Two-stage topological regression identification method for low-voltage substations

Abstract

The present invention discloses a two-stage topology regression identification method for low-voltage substations, which includes a first-stage identification of branch node-user node affiliation and a second-stage identification of branch node-main meter box node affiliation. When performing identification, a regression coefficient matrix and a candidate set are first established. By limiting the standard deviation correction amount, variable selection and variable screening are performed in turn, and it is determined whether there are unscreened candidate variables. This cycle is repeated to achieve the update of the regression coefficient matrix. The present invention fully explores the value of basic power measurement data and reduces dependence on physical models and prior knowledge. It efficiently identifies the substation branch node-user node association relationship, takes measurement errors into consideration, and constructs an error weight term coefficient adaptive adjustment model to improve the topology identification accuracy in the face of measurement errors, realize effective identification of substation topology connection relationships, thereby improving the overall observable performance of the distribution substation area, and providing a good topology transparency foundation for substation operation analysis.

Description

Technical Field

[0001] The present invention belongs to the field of topological regression identification, and in particular relates to a two-stage topological regression identification method for low-voltage stations. Background Art

[0002] Currently, a large number of distributed renewable energy sources are being widely connected to distribution networks. The random and intermittent nature of distributed energy sources increases operational uncertainty, making network topologies more complex and their operation more variable. This poses new challenges for network planning, scheduling, and operational management. Distribution substations, located at the end of the entire power grid, play a crucial role in connecting thousands of households and ensuring the implementation of the last mile of power supply services. However, these substations suffer from low levels of intelligent equipment, complex electrical structures, limited and underutilized monitoring equipment, and incomplete low-voltage substation topology information, making it difficult to meet the requirements for global observability of distribution substations.

[0003] Accurately identifying the topological structure and internal electrical connections of distribution substations can help clarify fault points and weak links in the power grid, which is of great significance for improving the efficiency of fault tracing and repair, and ensuring the stable operation of the power grid. The large scale and complex geographical structure of distribution network substations make traditional manual line mapping time-consuming and labor-intensive, and difficult to meet the requirements of accuracy and real-time performance. Through data analysis technology, the value contained in basic measurement data such as power and voltage can be fully analyzed and mined, and the topological connection relationships underlying electrical quantities can be directly identified without the need for additional prior knowledge or physical models. This is of great significance in reducing the complexity and difficulty of topology identification. Summary of the Invention

[0004] In order to solve the deficiencies in the prior art, the purpose of the present invention is to propose a two-stage topology regression identification method for low-voltage substations based on multivariate conditional evaluation. By constructing a two-stage topology regression identification model, the value of basic power measurement data can be fully tapped to effectively address the problem of difficult topology identification of distribution substations, reduce dependence on physical models and prior knowledge, and achieve effective identification of substation topology connection relationships, thereby improving the overall observable performance of distribution substations and supporting fault disturbance tracing.

[0005] The present invention adopts the following technical solutions:

[0006] A two-stage topology regression identification method for low-voltage substations includes the following steps:

[0007] (1) Obtain the number of users a, the number of branch nodes b, the power consumption data of user nodes, the power consumption data of branch nodes, and the power consumption data of main meter box nodes, standardize the power data, and perform time series segmentation on the processed power data; initialize the error weight σ and specify the error term coefficient adjustment limit;

[0008] (2) Carry out the first stage of identification of the relationship between branch nodes and user nodes: according to the number of users a, the number of branch nodes b, the power consumption data of user nodes, and the power consumption data of branch nodes, a regression coefficient matrix between branch nodes and users is established, and a zero matrix with b rows and a columns is constructed, with rows corresponding to branch nodes and columns corresponding to user nodes. If branch node i has a relationship with user j, the corresponding matrix element in row i and column j is set to 1, otherwise it is set to 0;

[0009] (3) Create b empty arrays A1, A2, ..., A i ,…,A b , named as the candidate set of users related to the branch node, and the candidate set of users related to the branch node i A i , used to store the user to which branch node i belongs;

[0010] (4) Calculate the current residual and obtain the standard deviation correction;

[0011] (5) Construct a branch node-user node association relationship identification model, with the objective function of minimizing the power difference between the branch node and the user node connected to it, perform the user node variable selection process for the current branch node i, calculate the F0 statistic after the variable screening, and select the user node with a correlation coefficient greater than the threshold F. out The variables are forward selected and added to the candidate set A i ;

[0012] (6) Select the variable with the smallest F0 statistic for backward elimination;

[0013] (7) Determine whether the number of variables in the current candidate set exceeds 2. If the number of variables is greater than 2, proceed to steps (8)-(9); otherwise, proceed to step (10);

[0014] (8) Calculate the F0 statistic and determination coefficient R after user node variable screening 2 And the prediction variance estimation coefficient PSE, if the prediction variance estimation coefficient PSE is less than or equal to the user node joining the candidate set A i The prediction variance estimation coefficient PSE before and the determination coefficient R 2 Greater than or equal to user nodes join candidate set A i The coefficient of determination R 2 And the F0 statistic is greater than the user node joining the candidate set A i If the F0 statistic before is not obtained, the current user variable is filtered out and the regression coefficient matrix is ​​updated; otherwise, proceed to step (9);

[0015] (9) Determine whether there are unscreened candidate variables. If so, proceed to steps (7)-(8) above; otherwise, proceed to step (10);

[0016] (10) Update and output the regression coefficient matrix based on the current candidate set variables;

[0017] (11) Perform steps (4) to (10) above for each branch node and finally output the regression coefficient matrix;

[0018] (12) According to steps (2)-(11), the second stage branch node-to-main meter box node ownership relationship identification is performed.

[0019] Furthermore, the method for identifying the relationship between branch nodes and master meter box nodes in the second stage is:

[0020] (1) According to the number of branch nodes b, the number of total meter boxes c, the power consumption of the total meter box nodes, and the power consumption data of the branch nodes, a regression coefficient matrix is ​​established between the branch nodes and the total meter box nodes. A zero matrix with c rows and b columns is constructed, and the rows correspond to the total meter box nodes and the columns correspond to the branch nodes. If the total meter box node l is in a relationship with the branch node i, the corresponding matrix element in row l and column i is set to 1, otherwise it is set to 0;

[0021] (2) Create c empty arrays B1, B2, ..., B l ,…,B c , named as the candidate set of branch nodes related to the total meter box node, and the candidate set of branch nodes related to the current total meter box node l B l , used to store the branch nodes to which the master meter box node l belongs;

[0022] (3) Calculate the current residual and obtain the standard deviation correction;

[0023] (4) Construct a main meter box node-branch node association relationship identification model, with the objective function of minimizing the power difference between the main meter box node and its connected branch nodes, perform the branch node variable selection process for the current main meter box node l, calculate the F0 statistic after the variable screening, and select the node with a correlation coefficient greater than the threshold F out The variables are forward selected and added to the candidate set B l ;

[0024] (5) Select the variable with the smallest F0 statistic for backward elimination;

[0025] (6) Determine whether the number of variables in the current candidate set exceeds 2. If the number of variables is greater than 2, proceed to steps (7)-(8); otherwise, proceed to step (9);

[0026] (7) Calculate the F0 statistic and determination coefficient R after the branch node variables are screened 2 And the prediction variance estimation coefficient PSE, if the prediction variance estimation coefficient PSE is less than or equal to the branch node, join the candidate set A iThe prediction variance estimation coefficient PSE before and the determination coefficient R 2 Greater than or equal to the branch node to join the candidate set A i The coefficient of determination R 2 And the F0 statistic is greater than the branch node to join the candidate set A i If the F0 statistic before is not obtained, the current branch node variable is filtered out and the regression coefficient matrix is ​​updated; otherwise, proceed to step (8);

[0027] (8) Determine whether there are candidate variables that have been screened. If so, proceed to steps (6)-(7) above; otherwise, proceed to step (9);

[0028] (9) Update and output the regression coefficient matrix based on the current candidate set variables;

[0029] (10) Perform steps (3) to (9) above for each branch node and finally output the regression coefficient matrix;

[0030] Furthermore, the prediction variance estimation coefficient PSE is calculated as follows:

[0031]

[0032]

[0033] Where, P i,t A is the power consumption of branch node i at time t; i is the set of user nodes associated with branch node i; P u j,t is the power consumption of user node j at time t; m is the number of users belonging to branch node i; PSE i is the prediction variance estimation coefficient of branch node i; N is the number of sampling time points; y i,t is the return power value of branch node i at time t, which is equal to the total power consumption of user nodes connected to branch node i; S i is the power variance of branch node i; is the mean power value of branch node i at each time point;

[0034] X l,t B is the power consumption of the main meter box node l at time t; l is the set of branch nodes associated with the main meter box node l; h is the number of branch nodes to which the main meter box node l belongs; PSE l is the prediction variance estimation coefficient of the total meter box node l; w l,t is the return power value of the main meter box node l at time t, which is equal to the total power consumption of the branch nodes connected to the main meter box node l; s l is the power variance of the main meter box node l; is the average power value of the main meter box node l at each time point;

[0035] The coefficient of determination R 2 The calculation method is:

[0036]

[0037] The calculation method of the F0 statistic is:

[0038]

[0039]

[0040] Where, is the branch node determination coefficient, F 0,bn is the F0 statistic parameter of the branch node, χ is the sum of squares of the power residual of the current branch node, χ1 and χ2 are the sum of squares of the power residual of the branch node before and after the addition of the significant user variable, respectively; p new is the number of newly added significant user variables; p2 is the number of user nodes screened by the current branch node; is the total meter box node determination coefficient, F 0,total is the F0 statistic parameter of the total meter box node, χ total is the sum of squares of the current total meter box node power residual, χ total,1 and χ total,2 are the residual square sums of the total meter box node power before and after adding significant branch node variables; p total,new is the number of newly added significant branch node variables; p total,2 The number of branch nodes filtered for the current main table box node.

[0041] Furthermore, the method for obtaining the standard deviation correction is:

[0042] 1) Initialization of standard deviation. The expression for calculating the initial standard deviation can be expressed as:

[0043]

[0044] Where: σ i,bn is the standard deviation of the power consumption of the i-th branch node; P i,t is the power consumption of the i-th branch node at time t; is the average power consumption of the i-th branch node; N is the total number of time points; σ l,total is the standard deviation of the power consumption of the lth main meter box node; X l,t is the power consumption of the lth main meter box node at time t; is the average power consumption of the lth main meter box node;

[0045] 2) Random error modeling: In each regression, the total table box regression result w l,t and branch node regression result y i,t Introducing a random error, the regression equation can be expressed as:

[0046]

[0047] in:

[0048] Ω user,t is the user power data matrix at time t;

[0049] k i,bn is the regression coefficient matrix k of the branch node bn The 1×a-dimensional matrix consisting of the elements in the i-th row;

[0050] ε bn ~N(0,1) is the random error term of normal distribution;

[0051] is the regression power value of branch node i considering the error term;

[0052] Ω bn,t is the branch node power data matrix at time t;

[0053] K l,total is the total meter box node regression coefficient matrix k total The l-th row of elements is a 1×b-dimensional matrix;

[0054] ε total ~N(0,1) is the random error term of normal distribution;

[0055] is the regressed power value of the total meter box node l considering the error term;

[0056] 3) Calculation of residuals: Calculate the residual of the current step:

[0057]

[0058] r i,bn Calculate the residual of branch node i considering the measurement error; r l,total To calculate the residual of the total meter box node l considering the measurement error;

[0059] 4) Standard deviation correction: recalculate the new standard deviation based on the residual

[0060] σ new,bn =std(r i,bn ) (58)

[0061] σ new,total =std(r l,total) (59)

[0062] Where, σ new,bn and σ new,total They are the corrected branch node standard deviation and total meter box node standard deviation respectively.

[0063] Furthermore, the error term coefficient adjustment limit is used to constrain the error standard deviation, and the upper and lower limit proportional coefficients are introduced to σ new Limit, σ new The maximum value of does not exceed 2 times the standard deviation before correction, and is not less than 0.5 times the standard deviation before correction. Its constraint expression can be expressed as:

[0064] σ min =0.5×σ (60)

[0065] σ max =2×σ (61)

[0066] The standard deviation is adjusted using the following formula:

[0067]

[0068] Furthermore, the method for constructing the branch node-user node association relationship identification model is as follows:

[0069] Based on the principle of energy conservation, the transmission power of a branch node is equal to the sum of the power consumed by the users connected to the node. The objective function of the branch node-user node association relationship identification model designed in this invention is to minimize the power difference between the branch node and the user nodes connected to it, which can be expressed as:

[0070]

[0071] Where, P i,t is the power consumption of branch node i at time t, y i,t is the total power of user nodes connected to branch node i at time t.

[0072] Furthermore, the method for constructing the main meter box node-branch node association relationship identification model is as follows:

[0073] Based on the principle of energy conservation, the transmission power of the main meter box node is equal to the sum of the power consumption of the branch nodes connected to the node. The objective function of the main meter box node-branch node association relationship identification model designed in this invention is to minimize the power difference between the main meter box node and the branch nodes connected to it, which can be expressed as:

[0074]

[0075] Where, X l,t is the power consumption of the main meter box node l at time t, w l,tis the total power of the branch nodes connected to the main meter box node l at time t.

[0076] Furthermore, the method for constructing the regression coefficient matrix and candidate set of the branch node-user relationship identification model is as follows:

[0077] 1) Create b empty arrays A1, A2, ..., A i ,…,A b , named as the candidate set of branch node related users, and construct the branch node-user association relationship matrix k with b rows and a columns bn Initialize k with rows corresponding to branch nodes and columns corresponding to user nodes bn is a zero matrix;

[0078] A i =[] (65)

[0079]

[0080] 2) Candidate vector set A of branch node i i Forward selection, statistics make the F0 statistic of branch node i greater than the threshold F out All user nodes of the branch node i are stored in the candidate set of the branch node i;

[0081]

[0082] Where, F out is the F0 statistic coefficient threshold, which is 3.5;

[0083] 3) Based on the branch node-user node regression identification algorithm, the PSE, F0, and R of each user node before and after screening are evaluated by multivariate conditions. 2 The results of multiple index changes are used to determine the user nodes related to the final branch node i;

[0084]

[0085] Where, PSE bn,old 、R 2 bn,old and F 0,bn,old are the predicted square error term, determination coefficient term and F0 statistical coefficient before user node j joins the user subset to which branch node i belongs; PSE bn 、R 2 bn and F 0,bn They are the prediction square error term, determination coefficient term and F0 statistical coefficient after node j joins the user subset to which branch node i belongs;

[0086] 4) According to the candidate vector set A of branch node i iAs a result, update the i-th row element of the regression coefficient matrix. If the user node j has a candidate vector set A i , then the corresponding element in row i and column j is set to 1;

[0087]

[0088] Furthermore, the method for constructing the regression coefficient matrix and candidate set of the total table box node-branch node relationship identification model is as follows:

[0089] 1) Create c empty arrays B1, B2, ..., B l ,…,B c , named as the candidate set of branch nodes related to the main table box node, and construct the main table box node-branch node association relationship matrix k with c rows and b columns total Initialize k with rows corresponding to the main table box nodes and columns corresponding to the branch nodes total is a zero matrix;

[0090] B l =[] (70)

[0091]

[0092] 2) Candidate vector set B of total table box nodes l Forward selection, statistics make the F0 statistic of the total table box node l greater than the threshold F out All branch nodes, and store the branch nodes in the candidate set of the total table box node l;

[0093]

[0094] Where i is the branch node, B l is the candidate set of the total table box node l;

[0095] 3) According to the total meter box node-branch node regression identification algorithm, by judging the PSE, F0, R before and after each branch node screening 2 The results of multiple index changes are used to determine the user nodes related to the final branch node i;

[0096]

[0097] Where, PSE total,old 、R 2 total,old and F 0,total,old are the predicted square error term, determination coefficient term and F0 statistical coefficient before branch node i is added to the branch node subset of the main table box node l; PSE total 、R 2 total and F 0,totalThey are respectively the prediction square error term, determination coefficient term and F0 statistical coefficient after branch node i is added to the branch node subset to which the total meter box node l belongs;

[0098] 4) According to the candidate vector set B of the total table box node l l The result of the update is to update the l-th row element of the total table box node-branch node regression coefficient matrix. If there is a candidate vector set B for branch node i, l , then the corresponding element in row l and column i is set to 1;

[0099]

[0100] A non-transitory computer-readable storage medium stores a computer program, which, when executed by a processor, implements the two-stage topological regression identification method for low-voltage substations as described above.

[0101] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the two-stage topological regression identification method for low-voltage substations as described above is implemented.

[0102] The beneficial technical effects of the present invention are:

[0103] The present invention proposes a substation topology regression identification method based on multivariate condition evaluation, which fully explores the value of basic power measurement data and reduces dependence on physical models and prior knowledge, efficiently identifies the relationship between substation branch nodes and user nodes, and considers measurement errors to construct an error weight term coefficient adaptive adjustment model to improve the topology identification accuracy in the face of measurement errors, and realize effective identification of substation topology connection relationships, thereby improving the overall observable performance of the distribution station area and providing a good topology transparency foundation for substation operation analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0104] Figure 1 Schematic diagram of the process of a two-stage topology regression identification method for low-voltage substations in an embodiment of the present invention;

[0105] Figure 2 A diagram of a two-stage topology identification model in an embodiment of the present invention;

[0106] FIG3( a ) is a topological structure of the station area 1 according to an embodiment of the present invention;

[0107] FIG3( b ) is a topological structure of the station area 2 according to an embodiment of the present invention;

[0108] FIG4( a ) is a topological diagram of active power of user nodes in area 1 according to an embodiment of the present invention;

[0109] FIG4( b ) is a topological diagram of the active power of branch nodes in area 1 according to an embodiment of the present invention;

[0110] FIG5( a ) is a topological diagram of active power of user nodes in area 2 according to an embodiment of the present invention;

[0111] FIG5( b ) is a topological diagram of the active power of the branch node in area 2 according to an embodiment of the present invention;

[0112] Figure 6(a) is the result of identifying the relationship between the main meter box and branch nodes in Area 1;

[0113] Figure 6(b) is the result of identifying the relationship between the main meter box and branch nodes in area 2;

[0114] Figure 7 Identify the heat map of the user-branch node relationship in area 1;

[0115] Figure 8 Identify the heat map of the user-branch node association relationship in area 2;

[0116] Figure 9 It is the active power of multiple area household nodes;

[0117] Figure 10 Heat map for identifying the relationship between users and branch nodes in multiple zones;

[0118] Figure 11 Heat map of identification of user-branch node association relationships in the area under measurement error. DETAILED DESCRIPTION

[0119] The following is a further clear and complete description of the method and device for real-time evaluation of distributed photovoltaic carrying capacity of a distribution network provided by the present invention in conjunction with the accompanying drawings:

[0120] like Figure 1 As shown in FIG, a two-stage topology regression identification method for low-voltage areas is provided, which includes the following steps:

[0121] (1) Obtain the number of users a, the number of branch nodes b, the power consumption data of user nodes, the power consumption data of branch nodes, and the power consumption data of main meter box nodes, standardize the power data, and perform time series segmentation on the processed power data; initialize the error weight σ and specify the error term coefficient adjustment limit;

[0122] (2) Carry out the first stage of identification of the relationship between branch nodes and user nodes: according to the number of users a, the number of branch nodes b, the power consumption data of user nodes, and the power consumption data of branch nodes, a regression coefficient matrix between branch nodes and users is established, and a zero matrix with b rows and a columns is constructed, with rows corresponding to branch nodes and columns corresponding to user nodes. If branch node i has a relationship with user j, the corresponding matrix element in row i and column j is set to 1, otherwise it is set to 0;

[0123] (3) Create b empty arrays A1, A2, ..., A i ,…,A b , named as the candidate set of users related to the branch node, and the candidate set of users related to the branch node i A i , used to store the user to which branch node i belongs;

[0124] (4) Calculate the current residual and obtain the standard deviation correction;

[0125] (5) Construct a branch node-user node association relationship identification model, with the objective function of minimizing the power difference between the branch node and the user node connected to it, perform the user node variable selection process for the current branch node i, calculate the F0 statistic after the variable screening, and select the user node with a correlation coefficient greater than the threshold F. out The variables are forward selected and added to the candidate set A i ;

[0126] (6) Select the variable with the smallest F0 statistic for backward elimination;

[0127] (7) Determine whether the number of variables in the current candidate set exceeds 2. If the number of variables is greater than 2, proceed to steps (8)-(9); otherwise, proceed to step (10);

[0128] (8) Calculate the F0 statistic and determination coefficient R after user node variable screening 2 And the prediction variance estimation coefficient PSE, if the prediction variance estimation coefficient PSE is less than or equal to the user node joining the candidate set A i The prediction variance estimation coefficient PSE before and the determination coefficient R 2 Greater than or equal to user nodes join candidate set A i The coefficient of determination R 2 And the F0 statistic is greater than the user node joining the candidate set A i If the F0 statistic before is not obtained, the current user variable is filtered out and the regression coefficient matrix is ​​updated; otherwise, proceed to step (9);

[0129] (9) Determine whether there are unscreened candidate variables. If so, proceed to steps (7)-(8) above; otherwise, proceed to step (10);

[0130] (10) Update and output the regression coefficient matrix based on the current candidate set variables;

[0131] (11) Perform steps (4) to (10) above for each branch node and finally output the regression coefficient matrix;

[0132] (12) According to steps (2)-(11), the second stage branch node-to-main meter box node ownership relationship identification is performed.

[0133] Specifically, the method for identifying the relationship between branch nodes and master meter box nodes in the second stage is:

[0134] (1) According to the number of branch nodes b, the number of total meter boxes c, the power consumption of the total meter box nodes, and the power consumption data of the branch nodes, a regression coefficient matrix is ​​established between the branch nodes and the total meter box nodes. A zero matrix with c rows and b columns is constructed, and the rows correspond to the total meter box nodes and the columns correspond to the branch nodes. If the total meter box node l is in a relationship with the branch node i, the corresponding matrix element in row l and column i is set to 1, otherwise it is set to 0;

[0135] (2) Create c empty arrays B1, B2, ..., B l ,…,B c , named as the candidate set of branch nodes related to the total meter box node, and the candidate set of branch nodes related to the current total meter box node l B l , used to store the branch nodes to which the master meter box node l belongs;

[0136] (3) Calculate the current residual and obtain the standard deviation correction;

[0137] (4) Construct a main meter box node-branch node association relationship identification model, with the objective function of minimizing the power difference between the main meter box node and its connected branch nodes, perform the branch node variable selection process for the current main meter box node l, calculate the F0 statistic after the variable screening, and select the node with a correlation coefficient greater than the threshold F out The variables are forward selected and added to the candidate set B l ;

[0138] (5) Select the variable with the smallest F0 statistic for backward elimination;

[0139] (6) Determine whether the number of variables in the current candidate set exceeds 2. If the number of variables is greater than 2, proceed to steps (7)-(8); otherwise, proceed to step (9);

[0140] (7) Calculate the F0 statistic and determination coefficient R after the branch node variables are screened 2 And the prediction variance estimation coefficient PSE, if the prediction variance estimation coefficient PSE is less than or equal to the branch node, join the candidate set A i The prediction variance estimation coefficient PSE before and the determination coefficient R 2 Greater than or equal to the branch node to join the candidate set A i The coefficient of determination R 2 And the F0 statistic is greater than the branch node to join the candidate set A i If the F0 statistic before is not obtained, the current branch node variable is filtered out and the regression coefficient matrix is ​​updated; otherwise, proceed to step (8);

[0141] (8) Determine whether there are candidate variables that have been screened. If so, proceed to steps (6)-(7) above; otherwise, proceed to step (9);

[0142] (9) Update and output the regression coefficient matrix based on the current candidate set variables;

[0143] (10) Perform steps (3) to (9) above for each branch node and finally output the regression coefficient matrix;

[0144] The traditional regression algorithm model has a single evaluation condition and has problems such as overfitting, improper variable selection and insufficient prediction accuracy. 2 The results of multiple evaluation criteria such as the coefficient of determination and prediction variance estimation are used to screen significant variables to improve the accuracy and robustness of model identification:

[0145] The calculation method of the prediction variance estimation coefficient PSE is:

[0146]

[0147]

[0148] Where, P i,t A is the power consumption of branch node i at time t; i is the set of user nodes associated with branch node i; P u j,t is the power consumption of user node j at time t; m is the number of users belonging to branch node i; PSE i is the prediction variance estimation coefficient of branch node i; N is the number of sampling time points; y i,t is the return power value of branch node i at time t, which is equal to the total power consumption of user nodes connected to branch node i; S i is the power variance of branch node i; is the mean power value of branch node i at each time point;

[0149] X l,t B is the power consumption of the main meter box node l at time t; l is the set of branch nodes associated with the main meter box node l; h is the number of branch nodes to which the main meter box node l belongs; PSE l is the prediction variance estimation coefficient of the total meter box node l; w l,t is the return power value of the main meter box node l at time t, which is equal to the total power consumption of the branch nodes connected to the main meter box node l; s l is the power variance of the main meter box node l; is the average power value of the main meter box node l at each time point;

[0150] The coefficient of determination R 2 The calculation method is:

[0151]

[0152] The calculation method of the F0 statistic is:

[0153]

[0154] Where, is the branch node determination coefficient, F 0,bn is the F0 statistic parameter of the branch node, χ is the sum of squares of the power residual of the current branch node, χ1 and χ2 are the sum of squares of the power residual of the branch node before and after the addition of the significant user variable, respectively; p new is the number of newly added significant user variables; p2 is the number of user nodes screened by the current branch node; is the total meter box node determination coefficient, F 0,total is the F0 statistic parameter of the total meter box node, χ total is the sum of squares of the current total meter box node power residual, χ total,1 and χ total,2 are the residual square sums of the total meter box node power before and after adding significant branch node variables; p total,new is the number of newly added significant branch node variables; p total,2 The number of branch nodes filtered for the current main table box node.

[0155] The methods for constructing the master meter box node-branch node association relationship identification model and the branch node-user node association relationship identification model are as follows:

[0156] Based on the principle of energy conservation, the transmission power of a branch node is equal to the sum of the power consumed by the users connected to the node. The objective function of the branch node-user node association relationship identification model designed in this invention is to minimize the power difference between the branch node and the user nodes connected to it, which can be expressed as:

[0157]

[0158] Where, P i,t is the power consumption of branch node i at time t, y i,t is the total power of user nodes connected to branch node i at time t.

[0159] Based on the principle of energy conservation, the transmission power of the main meter box node is equal to the sum of the power consumption of the branch nodes connected to the node. The objective function of the main meter box node-branch node association relationship identification model designed in this invention is to minimize the power difference between the main meter box node and the branch nodes connected to it, which can be expressed as:

[0160]

[0161] Where, X l,t is the power consumption of the main meter box node l at time t, w l,t is the total power of the branch nodes connected to the main meter box node l at time t.

[0162] In practical applications, the data acquisition process is often accompanied by various measurement errors and noise. These errors may arise from precision limitations of measurement equipment, environmental interference, or human factors. Directly using data containing these errors for modeling and analysis can lead to poor model fit and compromised prediction accuracy. To address this issue, error term weighting coefficients are introduced. By modeling and adjusting the error terms, the robustness and accuracy of the model are improved. These weighting coefficients primarily involve standard deviation initialization, random error modeling, residual calculation, and standard deviation correction.

[0163] 1) Initialization of standard deviation. The expression for calculating the initial standard deviation can be expressed as:

[0164]

[0165] Where: σ i,bn is the standard deviation of the power consumption of the i-th branch node; P i,t is the power consumption of the i-th branch node at time t; is the average power consumption of the i-th branch node; N is the total number of time points; σ l,total is the standard deviation of the power consumption of the lth main meter box node; X l,t is the power consumption of the lth main meter box node at time t; is the average power consumption of the lth main meter box node;

[0166] 2) Random error modeling: In each regression, the total table box regression result w l,t and branch node regression result y i,t Introducing a random error, the regression equation can be expressed as:

[0167]

[0168] in:

[0169] Ω user,t is the user power data matrix at time t;

[0170] k i,bn is the regression coefficient matrix k of the branch node bn The 1×a-dimensional matrix consisting of the elements in the i-th row;

[0171] ε bn ~N(0,1) is the random error term of normal distribution;

[0172] is the regression power value of branch node i considering the error term;

[0173] Ω bn,t is the branch node power data matrix at time t;

[0174] K l,total is the total meter box node regression coefficient matrix k total The l-th row of elements is a 1×b-dimensional matrix;

[0175] ε total ~N(0,1) is the random error term of normal distribution;

[0176] is the regressed power value of the total meter box node l considering the error term;

[0177] 3) Calculation of residuals: Calculate the residual of the current step:

[0178]

[0179] r i,bn Calculate the residual of branch node i considering the measurement error; r l,total To calculate the residual of the total meter box node l considering the measurement error;

[0180] 4) Standard deviation correction: recalculate the new standard deviation based on the residual

[0181] σ new,bn =std(r i,bn ) (97)

[0182] σ new,total =std(r l,total ) (98)

[0183] Where, σ new,bn and σ new,total are the corrected branch node standard deviation and total meter box node standard deviation respectively;

[0184] The error term coefficient adjustment limit is to constrain the error standard deviation, and the upper and lower limit proportional coefficients are introduced to σ new Limit, σ new The maximum value of does not exceed 2 times the standard deviation before correction, and is not less than 0.5 times the standard deviation before correction. Its constraint expression can be expressed as:

[0185] σ min =0.5×σ (99)

[0186] σ max =2×σ (100)

[0187] The standard deviation is adjusted using the following formula:

[0188]

[0189] Through the above steps, the standard deviation σ of the error term will be dynamically adjusted in each regression process, so that the regression model can adaptively update the error under different data.

[0190] Specifically, the method for constructing the regression coefficient matrix and candidate set of the branch node-user relationship identification model is as follows:

[0191] 1) Create b empty arrays A1, A2, ..., A i ,…,A b , named as the candidate set of branch node related users, and construct the branch node-user association relationship matrix k with b rows and a columns bn Initialize k with rows corresponding to branch nodes and columns corresponding to user nodes bn is a zero matrix;

[0192] A i =[] (102)

[0193]

[0194] 2) Candidate vector set A of branch node i i Forward selection, statistics make the F0 statistic of branch node i greater than the threshold F out All user nodes of the branch node i are stored in the candidate set of the branch node i;

[0195]

[0196] Where, F out is the F0 statistic coefficient threshold, which is 3.5;

[0197] 3) According to the branch node-user node regression identification algorithm, by judging the PSE, F0, R of each user node before and after screening 2 The results of multiple index changes are used to determine the user nodes related to the final branch node i;

[0198]

[0199] Where, PSE bn,old 、R 2 bn,old and F 0,bn,old are the predicted square error term, determination coefficient term and F0 statistical coefficient before user node j joins the user subset to which branch node i belongs; PSE bn 、R 2 bn and F 0,bnThey are the prediction square error term, determination coefficient term and F0 statistical coefficient after node j joins the user subset to which branch node i belongs;

[0200] 4) According to the candidate vector set A of branch node i i As a result, update the i-th row element of the regression coefficient matrix. If the user node j has a candidate vector set A i , then the corresponding element in row i and column j is set to 1;

[0201]

[0202] Specifically, the method for constructing the regression coefficient matrix and candidate set of the total table box node-branch node relationship identification model is as follows:

[0203] 1) Create c empty arrays B1, B2, ..., B l ,…,B c , named as the candidate set of branch nodes related to the main table box node, and construct the main table box node-branch node association relationship matrix k with c rows and b columns total Initialize k with rows corresponding to the main table box nodes and columns corresponding to the branch nodes total is a zero matrix;

[0204] B l =[] (107)

[0205]

[0206] 2) Candidate vector set B of total table box nodes l Forward selection, statistics make the F0 statistic of the total table box node l greater than the threshold F out All branch nodes, and store the branch nodes in the candidate set of the total table box node l;

[0207]

[0208] Where i is the branch node, B l is the candidate set of the total table box node l;

[0209] 3) According to the total meter box node-branch node regression identification algorithm, by judging the PSE, F0, R before and after each branch node screening 2 The results of multiple index changes are used to determine the user nodes related to the final branch node i;

[0210]

[0211] Where, PSE total,old 、R 2 total,old and F 0,total,oldare the predicted square error term, determination coefficient term and F0 statistical coefficient before branch node i is added to the branch node subset of the main table box node l; PSE total 、R 2 total and F 0,total They are respectively the prediction square error term, determination coefficient term and F0 statistical coefficient after branch node i is added to the branch node subset to which the total meter box node l belongs;

[0212] 4) According to the candidate vector set B of the total table box node l l The result of the update is to update the l-th row element of the total table box node-branch node regression coefficient matrix. If there is a candidate vector set B for branch node i, l , then the corresponding element in row l and column i is set to 1;

[0213]

[0214] As an example, in this embodiment, the method of the present invention is used to perform a two-stage topology regression identification for low-voltage areas, as follows:

[0215] 1. Construction of substation topology model

[0216] In order to identify the branch node-user node association relationship within a single substation and between different substations, two substation structure models with 12 branch nodes and 36 user nodes and 9 branch nodes and 37 user nodes were constructed respectively. The topological structure of the substation is as follows: Figure 3(a) 、 3(b) As shown;

[0217] 2. Node load configuration

[0218] Each user node is configured with a rated capacity of 3kW. Based on the load power change curve of the open source data set, the power consumption of each user node is set at a 15-minute time interval. The load changes of the user nodes and branch nodes in the generated area 1 and area 2 are as follows: Figure 4(a) 、 4(b) , 5(a), 5(b).

[0219] Based on the designed algorithm, the identification results of the main meter box-branch node association relationship in area 1 and area 2 are as follows: Figure 6(a) 、 6(b) As shown, the internal topology identification results of the single station area 1 and station area 2 are as follows Figure 7 、 8 As shown, the topological identification results of mixed multi-area substations 1 and 2 are as follows: Figure 10 As shown, the topology identification accuracy for a single station area is 100%, and the topology identification accuracy for a mixed station area is 95%;

[0220] The topological identification results of single station area 1 under different Gaussian random errors are as follows: Figure 11 As shown in Table 1, Figure 11 It can be seen that in a single station area, the Gaussian random error of 0.1-0.6 is set for the branch node power. The topology accuracy identification results are shown in the following table. Under the Gaussian random error of 0.1-0.5, the topology identification accuracy is 100%. Under the Gaussian random error of 0.6, the topology identification accuracy also reaches 83.3%, indicating that the identification model has certain robustness.

[0221] Table 1 Results of identification accuracy of user-branch node association relationship in different Gaussian distribution errors

[0222]

[0223] Example 2

[0224] This embodiment provides a non-transitory computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the two-stage topology regression identification method for low-voltage substations as described above is implemented.

[0225] Furthermore, the present invention adopts the following technical solutions:

[0226] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the two-stage topological regression identification method for low-voltage substations as described above is implemented.

[0227] Through the description of the above embodiments, it will be clear to those skilled in the art that the facilities of the present invention can be implemented by means of software plus the necessary general hardware platform. The embodiments of the present invention can be implemented using existing processors, or by a dedicated processor used for this or other purposes for an appropriate system, or by a hard-wired system. The embodiments of the present invention also include non-transitory computer-readable storage media, which include machine-readable media for carrying or having machine-executable instructions or data structures stored thereon; such machine-readable media can be any available medium that can be accessed by a general-purpose or special-purpose computer or other machine with a processor. For example, such machine-readable media can include RAM, ROM, EPROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store the required program code in the form of machine-executable instructions or data structures and can be accessed by a general-purpose or special-purpose computer or other machine with a processor. When information is transmitted or provided to a machine via a network or other communication connection (hard-wired, wireless, or a combination of hard-wired and wireless), the connection is also considered a machine-readable medium.

[0228] Thus far, the technical solutions of the present invention have been described in conjunction with the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art may make equivalent changes or substitutions to the relevant technical features, and the technical solutions after such changes or substitutions will fall within the scope of protection of the present invention.

Claims

1. A two-stage topological regression identification method for low-voltage areas, characterized by: The method comprises the following steps: (1) Obtain the number of users a, the number of branch nodes b, the power consumption data of user nodes, the power consumption data of branch nodes, and the power consumption data of main meter box nodes, standardize the power data, and perform time series segmentation on the processed power data; initialize the error weight σ and specify the error term coefficient adjustment limit; (2) Carry out the first stage of identification of the relationship between branch nodes and user nodes: according to the number of users a, the number of branch nodes b, the power consumption data of user nodes, and the power consumption data of branch nodes, a regression coefficient matrix between branch nodes and users is established, and a zero matrix with b rows and a columns is constructed, with rows corresponding to branch nodes and columns corresponding to user nodes. If branch node i has a relationship with user j, the corresponding matrix element in row i and column j is set to 1, otherwise it is set to 0; (3) Create b empty arrays A1, A2, ..., A i ,…,A b , named as the candidate set of users related to the branch node, and the candidate set of users related to the branch node i A i , used to store the user to which branch node i belongs; (4) Calculate the current residual and obtain the standard deviation correction; (5) Construct a branch node-user node association relationship identification model, with the objective function of minimizing the power difference between the branch node and the user node connected to it, perform the user node variable selection process for the current branch node i, calculate the F0 statistic after the variable screening, and select the user node with a correlation coefficient greater than the threshold F. out The variables are forward selected and added to the candidate set A i ; (6) Select the variable with the smallest F0 statistic for backward elimination; (7) Determine whether the number of variables in the current candidate set exceeds 2. If the number of variables is greater than 2, proceed to steps (8)-(9); otherwise, proceed to step (10); (8) Calculate the F0 statistic and determination coefficient R after user node variable screening 2 And the prediction variance estimation coefficient PSE, if the prediction variance estimation coefficient PSE is less than or equal to the user node joining the candidate set A i The prediction variance estimation coefficient PSE before and the determination coefficient R 2 Greater than or equal to user nodes join candidate set A i The coefficient of determination R 2 And the F0 statistic is greater than the user node joining the candidate set A i If the F0 statistic before is not obtained, the current user variable is filtered out and the regression coefficient matrix is ​​updated; otherwise, proceed to step (9); (9) Determine whether there are unscreened candidate variables. If so, proceed to steps (7)-(8) above; otherwise, proceed to step (10); (10) Update and output the regression coefficient matrix based on the current candidate set variables; (11) Perform steps (4) to (10) above for each branch node and finally output the regression coefficient matrix; (12) According to steps (2)-(11), the second stage branch node-to-main meter box node ownership relationship identification is performed.

2. The two-stage topology regression identification method for low-voltage substations according to claim 1 is characterized in that: The method for identifying the relationship between branch nodes and master meter box nodes in the second stage is: (1) According to the number of branch nodes b, the number of total meter boxes c, the power consumption of the total meter box nodes, and the power consumption data of the branch nodes, a regression coefficient matrix is ​​established between the branch nodes and the total meter box nodes. A zero matrix with c rows and b columns is constructed, and the rows correspond to the total meter box nodes and the columns correspond to the branch nodes. If the total meter box node l is in a relationship with the branch node i, the corresponding matrix element in row l and column i is set to 1, otherwise it is set to 0; (2) Create c empty arrays B1, B2, ..., B l ,…,B c , named as the candidate set of branch nodes related to the total meter box node, and the candidate set of branch nodes related to the current total meter box node l B l , used to store the branch nodes to which the master meter box node l belongs; (3) Calculate the current residual and obtain the standard deviation correction; (4) Construct a main meter box node-branch node association relationship identification model, with the objective function of minimizing the power difference between the main meter box node and its connected branch nodes, perform the branch node variable selection process for the current main meter box node l, calculate the F0 statistic after the variable screening, and select the node with a correlation coefficient greater than the threshold F out The variables are forward selected and added to the candidate set B l ; (5) Select the variable with the smallest F0 statistic for backward elimination; (6) Determine whether the number of variables in the current candidate set exceeds 2. If the number of variables is greater than 2, proceed to steps (7)-(8); otherwise, proceed to step (9); (7) Calculate the F0 statistic and determination coefficient R after the branch node variables are screened 2 And the prediction variance estimation coefficient PSE, if the prediction variance estimation coefficient PSE is less than or equal to the branch node, join the candidate set A i The prediction variance estimation coefficient PSE before and the determination coefficient R 2 Greater than or equal to the branch node to join the candidate set A i The coefficient of determination R 2 And the F0 statistic is greater than the branch node to join the candidate set A i If the F0 statistic before is not obtained, the current branch node variable is filtered out and the regression coefficient matrix is ​​updated; otherwise, proceed to step (8); (8) Determine whether there are candidate variables that have been screened. If so, proceed to steps (6)-(7) above; otherwise, proceed to step (9); (9) Update and output the regression coefficient matrix based on the current candidate set variables; (10) Repeat steps (3) to (9) for each branch node and finally output the regression coefficient matrix.

3. The two-stage topological regression identification method for low-voltage substations according to claim 1 is characterized in that: The calculation method of the prediction variance estimation coefficient PSE is: Where, P i,t A is the power consumption of branch node i at time t; i The set of user nodes associated with branch node i; is the power consumption of user node j at time t; m is the number of users belonging to branch node i; PSE i is the prediction variance estimation coefficient of branch node i; N is the number of sampling time points; y i,t is the return power value of branch node i at time t, which is equal to the total power consumption of user nodes connected to branch node i; S i is the power variance of branch node i; is the mean power value of branch node i at each time point; X l,t B is the power consumption of the main meter box node l at time t; l is the set of branch nodes associated with the main meter box node l; h is the number of branch nodes to which the main meter box node l belongs; PSE l is the prediction variance estimation coefficient of the total meter box node l; w l,t is the return power value of the main meter box node l at time t, which is equal to the total power consumption of the branch nodes connected to the main meter box node l; s l is the power variance of the main meter box node l; is the average power value of the main meter box node l at each time point; The coefficient of determination R 2 The calculation method is: The calculation method of the F0 statistic is: Where, is the branch node determination coefficient, F 0,bn is the F0 statistic parameter of the branch node, χ is the sum of squares of the power residual of the current branch node, χ1 and χ2 are the sum of squares of the power residual of the branch node before and after the addition of the significant user variable, respectively; p new is the number of newly added significant user variables; p2 is the number of user nodes screened by the current branch node; is the total meter box node determination coefficient, F 0,total is the F0 statistic parameter of the total meter box node, χ total is the sum of squares of the current total meter box node power residual, χ total,1 and χ total,2 are the residual square sums of the total meter box node power before and after adding significant branch node variables; p total,new is the number of newly added significant branch node variables; p total,2 The number of branch nodes filtered for the current main table box node.

4. The two-stage topology regression identification method for low-voltage substations according to claim 1 is characterized in that: The method for obtaining the standard deviation correction amount is: 1) Initialization of standard deviation. The expression for calculating the initial standard deviation can be expressed as: Where: σ i,bn is the standard deviation of the power consumption of the i-th branch node; P i,t is the power consumption of the i-th branch node at time t; is the average power consumption of the i-th branch node; N is the total number of time points; σ l,total is the standard deviation of the power consumption of the lth main meter box node; X l,t is the power consumption of the lth main meter box node at time t; is the average power consumption of the lth main meter box node; 2) Random error modeling: In each regression, the total table box regression result w l,t and branch node regression result y i,t Introducing a random error, the regression equation can be expressed as: in: Ω user,t is the user power data matrix at time t; k i,bn is the regression coefficient matrix k of the branch node bn The 1×a-dimensional matrix consisting of the elements in the i-th row; ε bn ~N(0,1) is the random error term of normal distribution; is the regression power value of branch node i considering the error term; Ω bn,t is the branch node power data matrix at time t; K l,total is the total meter box node regression coefficient matrix k total The l-th row of elements is a 1×b-dimensional matrix; ε total ~N(0,1) is the random error term of normal distribution; is the regressed power value of the total meter box node l considering the error term; 3) Calculation of residuals: Calculate the residual of the current step: r i,bn Calculate the residual of branch node i considering the measurement error; r l,total To calculate the residual of the total meter box node l considering the measurement error; 4) Standard deviation correction: recalculate the new standard deviation based on the residual s new,bn =std(r i,bn ) (21) s new,total =std(r l,total ) (22) Where, σ new,bn and σ new,total They are the corrected branch node standard deviation and total meter box node standard deviation respectively.

5. The two-stage topological regression identification method for low-voltage substations according to claim 4 is characterized in that: The error term coefficient adjustment limit is to constrain the error standard deviation, and the upper and lower limit proportional coefficients are introduced to σ new Limit, σ new The maximum value of does not exceed 2 times the standard deviation before correction, and is not less than 0.5 times the standard deviation before correction. Its constraint expression can be expressed as: s min =0.5×σ (23) s max =2×σ (24) The standard deviation is adjusted using the following formula:

6. The two-stage topology regression identification method for low-voltage substations according to claim 1 is characterized in that: The construction method of the branch node-user node association relationship identification model is as follows: Based on the principle of energy conservation, the transmission power of a branch node is equal to the sum of the power consumed by the users connected to the node. The objective function of the branch node-user node association relationship identification model designed in this invention is to minimize the power difference between the branch node and the user nodes connected to it, which can be expressed as: Where, P i,t is the power consumption of branch node i at time t, y i,t is the total power of user nodes connected to branch node i at time t.

7. The two-stage topology regression identification method for low-voltage substations according to claim 2 is characterized in that: The construction method of the main meter box node-branch node association relationship identification model is as follows: Based on the principle of energy conservation, the transmission power of the main meter box node is equal to the sum of the power consumption of the branch nodes connected to the node. The objective function of the main meter box node-branch node association relationship identification model designed in this invention is to minimize the power difference between the main meter box node and the branch nodes connected to it, which can be expressed as: Where, X l,t is the power consumption of the main meter box node l at time t, w l,t is the total power of the branch nodes connected to the main meter box node l at time t.

8. The two-stage topology regression identification method for low-voltage substations according to claim 1 is characterized in that: The method for constructing the regression coefficient matrix and candidate set of the branch node-user relationship identification model is as follows: 1) Create b empty arrays A1, A2, ..., A i ,…,A b , named as the candidate set of branch node related users, and construct the branch node-user association relationship matrix k with b rows and a columns bn Initialize k with rows corresponding to branch nodes and columns corresponding to user nodes bn is a zero matrix; A i ＝[] (28) 2) Candidate vector set A of branch node i i Forward selection, statistics make the F0 statistic of branch node i greater than the threshold F out All user nodes of the branch node i are stored in the candidate set of the branch node i; Where, F out is the F0 statistic coefficient threshold, which is 3.5; 3) Based on the branch node-user node regression identification algorithm, the PSE, F0, and R of each user node before and after screening are evaluated by multivariate conditions. 2 The results of multiple index changes are used to determine the user nodes related to the final branch node i; Where, PSE bn,old 、R 2 bn,old and F 0,bn,old are the predicted square error term, determination coefficient term and F0 statistical coefficient before user node j joins the user subset to which branch node i belongs; PSE bn 、R 2 bn and F 0,bn They are the prediction square error term, determination coefficient term and F0 statistical coefficient after node j joins the user subset to which branch node i belongs; 4) According to the candidate vector set A of branch node i i As a result, update the i-th row element of the regression coefficient matrix. If the user node j has a candidate vector set A i , then the corresponding element in row i and column j is set to 1; 9. The two-stage topology regression identification method for low-voltage substations according to claim 2 is characterized in that: The method for constructing the regression coefficient matrix and candidate set of the total table box node-branch node relationship identification model is as follows: 1) Create c empty arrays B1, B2, ..., B l ,…,B c , named as the candidate set of branch nodes related to the main table box node, and construct the main table box node-branch node association relationship matrix k with c rows and b columns total Initialize k with rows corresponding to the main table box nodes and columns corresponding to the branch nodes total is a zero matrix; B l ＝[] (33) 2) Candidate vector set B of total table box nodes l Forward selection, statistics make the F0 statistic of the total table box node l greater than the threshold F out All branch nodes, and store the branch nodes in the candidate set of the total table box node l; Where i is the branch node, B l is the candidate set of the total table box node l; 3) According to the total meter box node-branch node regression identification algorithm, by judging the PSE, F0, R before and after each branch node screening 2 The results of multiple index changes are used to determine the user nodes related to the final branch node i; Where, PSE total,old 、R 2 total,old and F 0,total,old are the predicted square error term, determination coefficient term and F0 statistical coefficient before branch node i is added to the branch node subset of the main table box node l; PSE total 、R 2 total and F 0,total They are respectively the prediction square error term, determination coefficient term and F0 statistical coefficient after branch node i is added to the branch node subset to which the total meter box node l belongs; 4) According to the candidate vector set B of the total table box node l l The result of the update is to update the l-th row element of the total table box node-branch node regression coefficient matrix. If there is a candidate vector set B for branch node i, l , then the corresponding element in row l and column i is set to 1; 10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the two-stage topology regression identification method for low-voltage substations is implemented as described in any one of claims 1 to 7.

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