CN111506874A - 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. Including steps: preset data acquisition matrix P _Ω (S), initialize parameters τ, μ, set maximum iteration times Max; initialize iteration matrix; solve sub-problem 1; solve sub-problem 2; determine the recovered sag source data matrix and recovery The two-sided noise matrix of ; performs 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

A method for estimating missing values in noisy sag source localization data

technical field

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.

Background technique

With the development of power electronic technology and computer technology, more and more sensitive loads are connected to the power system, which puts forward higher requirements on the power quality of the power grid. Voltage sag is one of the most serious power quality problems. The accurate location of the voltage sag source is not only conducive to timely discovery and removal of the disturbance source, but also provides a basis for defining the responsibilities of both the power supply and the consumer.

The location of the sag source depends on the coordination of multiple substations, which is based on the voltage/current/active/reactive power measurement data collected by multiple substations. However, due to the characteristics of PT, CT and other factors, as well as the power communication network and substation deployment environment and other factors, in the process of sag source monitoring, data loss and data errors usually occur during the data collection process. The accuracy and reliability of related applications bring great challenges. Therefore, it is of great significance to estimate the raw data collected by substations using incomplete data sets with missing elements collected in dispatch centers.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a method for estimating missing values of sag source location data containing noise in view of the above shortcomings, and the method is used to estimate the missing data so as to accurately reflect the location of the sag source.

The present invention adopts following technical scheme to realize:

A method for estimating missing values of noise-containing sag source positioning data, comprising the following steps:

(1) Suppose N sag source monitoring buses v ₁ , v ₂ ,...,v _N data acquisition matrix P _Ω (S) at T times, where Ω is the binary index set for measuring normal nodes, and the initialization parameters τ, μ, set the maximum number of iterations Max; N is a natural number other than 0, the data acquisition matrix is the measurement data of voltage, current, active power and reactive power; initialization dual variables τ=0.2, μ=1;

(2) Initialize the iterative matrix X ⁰ =0, Z ⁰ =0, V ^-1 =0, W ^-1 =0; where X is the measurement matrix, which is the row-form structured noise matrix; Z is the row-form Structured noise matrix; V and W are the matrices in the intermediate iteration steps of the calculation, respectively, and have no physical meaning;

(3) To solve sub-problem 1, the solution method is as follows:

FOR k=0toMax

Y ^k =V ^k-1 +δ _X P _Ω (SX ^k -Z ^k )

X ^k+1 =D _πδ (V ^k )

W ^k =W ^k-1 +δ _Z P _Ω (SX ^k+1 -Z ^k )

in

，

,

k is a natural number;

(4) According to the result of solving the kth sub-problem 1, then solve the sub-problem 2, and the solution method is as follows:

Among them, N is the number of sag source monitoring buses; max{} is the maximum operator.

(5) Determine the recovered dip source data matrix X _opt and the recovered two-side noise matrix Z _opt :

X _opt =X ^Max+1 , Z _opt =Z ^Max+1 ;

(6) Perform missing data estimation:

Monitor each acquisition time j of node i for each sag source, where i=1～N, j=1～T; if the measurement is not missing, then X _rec (i,j)=S(i,j ), otherwise the estimated value of the missing data is _Xrec (i,j)= _Xopt (i,j).

The method steps and the internal variables are described in detail below.

Suppose that N sag source monitoring buses v ₁ , v ₂ ,...,v _N are deployed in a certain power grid monitoring area, and N is a natural number that is not 0. In the present invention, it is assumed that any substation has only one monitoring bus, and the substation is periodically collected. For the sag source monitoring bus data, the collection time interval of each round is called a moment, and the total collection time is set as T moments; then the total sampling data can be expressed by the matrix X as:

；

;

where X is the measurement matrix, X(i,j) represents the original voltage, current, active power and reactive power measurement data of the bus node v _i corresponding to time j, where i=1～N, j=1～ However, due to data loss in the process of measurement acquisition and transmission, and due to the existence of noise, the grid dispatching center obtains an incomplete matrix S with many missing elements. In the present invention, the measurement data accounts for a The ratio is called the data volume rate.

其中[N]＝{1,…,N},T＝{1,…,T}，Ω为量测数据在量测矩阵中的下标索引集合(即前述的量测正常节点的二元下标集合)，P_Ω(·)为正交投影算子，表示当(i,j)∈Ω时S(i,j)为量测元素，即有：definition

Where [N]={1,...,N}, T={1,...,T}, Ω is the set of subscript indexes of the measurement data in the measurement matrix (that is, the aforementioned binary subscript of the normal node of the measurement scalar set), P _Ω (·) is an orthogonal projection operator, indicating that S(i, j) is the measurement element when (i, j) ∈ Ω, that is:

Due to data errors, the dispatching center may obtain the measurement data in two cases, namely the original data X(i,j) collected by the substation and the wrong data F(i,j), and the measurement data S(i,j) can be Expressed as:

；

;

The error data F(i,j) can be expressed as the superposition of the original acquisition 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 the noise value, the bus node of the collected erroneous data is called the data fault bus, and the proportion of the data fault bus is called the bus fault rate. In practical applications, some busbars are easy to become data fault busbars. The data rows corresponding to these nodes in the measurement matrix contain erroneous elements. For such row element errors, it can be considered that the measurement matrix is affected by a row-like structure. To reduce the pollution of noise, the measurement matrix can be further expressed as:

_PΩ (S)= _PΩ (X+Z),

where Z=(Z(i,j)) _N×T is the structured noise matrix in row form. In matrix Z, if node v _i collects wrong data at time j, then Z(i,j)≠0 , otherwise Z(i,j)=0.

The problem of missing measurement data with noise is to use the measurement matrix sent from the substation to the dispatch center to reconstruct the original acquisition data matrix of the substation. Using the low-rank characteristics of the data matrix collected by the substation, the data reconstruction problem can be modeled as matrix complementation. When solving the matrix completion problem, in order to effectively smooth the structured noise, the L 2,1 norm regularization term of the noise matrix Z is introduced into the standard matrix completion problem, so that the measurement data containing erroneous data is introduced into the standard matrix completion problem. The reconstruction problem is modeled as a structured noise matrix completion model based on L 2,1 norm regularization, namely:

Voltage sag is one of the most serious power quality problems. The accurate location of the voltage sag source is not only conducive to the timely discovery and removal of the disturbance source, but also provides a basis for defining the responsibilities of both power suppliers and consumers. However, the location of the sag source depends on Due to the coordination of multiple substations, and due to the constraints of PT, CT and other characteristics, as well as the power communication network and substation deployment environment, in the process of sag source monitoring, data loss and data errors usually occur in the process of data collection. Problems, data loss, and errors pose enormous challenges to the accuracy and reliability of the associated applications. The method of the invention takes advantage of the low rank characteristic of the measurement data based on the substation, models the missing data estimation problem as an L2,1 optimization problem, and uses the operator splitting method to solve the problem. Since the analytical expression is adopted, the solution speed is high and the convergence is good. , the missing data can be estimated with higher accuracy, thereby improving the sag source location accuracy.

Description of drawings

The present invention will be further described below in conjunction with the accompanying drawings:

Figure 1 is a flow chart of the method of the present invention.

Detailed ways

The technical solutions 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 variables appearing in the present invention have the same meaning before and after, and will not be changed by appearing in different formulas.

Referring to FIG. 1, a method for estimating missing values of noise-containing sag source positioning data of the present invention includes the following steps:

(1) Suppose N sag source monitoring buses v ₁ , v ₂ ,...,v _N data acquisition matrix P _Ω (S) at T times, where Ω is the binary index set for measuring normal nodes, and the initialization parameters τ, μ, set the maximum number of iterations Max; N is a natural number other than 0, the data acquisition matrix is voltage/current/active power/reactive power measurement data; initialization dual variables τ, μ, in this embodiment, τ=0.2, μ=1;

(2) Initialize the iterative matrix X ⁰ =0, Z ⁰ =0, V ^-1 =0, W ^-1 =0; where X is the measurement matrix, which is the row-form structured noise matrix; Z is the row-form structured noise matrix;

(3) To solve sub-problem 1, the solution method is as follows:

FOR k=0toMax

Y ^k =V ^k-1 +δ _X P _Ω (SX ^k -Z ^k )

X ^k+1 =D _πδ (V ^k )

W ^k =W ^k-1 +δ _Z P _Ω (SX ^k+1 -Z ^k )

in

，

,

k is a natural number;

(4) According to the result of solving the kth sub-problem 1, then solve the sub-problem 2, and the solution method is as follows:

Among them, N is the number of sag source monitoring buses; max{} is the maximum operator.

(5) Determine the recovered dip source data matrix X _opt and the recovered two-side noise matrix Z _opt :

X _opt =X ^Max+1 , Z _opt =Z ^Max+1 ;

(6) Perform missing data estimation:

Monitor each acquisition time j of node i for each sag source, where i=1～N, j=1～T; if the measurement is not missing, then X _rec (i,j)=S(i,j ), otherwise the estimated value of the missing data is _Xrec (i,j)= _Xopt (i,j).

The specific solution method of the optimization problem of the present invention will be described in detail below by means of embodiments.

Suppose that N sag source monitoring buses v ₁ , v ₂ ,...,v _N are deployed in a certain power grid monitoring area, and N is a natural number that is not 0. In the present invention, it is assumed that any substation has only one monitoring bus, and the substation is periodically collected. For the sag source monitoring bus data, the collection time interval of each round is called a moment, and the total collection time is set as T moments; then the total sampling data can be expressed by the matrix X as:

；

;

where X is the measurement matrix, X(i,j) represents the original voltage, current, active power and reactive power measurement data of the bus node v _i corresponding to time j, where i=1～N, j=1 ~T; however, due to data loss in the process of measurement acquisition and transmission, and due to noise, the grid dispatching center obtains an incomplete matrix S with many elements missing. In the present invention, the measurement data accounts for the total data volume. The ratio is called the data measurement rate.

其中[N]＝{1,…,N},T＝{1,…,T}，Ω为量测数据在量测矩阵中的下标索引集合(即前述的量测正常节点的二元下标集合)，P_Ω(·)为正交投影算子，表示当(i,j)∈Ω时S(i,j)为量测元素，即有：definition

Where [N]={1,...,N}, T={1,...,T}, Ω is the set of subscript indexes of the measurement data in the measurement matrix (that is, the aforementioned binary subscript of the normal node of the measurement scalar set), P _Ω (·) is an orthogonal projection operator, indicating that S(i, j) is the measurement element when (i, j) ∈ Ω, that is:

Due to data errors, there may be two situations in which the dispatching center obtains the measurement data. The substation collects the original data X(i,j) and the error data F(i,j). The measurement data S(i,j) can represent for:

；

;

The error data F(i,j) can represent that the substation is the superposition of the original collected data and the noise value, namely:

F(i,j)=X(i,j)+Z(i,j);

In the formula, Z(i,j) is the noise value, the bus node of the collected erroneous data is called the data fault bus, and the proportion of the data fault bus is called the bus fault rate. In practical applications, some buses are easy to It becomes the data fault bus. The data rows corresponding to these nodes in the measurement matrix contain erroneous elements. For such row element errors, it can be considered that the measurement matrix is polluted by the structured noise in the form of rows. The test matrix is expressed as:

_PΩ (S)= _PΩ (X+Z),

where Z=(Z(i,j)) _N×T is the structured noise matrix in row form. In matrix Z, if node v _i collects wrong data at time j, then Z(i,j)≠0 , otherwise Z(i,j)=0.

The problem of missing measurement data with noise is to use the measurement matrix sent from the substation to the dispatch center to reconstruct the original acquisition data matrix of the substation. Using the low-rank characteristics of the data matrix collected by the substation, the data reconstruction problem can be modeled as matrix complementation. When solving the matrix completion problem, in order to effectively smooth the structured noise, the L 2,1 norm regularization term of the noise matrix Z is introduced into the standard matrix completion problem, so that the measurement data containing erroneous data is introduced into the standard matrix completion problem. The reconstruction problem is modeled as a structured noise matrix completion model based on L 2,1 norm regularization, namely:

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

的奇异值分解为X＝UΣV^τ；hypothesis matrix

The singular value decomposition of is X=UΣV ^τ ;

where Σ=diag{σ _i |1≤i≤min(n ₁ ,n ₂ )},

；则有如下定义，and

; is defined as follows,

的F范数

(1) Matrix

The F norm of

的核范数

(2) Matrix

The nuclear norm of

的L2,1范数

(3) Matrix

The L2,1 norm of

，则其对应的奇异值阈值算子为D_γ(X)＝US_γ(Σ)V^T；(4) For any

, then its corresponding singular value threshold operator is D _γ (X)=US _γ (Σ)V ^T ;

where S _γ (Σ)=diag{max(0,σ _i -γ)|i=1,2,...,min(n ₁ ,n ₂ )}.

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

Then, transform equation (2) into solving two sub-problems, namely:

sub-question 1

，

,

为次微分

的一个次梯度，<·,·>表示矩阵的内积运算。in

sub-differential

A subgradient of , <·,·> represents the inner product operation of the matrix.

sub-question 2

，

,

为次微分

的一个次梯度。in

sub-differential

a subgradient of .

Then, solve subproblem 1;

按式(3)方法迭代生成序列收敛到该唯一解，即In subproblem 1, let

According to the method of formula (3), the iterative generation sequence converges to the unique solution, that is,

and should have

Let V ^k = V ^k-1 +δ _X P _Ω (SX ^k -Z ^k ), then equation (3) can be simplified as:

According to the correlation property of soft threshold, it can be known that for any τ, μ>0,

，则对式(4)有：

, then for formula (4) we have:

Therefore, sub-problem 1 can be solved iteratively as follows (5)

Then, solve subproblem 2;

Similar to the solution process of sub-problem 1, we can get:

，

,

取参数δ_Z＝1；where:

Take the parameter δ _Z = 1;

Let W ^k =W ^k-1 +δ _Z P _Ω (SX ^k+1 -Z ^k ), then:

存在全局最小点

，其中X⁽ⁱ⁾表示矩阵X的第i行，‖·‖₂表示向量2范数，根据该性质，则可知子问题2中Z更新如下：According to the correlation properties of the L2,1 norm corresponding to the soft threshold, it can be seen that for any

There is a global minimum

, where X ⁽ⁱ⁾ represents the i-th row of matrix X, and ‖·‖2 represents the vector ₂ norm. According to this property, it can be known that Z in sub-problem 2 is updated as follows:

Therefore, the iterative solution of sub-problem 2 is as follows:

Then, based on the solution methods of sub-problem 1 and sub-problem 2, after determining the parameters such as the maximum number of iterations of the algorithm, the optimal solution for estimating the missing data of the sag source can be obtained, that is, the restored sag source data matrix X _opt and the restored sag source data matrix X opt. The noise matrix Z _opt on both sides can be used to reconstruct the substation acquisition matrix X _rec by using the matrices X _opt and Z _opt . The specific method includes the following two steps:

(1) Fill the missing elements in the measurement matrix ' with the corresponding elements X _opt (i, j) in the recovered data matrix X _opt , that is, the reconstructed substation acquisition matrix X _rec satisfies:

(2) Identify the data fault bus through the restored noise matrix Z _opt . The bus corresponding to the row containing non-zero elements in Z _opt is the fault bus, and the bus corresponding to the row with all elements 0 is the normal sensor node. After the busbar fault occurs, the rows containing erroneous data in the acquisition matrix X _rec of the reconstructed substation can be replaced with the corresponding rows in the recovery data matrix X _opt , that is:

和

分别表示矩阵X_rec和X_opt的第i行数据。in the formula

and

represent the i-th row data of matrices X _rec and X _opt , respectively.

The embodiment is only to illustrate the technical idea of the present invention, and cannot limit the protection scope of the present invention. Any changes made on the basis of the technical solution according to the technical idea proposed by the present invention all fall within the protection scope of the present invention. .

Claims (9)

1. a noise-containing sag source positioning data missing value estimation method, is characterized in that, comprises the following steps: (1) Set the data acquisition matrix P _Ω (S) of N sag source monitoring buses v ₁ , v ₂ ,...,v _N at T times, where Ω is the binary index set for measuring normal nodes, and initialize the dual Variables τ, μ, set the maximum number of iterations Max; wherein, N is a natural number not 0, and the data acquisition matrix is voltage, current, active power and reactive power measurement data; (2) Initialize the iterative matrix X ⁰ =0, Z ⁰ =0, V ^-1 =0, W ^-1 =0; where X is the measurement matrix, which is the row-form structured noise matrix; Z is the row-form Structured noise matrix; V and W are the matrices in the intermediate iteration steps of the calculation, respectively, and have no physical meaning; (3) To solve sub-problem 1, the solution method is as follows:

in

,

k is a natural number; (4) According to the result of solving the kth sub-problem 1, then solve the sub-problem 2, and the solution method is as follows: FOR i=1toN

END FOR Among them, N is the number of sag source monitoring buses; max{} is the maximum operator. (5) Determine the recovered dip source data matrix X _opt and the recovered two-side noise matrix Z _opt : X _opt =X ^Max+1 , Z _opt =Z ^Max+1 ; (6) Perform missing data estimation: Monitor each acquisition time j of node i for each sag source, where i=1～N, j=1～T; if the measurement is not missing, then X _rec (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 sag source location data with noise according to claim 1 , wherein in step (1), the dual variables τ and μ are initialized, and the values τ=0.2 and μ=1. 3 . 3. The noise-containing sag source positioning data missing value estimation method according to claim 1, wherein the measurement matrix X described in the step (2), i.e. the total sampling data matrix, is expressed as:

; X(i,j) represents the original voltage, current, active power and reactive power measurement data of bus node v _i corresponding to time j, where i=1～N, j=1～T. 4. The method for estimating missing values of noise-containing sag source positioning data according to claim 3, characterized in that, in step (1)

Where [N]={1,...,N}, T={1,...,T}, Ω is the set of subscript indexes of the measurement data in the measurement matrix, that is, the binary subscript of the aforementioned normal node for measurement scalar set, P _Ω (·) is the orthogonal projection operator, which means that S(i, j) is the measurement element when (i, j) ∈ Ω, namely:

5. The method for estimating missing values of noise-containing sag source positioning data according to claim 4, characterized in that, due to data errors, there are two situations in which the dispatching center obtains the measurement data, namely the original data X collected by the substation (i,j) and error data F(i,j), so the measurement data S(i,j) is expressed as:

The error data F(i,j) is expressed as the superposition of the original acquisition data of the substation and the noise value, namely: F(i,j)=X(i,j)+Z(i,j); where Z(i,j) is the noise value. 6. The noise-containing sag source location data missing value estimation method according to claim 5, wherein the bus node of the collected error data is called a data fault bus, and the proportion of the data fault bus is called a data fault bus. is the bus failure rate, and the measurement matrix is further expressed as: _PΩ (S)= _PΩ (X+Z), where Z=(Z(i,j)) _N×T is the structured noise matrix in row form. In matrix Z, if node v _i collects wrong data at time j, then Z(i,j)≠0 , otherwise Z(i,j)=0. 7. The method for estimating missing values of noise-containing sag source positioning data according to claim 6, wherein the data reconstruction problem is modeled as a matrix completion problem by using the low-rank characteristic of the data matrix collected by the substation; The L 2,1 norm regularization term of matrix Z is introduced into the standard matrix completion problem to model the reconstruction problem of measurement data with erroneous data as a structured noise matrix completion based on L 2,1 norm regularization model, that is:

8. The noise-containing sag source location data missing value estimation method according to claim 7, wherein, based on the solution method of sub-problem 1 and sub-problem 2, after determining the parameter of the maximum number of iterations of the algorithm, the sag source is obtained The optimal solution for missing data estimation, namely the recovered sag source data matrix X _opt and the recovered two-sided noise matrix Z _opt , is used to reconstruct the substation acquisition matrix X _rec using the matrices X _opt and Z _opt . 9. The noise-containing sag source location data missing value estimation method according to claim 8, characterized in that, the concrete method for reconstructing the substation acquisition matrix X _rec using matrix X _opt and Z _opt comprises the following two steps: (6-1) Fill the missing elements in the measurement matrix with the corresponding elements X _opt (i,j) in the recovered data matrix X _opt , that is, the reconstructed substation acquisition matrix X _rec satisfies,

(6-2) Identify the data fault bus through the restored noise matrix Z _opt , the bus corresponding to the row containing non-zero elements in Z _opt is the fault bus, and the bus corresponding to the row with all elements of 0 is the normal sensor node, After the bus fault is identified, the rows containing erroneous data in the acquisition matrix X _rec of the reconstructed substation are replaced with the corresponding rows in the recovered data matrix X _opt , that is,

in the formula

and

represent the i-th row data of matrices X _rec and X _opt , respectively.

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