CN111553434A - Power system load classification method and system - Google Patents
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Abstract
The invention relates to a method and a system for classifying loads of a power system. The method comprises the following steps: acquiring load data of a power system to be analyzed to obtain a sample matrix; the load data of the power system comprises n load curves, and each load curve comprises power load data corresponding to p sampling points; the element of the ith row and the jth column in the sample matrix represents the power load value of the jth sampling point in the ith load curve; carrying out standardization processing on the load data of the power system to obtain standardized data; analyzing the standardized data by adopting a principal component analysis method to obtain a principal component matrix comprising m principal component components; determining k initial clusters by using a coacervation hierarchical clustering method according to the principal component matrix; and determining the classification result of each load curve in the load data of the power system by using a k-means clustering method according to the k initial clusters and the principal component matrix. The invention can reduce the operation time and improve the efficiency of the load classification of the power system.
Description
Technical Field
The invention relates to the field of power analysis, in particular to a method and a system for classifying loads of a power system.
Background
The power load classification refers to classifying the power grid load according to different methods. The power load classification is always the basis of power system planning, peak load shifting management, time-of-use electricity price and load prediction, and a good load classification method can provide correct basis and guidance for system planning, peak load shifting management and the like.
The classification of the power loads can provide a reference for effectively aggregating the loads participating in the power system scheduling. When classifying the power loads, a clustering method is generally adopted. At present, the application of clustering analysis in a power system is mainly focused on the aspect of load prediction, the clustering analysis is an optimization process, for example, the solving process of a k-means clustering algorithm is repeated iteration solving, so the global convergence of the k-means clustering algorithm cannot be accurately grasped, meanwhile, the k-means clustering algorithm has certain requirements on an initial clustering center, and the difference of the initial clustering center selection may cause a large difference of clustering results; other algorithms may obtain better clustering effect, but the required parameters are too much, the calculation time is too long, so that the operation efficiency is reduced, and the available value is not high when the practical problems are faced.
Disclosure of Invention
The invention aims to provide a method and a system for classifying loads of a power system, which are used for reducing the operation time and improving the efficiency of classifying the loads of the power system.
In order to achieve the purpose, the invention provides the following scheme:
a power system load classification method, comprising:
acquiring load data of a power system to be analyzed to obtain a sample matrix; the load data of the power system comprises n load curves, and each load curve comprises power load data corresponding to p sampling points; the element of the ith row and the jth column in the sample matrix represents the power load value of the jth sampling point in the ith load curve;
carrying out standardization processing on the load data of the power system to obtain standardized data;
analyzing the standardized data by adopting a principal component analysis method to obtain a principal component matrix comprising m principal component components; the principal component matrix comprises n rows and m columns, wherein m is less than p; the row vectors of the principal component matrix correspond to the n load curves one by one;
determining k initial clusters by using a coacervation hierarchical clustering method according to the principal component matrix;
and determining the classification result of each load curve in the load data of the power system by using a k-means clustering method according to the k initial clusters and the principal component matrix.
Optionally, the normalizing the load data of the power system to obtain normalized data specifically includes:
using formulas
Standardizing each data in the load data of the power system to obtain a standardized numerical matrix; the ith row vector in the standardized numerical matrix is standardized data corresponding to the ith load curve; wherein x isijIs the sample matrixRow i and column j;
is xijThe corresponding normalized value of the normalized value,
the element of the ith row and the jth column in the normalized numerical matrix;
is the average value of the j column in the sample matrix, sjIs the standard deviation of the j-th column in the sample matrix.
Optionally, the analyzing the normalized data by using a principal component analysis method to obtain a principal component matrix including m principal component components specifically includes:
analyzing the standardized data by adopting a principal component analysis method, and determining m principal component components according to the principal component accumulated variance contribution rate;
a principal component matrix comprising m principal component components is determined from the power system load data.
Optionally, the analyzing the normalized data by using a principal component analysis method, and determining m principal component components according to the principal component cumulative variance contribution rate specifically includes:
calculating a correlation coefficient matrix according to the normalized data; the matrix of correlation coefficients is
The correlation coefficient of the ith row and the jth column in the correlation coefficient matrix
The average value of the j column in the sample matrix is obtained;
for j column in the sample matrixAverage value;
calculating p eigenvalues of the correlation coefficient matrix and a unit eigenvector corresponding to each eigenvalue; each of the characteristic values is greater than or equal to 0;
constructing a feature vector matrix according to the p unit feature vectors; each row in the feature vector matrix corresponds to a unit feature vector, and the feature value corresponding to the unit feature vector of the ith row in the feature vector matrix is greater than the feature value corresponding to the unit feature vector of the (i + 1) th row;
calculating the variance contribution rate corresponding to each characteristic value;
calculating the cumulative variance contribution rate corresponding to the previous j feature values according to the variance contribution rate corresponding to each feature value; the first j characteristic values are characteristic values corresponding to the unit characteristic vectors of the first j rows;
and determining eigenvectors corresponding to the first m eigenvalues with the cumulative variance contribution ratio larger than the set threshold value as m principal component components.
Optionally, the determining a principal component matrix including m principal component components according to the power system load data specifically includes:
using formulas
Determining m comprehensive indexes of the principal component matrix; wherein the content of the first and second substances,
element l in ith row and jth columnijIn order to be the load,
λiis the ith characteristic value, eijIs the element of the ith row and the jth column in the feature vector matrix;
for each matrix of column vectors in the sample matrix, the ith element xiRepresenting the ith column vector in the sample matrix;
is a matrix composed of m synthetic indexes, i element ziA vector representing the ith integral index;
determining the principal component matrix as
Wherein the element z of the ith row and the jth columnijAnd the j index value in the i comprehensive index is shown.
Optionally, the determining k initial clusters by using a hierarchical clustering method according to the principal component matrix specifically includes:
acquiring n principal component curves and n initial cluster classes corresponding to the principal component matrix; the ith principal component curve is an ith row vector of the principal component matrix, and the ith principal component curve corresponds to an ith load curve in the load data of the power system; each load curve respectively forms an initial cluster;
calculating the Euclidean distance between any two principal component curves to obtain a first distance value;
sequencing all the first distance values in an ascending manner to obtain a distance sequence; the value of the ith element in the distance sequence is smaller than the value of the (i + 1) th element;
according to the element sequence in the distance sequence, judging the current element d in the distance sequenceijWhether the corresponding ith load curve and the jth load curve belong to different clusters or not; dijIs a first distance value between the ith principal component curve and the jth principal component curve;
when the current element dijWhen the corresponding ith load curve and the corresponding jth load curve belong to different clusters, condensing the cluster to which the ith load curve belongs and the cluster to which the jth load curve belongs to obtain an updated cluster; the updated cluster comprises the ith load curve and the jth load curve;
judging whether the total number of the current class clusters is k;
when the total number of the current class clusters is k, determining the k class clusters as k initial clusters;
when the total number of the current cluster is not k, updating the next element in the distance sequence to be the current element according to the element sequence in the distance sequence, and returning to judge the current element d in the distance sequenceijAnd whether the corresponding ith load curve and the corresponding jth load curve belong to different clusters.
Optionally, the determining, according to the k initial clusters and the principal component matrix, a classification result of each load curve in the load data of the power system by using a k-means clustering method specifically includes:
calculating the mean value of each principal component in the principal component curve corresponding to the initial clustering to obtain the initial clustering center of each cluster; the principal component curves corresponding to the initial clusters are all principal component curves corresponding to all load curves in the initial clusters;
calculating the Euclidean distance from the ith principal component curve to each clustering center to obtain a second distance value;
classifying the ith load curve corresponding to the ith principal component curve into a class cluster corresponding to the minimum value of the second distance value, and updating the class cluster;
calculating the updated clustering centers of all the clusters;
judging whether the cluster centers of all the updated clusters are consistent with the cluster centers of all the clusters before updating;
when the cluster centers of all the updated clusters are consistent with the cluster centers of all the clusters before updating, determining all the updated clusters as the classification result of each load curve in the load data of the power system;
and when the cluster centers of all the updated clusters are not consistent with the cluster centers of all the clusters before updating, updating the cluster center of each cluster, and returning to the step of calculating the Euclidean distance from the ith principal component curve to each cluster center to obtain a second distance value.
The invention also provides a system for classifying loads of an electric power system, comprising:
the power system load data acquisition module is used for acquiring power system load data to be analyzed to obtain a sample matrix; the load data of the power system comprises n load curves, and each load curve comprises power load data corresponding to p sampling points; the element of the ith row and the jth column in the sample matrix represents the power load value of the jth sampling point in the ith load curve;
the standardization module is used for carrying out standardization processing on the load data of the power system to obtain standardized data;
the principal component analysis module is used for analyzing the standardized data by adopting a principal component analysis method to obtain a principal component matrix comprising m principal component components; the principal component matrix comprises n rows and m columns, wherein m is less than p; the row vectors of the principal component matrix correspond to the n load curves one by one;
the initial clustering determining module is used for determining k initial clusters by using a coacervation hierarchical clustering method according to the principal component matrix;
and the classification result determining module is used for determining the classification result of each load curve in the load data of the power system by using a k-means clustering method according to the k initial clusters and the principal component matrix.
Optionally, the initial clustering determining module specifically includes:
a principal component curve and class cluster obtaining unit, configured to obtain n principal component curves and n initial class clusters corresponding to the principal component matrix; the ith principal component curve is an ith row vector of the principal component matrix, and the ith principal component curve corresponds to an ith load curve in the load data of the power system; each load curve respectively forms an initial cluster;
the first Euclidean distance calculating unit is used for calculating the Euclidean distance between any two principal component curves to obtain a first distance value;
the sorting unit is used for sorting all the first distance values in an ascending manner to obtain a distance sequence; the value of the ith element in the distance sequence is smaller than the value of the (i + 1) th element;
a cluster-like judging unit, configured to judge, according to an element order in the distance sequence, a current element d in the distance sequenceijWhether the corresponding ith load curve and the jth load curve belong to different clusters or not; dijIs a first distance value between the ith principal component curve and the jth principal component curve;
a condensing unit for condensing the current element dijWhen the corresponding ith load curve and the corresponding jth load curve belong to different clusters, condensing the cluster to which the ith load curve belongs and the cluster to which the jth load curve belongs to obtain an updated cluster; the updated cluster comprises the ith load curve and the jth load curve;
a cluster total number judging unit, configured to judge whether the current cluster total number is k;
an initial cluster determining unit, configured to determine k clusters as k initial clusters when the total number of current clusters is k;
a returning unit, configured to update a next element in the distance sequence to be a current element according to the element sequence in the distance sequence when the total number of the current class clusters is not k, and return to determine that the current element d in the distance sequence is the current element dijAnd whether the corresponding ith load curve and the corresponding jth load curve belong to different clusters.
Optionally, the classification result determining module specifically includes:
the clustering center calculating unit is used for calculating the mean value of each principal component in the principal component curve corresponding to the initial clustering to obtain the initial clustering center of each cluster; the principal component curves corresponding to the initial clusters are all principal component curves corresponding to all load curves in the initial clusters;
the second distance value calculating unit is used for calculating the Euclidean distance from the ith principal component curve to each clustering center to obtain a second distance value;
the class cluster updating unit is used for classifying the ith load curve corresponding to the ith principal component curve into a class cluster corresponding to the minimum value of the second distance value and updating the class cluster;
the cluster center calculating unit is used for calculating the updated cluster centers of all the clusters;
a cluster center judging unit, configured to judge whether the cluster centers of all the updated clusters are consistent with the cluster centers of all the clusters before updating;
a classification result determining unit, configured to determine all updated clusters as a classification result of each load curve in the load data of the power system when the cluster centers of all updated clusters are consistent with the cluster centers of all clusters before updating;
and the cluster center updating unit is used for updating the cluster center of each cluster when the updated cluster centers of all clusters are inconsistent with the cluster centers of all clusters before updating, and returning to the step of calculating the Euclidean distance from the ith principal component curve to each cluster center to obtain a second distance value.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
because the k-means clustering algorithm has certain requirements on the initial clustering centers, and the difference of the initial clustering centers can cause larger difference of clustering results, the invention selects the initial clustering centers by using the aggregation level clustering method in the division clustering, reduces the uncertainty of the algorithm, enables the clustering centers to be closer to the optimal classification compared with the traditional method, optimizes the iteration times of the k-means algorithm, shortens the operation time and further improves the classification efficiency of the power load data.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a schematic flow chart of a method for classifying loads of an electrical power system according to the present invention;
FIG. 2 is a schematic diagram of the agglomerative hierarchical clustering method of the present invention;
fig. 3 is a schematic structural diagram of the load classification system of the power system of the present invention.
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.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Fig. 1 is a schematic flow chart of a method for classifying loads of an electrical power system according to the present invention. As shown in fig. 1, the method for classifying loads of an electrical power system of the present invention includes the following steps:
step 100: and acquiring load data of the power system to be analyzed to obtain a sample matrix. The power system load data comprises n load curves, and each load curve comprises power load data corresponding to p sampling points. The sample matrix is
Element x of ith row and jth column in the sample matrixijAnd representing the power load value of the jth sampling point in the ith load curve. According to the actual demand, each load curve may represent a load curve corresponding to each energy source, or may represent a load curve corresponding to a certain time period (for example, one day); each sample point may represent a different sample point time or a different sample point location.
Step 200: and carrying out standardization processing on the load data of the power system to obtain standardized data. The concrete formula is as follows:
each data in the load data of the power system is standardized, and a standardized numerical matrix can be obtained. The ith row vector in the standardized numerical matrix is standardized data corresponding to the ith load curve; wherein x isijThe element of the ith row and the jth column in the sample matrix;
is xijThe corresponding normalized value of the normalized value,
the element of the ith row and the jth column in the normalized numerical matrix;
is the average value of the jth column in the sample matrix,
sjis the standard deviation of the jth column in the sample matrix,
step 300: and analyzing the standardized data by adopting a principal component analysis method to obtain a principal component matrix comprising m principal component components. The principal component matrix comprises n rows and m columns, wherein m is less than p; and the row vectors of the principal component matrix correspond to the n load curves one by one. The idea of the principal component analysis method is to use the mutual relationship existing between the original variables, replace the original more variables with less comprehensive indexes (i.e. new variables) to reduce the dimension, and simultaneously, to make the new variables retain the information reflected by the original variables as much as possible, and the reflection degree is reflected by the variance contribution rate corresponding to the characteristic value. Calculating the variance contribution rate and the cumulative variance contribution rate of the principal components, generally taking the characteristic value of which the cumulative contribution rate reaches 85% -95%, and respectively corresponding to m new variables, namely m principal components. The specific process is as follows:
(1) calculating a correlation coefficient matrix according to the normalized data; what is needed isThe correlation coefficient matrix is
The correlation coefficient of the ith row and the jth column in the correlation coefficient matrix
The average value of the j column in the sample matrix is obtained;
the average value of the j column in the sample matrix is obtained;
(2) and calculating p eigenvalues of the correlation coefficient matrix and a unit eigenvector corresponding to each eigenvalue. Obtaining p eigenvalues of a correlation coefficient matrix by solving an eigen equation of lambda I-R0, and enabling the eigenvalues to be in accordance with lambda1≥λ2≥…≥λpMore than or equal to 0.
(3) And constructing a feature vector matrix according to the p unit feature vectors. The feature vector matrix is:
each row in the eigenvector matrix corresponds to a unit eigenvector, ei(i ═ 1,2, …, p) is the characteristic value λiAnd the corresponding characteristic value of the unit characteristic vector of the ith row in the characteristic vector matrix is greater than the characteristic value of the unit characteristic vector of the (i + 1) th row.
(4) Calculate the variance contribution rate α corresponding to each eigenvaluei. The calculation formula is as follows:
(5) calculating the cumulative variance contribution rate corresponding to the previous j feature values according to the variance contribution rate corresponding to each feature value; the first j eigenvalues are the eigenvalues corresponding to the unit eigenvectors of the first j rows. Cumulative variance contribution of the first j eigenvalues
(6) And determining eigenvectors corresponding to the first m eigenvalues with the cumulative variance contribution rate larger than the set threshold value as m principal component components, and describing the power load data by using the m principal component components. The set threshold may be set according to actual conditions, and may be 85%, for example.
(7) Using formulas
Determining m synthetic indices z of a principal component matrix1，z2，…，zm(m.ltoreq.p). Wherein the content of the first and second substances,
element l in ith row and jth columnijIn order to be the load,
λiis the ith characteristic value, eijIs the element of the ith row and the jth column in the feature vector matrix;
for each matrix of column vectors in the sample matrix, the ith element xiRepresenting the ith column vector in the sample matrix;
is a matrix composed of m synthetic indexes, i element ziA vector representing the ith integral index. Due to the fact that
Each element in the index is a vector, so that m synthetic indexes determine a principal component matrix of
Wherein the element z of the ith row and the jth columnijAnd the j index value in the i comprehensive index is shown.
Step 400: and determining k initial clusters by using a coacervation hierarchical clustering method according to the principal component matrix. The specific process is as follows:
acquiring n principal component curves and n initial cluster classes corresponding to the principal component matrix; the ith principal component curve is an ith row vector of the principal component matrix, and the ith principal component curve corresponds to an ith load curve in the load data of the power system; each load curve respectively forms an initial cluster;
calculating the Euclidean distance between any two principal component curves to obtain a first distance value;
sequencing all the first distance values in an ascending manner to obtain a distance sequence; the value of the ith element in the distance sequence is smaller than the value of the (i + 1) th element;
according to the element sequence in the distance sequence, judging the current element d in the distance sequenceijWhether the corresponding ith load curve and the jth load curve belong to different clusters or not; dijIs a first distance value between the ith principal component curve and the jth principal component curve;
when the current element dijWhen the corresponding ith load curve and the corresponding jth load curve belong to different clusters, condensing the cluster to which the ith load curve belongs and the cluster to which the jth load curve belongs to obtain an updated cluster; the updated cluster comprises the ith load curve and the jth load curve;
judging whether the total number of the current class clusters is k;
when the total number of the current class clusters is k, determining the k class clusters as k initial clusters;
when the total number of the current cluster is not k, updating the next element in the distance sequence to be the current element according to the element sequence in the distance sequence, and returning to judge the current element d in the distance sequenceijAnd whether the corresponding ith load curve and the corresponding jth load curve belong to different clusters.
FIG. 2 is a schematic diagram of the agglomerative hierarchical clustering method of the present invention, as shown in FIG. 2, utilizingWhen clustering at a condensation level, firstly dividing n load curves into n clusters, and calculating Euclidean distances between every two clusters according to each principal component curve in the principal component matrix to obtain n (n-1)/2 Euclidean distances. Euclidean distance for ith and jth load curves
zi1,zj1,zi2,zj2,...,zim,zjmAre the corresponding principal component elements in the Z matrix.
Arranging the obtained n (n-1)/2 distances from small to large, then comparing whether the two load curves belong to different clusters or not for each distance according to the sequence, if the two load curves belong to different clusters, aggregating the two load curves into a cluster until the total cluster number is k, and stopping aggregation to finish hierarchical clustering. Taking the load curves a, b, c, d, e, f shown in fig. 2 as an example, d is calculated from the principal component curve in the principal component matrix corresponding to each load curveab＜dde＜def＜dfc＜dcb. First for dabThe load curves a and b belong to different clusters, so that the load curves a and b are condensed to form a cluster ab; then, d is judgeddeCorresponding load curves d and e belong to different clusters and are condensed to form a cluster de; then, d is judgedefCorresponding load curves e and f belong to different clusters, and the cluster de to which the load curve e belongs and the cluster f described by the cluster f are condensed to form a cluster def; then, d is judgedfcCorresponding load curves f and c which belong to different clusters are condensed to form a cluster cdef; then, d is judgedcbAnd corresponding load curves c and b belong to different clusters, and are condensed to form a cluster abcdef until the total number of the clusters is k.
Step 500: and determining the classification result of each load curve in the load data of the power system by using a k-means clustering method according to the k initial clusters and the principal component matrix. The specific process is as follows:
after k clusters are obtained, the mean value of each principal component of all principal component curves is obtained by using the principal component matrixAnd obtaining initial clustering centers of various clusters, wherein the initial clustering centers are in a vector form. Cluster center c for the kth clusterkTo say, ck＝[ck1ck2… ckm]，ckmAnd the mean value of the mth principal component of all the principal component curves corresponding to the kth class cluster is shown.
For the ith principal component curve, calculating the Euclidean distance D from the ith principal component curve to the center of each clusterik，
Wherein DikIs the Euclidean distance, z, from the ith curve to the kth class clusteri1,zi2,...,zimScore for the corresponding principal component in the Z matrix, ckmRepresents the mean of the mth principal component of the kth cluster class.
And classifying the ith load curve corresponding to the ith principal component curve into a class cluster corresponding to the minimum Euclidean distance, and updating the class cluster.
Calculating the updated clustering centers of all the clusters;
judging whether the cluster centers of all the updated clusters are consistent with the cluster centers of all the clusters before updating;
when the cluster centers of all the updated clusters are consistent with the cluster centers of all the clusters before updating, determining all the updated clusters as the classification result of each load curve in the load data of the power system;
and when the cluster centers of all the updated clusters are not consistent with the cluster centers of all the clusters before updating, updating the cluster center of each cluster, and returning to the step of calculating the Euclidean distance from the ith principal component curve to each cluster center to obtain a second distance value.
The method and the device can obtain the classification result of each load curve in the load data of the power system, and can be used for stabilizing the internal fluctuation of the system. Specifically, the peak-valley value and the time period of the cluster center are marked by analyzing the characteristics of the cluster centers, and then the load curves are subjected to peak staggering combination according to the difference of the peak-valley characteristics, so that the internal fluctuation of the system is stabilized.
The method obtains the classification result of each load curve in the load data of the power system, and can also provide a guidance basis for the load combination scheme of the virtual power plant. In research on VPP aggregation, power generation cost and risk are major considerations, and output characteristics and reliability of resources vary. Due to the load reduction or other uncertain factors, a part of resources can not participate in the aggregation, and at this time, a load combination suitable for participating in the current aggregation needs to be determined according to the resource characteristics. The VPP characteristics refer to characteristics of renewable energy sources such as wind power and photovoltaic and relevant to actual operation of the virtual power plant, for example, the economy and the environmental protection are considered, wherein the economy considers factors such as wind power, photovoltaic power generation income and energy abandonment cost of the virtual power plant, and the environmental protection is used for measuring the clean energy consumption level of the virtual power plant. The higher the economy and the environmental protection, the better the polymerization effect of the representative wind and light participating in the virtual power plant. The curve characteristics refer to the classification results obtained according to the method, namely a plurality of curve clusters, the curve characteristics of different clusters are analyzed, the curve characteristics and the scale of each cluster are used for measuring the self characteristics of the renewable energy, and the characteristics mainly comprise output characteristics and reliability, wherein the output characteristics consider the factors of the daily load rate, the daily peak-valley difference rate, the daily load fluctuation rate and the like of the energy, and the reliability considers the time ratio of the output of the cluster curve meeting the threshold value every day and the abnormal rate of the cluster curve in specific time. The better the output characteristic is and the higher the reliability is, the better the effect of representing the cluster curve participating in the virtual power plant polymerization is.
The invention also provides a power system load classification system, and fig. 3 is a schematic structural diagram of the power system load classification system of the invention. As shown in fig. 3, the load classification system of the power system of the present invention includes the following structures:
the power system load data acquisition module 301 is configured to acquire power system load data to be analyzed to obtain a sample matrix; the load data of the power system comprises n load curves, and each load curve comprises power load data corresponding to p sampling points; and an element in the ith row and the jth column in the sample matrix represents the power load value of the jth sampling point in the ith load curve.
A normalizing module 302, configured to perform normalization processing on the power system load data to obtain normalized data.
A principal component analysis module 303, configured to analyze the normalized data by using a principal component analysis method to obtain a principal component matrix including m principal component components; the principal component matrix comprises n rows and m columns, wherein m is less than p; and the row vectors of the principal component matrix correspond to the n load curves one by one.
An initial cluster determining module 304, configured to determine k initial clusters by using a coacervation hierarchical clustering method according to the principal component matrix.
And a classification result determining module 305, configured to determine a classification result of each load curve in the load data of the power system by using a k-means clustering method according to the k initial clusters and the principal component matrix.
As another embodiment, in the load classification system of an electrical power system of the present invention, the initial cluster determining module 304 specifically includes:
a principal component curve and class cluster obtaining unit, configured to obtain n principal component curves and n initial class clusters corresponding to the principal component matrix; the ith principal component curve is an ith row vector of the principal component matrix, and the ith principal component curve corresponds to an ith load curve in the load data of the power system; each load curve constitutes an initial cluster of classes.
And the first Euclidean distance calculating unit is used for calculating the Euclidean distance between any two principal component curves to obtain a first distance value.
The sorting unit is used for sorting all the first distance values in an ascending manner to obtain a distance sequence; the value of the ith element in the distance sequence is smaller than the value of the (i + 1) th element.
A cluster-like judging unit, configured to judge, according to an element order in the distance sequence, a current element d in the distance sequenceijWhether the corresponding ith load curve and the jth load curve belong to different clusters or not; dijIs the difference between the ith principal component curve and the jth principal component curveA first distance value therebetween.
A condensing unit for condensing the current element dijWhen the corresponding ith load curve and the corresponding jth load curve belong to different clusters, condensing the cluster to which the ith load curve belongs and the cluster to which the jth load curve belongs to obtain an updated cluster; the updated class cluster comprises the ith load curve and the jth load curve.
And the total number judging unit of the class clusters is used for judging whether the total number of the current class clusters is k or not.
And the initial cluster determining unit is used for determining the k clusters as k initial clusters when the total number of the current clusters is k.
A returning unit, configured to update a next element in the distance sequence to be a current element according to the element sequence in the distance sequence when the total number of the current class clusters is not k, and return to determine that the current element d in the distance sequence is the current element dijAnd whether the corresponding ith load curve and the corresponding jth load curve belong to different clusters.
As another embodiment, in the system for classifying loads in an electrical power system according to the present invention, the classification result determining module 305 specifically includes:
the clustering center calculating unit is used for calculating the mean value of each principal component in the principal component curve corresponding to the initial clustering to obtain the initial clustering center of each cluster; and the principal component curves corresponding to the initial clusters are all the principal component curves corresponding to all the load curves in the initial clusters.
And the second distance value calculating unit is used for calculating the Euclidean distance from the ith principal component curve to each cluster center to obtain a second distance value.
And the class cluster updating unit is used for classifying the ith load curve corresponding to the ith principal component curve into a class cluster corresponding to the minimum value of the second distance value, and updating the class cluster.
And the cluster center calculating unit is used for calculating the updated cluster centers of all the clusters.
And the cluster center judging unit is used for judging whether the cluster centers of all the updated clusters are consistent with the cluster centers of all the clusters before updating.
And the classification result determining unit is used for determining all the updated clusters as the classification result of each load curve in the load data of the power system when the cluster centers of all the updated clusters are consistent with the cluster centers of all the clusters before updating.
And the cluster center updating unit is used for updating the cluster center of each cluster when the updated cluster centers of all clusters are inconsistent with the cluster centers of all clusters before updating, and returning to the step of calculating the Euclidean distance from the ith principal component curve to each cluster center to obtain a second distance value.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (10)
1. A method of classifying a load in an electrical power system, comprising:
acquiring load data of a power system to be analyzed to obtain a sample matrix; the load data of the power system comprises n load curves, and each load curve comprises power load data corresponding to p sampling points; the element of the ith row and the jth column in the sample matrix represents the power load value of the jth sampling point in the ith load curve;
carrying out standardization processing on the load data of the power system to obtain standardized data;
analyzing the standardized data by adopting a principal component analysis method to obtain a principal component matrix comprising m principal component components; the principal component matrix comprises n rows and m columns, wherein m is less than p; the row vectors of the principal component matrix correspond to the n load curves one by one;
determining k initial clusters by using a coacervation hierarchical clustering method according to the principal component matrix;
and determining the classification result of each load curve in the load data of the power system by using a k-means clustering method according to the k initial clusters and the principal component matrix.
2. The method according to claim 1, wherein the normalizing the power system load data to obtain normalized data specifically comprises:
using formulas
Standardizing each data in the load data of the power system to obtain a standardized numerical matrix; the ith row vector in the standardized numerical matrix is standardized data corresponding to the ith load curve; wherein x isijThe element of the ith row and the jth column in the sample matrix;
is xijThe corresponding normalized value of the normalized value,
the element of the ith row and the jth column in the normalized numerical matrix;
is the average value of the j column in the sample matrix, sjIs the standard deviation of the j-th column in the sample matrix.
3. The method according to claim 1, wherein the analyzing the normalized data by principal component analysis to obtain a principal component matrix including m principal component components comprises:
analyzing the standardized data by adopting a principal component analysis method, and determining m principal component components according to the principal component accumulated variance contribution rate;
a principal component matrix comprising m principal component components is determined from the power system load data.
4. The method according to claim 3, wherein the analyzing the normalized data by principal component analysis and determining m principal component components according to the principal component cumulative variance contribution ratio comprises:
calculating a correlation coefficient matrix according to the normalized data; the matrix of correlation coefficients is
The correlation coefficient of the ith row and the jth column in the correlation coefficient matrix
The average value of the j column in the sample matrix is obtained;
the average value of the j column in the sample matrix is obtained;
calculating p eigenvalues of the correlation coefficient matrix and a unit eigenvector corresponding to each eigenvalue; each of the characteristic values is greater than or equal to 0;
constructing a feature vector matrix according to the p unit feature vectors; each row in the feature vector matrix corresponds to a unit feature vector, and the feature value corresponding to the unit feature vector of the ith row in the feature vector matrix is greater than the feature value corresponding to the unit feature vector of the (i + 1) th row;
calculating the variance contribution rate corresponding to each characteristic value;
calculating the cumulative variance contribution rate corresponding to the previous j feature values according to the variance contribution rate corresponding to each feature value; the first j characteristic values are characteristic values corresponding to the unit characteristic vectors of the first j rows;
and determining eigenvectors corresponding to the first m eigenvalues with the cumulative variance contribution ratio larger than the set threshold value as m principal component components.
5. The method according to claim 4, wherein the determining a principal component matrix including m principal component components according to the power system load data specifically includes:
using formulas
Determining m comprehensive indexes of the principal component matrix; wherein the content of the first and second substances,
element l in ith row and jth columnijIn order to be the load,
λiis the ith characteristic value, eijIs the element of the ith row and the jth column in the feature vector matrix;
for each matrix of column vectors in the sample matrix, the ith element xiRepresenting the ith column vector in the sample matrix;
is a matrix composed of m synthetic indexes, i element ziA vector representing the ith integral index;
determining the master according to the m comprehensive indexesThe component matrix is
Wherein the element z of the ith row and the jth columnijAnd the j index value in the i comprehensive index is shown.
6. The method according to claim 1, wherein the determining k initial clusters by using a hierarchical clustering method according to the principal component matrix specifically comprises:
acquiring n principal component curves and n initial cluster classes corresponding to the principal component matrix; the ith principal component curve is an ith row vector of the principal component matrix, and the ith principal component curve corresponds to an ith load curve in the load data of the power system; each load curve respectively forms an initial cluster;
calculating the Euclidean distance between any two principal component curves to obtain a first distance value;
sequencing all the first distance values in an ascending manner to obtain a distance sequence; the value of the ith element in the distance sequence is smaller than the value of the (i + 1) th element;
according to the element sequence in the distance sequence, judging the current element d in the distance sequenceijWhether the corresponding ith load curve and the jth load curve belong to different clusters or not; dijIs a first distance value between the ith principal component curve and the jth principal component curve;
when the current element dijWhen the corresponding ith load curve and the corresponding jth load curve belong to different clusters, condensing the cluster to which the ith load curve belongs and the cluster to which the jth load curve belongs to obtain an updated cluster; the updated cluster comprises the ith load curve and the jth load curve;
judging whether the total number of the current class clusters is k;
when the total number of the current class clusters is k, determining the k class clusters as k initial clusters;
when the total number of the current class clusters is not k, according to the resultUpdating the next element in the distance sequence to be the current element, and returning to judge the current element d in the distance sequenceijAnd whether the corresponding ith load curve and the corresponding jth load curve belong to different clusters.
7. The method for classifying loads of an electric power system according to claim 6, wherein the determining the classification result of each load curve in the load data of the electric power system by using a k-means clustering method according to the k initial clusters and the principal component matrix specifically comprises:
calculating the mean value of each principal component in the principal component curve corresponding to the initial clustering to obtain the initial clustering center of each cluster; the principal component curves corresponding to the initial clusters are all principal component curves corresponding to all load curves in the initial clusters;
calculating the Euclidean distance from the ith principal component curve to each clustering center to obtain a second distance value;
classifying the ith load curve corresponding to the ith principal component curve into a class cluster corresponding to the minimum value of the second distance value, and updating the class cluster;
calculating the updated clustering centers of all the clusters;
judging whether the cluster centers of all the updated clusters are consistent with the cluster centers of all the clusters before updating;
when the cluster centers of all the updated clusters are consistent with the cluster centers of all the clusters before updating, determining all the updated clusters as the classification result of each load curve in the load data of the power system;
and when the cluster centers of all the updated clusters are not consistent with the cluster centers of all the clusters before updating, updating the cluster center of each cluster, and returning to the step of calculating the Euclidean distance from the ith principal component curve to each cluster center to obtain a second distance value.
8. An electrical power system load classification system, comprising:
the power system load data acquisition module is used for acquiring power system load data to be analyzed to obtain a sample matrix; the load data of the power system comprises n load curves, and each load curve comprises power load data corresponding to p sampling points; the element of the ith row and the jth column in the sample matrix represents the power load value of the jth sampling point in the ith load curve;
the standardization module is used for carrying out standardization processing on the load data of the power system to obtain standardized data;
the principal component analysis module is used for analyzing the standardized data by adopting a principal component analysis method to obtain a principal component matrix comprising m principal component components; the principal component matrix comprises n rows and m columns, wherein m is less than p; the row vectors of the principal component matrix correspond to the n load curves one by one;
the initial clustering determining module is used for determining k initial clusters by using a coacervation hierarchical clustering method according to the principal component matrix;
and the classification result determining module is used for determining the classification result of each load curve in the load data of the power system by using a k-means clustering method according to the k initial clusters and the principal component matrix.
9. The power system load classification system of claim 8, wherein the initial cluster determination module specifically comprises:
a principal component curve and class cluster obtaining unit, configured to obtain n principal component curves and n initial class clusters corresponding to the principal component matrix; the ith principal component curve is an ith row vector of the principal component matrix, and the ith principal component curve corresponds to an ith load curve in the load data of the power system; each load curve respectively forms an initial cluster;
the first Euclidean distance calculating unit is used for calculating the Euclidean distance between any two principal component curves to obtain a first distance value;
the sorting unit is used for sorting all the first distance values in an ascending manner to obtain a distance sequence; the value of the ith element in the distance sequence is smaller than the value of the (i + 1) th element;
a cluster-like judging unit, configured to judge, according to an element order in the distance sequence, a current element d in the distance sequenceijWhether the corresponding ith load curve and the jth load curve belong to different clusters or not; dijIs a first distance value between the ith principal component curve and the jth principal component curve;
a condensing unit for condensing the current element dijWhen the corresponding ith load curve and the corresponding jth load curve belong to different clusters, condensing the cluster to which the ith load curve belongs and the cluster to which the jth load curve belongs to obtain an updated cluster; the updated cluster comprises the ith load curve and the jth load curve;
a cluster total number judging unit, configured to judge whether the current cluster total number is k;
an initial cluster determining unit, configured to determine k clusters as k initial clusters when the total number of current clusters is k;
a returning unit, configured to update a next element in the distance sequence to be a current element according to the element sequence in the distance sequence when the total number of the current class clusters is not k, and return to determine that the current element d in the distance sequence is the current element dijAnd whether the corresponding ith load curve and the corresponding jth load curve belong to different clusters.
10. The power system load classification system according to claim 9, wherein the classification result determination module specifically includes:
the clustering center calculating unit is used for calculating the mean value of each principal component in the principal component curve corresponding to the initial clustering to obtain the initial clustering center of each cluster; the principal component curves corresponding to the initial clusters are all principal component curves corresponding to all load curves in the initial clusters;
the second distance value calculating unit is used for calculating the Euclidean distance from the ith principal component curve to each clustering center to obtain a second distance value;
the class cluster updating unit is used for classifying the ith load curve corresponding to the ith principal component curve into a class cluster corresponding to the minimum value of the second distance value and updating the class cluster;
the cluster center calculating unit is used for calculating the updated cluster centers of all the clusters;
a cluster center judging unit, configured to judge whether the cluster centers of all the updated clusters are consistent with the cluster centers of all the clusters before updating;
a classification result determining unit, configured to determine all updated clusters as a classification result of each load curve in the load data of the power system when the cluster centers of all updated clusters are consistent with the cluster centers of all clusters before updating;
and the cluster center updating unit is used for updating the cluster center of each cluster when the updated cluster centers of all clusters are inconsistent with the cluster centers of all clusters before updating, and returning to the step of calculating the Euclidean distance from the ith principal component curve to each cluster center to obtain a second distance value.
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