CN113158135A - Noise-containing sag source positioning data missing value estimation method - Google Patents

Abstract

The invention belongs to the field of power quality analysis and control, and particularly relates to a method for estimating missing values of noise-containing sag source positioning data. It includes steps: preset data acquisition matrix S, initialize parameters τ, μ, set maximum iteration times Max; initialize iterative matrix; iterative solution; determine restored sag source data matrix and restored noise matrix; perform missing data estimation. Using the low-rank characteristic of measurement data based on substations, the missing data estimation problem is modeled as an L2,1 optimization problem, and the operator splitting method is used to solve it. Due to the use of analytical expressions, the solution speed is high, and the convergence is good. Missing data can be estimated with high accuracy, thereby improving the location accuracy of sag sources.

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 estimation method for a sag source positioning data missing value.

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 scheduling 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,…,v_NThe data acquisition matrix S, omega at the T moments is a binary subscript set for measuring normal nodes, dual variables tau, mu are initialized, and the maximum iteration times Max are 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＝S,Z⁰＝0,V^-1＝0,W^-10; wherein S is a measurement matrix; z is a noise matrix with the same size as S; v and W are respectively matrixes in the middle iteration step, and have no physical significance;

(3) the following calculations were performed:

FOR k＝0to MAX

W^k＝W^k-1+δ_ZP_Ω(S-X^k+1-Z^k-1)

wherein the description of the relevant variables is as follows:

δ_Xtaking the descending step length of X as 0.001;

δ_Ztaking the descending step length of Z as 0.001;

k is a natural number and is the iteration number;

V^kand W^kDenotes the result of the k-th iteration, V^k-1And W^k-1Denotes the result of the (k-1) th iteration, X^k+1Representing the result of the (k + 1) th iteration;

D_(τ,μ)(Z) for arbitrary τ, μ>0,Z∈R^N×T

‖L‖_F：‖L‖_FFor the F norm of the matrix L, the matrix L belongs to R according to the basic knowledge of the matrix^N×TF norm of

Note that the L matrix here is only an argument for describing the projection function, and has no practical physical meaning, L_ijIs the ith row and jth column position element of the matrix L;

‖L‖_*：‖L‖_*for the kernel norm of the matrix L, the matrix L belongs to R according to the basic knowledge of the matrix^N×TF norm of

Note that the L matrix here is only an argument for the projection function, and has no practical physical meaning, σ_iIs the ith singular value of the matrix L;

[P_Ω(L)]_ij: the function of projection of matrix L onto matrix S, note that the L matrix is only the argument for the projection function, and has no real objectTheory of significance, therefore P_Ω(S-X^k-Z^k) Is S-X^k-Z^kProjecting the result, P, onto the matrix S_Ω(S-X^k+1-Z^k-1) Is S-X^k+1-Z^k-1The result of the projection onto the matrix S.

[P_Ω(L)]_ijThe specific definition of (A) is as follows:

(4) according to the result of the kth solving in the step (3), the following calculation is carried out:

FOR i＝1to N

END

n is the number of the sag source monitoring buses; max { } is the maximum operator, (Z)^k+1)⁽ⁱ⁾Is Z^k+1The ith position element of (W)^k)⁽ⁱ⁾Is W^kThe ith position element of (1);

(5) determining a recovered sag source data matrix X_optAnd the recovered noise matrix Z_opt：

X_opt＝X^Max+1,Z_opt＝Z^Max+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 no defects are measured, then X_rec(i, j) S (i, j), otherwise the estimated value of the missing data is X_rec(i,j)＝X_opt(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,…,v_NN is a natural number different from 0, and the invention assumes that any substation has only one monitorThe method comprises the steps of measuring a bus, periodically collecting data of a sag source monitoring bus of the transformer substation, and setting a collection time interval of each round as a moment and setting total collection time as T moments; the total sampled data can be represented by a matrix S as:

wherein S is a measurement matrix, and S (i, j) represents a bus node v_iOriginal 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

Wherein [ N ] is]＝{1,…,N},[T_S]And Ω is a subscript index set of the metrology data in the metrology matrix {1, …, T }.

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:

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 structured noise, and further, the measurement matrix may be represented as:

P_Ω(S)＝P_Ω(X+Z)，

wherein Z is (Z (i, j))_N×TFor structuring the noise matrix, in matrix Z, if node v_iWhen error data is collected at time j, Z (i, j) ≠ 0, otherwise Z (i, j) ≠ 0.

The problem of the missing and completion of the measurement data containing noise is that a measurement matrix sent to a dispatching center on a transformer substation is utilized to reconstruct an original acquisition data matrix of the transformer substation, the low-rank characteristic of the acquisition data matrix of the transformer substation is utilized, the problem of data reconstruction can be modeled into a matrix completion problem, when the matrix completion problem is solved, in order to effectively smooth the structured noise, an L2 and 1 norm regularization item of a noise matrix Z is introduced into a standard matrix completion problem, so that the problem of the reconstruction of the measurement data containing error data is modeled into a structured noise matrix completion model based on L2 and 1 norm regularization, and the method comprises the following steps:

s.t.P_Ω(S)＝P_Ω(X+Z)

wherein, λ is penalty factor, and λ is 0.8. .

The voltage sag is one of the most serious power quality problems, accurate positioning of a voltage sag source is beneficial to timely finding and clearing disturbance sources and can provide basis for defining responsibilities of power supply and power utilization parties, but the positioning of the sag source depends on the cooperation of a plurality of transformer substations, and meanwhile due to the fact that the sag source is limited by characteristics such as PT (potential transformer), CT (current transformer), the deployment environment of a power communication network and the deployment environment of the transformer substations and the like, problems such as data loss, data errors and the like usually occur in the data collection process in the sag source monitoring process, and the data loss and errors bring huge challenges to the accuracy and the reliability of related applications. The method provided by the invention has the advantages that the low-rank characteristic based on the measured data of the transformer substation is utilized, the missing data estimation problem is modeled into an L2,1 optimization problem, an operator splitting method is utilized for solving, and due to the adoption of an analytic expression, the solving speed is high, the convergence is good, the missing data can be estimated with higher precision, and the positioning precision of the sag source is further improved.

Drawings

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,…,v_NThe data acquisition matrix S, omega at the T moments is a binary subscript set for measuring normal nodes, dual variables tau, mu are initialized, and the 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＝S,Z⁰＝0,V^-1＝0,W^-10; wherein S is a measurement matrix; z is a noise matrix with the same size as S; v and W are respectively matrixes in the middle iteration step, and have no physical significance;

(3) the following calculations were performed:

X^k+1＝D(_τ,μ)(V^k)

W^k＝W^k-1+δ_ZP_Ω(S-X^k+1-Z^k-1)

wherein the description of the relevant variables is as follows:

δ_Xtaking the descending step length of X as 0.001;

δ_Ztaking the descending step length of Z as 0.001;

k is a natural number and is the iteration number;

V^kand W^kDenotes the result of the k-th iteration, V^k-1And W^k-1The results of the (k-1) th iteration are shown. X^k+1Representing the result of the (k + 1) th iteration;

D_(τ,μ)(Z) for arbitrary τ, μ>0,Z∈R^N×T，

‖L‖_F：‖L‖_FFor the F norm of the matrix L, the matrix L belongs to R according to the basic knowledge of the matrix^N×TF norm of

Note that the L matrix here is only an argument for describing the projection function, and has no practical physical meaning, L_ijIs the ith row and jth column position element of the matrix L;

‖L‖_*：‖L‖_*for the kernel norm of the matrix L, the matrix L belongs to R according to the basic knowledge of the matrix^N×TF norm of

Note that the L matrix here is only an argument for the projection function, and has no practical physical meaning, σ_iIs the ith singular value of the matrix L;

[P_Ω(L)]_ijthe specific definition of (A) is as follows:

(4) according to the result of the kth solving in the step (3), the following calculation is carried out:

FORi＝1to N

END

n is the number of the sag source monitoring buses; max { } is the maximum operator, (Z)^k+1)⁽ⁱ⁾Is Z^k+1The ith position element of (W)^k)⁽ⁱ⁾Is W^kThe ith position element of (1);

(5) determining a recovered sag source data matrix X_optAnd the recovered noise matrix Z_opt：

X_opt＝X^Max+1,Z_opt＝Z^Max+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 no defects are measured, then X_rec(i, j) S (i, j), otherwise the estimated value of the missing data is X_rec(i,j)＝X_opt(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,…,v_NN 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 a matrix S as:

wherein S is a measurement matrix, and S (i, j) represents a bus node v_iMeasurement data of raw voltage, current, active power and reactive power corresponding to time jWherein 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 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

Wherein [ N ] is]＝{1,…,N},[T_S]＝{1,…,T}

Due to data errors, there may be two cases when the dispatching center acquires the measurement data, where the substation acquisition is original data X (i, j) and error data F (i, j), and the measurement data S (i, j) may be represented as:

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 fault buses, and a proportion occupied by the data fault buses is referred to as a bus fault rate, in practical applications, some buses are easy to become data fault buses, data rows corresponding to the nodes in the measurement matrix contain error elements, for error problems of such row elements, it can be considered that the measurement matrix is polluted by structured noise, and further, the measurement matrix can be represented as:

P_Ω(S)＝P_Ω(X+Z)，

wherein Z is (Z (i, j))_N×TFor structuring the noise matrix, in matrix Z, if node v_iWhen error data is collected at time j, Z (i, j) ≠ 0, otherwise Z (i, j) ≠ 0.

The problem of the missing and completion of the measurement data containing noise is that a measurement matrix sent to a dispatching center on a transformer substation is utilized to reconstruct an original acquisition data matrix of the transformer substation, the low-rank characteristic of the acquisition data matrix of the transformer substation is utilized, the problem of data reconstruction can be modeled into a matrix completion problem, when the matrix completion problem is solved, in order to effectively smooth the structured noise, an L2 and 1 norm regularization item of a noise matrix Z is introduced into a standard matrix completion problem, so that the problem of the reconstruction of the measurement data containing error data is modeled into a structured noise matrix completion model based on L2 and 1 norm regularization, and the method comprises the following steps:

s.t.P_Ω(S)＝P_Ω(X+Z)

wherein, λ is penalty factor, and λ is 0.8.

To solve the optimization problem of the above formula (1), the following definitions are first given:

suppose that the matrix X ∈ R^N×TIs decomposed into X ═ U ∑ V^τ；

Wherein Σ ═ diag { σ }_i|1≤i≤min(n₁,n₂)}，

And is

Then there is a definition as follows,

(1) the matrix X belongs to R^N×TF norm of

(2) The matrix X belongs to R^N×TNuclear norm of

(3) The matrix X belongs to R^N×TL2,1 norm

(4) For any X ∈ R^N×TThen its corresponding singular value threshold operator is

D_γ(X)＝US_γ(Σ)V^T；

Wherein S_γ(Σ)＝diag{max(0,σ_i-γ)|i＝1,2,…,min(N,T)}。

Then, the above equation (1) is relaxed as an unconstrained optimization problem:

then, equation (2) is transformed to solve 2 sub-problems, namely:

subproblem 1

Wherein

Is a sub-differential

Is measured in the direction of the first sub-gradient,<·,·>representing the inner product operation of the matrix.

The sub-problem 2 is that the sub-problem,

wherein

Is a sub-differential

A sub-gradient of (a).

Order to

Iteratively generating the sequence according to equation (3) converges to the unique solution, i.e.

And should be provided with

Let V^k＝V^k-1+δ_XP_Ω(S-X^k-Z^k) Then equation (3) can be simplified as:

according to the soft threshold correlation property, the method can know the correlation value of any tau and mu>0,Z∈R^N×T，

Then for equation (4):

thus, the solution can be iteratively solved as follows (5)

On the other hand:

in the formula:

taking the parameter delta_Z＝1；

Let W^k＝W^k-1+δ_ZP_Ω(S-X^k+1-Z^k) And then:

from L2,1 norm corresponding to soft threshold correlation property, it can be known that for any tau, mu>0,W∈R^N×T，

There is a global minimum

Wherein X⁽ⁱ⁾Represents the ith row, | | of matrix X₂Representing the vector 2 norm, from this property, Z is updated as follows:

the iterative solution method for sub-problem 2 is therefore as follows:

then, after parameters such as the maximum iteration times of the algorithm and the like are determined, the optimal solution of the estimation of the sag source missing data, namely the recovered sag source data matrix X, can be obtained_optAnd the recovered noise matrix Z_optUsing a matrix X_optAnd Z_optTransformer substation acquisition matrix X can be rebuilt_recThe specific method comprises the following two steps:

(1) with recovered data matrix X_optCorresponding element X in (1)_opt(i, j) to fill in missing elements in the measurement matrix', i.e. to reconstruct the substation acquisition matrix X_recSatisfies the following conditions:

(2) by the recovered noise matrix Z_optIdentification of data-failed bus at Z_optThe 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 used_recRecovery data matrix X for rows containing erroneous data_optThe corresponding row replacement in (1), namely:

in the formula

And

respectively represent matrix X_recAnd X_optThe 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,…,v_NThe data acquisition matrix at T moments (the specific definition of which is shown in claim 4) is obtained, wherein Ω is a binary subscript set for measuring normal nodes, dual variables τ and μ are initialized, and the 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) initialChange iteration matrix X⁰＝S,Z⁰＝0,V^-1＝0,W^-10; wherein S is a measurement matrix (the specific definition is shown in claim 3); z is a noise matrix with the same size as S; v and W are matrixes in the step of calculating intermediate iteration respectively, and have no physical significance;

(3) the following calculations were performed:

FOR k＝0 to MAX

wherein the description of the relevant variables is as follows:

δ_Xtaking the descending step length of X as 0.001;

δ_Ztaking the descending step length of Z as 0.001;

k is a natural number and is the iteration number;

V^kand W^kDenotes the result of the k-th iteration, V^k-1And W^k-1The results of the (k-1) th iteration are shown. X^k+1Representing the result of the (k + 1) th iteration;

D_(τ,μ)(Z) for arbitrary τ, μ>0,Z∈R^N×T，

‖L‖_F：‖L‖_FFor the F norm of the matrix L, the matrix L belongs to R according to the basic knowledge of the matrix^N×TF norm of

Note that the L matrix here is only an argument for describing the projection function, and has no practical physical meaning, L_ijIs the ith row and jth column position element of the matrix L;

‖L‖_*：‖L‖_*for the kernel norm of the matrix L, the matrix L belongs to R according to the basic knowledge of the matrix^N×TF norm of

Note that the L matrix here is only an argument for describing the projection function, and has no practical physical meaning, σ_iIs the ith singular value of the matrix L;

[P_Ω(L)]_ij: the function of projection of matrix L to matrix S, please note that L matrix here is only to explain the independent variable of projection function, and has no actual physical meaning, so P_Ω(S-X^k-Z^k) Is S-X^k-Z^kProjecting the result, P, onto the matrix S_Ω(S-X^k+1-Z^k-1) Is S-X^{k +1}-Z^k-1The result of the projection onto the matrix S.

[P_Ω(L)]_ijThe specific definition of (A) is as follows:

(4) according to the result of the kth solving in the step (3), the following calculation is carried out:

END

n is the number of the sag source monitoring buses; max { } is the maximum operator, (Z)^k+1)⁽ⁱ⁾Is Z^k+1Element of row i, (W)^k)⁽ⁱ⁾Is W^kThe ith position element of (1);

(5) determining a recovered sag source data matrix X_optAnd the recovered noise matrix Z_opt：

X_opt＝X^Max+1,Z_opt＝Z^Max+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, X_rec(i, j) S (i, j), otherwise the methodEstimate of missing data is X_rec(i,j)＝X_opt(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 S in step (2), i.e. the total sampled data matrix, is represented by:

s (i, j) represents bus node v_iRaw 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

Wherein [ N ] is]＝{1,…,N},[T_S]And Ω is a set of index indices of the measured data in the measurement matrix, i.e. the binary index set of the normal measurement nodes.

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:

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:

P_Ω(S)＝P_Ω(X+Z)，

wherein Z is (Z (i, j))_N×TAs a noise matrix, in matrix Z, if node v_iIf error data is collected at time j, Z (i, j) ≠ 0, otherwise Z (i, j) ≠ 0.

7. The method for estimating the missing value of the noisy sag source location data according to claim 6, wherein a data reconstruction problem is modeled as a matrix completion problem by using a low rank characteristic of a data matrix collected by a substation; namely, the L2, 1-norm regularization term of the noise matrix Z is introduced into the standard matrix completion problem, so as to model the measured data reconstruction problem containing error data into a structured noise matrix completion model based on L2, 1-norm regularization, that is, the following are provided:

wherein, λ is penalty factor, and λ is 0.8.

8. The method for estimating missing values of data of temporally-degraded noisy source-located data according to claim 7, wherein based on the solving method of sub-problem 1 and sub-problem 2, after determining the parameter of maximum iteration number of the algorithm, the optimal solution of the estimation of the missing data of the temporally-degraded source, namely the recovered temporally-degraded source, is obtainedData matrix X_optAnd the recovered noise matrix Z_optUsing matrix X_optAnd Z_optReconstruction of acquisition matrix X of transformer substation_rec。

9. The method of claim 8, wherein a matrix X is used to estimate missing values of noisy sag source-location data_optAnd Z_optReconstruction of acquisition matrix X of transformer substation_recThe specific method comprises the following two steps:

(9-1) temporally dropping the source data matrix X with recovery_optCorresponding element X in (1)_opt(i, j) to fill in missing elements in the measurement matrix, i.e. to reconstruct the substation acquisition matrix X_recThe requirements are met,

(9-2) noise matrix Z by recovery_optIdentification of data-failed bus at Z_optThe 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 reconstructed_recRecovery data matrix X for rows containing erroneous data_optThe corresponding row in (a) is replaced, i.e.,

in the formula

And

respectively represent matrix X_recAnd X_optThe ith row of data.

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