Two-stage topology regression identification method for low-voltage transformer area

Abstract

The invention discloses a two-stage topology regression identification method for a low-voltage transformer area, which comprises first-stage branch node-user node affiliation relation identification and second-stage branch node-general meter box node affiliation relation identification, and comprises the following steps: during identification, firstly, establishing a regression coefficient matrix and a candidate set; sequentially carrying out variable selection and variable screening by limiting the standard deviation correction, judging whether unscreened candidate variables exist or not, and circulating in this way to realize updating of the regression coefficient matrix; the power basic measurement data value is fully mined, the dependence on a physical model and prior knowledge is reduced, the transformer area branch node-user node incidence relation is efficiently identified, the measurement error is considered, an error weight item coefficient self-adaptive adjustment model is constructed, the topology identification accuracy in the face of the measurement error is improved, and the topology identification efficiency is improved. Effective identification of the topological connection relation of the transformer area is realized, so that the global observability of the power distribution transformer area is improved, and a good topological transparent basis is provided for transformer area 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 areas. Background Art

[0002] At present, a large number of distributed renewable energy sources are widely connected to the distribution network. The randomness and intermittent characteristics of distributed energy sources have increased the uncertainty factors of the distribution network operation, making the distribution network topology more complex and the operation mode changeable, which has brought new challenges to the planning, scheduling and operation management of the distribution network. The distribution substation is located at the end of the entire power grid. As the key to connecting thousands of households and ensuring the implementation of the last mile of power supply services, it plays a vital role. However, its equipment has a low degree of intelligence, a complex electrical structure, a limited number of monitoring equipment and insufficient utilization, and incomplete low-voltage substation topology information, which makes it difficult to meet the requirements of global observability of the distribution substation.

[0003] Accurately identifying the topological structure and internal electrical connection relationship of the distribution station area can help clarify the fault points and weak links in the power grid, which is of great significance to improving the efficiency of fault tracing and repair and ensuring the stable operation of the power grid. The huge scale and complex geographical structure of the distribution network area make it time-consuming and labor-intensive to rely on the traditional manual line survey method, and it is 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 relationship hidden behind the electrical quantity can be directly identified without the need for additional prior knowledge and physical models, which is of great significance to 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 condition evaluation. By constructing a two-stage topology regression identification model, the value of basic power measurement data can be fully explored 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 areas 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 total 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) Perform the first-stage branch node-user node affiliation identification: establish a regression coefficient matrix between branch nodes and users based on 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, and construct a zero matrix with b rows and a columns, with rows corresponding to branch nodes and columns corresponding to user nodes. If branch node i is in 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 is A i , used to store the user to which the 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 its connected user nodes. Perform the user node variable selection process for the current branch node i, 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 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 previous prediction variance estimation coefficient PSE and the determination coefficient R 2 Greater than or equal to the user node to join the 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 previous F0 statistic 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 candidate variables that have not been screened. 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 the above steps (4)-(10) 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 affiliation 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 total meter box nodes, and the power consumption data of branch nodes, a regression coefficient matrix between branch nodes and total meter box nodes is established, and a zero matrix with c rows and b columns is constructed, with rows corresponding to total meter box nodes and columns corresponding to branch nodes. If total meter box node l is in a relationship with 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 total meter box node-branch node association relationship identification model, with minimizing the power difference between the total meter box node and its connected branch nodes as the objective function, perform the branch node variable selection process on the current total meter box node l, calculate the F0 statistic after variable screening, and select the branch 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 branch 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 branch node, join the candidate set A iThe previous prediction variance estimation coefficient PSE 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 previous F0 statistic is not obtained, the current branch node variable is screened 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 the above steps (3) to (9) for each branch node, and finally output the regression coefficient matrix;

[0030] Furthermore, the calculation method of the prediction variance estimation coefficient PSE is:

[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; 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 average power value of branch node i at each time point;

[0034] X l,t B is the power consumption of the total meter box node l at time t; l is the set of branch nodes associated with the master meter box node l; h is the number of branch nodes to which the master 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 regressed power value of the total meter box node l at time t, which is equal to the total power consumption of the branch nodes connected to the total meter box node l; s l is the power variance of the total meter box node l; is the average power value of the total 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] In the formula, is the branch node determination coefficient, F 0,bn is the F0 statistic parameter of the branch node, χ is the residual sum of squares of the power of the current branch node, χ1 and χ2 are the residual sum of squares of the power of the branch node before and after the addition of significant user variables, 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 master 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: 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 total meter box node; X l,t is the power consumption of the lth total meter box node at time t; is the average power consumption of the lth total meter box node;

[0045] 2) Random error modeling: In each regression, the total table box regression result w l,t and the 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 total meter box node l regression power value 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] In the formula, 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 construction method of 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 by the present 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 construction method of 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 by the present 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 total meter box node l at time t, w l,tIt is 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 a branch node-user association relationship matrix k with b rows and a columns bn , and 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] In the formula, F out is the F0 statistic coefficient threshold, and its value 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 iThe result is to update the i-th row element of the regression coefficient matrix. If the user node j has a candidate vector set A i , 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 total table box node, and construct the total table box node-branch node association relationship matrix k with c rows and b columns total , and initialize k with rows corresponding to the total table box nodes and columns corresponding to the branch nodes total is a zero matrix;

[0090] B l =[] (70)

[0091]

[0092] 2) The candidate vector set B of the total table box node 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] In the formula, i is the branch node, B l is the candidate set of 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 to which node l belongs; PSE total , R 2 total and F 0,totalThey are respectively the prediction square error term, determination coefficient term and F0 statistical coefficient after the branch node i is added to the branch node subset to which the total table box node l belongs;

[0098] 4) According to the total table box node l candidate vector set B l The result 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 , 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 stations as described above.

[0101] An electronic device comprises 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 stations 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, thereby improving the topology identification accuracy in the face of measurement errors, and realizing 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 It is a flow chart of a two-stage topological regression identification method for low-voltage areas in an embodiment of the present invention;

[0105] Figure 2 A two-stage topology identification model diagram 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 structure diagram of 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 structure diagram of the active power of the branch node in area 2 according to an embodiment of the present invention;

[0112] FIG6( a ) is a diagram showing the identification result of the main meter box-branch node association relationship in area 1;

[0113] FIG6( b ) is a diagram showing the identification result of the main meter box-branch node association relationship in area 2;

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

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

[0116] Fig. 9 It is the active power of multiple user nodes;

[0117] Fig.10 Thermal map for identifying the association between users and branch nodes in multiple zones;

[0118] Fig.11 Heat map of identification of user-branch node association relationships in the platform 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, a two-stage topology regression identification method for low-voltage areas 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 total 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) Perform the first-stage branch node-user node affiliation identification: establish a regression coefficient matrix between branch nodes and users based on 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, and construct a zero matrix with b rows and a columns, with rows corresponding to branch nodes and columns corresponding to user nodes. If branch node i is in 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 is A i , used to store the user to which the 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 its connected user nodes. 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 previous prediction variance estimation coefficient PSE and the determination coefficient R 2 Greater than or equal to the user node to join the 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 previous F0 statistic 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 candidate variables that have not been screened. 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 the above steps (4)-(10) 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 affiliation relationship identification is performed.

[0133] Specifically, the method for identifying the branch node-to-main meter box node belonging relationship 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 total meter box nodes, and the power consumption data of branch nodes, a regression coefficient matrix between branch nodes and total meter box nodes is established, and a zero matrix with c rows and b columns is constructed, with rows corresponding to total meter box nodes and columns corresponding to branch nodes. If total meter box node l is in a relationship with 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 total meter box node-branch node association relationship identification model, with minimizing the power difference between the total meter box node and its connected branch nodes as the objective function, perform the branch node variable selection process on the current total meter box node l, calculate the F0 statistic after variable screening, and select the branch 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 branch 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 branch node, join the candidate set A i The previous prediction variance estimation coefficient PSE 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 previous F0 statistic is not obtained, the current branch node variable is screened 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 the above steps (3) to (9) 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 determination coefficient 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; 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 average power value of branch node i at each time point;

[0149] X l,t B is the power consumption of the total meter box node l at time t; l is the set of branch nodes associated with the master meter box node l; h is the number of branch nodes to which the master 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 total meter box node l; is the average power value of the total 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] In the formula, is the branch node determination coefficient, F 0,bn is the F0 statistic parameter of the branch node, χ is the residual sum of squares of the power of the current branch node, χ1 and χ2 are the residual sum of squares of the power of the branch node before and after the addition of significant user variables, 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 master box node.

[0155] The method for constructing the master meter box node-branch node association relationship identification model and the branch node-user node association relationship identification model is 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 by the present 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 by the present 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] In the formula, X l,t is the power consumption of the total meter box node l at time t, w l,t It 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 collection process is often accompanied by various measurement errors and noises. These errors may come from the accuracy limitations of the measuring equipment, environmental interference or human factors. If the data containing errors are directly used for modeling and analysis, the fitting effect of the model may be reduced and the prediction accuracy may be affected. In order to deal with this problem, the error term weight coefficient is introduced to improve the robustness and accuracy of the model by modeling and adjusting the error term, which mainly includes standard deviation initialization, random error modeling, residual calculation, standard deviation correction, etc.

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

[0164]

[0165] Where: 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 total meter box node; X l,t is the power consumption of the lth total meter box node at time t; is the average power consumption of the lth total meter box node;

[0166] 2) Random error modeling: In each regression, the total table box regression result w l,t and the 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 total meter box node l regression power value 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] In the formula, σ new,bn and σ new,total They 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 constrain 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 a branch node-user association relationship matrix k with b rows and a columns bn , and 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] In the formula, F out is the F0 statistic coefficient threshold, and its value is 3.5;

[0197] 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. 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 The result is to update the i-th row element of the regression coefficient matrix. If the user node j has a candidate vector set A i , 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 total table box node, and construct the total table box node-branch node association relationship matrix k with c rows and b columns total , and initialize k with rows corresponding to the total table box nodes and columns corresponding to the branch nodes total is a zero matrix;

[0204] B l =[] (107)

[0205]

[0206] 2) The candidate vector set B of the total table box node 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] In the formula, i is the branch node, B l is the candidate set of 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 to which the total table box node l belongs; 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 the branch node i is added to the branch node subset to which the total table box node l belongs;

[0212] 4) According to the total table box node l candidate vector set B l The result 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 , 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 two-stage topological regression identification for low-voltage areas, as follows:

[0215] 1. Construction of the 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. The topological structure of the substation is shown in the figure. Figure 3(a) , 3(b) As shown;

[0217] 2. Configuration of node load

[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 Areas 1 and 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 in the figure, the internal topology identification results of the single area of ​​area 1 and area 2 are as follows Figure 7 , 8 As shown in the figure, the topological identification results of mixed multi-area areas 1 and 2 are as follows: Fig.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 Fig.11 As shown in Table 1, Fig.11 It can be seen that in a single station area, the Gaussian random error of the branch node power is set to 0.1-0.6, and 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%, and 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 the area under different Gaussian distribution errors

[0222]

[0223] Example 2

[0224] The present 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 comprises 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 areas as described above is implemented.

[0227] Through the description of the above embodiments, it can be clearly understood by 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 an existing processor, or by a dedicated processor used for this purpose or other purposes for an appropriate system, or by a hard-wired system. The embodiments of the present invention also include a non-transitory computer-readable storage medium, which includes a machine-readable medium for carrying or having a machine-executable instruction or data structure stored thereon; such a machine-readable medium can be any available medium that can be accessed by a general or special-purpose computer or other machine with a processor. For example, such a machine-readable medium can include RAM, ROM, EPROM, EEPROM, CD-ROM or other optical disk storage, disk storage or other magnetic storage device, 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 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 wiring, or wireless, or a combination of hard wiring and wireless), the connection is also considered a machine-readable medium.

[0228] So far, the technical solutions of the present invention have been described in conjunction with the preferred embodiments shown in the accompanying drawings. However, it is easy for those skilled in the art to understand that the protection scope of the present invention is obviously not limited to these specific embodiments. Without departing from the principle of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will fall within the protection scope of the present invention.

Claims

1. A two-stage topological regression identification method for low-voltage areas, characterized in that: 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 total 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) Perform the first-stage branch node-user node affiliation identification: establish a regression coefficient matrix between branch nodes and users based on 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, and construct a zero matrix with b rows and a columns, with rows corresponding to branch nodes and columns corresponding to user nodes. If branch node i is in 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 is A i , used to store the user to which the 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 its connected user nodes. Perform the user node variable selection process for the current branch node i, 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 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 previous prediction variance estimation coefficient PSE and the determination coefficient R 2 Greater than or equal to the user node to join the 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 previous F0 statistic 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 candidate variables that have not been screened. 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 the above steps (4)-(10) 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 affiliation relationship identification is performed.

2. The two-stage topological regression identification method for low-voltage areas according to claim 1 is characterized in that: The method for identifying the relationship between branch nodes and master 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 total meter box nodes, and the power consumption data of branch nodes, a regression coefficient matrix between branch nodes and total meter box nodes is established, and a zero matrix with c rows and b columns is constructed, with rows corresponding to total meter box nodes and columns corresponding to branch nodes. If total meter box node l is in a relationship with 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 total meter box node-branch node association relationship identification model, with minimizing the power difference between the total meter box node and its connected branch nodes as the objective function, perform the branch node variable selection process on the current total meter box node l, calculate the F0 statistic after variable screening, and select the branch 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 branch 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 branch node, join the candidate set A i The previous prediction variance estimation coefficient PSE 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 previous F0 statistic is not obtained, the current branch node variable is screened 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) Perform the above steps (3)-(9) for each branch node and finally output the regression coefficient matrix.

3. The two-stage topological regression identification method for low-voltage areas 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 average power value of branch node i at each time point; X l,t B is the power consumption of the total meter box node l at time t; l is the set of branch nodes associated with the master meter box node l; h is the number of branch nodes to which the master 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 total meter box node l; is the average power value of the total 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: In the formula, is the branch node determination coefficient, F 0,bn is the F0 statistic parameter of the branch node, χ is the residual sum of squares of the power of the current branch node, χ1 and χ2 are the residual sum of squares of the power of the branch node before and after the addition of significant user variables, 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 master box node.

4. The two-stage topological regression identification method for low-voltage areas 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: 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 total meter box node; X l,t is the power consumption of the lth total meter box node at time t; is the average power consumption of the lth total meter box node; 2) Random error modeling: In each regression, the total table box regression result w l,t and the 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 total meter box node l regression power value 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) In the formula, 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 areas 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 constrain 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 topological regression identification method for low-voltage areas 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 by the present 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 topological regression identification method for low-voltage areas 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 by the present 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 total meter box node l at time t, w l,t It is the total power of the branch nodes connected to the main meter box node l at time t.

8. The two-stage topological regression identification method for low-voltage areas 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 a branch node-user association relationship matrix k with b rows and a columns bn , and 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; In the formula, F out is the F0 statistic coefficient threshold, and its value 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 The result is to update the i-th row element of the regression coefficient matrix. If the user node j has a candidate vector set A i , the corresponding element in row i and column j is set to 1; 9. The two-stage topology regression identification method for low-voltage areas 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 total table box node, and construct the total table box node-branch node association relationship matrix k with c rows and b columns total , and initialize k with rows corresponding to the total table box nodes and columns corresponding to the branch nodes total is a zero matrix; B l ＝[] (33) 2) The candidate vector set B of the total table box node 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; In the formula, i is the branch node, B l is the candidate set of 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 to which node l belongs; 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 the branch node i is added to the branch node subset to which the total table box node l belongs; 4) According to the total table box node l candidate vector set B l The result 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 , 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 areas is implemented as described in any one of claims 1 to 7.

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