithm Alg2 is an optimization algorithm that modifies, one by one, the position of at least one wind turbine from the first arrangement Disp1, preferably modifying the position of all the wind turbines from the first arrangement Disp1, in order to increase the annual energy produced by the farm by testing different possible discrete positions of each wind turbine around its initial position (or its last defined position).

[0078] To determine the annual energy produced, the second algorithm uses in particular the first discrete distribution RD1 of wind speeds, the second discrete distribution RD2 of wind directions.

[0079] Once all the wind turbines have been repositioned, a final arrangement DispF is obtained, containing the predetermined number of turbines within the predetermined space. The turbines can then be positioned (built / installed / erected) Pos within the physical site corresponding to the predetermined space.

[0080] There figure 2 illustrates, schematically and without limitation, a detailed view of a first embodiment of the method of positioning a predetermined number of wind turbines (or constructing a wind farm) in a predetermined space according to the invention.

[0081] This method includes, in particular, a first positioning algorithm, Alg1. This first positioning algorithm, Alg1, takes as input at least a first discrete distribution, RD1, of wind speeds, a second discrete distribution, RD2, of wind directions, and a first discrete mesh, RD3, of the predetermined space in which the predefined number of wind turbines and the probability of occurrence, Prob, of each wind speed in each wind direction can be placed. It can also use the characteristics of the wind turbines necessary for determining the annual energy produced. Wake models are used to determine this annual energy production.

[0082] Wind data, including speed, direction, and the probability of occurrence of each speed value in each direction, can be obtained from collection methods during a preliminary stage. This data can then be used to create a wind rose familiar to a person skilled in the art.

[0083] The first positioning algorithm, Alg1, determines an initial arrangement, Disp1, of the predefined number of wind turbines within the predetermined space. This initial arrangement, Disp1, can be improved but is of sufficient quality to allow for local optimizations in subsequent steps. This first positioning algorithm, Alg1, can be a greedy algorithm.

[0084] This first arrangement Disp1, obtained quickly using the greedy algorithm, is used as input data in a second algorithm Alg2. This second algorithm Alg2 is an optimization algorithm that modifies, one by one, the position of the different wind turbines of the first arrangement Disp1, in order to increase the annual energy produced by the farm by testing different possible discrete positions of each wind turbine around its initial position.

[0085] In more detail, the second algorithm, Alg2, comprises the following steps: A sequential order OS is defined for modifying the positions of the wind turbines, one by one. This sequential order OS can be obtained, in particular, by a random function. Then, iteratively, the position of at least one wind turbine i is modified, preferably each wind turbine i, by performing the following substeps: * possible discrete positions PDP_i are determined for wind turbine i, these possible discrete positions PDP_i being located in the vicinity of the position of wind turbine i to be repositioned (the other wind turbines remaining in their position, either the initial position from the first arrangement, or the position already repositioned). For example, a certain perimeter can be defined around the position of the wind turbine to be repositioned (a grid with one or two predetermined lengths, a square with a side of a certain length, a circle of a certain diameter, etc.).Discrete positions are determined within this perimeter, for example, by dividing it into cells. These discrete positions can then be the centers of the cells, the intersections of the cells, and / or the points defining the cells. Discrete positions that are too close to other wind turbines are removed from this perimeter; in other words, those located less than a minimum required distance are removed. For example, the minimum required distance could be at least twice the diameter of the wind turbine rotor. Positions located outside the predetermined space are also removed from this perimeter. The annual energy produced for each possible arrangement is then evaluated (for each possible discrete position, PDP_i of wind turbine i to be repositioned, with the other wind turbines remaining in their last assigned positions).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, one annual energy produced corresponds to each possible discrete position PDP_i of wind turbine i to be repositioned. * The position Pos_i of wind turbine i is retained as the discrete possible position PDP_i that corresponds to the maximum value of the annual energy produced at the Eval_i step. * This results in 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 Pos_i of wind turbine i.

[0086] Loop B1 then allows F1 to select the next wind turbine in the defined sequential order (i becomes i+1) in order to perform the same procedure for the following wind turbines.

[0087] Once all the wind turbines have been repositioned, a final arrangement DispF is obtained, consisting of the predetermined number of turbines within the predetermined space. The turbines can then be positioned (i.e., physically constructed, installed, or erected) Pos within the physical site corresponding to the predetermined space.

[0088] There figure 3 illustrates, schematically and without limitation, a variant of the figure 2 The references are identical to those of the figure 2 correspond to the same elements and will not be detailed again.

[0089] There figure 3 differs from figure 2 by adding a second loop B2 in the second algorithm Alg2.

[0090] Indeed, once all the wind turbines have been repositioned by loop B1, the plan is to modify the position of these wind turbines several times. To do this, the steps of determining the sequential order OS and loop B1 are repeated several times for each wind turbine, one by one. Loop B1 includes, for each wind turbine i to be repositioned, the determination of the possible discrete positions PDP_i, the evaluation of the annual energy produced Eval_i for each possible discrete position, the choice of the position Pos_i of wind turbine i to be repositioned, and the definition of the new arrangement Disp_N.

[0091] By repeating these steps several times, the positions of the wind turbines within the predetermined space can be refined, thus improving the annual energy produced by the farm. Changing the sequential order each time (for example, by randomizing the order) can further improve the annual energy output.

[0092] Loop B2 can end, for example, when the annual energy gain compared to the previous iteration is less than a certain value, for example less than 0.5%.

[0093] Once the B2 loop is completed, the last Disp_N arrangement obtained becomes the final DispF arrangement and we can then position (build / erect / install) Pos the wind turbines in the positions planned according to the final DispF arrangement to obtain a wind farm.

[0094] There figure 4 illustrates, schematically and without limitation, an example of a predetermined space suitable for implementing the positioning method of the invention (or for constructing a wind farm of the invention).

[0095] The predetermined space may include a first zone Z1 and a second zone Z2, represented by the vertical hatching. These zones Z1 and Z2 are not connected. Indeed, a non-zero minimum distance D exists between the two zones Z1 and Z2. Furthermore, zone Z1 is rectangular, and therefore convex. Zone Z2 has a complex, non-convex shape. In fact, if we consider the two points A and B, we observe that a portion of the segment Seg connecting points A and B lies outside zone Z2.

[0096] To identify the zones Z1 and Z2 of the predetermined space within a larger third zone ZE, encompassing these two zones Z1 and Z2, a Boolean matrix can be used. The third zone ZE is rectangular, which is easier to process computationally than non-connected and / or non-convex zones like Z1 and Z2. The Boolean matrix associates each discrete value (discrete position) in the zone ZE with a value of 1 if the discrete position is located within zone Z1 or Z2, and a value of 0 if it is located outside Z1 and Z2. This Boolean matrix defines 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 part of the boundary if its value in the Boolean matrix is ​​1 and if it has at least one direct neighbor with a Boolean value of 0.

[0097] There figure 5 illustrates, in a schematic and non-limiting way, an example of a first positioning algorithm according to the invention.

[0098] This first positioning algorithm is a greedy algorithm.

[0099] From the first discrete mesh RD3 of the predetermined space, the position of the first wind turbine P_E1 is defined, for example in an arbitrary way.

[0100] Then for each wind turbine j, we look for a position that maximizes the annual energy produced.

[0101] Thus, iteratively according to F3, potential positions PE_Ej are defined for each wind turbine, one by one, for the jth turbine to be positioned. These potential positions PE_Ej are delimited by the first discrete mesh RD3 of the predetermined space. For example, the potential positions may correspond to the positions in the first discrete mesh RD3 located between a minimum and a maximum distance from the wind turbines already positioned in the predetermined space, and / or to the corresponding positions at the boundary of the predetermined space.

[0102] Once these potential positions PE_Ej are defined for the wind turbine j to be positioned, the annual energy produced by the already positioned wind turbines and the wind turbine j to be positioned within the predetermined space is evaluated Eval_AEP for each of these potential positions PE_Ej. This Eval_AEP evaluation uses, in particular, 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. The characteristics of the wind turbines and the wake effects previously described in this document can be used in a known manner.

[0103] We can then choose the position Pos_j of the wind turbine j, the position corresponding to the maximum value of the annual energy produced in the previous step.

[0104] We can then define a new arrangement Disp_Ej of the positioned wind turbines (including turbine j) within 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 evaluating the annual energy produced Eval_AEP.

[0105] We perform the F3 loop for, j going 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 step-by-step manner at step P_E1.

[0106] Once all the wind turbines are positioned (i.e., when j=N-1), the last arrangement found, Disp_Ej, then corresponds to the first arrangement, Disp1. A wind farm can then be built by installing (erecting / constructing) the wind turbines at the positions of the last arrangement found, corresponding to the final arrangement, in order to produce energy from the wind, on the physical site of the predetermined space.

[0107] There figure 6 This schematically and non-exhaustively illustrates the positioning steps of the first three wind turbines using a first greedy positioning algorithm. Diagrams a), b), and c) correspond respectively to the positioning steps of the first, second, and third wind turbines.

[0108] The predetermined space Esp defined here is rectangular. The first wind turbine E1 is arbitrarily positioned at the bottom right corner of the rectangle of the predetermined space Esp. Thus, the first wind turbine E1 is positioned on the boundary of the predetermined space Esp.

[0109] Once this wind turbine is positioned, the potential positions for determining the position of the second wind turbine PE_E2 correspond to the discrete values ​​located on the boundary of the predetermined space Esp at a distance greater than a minimum distance from the first wind turbine E1, and the discrete values ​​located within the predetermined space Esp at a distance between the minimum and maximum distances. Here, the minimum distance is twice the diameter of the wind turbine rotors, and the maximum distance is four times the diameter of the wind turbine rotors.

[0110] Once the annual energy produced for each of the PE_E2 positions has been calculated, the position of the second wind turbine E2 is determined to be the position shown in diagram b). The second wind turbine is therefore on the boundary of the predetermined space Esp.

[0111] These positions of the first two wind turbines allow us to define the potential positions PE_E3 for the third wind turbine to be positioned. These potential positions PE_E3 include the discrete positions located within the predetermined space between the minimum and maximum distances of the already positioned wind turbines (the first and second wind turbines E1 and E2), as well as the discrete positions located on the boundary of the predetermined space Esp at a distance greater than the minimum distance of the wind turbines E1 and E2.

[0112] Once the annual energy produced for each of the PE_E3 positions has been calculated, the position of the third wind turbine E3 is determined to be the position shown in diagram c). The third wind turbine is therefore also on the boundary of the predetermined space Esp.

[0113] The positions of the first three wind turbines define the potential positions PE_E4 for the fourth turbine to be positioned. These potential PE_E4 positions include the discrete positions within the predetermined space located between the minimum and maximum distances of the already positioned turbines (turbines E1, E2, and E3). It should be noted that there are no discrete positions located on the boundary of the predetermined space Esp at a distance greater than the minimum distance of turbines E1, E2, and E3, outside the previously defined areas, because all other boundary values ​​no longer meet the minimum distance requirements with turbines E1 through E3.

[0114] There figure 7 This schematically and non-limitingly illustrates a variant of the positioning steps for the first three wind turbines using a first greedy positioning algorithm. Diagrams a), b), and c) correspond respectively to the positioning steps of the first, second, and third wind turbines.

[0115] There figure 7 differs from figure 6 This is because the potential positions are defined solely by the discrete values ​​of the space located between the minimum and maximum distances of the already positioned wind turbines. In other words, discrete values ​​located on the boundary of the predetermined space at a distance greater than the maximum distance of the already positioned wind turbines are no longer taken into account.

[0116] The predetermined space Esp defined here is rectangular. The first wind turbine E1 is arbitrarily positioned at the bottom right corner of the rectangle of the predetermined space Esp. Thus, the first wind turbine E1 is positioned on the boundary of the predetermined space Esp.

[0117] Once this wind turbine is positioned, the potential positions for determining the position of the second wind turbine PE_E2 correspond to discrete values ​​located within the predetermined space Esp (including the boundary) at a distance between the minimum and maximum distances. Here, the minimum distance is twice the diameter of the wind turbine rotors and the maximum distance is four times the diameter of the wind turbine rotors.

[0118] Once the annual energy produced for each position PE_E2 has been calculated, the position of the second wind turbine E2 is determined to be the position shown in diagram b). Therefore, the second wind turbine is not on the boundary of the predetermined space Esp, unlike the solution in diagram b). figure 6 , where the predetermined space is identical and the first and second discrete distributions and the first discrete mesh are identical, the probabilities of occurrence are identical and the position of the first wind turbine E1 is identical.

[0119] The positions of the first two wind turbines define the potential positions PE_E3 for the third wind turbine to be positioned. These potential positions PE_E3 include the discrete positions within the predetermined space located between the minimum and maximum distances of the wind turbines already positioned (the first and second wind turbines E1 and E2).

[0120] Once the annual energy produced for each of the PE_E3 positions has been calculated, the position of the third wind turbine E3 is determined to be the position shown in diagram c).

[0121] The positions of the first three wind turbines, E1 to E3, define the potential positions PE_E4 for the fourth wind turbine to be positioned. These potential positions PE_E4 include the discrete positions within the predetermined space located between the minimum and maximum distances of the wind turbines already positioned (wind turbines E1, E2, and E3).

[0122] It can be noted that the positions of the three wind turbines E1 to E3 of the figure 7 are very different from those of the figure 6 , even though all parameters are identical. The distinction is only related to the definition of the potential positions which integrate (according to the figure 6 ) or not (depending on the figure 7 ) the discrete positions of the boundary of the predetermined space Esp located at a distance greater than the maximum distance of all the wind turbines already positioned.

[0123] The advantage of the solution of the figure 7 compared to the figure 6 The advantage is that positioning the wind turbines one after the other allows for closer placement of the turbines, thus enabling more turbines to be positioned within a predetermined space. This is particularly beneficial when a large, predetermined number of turbines are required within a limited, predetermined space (relative to the predetermined number of turbines to be placed).

[0124] There figure 8 illustrates, schematically and without limitation, an example of the application of a local optimization process for the positioning of a wind turbine from a first arrangement.

[0125] This figure presents four diagrams a), b), c) and d) showing different stages of repositioning a wind turbine.

[0126] The method of positioning wind turbines applied here (or of constructing a wind farm) corresponds to the figure 3 .

[0127] In diagram a), we note a first arrangement of five wind turbines materialized by the small circles in a predetermined space Esp defined by the grey rectangle.

[0128] We seek to improve the position of the wind turbine Eol. To do this, we define a first grid Car 1, the grid being here a square centered on the wind turbine Eol and with side L1.

[0129] In diagram b), the grid Car1 is discretized into sixteen (but this could be a different number, for example, four, twenty-five, one hundred, etc.) cells Car2. Here, the Car2 cells are smaller squares than the grid Car1, thus discretizing the grid Car1. The possible discrete positions PDP_i are defined as the points of intersection of the Car2 cells. The possible discrete positions PDP_i are represented by crosses positioned at the points of intersection of the cells in the predetermined space Esp and at a sufficient distance from the other wind turbines. In diagram b), three discrete positions PDP_i are possible. Thus, after local optimization of the annual energy at the level of the three possible PDP_i positions, the position of the wind turbine Eol changes from position P_init to position P_modif1.

[0130] Once all the wind turbines have been repositioned, we can repeat step b) of the positioning method (or wind farm construction method).

[0131] We will then redefine a new grid (a new first square), with a side length L2 smaller than the side length L1 used in the previous iteration. This new grid, centered around the position P_modif1, is again discretized into the predetermined number of cells (here, sixteen second squares), and new possible discrete positions are defined, corresponding to the crosses positioned at the intersection points of the cells located in the predetermined space Esp and at a sufficient distance from the other wind turbines. It can be noted that the intersection points Pexc are located too close to the wind turbine EoI2 (their distance from the wind turbine EoI2 is less than the minimum distance). They are therefore not taken into account in the possible discrete positions for repositioning the wind turbine Eol. After this new iteration, the position of the wind turbine Eol is at position P_modif2.

[0132] Once all the wind turbines have been repositioned, we can iterate step b) of the positioning method (or wind farm construction method) once again.

[0133] In diagram d), a new local search for repositioning the wind turbine Eol is performed. A new grid (a new first square) is redefined, centered on the position P_modif2, with a side length L3 shorter than side length L2. The new grid is discretized into the predetermined number (identical to the grids of the previous iterations) of cells (here, sixteen second squares). Within these sixteen cells, sixteen intersection points are located in the predetermined space Esp and at a sufficient distance from the other wind turbines (greater than the minimum distance from the other wind turbines). These points then serve as possible discrete positions, represented by the crosses, for repositioning the wind turbine Eol.

[0134] Calculating the annual energy based on the position of the wind turbine Eol at these different possible discrete positions allows us to define the position P_modif3 corresponding to the maximum annual energy produced.

[0135] Note that for diagrams c) and d), the positions of the wind turbines other than Eol are unchanged, but they could be, given that diagrams c) and d) correspond to new iterations of step b) for which a new arrangement of the wind turbines is established as input to the new iteration.

[0136] There figure 9 , illustrates schematically and not exhaustively, several steps of the method of positioning a pre-established number of wind turbines (or constructing a wind farm) in a predetermined space Esp.

[0137] The predetermined space Esp is rectangular in shape here.

[0138] Diagram a) shows an initial arrangement of five wind turbines, represented by the dark gray dots, in the predetermined space Esp. This initial arrangement results from a first greedy algorithm like that of the figure 7 .

[0139] In diagram b), we aim to improve the position of wind turbine El1 in order to increase the annual energy produced. To do this, we proceed by determining a grid (a first square) centered on the position of wind turbine El1 and we discretize this grid into a predetermined number of cells (second squares for example) whose points of intersection located in the predetermined space Esp and at a sufficient distance from the other wind turbines (at a distance greater than the minimum distance of the other wind turbines, the minimum distance being for example twice the diameter of the wind turbine rotor) correspond to the possible discrete positions, represented by the small gray dots around wind turbine El1.

[0140] Diagram c) represents a new iteration of step b). In this new iteration, the arrangement of the wind turbines has been modified. Indeed, at the end of an iteration of step b), the wind turbines were repositioned one after the other.

[0141] In diagram c), we aim to reposition wind turbine EI2. To do this, we define a grid (first square) centered on the position of wind turbine EI2 and discretize this grid into a predetermined number of cells (here, the second set of squares). The intersections of these cells, located in the predetermined space Esp, at a distance greater than the minimum distance from the other wind turbines (twice the rotor diameter of the other turbines, for example), correspond to the possible discrete positions for wind turbine EI2. These possible discrete positions are represented by the small light gray dots surrounding wind turbine EI2.

[0142] There figure 10 illustrates, schematically and without limitation, an example of the application of the method of positioning wind turbines (or constructing a wind farm) in a complex predetermined space.

[0143] The predetermined space here consists of two non-connected zones Es1 and Es2. Furthermore, zone Es2 is non-convex given the triangular part of the boundary Ar towards the interior of zone Es2.

[0144] In diagram a), the grey dots represent the boundary of the predetermined space and correspond to the discrete locations where the first wind turbine can be installed.

[0145] In diagram b), a single wind turbine EE1 is positioned, represented by the isolated gray point, at the top of zone Es1. The clusters of dark gray points T2 represent the potential positions of the next wind turbine to be positioned within the predetermined space. They correspond to the discrete points on the boundaries of zones Es1 and Es2 located at a sufficient distance (i.e., greater than a minimum distance which can be twice the diameter of the wind turbine) from wind turbine EE1, as well as to the discrete positions within zone Es1 located at a distance between a minimum and a maximum distance from wind turbine EE1.

[0146] Diagram c) represents a stage where 20 wind turbines, represented by the isolated gray points, have been positioned by the first greedy positioning algorithm. The dark gray point clusters T21 correspond to the potential positions for the 21st wind turbine to be positioned by the first greedy positioning algorithm.

[0147] Diagram d) represents a stage where 50 wind turbines, represented by the isolated gray points, have been positioned by the first greedy positioning algorithm. The dark gray point clusters T51 correspond to the potential positions for the 51st wind turbine to be positioned by the first greedy positioning algorithm.

[0148] Diagram e) corresponds to a step where we seek to improve the position of an ELi wind turbine by a local optimization of its position. The arrangement of the 52 wind turbines was previously established by the first greedy positioning algorithm and the current positions of each of the 52 wind turbines correspond to the large isolated grey points in diagram e).

[0149] The small gray dots positioned around wind turbine ELi represent the possible discrete positions PDP_ELi for repositioning wind turbine ELi. The annual energy produced is estimated based on the positions of the wind turbines other than wind turbine ELi in the layout of diagram e) and on the different possible discrete positions PDP_ELi for wind turbine ELi.

[0150] There figure 11 illustrates, schematically and without limitation, a variant of the positioning method (or construction of a wind farm) for the predetermined complex space, identical to that of the figure 10 .

[0151] The predetermined space comprises two non-connected zones Es1 and Es2. Furthermore, zone Es2 is a non-convex zone given the triangular portion of the boundary Ar oriented towards the interior of zone Es2.

[0152] For the positioning of wind turbines using the first greedy positioning algorithm, the potential positions correspond to the discrete positions located within the predetermined space at a distance between a minimum and a maximum distance from the already positioned turbines. Points on the boundary located at a distance greater than the maximum distance from the already positioned turbines are not taken into account in order to maximize the number of turbines to be installed within the predetermined space, whereas they were taken into account in the first positioning algorithm. figure 10 , as can be seen in diagram b) of the figure 10 , by the potential positions T2 of the second wind turbine.

[0153] On diagram a) of the figure 11 Two wind turbines, EE1 and EE2, have been positioned. The potential positions of the third wind turbine, T3, correspond to the clusters of grey dots.

[0154] In diagram b) of the figure 11 Ten wind turbines, represented by the isolated grey dots, have been positioned. The potential positions of the eleventh wind turbine, T11, correspond to the clusters of grey dots. Exemples

[0155] A first example involves positioning the wind turbines in the predetermined space of the figure 7 , according to a continuous method (using continuous real data and not discrete values) of the prior art and according to the method of the figure 3 of the invention where the possible discrete positions are defined from a grid (a first square) centered on the position of the wind turbine to be repositioned, the grid being discretized into a pre-established number of meshes (which are here second squares), and the intersections of the meshes positioned in the predetermined space and at a sufficient distance (greater than a minimum distance) from the other wind turbines form the possible discrete positions.

[0156] The wind turbines to be installed are 2.5 MW wind turbines, the minimum distance between the wind turbines is 4 times the diameter of the wind turbine rotor.

[0157] For the method according to the invention, the maximum distance between the wind turbines used for the first greedy positioning algorithm is 8 times the diameter of the turbine rotor. The length of the first square in the first iteration is 500 m, the threshold for stopping the iterations in step b) is 5 m, the predetermined number is 4, and the ratio of the length of a first square to the length of the first square in the previous iteration of step b) is 0.8.

[0158] The prior art method is performed on the FarmShadow™ software (IFP Energies nouvelles, France).

[0159] The first wind speed distribution comprises discrete values ​​spaced 0.5m / s apart and the second wind direction distribution comprises discrete values ​​spaced 1° apart.

[0160] The method of the invention makes it possible to estimate a gain of approximately 2.2% on the annual energy produced compared to the prior art method, which shows the effectiveness of the method in improving the energy recovered by the farm while reducing the computation time and computer memory used.

[0161] The second application example is that of the figure 10 First, this application, which includes a predetermined space with non-convex and non-convex areas, is not applicable with a continuous method, which requires a convex and connected area, usually rectangular in shape. 52 10 MW wind turbines were positioned within this predetermined space.

[0162] The annual energy gain produced by the final wind turbine layout, compared to the initial layout obtained using the first greedy positioning algorithm, is approximately 2.84%. This demonstrates both the effectiveness of the initial layout obtained from the first algorithm and the efficiency of the local search process for optimizing the position of each wind turbine.

[0163] The method of positioning wind turbines in a predetermined space (or of constructing a wind farm) allows for quick, simple calculations while ensuring a precise and optimized position of the wind turbines in a predetermined space, a predetermined space which may be non-connected and / or non-convex in order to maximize the total annual energy produced by the wind farm.

Claims

1. Method for constructing a wind farm in a predetermined space (Esp) from 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), said predetermined space (Esp) being divided into a first discrete mesh (RD3), wherein at least the following successive steps are carried out: a) determining a first layout (Disp1) of said wind turbines in the first discrete mesh (RD3) of said predetermined space (Esp) using a first positioning algorithm (Alg1); b) defining a sequential order (OS) of modification of the positions of the wind turbines as determined by the first positioning algorithm (Alg1), and then carrying out at least the following steps iteratively for at least one wind turbine to be repositioned, one by one, in the defined sequential order (OS): b1) for each wind turbine to be repositioned, determining new possible discrete positions (PDP_i) of the wind turbine to be repositioned by establishing a grid of at least a first predefined length, the grid being centred on the position of the wind turbine to be repositioned, the grid being divided into a pre-established number of meshes, said new possible discrete positions comprising the points of intersection of the meshes, the points of intersection of the meshes being positioned in said predetermined space (Esp) and at a minimum distance from the positions of the other wind turbines; b2) calculating the average annual energy production (Eval_i) of the predefined number of wind turbines for each possible discrete position of the wind turbine to be repositioned from said first discrete wind speed distribution (RD1), said second discrete wind direction distribution (RD2) and said probability of occurrence (Prob); b3) choosing the position (Pos_i) of the wind turbine to be repositioned corresponding to the maximum calculated annual energy production value calculated in step b2); b4) defining a new layout of the wind turbines (Disp_N) in said predetermined space (Esp); and c) determining a final layout (DispF) corresponding to the last layout obtained, and constructing said wind farm by erecting said wind turbines at the positions of said final layout on the site of the predetermined space so as to generate energy from wind, steps a) and b) being implemented by computerized means, preferably a computer, a mobile telephone or a tablet.

2. Method for constructing a wind farm according to Claim 1, wherein, before step a), statistical wind data are collected by collection means, preferably a lidar sensor, in the predetermined space (Esp) in order 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).

3. Method for constructing a wind farm according to either of the preceding claims, wherein said predetermined space (Esp) is two-dimensional.

4. Method for constructing a wind farm according to one of the preceding claims, wherein said sequential order (OS) is obtained randomly.

5. Method for constructing a wind farm according to one of the preceding claims, wherein step b) is reiterated (B2) multiple times, preferably modifying the sequential order (OS) in each iteration.

6. Method for constructing a wind farm according to Claim 5, wherein, for each iteration (B2) of step b), a first predefined length smaller than the first predefined length from the preceding iteration is chosen, said pre-established number being the same from one iteration to another, and the iteration of step b) is stopped when the first predefined length becomes smaller than a first threshold.

7. Method for constructing a wind farm according to one of the preceding claims, wherein said predetermined space (Esp) comprises non-connected areas (Es1, Es2).

8. Method for constructing a wind farm according to one of the preceding claims, wherein said predetermined space (Esp) comprises non-convex areas (Z2, Es2).

9. Method for constructing a wind farm according to one of the preceding claims, wherein said first positioning algorithm (Alg1) carries out at least the following steps: - arbitrarily defining the position (P_E1) of the first wind turbine (EE1); - then, for each wind turbine to be positioned, successively: defining potential positions (PE_Ej) in said first discrete mesh (RD3) for the wind turbine to be positioned, said potential positions (PE_Ej) comprising discrete positions of the first discrete mesh (RD3) that are located between a minimum distance and a maximum distance from all positioned wind turbines and / or discrete positions of the boundary of the predetermined space (Esp) that are located at said minimum distance from all positioned wind turbines; calculating the annual energy production (Eval_AEP) of the positioned wind turbines and of the wind turbine to be positioned for the defined potential positions (PE_Ej) from said first discrete wind speed distribution (RD1), said second discrete wind direction distribution (RD2) and said probability of occurrence (Prob); choosing the position (Pos_j) of the wind turbine to be positioned corresponding to the maximum calculated annual energy production value: - determining said first layout (Disp_Ej) corresponding to the position of the predefined number of wind turbines in said predetermined space (Esp).

10. Method for constructing a wind farm according to Claim 9, wherein the arbitrary position corresponds to the greatest sum of the coordinates of the positions of said first discrete mesh (RD3).

11. Computer program product able to be downloaded from a communication network and / or recorded on a computer-readable medium and / or a medium able to be executed by a processor or a server, comprising program code instructions for implementing the method according to one of the preceding claims when the program is executed on a computer or a mobile telephone.

12. Wind farm obtained using the method for constructing a wind farm according to one of preceding Claims 1 to 10.