CN114022308A - Low-voltage distribution network topology self-adaptive identification method based on principal component analysis and convex optimization - Google Patents

Abstract

A low-voltage distribution network topology self-adaptive identification method based on principal component analysis and convex optimization belongs to the technical field of low-voltage distribution networks. The method is characterized in that: the method comprises the following steps: step 1, collecting electric energy data and forming a data matrix; step 2, performing principal component analysis on the power distribution network electric energy data; step 3, establishing a target function and constraint conditions of the topology identification model; step 4, introducing a relaxation variable, and converting the topology identification model into a convex optimization model; step 5, obtaining a regression matrix; and 6, obtaining the topological structure of the low-voltage distribution network through the regression matrix. In the low-voltage distribution network topology self-adaptive identification method based on principal component analysis and convex optimization, a data set matrix is processed by using the principal component analysis method, essential information among original data is reserved, the low-voltage distribution network topology identification problem is converted into a solvable convex optimization problem, the problem that other traditional optimization algorithms are prone to fall into a local solution is avoided, and the accuracy of topology identification is higher.

Description

Low-voltage distribution network topology self-adaptive identification method based on principal component analysis and convex optimization

Technical Field

A low-voltage distribution network topology self-adaptive identification method based on principal component analysis and convex optimization belongs to the technical field of low-voltage distribution networks.

Background

The low-voltage distribution network (namely, the low-voltage distribution network) is positioned at the tail end of the distribution system and directly provides services for users, and the operation reliability of the low-voltage distribution network directly determines the operation condition of the whole power grid and the service quality of the low-voltage distribution network for the users. The power distribution network has high differential rate, the structure changes due to reasons such as capacity increase, technical transformation, city construction and the like, the network topology and parameter configuration of the system need to be updated in time, and the system maintenance workload is large. Because the low-voltage distribution network lacks informatization and automation means, the identification of the topological structure of the low-voltage distribution network is incorrect, operation maintenance personnel cannot accurately master the operation condition of the current distribution network, the overhaul and repair of faults can not be carried out at once, and the electricity utilization experience of users is seriously influenced. With the advent of intermittent distributed power sources such as wind energy and photovoltaic and devices such as electric automobiles, the number of nodes of a low-voltage distribution network is increasing day by day, and the structure is also becoming more complex.

The power distribution network topology identification is an important component of high-level application software of a power distribution network management system, is a basis for realizing various high-level auxiliary software functions in a power distribution automatic system, and can provide a decision for power system scheduling. The topology of the low voltage distribution network provides connectivity among its numerous devices. The information of the underlying network topology facilitates efficient integration of renewable energy sources and efficient management of power distribution network faults. In addition, accurate network topology information is crucial to the estimation of reliable states in the power distribution network. Due to changes in power distribution network reconfiguration, repair, maintenance, load balancing, etc., it is not possible to ensure that network topology information is always accurate. Therefore, the power distribution network topology shows obvious changeability, and the accuracy of the power distribution network topology information is difficult to guarantee in real time.

Disclosure of Invention

The technical problem to be solved by the invention is as follows: the method overcomes the defects of the prior art, processes a data set matrix by using a principal component analysis method, retains essential information among original data, converts the low-voltage distribution network topology identification problem into a solvable convex optimization problem by using a norm approximation principle and convex relaxation, avoids the problem that other traditional optimization algorithms are easy to fall into a local solution, and is a low-voltage distribution network topology self-adaptive identification method based on principal component analysis and convex optimization, and the topology identification accuracy is higher.

The technical scheme adopted by the invention for solving the technical problems is as follows: the low-voltage distribution network topology self-adaptive identification method based on principal component analysis and convex optimization is characterized by comprising the following steps of: the method comprises the following steps:

step 1, collecting electric energy data of a transformer low-voltage side node intelligent electric meter, electric energy data of a distribution network node intelligent electric meter and electric energy data of a user node intelligent electric meter at fixed time intervals, and superposing the collected electric energy data to obtain a data matrix;

step 2, performing principal component analysis on the electric energy data acquired in the step 1, and decomposing the data to obtain a low-dimensional analysis object;

step 3, establishing a target function and constraint conditions of the topology identification model;

step 4, introducing a relaxation variable, and converting the topology identification model into a convex optimization model;

step 5, obtaining a regression matrix;

and 6, obtaining the topological structure of the low-voltage distribution network through the regression matrix.

Preferably, in step 1, the data matrix is:

Z＝[z_ij]_(n*N)

wherein z is_ijThe measured value of the ith node in the jth time interval is shown, N represents the number of nodes in the network, and N represents the number of measured values obtained by each node.

Preferably, in step 1, the fixed time interval is 15min or 30 min.

Preferably, in step 3, the objective function and the constraint condition of the topology identification model are:

R_mn∈{0,1}

wherein, | | U_2i+U_2d||_L1Represents the L1 norm, | U based on the objective function_2i+U_2d||_L2Representing the L2 norm based on the objective function.

Constraint 1: the corresponding formula is as follows:

constraint on a topological matrix R, wherein A is a row vector with the length of a and all elements of 1;

constraint 2: corresponding formula

The constraint on the elements in the matrix R, is a 0-1 programming problem_mnSetting U ═ {1, 2, … a } as a set of user nodes, T ═ 1, 2, … b } as a set of phase nodes, and m ∈ U for the connection relationship between the mth user and the nth phase node; n ∈ T.

Preferably, in step 4, the convex optimization model is:

min||U_2i+U_2d||_L1or||U_2i+U_2d||_L2

R_mn∈[0-σ，1+σ]

wherein, | | U_2i+U_2d||_L1Represents the L1 norm, | U based on the objective function_2i+U_2d||_L2Representing the L2 norm based on an objective function, σ being the relaxation vector, R_mnSetting U ═ {1, 2, … a } as a set of user nodes, T ═ 1, 2, … b } as a set of phase nodes, and m ∈ U for the connection relationship between the mth user and the nth phase node; n ∈ T.

Compared with the prior art, the invention has the beneficial effects that:

in the low-voltage distribution network topology self-adaptive identification method based on principal component analysis and convex optimization, the problem that other traditional optimization algorithms are easy to fall into local solutions is avoided, and the obtained solution is a global optimal solution; the data set matrix is processed by using a principal component analysis method, essential information among original data is reserved, the operation time of topology identification simulation is microsecond-level under the influence of the number of electric measurement sampling points, and the accuracy rate of topology identification is higher.

Drawings

Fig. 1 is a flow chart of a low-voltage distribution network topology adaptive identification method based on principal component analysis and convex optimization.

Detailed Description

Fig. 1 shows a preferred embodiment of the present invention, which is further described below with reference to fig. 1.

As shown in fig. 1, the low-voltage distribution network topology adaptive identification method based on principal component analysis and convex optimization includes the following steps:

step 1, collecting power distribution network electric energy data and voltage data;

acquiring electric energy data of the intelligent electric meter at the low-voltage side node of the transformer, electric energy data of the intelligent electric meter at the node of the distribution network and electric energy data of the intelligent electric meter at the user node at fixed time intervals (such as 15min or 30 min);

collecting and superposing the collected electric energy data to form a data matrix Z:

Z＝[z_ij]_(n*N)

wherein z is_ijThe measured value of the ith node at the jth time interval is shown, N represents the number of nodes in the network, and N represents the number of measured values obtained by each node.

Acquiring electric energy data of a low-voltage side of a transformer of a platform area, wherein the electric energy data is defined as a sample of m variables measured at the jth time:

the sample is subject to errors due to interference of the measured values due to random noise. Thus, the vector of measured variables is represented as:

z^m(j)＝z^t(j)+e(j)

wherein: z is a radical of^t(j) -a vector of actual values of the variables from the jth measurement; e (j) -noise induced error vector.

Step 2, performing principal component analysis on the power distribution network electric energy data, and decomposing the electric energy data to obtain a low-dimensional analysis object;

if the difference of the electricity consumption of the user to be identified is extremely small, a large amount of data needs to be adopted for analysis so as to ensure the accuracy of identification. The defects are that the calculation amount of the algorithm is large, and the recognition efficiency is low. The principal component analysis method is also called principal component analysis, the power distribution network electric energy data are analyzed through the principal component analysis method, the multi-index is converted into a few principal components through the idea of dimension reduction, each principal component can reflect most information of an original variable, and the contained information is not repeated. The method can lead the complex factors to be classified into a plurality of main components while introducing multi-aspect variables, simplify the problem and obtain more scientific and effective data information.

And forming a matrix by combining the electric energy data of the low-voltage side of the transformer area and the electric energy data of the electric meter to be identified, and constructing an (nxN) dimensional matrix Z. And analyzing the power distribution network electric energy data by using a principal component analysis method, namely estimating an (n-p) -dimensional real data subspace and a p-dimensional constraint subspace under the condition of a given data matrix Z.

In principal component analysis, the subspace is represented by a covariance matrix S_z＝ZZ^TIs obtained from the feature vector of (1). By dividing the variables into a number of dimensions (n)_dP) dependent variable z_dAnd the independent variable z_i(n_iN-p), a regression model can be obtained.

And z_dAnd z_iThe corresponding columns may also be divided as follows:

wherein the content of the first and second substances,

and

are respectively (n)_d*n_d) And (n)_d*n_i) The dimension matrix is a matrix of dimensions,

step 3, establishing a topology identification model, and setting a target function and constraint conditions;

each user is connected with one transformer only, the phase connection relation of the users has uniqueness, only one element in each column of the topological matrix R is 1, and the other elements are 0. The constraint relationship is shown in the following equation (1):

wherein, A represents a row vector with elements of 1 and length of a.

Let U ═ {1, 2, … a } be the set of user nodes, T ═ {1, 2, … b } be the set of phase nodes, R_mnObtaining the formula (2) for the connection relationship between the mth user and the nth phase node:

wherein m belongs to U; n ∈ T.

The topology identification problem of the power distribution network can be expressed as a semi-definite constraint optimization problem, and the objective function and constraint conditions for establishing the topology identification model are as follows:

R_mn∈{0,1}

wherein, | | U_2i+U_2d||_L1Represents the L1 norm, | U based on the objective function_2i+U_2d||_L2Representing the L2 norm based on the objective function, constraint 1: corresponding to the above formula:

constraints on the topology matrix R; constraint 2: corresponding to the above formula

The constraint on the elements in the matrix R is a 0-1 programming problem.

And 4, establishing a introduced relaxation variable, and converting the topology identification model into a convex optimization model.

The feasible domain of the 0-1 planning problem is discontinuous, so that the convex optimization requirement is not met, a relaxation variable sigma needs to be added to convert the feasible domain into inequality constraint, and the low-voltage distribution network topology identification problem is converted into a solvable convex optimization problem by utilizing norm approximation and a convex relaxation principle. Then the topology identification model in the step 3 is converted into the following convex optimization model:

min||U_2i+U_2d||_L1or||U_2i+U_2d||_L2

R_mn∈[0-σ，1+σ]

where σ is the relaxation vector.

Since the L1 norm and the L2 norm are both convex functions, the model is still a convex function after convex relaxation, and since the target function is easy to calculate partial derivatives, the optimal solution can be quickly calculated by adopting an interior point method.

Step 5, obtaining a regression matrix;

in step 2, since U is present_2dFull rank, hence the estimated regression matrix representation for the dependent and independent variables:

wherein the content of the first and second substances,

to represent(n_d*n_i) And (5) dimension regression matrix.

Regression matrix

The linear relation between the upper electric energy meter and the lower electric energy meter is expressed, and the correlation between the correlation matrix and the regression matrix is

Therefore, the relation between the upper electric energy meter and the lower electric energy meter in the low-voltage distribution network can be deduced.

And 6, obtaining the topological structure of the low-voltage distribution network through the regression matrix.

In the low-voltage distribution network topology self-adaptive identification method based on principal component analysis and convex optimization, the problem that other traditional optimization algorithms are easy to fall into local solutions is avoided, and the obtained solution is a global optimal solution; the data set matrix is processed by using a principal component analysis method, essential information among original data is reserved, the operation time of topology identification simulation is microsecond-level under the influence of the number of electric measurement sampling points, and the accuracy rate of topology identification is higher.

Collecting data of a transformer low-voltage side node, a power distribution network node and a user node intelligent electric meter, and reducing the dimension of the collected data by using a principal component analysis method; and converting the low-voltage distribution network topology identification problem into a solvable convex optimization problem by utilizing norm approximation and convex relaxation principles to obtain a regression matrix R. And successively identifying the connection relation of the upper and lower nodes, and finally obtaining the topological structure from the low-voltage side of the transformer to the whole low-voltage distribution network of the user.

The foregoing is directed to preferred embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow. However, any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention are within the protection scope of the technical solution of the present invention.

Claims (5)

1. A low-voltage distribution network topology self-adaptive identification method based on principal component analysis and convex optimization is characterized by comprising the following steps: the method comprises the following steps:

step 1, collecting electric energy data of a transformer low-voltage side node intelligent electric meter, electric energy data of a distribution network node intelligent electric meter and electric energy data of a user node intelligent electric meter at fixed time intervals, and superposing the collected electric energy data to obtain a data matrix;

step 2, performing principal component analysis on the electric energy data acquired in the step 1, and decomposing the data to obtain a low-dimensional analysis object;

step 3, establishing a target function and constraint conditions of the topology identification model;

step 4, introducing a relaxation variable, and converting the topology identification model into a convex optimization model;

step 5, obtaining a regression matrix;

and 6, obtaining the topological structure of the low-voltage distribution network through the regression matrix.

2. The low-voltage distribution network topology self-adaptive identification method based on principal component analysis and convex optimization according to claim 1, characterized in that: in step 1, the data matrix is:

Z＝[z_ij]_(n*N)

wherein z is_ijThe measured value of the ith node in the jth time interval is shown, N represents the number of nodes in the network, and N represents the number of measured values obtained by each node.

3. The low-voltage distribution network topology self-adaptive identification method based on principal component analysis and convex optimization according to claim 1, characterized in that: in step 1, the fixed time interval is 15min or 30 min.

4. The low-voltage distribution network topology self-adaptive identification method based on principal component analysis and convex optimization according to claim 1, characterized in that: in step 3, the objective function and the constraint condition of the topology identification model are as follows:

R_mn∈{0,1}

wherein, | | U_2i+U_2d||_L1Represents the L1 norm, | U based on the objective function_2i+U_2d||_L2Representing the L2 norm based on the objective function.

Constraint 1: the corresponding formula is as follows:

constraint on a topological matrix R, wherein A is a row vector with the length of a and all elements of 1;

constraint 2: corresponding formula

The constraint on the elements in the matrix R, is a 0-1 programming problem_mnSetting U ═ {1, 2, … a } as a set of user nodes, T ═ 1, 2, … b } as a set of phase nodes, and m ∈ U for the connection relationship between the mth user and the nth phase node; n ∈ T.

5. The low-voltage distribution network topology self-adaptive identification method based on principal component analysis and convex optimization according to claim 1, characterized in that: in step 4, the convex optimization model is:

min||U_2i+U_2d||_L1or||U_2i+U_2d||_L2

R_mn∈[0-σ，1+σ]

wherein, | | U_2i+U_2d||_L1Represents the L1 norm, | U based on the objective function_2i+U_2d||_L2Representing the L2 norm based on an objective function, σ being the relaxation vector, R_mnSetting U ═ {1, 2, … a } as a set of user nodes, T ═ 1, 2, … b } as a set of phase nodes, and m ∈ U for the connection relationship between the mth user and the nth phase node; n ∈ T.

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