CN115344996A - Wind power typical scene construction method and system based on multi-characteristic quantity indexes of improved K-means algorithm - Google Patents
Wind power typical scene construction method and system based on multi-characteristic quantity indexes of improved K-means algorithm Download PDFInfo
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Abstract
The invention discloses a wind power typical scene construction method under multiple characteristic quantity indexes based on an improved K-means algorithm, which comprises the following steps: establishing a sample set with wind power multi-feature quantity according to the selected feature index of the wind power electro-fluctuation characteristic; based on the improvement of a K-means clustering algorithm, carrying out clustering analysis on the sample set, optimizing each clustering result according to a clustering effectiveness index, and finding out the optimal clustering result of the sample set; obtaining initial clustering centers of various clusters according to the optimal clustering result by combining the density degree and the maximum and minimum distance principle; and clustering and analyzing the wind power output scene by adopting an improved K-means clustering algorithm so as to reduce the wind power output scene and construct a typical wind power output scene. Compared with the traditional K-means clustering algorithm, the method reduces the randomness of the clustering center and the blindness of the clustering number setting, improves the accuracy of wind power generation clustering, and provides reference for actually making the operation planning and development of high-proportion wind power generation access power grid.
Description
Technical Field
The invention relates to the field of analysis of wind power generation scenes of a power system, in particular to a method and a system for constructing a typical wind power scene under multiple characteristic quantity indexes based on an improved K-means algorithm.
Background
With the large-scale development and utilization of clean energy, the generated energy of the clean energy is continuously and rapidly developed, and the increase of installed capacity is continuously enlarged. The clean energy has the advantages of environmental protection, abundance, wide distribution and the like, but the stability of the clean energy is poorer, and the energy density is lower. According to the statistics of the world meteorological organization, wind power generation is one of the most mature and fastest-developed clean energy sources. According to the statistics of the national energy bureau, the installed capacity of the national power generation is about 23.8 hundred million kilowatts by 12 months in 2021, and the installed capacity is increased by 7.9 percent on a same scale. Wherein, the installed capacity of wind power is about 3.3 hundred million kilowatts, the year-on-year increase is 16.6%, and the great progress is made in the aspect of clean energy consumption, and the wind power utilization rate is up to 96.9%. Wherein the terrestrial wind power accumulation assembly machine is 3.02 hundred million kilowatts, the offshore wind power accumulation assembly machine is 2639 thousand kilowatts, and the wind power accumulation assembly machine accounts for about 13 percent of the whole power generation assembly machine. In 2021, the wind power generation amount is 6526 hundred million kilowatt hours, and the wind power generation amount breaks through 6000 million kilowatt hours and is increased by 40.5 percent on the same basis. In 2021, 206.1 hundred million kilowatts of wind electricity abandoned by the whole country, the national average wind electricity utilization rate is 96.9 percent, the percentage is improved by 0.4 percent, and the wind electricity abandoning and limiting conditions are further relieved.
Taking Jiangsu province as an example, 2987 ten thousand kilowatts are installed in the renewable energy accumulation machine of the Jiangsu province by the end of 2021 year. The photovoltaic power generation accumulation installation 1916 ten thousand kilowatts, wherein the concentrated photovoltaic 941.08 ten thousand kilowatts accounts for 49.12%; the distributed photovoltaic 974.9 ten thousand kilowatts accounts for 50.88 percent and is located the third part of the country. The wind power is accumulated to be 2234 ten thousand kilowatts, and accounts for 50.44 percent of the total installed capacity of the new energy power generation. By the end of 12 months in 2021, the annual wind power generation amount of the Jiangsu province is 415.66 hundred million kilowatt hours, which is increased by 81.5 percent in the same way and accounts for 56 percent of the total new energy generation amount of the Jiangsu province.
With the continuous increase of installed capacity of wind power, the proportion of wind power generation in the power supply of a power grid is continuously improved, the consumption requirement of wind power energy puts forward higher requirements on the economic operation of a power system, the evaluation of the wind power consumption capability of the power grid, the formulation of a power grid dispatching plan and the like, and relevant research and technical countermeasures need to be developed urgently. At present, in a conventional research wind power typical output scene, a sample set is established only based on wind power output characteristics to realize wind power typical scene construction, the obtained wind power typical scene is not accurate enough, and the calculation efficiency is not high.
Disclosure of Invention
In order to solve the problems, the invention provides a wind power typical scene construction method under multiple characteristic quantity indexes based on an improved K-means algorithm. Meanwhile, compared with the traditional K-means clustering algorithm, the method has the advantages that the defects of randomness of a clustering center and blindness of clustering number setting are optimized, the accuracy of wind power generation clustering is improved, and reference is provided for actually making operation planning and development of high-proportion wind power generation access power grids.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention relates to a wind power typical scene construction method under multiple characteristic quantity indexes based on an improved K-means algorithm, which comprises the following steps:
establishing a sample set with wind power multi-feature quantity according to the selected feature index of the wind power electro-fluctuation characteristic; based on a K-means clustering algorithm, carrying out clustering analysis on the sample set, optimizing each clustering result according to a clustering effectiveness index, and finding out an optimal clustering result of the sample set;
obtaining initial clustering centers of various clusters according to the optimal clustering result by combining the density degree and the maximum and minimum distance principle;
and clustering analysis is carried out on the wind power output scene by adopting an improved K-means clustering algorithm so as to realize reduction of the wind power output scene and construct a typical wind power output scene.
The invention is further improved in that: the characteristic indexes comprise a wind power output ratio, a wind power output change rate and a wind power output imbalance rate, wherein the wind power output ratio is expressed as follows:
the wind power output ratio is expressed as:
in the formula, P (t) is the actual value of the wind power active power output at a certain moment, P GN The rated installed capacity of the fan; the wind power output change rate is expressed as:
in the formula, delta P v (t) is the wind power output change rate at a certain moment, and delta P (t) is the difference value of the wind power output at the moment and the wind power output at the previous moment.
The wind power output imbalance ratio is expressed as:
in the formula, DP (i) represents the imbalance rate of wind power output at the ith hour; p a (i) The average output of the wind power in the ith time is obtained; p amax The maximum value of the average output power in wind power generation;
according to the selected characteristic indexes of the wind power electro-fluctuation characteristics, a sample set with wind power multi-characteristic quantities is established, and the method comprises the following steps:
and obtaining the output ratio value and the output change rate value of the wind power at each moment based on a wind power output ratio and wind power output change rate calculation formula and combining historical data of the wind power at each moment, and constructing a wind power multi-characteristic quantity sample set X.
The invention is further improved in that: the specific operation of finding out the optimal clustering result of the sample set is as follows:
1) Determining the search range of the clustering number, and calling a traditional K-means clustering algorithm for different clustering numbers K respectively to obtain clustering results of the wind power sample sets under different K values;
2) According to the clustering result, calculating the clustering effectiveness indexes under different k values;
3) And comparing the sizes of the clustering effectiveness indexes under different k values, and when the clustering effectiveness index value reaches the optimal solution, selecting the k value corresponding to the optimal solution as the optimal value of the clustering result, and determining the optimal clustering number.
The invention is further improved in that: the clustering effectiveness index expression is as follows:
in the formula, S max (i),S max (j) Representing the similarity in the cluster, wherein the meaning is the distance value with the maximum Euclidean distance from the final cluster center of the cluster in the same class after the clustering is finished; m (i, j) represents the similarity between the classes, and refers to the sum of squared deviations of final clustering centers of different classes after clustering is finished.
The invention is further improved in that: the specific steps for obtaining the initial clustering centers of various clusters are as follows:
a, the content of the first and second groups is determined, input wind power fluctuation sample set X = { X = { X } 1 ,x 2 ,…,x n And the optimal clustering number k;
b, calculating the distance between different samples in the sample set X by adopting an Euclidean distance function, and storing the distance in a sample distance matrix D dist In, the expression is:
D dist ＝{d(x i ,x j )|1≤i,j≤n}
in the formula, x i And x j Two data samples in X;
wherein the distance matrix D dist In D dist The (i, j) element represents the sample x i And sample x j The size of the distance between the two; i.e. D dist The ith row represents the set of distances between each sample in the sample set and the ith data sample.
c, distance matrix D dist Calculating the density of each row, and respectively calculating D dist The row elements are sorted in positive sequence to obtain a distance sorting matrix D sort The expression is as follows:
in the formula, sort {. Cndot } operator represents the pair D dist Each row of elements performs positive sequence sorting work; d sort (i, j) denotes the distance sample x i A jth distance value;
d, giving the requirement of the m-th neighborhood sample for comparing the density degree of each sample, and taking a distance sorting matrix D sort The m column data is obtained to obtain the density distance D between each sample and the rest samples m The expression is as follows:
D m ＝[d sort (1,m),d sort (2,m),…,d sort (n,m)] T
comparing the density distance D m The value of each element in (1), wherein the minimum value of the element min (D) m ) The corresponding sample is the sample with the most dense samples in the sample set and is used as the first-class initial clustering center V 1 ；
e, selecting initial centers in the rest clusters based on the maximum and minimum distance principle, and finding V from X 1 The sample with the largest distance is taken as the initial clustering center V of the second class 2 ；
f, calculating the rest scenes x respectively i And V 1 、V 2 Distance therebetween, comparative analysis x i And V 1 、V 2 Maximum value L of minimum distance dist_i ，L dist_i Corresponding scene x i I.e. the initial cluster center V of the third type 3 Wherein, in the process,
L dist_i ＝max(min(d(x i ,V 1 ),d(x i ,V 2 )))
g, scene x of the remaining initial clustering center re Distance from the determined initial center and find x re Maximum value L of minimum distance from determined initial clustering center re The corresponding scene is the k-th initial clustering center V k ，
L re ＝max(min(d(x r ,V 1 ),…,d(x r ,V k-1 )))。
The invention discloses a system for constructing a wind power typical scene under multiple characteristic quantity indexes based on an improved K-means algorithm, which comprises a sample acquisition module, a sample set clustering analysis module, an initial clustering center determining module and a wind power output typical scene constructing module, wherein the sample acquisition module is used for acquiring a plurality of characteristic quantity indexes of wind power;
the sample acquisition module is used for acquiring characteristic indexes of the wind power electrokinetic characteristics and establishing a sample set with wind power multi-characteristic quantity;
the sample set clustering analysis module is used for determining the searching range of the clustering number, calling the traditional K-means clustering algorithm for different clustering numbers K respectively and obtaining the clustering result of the wind power sample set under different K values; calculating effectiveness indexes under different k values according to the clustering result; comparing the sizes of the clustering effectiveness indexes under different k values, when the clustering effectiveness index value reaches the optimal solution, selecting the k value corresponding to the optimal solution as the optimal value of the clustering result, and determining the optimal clustering number;
the initial clustering center determining module is used for obtaining the initial clustering centers of all clusters according to the optimal clustering result of the sample set found by the sample set clustering analysis module and by combining the density degree and the maximum and minimum distance principle;
and the wind power output typical scene construction module is used for performing clustering analysis on the wind power output scene based on the initial clustering center by using an improved K-means clustering algorithm so as to realize wind power output scene reduction and construct a wind power output typical scene.
The invention has the beneficial effects that: 1. the invention provides an improved idea of 'two-step walking' on the basis of the traditional K-means algorithm, introduces the clustering effectiveness index in the first step, and obtains the optimal clustering number of a sample set by comparing and analyzing the effectiveness index values under different K values. The method can solve the problem that the traditional K-means algorithm needs to artificially give the clustering number when the parameters are initialized, and has blindness. The second step introduces the density degree and the maximum and minimum distance principle on the basis of the first step, and obtains various cluster centers based on the optimal cluster number, thereby being beneficial to improving the calculation efficiency.
2. According to the method, the time sequence and the similarity of the wind power output are considered, the input data sample set is established on the basis of the wind power multi-characteristic quantity indexes, the construction of a wind power typical scene is realized on the basis of an improved K-means clustering algorithm, and a scientific basis is provided for researching the safety of a wind power access electric power system and formulating a scheduling plan. On the basis of ensuring the calculation precision, the wind power typical scene obtained by the method is more comprehensive and accurate, and the calculation efficiency is higher.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a schematic flow chart based on an improved K-means clustering algorithm;
FIG. 3 is a graph of the change in the cluster validity indicator;
FIG. 4 is a clustering result of a multi-feature quantity sample set in each season based on an improved K-means algorithm;
fig. 5 is typical scene occurrence probabilities for each season.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.
The invention relates to a system for constructing a wind power typical scene under multiple characteristic indexes based on an improved K-means algorithm, which comprises a sample acquisition module, a sample set clustering analysis module, an initial clustering center determining module and a wind power output typical scene constructing module, wherein the sample acquisition module is used for acquiring a sample set of wind power output typical scenes;
the sample acquisition module is used for acquiring characteristic indexes of the wind power electrokinetic characteristics and establishing a sample set with wind power multi-characteristic quantity;
the sample set clustering analysis module is used for determining the searching range of the clustering number, and calling the traditional K-means clustering algorithm for different clustering numbers K respectively to obtain the clustering results of the wind power sample sets under different K values; calculating the effectiveness indexes under different k values according to the clustering result; comparing the sizes of the clustering effectiveness indexes under different k values, when the clustering effectiveness index value reaches the optimal solution, selecting the k value corresponding to the optimal solution as the optimal value of the clustering result, and determining the optimal clustering number;
wherein, the expression of the clustering effectiveness index is as follows:
in the formula, S max (i),S max (j) Representing the similarity in the same type, wherein the meaning is the distance value with the maximum Euclidean distance from the final clustering center of the same type in the same type of cluster after the clustering is finished; m (i, j) represents the similarity between the classes, and refers to the sum of squared deviations of final clustering centers of different classes after clustering is finished;
the initial clustering center determining module is used for obtaining the initial clustering centers of all clusters according to the optimal clustering result of the sample set found by the sample set clustering analysis module and by combining the density degree and the maximum and minimum distance principle;
and the wind power output typical scene construction module is used for performing clustering analysis on the wind power output scene based on the initial clustering center by using an improved K-means clustering algorithm so as to realize wind power output scene reduction and construct a wind power output typical scene.
The characteristic indexes comprise a wind power output ratio, a wind power output change rate and a wind power output unbalance rate, wherein the wind power output ratio is expressed as:
in the formula, P (t) is the actual value of wind power active power output at a certain moment, P GN The rated installed capacity of the fan; the wind power output change rate is expressed as:
in the formula, delta P v (t) is the wind power output change rate at a certain moment, and delta P (t) is the difference value of the wind power output at the moment and the wind power output at the previous moment;
the wind power output imbalance ratio is expressed as:
in the formula, DP (i) representsThe imbalance rate of wind power output at the ith hour; p a (i) The average output of the wind power at the ith time is obtained; p amax The maximum value of the average output power in wind power generation;
according to the selected characteristic indexes of the wind power electrokinetic characteristics, a sample set with wind power multi-characteristic quantities is established, and the method comprises the following steps: based on a wind power output proportion and a wind power output change rate calculation formula, combining historical data of wind power at each moment to obtain a wind power output proportion value and a wind power output change rate value of the wind power at each moment, and constructing a wind power multi-feature quantity sample set X.
The initial clustering center determining module is specifically configured to:
a, inputting an original wind power fluctuation sample set X = { X = { X = } 1 ,x 2 ,…,x n And the optimal clustering number k;
b, calculating the distance between different samples in the sample set X by adopting an Euclidean distance function, and storing the distance in a sample distance matrix D dist In, the expression is:
D dist ＝{d(x i ,x j )|1≤i,j≤n}
in the formula, x i And x j Two data samples in X;
wherein the distance matrix D dist In D dist The (i, j) element represents the sample x i And sample x j The size of the distance between the two plates; i.e. D dist The ith row represents a set of distances between each sample in the sample set and the ith data sample;
c, distance matrix D dist Calculating the density of each row, and respectively calculating D dist The row elements are sorted in positive sequence to obtain a distance sorting matrix D sort The expression is as follows:
in the formula, sort {. Cndot } operator represents the pair D dist Each row of elements performs positive sequence sorting work; d sort (i, j) denotes the distance sample x i The jth sample distance value;
d, giving the requirement of the m-th neighborhood sample for comparing the density degree of each sample, and taking a distance sorting matrix D sort The m column data is obtained to obtain the density distance D between each sample and the rest samples m The expression is as follows:
D m ＝[d sort (1,m),d sort (2,m),…,d sort (n,m)] T
comparing the density distance D m The value of each element in (1), wherein the minimum value of the element min (D) m ) The corresponding sample is the sample with the most dense samples in the sample set and is used as the first-class initial clustering center V 1 ；
e, selecting initial centers in the rest clusters based on the maximum and minimum distance principle, and finding V from X 1 The sample with the largest distance is taken as the initial clustering center V of the second class 2 ；
f, calculating the rest scenes x respectively i And V 1 、V 2 Distance therebetween, comparative analysis x i And V 1 、V 2 Maximum value L of minimum distance dist_i ，L dist_i Corresponding scene x i I.e. the third type initial clustering center V 3 Wherein
L dist_i ＝max(min(d(x i ,V 1 ),d(x i ,V 2 )))
g, scene x of the remaining initial clustering center re Distance from the determined initial center and find x re Maximum value L of minimum distance from determined initial clustering center re The corresponding scene is the k-th initial clustering center V k ，
L re ＝max(min(d(x r ,V 1 ),…,d(x r ,V k-1 )))。
The invention relates to a wind power typical scene construction method under multiple characteristic quantity indexes based on an improved K-means algorithm, which comprises the steps of constructing a multiple index sample set for depicting wind power characteristics, improving the traditional K-means clustering algorithm, carrying out clustering analysis on a wind power output scene by adopting the improved K-means clustering algorithm, and constructing a wind power typical scene; the method comprises the steps of carrying out parameter initialization on a K-means clustering algorithm, carrying out parameter initialization on the K-means clustering algorithm, and carrying out parameter initialization on the K-means clustering algorithm. In order to solve the problem that the selection of the clustering center is random when the traditional K-means clustering algorithm is initialized, a method for determining the initial centers of various clusters based on the curve density degree and the maximum and minimum distance principle is provided.
Taking wind power output in a certain area of Jiangsu province as an example, the output data of wind power generation from 1 month and 1 day of 2015 to 1 month and 1 day of 2016 in the area is selected as a sample, and considering that the wind power output has time sequence periodicity, in the example, the historical output data samples of the wind power generation are divided into four types of samples of spring, summer, autumn and winter for clustering simulation, wherein the number of the sample scenes in spring and autumn is 170, the number of the sample scenes in summer is 92, the number of the sample scenes in winter is 89, and the number of the samples is 351.
In the part established by the wind power output characteristic index system, the existing wind power characteristic indexes are combined, the time sequence and periodicity of wind power output are considered, and the wind power output, the wind power output change and the wind power fluctuation index of wind power unbalance are considered. In order to improve the calculation speed, the wind power output historical data is simplified by taking the wind power rated installed capacity as a reference, and the volatility characteristic indexes of the wind power output ratio, the wind power output change rate and the wind power imbalance rate are correspondingly obtained.
The definition of the wind power output ratio is the percentage of the active power output measured by wind power and the rated capacity of a fan:
in the formula, P (t) is the actual value of wind power active power output at a certain moment, P GN The rated installed capacity of the fan;
the definition of the wind power output change rate is the ratio of the difference value of the wind power output at the current moment and the wind power output at the previous moment to the rated capacity of the fan:
in the formula, delta P v (t) is the wind power output change rate at a certain moment; and delta P (t) is the difference value of the wind power output at the moment and the wind power output at the previous moment.
The wind power output imbalance ratio is expressed as:
in the formula, DP (i) represents the imbalance rate of wind power output at the ith hour; p a (i) The average output of the wind power at the ith time is obtained; p is amax The maximum value of the average output in wind power generation.
Dividing wind power output data by taking hours as a unit, calculating the output ratio and the output change rate of wind power per hour according to the wind power output ratio and the output change rate, and establishing a sample data set containing multiple characteristic quantities, namely a wind power volatility sample set X, wherein the expression is as follows:
wherein, 1-24 rows in the wind power fluctuation sample set X represent the wind power output ratio at each moment of a certain day of wind power, and 25-48 rows represent the wind power change rate at each moment of the certain day of wind power.
And optimizing the clustering result of the wind power scene according to the clustering effectiveness index of the wind power volatility sample set X containing the multi-feature quantity, and finding out the optimal clustering result. The specific operation is as follows: firstly, setting the variation range of a clustering number k; and then calling a traditional K-means clustering algorithm for different K values respectively according to the search range of the clustering number to obtain the clustering result of the wind power sample set under different K values. And calculating the effectiveness index value under each clustering number in the search range according to the clustering result. And then comparing the sizes of the effectiveness indexes under different k values, selecting the k value corresponding to the optimal index solution as the optimal value of the clustering result, and determining the optimal clustering number. And finally, outputting a wind power typical scene clustering result under the optimal clustering number. Wherein the effectiveness index is calculated as follows:
in the formula, S max (i),S max (j) Representing the similarity in the same type, wherein the meaning is the distance value with the maximum Euclidean distance from the final clustering center of the same type in the same type of cluster after the clustering is finished; m (i, j) represents the similarity between the classes, and refers to the sum of squared deviations of final clustering centers of different classes after clustering is finished. Therefore, the index magnitude is positively correlated with the intra-class similarity and negatively correlated with the inter-class similarity. I.e. the smaller the significance index value, the better the clustering result obtained.
And determining the initial centers of various clusters according to the density degree and the maximum and minimum distance principle in the aspect of selecting the cluster centers during parameter initialization. In the clustering algorithm, the distance between any two samples in a sample set is calculated by adopting an Euclidean distance function, the mutual influence degree between the two samples is represented, and the calculation formula is as follows:
in the formula, x i And x j Two data samples in X are represented.
The invention provides a scene density degree representing the curve density between each sample and the rest samples. The curve density information is defined as the maximum distance value of the mth sample which is closest to the sample scene. And characterizing the sample density of the position of each sample scene according to the maximum distance value, wherein the sample with the smaller mth maximum distance value is more dense with the rest samples. The method comprises the following specific steps:
(1) The initial sample set X = { X obtained by the above calculation is input 1 ,x 2 ,…,x n }。
(2) Adopting an equation (6), calculating the distance between different samples in the sample set X, and storing the distance matrix D of the samples dist In, the expression is:
D dist ＝{d(x i ,x j )|1≤i,j≤n} (7)
(3) To distance matrix D dist The density of each row is calculated, D dist Row i of (a) represents a sample x i Distance from all samples in set X. Are respectively to D dist The row elements are sorted in positive sequence to obtain a distance sorting matrix D sort The expression is as follows:
in the formula, sort {. Cndot } operator represents the pair D dist Each row of elements performs positive sequence sorting work; d sort (i, j) denotes the distance sample x i The jth distance value.
(4) Given the requirement of the mth neighborhood sample for comparing the density degree of each sample, a distance ordering matrix D is taken sort In the mth column, the density distance D between each sample and the rest samples is obtained m The expression is as follows:
D m ＝[d sort (1,m),d sort (2,m),…,d sort (n,m)] T (9)
comparing the density distance D m The value of each element in (1), wherein the minimum value of the element min (D) m ) The corresponding sample is the most dense sample in the sample set and is used as the first-class initial clustering center V 1 ；
(5) Finding out the sum V from X 1 Taking the sample with the largest distance as the initial clustering center V of the second class 2 ；
(6) Computing the remaining scenes x separately i And V 1 、V 2 Distance between, comparative analysis x i And V 1 、V 2 Maximum value L of minimum distance i ，L i Corresponding scene x i I.e. the third type initial clustering center V 3 ；
L i ＝max(min(d(x i ,V 1 ),d(x i ,V 2 ))) (10)
(7) Scene x with remaining initial cluster centers re Distance from the determined initial cluster center and finding x re Maximum value L of minimum distance from determined initial clustering center re The corresponding scene is the kth initial clustering center V k (ii) a Wherein,
L re ＝max(min(d(x re ,V 1 ),…,d(x re ,V k-1 ))) (11)
(8) And finally, dividing all scenes in the set X into different clusters according to a minimum distance principle.
And constructing a part in a typical scene of wind power. Through the optimal clustering number selected by the two-step walking idea and the clustering centers in the initialization parameters of various clusters, improved K-means clustering calculation is carried out on the sample set containing multiple characteristic quantities, wind power scene reduction is realized, and therefore typical scenes of wind power output are established and the occurrence probability of each typical scene is obtained. FIG. 4 shows typical output scenes of wind power in different seasons.
The wind power data are divided according to seasons, and the construction of a wind power typical scene in each season is realized. As shown in fig. 3, in the case of the optimal cluster numbers of different seasons, table 1 summarizes the optimal cluster numbers of the wind power data and the initial cluster centers of all seasons.
TABLE 1 optimal clustering number and initial clustering center for wind power in each season
And the final clustering result is to analyze the operation stability after the wind power is accessed into the power grid, more consider the situation of universal operation, and compare the variance, the iteration times and the complexity O (nmkT) of different clustering clusters obtained by clustering by adopting an improved K-means algorithm. Taking the summer multi-feature sample set as an example, the comparison result of each index is shown in table 2. Wherein n in the complexity O (nmkT) represents the size of the data set, m represents the characteristic dimension of the data object, k represents the number of clusters, and T represents the total iteration number.
As can be seen from table 2, the variance, the number of iterations, and the complexity obtained by the algorithm herein have smaller error variance, fewer iterations, and lower complexity compared to the conventional algorithm. Compared with the traditional K-means algorithm, the improved K-means algorithm has more superiority to the clustering result, and meanwhile, the improved K-means algorithm can effectively reduce the volatility of sample data. In terms of iteration times and complexity, the improved K-means algorithm is also superior to the traditional algorithm, and the calculation time of clustering can be shortened.
TABLE 2 evaluation index of clustering results
When the optimal cluster number is 4, the output curve of the four seasons of spring, summer, autumn and winter as shown in fig. 4 can visually represent the wind power output magnitude and the change trend, a typical spring scene can be defined as a convex fluctuation type, a descending type and an ascending type from top to bottom according to the curve shape, and can be defined as a high output type and a low output type according to the output magnitude; the output value of a typical wind power scene in summer is smaller than that in spring, the trend is relatively gentle, and the output scene can be divided into a high-level fluctuation mode, a medium-level fluctuation mode and a low-level fluctuation mode; autumn and winter can be divided into convex fluctuation type, descending type and ascending type. The method shows that the wind power solar output has stronger volatility and regularity. The occurrence probability of each typical scene is obtained by improving the K-means clustering result, so that the occurrence possibility of the wind power output time sequence scene can be judged.
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein. The scheme in the embodiment of the invention can be realized by adopting various computer languages, such as object-oriented programming language Java and transliteration scripting language JavaScript.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including the preferred embodiment and all changes and modifications that fall within the scope of the invention.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.
Claims (10)
1. A wind power typical scene construction method under multiple characteristic quantity indexes based on an improved K-means algorithm is characterized by comprising the following steps: the method comprises the following steps:
establishing a sample set with wind power multi-feature quantity according to the selected feature index of the wind power electro-fluctuation characteristic;
based on a K-means clustering algorithm, carrying out clustering analysis on the sample set, optimizing each clustering result according to a clustering effectiveness index, and finding out an optimal clustering result of the sample set;
obtaining initial clustering centers of various clusters according to the optimal clustering result by combining the density degree and the maximum and minimum distance principle;
and clustering and analyzing the wind power output scene based on the initial clustering center by adopting an improved K-means clustering algorithm so as to reduce the wind power output scene and construct a typical wind power output scene.
2. The method for constructing the wind power typical scene under the multi-characteristic quantity index based on the improved K-means algorithm is characterized by comprising the following steps of: the characteristic indexes comprise a wind power output ratio, a wind power output change rate and a wind power output unbalance rate, wherein the wind power output ratio is expressed as:
in the formula, P (t) is the actual value of wind power active power output at a certain moment, P GN The rated installed capacity of the fan;
the wind power output change rate is expressed as:
in the formula, delta P v (t) is the wind power output change rate at a certain moment, and delta P (t) is the difference value of the wind power output at the moment and the wind power output at the previous moment;
the wind power output imbalance ratio is expressed as:
in the formula, DP (i) represents the imbalance rate of wind power output at the ith hour; p a (i) The average output of the wind power in the ith time is obtained; p amax The maximum value of the average output in wind power generation;
according to the selected characteristic indexes of the wind power electro-fluctuation characteristics, a sample set with wind power multi-characteristic quantities is established, and the method comprises the following steps:
based on a wind power output proportion and a wind power output change rate calculation formula, combining historical data of wind power at each moment to obtain a wind power output proportion value and a wind power output change rate value of the wind power at each moment, and constructing a wind power multi-feature quantity sample set X.
3. The method for constructing the wind power typical scene based on the multi-characteristic quantity indexes of the improved K-means algorithm as claimed in claim 1, is characterized in that: based on a K-means clustering algorithm, performing clustering analysis on the sample set, optimizing each clustering result according to a clustering effectiveness index, and finding out the optimal clustering result of the sample set by the specific operations of:
1) Determining the search range of the clustering number, and calling a traditional K-means clustering algorithm for different clustering numbers K respectively to obtain clustering results of the wind power sample sets under different K values;
2) Calculating the effectiveness indexes under different k values according to the clustering result;
3) And comparing the sizes of the clustering effectiveness indexes under different k values, when the clustering effectiveness index value reaches the optimal solution, selecting the k value corresponding to the optimal solution as a clustering result optimal value, and determining the optimal clustering number.
4. The method for constructing the wind power typical scene based on the multi-characteristic quantity indexes of the improved K-means algorithm as claimed in claim 1, is characterized in that: the clustering validity index expression is:
in the formula, S max (i),S max (j) Representing the similarity in the cluster, wherein the meaning is the distance value with the maximum Euclidean distance from the final cluster center of the cluster in the same class after the clustering is finished; m (i, j) represents the similarity between the classes, and refers to the sum of squared deviations of final clustering centers of different classes after clustering is finished.
5. The method for constructing the wind power typical scene under the multi-characteristic quantity index based on the improved K-means algorithm is characterized in that the specific steps for obtaining the initial clustering centers of various clusters are as follows:
a, inputting an original wind power fluctuation sample set X = { X = { X = } 1 ,x 2 ,…,x n H, and an optimal clustering number k;
b, calculating the distance between different samples in the sample set X by adopting an Euclidean distance function, and storing the distance in a sample distance matrix D dist In, the expression is:
D dist ＝{d(x i ,x j )|1≤i,j≤n}
in the formula, x i And x j Two data samples in X;
wherein the distance matrix D dist In D dist The (i, j) element represents the sample x i And sample x j The size of the distance between the two; i.e. D dist The ith row represents a set of distances between each sample in the sample set and the ith data sample;
c, distance matrix D dist Calculating the density of each line, and respectively calculating D dist Each line element of (1)Sequencing in positive sequence to obtain a distance sequencing matrix D sort The expression is as follows:
in the formula, sort {. Cndot } operator represents the pair D dist Each row of elements performs positive sequence sorting work; d sort (i, j) denotes the distance sample x i The jth sample distance value;
d, giving the requirement of the mth neighborhood sample for comparing the density degree of each sample, and taking a distance sorting matrix D sort The m column data is obtained to obtain the density distance D between each sample and the rest samples m The expression is as follows:
D m ＝[d sort (1,m),d sort (2,m),…,d sort (n,m)] T
comparing the density distance D m The size of the numerical value of each element in the formula (II), wherein the minimum value of the element is min (D) m ) The corresponding sample is the sample with the most dense samples in the sample set and is used as the first-class initial clustering center V 1 ；
e, selecting initial centers in the rest clusters based on the maximum and minimum distance principle, and finding V from X 1 Taking the sample with the largest distance as the initial clustering center V of the second class 2 ；
f, calculating the rest scenes x respectively i And V 1 、V 2 Distance between, comparative analysis x i And V 1 、V 2 Maximum value L of minimum distance dist_i ，L dist_i Corresponding scene x i I.e. the initial cluster center V of the third type 3 Wherein, in the process,
L dist_i ＝max(min(d(x i ,V 1 ),d(x i ,V 2 )))
g, the remaining scene x of the initial clustering center re Distance from the determined initial center and find x re Maximum value L of minimum distance from determined initial clustering center re The corresponding scene is the k-th initial clustering center V k ，
L re ＝max(min(d(x r ,V 1 ),…,d(x r ,V k-1 )))。
6. A system for constructing a wind power typical scene under multiple characteristic quantity indexes based on an improved K-means algorithm is characterized in that: the system comprises a sample acquisition module, a sample set clustering analysis module, an initial clustering center determining module and an air-out electricity output typical scene constructing module;
the sample acquisition module is used for acquiring characteristic indexes of the electro-aerodynamic characteristics of the wind power and establishing a sample set with wind power multiple characteristic quantities;
the sample set clustering analysis module is used for determining the searching range of the clustering number, and calling the traditional K-means clustering algorithm for different clustering numbers K respectively to obtain the clustering results of the wind power sample sets under different K values; calculating effectiveness indexes under different k values according to the clustering result; comparing the sizes of the clustering effectiveness indexes under different k values, when the clustering effectiveness index value reaches the optimal solution, selecting the k value corresponding to the optimal solution as a clustering result optimal value, and determining the optimal clustering number;
the initial clustering center determining module is used for obtaining the initial clustering centers of all clusters according to the optimal clustering result of the sample set found by the sample set clustering analysis module and by combining the density degree and the maximum and minimum distance principle;
and the wind power output typical scene construction module is used for performing clustering analysis on the wind power output scene based on the initial clustering center by using an improved K-means clustering algorithm so as to reduce the wind power output scene and construct the wind power output typical scene.
7. The system for constructing the wind power typical scene under the multi-characteristic quantity index based on the improved K-means algorithm as claimed in claim 6, wherein: the characteristic indexes comprise a wind power output ratio, a wind power output change rate and a wind power output imbalance rate, wherein the wind power output ratio is expressed as:
in the formula, P (t) is the actual value of wind power active power output at a certain moment, P GN The rated installed capacity of the fan; the wind power output change rate is expressed as:
in the formula, delta P v (t) is the wind power output change rate at a certain moment, and delta P (t) is the difference value of the wind power output at the moment and the wind power output at the previous moment;
the wind power output imbalance ratio is expressed as:
in the formula, DP (i) represents the imbalance rate of wind power output at the ith hour; p a (i) The average output of the wind power in the ith time is obtained; p is amax The maximum value of the average output in wind power generation;
according to the selected characteristic indexes of the wind power electro-fluctuation characteristics, a sample set with wind power multi-characteristic quantities is established, and the method comprises the following steps: based on a wind power output proportion and a wind power output change rate calculation formula, combining historical data of wind power at each moment to obtain a wind power output proportion value and a wind power output change rate value of the wind power at each moment, and constructing a wind power multi-feature quantity sample set X.
8. The system for constructing the wind power typical scene based on the multi-feature quantity indexes of the improved K-means algorithm as claimed in claim 6, wherein: the clustering effectiveness index expression is as follows:
in the formula, S max (i),S max (j) Representing degree of similarity within the classThe meaning is the distance value with the maximum Euclidean distance from the final clustering center of the cluster in the same class after the clustering is finished; m (i, j) represents the similarity between the classes, and refers to the sum of squared deviations of final clustering centers of different classes after clustering is finished.
9. The system for constructing the wind power typical scene under the multi-characteristic quantity index based on the improved K-means algorithm as claimed in claim 6, wherein: the initial clustering center determining module is specifically configured to:
a, inputting an original wind power fluctuation sample set X = { X = { X = } 1 ,x 2 ,…,x n H, and an optimal clustering number k;
b, calculating the distance between different samples in the sample set X by adopting an Euclidean distance function, and storing the distance in a sample distance matrix D dist In, the expression is:
D dist ＝{d(x i ,x j )|1≤i,j≤n}
in the formula, x i And x j Represents two data samples in X;
wherein the distance matrix D dist In D dist The (i, j) element represents the sample x i And sample x j The size of the distance between the two; i.e. D dist The ith row represents a set of distances between each sample in the sample set and the ith data sample;
c, distance matrix D dist Calculating the density of each line, and respectively calculating D dist The elements of each row are subjected to positive sequence sorting to obtain a distance sorting matrix D sort The expression is as follows:
in the formula, sort {. Cndot } operator represents the pair D dist Each row of elements performs positive sequencing work; d sort (i, j) denotes the distance sample x i The jth sample distance value;
d, giving the requirement of the m-th neighborhood sample for comparing the density degree of each sample, and taking a distance sorting matrix D sort In the mth column, the density distance D between each sample and the rest samples is obtained m The expression is as follows:
D m ＝[d sort (1,m),d sort (2,m),…,d sort (n,m)] T
comparing the density distance D m The value of each element in (1), wherein the minimum value of the element min (D) m ) The corresponding sample is the sample with the most dense samples in the sample set and is used as the first-class initial clustering center V 1 ；
e, selecting initial centers in the rest clusters based on the maximum and minimum distance principle, and finding V from X 1 Taking the sample with the largest distance as the initial clustering center V of the second class 2 ；
f, calculating the rest scenes x respectively i And V 1 、V 2 Distance between, comparative analysis x i And V 1 、V 2 Maximum value L of minimum distance dist_i ，L dist_i Corresponding scene x i I.e. the third type initial clustering center V 3 Wherein
L dist_i ＝max(min(d(x i ,V 1 ),d(x i ,V 2 )))
g, scene x of the remaining initial clustering center re Distance from the determined initial center and find x re Maximum value L of minimum distance from determined initial clustering center re The corresponding scene is the k-th initial clustering center V k ，
L re ＝max(min(d(x r ,V 1 ),…,d(x r ,V k-1 )))。
10. A computer-readable storage medium having computer instructions stored thereon, characterized in that: the computer instructions execute the wind power typical scene construction method based on the multi-characteristic quantity indexes of the improved K-means algorithm in the claims 1 to 5 when running.
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