CN111553398A - Wind power scene uncertain continuous interval obtaining method based on multidimensional normal distribution - Google Patents

Wind power scene uncertain continuous interval obtaining method based on multidimensional normal distribution Download PDF

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CN111553398A
CN111553398A CN202010318642.1A CN202010318642A CN111553398A CN 111553398 A CN111553398 A CN 111553398A CN 202010318642 A CN202010318642 A CN 202010318642A CN 111553398 A CN111553398 A CN 111553398A
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李彬
阳同光
黎灿兵
黄志亮
李文芳
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Abstract

The invention relates to the field of wind power, and discloses a method for acquiring an uncertain continuous interval of a wind power scene based on multidimensional normal distribution, which specifically comprises the following steps: s1: according to research data, the day-ahead prediction error sequence of wind power of the wind power plant is shown to obey multidimensional normal distribution, and a random vector about the multidimensional normal distribution is generated to serve as a wind power output scene, namely a preliminary wind power output uncertain continuous interval; s2: and improving K-means clustering on the wind power output scene, reducing the wind power output scene, and obtaining a final more accurate uncertain continuous interval of wind power output. After a large number of scene samples are generated, improved K-means clustering is carried out on each generated scene to properly smooth the generated interval, the influence of the extreme value on the generated interval is reduced, and the interval range is reduced as much as possible on the premise of ensuring that the interval contains the range of wind power.

Description

Wind power scene uncertain continuous interval obtaining method based on multidimensional normal distribution
Technical Field
The invention relates to the field of wind power, in particular to a wind power scene uncertain continuous interval obtaining method based on multidimensional normal distribution.
Background
The essential difference between wind power generation and traditional power generation is that the energy source can not be stored and is influenced by various factors such as weather and terrain, and the difference determines that the wind power output has obvious fluctuation, randomness and uncontrollable property. The large-scale participation of wind power in grid connection brings great challenges to the scheduling of traditional power systems based on reliable power sources (such as thermal power and hydroelectric power). In the face of the change of a power supply structure, under the current large background of rapid wind power development, the method for finding out the power system dispatching mode which can not only give play to the environmental protection benefits of wind power, but also give consideration to the safety of a power grid has important significance.
The day-ahead combined dispatching of wind power, hydropower and thermal power of an electric power system refers to an optimization problem of determining the output of a wind power plant, a hydropower station and a thermal power plant unit in a certain dispatching range, and the problem is to minimize the total fuel cost of the thermal power plant in a dispatching cycle on the premise of meeting the requirements of power balance, water balance, unit constraint and the like of the electric power system.
A flexible and steady model is found to describe the actual wind power output, and at present, four main models for processing the wind power uncertainty are provided, namely a fuzzy set model, a robust optimization model, a probability sampling model and an interval optimization model.
In the fuzzy set model, wind power with uncertainty is used as a fuzzy variable, the model has the advantages that the obtained optimal scheduling scheme can change well according to the scheduling emphasis point, and the disadvantage is that the setting of the membership function of the model has certain subjectivity and cannot well reflect objective conditions.
For the robust optimization model, wind power with uncertainty is used as an uncertain parameter set, and the set is used for giving an optimization result under the worst condition. The model has the advantages that a feasible solution meeting extreme conditions is obtained under uncertain factors, and the feasible solution is over conservative sometimes and is not beneficial to saving cost.
In the probability sampling model, wind power with uncertainty is used as a random variable, and the occurrence probability of the wind power output situation is simulated by depending on a sampling method. The model mainly adopts a Monte Carlo method for sampling, has the advantages that probability information of random variables can be obtained by bypassing a distribution function, and has the disadvantages that the sampling times are not easy to set, the probability result can be influenced by the amount of the sampling times, in addition, the final scheduling result in the probability sampling model is usually an expected average value under a scheme of a plurality of wind power output situations, and the specific output of a unit is difficult to guide.
For the interval model, the wind power with uncertainty is designed as a continuous interval variable. Therefore, the interval model mainly depends on the lower bound and the upper bound of the interval variable to participate in the calculation of the scheduling result. The interval model has the advantages that uncertain factors can be quantized in an interval, the optimal solution under the constraint of the interval can be obtained through a conventional method, and the interval model has the defects that the continuous interval of wind power is not easy to obtain, and the scheduling result is very sensitive to the interval value.
There are two main methods for solving the interval of the random variable, an interval estimation method and a scene simulation method. The interval estimation method is to construct variable estimation intervals based on a certain confidence level through a probability distribution function of random variables. The interval estimation method has a perfect mathematical theory, but the selection of the confidence level lacks clear regulation. The scene simulation method is to generate a plurality of variable scenes based on the probability distribution function of random variables and obtain the upper and lower bounds of the random variables. When enough scenes are generated, the upper and lower bounds can completely cover the variation range of the random variable, but the individual extreme scenes are easy to cause large deviation of the upper or lower bounds. The problem of joint scheduling of wind power, hydropower and thermal power day ahead still faces some challenges caused by wind power uncertainty, hydropower and thermal power start-stop limits.
In view of the above, the modeling and solving of the day-ahead joint scheduling problem of wind power, hydropower and thermal power are mainly researched from the perspective of the power generation cost of the system. Aiming at the acquisition of the wind power uncertain continuous interval, a scene interval method based on multidimensional normal distribution is provided. The wind power output is difficult to predict completely, so the uncertainty of the wind power output needs to be considered during scheduling. The conventional method is to obtain a distribution function of a wind power output prediction value or a distribution function of a prediction error, and randomly sample to generate a series of scenes which accord with the distribution, wherein each scene has a corresponding occurrence probability value. In order to fully simulate the possible change situation of wind power output, a large number of wind power output error scenes need to be generated. The more the number of scenes is, the more possible the scenes cover the real output situation, but the time for solving the random variable problem is extremely long; the smaller the number, the easier it is to save solution time, but the result accuracy will be inevitably affected.
For example, chinese patent publication No. CN 106230028B, 2019, 1 month and 22 days, discloses a multi-objective optimization method for a wind power-pumped storage combined system, which is based on that a predicted value of wind power is known and a load is determined in the past, and includes the steps of: based on wind power output power prediction and probability distribution of prediction errors, performing scene sampling by adopting an autoregressive moving average model and establishing a group of initial scenes; processing an initial scene by adopting scene reduction to obtain an optimal wind power scene tree; and establishing a mathematical optimization model with low carbon and low cost as targets, taking the starting and stopping states of the unit and the active power output distribution of the unit in each period as decision variables, optimizing the optimal wind power scene tree by adopting a second-order random optimization model, and outputting optimal unit scheduling. A method for effectively reducing a wind power scene is not adopted, and the deviation of the upper and lower boundaries of an influence interval with an overlarge extreme value cannot be avoided.
Disclosure of Invention
The method aims to solve the technical problem that an interval model is improved, in order to avoid the deviation of the extreme value from the upper bound and the lower bound of an influence interval, after a large number of enough scene samples are generated, improved K-means clustering is carried out on each generated scene to properly smooth the generation interval, the influence of the extreme value on the generation interval is reduced, and the interval range is reduced as much as possible on the premise of ensuring that the interval contains the range of wind power.
In order to solve the problems, a wind power scene uncertain continuous interval obtaining method based on multidimensional normal distribution is adopted, and the method is characterized by comprising the following steps:
s1: according to research data, the day-ahead prediction error sequence of wind power of the wind power plant is shown to obey multidimensional normal distribution, and a random vector about the multidimensional normal distribution is generated to serve as a wind power output scene, namely a preliminary wind power output uncertain continuous interval;
s2: and improving K-means clustering (K-means clustering algorithm) on the wind power output scene, reducing the wind power output scene, and obtaining a final more accurate uncertain continuous interval of wind power output.
As a further improvement of the present invention, in step S1, the specific steps of generating the random vector about the multidimensional normal distribution are:
(1) respectively and independently generating normal distribution random numbers on respective dimensionalities according to the mean value and the standard deviation of given edge distribution, and synthesizing a vector Y according to component positions, wherein Y is an independent multi-dimensional normal distribution random vector;
(2) performing Cholesky decomposition on the correlation number matrix rho;
(3) multiplying the matrix obtained by decomposition by the vector Y generated in the step (1) to obtain a random vector X under the solved joint distribution;
(4) considering the situation that X falls in a non-sample statistical region, an X acceptable interval is introduced as a standard for selecting acceptance, and the boundary value of the acceptable interval is determined by the maximum Euclidean distance D between an error sequence and an error mean sequence in a statistical samplemaxAnd a minimum Euclidean distance DminIt is determined that the final effective scene is X ═ X (D)min＜X＜Dmax)。
As a further improvement of the present invention, in the step (2), the cholesky decomposition is as follows:
ρ＝RRT(1)
wherein, R is a lower triangular matrix, and the formula is as follows:
Figure BDA0002460495840000031
as a further improvement of the invention, in the step (3), the specific process is as follows:
X＝RY
as a further improvement of the present invention, in step (3), Y ═ R is allowed-1X, proving that all components of the random vector Y are not related to each other, and specifically comprising the following steps:
Figure BDA0002460495840000041
the cause covariance matrix of the above formula has the following properties:
Cov(Ax,By)＝ACov(x,y)BT(4)
since Y is a random variable in normal distribution, every two components in Y are independent from each other, and according to the formula, the random vector X which is not independent can be obtained as long as an independent multi-dimensional normal distribution random vector Y is generated and then is transformed to make X equal to RY.
As a further improvement of the present invention, in step S2, the specific steps of improving K-means clustering for reducing the output scene are as follows:
given sample set is { X'1,X′2,...,X′n}, vector sequence
Figure BDA0002460495840000042
Figure BDA0002460495840000043
Representing the n-dimensional space of the real number domain, and the process of the k-means clustering algorithm of each sample in the sample set is as follows:
1) giving the number k of the cluster categories, and giving k cluster centers C ∈ { C } randomly in the sample set1,...,ck}；
2) Calculating the distance D (x) from all samples to the center of each clusteri,cj)；
3) Distributing each sample to a nearest clustering center to form a cluster;
4) the mean value of all samples in the k clusters is classified and calculated as the clustering center C ∈ { C }1,...,ckReplace the previous cluster center;
5) repeating the process of 2) -4) until the new cluster center and the old cluster center are approximately equidistant.
As a further improvement of the present invention, the distance index of the k-means cluster is an euclidean distance, and the calculation steps of the euclidean distance are as follows:
according to vector sequence X'i＝(x1,x2,…xn) And the vector sequence Y ═ Y1,y2,…,yn) The Euclidean distance is as shown in formula (5):
Figure BDA0002460495840000051
as a further improvement of the present invention, the distance index of the k-means cluster is a DTW distance improved based on euclidean distance, and the DTW distance is calculated by the following steps:
in the matrix D of equation (5), the set of each group of adjacent elements is called a curved path, and the boundary, continuity and monotonicity constraints are satisfied, and is denoted as P ═ P1,p2,…ps…,pgWhere g denotes the total number of elements in the path, element psIs the coordinate of the s-th point on the path, i.e. ps＝(i,j)；
The path P has a plurality of paths, and the purpose of DTW is to find an optimal curved path, so that the vector sequence Xi'＝(x1,x2,…xn) And the vector sequence Y ═ Y1,y2,…,yn) Has the smallest total cost of bending, i.e.
Figure BDA0002460495840000052
In order to solve the above equation, an accumulated cost matrix L is constructed by a dynamic programming method, wherein each element is:
Figure BDA0002460495840000053
wherein i is 1,2, …, n; j is 1,2, …, m; l (0,0) ═ 0, L (i,0) ═ L (0, j) ± ∞;
in the process of searching the curved path P, if the path is continuously bent for 2 times or more in the horizontal or vertical direction, the path is called continuous bending, in order to avoid the phenomenon of excessive bending in the process of searching the curved path, the DTW algorithm is improved by adding the constraint on the continuous bending number r on the basis of the original three constraints, namely the boundary property, the continuity and the monotonicity, and the DTW algorithm is improved, namely
rx≤rx_max,ry≤ry_max(8)
In the formula, rxAnd ryRespectively, path P in vector sequence Xi'＝(x1,x2,…xn) And the vector sequence Y ═ Y1,y2,…,yn) Number of consecutive bends in direction; r isx_maxAnd ry_maxAre respectively in vector sequence Xi'＝(x1,x2,…xn) And the vector sequence Y ═ Y1,y2,…,yn) The maximum continuous bending number allowed in the direction is determined according to the vector sequence X'i＝(x1,x2,…xn) And the vector sequence Y ═ Y1,y2,…,yn) Determining the dimension and the sequence characteristics of the target sequence;
thus, the formula (7) becomes a form of the following formula (9):
Figure BDA0002460495840000061
then vector sequence X'i＝(x1,x2,…xn) And Y ═ Y1,y2,…,yn) The improved dynamic time bending distance is as follows:
DTW′(X,Y)＝L′(n,m) (10)
in the formula (10), L '(n, m) is a vector sequence X'i＝(x1,x2,…xn) And Y ═ Y1,y2,…,yn) The higher the minimum total cost value of the curve, the greater the difference between the trend characteristics of the two sequences, and the more dissimilar the two curves.
As a further improvement of the method, the number of the K-means clusters after the wind power scene is reduced is 10 to 100.
As a further improvement of the method, the number of the K-means clusters after the wind power scene is reduced is 50 to 100.
According to the method, on the basis of K-means, the sample distance judgment method is changed into a DTW (dynamic Time warping) distance, so that the method can be better suitable for wind power scene sequence clustering, the influence of extreme values on a generation interval can be reduced, and the interval range can be reduced as much as possible on the premise that the interval contains the range where wind power appears.
Drawings
FIG. 1 is a generated and reduced wind farm output error scenario.
FIG. 2 is a wind farm output scene envelope curve under different cluster numbers.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
A wind power scene uncertain continuous interval obtaining method based on multidimensional normal distribution comprises two parts of wind power output scene generation and wind power processing scene clustering.
Wherein the improved K-means clustering is used to reduce the contribution scenario.
The method comprises the following steps: 1. and 2, generating a wind power output scene, and performing improved K-means clustering on the wind power output scene.
According to the scheme, the improved K-means clustering is carried out on the output scene, and the problem that the upper bound or the lower bound of the interval is greatly deviated easily due to the fact that the wind power output scene contains individual extreme scenes is solved.
1. Wind power output scene generation
According to previous researches, the wind power day-ahead prediction error sequence of the wind power plant is shown to be subjected to multidimensional normal distribution. The random vector generation procedure for multidimensional normal distribution is as follows:
(1) respectively and independently generating normal distribution random numbers on respective dimensionality according to the mean value and standard deviation of given edge distribution, and synthesizing a vector Y according to component positions;
(2) performing Cholesky decomposition on the correlation number matrix rho to make rho equal to RRT；
(3) And (3) multiplying the vector Y generated in the step (1) by the matrix obtained by decomposition, namely X is RY, and X is the random vector under the obtained joint distribution.
(4) Considering the situation that X falls in a non-sample statistical region, an X acceptable interval is introduced as a standard for selecting acceptance, and the boundary value of the acceptable interval is determined by the maximum Euclidean distance and the minimum Euclidean distance between an error sequence and an error mean sequence in a statistical sample. The final effective scene is X ═ X (D)min＜X＜Dmax)。
The generation process is derived as follows:
and (3) setting a random vector of multi-dimensional normal distribution as X and a correlation coefficient matrix as rho, and performing Cholesky (Cholesky) decomposition on the random vector:
ρ＝RRT(1)
where R is the lower triangular matrix, the formula is as follows.
Figure BDA0002460495840000071
Let Y be R-1X, it is easy to prove that the components of the random vector Y are uncorrelated with each other.
The mutual independence proves to be as follows:
Cov(Y)＝Cov(R-1X,(R-1X)T)＝R-1Cov(X,XT)(R-1)T
＝R-1ρ(R-1)T＝I
the cause covariance matrix of the above formula has the following properties:
Cov(Ax,By)＝ACov(x,y)BT(4)
since Y is a normally distributed random variable, every two components in Y are independent. According to the formula, it is proved that the random vector X which is not independent can be obtained by generating the independent multi-dimensional normal distribution random vector Y and then converting the vector into X which is equal to RY.
2. Improved K-means clustering for wind power output scene
Given sample set is { X'1,X′2,...,X′n}, vector sequence
Figure BDA0002460495840000082
Figure BDA0002460495840000083
Representing the n-dimensional space of the real number domain, and the process of the k-means clustering algorithm of each sample in the sample set is as follows:
1) giving the number k of the cluster categories, and giving k cluster centers C ∈ { C } randomly in the sample set1,...,ck}。
2) Calculating the distance D (x) from all samples to the center of each clusteri,cj)。
3) Each sample is assigned to the nearest cluster center, forming a cluster.
4) The mean value of all samples in the k clusters is classified and calculated as the clustering center C ∈ { C }1,...,ckReplace the previous cluster center.
5) Repeating the process of 2) -4) until the new cluster center and the old cluster center are approximately equidistant.
k-means clustering commonly uses Euclidean distance formula as a distance index, but Euclidean distance has very limitation on similarity measurement of time series, so the invention replaces the distance index in k-means with improved DTW distance similarity measurement.
The specific calculation of the two distances is as follows:
1) european distance
According to vector sequence X'i＝(x1,x2,…xn) And Y ═ Y1,y2,…,yn) The Euclidean distance is as shown in formula (5).
Figure BDA0002460495840000081
2) Improved DTW (dynamic Time warping) distance
Formula (5) is xiAnd yjThe euclidean distance between them. In matrix D, the set of each group of adjacent elements is called a curved path, and the boundary, continuity and monotonicity constraints are satisfied, and is denoted as P ═ P1,p2,…ps…,pgWhere g denotes the total number of elements in the path, element psIs the coordinate of the s-th point on the path, i.e. ps＝(i,j)。
The paths P are multiple, DTW aims to find an optimal curved path, such that the sequence X'i＝(x1,x2,…xn) And Y ═ Y1,y2,…,yn) Has the smallest total cost of bending, i.e.
Figure BDA0002460495840000091
In order to solve the above equation, an accumulated cost matrix L is constructed by a dynamic programming method, wherein each element is:
Figure BDA0002460495840000092
wherein i is 1,2, …, n; j is 1,2, …, m; l (0,0) ═ 0, L (i,0) ═ L (0, j) ∞.
In searching for the curved path P, if the path is continuously curved 2 times or more in the horizontal or vertical direction, it is called continuous curving. In order to avoid the phenomenon of excessive bending in the process of searching a bending path, the DTW algorithm is improved by adding the constraint of a continuous bending number r on the basis of the original three constraints (boundary, continuity and monotonicity), namely
rx≤rx_max,ry≤ry_max(8)
In the formula, rxAnd ryRespectively, path P in vector sequence X'i＝(x1,x2,…xn) And the vector sequence Y ═ Y1,y2,…,yn) Number of consecutive bends in direction; r isx_maxAnd ry_maxAre respectively in vector sequence X'i＝(x1,x2,…xn) And the vector sequence Y ═ Y1,y2,…,yn) The maximum continuous bending number allowed in the direction is determined according to the vector sequence X'i＝(x1,x2,…xn) And the vector sequence Y ═ Y1,y2,…,yn) Is determined, as well as the sequence characteristics.
Thus, the formula (7) becomes a form of the following formula (9):
Figure BDA0002460495840000101
then vector sequence X'i＝(x1,x2,…xn) And Y ═ Y1,y2,…,yn) The improved dynamic time bending distance is as follows:
DTW′(X,Y)＝L′(n,m) (10)
in the formula (10), L '(n, m) is the sequence X'i＝(x1,x2,…xn) And Y ═ Y1,y2,…,yn) The minimum total cost value of bending, through the above formula, can effectively carve the trend similarity distance between the sequences. The larger the value, the greater the difference between the trend characteristics of the two sequences, and the more dissimilar the two curves.
Aiming at the day-ahead prediction result of the wind power, the potential error interval of the power system is expected to be known as much as possible in the power system scheduling, and the more accurate the power system scheduling, the better the potential error interval. Taking the wind power plant wind power prediction result of a certain day of a certain place as an example, 1605 error sequence scenes are generated according to the error statistical parameters, and the reduced wind power plant output error scene result is drawn and generated, as shown in fig. 1. And drawing the output scene envelope lines of the wind power plants under different clustering numbers according to the reduced error scene result, as shown in FIG. 2.
As can be seen from fig. 1, the 1605 effective scenes obtained in the diagram (a) have an overall shape similar to an inverted funnel and two sides with saw teeth, which indicates that individual extreme points may appear in each dimension during the generation of the error sequence scenes. The graph (b) is the case of reducing the error scene to 10, and the coverage range is obviously smaller than that of the graph (a), but the overall trend is still an inverted funnel, and only two sides have no obvious saw teeth, which shows that the edge scene is replaced by the central scene in the process of scene reduction. In the case that the error scenes are reduced to 20, 50 and 100 in the graphs (c), (d) and (e), respectively, it can be found that the range covered by the reduced scenes is enlarged and is closer to the original scene range as the number of clusters increases.
The effect of bringing the error scene into the predicted value of the wind power plant output can be seen from fig. 2. In the figure, a gray shaded area is wind power rotating reserve capacity prepared according to 25% installed capacity in a conventional mode, and lines in the figure respectively represent an actual output value of a wind power plant, a predicted output value of the wind power plant, a reduced wind power plant output scene envelope line and an unreduced wind power plant output scene envelope line.
In the graph (a), the error scene is clustered to 10 wind farm output envelope ranges, and it can be found that the reduced wind farm output range is obviously smaller than the spare capacity range in the conventional mode, but the actual output is not effectively covered by the range, and the actual output obviously jumps out of the reduced envelope ranges in multiple prediction time periods such as 2 nd, 3 rd, 4 th, 7 th, 11 th, 12 th, 13 th, 23 th and the like.
Graph (b) is the wind farm output envelope range clustered to 20 in the error scene, and it can be found that the envelope range is enlarged compared with graph (a), the actual output jumps out of the envelope only in the 2 nd, 4 th and 7 th prediction periods, and the rest of the time does not cross the line.
Graph (c) is a range of wind farm output envelopes clustered to 50 in the error scenario, and it can be found that this envelope range can effectively cover the actual output (except for the 2 nd prediction period).
And (d) is the output envelope range of the wind power plant clustered to 100 in the error scene, and the envelope range is found to be expanded compared with the envelope range of the wind power plant clustered to 100 in the error scene, so that the actual output is effectively covered (except for the 2 nd prediction period).
In summary, although the original error scene envelope can cover the actual output situation by 100%, the wind power scheduling based on this envelope range may result in an excessively high wind power rotation reserve capacity. On the premise of not expanding the scheduling risk, the scene reduction method is adopted to shrink the envelope range of the error scene, so that the wind power rotating reserve capacity can be effectively reduced, and the clustering number is preferably 50 to 100.
In the conventional manner, the predicted value is supplemented with the fixed rotation reserve capacity, and although the situation that part of the predicted value of the wind power deviates from the actual value can be solved, in the prediction of the wind power day ahead, the more the prediction time interval is, the larger the prediction error is, and the actual output is likely to jump out of the fixed rotation reserve capacity. The output envelope curve of the wind power plant drawn according to the error scene can be expanded along with the increase of the prediction time period, the rotation reserve capacity can be effectively saved in the early stage of prediction, and the actual output can be effectively covered in the later stage of prediction.
Different from the existing wind power interval generation model, the method selects a clustering method in a reduced scene, greatly reduces the interval range, and is beneficial to reducing wind power rotation standby and improving the scheduling economy of a power system.
In addition, on the basis of K-means, the method for judging the sample distance is changed into the DTW (dynamic time warping) distance, so that the method can be better suitable for clustering the wind power scene sequence.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several equivalent substitutions or obvious modifications can be made without departing from the spirit of the invention, and all the properties or uses are considered to be within the scope of the invention.

Claims (10)

1. A wind power scene uncertain continuous interval obtaining method based on multidimensional normal distribution is characterized by comprising the following steps:
s1: according to research data, the day-ahead prediction error sequence of wind power of the wind power plant is shown to obey multidimensional normal distribution, and a random vector about the multidimensional normal distribution is generated to serve as a wind power output scene, namely a preliminary wind power output uncertain continuous interval;
s2: and improving K-means clustering on the wind power output scene, reducing the wind power output scene, and obtaining a final more accurate uncertain continuous interval of wind power output.
2. The wind power scene uncertain continuous interval obtaining method based on multi-dimensional normal distribution according to claim 1, wherein in step S1, the specific steps of generating random vectors about the multi-dimensional normal distribution are as follows:
(1) respectively and independently generating normal distribution random numbers on respective dimensionalities according to the mean value and the standard deviation of given edge distribution, and synthesizing a vector Y according to component positions, wherein Y is an independent multi-dimensional normal distribution random vector;
(2) performing Cholesky decomposition on the correlation number matrix rho;
(3) multiplying the matrix obtained by decomposition by the vector Y generated in the step (1) to obtain a random vector X under the solved joint distribution;
(4) considering the situation that X falls in a non-sample statistical region, an X acceptable interval is introduced as a standard for selecting acceptance, and the boundary value of the acceptable interval is determined by the maximum Euclidean distance D between an error sequence and an error mean sequence in a statistical samplemaxAnd a minimum Euclidean distance DminDetermining that the final effective scene is
X′＝X(Dmin＜X＜Dmax)。
3. The wind power scene uncertain continuous interval obtaining method based on multidimensional normal distribution as claimed in claim 2, wherein in step (2), the cholesky decomposition is as follows:
ρ＝RRT(1)
wherein, R is a lower triangular matrix, and the formula is as follows:
Figure FDA0002460495830000011
4. the wind power scene uncertain continuous interval obtaining method based on multi-dimensional normal distribution as claimed in claim 3, wherein in step (3), the specific process is as follows:
X＝RY。
5. the method for acquiring the uncertain continuous interval of wind power scene based on multidimensional normal distribution as claimed in claim 4, wherein in step (3), let Y-R-1X, proving that all components of the random vector Y are not related to each other, and specifically comprising the following steps:
Figure FDA0002460495830000021
the cause covariance matrix of the above formula has the following properties:
Cov(Ax,By)＝ACov(x,y)BT(4)
since Y is a random variable in normal distribution, every two components in Y are independent from each other, and according to the formula, the random vector X which is not independent can be obtained as long as an independent multi-dimensional normal distribution random vector Y is generated and then is transformed to make X equal to RY.
6. The method for acquiring the uncertain continuous interval of the wind power scene based on the multidimensional normal distribution as claimed in any one of claims 2 to 5, wherein in the step S2, the specific step of improving the K-means clustering for reducing the output scene is as follows:
given sample set is { X'1,X'2,...,X'n}, vector sequence
Figure FDA0002460495830000022
Figure FDA0002460495830000023
Representing the n-dimensional space of the real number domain, and the process of the k-means clustering algorithm of each sample in the sample set is as follows:
1) giving the number k of the cluster categories, and giving k cluster centers C ∈ { C } randomly in the sample set1,...,ck}；
2) Calculating the distance D (x) from all samples to the center of each clusteri,cj)；
3) Distributing each sample to a nearest clustering center to form a cluster;
4) the mean value of all samples in the k clusters is classified and calculated as the clustering center C ∈ { C }1,...,ckReplace the previous cluster center;
5) repeating the process of 2) -4) until the new cluster center and the old cluster center are approximately equidistant.
7. The method for acquiring the uncertain continuous interval of the wind power scene based on the multidimensional normal distribution as claimed in claim 6, wherein the distance index of the k-means cluster is Euclidean distance, and the calculation steps of the Euclidean distance are as follows:
for vector sequence X'i＝(x1,x2,…xn) And the vector sequence Y ═ Y1,y2,…,yn) The Euclidean distance is as shown in formula (5):
Figure FDA0002460495830000031
8. the method for acquiring the uncertain continuous interval of the wind power scene based on the multidimensional normal distribution as claimed in claim 7, wherein the distance index of the k-means cluster is a DTW distance improved based on Euclidean distance, and the DTW distance is calculated by the following steps:
in the matrix D of equation (5), the set of each group of adjacent elements is called a curved path, and the boundary, continuity and monotonicity constraints are satisfied, and is denoted as P ═ P1,p2,…ps…,pgWhere g denotes the total number of elements in the path, element psIs the coordinate of the s-th point on the path, i.e. ps＝(i,j)；
The paths P are multiple, DTW aims to find an optimal curved path, so that the vector sequence X'i＝(x1,x2,…xn) And the vector sequence Y ═ Y1,y2,…,yn) Has the smallest total cost of bending, i.e.
Figure FDA0002460495830000032
In order to solve the above equation, an accumulated cost matrix L is constructed by a dynamic programming method, wherein each element is:
Figure FDA0002460495830000033
wherein i is 1,2, …, n; j is 1,2, …, m; l (0,0) ═ 0, L (i,0) ═ L (0, j) ± ∞;
in the process of searching the curved path P, if the path is continuously bent for 2 times or more in the horizontal or vertical direction, the path is called continuous bending, in order to avoid the phenomenon of excessive bending in the process of searching the curved path, the DTW algorithm is improved by adding the constraint on the continuous bending number r on the basis of the original three constraints, namely the boundary property, the continuity and the monotonicity, and the DTW algorithm is improved, namely
rx≤rx_max,ry≤ry_max(8)
In the formula, rxAnd ryRespectively, path P in vector sequence X'i＝(x1,x2,…xn) And the vector sequence Y ═ Y1,y2,…,yn) Number of consecutive bends in direction; r isx_maxAnd ry_maxAre respectively in vector sequence X'i＝(x1,x2,…xn) And Y ═ Y1,y2,…,yn) Maximum number of consecutive bends allowed in direction, bothIs taken according to a vector sequence X'i＝(x1,x2,…xn) And Y ═ Y1,y2,…,yn) Determining the dimension and the sequence characteristics of the target sequence;
thus, the formula (7) becomes a form of the following formula (9):
Figure FDA0002460495830000041
then vector sequence X'i＝(x1,x2,…xn) And Y ═ Y1,y2,…,yn) The improved dynamic time bending distance is as follows:
DTW′(X,Y)＝L′(n,m) (10)
in the formula (10), L '(n, m) is a vector sequence X'i＝(x1,x2,…xn) And Y ═ Y1,y2,…,yn) The higher the minimum total cost value of the curve, the greater the difference between the trend characteristics of the two sequences, and the more dissimilar the two curves.
9. The wind power scene uncertain continuous interval obtaining method based on multi-dimensional normal distribution as claimed in claim 1, wherein the number of the K-means cluster reduced wind power scenes is 10 to 100.
10. The wind power scene uncertain continuous interval obtaining method based on multi-dimensional normal distribution as claimed in claim 9, wherein the number of the K-means cluster reduced wind power scenes is 50 to 100.
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