CN111506874A - Noise-containing sag source positioning data missing value estimation method - Google Patents

Noise-containing sag source positioning data missing value estimation method Download PDF

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CN111506874A
CN111506874A CN202010297529.XA CN202010297529A CN111506874A CN 111506874 A CN111506874 A CN 111506874A CN 202010297529 A CN202010297529 A CN 202010297529A CN 111506874 A CN111506874 A CN 111506874A
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万新强
王洪寅
王秀茹
赖勇
张科
邱冬
韩少华
万苏磊
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State Grid Jiangsu Electric Power Co ltd Suqian Power Supply Branch
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State Grid Corp of China SGCC
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Abstract

The invention belongs to the field of power quality analysis and control, and particularly relates to a noise-containing sag source positioning data missing value estimation method. The method comprises the following steps: presetting a data acquisition matrix PΩThe method comprises the steps of (S), initializing parameters tau and mu, setting maximum iteration times Max, initializing an iteration matrix, solving a subproblem 1, solving a subproblem 2, determining a recovered sag source data matrix and recovered two-side noise matrices, carrying out missing data estimation, modeling a missing data estimation problem into an L2, 1 optimization problem by using the low-rank characteristic based on measured data of a transformer substation, and solving by using an operator splitting method.

Description

Noise-containing sag source positioning data missing value estimation method
Technical Field
The invention belongs to the field of power quality analysis and control, and particularly relates to a noise-containing sag source positioning data missing value estimation method.
Background
With the development of power electronic technology and computer technology, more and more sensitive loads are connected into a power system, and further higher requirements are put forward on the power quality of a power grid. The voltage sag is one of the most serious power quality problems, and the accurate positioning of the voltage sag source is not only beneficial to timely finding and eliminating disturbance sources, but also can provide a basis for defining the responsibilities of power supply and power utilization parties.
The localization of sag sources relies on the coordination of multiple substations, which are based on voltage/current/active/reactive measurement data collected by the multiple substations. However, due to the characteristics of PT, CT, etc., and the constraints of factors such as the deployment environments of the power communication network and the substation, in the sag source monitoring process, problems such as data loss and data errors usually occur in the data collection process, and the data loss and errors bring huge challenges to the accuracy and reliability of related applications, so that it is very important to estimate the original data collected by the substation by using the collected incomplete data set containing the missing elements in the dispatching center.
Disclosure of Invention
The invention aims to provide a method for estimating the missing value of the data of the sag source containing noise, aiming at the defects.
The invention is realized by adopting the following technical scheme:
a method for estimating a missing value of sag source positioning data containing noise comprises the following steps,
(1) n sag source monitoring buses v1,v2,…,vNData acquisition matrix P of T momentsΩ(S), omega is a binary subscript set for measuring normal nodes, parameters tau and mu are initialized, and maximum iteration times Max are set; n is a natural number different from 0, and the data acquisition matrix is voltage, current, active power and reactive power measurement data; initializing a dual variable tau to 0.2 and a variable mu to 1;
(2) initializing an iteration matrix X0＝0,Z0＝0,V-1＝0,W-10; wherein, X is a measuring matrix and is a row-form structured noise matrix; z is a row-wise structured noise matrix; v and W are matrixes in the step of calculating intermediate iteration respectively, and have no physical significance;
(3) solving the subproblem 1, the solving method is as follows:
FOR k＝0to Max
Yk＝Vk-1+XPΩ(S-Xk-Zk)
Xk+1＝Dπ(Vk)
Wk＝Wk-1+ZPΩ(S-Xk+1-Zk)
wherein
Figure BDA0002451250240000021
，
Figure BDA0002451250240000022
k is a natural number;
(4) and according to the result of solving the k-th sub-problem 1, then solving a sub-problem 2, wherein the solving method comprises the following steps:
Figure BDA0002451250240000031
n is the number of the sag source monitoring buses; max is the maximum operator.
(5) Determining a recovered sag source data matrix XoptAnd the recovered two-sided noise matrix Zopt：
Xopt＝XMax+1,Zopt＝ZMax+1；
(6) And (3) missing data estimation:
acquiring a moment j of each sag source monitoring node i, wherein i is 1-N, and j is 1-T; if the measurement is not missing, Xrec(i, j) S (i, j), otherwise the estimated value of the missing data is Xrec(i,j)＝Xopt(i,j)。
The method steps and internal variables are described in detail below.
N sag source monitoring buses v are arranged in a certain power grid monitoring area1,v2,…,vNN is a natural number different from 0, the invention assumes that any transformer substation only has one monitoring bus, periodically collects the data of the transformer substation sag source monitoring bus, and sets the collection time interval of each round as a moment and the total collection time as T moments; the total sampled data can be represented by matrix X as:
Figure BDA0002451250240000041
；
wherein X is a measurement matrix, and X (i, j) represents a bus node viOriginal voltage, current, active power and reactive power measurement data corresponding to a time j, wherein i is 1 to N, and j is 1 to T; however, due to data loss in the measurement acquisition and transmission processes and noise, the power grid dispatching center obtains an incomplete matrix S with a lot of elements lost, and the proportion of the measurement data in the total data volume is called data measurement rate in the invention.
Definition of
Figure BDA0002451250240000044
Wherein [ N ] is]Where, T is {1, …, N }, and Ω is a subscript index set of the measured data in the measurement matrix (i.e. the aforementioned binary subscript set of the normal measurement nodes), PΩ(. cndot.) is an orthographic projection operator, which means that S (i, j) is a measure element when (i, j) ∈ Ω, i.e. there are:
Figure BDA0002451250240000042
due to data errors, there may be two cases when the scheduling center acquires the measured data, that is, the original data X (i, j) and the error data F (i, j) acquired by the substation, where the measured data S (i, j) may be represented as:
Figure BDA0002451250240000043
；
the error data F (i, j) can be expressed as the superposition of the original collected data of the substation and the noise value, namely:
F(i,j)＝X(i,j)+Z(i,j)；
in the formula, Z (i, j) is a noise value, a bus node of the collected error data is referred to as a data fault bus, and the proportion of the data fault bus is referred to as a bus fault rate. In practical applications, some buses are prone to become data failure buses, and data rows corresponding to these nodes in the measurement matrix contain error elements, and for the error problem of such row elements, the measurement matrix may be considered to be contaminated by row-form structured noise, and further may be represented as:
PΩ(S)＝PΩ(X+Z)，
wherein Z is (Z (i, j))N×TIn the form of a structured noise matrix in the form of rows, in matrix Z, if node viIf an error is collected at time j, Z (i, j) ≠ 0, otherwise Z (i, j) ≠ 0.
The problem of the missing and completion of the noisy measured data is that a measured matrix sent to a dispatching center on a transformer substation is used for reconstructing an original collected data matrix of the transformer substation, the low-rank characteristic of the collected data matrix of the transformer substation is used for modeling the data reconstruction problem into a matrix completion problem, and when the matrix completion problem is solved, in order to effectively smooth the structured noise, L2 and 1 norm regularization items of a noise matrix Z are introduced into a standard matrix completion problem, so that the measured data reconstruction problem containing wrong data is modeled into a structured noise matrix completion model based on L2 and 1 norm regularization, namely:
Figure BDA0002451250240000051
the method utilizes the low-rank characteristic based on the measured data of the transformer substations to model the missing data estimation problem into L2, 1 optimization problem, and utilizes an operator splitting method to solve the problem, and has the advantages of high solving speed and good convergence due to the adoption of an analytic expression, and can estimate the missing data with higher precision, thereby improving the positioning precision of the sag source.
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The invention will be further explained with reference to the drawings, in which:
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
It should be noted that the variable appearing in the present invention has the same meaning before and after, and will not change due to the appearance in different formulas.
Referring to fig. 1, the method for estimating missing values of data of sag source locations containing noise according to the present invention includes the following steps:
(1) n sag source monitoring buses v1,v2,…,vNData acquisition matrix P of T momentsΩ(S), omega is a binary subscript set for measuring normal nodes, parameters tau and mu are initialized, and maximum iteration times Max are set; n is a natural number different from 0, and the data acquisition matrix is voltage/current/active power/reactive power measurement data; initializing a dual variable tau, mu, wherein in the embodiment, tau is 0.2, and mu is 1;
(2) initializing an iteration matrix X0＝0,Z0＝0,V-1＝0,W-10; wherein, X is a measuring matrix and is a row-form structured noise matrix; z is a row-wise structured noise matrix;
(3) solving the subproblem 1, the solving method is as follows:
FOR k＝0to Max
Yk＝Vk-1+XPΩ(S-Xk-Zk)
Xk+1＝Dπ(Vk)
Wk＝Wk-1+ZPΩ(S-Xk+1-Zk)
wherein
Figure BDA0002451250240000071
，
Figure BDA0002451250240000072
k is a natural number;
(4) and according to the result of solving the k-th sub-problem 1, then solving a sub-problem 2, wherein the solving method comprises the following steps:
Figure BDA0002451250240000073
n is the number of the sag source monitoring buses; max is the maximum operator.
(5) Determining a recovered sag source data matrix XoptAnd the recovered two-sided noise matrix Zopt：
Xopt＝XMax+1,Zopt＝ZMax+1；
(6) And (3) missing data estimation:
acquiring a moment j of each sag source monitoring node i, wherein i is 1-N, and j is 1-T; if the measurement is not missing, Xrec(i, j) S (i, j), otherwise the estimated value of the missing data is Xrec(i,j)＝Xopt(i,j)。
The concrete solving method of the optimization problem of the present invention will be described in detail by examples.
N sag source monitoring buses v are arranged in a certain power grid monitoring area1,v2,…,vNN is a natural number different from 0, the invention assumes that any transformer substation only has one monitoring bus, periodically collects the data of the transformer substation sag source monitoring bus, and sets the collection time interval of each round as a moment and the total collection time as T moments; the total sampled data can be represented by matrix X as:
Figure BDA0002451250240000081
；
wherein X is a measurement matrix, and X (i, j) represents a bus node viMeasuring data of original voltage, current, active power and reactive power corresponding to a moment j, wherein i is 1-N, and j is 1-T; however, due to data loss during measurement acquisition and transmission and due to noise, power grid schedulingThe incomplete matrix S with a plurality of lost elements is obtained at the center, and the proportion of the measured data in the total data volume is called data measurement rate in the invention.
Definition of
Figure BDA0002451250240000091
Wherein [ N ] is]Where, T is {1, …, N }, and Ω is a subscript index set of the measured data in the measurement matrix (i.e. the aforementioned binary subscript set of the normal measurement nodes), PΩ(. cndot.) is an orthographic projection operator, which means that S (i, j) is a measure element when (i, j) ∈ Ω, i.e. there are:
Figure BDA0002451250240000092
due to data errors, there may be two situations when the dispatching center acquires the measurement data, where the substation acquires the original data X (i, j) and the error data F (i, j), and the measurement data S (i, j) may be represented as:
Figure BDA0002451250240000093
；
the error data F (i, j) may represent the superposition of the original collected data and the noise value for the substation, i.e.:
F(i,j)＝X(i,j)+Z(i,j)；
in the formula, Z (i, j) is a noise value, bus nodes of the collected error data are referred to as data failure buses, and a proportion occupied by the data failure buses is referred to as a bus failure rate, in practical applications, some buses are easy to become data failure buses, and data rows corresponding to the nodes in the measurement matrix contain error elements, and regarding error problems of the row elements, the measurement matrix can be considered to be polluted by row-form structured noise, and further, the measurement matrix can be represented as:
PΩ(S)＝PΩ(X+Z)，
wherein Z is (Z (i, j))N×TIn the form of a structured noise matrix in the form of rows, in matrix Z, if node viIn the case where error data is collected at time j, Z (i, j) ≠ 0Otherwise, Z (i, j) is 0.
The problem of the missing and completion of the noisy measured data is that a measured matrix sent to a dispatching center on a transformer substation is used for reconstructing an original collected data matrix of the transformer substation, the low-rank characteristic of the collected data matrix of the transformer substation is used for modeling the data reconstruction problem into a matrix completion problem, and when the matrix completion problem is solved, in order to effectively smooth the structured noise, L2 and 1 norm regularization items of a noise matrix Z are introduced into a standard matrix completion problem, so that the measured data reconstruction problem containing wrong data is modeled into a structured noise matrix completion model based on L2 and 1 norm regularization, namely:
Figure BDA0002451250240000101
to solve the optimization problem of the above formula (1), the following definitions are first given:
hypothesis matrix
Figure BDA0002451250240000103
Is decomposed into X ═ U ∑ Vτ；
Wherein Σ ═ diag { σ }i|1≤i≤min(n1,n2)}，
And is
Figure BDA0002451250240000104
(ii) a Then there is a definition as follows,
(1) matrix array
Figure BDA0002451250240000105
F norm of
Figure BDA0002451250240000102
(2) Matrix array
Figure BDA0002451250240000117
Nuclear norm of
Figure BDA0002451250240000111
(3) Matrix array
Figure BDA0002451250240000118
L2, 1 norm of
Figure BDA0002451250240000112
(4) For any purpose
Figure BDA0002451250240000119
If the corresponding singular value threshold operator is Dγ(X)＝USγ(Σ)VT；
Wherein Sγ(Σ)＝diag{max(0,σi-γ)|i＝1,2,…,min(n1,n2)}。
Then, the above equation (1) is relaxed as an unconstrained optimization problem:
Figure BDA0002451250240000113
then, equation (2) is transformed to solve 2 sub-problems, namely:
subproblem 1
Figure BDA0002451250240000114
，
Wherein
Figure BDA0002451250240000115
Is a sub-differential
Figure BDA0002451250240000116
Is measured in the direction of the first sub-gradient,<·,·>representing the inner product operation of the matrix.
Subproblem 2
Figure BDA0002451250240000121
，
Wherein
Figure BDA0002451250240000122
Is a sub-differential
Figure BDA0002451250240000123
A sub-gradient of (a).
Then, solving the subproblem 1;
in sub-problem 1, let
Figure BDA0002451250240000124
Iteratively generating the sequence according to equation (3) converges to the unique solution, i.e.
Figure BDA0002451250240000125
And should be provided with
Figure BDA0002451250240000126
Let Vk＝Vk-1+XPΩ(S-Xk-Zk) Then equation (3) can be simplified as:
Figure BDA0002451250240000127
from the soft threshold correlation property, it can be seen that for any τ, μ > 0,
Figure BDA0002451250240000128
Figure BDA0002451250240000129
then, for formula (4):
Figure BDA0002451250240000131
therefore, sub-problem 1 can be solved iteratively as follows (5)
Figure BDA0002451250240000132
Then, solving a subproblem 2;
similar to the solving process of sub-problem 1, we can obtain:
Figure BDA0002451250240000133
，
in the formula:
Figure BDA0002451250240000134
taking parametersZ＝1；
Let Wk＝Wk-1+ZPΩ(S-Xk+1-Zk) And then:
Figure BDA0002451250240000135
from L2, the soft threshold correlation property corresponding to 1 norm can be known for any arbitrary
Figure BDA0002451250240000136
There is a global minimum point
Figure BDA0002451250240000137
Wherein X is(i)Represents the ith row, | | of matrix X2Representing the vector 2 norm, from this property, we know that Z in sub-problem 2 is updated as follows:
Figure BDA0002451250240000141
the iterative solution method for sub-problem 2 is therefore as follows:
Figure BDA0002451250240000142
then, based on the solving method of the subproblems 1 and 2, after parameters such as the maximum iteration times of the algorithm are determined, the optimal solution of the estimation of the sag source missing data, namely the recovered sag source data matrix X, can be obtainedoptAnd the recovered two-sided noise matrix ZoptUsing matrix XoptAnd ZoptTransformer substation acquisition matrix X can be rebuiltrecThe specific method comprises the following two steps:
(1) with recovered data matrix XoptCorresponding element X in (1)opt(i, j) to fill in missing elements in the measurement matrix', i.e. to reconstruct the substation acquisition matrix XrecSatisfies the following conditions:
Figure BDA0002451250240000143
(2) by the recovered noise matrix ZoptIdentification of data-failed bus at ZoptThe buses corresponding to the rows containing the non-zero elements are fault buses, the buses corresponding to the rows with all the elements of 0 are normal sensor nodes, and after the bus faults are identified, the reconstructed substation acquisition matrix X can be usedrecRecovery data matrix X for rows containing erroneous dataoptThe corresponding row replacement in (1), namely:
Figure BDA0002451250240000151
in the formula
Figure BDA0002451250240000152
And
Figure BDA0002451250240000153
respectively represent matrix XrecAnd XoptThe ith row of data.
The embodiments are only for illustrating the technical idea of the present invention, and the technical idea of the present invention is not limited thereto, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the scope of the present invention.

Claims (9)

1. A method for estimating a missing value of sag source positioning data containing noise is characterized by comprising the following steps:
(1) n sag source monitoring buses v1,v2,…,vNOf T timesData acquisition matrix PΩ(S), omega is a binary subscript set for measuring normal nodes, a dual variable tau, mu is initialized, and a maximum iteration number Max is set; wherein N is a natural number different from 0, and the data acquisition matrix is voltage, current, active power and reactive power measurement data;
(2) initializing an iteration matrix X0＝0,Z0＝0,V-1＝0,W-10; wherein, X is a measuring matrix and is a row-form structured noise matrix; z is a row-wise structured noise matrix; v and W are matrixes in the step of calculating intermediate iteration respectively, and have no physical significance;
(3) solving the subproblem 1, the solving method is as follows:
Figure FDA0002451250230000011
wherein
Figure FDA0002451250230000012
，
Figure FDA0002451250230000013
k is a natural number;
(4) and according to the result of solving the k-th sub-problem 1, then solving a sub-problem 2, wherein the solving method comprises the following steps:
FOR i＝1to N
Figure FDA0002451250230000021
END FOR
n is the number of the sag source monitoring buses; max is the maximum operator.
(5) Determining a recovered sag source data matrix XoptAnd the recovered two-sided noise matrix Zopt：
Xopt＝XMax+1,Zopt＝ZMax+1；
(6) And (3) missing data estimation:
acquiring a moment j of each sag source monitoring node i, wherein i is 1-N, and j is 1-T; if the measurement is not missing, Xrec(i, j) S (i, j), otherwise the estimated value of the missing data is Xrec(i,j)＝Xopt(i,j)。
2. The method for estimating missing values of noisy dip-in source location data according to claim 1, wherein in step (1), a dual variable τ, μ, is initialized, and the value τ is 0.2 and μ is 1.
3. The method of claim 1, wherein the measurement matrix X in step (2), i.e. the total sampled data matrix, is represented by:
Figure FDA0002451250230000031
；
x (i, j) represents bus node viRaw voltage, current, active power and reactive power measurement data corresponding to time j, where i is 1-N and j is 1-T.
4. The method according to claim 3, wherein the step (1) comprises
Figure FDA0002451250230000034
Wherein [ N ] is]Where, T is {1, …, N }, and Ω is a set of index indices of the measured data in the measurement matrix, i.e. the aforementioned binary index set of normal nodes, PΩ(. cndot.) is an orthographic projection operator, which means that S (i, j) is a measure element when (i, j) ∈ Ω, i.e. there are:
Figure FDA0002451250230000032
5. the method for estimating the missing value of the noisy sag source positioning data according to claim 4, wherein due to data errors, the dispatching center obtains the measured data in two cases, namely original data X (i, j) and error data F (i, j) collected by the substation, so that the measured data S (i, j) is represented as:
Figure FDA0002451250230000033
the error data F (i, j) is expressed as superposition of the original collected data of the transformer substation and a noise value, namely:
F(i,j)＝X(i,j)+Z(i,j)；
wherein Z (i, j) is a noise value.
6. The method of claim 5, wherein the bus node of the collected error data is called a data-faulty bus, and the ratio of the data-faulty bus is called a bus fault rate, and the measurement matrix is further represented as:
PΩ(S)＝PΩ(X+Z)，
wherein Z is (Z (i, j))N×TIn the form of a structured noise matrix in the form of rows, in matrix Z, if node viIf an error is collected at time j, Z (i, j) ≠ 0, otherwise Z (i, j) ≠ 0.
7. The method for estimating the missing value of the sag source positioning data containing the noise according to claim 6, wherein the data reconstruction problem is modeled as a matrix completion problem by using the low-rank characteristic of a data matrix collected by a transformer substation, namely, an L2, 1 norm regularization item of a noise matrix Z is introduced into a standard matrix completion problem so as to model the measured data reconstruction problem containing the error data as a structural noise matrix completion model based on L2, 1 norm regularization, namely:
Figure FDA0002451250230000041
8. the method according to claim 7, wherein the optimal solution of the estimation of the data missing from the temporally-degraded source, i.e. the recovered data matrix X of the temporally-degraded source, is obtained after determining the parameter of the maximum iteration number of the algorithm based on the solving method of the sub-problem 1 and the sub-problem 2optAnd the recovered two-sided noise matrix ZoptUsing matrix XoptAnd ZoptReconstruction of acquisition matrix X of transformer substationrec。
9. The method of claim 8, wherein a matrix X is used to estimate missing values of noisy sag source-location dataoptAnd ZoptReconstruction of acquisition matrix X of transformer substationrecThe specific method comprises the following two steps:
(6-1) with the recovered data matrix XoptCorresponding element X in (1)opt(i, j) to fill in missing elements in the measurement matrix, i.e. to reconstruct the substation acquisition matrix XrecThe requirements are met,
Figure FDA0002451250230000051
(6-2) noise matrix Z by recoveryoptIdentification of data-failed bus at ZoptThe bus corresponding to the row containing the non-zero element is a fault bus, the buses corresponding to the rows with all the elements of 0 are normal sensor nodes, and after the bus fault is identified, the substation acquisition matrix X is reconstructedrecRecovery data matrix X for rows containing erroneous dataoptThe corresponding row in (a) is replaced, i.e.,
Figure FDA0002451250230000052
in the formula
Figure FDA0002451250230000053
And
Figure FDA0002451250230000054
respectively represent matrix XrecAnd XoptThe ith row of data.
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