CN113220671A - Power load missing data restoration method based on power utilization mode decomposition and reconstruction - Google Patents

Power load missing data restoration method based on power utilization mode decomposition and reconstruction Download PDF

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CN113220671A
CN113220671A CN202110409685.5A CN202110409685A CN113220671A CN 113220671 A CN113220671 A CN 113220671A CN 202110409685 A CN202110409685 A CN 202110409685A CN 113220671 A CN113220671 A CN 113220671A
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林振智
卢峰
金伟超
刘晟源
杨莉
崔雪原
林之岸
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Zhejiang University ZJU
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Abstract

The invention discloses a power load missing data restoration method based on power consumption mode decomposition and reconstruction, and relates to the field of analysis and processing of large power data. The method comprises the steps of firstly, acquiring power load data of a power consumer, and dividing a data set into a complete load data set and a load data set to be repaired; based on the sparsity and diversity of the user power load, a K singular value decomposition dictionary learning algorithm is adopted to extract a base vector dictionary matrix representing the user power electronic mode from the complete load data set; decomposing and coding the load curve to be repaired based on the basis of the base vector dictionary matrix, and determining the load curve to be repaired to be composed of electronic modes; and finally, reconstructing the load curve according to the coding vector of the load curve to be repaired based on the base vector dictionary matrix, and filling and repairing the data of the missing part of the power load. The method can be applied to multi-day load data loss or load data loss repair in continuous time periods.

Description

Power load missing data restoration method based on power utilization mode decomposition and reconstruction
Technical Field
The invention relates to the field of analysis and processing of big electric power data, in particular to a power load missing data repairing method based on power utilization mode decomposition and reconstruction.
Background
The wide popularization of the intelligent electric meter and the construction of the electricity utilization information acquisition system provide a data base for the research and analysis of the large load data of the user side. However, the load data is not complete due to problems such as meter failure or communication errors. The method for repairing the missing load data can improve the data quality, is a precondition for analyzing the load data, and has important significance for intelligent power grids and intelligent power utilization. The power load has the characteristics of fast change, no fixed rule and the like due to the randomness of power consumption of users and the start-stop characteristic of equipment. Meanwhile, load data loss can be divided into three loss types of isolated loss, continuous loss and total loss, and a conventional interpolation algorithm is not suitable for repairing the condition of continuous distribution of the lost load data. And therefore the difficulty of load-miss data repair is greater than that of geospatial data repair and image repair.
User load data has two main features: sparsity and diversity. Sparsity means that the daily load of a user can be basically linearly composed of several sub-modes, for example, the load can be decomposed into power curves of various devices of the user; diversity refers to a set of electronic patterns that can be reconstructed into different daily load curves by different codes. Based on the sparsity and diversity of the load of the power user, the daily load curve is decomposed into different load sub-modes by adopting a sparse coding technology, and the different load curves are described as linear combination of the sub-modes so as to realize load reconstruction, thereby restoring the load missing data.
Disclosure of Invention
The technical problem to be solved and the technical task to be solved by the invention are to perfect and improve the prior technical scheme and provide a power load missing data restoration method based on power utilization mode decomposition and reconstruction so as to realize effective restoration of continuously missing load data. Therefore, the invention adopts the following technical scheme.
A power load missing data restoration method based on power utilization mode decomposition and reconstruction is characterized by comprising the following steps:
1) acquiring power load data of a power consumer from a power information acquisition system, and dividing a data set into a complete load data set and a load data set to be repaired according to whether daily load data is completely acquired;
2) extracting a base vector dictionary matrix representing the electronic mode for the user from the complete load data set by adopting a K singular value decomposition dictionary learning algorithm;
3) decomposing and coding the load curve to be repaired based on the basis of the base vector dictionary matrix, and determining the load curve to be repaired to be composed of electronic modes;
4) and reconstructing the load curve according to the coding vector of the load curve to be repaired based on the base vector dictionary matrix, and performing filling repair on the data of the missing part of the power load, namely using the power utilization data at the corresponding moment in the reconstructed load curve as the repair value of the data of the missing part of the load.
According to the technical scheme, a K singular value decomposition dictionary learning algorithm is adopted, the power load data of the power consumer is firstly acquired, and the data set is divided into a complete load data set and a load data set to be repaired according to whether the daily load data is completely acquired or not. Based on sparseness and diversity of power user loads, a K singular value decomposition dictionary learning algorithm is adopted to extract a base vector dictionary matrix representing a user power electronic mode from complete load data set; then, decomposing and coding the load curve to be repaired based on the basis of the base vector dictionary matrix, and determining the load curve to be repaired to be composed of electronic modes; and finally reconstructing the load curve according to the coding vector of the load curve to be repaired based on the base vector dictionary matrix, and performing filling repair on the data of the missing part of the power load, namely taking the power utilization data at the corresponding moment in the reconstructed load curve as the repair value of the data of the missing part of the load. Therefore, effective repair of continuously missing load data is achieved.
As a preferable technical means: in the step 1), power consumption load data of power consumers are acquired from a power consumption information acquisition system, and the load data are divided into a complete load data set and a load data set to be repaired according to whether the daily load data are completely acquired or not, wherein a complete daily load acquisition sample set X of a certain userN×MCan be expressed as:
Figure BDA0003023665240000031
Figure BDA0003023665240000032
in the formula: n is daily load collection points; m is the number of load acquisition days;
Figure BDA0003023665240000033
the daily load curve of the j day is an N-dimensional characteristic vector;
Figure BDA0003023665240000034
the power vector at the ith acquisition time of the whole load curve. For the load curve x to be restored ═ x1,x2,…,xN]T，
Figure BDA0003023665240000035
Figure BDA0003023665240000036
For the null value, i ∈ Ωnan＝{c1,c2,...,cL}，clNumber of the l-th missing point, ΩnanAnd acquiring a sequence number set of missing points, wherein L is the number of missing points acquired by the load curve.
As a preferable technical means: in step 2), a K singular value decomposition dictionary learning algorithm is adopted to extract a base vector dictionary matrix representing the electronic mode for the user from the complete load data set, and the dictionary learning aims at learning a dictionary matrix B so that X isN×MIs approximately decomposed into:
X≈BZ
in the formula: b is belonged to RN×KIs a dictionary matrix, K is the size of the dictionary, and each column of B
Figure BDA0003023665240000037
Is a unitized atom vector, and is also an M-dimensional feature vector; z ═ Z1,z2,…,zM]∈RK×MIs a sparse coding matrix. When Z is to be satisfied as sparsely as possible while performing approximate decomposition, the expression of the approximate decomposition problem is:
Figure BDA0003023665240000038
in the formula: i | · | purple windFIs Frobenius norm whose value is the square sum root of the matrix elements and represents the reconstruction error EBSize of (D), reconstruction error EBThe smaller the dictionary, the better the dictionary learning effect; i | · | purple wind0Is a 0 norm whose value is the number of non-zero entries in the matrix; t is0For sparsity constraint threshold, for constraining the coded vector ziThe equation can be solved by an orthogonal matching pursuit algorithm.
As a preferable technical means: in step 3), on the basis of dictionary learning by adopting a K singular value decomposition algorithm, decomposing and encoding a load curve to be repaired based on a base vector, determining that the load curve to be repaired is formed by an electronic mode, and encoding the load curve to be repaired by using a load data part successfully acquired by the load curve to be repaired and a dictionary matrix at a corresponding moment, wherein the encoding expression is as follows:
Figure BDA0003023665240000041
Figure BDA0003023665240000042
x/Ω＝x-{xi|i∈Ωnan}
Figure BDA0003023665240000043
in the formula: x is the number of/ΩSuccessfully collected load data in the load curve x, wherein the length of the load data is N-L;
Figure BDA0003023665240000044
is the ith dimension (row) feature vector in B; b is/ΩRemoving the dictionary matrix after collecting the corresponding characteristic row vectors at the missing moment for the complete dictionary matrix B,
Figure BDA0003023665240000045
zgto reconstruct the vector, is x/ΩBased on B/ΩAnd decomposing the obtained sparse coding vector, wherein the value of the sparse coding vector is formed by an electronic mode determined based on the successfully collected load data, and the sparse coding vector represents a possible power utilization mode of the load curve to be repaired.
As a preferable technical means: in step 4), based on the basis of the base vector dictionary matrix, reconstructing the load curve according to the coding vector of the load curve to be repaired, wherein the expression is as follows:
xg＝Bzg
in the formula xgFor reconstructing the load curve, from the reconstructed vector zgAnd reconstructing the complete dictionary matrix B. On the basis, filling and repairing the data of the missing part of the power load, namely, taking the power utilization data at the corresponding moment in the reconstructed load curve as a repairing value of the data of the missing part of the power load, wherein the expression is as follows:
Figure BDA0003023665240000046
in the formula
Figure BDA0003023665240000051
To reconstruct the load xgCorrespondingly acquiring load data at the missing moment.
Has the advantages that:
the invention provides a power load missing data restoration method based on power utilization mode decomposition and reconstruction. The method comprises the steps of firstly, acquiring power load data of a power consumer, and dividing a data set into a complete load data set and a load data set to be repaired according to whether daily load data are completely acquired. Based on sparseness and diversity of power user loads, a K singular value decomposition dictionary learning algorithm is adopted to extract a base vector dictionary matrix representing a user power electronic mode from complete load data set; then, decomposing and coding the load curve to be repaired based on the basis of the base vector dictionary matrix, and determining the load curve to be repaired to be composed of electronic modes; and finally reconstructing the load curve according to the coding vector of the load curve to be repaired based on the base vector dictionary matrix, and performing filling repair on the data of the missing part of the power load, namely taking the power utilization data at the corresponding moment in the reconstructed load curve as the repair value of the data of the missing part of the load. Therefore, effective repair of continuously missing load data is achieved. According to the method, the power utilization habits of the users and the relative fixation of the power utilization equipment are considered, the user load is divided into a plurality of typical power utilization modes based on historical load data, and the missing load data is repaired based on the power utilization modes. The power load data management personnel can apply the method to the load data missing repair of multi-day load data missing or continuous time periods according to the actual needs.
Drawings
FIG. 1 is a flow chart of the present invention.
FIG. 2 is the load curve 1 missing data repair result;
FIG. 3 is the load curve 2 missing data repair result;
FIG. 4 is the load curve 3 missing data repair result;
FIG. 5 shows the actual encoding and reconstruction encoding results of the load curve 1;
FIG. 6 shows the actual encoding and reconstruction encoding results of the load curve 2;
FIG. 7 shows the actual encoding and reconstruction encoding results of the load curve 3;
FIG. 8 shows the corresponding basis vectors of the actual encoding and the reconstructed encoding of the load curve 1;
FIG. 9 shows the corresponding basis vectors of the actual encoding and the reconstructed encoding of the load curve 2;
fig. 10 shows the base vectors corresponding to the actual encoding and the reconstructed encoding of the load curve 3.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the drawings in the specification.
As shown in fig. 1, fig. 1 is a flow chart of the method of the present invention: the method comprises the steps of firstly, acquiring power load data of a power consumer, and dividing a data set into a complete load data set and a load data set to be repaired according to whether daily load data are completely acquired. Based on sparseness and diversity of power user loads, a K singular value decomposition dictionary learning algorithm is adopted to extract a base vector dictionary matrix representing a user power electronic mode from complete load data set; then, decomposing and coding the load curve to be repaired based on the basis of the base vector dictionary matrix, and determining the load curve to be repaired to be composed of electronic modes; and finally reconstructing the load curve according to the coding vector of the load curve to be repaired based on the base vector dictionary matrix, and performing filling repair on the data of the missing part of the power load, namely taking the power utilization data at the corresponding moment in the reconstructed load curve as the repair value of the data of the missing part of the load. Therefore, effective repair of continuously missing load data is achieved. The method comprises the following specific steps:
step 1, acquiring power consumption load data of power users from a power consumption information acquisition system, dividing the load data into a complete load data set and a load data set to be repaired according to whether the daily load data is completely acquired or not, wherein a complete daily load acquisition sample set X of a certain userN×MCan be expressed as:
Figure BDA0003023665240000061
Figure BDA0003023665240000071
in the formula: n is daily load collection points; m is the number of load acquisition days;
Figure BDA0003023665240000072
the daily load curve of the j day is an N-dimensional characteristic vector;
Figure BDA0003023665240000073
the power vector at the ith acquisition time of the whole load curve. For the load curve x to be restored ═ x1,x2,…,xN]T，
Figure BDA0003023665240000074
Figure BDA0003023665240000075
For the null value, i ∈ Ωnan＝{c1,c2,...,cL}，clNumber of the l-th missing point, ΩnanAnd acquiring a sequence number set of missing points, wherein L is the number of missing points acquired by the load curve.
And extracting a base vector dictionary matrix representing the electronic mode for the user from the complete load data set by adopting a K singular value decomposition dictionary learning algorithm.
Step 2, extracting a base vector dictionary matrix representing the electronic mode for the user from the complete load data set by adopting a K singular value decomposition dictionary learning algorithm, wherein the dictionary learning aim is to learn a dictionary matrix B so that X isN×MIs approximately decomposed into:
X≈BZ
in the formula: b is belonged to RN×KIs a dictionary matrix, K is the size of the dictionary, and each column of B
Figure BDA0003023665240000076
Is a unitized atom vector, and is also an M-dimensional feature vector; z ═ Z1,z2,…,zM]∈RK×MFor sparse codingAnd (4) matrix. When Z is to be satisfied as sparsely as possible while performing approximate decomposition, the expression of the approximate decomposition problem is:
Figure BDA0003023665240000077
in the formula: i | · | purple windFIs Frobenius norm whose value is the square sum root of the matrix elements and represents the reconstruction error EBSize of (D), reconstruction error EBThe smaller the dictionary, the better the dictionary learning effect; i | · | purple wind0Is a 0 norm whose value is the number of non-zero entries in the matrix; t is0For sparsity constraint threshold, for constraining the coded vector ziThe equation can be solved by an orthogonal matching pursuit algorithm.
And 3, decomposing and coding the load curve to be repaired based on the basis of the base vector on the basis of dictionary learning by adopting a K singular value decomposition algorithm, determining the load curve to be repaired to be formed by an electronic mode, and coding the load curve to be repaired by utilizing a load data part successfully acquired by the load curve to be repaired and a dictionary matrix at a corresponding moment, wherein the coded expression is as follows:
Figure BDA0003023665240000081
Figure BDA0003023665240000082
x/Ω＝x-{xi|i∈Ωnan}
Figure BDA0003023665240000083
in the formula: x is the number of/ΩSuccessfully collected load data in the load curve x, wherein the length of the load data is N-L;
Figure BDA0003023665240000084
is the ith dimension (row) feature vector in B; b is/ΩRemoving the dictionary matrix after collecting the corresponding characteristic row vectors at the missing moment for the complete dictionary matrix B,
Figure BDA0003023665240000085
zgto reconstruct the vector, is x/ΩBased on B/ΩAnd decomposing the obtained sparse coding vector, wherein the value of the sparse coding vector is formed by an electronic mode determined based on the successfully collected load data, and the sparse coding vector represents a possible power utilization mode of the load curve to be repaired.
And 4, reconstructing the load curve according to the coding vector of the load curve to be restored based on the base vector dictionary matrix, wherein the expression is as follows:
xg＝Bzg
in the formula xgFor reconstructing the load curve, from the reconstructed vector zgAnd reconstructing the complete dictionary matrix B. On the basis, filling and repairing the data of the missing part of the power load, namely, taking the power utilization data at the corresponding moment in the reconstructed load curve as a repairing value of the data of the missing part of the power load, wherein the expression is as follows:
Figure BDA0003023665240000086
in the formula
Figure BDA0003023665240000087
To reconstruct the load xgCorrespondingly acquiring load data at the missing moment.
The invention is further illustrated by the following specific examples:
one, data source
The example data mainly comes from 48-point daily load data of 5-10 months in 2019 of a certain resident user, a load curve of three days is randomly selected to construct missing samples, and the missing samples are set to be load data missing at 10 continuous collection times.
Second, load missing data repair result
The technical proposal provided by the invention is adopted to repair the three load curves, and other users are selected to adoptCollecting 100 complete daily load curves (namely M is 100) as a training set for dictionary learning, setting the dictionary size to be 20, namely K is 20, and setting a sparsity constraint threshold T 05. The repairing results of the three load curves are respectively shown in fig. 2, fig. 3 and fig. 4, the sparse coding of the actual load curve and the reconstructed load curve is respectively shown in fig. 5, fig. 6 and fig. 7, and the coding of the corresponding base vectors is respectively shown in fig. 8, fig. 9 and fig. 10.
From fig. 2, fig. 3 and fig. 4, the algorithm provided in this chapter can better repair the missing load data no matter the load is flat or there is a large rise and fall during the data missing period. As can be seen from fig. 5, 6, and 7, after the load curve with missing part of the data is encoded based on the dictionary, the encoding result is close to the actual complete load curve encoding result, and the part with a larger encoding value is substantially consistent, which indicates that the missing load curve can still obtain the encoding consistent with the actual complete load curve based on the dictionary matrix based on the part of the data successfully acquired by the missing load curve. Due to the consistency of the reconstruction codes and the original load decomposition codes, the load curve obtained based on the reconstruction codes and the reconstruction of the complete dictionary is basically consistent with the actual complete load curve, and therefore the missing load data can be repaired. As shown in fig. 8, 9 and 10, the basis vectors corresponding to the largest codes (i.e., the basis vector 13 in fig. 8, the basis vector 18 in fig. 9 and the basis vector 16 in fig. 10) are closer to the actual full load curve, and the basis vectors corresponding to the remaining codes are further repaired and approximated, and finally can pass through the dictionary basis vectors.
The method for repairing the missing data of the power load based on the power consumption mode decomposition and reconstruction shown in fig. 1 is a specific embodiment of the present invention, has shown the substantial features and the progress of the present invention, and can make equivalent modifications in the aspects of shape, structure, etc. according to the practical use requirements, and is within the protection scope of the present solution.

Claims (5)

1. A power load missing data restoration method based on power utilization mode decomposition and reconstruction is characterized by comprising the following steps:
1) acquiring power load data of a power consumer from a power information acquisition system, and dividing a data set into a complete load data set and a load data set to be repaired according to whether daily load data is completely acquired;
2) extracting a base vector dictionary matrix representing the electronic mode for the user from the complete load data set by adopting a K singular value decomposition dictionary learning algorithm;
3) decomposing and coding the load curve to be repaired based on the basis of the base vector dictionary matrix, and determining the load curve to be repaired to be composed of electronic modes;
4) and reconstructing the load curve according to the coding vector of the load curve to be repaired based on the base vector dictionary matrix, and performing filling repair on the data of the missing part of the power load, namely using the power utilization data at the corresponding moment in the reconstructed load curve as the repair value of the data of the missing part of the load.
2. The method for restoring the missing data of the power load based on the power utilization pattern decomposition reconstruction as claimed in claim 1, wherein: in the step 1), acquiring power load data of a power consumer from a power information acquisition system, dividing the load data into a complete load data set and a load data set to be repaired according to whether the daily load data is completely acquired, wherein the complete daily load acquisition sample set X of the userN×MComprises the following steps:
Figure FDA0003023665230000011
Figure FDA0003023665230000012
in the formula: n is daily load collection points; m is the number of load acquisition days;
Figure FDA0003023665230000013
the daily load curve of the j day is an N-dimensional characteristic vector;
Figure FDA0003023665230000021
the power vector at the ith acquisition moment of all load curves is obtained; for the load curve x to be restored ═ x1,x2,…,xN]T，
Figure FDA0003023665230000022
Figure FDA0003023665230000023
For the null value, i ∈ Ωnan＝{c1,c2,...,cL}，clNumber of the l-th missing point, ΩnanAnd acquiring a serial number set of the missing points, wherein L is the number of the missing points acquired by the load curve.
3. The method for restoring the missing data of the power load based on the power utilization pattern decomposition reconstruction as claimed in claim 1, wherein: in step 2), a K singular value decomposition dictionary learning algorithm is adopted to extract a base vector dictionary matrix representing the electronic mode for the user from the complete load data set, and the dictionary learning aims at learning a dictionary matrix B so that X isN×MIs approximately decomposed into:
X≈BZ
in the formula: b is belonged to RN×KIs a dictionary matrix, K is the size of the dictionary, and each column of B
Figure FDA0003023665230000024
Is a unitized atom vector, and is also an M-dimensional feature vector; z ═ Z1,z2,…,zM]∈RK×MIs a sparse coding matrix; when Z is to be satisfied as sparsely as possible while performing approximate decomposition, the expression of the approximate decomposition problem is:
Figure FDA0003023665230000025
in the formula: i | · | purple windFIs Frobenius norm ofThe square sum root of the matrix elements, representing the reconstruction error EBSize of (D), reconstruction error EBThe smaller the dictionary, the better the dictionary learning effect; i | · | purple wind0Is a 0 norm whose value is the number of non-zero entries in the matrix; t is0For sparsity constraint threshold, for constraining the coded vector ziThe equation can be solved by an orthogonal matching pursuit algorithm.
4. The method for restoring the missing data of the power load based on the power utilization pattern decomposition reconstruction as claimed in claim 1, wherein: in step 3), on the basis of dictionary learning by adopting a K singular value decomposition algorithm, decomposing and encoding a load curve to be repaired based on a base vector, determining that the load curve to be repaired is formed by an electronic mode, and encoding the load curve to be repaired by using a load data part successfully acquired by the load curve to be repaired and a dictionary matrix at a corresponding moment, wherein the encoding expression is as follows:
Figure FDA0003023665230000031
Figure FDA0003023665230000032
x/Ω＝x-{xi|i∈Ωnan}
Figure FDA0003023665230000033
in the formula: x is the number of/ΩSuccessfully collected load data in the load curve x, wherein the length of the load data is N-L;
Figure FDA0003023665230000034
is the ith dimension (row) feature vector in B; b is/ΩRemoving the dictionary matrix after collecting the corresponding characteristic row vectors at the missing moment for the complete dictionary matrix B,
Figure FDA0003023665230000035
zgto reconstruct the vector, is x/ΩBased on B/ΩAnd decomposing the obtained sparse coding vector, wherein the value of the sparse coding vector is formed by an electronic mode determined based on the successfully collected load data, and the sparse coding vector represents a possible power utilization mode of the load curve to be repaired.
5. The method for restoring the missing data of the power load based on the power utilization pattern decomposition reconstruction as claimed in claim 1, wherein: in step 4), based on the basis of the base vector dictionary matrix, reconstructing the load curve according to the coding vector of the load curve to be repaired, wherein the expression is as follows:
xg＝Bzg
in the formula xgFor reconstructing the load curve, from the reconstructed vector zgAnd reconstructing a complete dictionary matrix B; on the basis, filling and repairing the data of the missing part of the power load, namely, taking the power utilization data at the corresponding moment in the reconstructed load curve as a repairing value of the data of the missing part of the power load, wherein the expression is as follows:
Figure FDA0003023665230000036
in the formula
Figure FDA0003023665230000037
To reconstruct the load xgCorrespondingly acquiring load data at the missing moment.
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