A method and system for combined estimation of power grid topology and impedance

Abstract

The application provides a method and system for combined estimation of power grid topology and impedance, comprising: abstracting the power grid into an undirected graph, collecting electrical energy parameters of each observable node, and constructing a data set; constructing a power flow calculation model with an impedance distance intersection matrix as a parameter, and introducing a physical information neural network (PINN) with physical constraints to estimate the impedance distance intersection matrix, and then obtaining an impedance distance matrix d ; introducing a node level concept according to the impedance distance matrix d , and adopting a hierarchical iterative grouping algorithm to jointly estimate the topology and line impedance of the power grid. The application only uses smart meters with actual terminal configurations, improves the estimation accuracy of the topology and impedance parameters of the power grid, and reduces the operation complexity of the algorithm.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of power grid modeling, in particular to a method and system for combined estimation of power grid topology and impedance. BACKGROUND

[0002] With large-scale deployment of renewable energy and other distributed energy, the operation state of distribution network is becoming more and more complex, and current distribution network needs efficient operation and control method. Topology and line parameter information is a prerequisite for advanced planning, operation and control such as power flow calculation and voltage control of distribution / micro-grid. However, unknown changes such as maintenance, repair and load balancing in distribution / micro-grid may cause great deviation between real topology and line parameters and records. Therefore, accurate topology identification and accurate line parameter estimation are crucial for distribution / micro-grid.

[0003] Traditional methods use additional measurement devices such as line current sensors or phasor measurement units to identify the topology and line parameters of the power grid. However, line current sensors or switch state detection are used to infer network topology. These methods can provide high accuracy, but due to the need to deploy additional hardware devices, the cost is high, and the installation location and maintenance optimization also require additional work. In addition, in large-scale low-voltage distribution networks, it is often difficult to obtain all the necessary sensor data, resulting in missing topology information for some nodes or lines, affecting the accurate modeling of the overall network.

[0004] The wide installation of smart meters promotes the development of new technologies for distribution / micro-grid topology and impedance estimation. In order to solve the above problems, existing technologies usually use inference methods based on smart meter data analysis. By analyzing the covariance matrix of voltage changes at all nodes or using correlation analysis of voltage and power to infer the relationship between nodes and network connections. However, smart meters are often installed only at some nodes, so the accuracy of the above analysis and inference results is not high. In addition, the existing combined estimation method of distribution / micro-grid topology and line impedance has the disadvantages of high computational complexity and low accuracy. SUMMARY

[0005] The technical problem to be solved by the present application is how to use the actual terminal configuration of the smart meter to improve the accuracy of estimating the topology and impedance parameters of the power grid.

[0006] The present application solves the above technical problems by the following technical means:

[0007] The present application provides a method for combined estimation of power grid topology and impedance, comprising:

[0008] S1, abstracting the power grid into an undirected graph, and collecting the electrical energy parameters of each observable node to build a data set;

[0009] S2. Construct a power flow calculation model with the impedance distance intersection matrix as a parameter, and introduce a physical information neural network (PINN) with physical constraints to estimate the impedance distance intersection matrix, thereby obtaining the impedance distance matrix. d ;

[0010] S3, based on the impedance distance matrix d The concept of node level is introduced, and a hierarchical iterative grouping algorithm is used to jointly estimate the topology and line impedance of the power grid.

[0011] Further, step S1 includes the following steps:

[0012] S11. Treat the power grid as an undirected graph. ;in, Represents the set of nodes in the power grid. Let the set of lines in the power grid be represented; Represents the set of observable nodes in the power grid. , Represents the power source node in the power grid. arrive This represents the observable nodes in the power grid, where N is the total number of observable nodes;

[0013] S12. Collect the power parameters of each observable node in the power grid, including voltage amplitude data. Active power data reactive power data ,in , , They represent the first Voltage amplitude, active power, and reactive power of each observable node;

[0014] S13. Construct the dataset, let ;in, , , , This represents the transpose of a matrix, and , Indicates the number of sampling points. Indicates the first The observable node at the th ... Voltage amplitude at each sampling point; ,in Indicates the first The observable node at the th ... Active power at each sampling point; , Indicates the first The observable node at the th ... Reactive power at each sampling point.

[0015] Further, the step S2 comprises the following steps:

[0016] S21, adopt formula (1)-formula (3) to describe the power flow calculation model of power grid:

[0017] (1)

[0018] (2)

[0019] (3)

[0020] Wherein, The voltage amplitude of node , The voltage amplitude of node ; The resistance and reactance of line between node And node ; Node Represents the upstream node of node , and node Represents the downstream node of node ; Respectively represent the active power and reactive power flowing out of node ; , Node set of all downstream nodes of node ; Substituting formula (1) and formula (2) into formula (3) can obtain formula (4):

[0021] (4)

[0022] The voltage square of power supply node and the voltage square difference of each node can be obtained by using formula (4) to list:

[0023] (5)

[0024] Wherein, Indicates Row 1 column vector, all elements in the vector are 1; ; ; ; Respectively are resistance distance intersection matrix and reactance distance intersection matrix, , Respectively represent the line set between node To And the line set between node To ;

[0025] S22, introducing a physical information loss term in the framework of deep neural network, estimating by a physical information neural network (PINN) matrix, obtaining matrix; the physical information neural network (PINN) is composed of 1 input layer, L hidden layers, 1 output layer and 1 clustering layer;

[0026] S23, according to the obtained matrix, obtaining the resistance distance matrix and the reactance distance matrix :

[0027] (9)

[0028] wherein, represents the sum of the resistance of all lines between and , and represents the sum of the reactance of all lines between and ; the resistance distance matrix and the reactance distance matrix are collectively represented by the impedance distance matrix d .

[0029] Further, the step S22 comprises the following steps:

[0030] S221, in the input layer, hidden layer and output layer of the PINN, the signal processing process is shown in formula (6):

[0031] (6)

[0032] wherein, is the weight matrix of the l layer, ; is the bias vector of the l layer; when , is the output of the layer, when , , is the activation function;

[0033] S222, the clustering layer of the PINN uses a density-based spatial clustering algorithm to cluster similar values in the output layer of the PINN together, and replaces these similar values with cluster centers; after the clustering process, the weighted average method of formula (7) is used to calculate the cluster center of each class as follows:

[0034] (7)

[0035] where C is a certain cluster; is the i-th data point in cluster C; is the weight of data point is inversely proportional to the distance of data point to the mean of data points in cluster C; , is a very small positive number to avoid division by zero error;

[0036] S223, calculate the loss function of the physical information neural network using formula (8) Loss ; the loss function Loss contains the prediction error of the neural network Loss1 and the error caused by the prediction result not satisfying the physical law Loss2 :

[0037] (8.a)

[0038] (8.b)

[0039] (8.c)

[0040] where is the weight of Loss1 and Loss2 in the total loss; is the impedance intersection distance matrix estimated by the physical information neural network; the gradient of the loss function with respect to , is calculated by the chain rule using the back propagation algorithm, and finally the calculated gradient is used to adjust the weights and biases of each layer;

[0041] S224, repeat steps S221 to S223 until the loss function Loss is less than the set threshold value.

[0042] Further, the step S3 comprises the following steps:

[0043] S31, input the set of observable nodes , and the impedance distance matrix composed of the impedance distances between these nodes d ;

[0044] S32, introduce the concept of node level, the node level of node is equal to the i-th column of the matrix ​​The number of unique elements in a row; for distribution / microgrids, the parent node has a node level one higher than the child node, and the two nodes in a pair of sibling nodes have the same node level; if the node levels of two nodes are... and If the difference is 1, then the node For nodes To form a candidate parent-child node pair; if the node levels of the two nodes are... and If they are equal, then the nodes For nodes Form candidate sibling node pairs;

[0045] S33. For any node pair in the candidate node pair set and Calculate the distance difference : ;in

[0046] S34, if , Then the node For nodes The parent node;

[0047] S35, if , Then the node With nodes For sibling nodes;

[0048] S36. Based on the judgment results of steps S33 and S34, construct a preliminary topological relationship; if the node With nodes If it is a parent-child node pair, then in the node With nodes Add an edge between them and update the set of lines. If node With nodes If they are sibling nodes, then they are nodes. With nodes Create a new parent node and at the nodes respectively and nodes ,node and nodes Add an edge between them and update the set of lines. ;

[0049] S37. If no new parent node is added. If a new parent node exists, proceed to step S38; Then update the impedance distance matrix. d ;for child nodes :

[0050] ,

[0051] for Non-child nodes :

[0052] ;

[0053] S38, Remove Node Set The node set will include nodes that already have parent-child or sibling relationships, and the newly added node will be merged into the node set. In the middle; when the set When the number of nodes in the set is greater than 2, repeat steps S33 to S38; when the set... When the number of nodes in the set is equal to 2, connect the two remaining nodes, the iteration process terminates, and the topology is restored; when the set... When the number of nodes in the algorithm equals 1, the iteration process terminates, and the topology is restored.

[0054] S39. According to the impedance distance matrix d Calculate the first Resistance of the line Reactance .

[0055] This invention also provides a system for joint estimation of power grid topology and impedance. The system operates using the above-described method and includes the following modules:

[0056] The dataset building module is used to abstract the power grid into an undirected graph and collect the power parameters of each observable node to build the dataset;

[0057] The impedance distance matrix calculation module is used to construct a power flow calculation model with the impedance distance intersection matrix as a parameter. It introduces a physical information neural network (PINN) with physical constraints to estimate the impedance distance intersection matrix, thereby obtaining the impedance distance matrix. d ;

[0058] Topology and impedance output module, used to output impedance distance matrix d The concept of node level is introduced, and a hierarchical iterative grouping algorithm is used to jointly estimate the topology and line impedance of the power grid.

[0059] The advantages of this invention are:

[0060] (1) This invention can use existing terminal smart meter devices to infer the topology and line parameters of low-voltage power distribution networks. It avoids the high cost of deploying additional sensors for each node, while improving the universality and operability of the system.

[0061] (2) The traditional deep learning method cannot effectively capture the relationship between the electrical energy parameters of the observable nodes and the impedance distance intersection matrix , and it is difficult to accurately estimate the values of and The matrix may produce solutions inconsistent with physical laws. The present application estimates the impedance distance intersection matrix using PINN, fully combines the nonlinear relationship of the electrical energy data between the observable nodes and considers the physical characteristics of the underlying power distribution network, providing an accurate impedance distance matrix for the subsequent iterative grouping algorithm.

[0062] (3) Since the impedance distance intersection matrix and is a symmetric matrix, and many elements in the matrix have equal values. Therefore, the present application introduces a clustering layer inside the PINN, and proposes a weighted average method to calculate the cluster center of each cluster. The introduction of the clustering layer not only provides accurate node levels for the subsequent algorithm, but also eliminates the influence of data noise on the impedance distance intersection matrix, improving the robustness of the method of the present application.

[0063] (4) Since the iterative grouping algorithm needs to judge the relationship between all node pairs when judging the topological relationship between nodes, the computational complexity is very high. In order to improve the computational efficiency of the iterative grouping algorithm, the present application introduces the concept of node level and proposes a hierarchical iterative grouping algorithm. This algorithm only needs to find the connection relationship between all nodes in the candidate sibling node pairs and the candidate parent-child node pairs, greatly reducing the computational complexity. BRIEF DESCRIPTION OF DRAWINGS

[0064] Figure 1 is a flowchart of a power grid topology and impedance joint estimation method according to an embodiment of the present application;

[0065] Figure 2 is a comparison diagram of simulation experimental data of estimating impedance and actual impedance according to an embodiment of the present application. DETAILED DESCRIPTION

[0066] In order to make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme in the embodiments of the present application will be described clearly and completely below, obviously, the described embodiments are part of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0067] Embodiment 1

[0068] This embodiment provides a method for joint estimation of power grid topology and impedance, such as... Figure 1 As shown, it includes:

[0069] S1. Abstract the power grid into an undirected graph and collect the power parameters of each observable node to construct a dataset. This includes the following implementation steps:

[0070] S11. Treat the power grid as an undirected graph. ;in, Represents the set of nodes in the power grid. Let the set of lines in the power grid be represented; Represents the set of observable nodes in the power grid. , Represents the power source node in the power grid. arrive This represents the observable nodes in the power grid, where N is the total number of observable nodes;

[0071] S12. Collect the power parameters of each observable node in the power grid, including voltage amplitude data. Active power data reactive power data ,in , , They represent the first Voltage amplitude, active power, and reactive power of each observable node;

[0072] S13. Construct the dataset, let ;in, , , , This represents the transpose of a matrix, and , Indicates the number of sampling points. Indicates the first The observable node at the th ... Voltage amplitude at each sampling point; ,in Indicates the first The observable node at the th ... Active power at each sampling point; , Indicates the first The observable node at the th ... Reactive power at each sampling point.

[0073] S2. Construct a power flow calculation model with the impedance distance intersection matrix as a parameter, and introduce a physical information neural network (PINN) with physical constraints to estimate the impedance distance intersection matrix, thereby obtaining the impedance distance matrix. d. Specifically comprising the following implementation steps:

[0074] S21, using formula (1) - formula (3) to describe the power flow calculation model of the power grid:

[0075] (1)

[0076] (2)

[0077] (3)

[0078] Wherein, The voltage amplitude of node , The voltage amplitude of node ; Respectively represent the resistance and reactance of the line between node And node ; Node Represents the upstream node of node , and node Represents the downstream node of node ; Respectively represent the active power and reactive power flowing out of node ; , Node set of all downstream nodes of node ; Substituting formula (1) and formula (2) into formula (3) can obtain formula (4):

[0079] (4)

[0080] Using formula (4) to list the voltage square of the power supply node and the voltage square difference of each node, formula (5) can be obtained:

[0081] (5)

[0082] Wherein, Indicates The row 1 column vector, all elements in the vector are 1; ; ; ; Respectively are the resistance distance intersection matrix and the reactance distance intersection matrix, , Respectively represent the line set between node To And the line set between node To ;

[0083] S22, introducing a physical information loss term in the framework of deep neural network, using a physical information neural network PINN to estimate matrix, obtaining matrix; the physical information neural network PINN is composed of 1 input layer, L hidden layers, 1 output layer and 1 clustering layer; specifically including the following implementation steps:

[0084] S221, the input layer, hidden layer and output layer of PINN, the signal processing process is shown in formula (6):

[0085] (6)

[0086] wherein, is the weight matrix of the i-th layer, l ; is the bias vector of the i-th layer; when l , is the output of the i-th layer, when , , is an activation function; S222, the clustering layer of PINN uses a density-based spatial clustering algorithm to cluster similar values in the output layer of PINN together, and replaces these similar values with cluster centers; after the clustering process, the weighted average method of formula (7) is used to calculate the cluster center of each class

[0087] as follows:

[0088] (7)

[0089] wherein, C is a certain cluster; is the i-th data point in the cluster C; is the weight of the data point , which is inversely proportional to the distance of the data point to the mean value of the data points in the cluster C, , is a very small positive number, used to avoid division by zero error;

[0090] S223, the loss function of the physical information neural network is calculated by formula (8) Loss ; the loss function Loss includes the prediction error of the neural network Loss1 and the error caused by the fact that the prediction result does not satisfy the physical law Loss2 :

[0091] (8.a)​​​​

[0092] (8.b)

[0093] (8.c)

[0094] wherein, is the weight of the total loss occupied by Loss1 and Loss2 ; is the impedance intersection distance matrix estimated by the physical information neural network; the loss function is calculated by the chain rule through the back propagation algorithm, and the gradient of , is calculated, and finally the weight and bias of each layer are adjusted according to the calculated gradient;

[0095] S224, repeating steps S221 to S223 until the loss function Loss is less than the set threshold value.

[0096] S23, according to the obtained matrix, the resistance distance matrix and the reactance distance matrix are obtained by formula (9):

[0097] (9)

[0098] wherein, represents the sum of the resistance of all lines between and , represents the sum of the reactance of all lines between and ; the resistance distance matrix and the reactance distance matrix are uniformly represented by the impedance distance matrix d .

[0099] S3, according to the impedance distance matrix d , the concept of node level is introduced, and the hierarchical iterative grouping algorithm is used to jointly estimate the topology and line impedance of the power grid. Specifically, the following implementation steps are included:

[0100] S31, input the observable node set , , and the impedance distance matrix d composed of the impedance distance between these nodes;

[0101] S32, in judging the exact relationship between nodes, in order to avoid listing all node pairs, resulting in high complexity of operation, need to make a preliminary screening of node pairs to get the candidate node pair set, subsequent only from the candidate node pair to judge the connection between nodes, can improve the operation efficiency of algorithm. Therefore, the concept of node level is introduced, and the node The node level of the node is equal to the number of unique elements in the first row of the matrix; for microgrid, the node level of the parent node is higher than that of the child node by 1, and the node level of the two nodes of the brother node pair is the same; if the node level of the two nodes and differs by 1, then the node is a candidate parent-child node pair with the node ; if the node level of the two nodes and is equal, then the node is a candidate brother node pair with the node ;

[0102] S33, for any node pair and in the candidate node pair set, calculate the distance difference : ; wherein

[0103] S34, if , , then the node is the parent node of the node ;

[0104] S35, if , , then the node and the node are a brother node pair;

[0105] S36, according to the judgment results of steps S33 and S34, construct a preliminary topological relationship; if the node and the node are a parent-child node pair, add an edge between the node and the node , and update the line set ; if the node and the node are a brother node pair, create a new parent node for the node and the node , and add an edge between the node and the node ,node and nodes Add an edge between them and update the set of lines. ;

[0106] S37. If no new parent node is added. Then proceed to step S38; if a new parent node exists. Then update the impedance distance matrix. d ;for child nodes :

[0107] ,

[0108] for Non-child nodes :

[0109] ;

[0110] S38, Remove Node Set The node set will include nodes that already have parent-child or sibling relationships, and the newly added node will be merged into the node set. In the middle; when the set When the number of nodes in the set is greater than 2, repeat steps S33 to S38; when the set... When the number of nodes in the set is equal to 2, connect the two remaining nodes, the iteration process terminates, and the topology is restored; when the set... When the number of nodes in the algorithm equals 1, the iteration process terminates, and the topology is restored.

[0111] S39. According to the impedance distance matrix d Calculate the first Resistance of the line Reactance .

[0112] This embodiment also demonstrates a simulation experiment of the above method on an IEEE 33-node network. To simulate power system operation measurement data, the dataset D used by the physical information neural network in the experiment was generated using MATPOWER. The PINN prediction results were input into iterative grouping for joint topology and impedance estimation, obtaining estimated resistance and reactance data for each edge. To quantify the performance of the method in this application, as... Figure 2 As shown, the mean percentage error (MAPE) is selected as the performance index for impedance calculation; the mean percentage error of impedance estimation in this embodiment is 0.6640%.

[0113] Example 2

[0114] The embodiment provides a system for combined estimation of power grid topology and impedance, which adopts the method described in the embodiment 1 during system operation, and comprises the following modules.

[0115] A data set construction module is used for abstracting the power grid into a non-directional graph, collecting the electric energy parameters of each observable node, and constructing a data set.

[0116] The data set construction module comprises the following units.

[0117] A graph abstraction unit is used for regarding the power grid as a non-directional graph. Wherein, represents a set of nodes in the power grid, represents a set of lines in the power grid; it is assumed that represents a set of observable nodes in the power grid, , represents a power supply node in the power grid, to represents an observable node in the power grid, and N represents the total number of observable nodes.

[0118] A data collection unit is used for collecting the electric energy parameters of each observable node in the power grid, including voltage amplitude data , active power data and reactive power data , wherein , respectively represents the voltage amplitude, the active power and the reactive power of the i-th observable node. , ,

[0119] A data set construction unit is used for constructing a data set, and ; wherein, , , , represents the transpose of a matrix, and , represents the number of sampling points, represents the voltage amplitude of the i-th observable node at the j-th sampling point. , wherein represents the active power of the i-th observable node at the j-th sampling point. , represents the reactive power of the i-th observable node at the j-th sampling point.

[0120] ​​​​​​​An impedance distance matrix calculation module is configured to construct a power flow calculation model with an impedance distance intersection matrix as a parameter, and introduce a physical information neural network (PINN) with physical constraints to estimate the impedance distance intersection matrix, and further obtain the impedance distance matrix d ;

[0121] The impedance distance matrix calculation module comprises the following units:

[0122] A power flow calculation model construction unit is configured to describe a power flow calculation model of the power grid by using formula (1)-formula (3):

[0123] (1)

[0124] (2)

[0125] (3)

[0126] wherein, denotes a voltage amplitude of a node ; denotes a voltage amplitude of a node ; denote a resistance and a reactance of a line between a node and a node , respectively; denote upstream nodes of a node and downstream nodes of a node , respectively; denote active power and reactive power flowing out of a node , respectively; , denote a node set of all downstream nodes of a node ; ;

[0127] (4)

[0128] A voltage square of a power source node and a voltage square difference of each node are listed by using formula (4), and formula (5) can be obtained:

[0129] (5)

[0130] wherein, denotes a row 1 column vector, and all elements in the vector are 1, ; ; ; ; denote a resistance distance intersection matrix and a reactance distance intersection matrix, respectively, , respectively represent a set of lines and a node between nodes a set of lines between nodes ;

[0131] The distance intersection matrix estimation unit is used for introducing a physical information loss term in the framework of a deep neural network, adopting a physical information neural network (PINN) to estimate matrix, obtaining matrix; the physical information neural network (PINN) is composed of 1 input layer, L hidden layers, 1 output layer and 1 clustering layer;

[0132] The distance intersection matrix estimation unit specifically performs the following process:

[0133] (1) In the input layer, the hidden layer and the output layer of the PINN, the signal processing process is as shown in formula (6):

[0134] (6)

[0135] wherein, W is a weight matrix of the i-th layer, ; l is a bias vector of the i-th layer; when i = L, y is an output of the i-th layer, when i = 1, x is an input of the i-th layer, , is an activation function; l (2) The clustering layer of the PINN adopts a density-based spatial clustering algorithm to cluster similar values in the output layer of the PINN together, and replace these similar values with clustering centers; after the clustering process, the clustering center of each class is calculated by using the weighted average method of formula (7) as follows: (7) wherein, C is a certain cluster; xi is the i-th data point in the cluster C; di is a distance between the data point xi and the cluster center of the cluster C; di is inversely proportional to the distance between the data point xi and the mean value of the data points in the cluster C, and di is a very small positive number for avoiding division by zero error;

[0136]

[0137] (7)

[0138] wherein, C is a certain cluster; xi is the i-th data point in the cluster C; di is a distance between the data point xi and the cluster center of the cluster C; di is inversely proportional to the distance between the data point xi and the mean value of the data points in the cluster C, and di is a very small positive number for avoiding division by zero error;

[0139] ​​​​​​​​​​​​​​​​(3) calculating the loss function of the physical information neural network by using formula (8) Loss ; the loss function Loss includes the prediction error of the neural network Loss1 and the error caused by the prediction result not satisfying the physical law Loss2 :

[0140] (8.a)

[0141] (8.b)

[0142] (8.c)

[0143] wherein, is the weight of the total loss Loss1 of and Loss2 ; is the impedance intersection distance matrix estimated by the physical information neural network; the gradient of the loss function with respect to , is calculated by using the chain rule through the back propagation algorithm, and finally the calculated gradient is used to adjust the weight and bias of each layer;

[0144] (4) repeating the above processes (1) to (3) until the loss function Loss is less than the set threshold value.

[0145] The distance matrix calculation unit is configured to obtain the resistance distance matrix and the reactance distance matrix by using formula (9) according to the obtained :

[0146] (9)

[0147] wherein, represents the sum of the resistance of all lines between and , and represents the sum of the reactance of all lines between and ; the resistance distance matrix and the reactance distance matrix are collectively represented by the impedance distance matrix d .

[0148] The topology and impedance output module is configured to introduce the concept of node level according to the impedance distance matrix d , and jointly estimate the topology and line impedance of the power grid by using a hierarchical iterative grouping algorithm.

[0149] The topology and impedance output module specifically performs the following process:

[0150] (1) Input the set of observable nodes , and the impedance distance matrix composed of the impedance distances between these nodes d ;

[0151] (2) Introduce the concept of node level, the node level of node is equal to the number of unique elements in the th row of the matrix; for a distribution / microgrid, the node level of a parent node is one higher than that of a child node, and the node levels of two sibling nodes are the same; if the node levels of two nodes differ by one, i.e., the node level of node is one higher than that of node , then node and node form a candidate parent-child node pair; if the node levels of two nodes are the same, i.e., the node level of node is equal to that of node , then node and node form a candidate sibling node pair;

[0152] (3) For any node pair and in the set of candidate node pairs, calculate the distance difference : ; where

[0153] (4) If , , then node is the parent node of node ;

[0154] (5) If , , then node and node are a sibling node pair;

[0155] (6) According to the results of steps S33 and S34, construct the preliminary topological relationship; if node and node are a parent-child node pair, add an edge between node and node , and update the line set ; if node and node are a sibling node pair, create a new parent node for node and node , and add an edge between node and node , and nodes ,node and nodes Add an edge between them and update the set of lines. ;

[0156] (7) If no new parent node is added Then proceed to step S38; if a new parent node exists. Then update the impedance distance matrix. d ;for child nodes :

[0157] ,

[0158] for Non-child nodes :

[0159] ;

[0160] (8) Remove the set of nodes The node set will include nodes that already have parent-child or sibling relationships, and the newly added node will be merged into the node set. In the middle; when the set When the number of nodes in the set is greater than 2, repeat steps S33 to S38; when the set... When the number of nodes in the set is equal to 2, connect the two remaining nodes, the iteration process terminates, and the topology is restored; when the set... When the number of nodes in the algorithm equals 1, the iteration process terminates, and the topology is restored.

[0161] (9) Based on the impedance distance matrix d Calculate the first Resistance of the line Reactance .

[0162] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for power grid topology and impedance joint estimation, characterized in that, Comprise: S1, the power grid is abstracted into an undirected graph, and the electrical energy parameters of each observable node are collected to construct a data set; comprising: S11. Consider the power grid as an undirected graph ; wherein, denotes a set of nodes in the power grid, denotes a set of lines in the power grid; let denotes a set of observable nodes in the power grid, , denotes a set of source nodes in the power grid, to denotes an observable node in the power grid, N is the total number of observable nodes; S12. Collect the power parameters of each observable node in the power grid, including voltage amplitude data. Active power data reactive power data ,in , , They represent the first Voltage amplitude, active power, and reactive power of each observable node; S13, constructing a data set, let ; wherein, , , , denotes the transpose of the matrix, and , denotes the number of sampling points, denotes the voltage amplitude of the first observable node at the first sampling point; , wherein denotes the active power of the first observable node at the first sampling point; , denotes the reactive power of the first observable node at the first sampling point; S2, construct a power flow calculation model with impedance distance intersection matrix as a parameter, and introduce a physical information neural network (PINN) with physical constraints to estimate the impedance distance intersection matrix, and then obtain the impedance distance matrix d ; comprising: S21, the power flow calculation model of the power grid is described by formula (1)-formula (3): (1) (2) (3) wherein denotes the voltage amplitude at node , denotes the voltage amplitude at node ; denote the resistance and the reactance of the line between node and node , respectively; node represents an upstream node of node , and node represents a downstream node of node ; represent the active power and the reactive power flowing out of node , respectively; , denotes the set of all downstream nodes of node ; substituting equations (1) and (2) into equation (3) gives equation (4): (4) The voltage square of the power supply node and the voltage square difference of each node can be obtained by formula (4): (5) wherein denotes a vector of size 1 x n with all elements equal to 1 ; ; ; ; are the resistance distance intersection matrix and the reactance distance intersection matrix, respectively, , represent the set of lines between nodes and and the set of lines between nodes and , respectively. S22, introducing a physical information loss term in the framework of a deep neural network, using a physical information neural network PINN to estimate matrix, obtaining matrix; the physical information neural network PINN is composed of 1 input layer, L hidden layers, 1 output layer and 1 clustering layer; S23. According to the obtained matrix, the resistance distance matrix is obtained by equation (9) and the reactance distance matrix : (9) wherein denotes the sum of the resistances of all lines between and denotes the sum of the reactances of all lines between ; the resistance distance matrix and the reactance distance matrix are unified in the impedance distance matrix d denoted by S3、According to the impedance distance matrix d , the node level concept is introduced, and the hierarchical iterative grouping algorithm is used to jointly estimate the topology and line impedance of the power grid.

2. The method of grid topology and impedance joint estimation according to claim 1, characterized in that, The step S22 comprises the following steps: S221, in the input layer, hidden layer and output layer of PINN, the signal processing process is as shown in formula (6): (6) wherein, is the weight matrix of the l layer, ; is the bias vector of the l layer; when , is the output of the layer, when , , is the activation function; S222、The clustering layer of the PINN adopts a density-based spatial clustering algorithm to cluster similar values in the results of the output layer of the PINN together, and replace these similar values with cluster centers; after the clustering process is completed, the cluster centers of each class are calculated by using the weighted average method of formula (7) As follows: (7) where C is some cluster; is the i-th data point in cluster C; is the i-th data point in cluster C; is the weight of data point is inversely proportional to the distance of data point to the mean of data points in cluster C; , is a very small positive number to avoid division by zero error;​ S223, calculating the loss function of the physical information neural network by using formula (8) Loss ; loss function Loss prediction error containing the neural network Loss1 error caused by the prediction result not satisfying the physical law Loss2 : (8.a) (8.b) (8.c) wherein, is Loss1 and Loss2 a weight of the total loss; is an impedance intersection distance matrix estimated by the physical information neural network; the gradient of the loss function with respect to , is calculated by using the chain rule through the backpropagation algorithm, and finally the weights and biases of each layer are adjusted according to the calculated gradient; S224, repeatedly performing steps S221 to S223 until the loss function Loss is less than a set threshold.

3. The method of grid topology and impedance joint estimation according to claim 2, characterized in that, The step S3 comprises the following steps: S31, input observable node set , , and the impedance distance matrix composed of the impedance distances between these nodes d ; S32. Introduce the concept of node levels, nodes... Node level equal The first in the matrix The number of unique elements in a row; for distribution / microgrids, the parent node has a node level one higher than the child node, and the two nodes in a pair of sibling nodes have the same node level; if the node levels of two nodes are... and If the difference is 1, then the node For nodes To form a candidate parent-child node pair; if the node levels of the two nodes are... and If they are equal, then the nodes For nodes Form candidate sibling node pairs; S33, for any one node pair in the candidate node pair set and , calculate the distance difference : ; wherein S34, if , then node is the parent node of node ; S35、if , then the nodes and the nodes are sibling pairs; S36, constructing a preliminary topology relationship according to the judgment results of step S33 and step S34; if the node and the node are a parent-child node pair, then adding an edge between the node and the node , and updating the line set ; if the node and the node are a brother node pair, then creating a new parent node for the node and the node , and adding an edge between the node and the node , the node and the node respectively, and updating the line set ; S37, if there is no new parent node , then go to step S38; if there is a new parent node , then update the impedance distance matrix d ; for the child nodes of the node : ， For non-child nodes of ； S38, remove the node set nodes which have established parent-child or sibling relationship, and incorporate the new node into the node set ; when the number of nodes in the set is greater than 2, steps S33 to S38 are executed in a loop; when the number of nodes in the set is equal to 2, the two remaining nodes are connected, and the iteration process is terminated, completing the recovery of the topology structure; when the number of nodes in the set is equal to 1, the iteration process is terminated, completing the recovery of the topology structure; S39. The impedance distance matrix is calculated d The first The resistance of the line The reactance .

4. A system for joint estimation of power grid topology and impedance, characterized in that, Comprise the following modules: The data set construction module is used for abstracting the power grid into an undirected graph, collecting the electrical energy parameters of each observable node, and constructing a data set; Comprise the following units: a graph abstraction unit for viewing the power grid as an undirected graph ; wherein denotes a set of nodes in the power grid, denotes a set of lines in the power grid; let denotes a set of observable nodes in the power grid, , denotes a set of source nodes in the power grid, to denotes an observable node in the power grid, N being the total number of observable nodes; The data acquisition unit is used to collect electrical parameters from each observable node in the power grid, including voltage amplitude data. Active power data reactive power data ,in , , They represent the first Voltage amplitude, active power, and reactive power of each observable node; a data set construction unit configured to construct a data set, let ; wherein, , , , denotes the transpose of a matrix, and , denotes the number of sampling points, denotes the voltage amplitude of the th observable node at the th sampling point; , wherein denotes the active power of the th observable node at the th sampling point; , denotes the reactive power of the th observable node at the th sampling point; The impedance distance matrix calculation module is configured to construct a power flow calculation model with an impedance distance intersection matrix as a parameter, and introduce a physical information neural network (PINN) with physical constraints to estimate the impedance distance intersection matrix, and then obtain the impedance distance matrix d ; comprising the following units: The power flow calculation model construction unit is used for describing the power flow calculation model of the power grid by formula (1)-formula (3): (1) (2) (3) wherein denotes the voltage amplitude at node , denotes the voltage amplitude at node ; denote the resistance and the reactance of the line between node and node , respectively; node represents an upstream node of node , and node represents a downstream node of node ; denote the active power and the reactive power flowing out of node , respectively; , denotes the set of all downstream nodes of node ; substituting equations (1) and (2) into equation (3) gives equation (4): (4) The voltage square of the power supply node and the voltage square difference of each node can be obtained by formula (4): (5) wherein, denotes a vector of size 1 x n with all elements equal to 1 ; ; ; ; are the resistance distance intersection matrix and the reactance distance intersection matrix, respectively, , represent the set of lines between nodes and and the set of lines between nodes and , respectively. The distance intersection matrix estimation unit is used for introducing a physical information loss term in a framework of a deep neural network, and a physical information neural network (PINN) is used for estimation matrix, obtain matrix; the physical information neural network (PINN) is composed of 1 input layer, L hidden layers, 1 output layer and 1 clustering layer a distance matrix calculation unit for calculating a distance matrix from the obtained matrix, the resistance distance matrix and the reactance distance matrix are obtained by formula (9) and formula (10) : (9) wherein denotes the sum of the resistances of all lines between and denotes the sum of the reactances of all lines between and the resistance distance matrix and the reactance distance matrix d are unified in the impedance distance matrix Topology and impedance output module for determining topology and impedance distance matrix d The hierarchical iteration grouping algorithm is adopted to jointly estimate the topology and line impedance of the power grid by introducing the concept of node level.

5. The system for combined estimation of grid topology and impedance according to claim 4, characterized in that, The distance intersection matrix estimation unit specifically executes the process as follows: (1) in the input layer, hidden layer and output layer of PINN, the signal processing process is as shown in formula (6): (6) wherein, is the weight matrix of the l layer, ; is the bias vector of the l layer; when , is the output of the layer, when , , is an activation function; (2) The clustering layer of PINN adopts a density-based spatial clustering algorithm to cluster similar values in the output layer of PINN together and replace these similar values with a cluster center; after the clustering process, the cluster center of each class is calculated by using the weighted average method of formula (7) As follows: (7) where C is some cluster; is the mean of the data points in cluster C; is the weight of data point is the distance of data point to the mean of the data points in cluster C is inversely proportional to the distance , , is a very small positive number to avoid division by zero error; (3) calculating the loss function of the physical information neural network by using formula (8) Loss ; the loss function Loss comprises a prediction error of the neural network Loss1 an error caused by the prediction result not satisfying the physical law Loss2 : (8.a) (8.b) (8.c) wherein, is Loss1 and Loss2 a weight in the total loss; is the impedance intersection distance matrix estimated by the physical information neural network; the gradient of the loss function with respect to , is calculated by using the chain rule through the backpropagation algorithm, and finally the weights and biases of each layer are adjusted according to the calculated gradient; (4) repeat the above processes (1) to (3) until the loss function Loss is less than a set threshold.

6. The system for combined estimation of grid topology and impedance according to claim 5, characterized in that, The topology and impedance output module specifically executes the process as follows: (1) input a set of observable nodes , , and an impedance distance matrix of impedance distances between these nodes d ; (2) Introduce the concept of node level, node Node level equal The first in the matrix The number of unique elements in a row; for distribution / microgrids, the parent node has a node level one higher than the child node, and the two nodes in a pair of sibling nodes have the same node level; if the node levels of two nodes are... and If the difference is 1, then the node For nodes To form a candidate parent-child node pair; if the node levels of the two nodes are... and If they are equal, then the nodes For nodes Form candidate sibling node pairs; (3) For any node pair in the candidate node pair set and , calculate the distance difference : ; wherein (4) If , , then node is the parent of node ; (5) If , , then nodes and nodes are sibling pairs; (6) According to the judging results of step S33 and step S34, a preliminary topological relationship is constructed; if the node and the node are a parent-child node pair, an edge is added between the node and the node , and the line set is updated; if the node and the node are a brother node pair, a new parent node is created for the node and the node , and an edge is added between the node and the node , the node and the node , and the line set is updated; (7) If there is no new parent node , go to step S38; if there is a new parent node , update the impedance distance matrix d ; for the child nodes of : ， For non-child nodes of ； (8) removing the node set nodes having established parent-child or sibling relationship, and incorporating the new node into the node set ; when the number of nodes in the node set is greater than 2, steps S33 to S38 are executed in a loop; when the number of nodes in the node set is equal to 2, the two remaining nodes are connected, and the iteration process is terminated, completing the recovery of the topology structure; when the number of nodes in the node set is equal to 1, the iteration process is terminated, completing the recovery of the topology structure; (9) According to the impedance distance matrix d The resistance , reactance of the line of the i-th section is calculated .

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