Matrix decomposition-based power distribution data missing completion method and device

Abstract

The invention discloses a power distribution data missing complementing method and device based on matrix decomposition, and the method comprises the steps: constructing a data feature matrix of a power system according to network parameters of the power system; setting an arrangement form of a power distribution data matrix according to the data characteristic matrix and the type and scale of the power distribution data measurement value; constructing a power distribution data matrix completion problem model according to the power distribution data matrix; and solving the power distribution data matrix completion problem model by using a block coordinate descent algorithm to complete power distribution data missing completion. The method can be applied to state estimation under the condition of low measurement of the power distribution system, and can flexibly adapt to estimation and complementation of the power flow data of the power distribution system at the single moment of the measured data characteristic value of the power system.

Description

Technical Field

[0001] The present invention relates to the technical field of power distribution network, and in particular to a method and device for completing missing power distribution data based on matrix decomposition. Background Art

[0002] Guided by mathematics, control theory and other emerging theories, the state estimation technology of distribution system combined with the characteristics of the power system itself has become the key to the operation of distribution system. With the popularization of distributed energy resources, due to the scarcity of sensors and low measurement quality, traditional state estimation technology is difficult to cope with the current low-measurement distribution system, because the standard least squares method cannot operate when there is less known data.

[0003] At present, the existing algorithms have poor completion ability, limited accuracy and low credibility when applied to the completion of power flow data of low-measurement distribution systems. Moreover, the existing matrix completion algorithm needs to calculate the singular value decomposition (SVD) at each iteration during the operation process, which has low computational efficiency and high computational cost. Artificial intelligence algorithms are also commonly used for power system state estimation, but the data needs to be divided into training sets and test sets, and there are certain requirements for data quality and quantity to ensure high accuracy and credibility, and the use process is relatively complicated.

[0004] Therefore, how to invent a technical solution to complete missing distribution data has become an urgent problem to be solved. Summary of the invention

[0005] To this end, the present invention provides a method and device for completing missing distribution data based on matrix decomposition, which can be used for state estimation under low measurement conditions of the distribution system, and flexibly adapt to the distribution system flow data of the power system measurement data at a single moment for estimation and completion.

[0006] In order to achieve the above object, the present invention provides the following technical solution: a method for completing missing distribution data based on matrix decomposition, comprising:

[0007] According to the network parameters of the power system, construct the data feature matrix of the power system;

[0008] According to the data characteristic matrix and the type and scale of the power distribution data measurement value, setting the arrangement form of the power distribution data matrix;

[0009] According to the power distribution data matrix, a power distribution data matrix completion problem model is constructed;

[0010] The block coordinate descent algorithm is used to solve the distribution data matrix completion problem model to complete the missing distribution data.

[0011] As a preferred solution of a method for completing missing distribution data based on matrix decomposition, in the process of constructing a data feature matrix of the power system according to the network parameters of the power system, the expression of the data feature matrix is:

[0012]

[0013] In the formula, for all unbalanced nodes; is a collection of lines; is the node admittance matrix.

[0014] As a preferred solution of a method for completing missing power distribution data based on matrix decomposition, the arrangement form of the power distribution data matrix includes branch index arrangement and node index arrangement;

[0015] In the branch index arrangement, for each branch matrix The corresponding line in is of the form:

[0016]

[0017] In the formula, and are the real and imaginary parts of the complex variable respectively; V f is the voltage at the branch end point f; S f The power injected into the branch end point f; V t is the voltage at the branch end t; S t The power injected into the branch end point t; i ft For the branch The current;

[0018] In the node index arrangement, for each node matrix The corresponding line in is of the form:

[0019]

[0020] Where V n is the voltage at node n; S n Inject power into node n.

[0021] As a preferred solution of a method for completing missing power distribution data based on matrix decomposition, the expression of the power distribution data matrix completion problem model is:

[0022]

[0023]

[0024] In the formula, ||X|| *is the nuclear norm of X; σ i (X) is the i-th largest singular value of X; is the matrix to be completed; is the set of known elements in the matrix M; P Ω (X) is the matrix containing the known data set Ω after completion; P Ω (M) is the matrix to be completed containing the known data set Ω; F refers to the Frobenius norm representation; is the completed matrix.

[0025] As a preferred solution of the distribution data missing completion method based on matrix decomposition, in the process of solving the distribution data matrix completion problem model using the block coordinate descent algorithm, the distribution data matrix completion problem model is rewritten as follows using the matrix decomposition strategy:

[0026]

[0027] In the formula, and U and V are respectively decomposed into two parts by processing the matrix X through matrix decomposition method.

[0028] The present invention also provides a power distribution data missing completion device based on matrix decomposition, based on the above power distribution data missing completion method based on matrix decomposition, comprising:

[0029] A data feature matrix construction module is used to construct a data feature matrix of the power system according to network parameters of the power system;

[0030] A power distribution data matrix arrangement form setting module, used to set the arrangement form of the power distribution data matrix according to the type and scale of the data feature matrix and the power distribution data measurement value;

[0031] A power distribution data matrix completion problem model construction module, used to construct a power distribution data matrix completion problem model according to the power distribution data matrix;

[0032] The distribution data matrix completion problem model solving module is used to solve the distribution data matrix completion problem model using a block coordinate descent algorithm to complete the missing distribution data completion.

[0033] As a preferred solution of a power distribution data missing completion device based on matrix decomposition, in the data feature matrix construction module, in the process of constructing the data feature matrix of the power system according to the network parameters of the power system, the expression of the data feature matrix is:

[0034]

[0035] In the formula, for all unbalanced nodes; is a collection of lines; is the node admittance matrix.

[0036] As a preferred solution of a power distribution data missing completion device based on matrix decomposition, in the power distribution data matrix arrangement form setting module, the arrangement form of the power distribution data matrix includes branch index arrangement and node index arrangement;

[0037] In the branch index arrangement, for each branch matrix The corresponding line in is of the form:

[0038]

[0039] In the formula, and are the real and imaginary parts of the complex variable respectively; V f is the voltage at the branch end point f; S f The power injected into the branch end point f; V t is the voltage at the branch end t; S t The power injected into the branch end point t; i ft For the branch The current;

[0040] In the node index arrangement, for each node matrix The corresponding line in is of the form:

[0041]

[0042] Where V n is the voltage at node n; S n Inject power into node n.

[0043] As a preferred solution of a power distribution data missing completion device based on matrix decomposition, in the power distribution data matrix completion problem model construction module, the expression of the power distribution data matrix completion problem model is:

[0044]

[0045]

[0046] In the formula, ||X|| * is the nuclear norm of X; σ i (X) is the i-th largest singular value of X; is the matrix to be completed; is the set of known elements in the matrix M; P Ω (X) is the matrix containing the known data set Ω after completion; PΩ (M) is the matrix to be completed containing the known data set Ω; F refers to the Frobenius norm representation; is the completed matrix.

[0047] As a preferred solution of a power distribution data missing completion device based on matrix decomposition, in the power distribution data matrix completion problem model solving module, in the process of using the block coordinate descent algorithm to solve the power distribution data matrix completion problem model, the matrix decomposition strategy is used to rewrite the power distribution data matrix completion problem model as follows:

[0048]

[0049] In the formula, and U and V are respectively decomposed into two parts by processing the matrix X through matrix decomposition method.

[0050] The present invention has the following advantages: constructing a data feature matrix of the power system according to the network parameters of the power system; setting the arrangement form of the distribution data matrix according to the type and scale of the data feature matrix and the distribution data measurement value; constructing a distribution data matrix completion problem model according to the distribution data matrix; solving the distribution data matrix completion problem model using a block coordinate descent algorithm to complete the missing distribution data completion. The present invention uses matrix completion based on matrix decomposition to complete the missing data of the distribution system at a single moment. First, a standard matrix completion model is given; then, a structured data matrix is ​​formed to adapt to the data characteristics of the power system; finally, the completion model is solved using a block coordinate descent method based on the principle of matrix decomposition. The present invention uses a block coordinate descent method based on the principle of matrix decomposition to solve the completion model. The block coordinate descent method avoids calculating the singular value decomposition (SVD) in each iteration during the calculation process, improves the calculation efficiency, and reduces the calculation cost. Considering the data characteristics of the power system on the basis of the standard matrix completion model, the present invention can well adapt to the power flow data under the low measurement state of the distribution system. Compared with the least squares method, the present invention has lower requirements on the amount of known data, better data completion capability and higher accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the implementation methods of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the implementation methods or the description of the prior art. Obviously, the drawings in the following description are only exemplary, and for ordinary technicians in this field, other implementation drawings can be derived from the provided drawings without creative work.

[0052] The structures, proportions, sizes, etc. illustrated in this specification are only used to match the contents disclosed in the specification so as to facilitate understanding and reading by persons familiar with the technology. They are not used to limit the conditions under which the present invention can be implemented, and therefore have no substantial technical significance. Any structural modification, change in proportion or adjustment of size shall still fall within the scope of the technical contents disclosed in the present invention without affecting the effects and purposes that can be achieved by the present invention.

[0053] Figure 1 A schematic flow chart of a method for completing missing power distribution data based on matrix decomposition provided in Embodiment 1 of the present invention;

[0054] Figure 2 A graph of IEEE-33 node voltage amplitude completion error rate in a possible embodiment provided in Embodiment 1 of the present invention;

[0055] Figure 3 A schematic diagram of IEEE-33 node system data completion error results in a possible embodiment provided in Embodiment 1 of the present invention;

[0056] Figure 4 This is a schematic diagram of the architecture of a power distribution data missing completion device based on matrix decomposition provided in Example 2 of the present invention. DETAILED DESCRIPTION

[0057] The following is a description of the implementation of the present invention by specific embodiments. People familiar with the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0058] Example 1

[0059] See also Figure 1 Embodiment 1 of the present invention provides a method for completing missing power distribution data based on matrix decomposition, comprising the following steps:

[0060] S1. Construct a data feature matrix of the power system according to the network parameters of the power system;

[0061] S2. according to the data feature matrix and the type and scale of the power distribution data measurement value, setting the arrangement form of the power distribution data matrix;

[0062] S3. Constructing a distribution data matrix completion problem model according to the distribution data matrix;

[0063] S4. Use a block coordinate descent algorithm to solve the distribution data matrix completion problem model to complete the missing distribution data completion.

[0064] In this embodiment, in step S1, a data feature matrix of the power system is constructed according to the network parameters of the power system;

[0065] Specifically, the expression of the data feature matrix is:

[0066]

[0067] In the formula, for all unbalanced nodes; is a collection of lines; is the node admittance matrix;

[0068] make is the node voltage, is the injected power. Assuming that the balanced node voltage v1 and the injected power s1 are known, the unbalanced node voltage V n and the injected power S n Provided by the Supervisory Control and Data Acquisition (SCADA) system and partially missing. represents the current in each branch, f represents the beginning of the line, t represents the end of the line,

[0069] In this embodiment, in step S2, the arrangement form of the power distribution data matrix is ​​set according to the type and scale of the data feature matrix and the power distribution data measurement value;

[0070] Specifically, the specific data arrangement form of the data matrix M can be set according to the type and scale of the distribution data measurement value. In order to adapt to the data characteristics of the power system, two feasible arrangement forms are proposed as follows, one is arranged according to the branch index, and the other is arranged according to the node index. The matrix completion algorithm is not limited to the above two matrix structures because it is applicable to random data and various types of data sets. As long as there is a linear relationship between the data in the matrix, the structure of the data matrix M can be flexibly changed according to actual needs.

[0071] Branch index arrangement: The branch index arrangement method uses both node and branch related data. Each row of M represents a branch, and each column represents the data related to the branch. For each branch matrix The corresponding line in is of the form:

[0072]

[0073] In the formula, and are the real and imaginary parts of the complex variable respectively; Vf is the voltage at the branch end point f; S f The power injected into the branch end point f; V t is the voltage at the branch end t; S t The power injected into the branch end point t; i ft For the branch The current;

[0074] Node index arrangement: The node index arrangement method uses node-related data. Each row of M represents a node, and each column represents the data related to the node. For each node matrix The corresponding line in is of the form:

[0075]

[0076] Where V n is the voltage at node n; S n Inject power into node n.

[0077] In this embodiment, in step S3, a distribution data matrix completion problem model is constructed according to the distribution data matrix;

[0078] Specifically, is the matrix to be completed, let Represents the set of known elements in the matrix M. When a large number of elements in the matrix M are lost and cannot be obtained, leaving only a small number of elements Ω, the problem of how to fill these missing data reasonably and as accurately as possible can be modeled as a rank minimization optimization problem:

[0079]

[0080] sP Ω (X) = P Ω (M)

[0081] in, is the orthogonal projection operator, which means that when (i, j)∈Ω, P Ω (M) ij =M ij ; otherwise it is 0, that is

[0082]

[0083] However, the above formula has no practical application value because the rank function is non-convex and non-smooth, so the standard matrix completion problem is an NP-hard problem, that is, a non-deterministic polynomial problem. The most common way to solve this problem is to relax the nuclear norm. represents the nuclear norm of X, where σ i(X) is the i-th largest singular value of X. The distribution data matrix completion problem model can be expressed as:

[0084]

[0085] In the formula, ||X|| * is the nuclear norm of X; σ i (X) is the i-th largest singular value of X; is the matrix to be completed; is the set of known elements in the matrix M; P Ω (X) is the matrix containing the known data set Ω after completion; P Ω (M) is the matrix to be completed containing the known data set Ω; F refers to the Frobenius norm representation; is the completed matrix.

[0086] In this embodiment, in step S4, a block coordinate descent algorithm is used to solve the power distribution data matrix completion problem model to complete the missing power distribution data completion.

[0087] Specifically, the block coordinate descent algorithm is used to solve the matrix completion problem. The block coordinate descent algorithm is commonly known as the alternating minimization algorithm. Since the solution method based on nuclear norm relaxation involves complex matrix singular value decomposition, it may lead to a decrease in the efficiency of solving the matrix completion model and also have certain limitations on the amount of data processed. Therefore, matrix decomposition is used to modify the target matrix into the product of two low-rank matrices:

[0088]

[0089] Among them, r is the rank upper limit of X. Using this representation method can also greatly reduce the scale of the problem and speed up the solution.

[0090] Using the block coordinate descent algorithm, the above matrix completion model is rewritten as:

[0091]

[0092] In the formula, and U and V are respectively decomposed into two parts by processing the matrix X through matrix decomposition method.

[0093] However, since the distribution data matrix completion problem model is non-convex, this problem may have a non-globally optimal stationary point solution. However, as long as the following relatively loose conditions are met:

[0094] ||P Ω (UV-M)|| F ≤λ

[0095] but The solution X=UV is the global optimal solution.

[0096] Algorithm 1 The specific process of solving the model by block coordinate descent method is shown in Table 1:

[0097]

[0098] Table 1 Algorithm 1 Block coordinate descent method model solution process

[0099] In a possible embodiment, an example of IEEE-33 node system data completion is provided as follows:

[0100] like Figure 2 As shown in the figure, the error rate of each node completion result of the IEEE-33 node system when the amount of known data is 55% is shown. Among them, the known data nodes are white, and the accuracy of the completion results of the remaining nodes with missing data is represented by color. It can be seen that the average accuracy is about 3.5%.

[0101] like Figure 3 As shown in the figure, the completion accuracy of the IEEE-33 node system when the data is missing 10%-70%. When the amount of known data is greater than 70%, the error of the algorithm in this paper is less than 1%, which is lower than the least squares method; when the amount of known data is less than 70%, the least squares method is no longer operational. Therefore, the algorithm in this paper performs better than the least squares method in processing the scale of missing data, and the algorithm has high accuracy and good reliability.

[0102] In summary, the present invention constructs a data feature matrix of the power system according to the network parameters of the power system; sets the arrangement form of the distribution data matrix according to the type and scale of the data feature matrix and the distribution data measurement value; constructs a distribution data matrix completion problem model according to the distribution data matrix; uses a block coordinate descent algorithm to solve the distribution data matrix completion problem model to complete the missing distribution data completion. The present invention uses matrix completion based on matrix decomposition to complete the missing data of the distribution system at a single moment. First, a standard matrix completion model is given; then, a structured data matrix is ​​formed to adapt to the data characteristics of the power system; finally, the completion model is solved by using the block coordinate descent method based on the principle of matrix decomposition. The present invention uses the block coordinate descent method to solve the completion model based on the principle of matrix decomposition. The block coordinate descent method avoids calculating the singular value decomposition (SVD) in each iteration during the calculation process, improves the calculation efficiency, and reduces the calculation cost. Considering the data characteristics of the power system on the basis of the standard matrix completion model, the present invention can well adapt to the flow data under the low measurement state of the distribution system. Compared with the least squares method, the present invention has lower requirements on the amount of known data, better data completion capability and higher accuracy.

[0103] It should be noted that the method of the embodiment of the present disclosure can be performed by a single device, such as a computer or a server. The method of the present embodiment can also be applied in a distributed scenario and completed by multiple devices cooperating with each other. In the case of such a distributed scenario, one of the multiple devices can only perform one or more steps in the method of the embodiment of the present disclosure, and the multiple devices will interact with each other to complete the described method.

[0104] It should be noted that the above describes some embodiments of the present disclosure. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in an order different from that in the above embodiments and still achieve the desired results. In addition, the processes depicted in the accompanying drawings do not necessarily require the specific order or continuous order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0105] Example 2

[0106] See also Figure 4 Embodiment 2 of the present invention further provides a power distribution data missing completion device based on matrix decomposition, comprising:

[0107] The data characteristic matrix construction module 001 is used to construct the data characteristic matrix of the power system according to the network parameters of the power system;

[0108] The power distribution data matrix arrangement form setting module 002 is used to set the arrangement form of the power distribution data matrix according to the type and scale of the data feature matrix and the power distribution data measurement value;

[0109] A power distribution data matrix completion problem model construction module 003 is used to construct a power distribution data matrix completion problem model according to the power distribution data matrix;

[0110] The distribution data matrix completion problem model solving module 004 is used to solve the distribution data matrix completion problem model using a block coordinate descent algorithm to complete the missing distribution data completion.

[0111] In this embodiment, in the data feature matrix construction module 001, in the process of constructing the data feature matrix of the power system according to the network parameters of the power system, the expression of the data feature matrix is:

[0112]

[0113] In the formula, for all unbalanced nodes; is a collection of lines; is the node admittance matrix.

[0114] In this embodiment, in the power distribution data matrix arrangement form setting module 002, the arrangement form of the power distribution data matrix includes branch index arrangement and node index arrangement;

[0115] In the branch index arrangement, for each branch matrix The corresponding line in is of the form:

[0116]

[0117] In the formula, and are the real and imaginary parts of the complex variable respectively; V f is the voltage at the branch end point f; S f The power injected into the branch end point f; V t is the voltage at the branch end t; S t The power injected into the branch end point t; i ft For the branch The current;

[0118] In the node index arrangement, for each node matrix The corresponding line in is of the form:

[0119]

[0120] Where V n is the voltage at node n; S n Inject power into node n.

[0121] In this embodiment, in the power distribution data matrix completion problem model construction module 003, the expression of the power distribution data matrix completion problem model is:

[0122]

[0123]

[0124] In the formula, ||X|| * is the nuclear norm of X; σ i (X) is the i-th largest singular value of X; is the matrix to be completed; is the set of known elements in the matrix M; P Ω (X) is the matrix containing the known data set Ω after completion; P Ω (M) is the matrix to be completed containing the known data set Ω; F refers to the Frobenius norm representation; is the completed matrix.

[0125] In this embodiment, in the power distribution data matrix completion problem model solving module 004, in the process of using the block coordinate descent algorithm to solve the power distribution data matrix completion problem model, the power distribution data matrix completion problem model is rewritten as follows using a matrix decomposition strategy:

[0126]

[0127] In the formula, and U and V are respectively decomposed into two parts by processing the matrix X through matrix decomposition method.

[0128] It should be noted that the information interaction, execution process and other contents between the modules of the above-mentioned system are based on the same concept as the method embodiment in Example 1 of the present application, and the technical effects they bring are the same as those of the method embodiment of the present application. For specific contents, please refer to the description in the method embodiment shown above in the present application, and will not be repeated here.

[0129] Example 3

[0130] Embodiment 3 of the present invention provides a non-transitory computer-readable storage medium, in which a program code for a method for completing missing power distribution data based on matrix decomposition is stored. The program code includes instructions for executing a method for completing missing power distribution data based on matrix decomposition of embodiment 1 or any possible implementation thereof.

[0131] The computer-readable storage medium may be any available medium that can be accessed by a computer or a data storage device such as a server or a data center that includes one or more available media. The available medium may be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid-state drive (SSD)).

[0132] Example 4

[0133] Embodiment 4 of the present invention provides an electronic device, including: a memory and a processor;

[0134] The processor and the memory communicate with each other via a bus; the memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute a method for completing missing power distribution data based on matrix decomposition in Example 1 or any possible implementation thereof.

[0135] Specifically, the processor can be implemented by hardware or by software. When implemented by hardware, the processor can be a logic circuit, an integrated circuit, etc.; when implemented by software, the processor can be a general-purpose processor implemented by reading software codes stored in a memory. The memory can be integrated in the processor or can be located outside the processor and exist independently.

[0136] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the process or function described in the embodiment of the present invention is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable systems. The computer instructions can be stored in a computer-readable storage medium, or transmitted from a computer-readable storage medium to another computer-readable storage medium, for example, the computer instructions can be transmitted from a website site, computer, server or data center by wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) mode to another website site, computer, server or data center.

[0137] Obviously, those skilled in the art should understand that the above modules or steps of the present invention can be implemented by a general computing system, they can be concentrated on a single computing system, or distributed on a network composed of multiple computing systems, and optionally, they can be implemented by a program code executable by a computing system, so that they can be stored in a storage system and executed by the computing system, and in some cases, the steps shown or described can be executed in a different order than here, or they can be made into individual integrated circuit modules, or multiple modules or steps therein can be made into a single integrated circuit module for implementation. Thus, the present invention is not limited to any specific combination of hardware and software.

[0138] Although the present invention has been described in detail above by general description and specific embodiments, it is obvious to those skilled in the art that some modifications or improvements can be made to the present invention. Therefore, these modifications or improvements made without departing from the spirit of the present invention all belong to the scope of protection claimed by the present invention.

Claims

1. A method for completing missing power distribution data based on matrix decomposition, characterized in that: include: According to the network parameters of the power system, construct the data feature matrix of the power system; According to the data characteristic matrix and the type and scale of the power distribution data measurement value, setting the arrangement form of the power distribution data matrix; According to the power distribution data matrix, a power distribution data matrix completion problem model is constructed; The block coordinate descent algorithm is used to solve the distribution data matrix completion problem model to complete the missing distribution data.

2. A method for completing missing power distribution data based on matrix decomposition according to claim 1, characterized in that: In the process of constructing the data characteristic matrix of the power system according to the network parameters of the power system, the expression of the data characteristic matrix is: In the formula, for all unbalanced nodes; is a collection of lines; is the node admittance matrix.

3. The method for completing missing power distribution data based on matrix decomposition according to claim 2, characterized in that: The arrangement form of the power distribution data matrix includes branch index arrangement and node index arrangement; In the branch index arrangement, for each branch matrix The corresponding line in is of the form: In the formula, and are the real and imaginary parts of the complex variable respectively; V f is the voltage at the branch end point f; S f The power injected into the branch end point f; V t is the voltage at the branch end t; S t The power injected into the branch end point t; i ft For the branch The current; In the node index arrangement, for each node matrix The corresponding line in is of the form: Where V n is the voltage at node n; S n Inject power into node n.

4. The method for completing missing power distribution data based on matrix decomposition according to claim 3, characterized in that: The expression of the distribution data matrix completion problem model is: In the formula, ||X|| * is the nuclear norm of X; σ i (X) is the i-th largest singular value of X; is the matrix to be completed; is the set of known elements in the matrix M; P Ω (X) is the matrix containing the known data set Ω after completion; P Ω (M) is the matrix to be completed containing the known data set Ω; F refers to the Frobenius norm representation; is the completed matrix.

5. The method for completing missing power distribution data based on matrix decomposition according to claim 4, characterized in that: In the process of solving the distribution data matrix completion problem model using the block coordinate descent algorithm, the distribution data matrix completion problem model is rewritten as follows using a matrix decomposition strategy: In the formula, and U and V are respectively decomposed into two parts by processing the matrix X through matrix decomposition method.

6. A power distribution data missing completion device based on matrix decomposition, adopting a power distribution data missing completion method based on matrix decomposition according to any one of claims 1 to 5, characterized in that: include: A data feature matrix construction module is used to construct a data feature matrix of the power system according to network parameters of the power system; A power distribution data matrix arrangement form setting module, used to set the arrangement form of the power distribution data matrix according to the type and scale of the data feature matrix and the power distribution data measurement value; A power distribution data matrix completion problem model construction module, used to construct a power distribution data matrix completion problem model according to the power distribution data matrix; The distribution data matrix completion problem model solving module is used to solve the distribution data matrix completion problem model using a block coordinate descent algorithm to complete the missing distribution data completion.

7. The device for completing missing power distribution data based on matrix decomposition according to claim 6, characterized in that: In the data feature matrix construction module, in the process of constructing the data feature matrix of the power system according to the network parameters of the power system, the expression of the data feature matrix is: In the formula, for all unbalanced nodes; is a collection of lines; is the node admittance matrix.

8. The device for completing missing power distribution data based on matrix decomposition according to claim 7, characterized in that: In the power distribution data matrix arrangement form setting module, the arrangement form of the power distribution data matrix includes branch index arrangement and node index arrangement; In the branch index arrangement, for each branch matrix The corresponding line in is of the form: In the formula, and are the real and imaginary parts of the complex variable respectively; V f is the voltage at the branch end point f; S f The power injected into the branch end point f; V t is the voltage at the branch end t; S t The power injected into the branch end point t; i ft For the branch The current; In the node index arrangement, for each node matrix The corresponding line in is of the form: Where V n is the voltage at node n; S n Inject power into node n.

9. The device for completing missing power distribution data based on matrix decomposition according to claim 8, characterized in that: In the power distribution data matrix completion problem model construction module, the expression of the power distribution data matrix completion problem model is: In the formula, ||X|| * is the nuclear norm of X; σ i (X) is the i-th largest singular value of X; is the matrix to be completed; is the set of known elements in the matrix M; P Ω (X) is the matrix containing the known data set Ω after completion; P Ω (M) is the matrix to be completed containing the known data set Ω; F refers to the Frobenius norm representation; is the completed matrix.

10. The device for completing missing power distribution data based on matrix decomposition according to claim 9, characterized in that: In the distribution data matrix completion problem model solving module, in the process of using the block coordinate descent algorithm to solve the distribution data matrix completion problem model, the distribution data matrix completion problem model is rewritten as follows using a matrix decomposition strategy: In the formula, and U and V are respectively decomposed into two parts by processing the matrix X through matrix decomposition method.

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