CN109995374A - A kind of principal component component iteration selection method for electric power system data compression - Google Patents
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Abstract
The present invention provides a kind of principal component component iteration selection methods for electric power system data compression, the method is on the basis of traditional principle component analysis data compression method, setting principal component number of components N ' is 1 first, and then calculate the principal component matrix of iteration, rebuild estimated data matrix, all reconstruct phasor datas are calculated again to compare and the maximum total vector error value of original phasor data, and judge whether to meet reconstruct data precision accordingly, the further iteration if precision is unsatisfactory for, until obtaining the principal component number of components for meeting reconstruction accuracy.The present invention can be applied to the phasor data compression in complex field independent of data sample normalized；Simultaneously, iterative process will not increase the calculation amount of principal component analytical method significantly, when compressing using principal component analytical method to synchronized phasor data, the compression ratio and reconstruct data precision of data, the selection of the principal component component of the data compression suitable for electric system are effectively improved.
Description
Technical field
The invention belongs to interconnected network fields, and in particular to a kind of principal component component for electric power system data compression
Iteration selection method.
Background technique
In recent years, as the scale development of interconnected network is increasing, the dynamic characteristic of electric system becomes increasingly complex,
The dynamic security stable problem of electric system is also increasingly severeer.Electric system synchronized measurement system (Wide-area
Measurement System, WAMS) appearance for solve bulk power grid dynamic security stable problem provide extremely advantageous number
According to basis.Synchro measure data are based on the phasor of voltage and current in electric system, while further comprising active power, nothing
Other data such as function power；Wherein the phasor of voltage and current is divided into A, B, C three-phase and positive sequence, negative phase-sequence, zero sequence, data again
It measures huge.With the expansion of electric system scale, the amount of synchro measure data is also increasing, the increased data volume of explosion type
The bottleneck for further developing and applying as limits synchronization measuring system.The phasor data being effectively compressed in synchro measure can have
Effect reduces the data volume of synchro measure, helps to find the dynamic security problem that electric system occurs in time.
The data compression method generallyd use in power measurement system is principal component analytical method.Principal component analysis, also referred to as
Principal component analysis is that multiple original variables are converted into several masters under the premise of losing little information using the thought of dimensionality reduction
The method of ingredient only considers a few principal component and is unlikely to lose too many information, to catch principal contradiction, discloses thing
Regularity between object built-in variable, while it is simplified problem, improve analysis efficiency.According to phasor in electric system
The correlation of amplitude and phase angle suitably chooses principal component component for effective compression realized to synchro measure data, and significantly
Reduce synchro measure data volume.
In the prior art, principal component component selection method includes accumulation contribution rate method and Kaiser-Guttman criterion
Method, both methods both for sample be real number under conditions of, based on the normalizing that real number sample average is 0, variance is 1
Change what processing was realized.When carrying out the compression of electric system phasor data, the sample of principal component analysis is plural number.Due in plural number
The not samples normalization definition of standard in domain, it is difficult to use the method choice principal component component based on samples normalization；Separately
Outside, since the sample of processing is real number, using both methods, when phasor data compresses, selection principal component component need to be by phase
The amplitude and phase angle of amount are respectively processed, and the amplitude and phase angle of phasor carry out data compression as the amount independently measured respectively
The correlation having between two amounts of strict physical meaning originally will be destroyed, in turn results in extra error.Meanwhile both
Choosing method be all using the characteristic value of initial data covariance matrix as judgment basis, therefore not can guarantee rebuild after data
Precision is not properly suited for the data compression of phasor principal component analysis.
Summary of the invention
In order to improve the efficiency of data compression of electric system, overcome the problems, such as that DATA REASONING precision is low, the present invention provides
It is a kind of for electric power system data compression principal component component iteration selection method, the method phasor compressed data it is main at
Divide on the basis of analysis method, chooses individual features phasor from proper phasor matrix according to principal component number of components and calculating changes
The corresponding principal component matrix in generation, and from which further follow that the principal component number of components for meeting reconstruction accuracy, it can be applied in complex field
Phasor data compression can effectively improve the compression ratio and reconstruct data precision of data.
To achieve the goals above, this invention takes following technical solutions.
A kind of principal component component iteration selection method for electric power system data compression, the method includes following steps
It is rapid:
Step S0 constructs the original of M row N column according to the N group voltage/current phasor at M moment of measurement data to be compressed
Beginning data matrix Dr, DrFor the complex matrix of M × N；According toBy DrIt is normalized to the normalization data that modulus value is 1
Matrix D, D are the complex matrix of M × N, wherein1≤j≤
N；According to C=DHThe covariance matrix C, C that D calculates D are the complex matrix of N × N, and covariance matrix C is Hermitian matrix
And positive semidefinite matrix, and further calculate the All Eigenvalues λ of Ci, i=1......N, and λ1≥λ2≥…≥λN>=0, due to
C is Hermitian matrix and positive semidefinite matrix, the then eigenvalue λ of CiIt is real number；Seek system of linear equations λiThe basis of I-C=0
Solution system, obtains C for λiOne group of proper phasor ui, obtain proper phasor matrix U=[u1,u2,…,uN], U is answering for N × N
Matrix number, and meet UHCU=Λ, wherein Λ=diag (λ1,λ2,…,λN)；
Step S1, enabling the initial value of iteration is principal component number of components N '=0, estimated data matrix
Step S2 chooses a proper phasor u of N ' according to principal component number of components N ' from proper phasor matrix UN′；According to
pN′=DuN′Calculate a principal component matrix p of N ' of iterationN′, pN′For the complex matrix of M × 1；
Step S3, according to iterative formulaRebuild estimated data matrix For the plural number of M × N
Matrix；
Step S4 calculates estimated data matrixIt is missed with the synthetic vector of corresponding phasors all in normalization data matrix D
Poor TVE value, and take the maximum value of total vector error TVE；
Step S5 determines whether N ' meets the criterion of reconstruct data precision according to the TVE maximum value, if differentiating
Condition is set up, and S7 is thened follow the steps；Otherwise, step S6 is executed；
Step S6, to principal component number of components N ' increase by 1, return step S2；
Step S7 retains current principal component number of components N ', as the principal component number of components for meeting reconstruction accuracy.
Further, in the step S4, all corresponding total vector error TVE values for calculating phasor pass through formula
(1) it calculates
The formula for taking the maximum value of total vector error TVE is
εTVE=max { εij} (2)
In formula (1),It is the estimated data matrix after reconstructIn element, DijIt is in normalized data matrix D
Element；In formula (2), εTVEFor all εijMaximum value.
Further, in the step S5, the criterion is εTVE< εTVE,MAX；Wherein, εTVEFor all εij's
Maximum value, εTVE,MAXFor the maximum value of the total vector error TVE of data compression condition, εTVE.MAXValue set by actual demand
It is fixed.
As can be seen from the technical scheme provided by the above-mentioned embodiment of the present invention, the embodiment of the present invention based on power train
The principal component component iteration selection method of system data compression, base of the method in phasor compressed data principal component analytical method
On plinth, a proper phasor of N ' is chosen from proper phasor matrix U using the principal component number of components N ' of iteration and calculates iteration
A principal component matrix of N ', rebuilds estimated data matrix, then calculates the maximum synthetic vector of all corresponding phasors and miss
Difference, and judge whether to meet reconstruct data precision accordingly, obtain the principal component number for meeting reconstruction accuracy.The present invention disobeys
The phasor data that can be applied in complex field in data sample normalized is relied to compress；Meanwhile iterative process will not be significant
Ground increases the calculation amount of principal component analytical method, when use principal component analytical method carries out data compression to synchronized phasor data
When, effectively improve the compression ratio and reconstruct data precision of data, the principal component point of the data compression suitable for electric system
The selection of amount.
The additional aspect of the present invention and advantage will be set forth in part in the description, these will from the following description
Become obvious, or practice through the invention is recognized.
Detailed description of the invention
In order to illustrate the technical solution of the embodiments of the present invention more clearly, making required in being described below to embodiment
Attached drawing is briefly described, it should be apparent that, drawings in the following description are only some embodiments of the invention, right
For those of ordinary skill in the art, without creative efforts, it can also be obtained according to these attached drawings
His attached drawing.
Fig. 1 is that principal component component iteration selection method process of the embodiment of the present invention for electric power system data compression is shown
It is intended to.
Specific embodiment
Embodiments of the present invention are described below in detail, the example of the embodiment is shown in the accompanying drawings, wherein from beginning
Same or similar element or element with the same or similar functions are indicated to same or similar label eventually.Below by
The embodiment being described with reference to the drawings is exemplary, and for explaining only the invention, and cannot be construed to limit of the invention
System.
Those skilled in the art of the present technique are appreciated that unless expressly stated, singular " one " used herein, " one
It is a ", " described " and "the" may include plural form.It is to be further understood that wording used in specification of the invention
" comprising " refers to that there are the feature, integer, step, operation, element and/or component, but it is not excluded that in the presence of or addition one
Other a or multiple features, integer, step, operation, element, component and/or their group.It should be understood that when we claim element
It is " connected " or when " coupling " another element, it can be directly connected or coupled to other elements, or there may also be centres
Element.In addition, " connection " used herein or " coupling " may include being wirelessly connected or coupling.Wording used herein " and/
Or " it include one or more associated any cells for listing item and all combinations.
Those skilled in the art of the present technique are appreciated that unless otherwise defined, all terms used herein (including technology
Term and scientific term) there is meaning identical with the general understanding of those of ordinary skill in fields of the present invention.Also answer
It should be appreciated that those terms such as defined in the general dictionary should be understood that have in the context of the prior art
The consistent meaning of meaning will not be explained in an idealized or overly formal meaning and unless defined as here.
In order to facilitate understanding of embodiments of the present invention, it is done by taking several specific embodiments as an example into one below in conjunction with attached drawing
The explanation of step, and each embodiment does not constitute the restriction to the embodiment of the present invention.
According to one embodiment of present invention, provide it is a kind of for electric power system data compression principal component component change
It is a kind of iteration selection method for selection method, Fig. 1 show the master described in the present embodiment for electric power system data compression
Ingredient component iteration selection method flow diagram.
Voltage and current phasor sequence in the phasor data of electric power synchronized measurement system by one-to-one amplitude and
Phase forms, and generally comprises several groups voltage phasor and several groups electric current phasor in synchro measure data.With electricity in the present embodiment
It is illustrated for voltage phasor in Force system, the step of the present embodiment is equally applicable to electric current phasor.
As shown in Figure 1, the component selection method includes the following steps:
Step S0 constructs the initial data of M row N column according to the N group voltage phasor at M moment of measurement data to be compressed
Matrix Dr,DrFor the complex matrix of M × N；According to D=DrΛN -1By DrBeing normalized to modulus value is 1
Normalization data matrix D, D be M × N complex matrix, wherein1≤j≤N；According to C=DHThe covariance matrix of D calculating D
C, C are the complex matrix of N × N, and covariance matrix C is Hermitian matrix and positive semidefinite matrix；And further calculate the complete of C
Portion's eigenvalue λi, i=1......N, and λ1≥λ2≥…≥λN>=0, due to C be Hermitian matrix and positive semidefinite matrix,
The then eigenvalue λ of CiIt is real number；Seek system of linear equations λiThe basic course laboratory of I-C=0 obtains C for λiOne group of feature phase
Measure ui, obtain proper phasor matrix U=[u1,u2,…,uN], U is the complex matrix of N × N, and meets UHCU=Λ, wherein Λ
=diag (λ1,λ2,…,λN)。
In this step, voltage phasor is respectively In corresponding synchro measure data
A voltage measurement point (such as bus A phase voltage, bus positive sequence voltage etc.), VjAnd αjRespectively voltage phasor corresponds
Amplitude sequence and phase sequence；Measurement data to be compressed shares the data at M moment, then has Vj=[V1j,V2j,…,
VMj]T, αj=[α1j,α2j,…,αMj]T, Vij∠αijPhasor of corresponding j-th of the voltage phasor i-th of moment, 1≤i≤M, 1
≤j≤N。
Step S1 sets the initial value of iteration as principal component number of components N '=0, estimated data matrix
Step S2 chooses a proper phasor u of N ' according to principal component number of components N ' from proper phasor matrix UN′；According to
pN′=DuN′Calculate a principal component matrix p of N ' of iterationN′, pN′For the complex matrix of M × 1.
Step S3, according to iterative formulaRebuild estimated data matrixFor
The complex matrix of M × N.
Step S4 calculates estimated data matrixIt is missed with the synthetic vector of corresponding phasors all in normalization data matrix D
Poor (total vector error, TVE) value, and take maximum TVE value.
Further, all corresponding TVE values for calculating phasor, are calculated by formula (1)
The formula for taking TVE maximum value is
εTVE=max { εij} (2)
In formula (1),It is the estimated data matrix after reconstructIn element, DijIt is in normalized data matrix D
Element；In formula (2), εTVEFor all εijMaximum value.
Step S5, determines whether N ' meets the criterion of reconstruct data precision, if criterion is set up, executes step
Rapid S7；Otherwise, step S6 is executed.
Further, the criterion in this step is εTVE< εTVE,MAX；Wherein, εTVEFor all εijMaximum
Value, εTVE,MAXFor the maximum TVE value of data compression condition, εTVE.MAXValue set by actual demand.
Step S6, to principal component number of components N ' increase by 1, return step S2.
Step S7 retains current principal component number of components N ', as the principal component number of components for meeting reconstruction accuracy.
Principal component point of the embodiment of the present invention for electric power system data compression it can be seen from above-mentioned technical proposal
Iteration selection method is measured, is had the following beneficial effects: independent of data sample normalized, not by no strict mathematical
The complex field phasor of definition it is normalized limitation and can be applied to the phasor data in complex field compression；Efficiently control reconstruction
Data precision, the more focus of principal component analytical method statistically are the Characteristic Extractions for being statistical data.This
Outside, although the present embodiment realizes the selection course of principal component component by alternative manner, iterative process can't be significant
Ground increases the calculation amount of principal component analytical method, because in substation, the synchronized phasor number that measures under steady state conditions
According to being three-phase symmetrical, and since electrical distance is very close, variation tendency is also similar between synchronized phasor data, also
It is to say, principal component component is 1 at most of conditions, and iterative process only needs once meet reconstruct data precision
Requirement just need iteration to meet weight several times in addition, only in extremely few situation, such as when short trouble occurs for system
The precision of structure data.When the technical solution of the present embodiment is applied to principal component analytical method to the synchronization in power measurement system
When phasor data is compressed, the compression ratio and reconstruct two performance indicators of data precision of data can be effectively improved, it is more suitable
Together in the selection of the principal component component of data compression in the power system.
Those of ordinary skill in the art will appreciate that: attached drawing is the schematic diagram of one embodiment, module in attached drawing or
Process is not necessarily implemented necessary to the present invention.
All the embodiments in this specification are described in a progressive manner, same and similar between each embodiment
Part may refer to each other, and each embodiment focuses on the differences from other embodiments.Especially for dress
Set or system embodiment for, since it is substantially similar to the method embodiment, so describe fairly simple, related place ginseng
See the part explanation of embodiment of the method.Apparatus and system embodiment described above is only schematical, wherein institute
Stating unit as illustrated by the separation member may or may not be physically separated, component shown as a unit
It may or may not be physical unit, it can it is in one place, or may be distributed over multiple network units
On.Some or all of the modules therein can be selected to achieve the purpose of the solution of this embodiment according to the actual needs.Ability
Domain those of ordinary skill can understand and implement without creative efforts.
Those of ordinary skill in the art will appreciate that: the component in device in embodiment can be described according to embodiment
It is distributed in the device of embodiment, corresponding change can also be carried out and be located in one or more devices different from the present embodiment.
The component of above-described embodiment can be merged into a component, can also be further split into multiple subassemblies.
The foregoing is only a preferred embodiment of the present invention, but protection scope of the present invention be not limited to
This, anyone skilled in the art in the technical scope disclosed by the present invention, the variation that can readily occur in or replaces
It changes, should be covered by the protection scope of the present invention.Therefore, protection scope of the present invention should be with the protection of claim
Subject to range.
Claims (3)
1. a kind of principal component component iteration selection method for electric power system data compression, which is characterized in that the method packet
Include following steps:
Step S0 constructs the initial data of M row N column according to the N group voltage/current phasor at M moment of measurement data to be compressed
Matrix Dr, DrFor the complex matrix of M × N；According toBy DrIt is normalized to the normalization data matrix D that modulus value is 1, D is
The complex matrix of M × N, whereinAccording to C
=DHThe covariance matrix C, C that D calculates D are the complex matrix of N × N, and covariance matrix C is Hermitian matrix and positive semidefinite
Matrix, and further calculate the All Eigenvalues λ of Ci, i=1......N, and λ1≥λ2≥…≥λN>=0, since C is
Hermitian matrix and positive semidefinite matrix, the then eigenvalue λ of CiIt is real number；Seek system of linear equations λiThe Basic Solutions of I-C=0
System, obtains C for λiOne group of proper phasor ui, obtain proper phasor matrix U=[u1,u2,…,uN], U is the plural square of N × N
Battle array, and meet UHCU=Λ, wherein Λ=diag (λ1,λ2,…,λN)；
Step S1, enabling the initial value of iteration is principal component number of components N '=0, estimated data matrix
Step S2 chooses a proper phasor u of N ' according to principal component number of components N ' from proper phasor matrix UN′；According to pN′=
DuN′Calculate a principal component matrix p of N ' of iterationN′, pN′For the complex matrix of M × 1；
Step S3, according to iterative formulaRebuild estimated data matrix For the complex matrix of M × N；
Step S4 calculates estimated data matrixWith the total vector error value of corresponding phasors all in normalization data matrix D,
And take the maximum value of total vector error；
Step S5 determines whether N ' meets the criterion of reconstruct data precision according to the maximum value of the total vector error,
If criterion is set up, S7 is thened follow the steps；Otherwise, step S6 is executed；
Step S6, to principal component number of components N ' increase by 1, return step S2；
Step S7 retains current principal component number of components N ', as the principal component number of components for meeting reconstruction accuracy.
2. the principal component component iteration selection method of data compression according to claim 1, which is characterized in that the step
In S4, all corresponding total vector error value TVE for calculating phasor are calculated by formula (1)
The formula for taking the maximum value of total vector error value TVE is
εTVE=max { εij} (2)
In formula (1),It is the estimated data matrix after reconstructIn element, DijIt is the element in normalization data matrix D；Formula
(2) in, εTVEFor all εijMaximum value.
3. the principal component component iteration selection method according to claim 1 for data compression, which is characterized in that described
In step S5, the criterion is εTVE< εTVE,MAX；Wherein, εTVEFor all εijMaximum value；εTVE,MAXFor data compression
The maximum value of the total vector error of condition, εTVE.MAXValue set by actual demand.
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