CN106056470A - Electrical equipment load curve separation method based on principal component analysis and stepwise regression - Google Patents
Electrical equipment load curve separation method based on principal component analysis and stepwise regression Download PDFInfo
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Abstract
The invention provides an electrical equipment load curve separation method based on principal component analysis and stepwise regression. The electrical equipment load curve separation method comprises the steps of: filtering annual electricity load data of residents to obtain a low frequency component in electricity-utilization data of each user; converting each obtained low frequency component into a high dimension vector; calculating electricity consumption characteristics of each user; fitting statistical data of the number of household appliances with the electricity consumption characteristics to obtain a linear relation between the number of household appliances and electricity consumption characteristic quantity, and calculating a fitting coefficient; restoring the fitting coefficient to a high dimensional space by means of a coordinate transformation matrix, so as to obtain a high dimension vector which is a load curve of electrical equipment; and establishing an energy-saving scheme for users in a region according to load curve of the electrical equipment. The electrical equipment load curve separation method can be used for analyzing various kinds of electrical equipment load curves in the specified region, acquiring electricity-utilization habits of the electricity consumers in the specific region, customizing an electricity price scheme for the users in the region, guiding the users to change the electricity-utilization habits in a targeted manner, and achieving the purpose of saving electric energy.
Description
Technical field
The present invention relates to Power Electronic Technique, in particular it relates to a kind of based on principal component analysis with the electrical equipment of successive Regression
Machine utilization curve separation method.
Background technology
Demand Side Response i.e. power consumer adjusts its original custom according to power price, dynamically changing of Power policy
With power mode, reach to reduce or elapse the power load of certain period and respond supply of electric power, thus ensure the safety of network system
Economy.
Demand response policy making is set up on understanding user power utilization behavior in depth.User power utilization behavior includes
How user's current power behavior and user respond the corresponding policy of demand.For the electrical equipment in every resident family, electricity is installed
User power utilization behavior can be made and measuring accurately by table, but need to pay high construction installation and operation and maintenance expenses use.Use load
Curve isolation technics is not required to be all electrical appliances of every resident and installs ammeter, it is only necessary to gather subscriber household total electricity consumption curve
User's difference electrical equipment electricity consumption curve can be analyzed.Use resident's difference electrical equipment electricity consumption curve can analyze spy
Fixed area power consumer consumption habit, customizes electricity price scheme for this area user, guides user to change electricity consumption targetedly and practises
Used, reduce power system load peak value.Separating for realizing load curve, the computational methods that the present invention is given comprehensively employ two kinds
Method, principal component analysis and polynary gradually linear regression.
Principal component analysis (Principal Componential Analysis, PCA), is a kind of multi-variate statistical analysis skill
Art.Its centrales is by Data Dimensionality Reduction, extracts the main component of information in data, ignores the accessory constituent of information in data.
The dimension of initial data can be reduced by principal component analysis, remove the random disturbance in data, simplify subsequent calculations.
Polynary gradually linear regression analysis refers to the regression analysis to two or more linear variables, compares common
Multiple linear regression, polynary gradually linear regression is analyzed each step and is first chosen the most significant independent variable of impact and introduce, then to
There is variable to test one by one, reject impact least significantly variable, finally set up gradually linear regression predictive equation.Progressively
Linear regression can preferably overcome the generation of multicollinearity phenomenon, is the most frequently used analysis method exploring multivariate relationship.
Summary of the invention
For defect of the prior art, it is an object of the invention to provide a kind of based on principal component analysis and successive Regression
Electric equipment load curve separation method.
The electric equipment load curve separation method based on principal component analysis and successive Regression provided according to the present invention, bag
Include following steps:
Step 1: set up according to the statistical data of user household electrical equipment quantity got, the resident's Power system load data whole year
Data sample set；
Step 2: be filtered the annual Power system load data of every user, obtains the annual electric load of every user
Low frequency component in data；
Step 3: the low frequency component obtained is converted into the first high dimension vector；
Step 4: high dimension vector is merged into the first matrix, uses PCA to obtain this matrix after decomposing this matrix
Eigen vector, eigenvalue is sorted from big to small, from the beginning of at maximum eigenvalue, takes multiple eigenvalue conduct
Described bigger eigenvalue, becomes the second matrix by the combination of eigenvectors corresponding to bigger eigenvalue, as higher dimensional space with
The transformation matrix of coordinates of lower dimensional space；
Step 5: the first corresponding for every user high dimension vector is mapped to lower dimensional space by transformation matrix of coordinates, calculates
First high dimension vector of every user is mapped to the coordinate of lower dimensional space, and described coordinate is as power consumption feature；
Step 6: use gradually linear regression to analyze statistical data and the power consumption feature of matching household electrical appliance quantity, obtain
Household electrical appliance quantity and the linear relationship of power consumption characteristic quantity, and digital simulation coefficient；
Step 7: fitting coefficient is reduced to higher dimensional space by transformation matrix of coordinates, obtains the second high dimension vector, described
Second high dimension vector is the load curve of electrical equipment；
Step 8: the load curve according to electrical equipment is that user formulates energy-saving scheme.
Preferably, described step 1 includes: collects user's Urban Annual Electrical Power Consumption data, gathers more than one data point per hour,
Read user's Urban Annual Electrical Power Consumption data and preserve into the form of matrix, specifically,
Read the electricity consumption data of n-th day whole day, be combined as a column vector according to time sequencing, and use symbol dnTable
Show, calculate column vector d representing electricity consumption every day datan, it is combined as a matrix according to chronological order, and uses symbol D table
Show as follows:
D=(d1,d2,…,dn)
Calculate the electricity consumption data matrix D of every user, collect electrical equipment incremental data to be analyzed, by the use of same user
Electricity data matrix and electrical equipment incremental data are mapped, and collectively form a sample, the data sample gathering all users
The data sample set of this composition.
Preferably, described step 2 includes: in choosing adjacent 50 days, the meansigma methods of electricity consumption data is as the centre electricity consumption of a day
Data, operation of wherein averaging can produce the effect of low pass filter；Computing formula is as follows:
In formula:Represent low frequency component matrix, diRepresenting the column vector of i-th day electricity consumption data, n represents total natural law.
Preferably, described step 3 includes: by low frequency component matrixIt is converted into following form:
Preferably, the PCA in described step 4 refers to: first high dimension vector of every user is merged into
One matrix, uses symbol M to represent, M principal component analysis obtains eigenvalue matrix A and eigenvectors matrix U:
MM*=UAU*
U=(U1,U2,…,Um)
Front S vector in selected characteristic vector matrix U, uses symbol USRepresent, in formula: m represents number of users, U*Represent
The conjugate transpose of matrix U, M*The conjugate transpose of representing matrix M；
US=(U1,U2,…,US)
Choose USTransformation matrix of coordinates as higher dimensional space Yu lower dimensional space.
Preferably, described step 5 includes: by first high dimension vector of every userWith transformation matrix of coordinates USDo inner product
As the power consumption characteristic quantity of this user, computing formula is as follows:
In formula: vector f represents a user power utilization measure feature amount, matrix F represents all user power utilization measure feature amounts,Table
Show matrix USConjugate transpose；
Preferably, described step 6 includes: use gradually linear regression to analyze matching vector l and matrix F, is calculated S dimension
Vector fitting coefficient w,；Vector l is used to represent household electrical appliance quantity.
Preferably, described step 7 includes: use transformation matrix of coordinates USFitting coefficient w is converted into higher dimensional space, calculates
Formula is as follows:
W=USw；
In formula: the element in vector W is for representing the power consumption of the time period corresponding to electrical equipment element in vector W
Amount.
Preferably, described step 8 includes: analyzes regional multiple electrical equipment load curve, obtains this area's power consumer
Consumption habit, customizes electricity price scheme for this area user.
Compared with prior art, the present invention has a following beneficial effect:
The present invention can analyze designated area multiple electrical equipment load curve, obtains particular locality power consumer electricity consumption and practises
Used, customize electricity price scheme for this area user, guide user to change consumption habit targetedly, reach the mesh of saves energy
's.
Accompanying drawing explanation
By the detailed description non-limiting example made with reference to the following drawings of reading, the further feature of the present invention,
Purpose and advantage will become more apparent upon:
Fig. 1 is the Urban Annual Electrical Power Consumption data and curves figure of electromagnetic oven；
The electric equipment load curve separation method based on principal component analysis and successive Regression that Fig. 2 provides for the present invention
Schematic flow sheet.
Detailed description of the invention
Below in conjunction with specific embodiment, the present invention is described in detail.Following example will assist in the technology of this area
Personnel are further appreciated by the present invention, but limit the present invention the most in any form.It should be pointed out that, the ordinary skill to this area
For personnel, without departing from the inventive concept of the premise, it is also possible to make some changes and improvements.These broadly fall into the present invention
Protection domain.
A kind of domestic electric appliance load curve separation method based on principal component analysis and polynary gradually linear regression, bag
Include following steps:
(1) obtain the statistical data of user household electrical equipment quantity, obtain the resident's Power system load data whole year, build data sample
This set.
(2) the electricity consumption data filtering to every user, obtains the low frequency component in every user power utilization data.Again will be to often
The low frequency component that position user power utilization data filtering obtains is converted into a high dimension vector.
(3) high dimension vector of every user in (2) is merged into a matrix, and use PCA to decompose this
Matrix, obtains eigen vector.Choose the matrix of bigger eigenvalue characteristic of correspondence vector composition, empty as higher-dimension
Between with the transformation matrix of coordinates of lower dimensional space.
(4) use the transformation matrix of coordinates in (3) that the high dimension vector of every user is mapped to lower dimensional space, and calculate it
Coordinate in lower dimensional space, is defined as power consumption characteristic quantity.
(5) gradually linear regression is used to analyze in statistical data and (4) of matching household electrical appliance quantity in lower dimensional space
Coordinate, obtains the linear relationship of household electrical appliance quantity and power consumption characteristic quantity, and digital simulation coefficient.
(6) use the transformation matrix of coordinates in (3) that fitting coefficient is reduced to higher dimensional space, choose this high dimension vector and represent
The load curve of this electrical equipment.
In described step (1), method particularly includes: collect user's Urban Annual Electrical Power Consumption data, the most at least gather data
Point.Read user's Urban Annual Electrical Power Consumption data and preserve into the form of matrix:
Read the electricity consumption data of n-th day whole day, be combined as a column vector according to time sequencing, and use symbol dnTable
Show.Calculate column vector d representing electricity consumption every day datan, it is combined as a matrix according to chronological order, and uses symbol D table
Show.
D=(d1,d2,…,dn)
Calculate the electricity consumption data matrix D of every user.Collect electrical equipment incremental data to be analyzed, by the use of same user
Electricity data matrix and electrical equipment incremental data are mapped, and collectively form a sample, the data sample gathering all users
The data sample set of this composition.
In described step (2), obtain electricity consumption data low frequency components method particularly includes: choose electricity consumption number in adjacent 50 days
According to meansigma methods as the electricity consumption data of middle a day.Operation of averaging produces the effect of low pass filter, it is possible to take it
His filtering mode.
In described step (2), would indicate that the matrix of electricity consumption data low frequency componentsIt is converted into the concrete side of high dimension vector
Method is:
If
Picks symbolsRepresent this high dimension vector, order
In described step (3), use PCA method particularly includes: by every user (setting total m position user)
High dimension vector merge into a matrix, use symbol M to represent, M principal component analysis is obtained eigenvalue matrix A and feature to
Moment matrix U:
MM*=UAU*
U=(U1,U2,…,Um)
Front S vector in selected characteristic vector matrix U, uses symbol USRepresent
US=(U1,U2,…,US)
Choose USTransformation matrix of coordinates as higher dimensional space Yu lower dimensional space.
In described step (4), calculate power consumption characteristic quantity method particularly includes: by the high dimension vector of every userWith seat
Mark transformation matrix USDo the inner product power consumption characteristic quantity as this user.
Choose vector f and represent a user power utilization measure feature amount,
Choose matrix F and represent all user power utilization measure feature amounts,
In described step (5), method particularly includes: use gradually linear regression to analyze matching household electrical appliance quantity and use with user
Electricity characteristic quantity.
Vector l is used to represent household electrical appliance quantity.
Use gradually linear regression to analyze matching vector l and matrix F, be calculated S dimensional vector fitting coefficient w so that l ≈
wF。
In described step (6), method particularly includes: use transformation matrix of coordinates USFitting coefficient w is converted into higher dimensional space,
And use symbol W to represent.
W=USw
This electrical equipment of element approximate representation in vector W is at the power consumption of the time period corresponding to this element.
Domestic electric appliance load curve separation method based on principal component analysis and polynary gradually linear regression is used to divide
The electricity consumption curve of electromagnetic oven in analysis domestic electric appliance.
(1) obtain the statistical data of electromagnetic oven quantity, obtain residential power load data, build data sample set.
Sample: 581 families in area, Ireland, m=581.
Power system load data: the electricity consumption data in July, 2009 in December, 2010, measures 48 power consumption data every day
(per half an hour measures once), measures 536 days, n=536, D=(d altogether1,d2,…,d536)。
Electromagnetic oven quantity statistics data refer to add up quantity l of each family electromagnetic oven.Value possible for l can be divided into three kinds of feelings
Condition: 1. do not have；2. one；3. two and more than.
(2) the electricity consumption data filtering to every domestic consumer, obtains the low frequency component in every user power utilization data.Use
The power consumption of one day in the middle of the meansigma methods approximate representation of adjacent 50 days electricity consumption data.
Filtering operation cause testing just start after the measurement data of initial 24 days and experiment terminate before last 25 days
Measurement data disappearance, measurement data is reduced to 487 days, every day 48 measure point.
Above-mentioned 487 × 48 data points being placed in a vector, this vector has 23376 elements, and all data points depend on
Arrange according to time sequencing, from the 23:30-24:00 of the 0:00-0:30 of first day to last day.
(3) high dimension vector of every user in (2) being merged into a matrix M, M has 23376 row 581 and arranges.
Use PCA to decompose this matrix, obtain eigen vector.Choose bigger eigenvalue pair
The matrix of the characteristic vector composition answered, as the transformation matrix of coordinates of higher dimensional space Yu lower dimensional space.
MM*=UAU*
U is the square formation of 23376 row 23376 row, and A is the square formation of 23376 row 23376 row.
Front S vector in selected characteristic vector matrix U, uses symbol USRepresent, S=10.
US=(U1,U2,…,U10)
USIt it is the matrix of 23376 row 10 row.
(4) use the transformation matrix of coordinates in (3) that the high dimension vector of every user is mapped to lower dimensional space, and calculate it
Coordinate in lower dimensional space, is defined as power consumption characteristic quantity,F is the matrix of 10 row 581 row.
(5) use gradually linear regression to analyze matching vector l and matrix F, be calculated S dimensional vector fitting coefficient w so that
l≈wF。
(6) transformation matrix of coordinates U is usedSFitting coefficient w is converted into higher dimensional space.
W=USw
This electrical equipment of element approximate representation in vector W is at the power consumption of the time period corresponding to this element.
W vector is reduced to the matrix form of 487 × 48, and uses contour map to represent, as it is shown in figure 1, shown in figure
Numerical value is relative value.
In figure, the electromagnetic oven time concentrates on noon with at dusk, and result rule of typically working and resting with family life is kissed completely
Close.
Above the specific embodiment of the present invention is described.It is to be appreciated that the invention is not limited in above-mentioned
Particular implementation, those skilled in the art can make a variety of changes within the scope of the claims or revise, this not shadow
Ring the flesh and blood of the present invention.In the case of not conflicting, the feature in embodiments herein and embodiment can any phase
Combination mutually.
Claims (9)
1. an electric equipment load curve separation method based on principal component analysis and successive Regression, it is characterised in that include
Following steps:
Step 1: set up data according to the statistical data of user household electrical equipment quantity got, the resident's Power system load data whole year
Sample set；
Step 2: be filtered the annual Power system load data of every user, obtains the annual Power system load data of every user
In low frequency component；
Step 3: the low frequency component obtained is converted into the first high dimension vector；
Step 4: high dimension vector is merged into the first matrix, uses PCA to obtain the spy of this matrix after decomposing this matrix
Value indicative and characteristic vector, sort from big to small by eigenvalue, from the beginning of at maximum eigenvalue, takes multiple eigenvalue as described
Bigger eigenvalue, becomes the second matrix by the combination of eigenvectors corresponding to bigger eigenvalue, as higher dimensional space and low-dimensional
The transformation matrix of coordinates in space；
Step 5: by transformation matrix of coordinates, the first corresponding for every user high dimension vector is mapped to lower dimensional space, calculates every
First high dimension vector of user is mapped to the coordinate of lower dimensional space, and described coordinate is as power consumption feature；
Step 6: use gradually linear regression to analyze statistical data and the power consumption feature of matching household electrical appliance quantity, obtain domestic
Electrical equipment quantity and the linear relationship of power consumption characteristic quantity, and digital simulation coefficient；
Step 7: fitting coefficient is reduced to higher dimensional space by transformation matrix of coordinates, obtains the second high dimension vector, and described second
High dimension vector is the load curve of electrical equipment；
Step 8: the load curve according to electrical equipment is that user formulates energy-saving scheme.
Electric equipment load curve separation method based on principal component analysis and successive Regression the most according to claim 1,
It is characterized in that, described step 1 includes: collects user's Urban Annual Electrical Power Consumption data, gathers more than one data point per hour, reads
User's Urban Annual Electrical Power Consumption data also preserve into the form of matrix, specifically,
Read the electricity consumption data of n-th day whole day, be combined as a column vector according to time sequencing, and use symbol dnRepresent, calculate
Represent column vector d of electricity consumption every day datan, it is combined as a matrix according to chronological order, and uses symbol D to be expressed as follows:
D=(d1,d2,…,dn)
Calculate the electricity consumption data matrix D of every user, collect electrical equipment incremental data to be analyzed, by the electricity consumption number of same user
It is mapped according to matrix and electrical equipment incremental data, collectively forms a sample, the data sample structure that all users are gathered
Become data sample set.
Electric equipment load curve separation method based on principal component analysis and successive Regression the most according to claim 2,
It is characterized in that, described step 2 includes: in choosing adjacent 50 days, the meansigma methods of electricity consumption data is as the centre electricity consumption number of a day
According to, operation of wherein averaging can produce the effect of low pass filter；Computing formula is as follows:
In formula:Represent low frequency component matrix, diRepresenting the column vector of i-th day electricity consumption data, n represents total natural law.
Electric equipment load curve separation method based on principal component analysis and successive Regression the most according to claim 3,
It is characterized in that, described step 3 includes: by low frequency component matrixIt is converted into following form:
Electric equipment load curve separation method based on principal component analysis and successive Regression the most according to claim 1,
It is characterized in that, the PCA in described step 4 refers to: first high dimension vector of every user is merged into the first square
Battle array, uses symbol M to represent, M principal component analysis obtains eigenvalue matrix A and eigenvectors matrix U:
MM*=UAU*
U=(U1,U2,…,Um)
Front S vector in selected characteristic vector matrix U, uses symbol USRepresent, in formula: m represents number of users, U*Representing matrix U
Conjugate transpose, M*The conjugate transpose of representing matrix M；
US=(U1,U2,…,US)
Choose USTransformation matrix of coordinates as higher dimensional space Yu lower dimensional space.
Electric equipment load curve separation method based on principal component analysis and successive Regression the most according to claim 1,
It is characterized in that, described step 5 includes: by first high dimension vector of every userWith transformation matrix of coordinates USDo inner product conduct
The power consumption characteristic quantity of this user, computing formula is as follows:
In formula: vector f represents a user power utilization measure feature amount, matrix F represents all user power utilization measure feature amounts,Represent square
Battle array USConjugate transpose.
Electric equipment load curve separation method based on principal component analysis and successive Regression the most according to claim 1,
It is characterized in that, described step 6 includes: uses gradually linear regression to analyze matching vector l and matrix F, is calculated S dimensional vector
Fitting coefficient w,；Vector l is used to represent household electrical appliance quantity.
Electric equipment load curve separation method based on principal component analysis and successive Regression the most according to claim 1,
It is characterized in that, described step 7 includes: use transformation matrix of coordinates USFitting coefficient w is converted into higher dimensional space, computing formula
As follows:
W=USw；
In formula: the element in vector W is for representing the power consumption of the time period corresponding to electrical equipment element in vector W.
Electric equipment load curve separation method based on principal component analysis and successive Regression the most according to claim 1,
It is characterized in that, described step 8 includes: analyzes regional multiple electrical equipment load curve, obtains this area's power consumer electricity consumption
Custom, customizes electricity price scheme for this area user.
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| CN108197425A (en) * | 2018-01-19 | 2018-06-22 | 北京工业大学 | A kind of intelligent grid data resolving method based on Non-negative Matrix Factorization |
| CN112327004A (en) * | 2020-10-20 | 2021-02-05 | 北京嘀嘀无限科技发展有限公司 | Vehicle acceleration determination method and device, storage medium and electronic equipment |
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108197425A (en) * | 2018-01-19 | 2018-06-22 | 北京工业大学 | A kind of intelligent grid data resolving method based on Non-negative Matrix Factorization |
| CN108197425B (en) * | 2018-01-19 | 2019-09-03 | 北京工业大学 | A kind of smart grid data resolving method based on Non-negative Matrix Factorization |
| CN112327004A (en) * | 2020-10-20 | 2021-02-05 | 北京嘀嘀无限科技发展有限公司 | Vehicle acceleration determination method and device, storage medium and electronic equipment |
| CN113159988A (en) * | 2021-04-14 | 2021-07-23 | 杭州电力设备制造有限公司 | User electric appliance load state analysis method, device, equipment and readable storage medium |
| CN113159988B (en) * | 2021-04-14 | 2022-08-02 | 杭州电力设备制造有限公司 | User electric appliance load state analysis method, device, equipment and readable storage medium |
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Application publication date: 20161026 |