CN108932554B - Configuration optimization method and device for wind power plant flow field measurement points - Google Patents
Configuration optimization method and device for wind power plant flow field measurement points Download PDFInfo
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Abstract
The embodiment of the application discloses a method and a device for optimizing configuration of wind power plant flow field measurement points, and the method comprises the steps of constructing an initial sample space, wherein the initial sample space comprises at least one sample of a wind power plant flow field measurement point position deployment decision, the sample of the wind power plant flow field measurement point position deployment decision comprises at least one position of a wind power plant flow field measurement point, and the wind power plant flow field measurement point is configured on a fan and/or a wind measuring tower; obtaining N samples of a wind power plant flow field measurement point position deployment decision from an initial sample space; sequencing the N samples according to the linear approximation error result of the one-dimensional flow field curve of the wind power plant, and selecting the sample with the linear approximation error result smaller than a preset value from the N samples to form an ideal sample space S; and carrying out accurate simulation evaluation on the prediction precision of the wind power plant output power on the sample of the ideal sample space S to obtain the position optimal solution omega of the wind power plant flow field measurement point.
Description
Technical Field
The application relates to the field of wind power generation, in particular to a configuration optimization method and device for wind power plant flow field measurement points.
Background
The installed capacity of Chinese wind power is at the first place in the world. Meanwhile, the annual wind abandoning power is rapidly increased, the average wind abandoning rate reaches 21 percent at present, and the wind abandoning limit power is developed towards normalization and malignancy. The large uncertainty of the power of the wind power plant is an important factor influencing wind power integration so as to cause the increase of the wind power curtailment. And optimizing the power prediction effect of the wind power plant is vital to improving the stability of wind power integration and reducing the wind curtailment amount. The energy industry standard stipulates that the error of the monthly square root of the predicted value of the 4 th h predicted value of the ultra-short term prediction is less than 0.15. The root mean square error of the prediction result of the current mainstream wind power plant power prediction method (including a physical method and a statistical method) is generally between 0.1 and 2.0. One of the main problems of low prediction accuracy is: the deployment position of the wind power plant flow field measuring point is not reasonable enough, so that the characteristics of a sensor of the wind power plant flow field measuring point can not be well utilized.
The acquisition and analysis of multi-source information such as geography, weather, environment, energy and the like of the wind power plant are the basis of the accurate perception and perception of the environment of the wind power plant. As a premise of wind power generation, direct perception of the dynamics (wind speed and wind direction) of a near-current flow field in a wind power plant is the core of power uncertainty analysis of the wind power plant. The quantity and the positions of the flow field measuring points of the wind power plant are optimally configured in an area of dozens of square kilometers of the large-scale wind power plant, so that the power sensing efficiency and the prediction precision of the wind power plant can be improved, and the construction cost and the engineering period of the flow field measuring points and an information system thereof are reduced.
At present, a flow field measurement point in a wind power plant construction standard is mainly configured in a cabin or a anemometer tower of a fan, and in the wind power plant, the specific configuration position of the flow field measurement point is mainly set according to a multi-fan similar classification configuration method; for example, based on similarity of historical meteorological information at a plurality of wind turbines in a wind farm, dividing the plurality of wind turbines in the wind farm into at least one group; flow field measurement points are configured from one packet, for example: and selecting a sensor representing the configuration of the fan in the group or arranging a wind measuring tower at a proper position in the group, and acquiring a measured value of the flow field measuring point to the group. The output power of a plurality of wind turbines in a wind farm is analyzed based on measured values of flow field measurement points configured in a plurality of groups divided in the wind farm. Certainly, the grouping rule for the fans may further include that the distance between the fans in the group is smaller than a predetermined distance, and the models of the fans in the group are consistent; the rule for adjusting the fan grouping may be: whether the fans in a group satisfy a grouping rule, based on the adjusted similarities, divide the plurality of fans in the wind farm into new groups, and so on. The sensor on the fan or anemometer tower includes: meteorological sensor, fan state sensor and fan output power sensor. After the fans are grouped, the types and the number of sensors required in power prediction are reduced by utilizing the similarity of meteorological information at each fan in a wind field, the sensors can be deployed only at a representative fan in a plurality of fans with the similarity, and further, the cost required when the sensors are deployed can be greatly reduced.
However, this solution is directed to reduce the types and the number of sensors required in power prediction based on the existing sensors, that is, the configuration of the flow field measurement points in the prior art is mainly implemented by means of the grouping of the wind turbines and adjusting the grouping rules, and in order to further improve the prediction accuracy of the power of the wind farm, it does not relate to how to specifically optimize the positions of the flow field measurement points, for example, in the wind farm or in each group, to which wind turbine nacelle the flow field measurement points are specifically configured or on which wind tower the flow field measurement points are configured.
Disclosure of Invention
The embodiment of the application provides a configuration optimization method and device for wind power plant flow field measurement points, which can optimize the positions of the flow field measurement points and improve the prediction precision of wind power plant power.
In order to achieve the above purpose, the embodiment of the present application adopts the following technical solutions:
the method comprises the steps that an initial sample space is constructed, the initial sample space comprises a sample of a wind power plant flow field measurement point position deployment decision, the sample of the wind power plant flow field measurement point position deployment decision comprises at least one position of a wind power plant flow field measurement point, and the wind power plant flow field measurement point is configured on a fan and/or a wind measuring tower; obtaining N samples of a wind power plant flow field measurement point position deployment decision from an initial sample space; sequencing the N samples according to the linear approximation error result of the one-dimensional flow field curve of the wind power plant, and selecting the sample with the linear approximation error result smaller than a preset value from the N samples to form an ideal sample space S; the sample space S comprises S samples, S is less than or equal to N, accurate simulation evaluation of the wind power plant output power prediction precision is conducted on the samples in the sample space S, and the position optimal solution omega of the wind power plant flow field measurement point is obtained. In the scheme, N samples are obtained from an initial sample space formed by a wind power plant flow field measurement point position deployment decision, the N samples are sequenced according to the linear approximation error result of a one-dimensional flow field curve of the wind power plant, then accurate simulation evaluation of the wind power plant output power prediction precision is carried out on the samples in the ideal sample space S, and the position optimal solution omega of the wind power plant flow field measurement point is obtained.
One example is that accurate simulation evaluation of the wind farm output power prediction accuracy is performed on a sample of an ideal sample space S to obtain a position optimal solution Ω of a wind farm flow field measurement point, and the method includes: and carrying out accurate simulation evaluation on the prediction precision of the output power of the wind power plant on the sample of the ideal sample space S according to root-mean-square error (RMSE), and obtaining the position optimal solution omega of the flow field measuring point of the wind power plant. In the scheme, N samples are sequenced according to the result of linear approximation error of a one-dimensional flow field curve of the wind power plant, and then an ideal sample space S is obtained from the N samples, so that the number of samples for wind power plant output power prediction is reduced, and the calculation cost is reduced.
In addition, the initial sample space may be a two-dimensional sample space or a one-dimensional sample space, but in order to implement sorting of N samples according to an optimal linear approximation error result for a one-dimensional flow field curve of a wind farm, if the initial sample space is the two-dimensional sample space, it is necessary to perform dimension reduction processing on the two-dimensional sample space first, and one example is: the position of the wind power plant flow field measuring point is a two-dimensional coordinate of the wind power plant flow field measuring point; constructing the initial sample space includes: generating uniformly distributed random two-dimensional coordinates of wind power plant flow field measurement points in a two-dimensional space according to a uniformly distributed random function to form an initial sample space; obtaining N samples of a deployment decision of a wind power plant flow field measurement point position from an initial sample space, wherein the N samples comprise: selecting N samples from an initial sample space; acquiring wind field data, wherein the wind field data at least comprises: the wind direction of the wind power plant flow field measuring point and the position of the wind power plant flow field measuring point in the wind power plant; acquiring a main wind direction in a preset time period according to wind field data; determining the projection distance of the wind power plant flow field measuring point on the main wind direction according to the coordinate of the wind power plant flow field measuring point and the main wind direction; and traversing N samples in the initial sample space to obtain a one-dimensional sample space, wherein the one-dimensional sample space comprises the N samples.
If the initial sample space is a two-dimensional sample space, another example is: the method comprises the following steps that an initial sample space is a two-dimensional sample space, and the position of a wind power plant flow field measuring point is a two-dimensional coordinate of the wind power plant flow field measuring point; constructing the initial sample space includes: generating uniformly distributed random two-dimensional coordinates of wind power plant flow field measurement points in a two-dimensional space according to a uniformly distributed random function to form an initial sample space; obtaining N samples of a deployment decision of a wind power plant flow field measurement point position from an initial sample space, wherein the N samples comprise: acquiring wind field data, wherein the wind field data at least comprises: the wind direction of the wind power plant flow field measuring point and the position of the wind power plant flow field measuring point in the wind power plant; acquiring a main wind direction in a preset time period according to the wind field data; determining the projection distance of the wind power plant flow field measuring point on the main wind direction according to the coordinate of the wind power plant flow field measuring point and the main wind direction; traversing the wind power plant flow field measurement points of the initial sample space to obtain a one-dimensional sample space; and selecting N samples in the one-dimensional sample space.
In the above two examples in which the initial sample space is a two-dimensional sample space, the difference between the first example and the second example is: in the first example, N samples are selected in a two-dimensional initial sample space, and then the sample space formed by the N samples is subjected to dimensionality reduction to form a one-dimensional sample space containing the N samples, so that the process of selecting the N samples in the initial sample space is realized; in the second example, a two-dimensional initial sample space is first reduced to form a one-dimensional sample space, and then N samples are selected from the one-dimensional sample space, so as to realize the process of selecting N samples from the initial sample space.
If the initial sample space is a one-dimensional sample space, one example is: constructing an initial sample space, comprising: generating uniformly distributed random two-dimensional coordinates of the wind power plant flow field measuring points in a two-dimensional space according to a uniformly distributed random function to form a random sample space; acquiring wind field data, wherein the wind field data at least comprises: the wind direction of the wind power plant flow field measuring point and the position of the wind power plant flow field measuring point in the wind power plant; acquiring a main wind direction in a preset time period according to wind field data; determining the projection distance of the wind power plant flow field measuring point on the main wind direction according to the coordinate of the wind power plant flow field measuring point and the main wind direction; traversing the wind power plant flow field measurement points of the initial sample space to obtain a one-dimensional sample space; obtaining N samples of a deployment decision of a wind power plant flow field measurement point position from a random sample space, wherein the N samples comprise: n samples are taken in a one-dimensional sample space.
One example is that before performing accurate simulation evaluation on the prediction accuracy of the output power of the wind farm on a sample of an ideal sample space S according to a root mean square error RMSE and obtaining an optimal solution Ω of a position of a wind farm flow field measurement point, the method further includes: dividing an ideal sample space S into a depth-first Search (SD) subset and a breadth-first Search (SB) subset according to the characteristics of a one-dimensional sample space; according to the result of linear approximation error of the one-dimensional flow field curve of the wind power plant, samples in the depth-first search subset and the breadth-first search subset are sorted respectively; carrying out accurate simulation evaluation on the prediction precision of the wind power plant output power on the sample of the ideal sample space S according to the root mean square error RMSE to obtain the position optimal solution omega of the wind power plant flow field measurement point, wherein the method comprises the following steps: and according to a preset sequence, carrying out accurate simulation evaluation on the output power prediction precision of the wind power plant on the samples in the depth-first search subset and the breadth-first search subset, and obtaining a position optimal solution omega of a flow field measuring point of the wind power plant, wherein in the preset sequence, the samples in the depth-first search subset and the samples in the breadth-first search subset are arranged in an inserting manner, the samples in the depth-first search subset are arranged according to the ascending order of the results of linear approximation errors of the one-dimensional flow field curve of the wind power plant, and the samples in the breadth-first search subset are arranged according to the ascending order of the results of linear approximation errors of the one-dimensional flow field curve of the wind power plant. In the scheme, the sample space is reduced to the one-dimensional sample space processed to the main wind direction, so that the samples in the breadth-first search subset can predict the power of the wind farm according to the density of the wind farm flow field measurement points on the main wind direction, the samples in the depth-first search subset can predict the power of the wind farm according to the number of the wind farm flow field measurement points near the projection of one wind farm flow field measurement point on the main wind direction, and the distribution density and the number of the wind farm flow field measurement points can be considered when the wind farm power prediction precision is improved.
In a second aspect, a device for optimizing configuration of wind farm flow field measurement points is provided, including: the system comprises an initialization module, a wind power plant flow field measurement point deployment module and a wind power plant flow field measurement point deployment module, wherein the initialization module is used for constructing an initial sample space which comprises a wind power plant flow field measurement point position deployment decision, the wind power plant flow field measurement point position deployment decision comprises a position of the wind power plant flow field measurement point, and the wind power plant flow field measurement point is configured on a fan and/or a wind measuring tower; the sampling module is used for acquiring N samples of a wind power plant flow field measurement point position deployment decision from the initial sample space constructed by the initialization module; the calculation module is used for sequencing the N samples acquired by the sampling module according to the optimal linear approximation error result of the one-dimensional flow field curve of the wind power plant, and selecting the sample with the approximation error result smaller than a preset value from the N samples to form an ideal sample space S; and the solving module is used for carrying out accurate simulation evaluation on the prediction precision of the output power of the wind power plant on the sample of the ideal sample space S acquired by the calculating module to acquire the position optimal solution omega of the flow field measurement point of the wind power plant.
In a third aspect, a device for optimizing configuration of wind farm flow field measurement points is provided, including: a processor, a memory, and a bus; the memory is used for storing computer execution instructions, the processor is connected with the memory through the bus, and when the configuration optimization device of the wind farm flow field measurement point runs, the processor executes the computer execution instructions stored in the memory, so that the control device executes the method according to the first aspect.
In a fourth aspect, there is provided a computer storage medium comprising instructions which, when run on a computer, cause the computer to perform the method of the first aspect.
In a fifth aspect, the present application also provides a computer program product which, when run on a computer, causes the computer to perform the method of the first aspect described above.
It can be understood that any one of the above-mentioned configuration optimization devices, computer storage media, or computer program products for wind farm flow field measurement points is used to execute the above-mentioned configuration optimization method for corresponding wind farm flow field measurement points, and therefore, the beneficial effects that can be achieved by the configuration optimization method for wind farm flow field measurement points and the beneficial effects of the corresponding solutions in the following specific embodiments may be referred to, and are not described herein again.
Drawings
Fig. 1 is a schematic flow chart of a configuration optimization method for wind farm flow field measurement points according to an embodiment of the present application;
fig. 2 is an ideal sample space S provided by the embodiment of the present application, which is the first k% samples with the minimum linear approximation error result among N samples;
fig. 3 is a schematic diagram of linear approximation of positions of wind field flow field measurement points in three scenes to a one-dimensional flow field curve provided in the embodiment of the present application;
fig. 4 is a schematic diagram of acquiring a main wind direction according to an embodiment of the present application;
FIG. 5 is a schematic diagram of mapping a spatial position of a wind farm flow field measurement point to a projection along a main wind direction according to an embodiment of the present application;
FIG. 6 is a schematic diagram of a spatial dimension reduction process of a two-dimensional wind farm provided by the embodiment of the application;
fig. 7 is a schematic flowchart of a process for performing accurate simulation evaluation on the prediction accuracy of the wind farm output power on a sample of an ideal sample space S according to the embodiment of the present application;
FIG. 8 is a diagram of a prior art arrangement of any three wind farm flow field measurement points for ultra-short term (one hour in advance) prediction of wind farm output power;
FIG. 9 is a diagram of ultra-short term (one hour in advance) prediction of wind farm output power from any one of three wind farm flow field measurement points provided in the embodiment of the present application;
fig. 10 is a schematic structural diagram of an apparatus for optimizing configuration of a wind farm flow field measurement point according to an embodiment of the present disclosure;
fig. 11 is a schematic structural diagram of an apparatus for optimizing configuration of a wind farm flow field measurement point according to another embodiment of the present disclosure;
fig. 12 is a schematic structural diagram of an apparatus for optimizing configuration of wind farm flow field measurement points according to still another embodiment of the present disclosure.
Detailed Description
Embodiments of the present application are described below with reference to the accompanying drawings.
First, a brief introduction is made to the technical background involved herein to facilitate the reader's understanding:
the embodiment of the invention is applied to configuration optimization of wind power plant flow field measurement points, wherein the wind power plant flow field measurement points refer to positions of sensors used for collecting data of wind power plant power prediction, the sensors can be specifically installed on an engine room of a fan or a wind measuring tower, and the configuration of the wind power plant flow field measurement points refers to the following steps: specifically arranging sensors on the engine rooms or anemometers of the wind turbines in the wind power plant; the sensor may include: meteorological sensor, fan state sensor and fan output power sensor.
When mounting the sensor to the nacelle of a wind turbine, one typical sensor is: the wind turbine comprises a wind turbine cabin and a wind turbine cabin, wherein each wind turbine cabin is provided with a wind turbine cabin wind speed indicator, and the wind turbine cabin wind speed indicator is generally arranged on the top of the rear portion of the wind turbine cabin. The wind power generation system is used for monitoring the wind turbine in real time, controlling yaw and providing a real-time data source for power prediction of the wind power plant. The scheme for realizing the carrying of the sensor through the anemometer tower comprises the following steps: the position of the anemometer tower is preferably configured within the range of 1 km-5 km outside the wind power plant, and in order to avoid the influence of wake effect of the wind power plant as much as possible, the anemometer tower is preferably constructed at the representative position of the upwind direction of the main wind direction of the wind power plant. The anemometer tower is mainly used for early-stage micro site selection of the wind power plant, but real-time data collected by the anemometer tower is also an important data source for power prediction of the wind power plant. Among them, the advantages of the cabin anemometer are: because the top of the engine room is relatively close to the center of the wind wheel of the wind generating set, the time delay between the measured value and the actual wind on the wind wheel is small, and the influence of the surrounding terrain is small. The advantages of the anemometer tower are as follows: the influence of wake effect of the wind power plant is considered to be reduced as much as possible in the site selection stage, so that the measurement accuracy of the wind measuring tower sensor on free wind is high. However, the nacelle anemometer: the anemoscope is greatly influenced by the wake effect of the wind turbine and the disturbance of the wind turbine, the wind speed of the free flow which is actually captured in front of the wind turbine cannot be represented, and the measurement result has high randomness. Uncertainty caused by wake effect is +/-1.5 m/s; wind measuring tower: at present, the position of the wind measuring tower is configured to be standard, and the wind measuring tower has the defects of multiple pairs of previous micro site selection, less measuring points, too far distance between the measuring points and most of fans and insufficient space density. Measurement precision: . + -. 0.5m/s (3 m/s-30 m/s).
The mathematical model of the prediction precision evaluation function for the wind power plant power is as follows:
wherein minJ is an evaluation target, J is the number of evaluation scenes, fj(Ωn)＝RMSETAs a function of the prediction accuracy evaluation of the wind farm power, omegan＝{(xi,yi)}i＝1,2,…,nA set of wind-field flow field measurement points, RMSE (root-mean-square error), in scene j.
Wherein:
Pmfthe actual average power of the wind power plant in the period i;
Ppithe predicted power of the wind power plant in the period i;
Cistarting up total capacity of the wind power plant at the time period i;
and n is the number of all samples in the wind power plant.
The technical scheme provided by the application is described below with reference to the accompanying drawings.
Referring to fig. 1, an embodiment of the present invention provides a configuration optimization method for wind farm flow field measurement points, including the following steps:
101. and constructing an initial sample space, wherein the initial sample space comprises at least one sample of a wind power plant flow field measurement point position deployment decision, the sample of the wind power plant flow field measurement point position deployment decision comprises at least one position of the wind power plant flow field measurement point, and the wind power plant flow field measurement point is configured on a fan and/or a wind measuring tower.
102. And obtaining N samples of the deployment decision of the position of the flow field measuring point of the wind power plant from the initial sample space.
103. And sequencing the N samples according to the linear approximation error result of the one-dimensional flow field curve of the wind power plant, and selecting the sample with the linear approximation error result smaller than a preset value from the N samples to form an ideal sample space S.
In step 103, a plurality of samples with the minimum approximation error result from the N samples may be selected to form an ideal sample space S, which is used as an input of the accurate simulation evaluation of the wind power field output power prediction accuracy in step 104, thereby further reducing the computational complexity of the accurate simulation evaluation. Step 103 can be described as determining the position of the segmentation point (the position of the wind farm flow field measurement point) of the function on the premise of a given segmentation number (the configuration number of the wind farm flow field measurement points), so that the result of the linear approximation error is minimum in a given scene set (one-dimensional flow field curve). The solving model is as follows:
s.t.-εj≤αP(j)+β-C(j)≤εj，0≤εj≤εM+1wherein, alpha and beta are linear approximation undetermined coefficients epsilonjFor approximation error, P(j)Representing the first order of a linear approximation function, C(j)Represents the constant term of the linear approximation function, M refers to the number of segments of the linear approximation.
As shown in fig. 2, the ideal sample space S preferably takes the first k% of the minimum linear approximation error result from the N samples, that is, as shown in fig. 3, the minimum linear approximation error result is obtained at positions d1, d2, and d3 of the wind farm flow field measurement points included in the samples in the ideal sample space S in the first, second, and third scenarios.
104. And carrying out accurate simulation evaluation on the prediction precision of the wind power plant output power on the sample of the ideal sample space S to obtain the position optimal solution omega of the wind power plant flow field measurement point.
In the scheme, N samples are obtained from an initial sample space formed by a wind power plant flow field measurement point position deployment decision, the N samples are sequenced according to the linear approximation error result of a one-dimensional flow field curve of the wind power plant, then accurate simulation evaluation of the wind power plant output power prediction precision is carried out on the samples in the ideal sample space S, and the position optimal solution omega of the wind power plant flow field measurement point is obtained.
Because the optimal linear approximation needs to be performed on the N samples by using the one-dimensional flow field curve of the wind power plant in step 103 to obtain an error result, the dimension reduction processing needs to be performed on the two-dimensional wind power plant space in the previous step; the specific principle is as follows:
in a wind power plant, the fluctuation of wind energy is a dynamic propagation process with time lag, and the output power of a fan and the output power of the fan have an up-down and down-stream space-time coupling relation. In the micro site selection and design stage of the wind power plant, the arrangement of the fans is optimized mainly according to the main wind direction and the vertical main wind direction. Under the condition of determining the main wind direction, the fluctuation of the output power of the fan presents the situation of upstream and downstream propagation of the main wind direction. In the process of considering the propagation of wind energy, the measurement values of the wind farm flow field measurement points which are the same as or similar to the main wind direction projection have greater similarity, so that the two-dimensional problem of deploying the wind farm flow field measurement points in the wind farm area can be converted into a one-dimensional problem arranged according to the main wind direction, as shown in fig. 4, a two-dimensional wind farm space is formed by the intersection plane of X, Y two axis coordinates, which is shown by an arrow in the figureThe main wind direction is shown, and the wind farm flow field measurement points (shown by circles) are randomly distributed. The dimension reduction is performed on the two-dimensional wind power plant space, as shown in fig. 5, the dynamic propagation process of wind energy change can be described by using a one-dimensional advection equation, and the decision variable (x) of the space position of the wind power plant flow field measuring point is obtainedi,yi) Mapped as a projection d along the prevailing wind directioniAnd dimension reduction of the decision space is realized. Therefore, the following conversion is realized on the wind field flow field measurement point set in the scene j:
the specific dimension reduction of the two-dimensional wind farm space comprises the following steps, as shown in fig. 6:
s1: acquiring wind field data, wherein the wind field data at least comprises: the wind direction of the wind power plant flow field measuring point and the position of the wind power plant flow field measuring point in the wind power plant; the wind field data can be read by a GIS (Geographic Information System) and an EMS (Energy Management System).
And S2, acquiring the main wind direction in a preset time period according to the wind field data.
And S3, determining the projection distance of the wind farm flow field measuring point on the main wind direction according to the coordinate of the wind farm flow field measuring point and the main wind direction.
According to GIS data and basic requirements of deployment of measuring points, if the projection distance can be configured with wind power plant flow field measuring points, recording the projection distance of the wind power plant flow field measuring points on the main wind direction, otherwise, recording the wind power plant flow field measuring points as infeasible points. All measurement points in the wind farm are traversed according to step S3.
According to the dimension reduction principle, the initial sample space in step 101 may be a two-dimensional sample space or a one-dimensional sample space, but in order to realize the ordering of N samples according to the optimal linear approximation error result of the one-dimensional flow field curve of the wind farm, if the initial sample space is the two-dimensional sample space, the dimension reduction processing on the two-dimensional sample space is needed first.
In the first example, the position of the wind farm flow field measurement point is a two-dimensional coordinate of the wind farm flow field measurement point;
step 101 of constructing an initial sample space comprises: generating uniformly distributed random two-dimensional coordinates of wind power plant flow field measurement points in a two-dimensional space according to a uniformly distributed random function to form an initial sample space; step 102, obtaining N samples of a wind farm flow field measurement point position deployment decision from an initial sample space, including: s1: selecting N samples from an initial sample space; specifically, N samples are selected in an initial sample space according to a probability equality principle; s2: acquiring wind field data, wherein the wind field data at least comprises: the wind direction of the wind power plant flow field measuring point and the position of the wind power plant flow field measuring point in the wind power plant; acquiring a main wind direction in a preset time period according to wind field data; determining the projection distance of the wind power plant flow field measuring point on the main wind direction according to the coordinate of the wind power plant flow field measuring point and the main wind direction; and traversing N samples in the initial sample space to obtain a one-dimensional sample space, wherein the one-dimensional sample space comprises the N samples.
In example two, if the initial sample space is a two-dimensional sample space, and the position of the wind farm flow field measurement point is a two-dimensional coordinate of the wind farm flow field measurement point; step 101 of constructing an initial sample space comprises: generating uniformly distributed random two-dimensional coordinates of wind power plant flow field measurement points in a two-dimensional space according to a uniformly distributed random function to form an initial sample space; step 102, obtaining N samples of a wind farm flow field measurement point position deployment decision from an initial sample space, including: acquiring wind field data, wherein the wind field data at least comprises: the wind direction of the wind power plant flow field measuring point and the position of the wind power plant flow field measuring point in the wind power plant; acquiring a main wind direction in a preset time period according to the wind field data; determining the projection distance of the wind power plant flow field measuring point on the main wind direction according to the coordinate of the wind power plant flow field measuring point and the main wind direction; traversing the wind power plant flow field measurement points of the initial sample space to obtain a one-dimensional sample space; and selecting N samples in the one-dimensional sample space, and specifically selecting N samples in the one-dimensional sample space according to a probability equality principle.
In the above two examples in which the initial sample space is a two-dimensional sample space, the difference between the first example and the second example is: in the first example, N samples are selected in a two-dimensional initial sample space, and then the sample space formed by the N samples is subjected to dimensionality reduction to form a one-dimensional sample space containing the N samples, so that the process of selecting the N samples in the initial sample space is realized; in the second example, a two-dimensional initial sample space is first reduced to form a one-dimensional sample space, and then N samples are selected from the one-dimensional sample space, so as to realize the process of selecting N samples from the initial sample space.
In example three: if the initial sample space is a one-dimensional sample space, step 101 constructs an initial sample space, including: generating uniformly distributed random two-dimensional coordinates of the wind power plant flow field measuring points in a two-dimensional space according to a uniformly distributed random function to form a random sample space; acquiring wind field data, wherein the wind field data at least comprises: the wind direction of the wind power plant flow field measuring point and the position of the wind power plant flow field measuring point in the wind power plant; acquiring a main wind direction in a preset time period according to wind field data; determining the projection distance of the wind power plant flow field measuring point on the main wind direction according to the coordinate of the wind power plant flow field measuring point and the main wind direction; traversing the wind power plant flow field measurement points of the initial sample space to obtain a one-dimensional sample space; step 102, obtaining N samples of a wind farm flow field measurement point position deployment decision from a random sample space, including: n samples are taken in a one-dimensional sample space.
The similarity of wind power field flow field measurement points in the vertical direction of the main wind direction is utilized to convert the two-dimensional problem of deploying the wind power field flow field measurement points in the wind power field area into a one-dimensional problem of arrangement according to the main wind direction. The following are exemplary: for an ideal wind farm measurement area over a ten kilometer range, the decision space may be compressed by 85%.
Wherein step 103 is: and carrying out accurate simulation evaluation on the prediction precision of the output power of the wind power plant on the sample of the ideal sample space S according to the root mean square error RMSE, and obtaining the position optimal solution omega of the flow field measurement point of the wind power plant. In the scheme, N samples are sequenced according to the optimal linear approximation error result of the one-dimensional flow field curve of the wind power plant, and then an ideal sample space S is obtained from the N samples, so that the number of samples for predicting the output power of the wind power plant is reduced, and the calculation cost is reduced.
According to the scheme, the sample space is reduced to the one-dimensional sample space processed to the main wind direction, so that the ideal sample space S can be divided into the breadth-first search subset and the depth-first search subset, the samples in the breadth-first search subset can be used for predicting the power of the wind farm according to the density of the wind farm flow field measuring points on the main wind direction, the samples in the depth-first search subset can be used for predicting the power of the wind farm according to the number of the wind farm flow field measuring points near the projection of one wind farm flow field measuring point on the main wind direction, and therefore when the power prediction accuracy of the wind farm is improved, the distribution density and the number of the wind farm flow field measuring points can be considered. Specifically, after obtaining the ideal sample space S, the following processing steps are included, as shown in fig. 7:
s11: the ideal sample space S is divided into a depth-first search subset and a breadth-first search subset according to the characteristics of the one-dimensional sample space.
S12: and respectively sequencing the samples in the depth-first search subset and the breadth-first search subset according to the result of the linear approximation error of the one-dimensional flow field curve of the wind power plant.
S13: and according to a preset sequence, carrying out accurate simulation evaluation on the output power prediction precision of the wind power plant on samples in the depth-first search subset and the breadth-first search subset, and obtaining the position optimal solution omega of the flow field measurement point of the wind power plant. In the preset sequence, the samples in the depth-first search subset and the samples in the breadth-first search subset are arranged alternately, the samples in the depth-first search subset are arranged according to the ascending order of the optimal linear approximation error result of the one-dimensional flow field curve of the wind power plant, and the samples in the breadth-first search subset are arranged according to the ascending order of the optimal linear approximation error result of the one-dimensional flow field curve of the wind power plant.
In step S13, a random number r is generated according to [0,1] even distribution for an arbitrary sample S in the ideal sample space S, for example, the first sample S is 1, and if r is less than 0.6, the accurate simulation evaluation of the wind farm output power prediction accuracy is performed for the sample S of the SB subset is 1; otherwise, carrying out accurate simulation evaluation on the output power prediction precision of the wind power plant on the sample s of the SD subset to be 1; and traversing the SB subset and the SD subset to obtain the position optimal solution omega of the wind power plant flow field measuring point. In the SB subset, the order of the accurate simulation evaluation is sorted according to the root mean square error RMSE, and similarly, in the SD subset, the order of the accurate simulation evaluation is sorted according to the root mean square error RMSE.
The embodiment of the application provides a prediction map of any three wind farm flow field measurement points arranged in the prior art for the ultra-short term (one hour in advance) of the output power of the wind farm, as shown in fig. 8; the coordinates of flow field measurement points of the three wind power plants, the prediction results of the output power of the wind power plants and the RMSE of the actual output power are shown in a table I:
| Wind power plant flow field measurement point coordinate | RMSE |
| (3678,541)，(3898,6258)，(1525,520) | 0.12 |
| (2382,4521)，(596,4916)，(1666,314) | 0.15 |
| (6515，6397)，(2987,1748)，(4993,4351) | 0.11 |
| (296,3973)，(1406,2427)，(6190,5091) | 0.11 |
After the configuration of the electric field flow field measurement points is optimized according to the scheme provided by the application, any three wind farm flow field measurement points are used for predicting the ultra-short term (one hour in advance) output power of the wind farm, as shown in fig. 9; the coordinates of flow field measurement points of the three wind power plants, the prediction results of the output power of the wind power plants and the RMSE of the actual output power are shown in a table two:
watch two
| Wind power plant flow field measurement point coordinate | RMSE |
| (296,3973)(1406,2427)(6190,5091) | 0.08 |
Comparing the first table and the second table, the predicted RMSE of the wind power plant output power is reduced to 0.08.
The embodiment of the application provides a configuration optimization device for wind power plant flow field measurement points, which is used for executing the configuration optimization method for the wind power plant flow field measurement points. According to the method, the functional modules of the configuration optimization device of the wind farm flow field measurement point can be divided, for example, the functional modules can be divided corresponding to the functions, or two or more functions can be integrated into one processing module. The integrated module can be realized in a hardware mode, and can also be realized in a software functional module mode. It should be noted that, in the embodiment of the present application, the division of the module is schematic, and is only one logic function division, and there may be another division manner in actual implementation.
In the case of dividing each functional module according to each function, fig. 10 shows a schematic structural diagram of a configuration optimization device 100 of a wind farm flow field measurement point according to the foregoing embodiment, where the configuration optimization device 100 of the wind farm flow field measurement point includes: an initialization module 101, a sampling module 102, a calculation module 103, and a solving module 104. The initialization module 101 is used for supporting the configuration optimization device of the wind power plant flow field measurement point to execute the step 101; the sampling module 102 is used for supporting the configuration optimization device of the wind power plant flow field measurement point to execute the step 102; the calculation module 103 is used for supporting the configuration optimization device of the wind power plant flow field measurement point to execute the step 103; the solving module 104 is used for supporting the configuration optimization device of the wind power plant flow field measurement point to execute the step 104; in addition, the calculation module 103 is configured to support the configuration optimization device of the wind farm flow field measurement point to execute steps S11 and S12; the solving module 104 is used for supporting the configuration optimization device of the wind farm flow field measurement point to execute the step S13; all relevant contents of each step related to the above method embodiment may be referred to the functional description of the corresponding functional module, and are not described herein again.
In the case of an integrated unit, fig. 11 shows a schematic diagram of a possible configuration of the configuration optimization device 110 of the wind farm flow field measurement point involved in the above embodiment. The configuration optimization device 110 for the wind farm flow field measurement point includes: a communication unit 111, a processing unit 112 and a storage unit 113. The processing unit 112 is configured to control and manage actions of the configuration optimization device of the wind farm flow field measurement point, for example, the processing unit 112 is configured to support the configuration optimization device of the wind farm flow field measurement point to execute the processes 101, 102, 103, and 104 in the foregoing method; the communication unit 111 is configured to support connection of a configuration optimization device of the wind farm flow field measurement point and an external device for data interaction, and is configured to perform a part of functions of the sampling module 102, for example, acquiring wind farm data. The storage unit 2413 is configured to store program codes and data of the configuration optimization device of the wind farm flow field measurement point.
The processing unit 112 may be a processor or a controller, and may be, for example, a Central Processing Unit (CPU), a general purpose processor, a Digital Signal Processor (DSP), an application-specific integrated circuit (ASIC), a Field Programmable Gate Array (FPGA) or other programmable logic device, a transistor logic device, a hardware component, or any combination thereof. Which may implement or perform the various illustrative logical blocks, modules, and circuits described in connection with the disclosure. The processor may also be a combination of computing functions, e.g., comprising one or more microprocessors, DSPs, and microprocessors, among others. The communication unit 111 may be a communication interface or the like. The storage unit 113 may be a memory.
When the processing unit 112 is a processor, the communication unit 111 is an interface circuit, and the storage unit 113 is a memory, the configuration optimization device for wind farm flow field measurement points according to the embodiment of the present application may be the following configuration optimization device for wind farm flow field measurement points.
Referring to fig. 12, the configuration optimization device 120 for wind farm flow field measurement points includes: a processor 121, a memory 122, a bus 123, and an interface circuit 124; the memory 122 is configured to store a computer execution instruction, the interface circuit 124 and the processor 121 are connected to the memory 122 through the bus 123, and when the configuration optimization device 120 for wind farm flow field measurement points operates, the processor 121 executes the computer execution instruction stored in the memory 122, so that the control device of the optical switch chip executes the configuration optimization method for wind farm flow field measurement points as described above. The bus 123 may be a Peripheral Component Interconnect (PCI) bus, an Extended Industry Standard Architecture (EISA) bus, or the like. The bus 2503 may be divided into an address bus, a data bus, a control bus, and the like. For ease of illustration, only one thick line is shown in FIG. 12, but this is not intended to represent only one bus or type of bus.
The embodiment of the present application also provides a storage medium, which may include a memory 122.
The configuration optimization device for the wind farm flow field measurement points provided by the embodiment of the application can be used for executing the configuration optimization method for the wind farm flow field measurement points, so that the technical effect obtained by the configuration optimization device can refer to the method embodiment, and the details of the method embodiment are not repeated herein.
In the above embodiments, the implementation may be wholly or partially realized by software, hardware, firmware, or any combination thereof. When implemented using a software program, may be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. The procedures or functions described in accordance with the embodiments of the present application are all or partially generated upon loading and execution of computer program instructions on a computer. The computer may be a general purpose computer, a special purpose computer, a network of computers, or other programmable device. The computer instructions may be stored on a computer readable storage medium or transmitted from one computer readable storage medium to another, for example, from one website, computer, server, or data center to another website, computer, server, or data center via wire (e.g., coaxial cable, fiber optic, Digital Subscriber Line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium that can be accessed by a computer or can comprise one or more data storage devices, such as a server, a data center, etc., that can be integrated with the medium. The usable medium may be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., Solid State Disk (SSD)), among others.
While the present application has been described in connection with various embodiments, other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed application, from a review of the drawings, the disclosure, and the appended claims. In the claims, the word "comprising" does not exclude other elements or steps, and the word "a" or "an" does not exclude a plurality. A single processor or other unit may fulfill the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.
Although the present application has been described in conjunction with specific features and embodiments thereof, it will be evident that various modifications and combinations can be made thereto without departing from the spirit and scope of the application. Accordingly, the specification and figures are merely exemplary of the present application as defined in the appended claims and are intended to cover any and all modifications, variations, combinations, or equivalents within the scope of the present application. It will be apparent to those skilled in the art that various changes and modifications may be made in the present application without departing from the spirit and scope of the application. Thus, if such modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is intended to include such modifications and variations as well.
Claims (12)
1. A method for optimizing the configuration of wind field measurement points in a wind farm is characterized in that,
constructing an initial sample space, wherein the initial sample space comprises at least one sample of a wind power plant flow field measurement point position deployment decision, the sample of the wind power plant flow field measurement point position deployment decision comprises at least one position of the wind power plant flow field measurement point, and the wind power plant flow field measurement point is configured on a fan and/or a anemometer tower;
obtaining N samples of a wind power plant flow field measurement point position deployment decision from the initial sample space;
sequencing the N samples according to the linear approximation error result of the one-dimensional flow field curve of the wind power plant, and selecting the sample with the linear approximation error result smaller than a preset value from the N samples to form an ideal sample space S;
carrying out accurate simulation evaluation on the prediction precision of the wind power plant output power on the sample of the ideal sample space S to obtain an optimal position solution omega of a wind power plant flow field measurement point;
the method comprises the following steps of carrying out accurate simulation evaluation on the output power prediction precision of the wind power plant on a sample of the ideal sample space S, and obtaining a position optimal solution omega of a wind power plant flow field measurement point, wherein the method comprises the following steps: and carrying out accurate simulation evaluation on the prediction precision of the output power of the wind power plant on the sample of the ideal sample space S according to the root mean square error RMSE, and obtaining the position optimal solution omega of the flow field measurement point of the wind power plant.
2. The method of claim 1, wherein the initial sample space is a two-dimensional sample space and the location of the wind farm flow field measurement point is a two-dimensional coordinate of the wind farm flow field measurement point;
the constructing an initial sample space comprises: generating uniformly distributed random two-dimensional coordinates of the wind power plant flow field measuring points in a two-dimensional space according to a uniformly distributed random function to form an initial sample space;
the obtaining of N samples of a wind farm flow field measurement point location deployment decision from the initial sample space includes:
selecting N samples from the initial sample space;
acquiring wind field data, wherein the wind field data at least comprises: the wind direction of the wind power plant flow field measuring point and the position of the wind power plant flow field measuring point in the wind power plant;
acquiring a main wind direction in a preset time period according to the wind field data;
determining the projection distance of the wind power plant flow field measuring point on the main wind direction according to the coordinate of the wind power plant flow field measuring point and the main wind direction;
and traversing the N samples in the initial sample space to obtain a one-dimensional sample space, wherein the one-dimensional sample space comprises the N samples.
3. The method of claim 1, wherein the initial sample space is a two-dimensional sample space and the location of the wind farm flow field measurement point is a two-dimensional coordinate of the wind farm flow field measurement point;
the constructing an initial sample space comprises: generating uniformly distributed random two-dimensional coordinates of the wind power plant flow field measuring points in a two-dimensional space according to a uniformly distributed random function to form an initial sample space;
the obtaining of N samples of a wind farm flow field measurement point location deployment decision from the initial sample space includes:
acquiring wind field data, wherein the wind field data at least comprises: the wind direction of the wind power plant flow field measuring point and the position of the wind power plant flow field measuring point in the wind power plant;
acquiring a main wind direction in a preset time period according to the wind field data;
determining the projection distance of the wind power plant flow field measuring point on the main wind direction according to the coordinate of the wind power plant flow field measuring point and the main wind direction;
traversing the wind power plant flow field measurement points of the initial sample space to obtain a one-dimensional sample space;
and selecting N samples in the one-dimensional sample space.
4. The method of claim 1, wherein the initial sample space is a one-dimensional sample space, and wherein constructing the initial sample space comprises:
generating uniformly distributed random two-dimensional coordinates of the wind power plant flow field measuring points in a two-dimensional space according to a uniformly distributed random function to form a random sample space;
acquiring wind field data, wherein the wind field data at least comprises: the wind direction of the wind power plant flow field measuring point and the position of the wind power plant flow field measuring point in the wind power plant;
acquiring a main wind direction in a preset time period according to the wind field data;
determining the projection distance of the wind power plant flow field measuring point on the main wind direction according to the coordinate of the wind power plant flow field measuring point and the main wind direction;
traversing the wind power plant flow field measurement points of the random sample space to obtain a one-dimensional sample space;
obtaining N samples of a deployment decision of a wind power plant flow field measurement point position from the initial sample space, wherein the N samples comprise: and selecting N samples in the one-dimensional sample space.
5. The method according to any one of claims 2 to 4, wherein before the accurate simulation evaluation of the wind farm output power prediction accuracy is performed on the samples of the ideal sample space S according to the root mean square error RMSE and the position optimal solution Ω of the wind farm flow field measurement point is obtained, the method further comprises:
dividing the ideal sample space S into a depth-first search subset and a breadth-first search subset according to the characteristics of the one-dimensional sample space;
according to the result of the linear approximation error of the one-dimensional flow field curve of the wind power plant, respectively sequencing the samples in the depth-first search subset and the breadth-first search subset;
the accurate simulation evaluation of the prediction precision of the output power of the wind power plant is carried out on the sample of the ideal sample space S according to the root mean square error RMSE, and the position optimal solution omega of the flow field measurement point of the wind power plant is obtained, and the method comprises the following steps: and according to a preset sequence, performing accurate simulation evaluation on the output power prediction precision of the wind power plant on samples in the depth-first search subset and the breadth-first search subset to obtain a position optimal solution omega of a flow field measurement point of the wind power plant, wherein in the preset sequence, the samples in the depth-first search subset and the samples in the breadth-first search subset are arranged alternately, the samples in the depth-first search subset are arranged according to the ascending order of the results of the linear approximation errors of the one-dimensional flow field curve of the wind power plant, and the samples in the breadth-first search subset are arranged according to the ascending order of the results of the optimal linear approximation errors of the one-dimensional flow field curve of the wind power plant.
6. An allocation optimization device for wind power plant flow field measurement points is characterized in that,
the system comprises an initialization module, a calculation module and a calculation module, wherein the initialization module is used for constructing an initial sample space, the initial sample space comprises at least one sample of a wind farm flow field measurement point position deployment decision, the sample of the wind farm flow field measurement point position deployment decision comprises at least one position of the wind farm flow field measurement point, and the wind farm flow field measurement point is configured on a fan and/or a wind measuring tower;
the sampling module is used for acquiring N samples of a wind power plant flow field measurement point position deployment decision from the initial sample space constructed by the initialization module;
the calculation module is used for sequencing the N samples acquired by the sampling module according to the linear approximation error result of the one-dimensional flow field curve of the wind power plant, and selecting the sample with the linear approximation error result smaller than a preset value from the N samples to form an ideal sample space S;
the solving module is used for carrying out accurate simulation evaluation on the prediction precision of the output power of the wind power plant on the sample of the ideal sample space S obtained by the calculating module to obtain the position optimal solution omega of the flow field measurement point of the wind power plant; the solving module is specifically configured to perform accurate simulation evaluation on the prediction accuracy of the output power of the wind farm on the sample of the ideal sample space S according to the root mean square error RMSE, and obtain the position optimal solution Ω of the wind farm flow field measurement point.
7. The apparatus of claim 6, wherein the initial sample space is a two-dimensional sample space and the location of the wind farm flow field measurement point is a two-dimensional coordinate of the wind farm flow field measurement point;
the initialization module is specifically used for generating uniformly distributed random two-dimensional coordinates of wind power plant flow field measurement points in a two-dimensional space according to a uniformly distributed random function to form an initial sample space;
the sampling module is specifically used for selecting N samples in the initial sample space; acquiring wind field data, wherein the wind field data at least comprises: the wind direction of the wind power plant flow field measuring point and the position of the wind power plant flow field measuring point in the wind power plant; acquiring a main wind direction in a preset time period according to the wind field data; determining the projection distance of the wind power plant flow field measuring point on the main wind direction according to the coordinate of the wind power plant flow field measuring point and the main wind direction; and traversing the N samples in the initial sample space to obtain a one-dimensional sample space, wherein the one-dimensional sample space comprises the N samples.
8. The apparatus of claim 6, wherein the initial sample space is a two-dimensional sample space and the location of the wind farm flow field measurement point is a two-dimensional coordinate of the wind farm flow field measurement point;
the initialization module is specifically used for generating uniformly distributed random two-dimensional coordinates of wind power plant flow field measurement points in a two-dimensional space according to a uniformly distributed random function to form an initial sample space;
the sampling module is specifically used for acquiring wind field data, and the wind field data at least comprises: the wind direction of the wind power plant flow field measuring point and the position of the wind power plant flow field measuring point in the wind power plant; acquiring a main wind direction in a preset time period according to the wind field data; determining the projection distance of the wind power plant flow field measuring point on the main wind direction according to the coordinate of the wind power plant flow field measuring point and the main wind direction; traversing the wind power plant flow field measurement points of the initial sample space to obtain a one-dimensional sample space; and selecting N samples in the one-dimensional sample space.
9. The apparatus of claim 6,
the initialization module is specifically used for generating uniformly distributed random two-dimensional coordinates of wind power plant flow field measurement points in a two-dimensional space according to a uniformly distributed random function to form a random sample space; acquiring wind field data, wherein the wind field data at least comprises: the wind direction of the wind power plant flow field measuring point and the position of the wind power plant flow field measuring point in the wind power plant; acquiring a main wind direction in a preset time period according to the wind field data; determining the projection distance of the wind power plant flow field measuring point on the main wind direction according to the coordinate of the wind power plant flow field measuring point and the main wind direction; traversing the wind power plant flow field measurement points of the random sample space to obtain a one-dimensional sample space;
the sampling module is specifically configured to select N samples in the one-dimensional sample space.
10. The apparatus according to any one of claims 7-9, wherein the computing module is further configured to divide the ideal sample space S into a depth-first search subset and a breadth-first search subset according to the characteristics of the one-dimensional sample space; according to the result of the linear approximation error of the one-dimensional flow field curve of the wind power plant, respectively sequencing the samples in the depth-first search subset and the breadth-first search subset;
the solving module is specifically used for carrying out accurate simulation evaluation on the output power prediction precision of the wind power plant on the solutions of the samples in the depth-first search subset and the breadth-first search subset according to a preset sequence, and obtaining a position optimal solution omega of a wind power plant flow field measurement point; in the preset sequence, the samples in the depth-first search subset and the samples in the breadth-first search subset are arranged alternately, the samples in the depth-first search subset are arranged according to the ascending result of the linear approximation error of the one-dimensional flow field curve of the wind power plant, and the samples in the breadth-first search subset are arranged according to the ascending result of the linear approximation error of the one-dimensional flow field curve of the wind power plant.
11. A configuration optimization device for wind power plant flow field measurement points is characterized by comprising: a processor, a memory, and a bus; the memory is used for storing computer-executable instructions, the processor is connected with the memory through the bus, and when the configuration optimization device of the wind farm flow field measurement point runs, the processor executes the computer-executable instructions stored in the memory to enable the control device to execute the method according to any one of claims 1 to 5.
12. A computer storage medium comprising instructions which, when run on a computer, cause the computer to perform the method of any one of claims 1-5.
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