CN113341275B - Method for positioning single-phase earth fault of power distribution network - Google Patents

Method for positioning single-phase earth fault of power distribution network Download PDF

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CN113341275B
CN113341275B CN202110648837.7A CN202110648837A CN113341275B CN 113341275 B CN113341275 B CN 113341275B CN 202110648837 A CN202110648837 A CN 202110648837A CN 113341275 B CN113341275 B CN 113341275B
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power distribution
fault
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CN113341275A (en
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党建
闫运江
贾嵘
王晓卫
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Shaanxi Tianhong Bochen Electric Power Construction Co.,Ltd.
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Xian University of Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/08—Locating faults in cables, transmission lines, or networks
    • G01R31/081—Locating faults in cables, transmission lines, or networks according to type of conductors
    • G01R31/086—Locating faults in cables, transmission lines, or networks according to type of conductors in power transmission or distribution networks, i.e. with interconnected conductors
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/08—Locating faults in cables, transmission lines, or networks
    • G01R31/088—Aspects of digital computing
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/23—Clustering techniques
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/70—Smart grids as climate change mitigation technology in the energy generation sector
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/22—Flexible AC transmission systems [FACTS] or power factor or reactive power compensating or correcting units

Abstract

The invention discloses a method for positioning a single-phase earth fault of a power distribution network, which comprises the steps of starting to allocate D-PMU at intervals from a head-end node of a power distribution network model, and calculating a three-phase current sequence of nodes which are not allocated with the D-PMU and a standard deviation of fault phase current of each node in a time window when a fault occurs; and establishing a power distribution network graph model on a graph database according to a power distribution network model topological structure, operating the IPLM after each edge obtains corresponding weight, finally, inquiring a first vertex of the fault section from top to bottom on the basis of an IPLM operation result, and determining an accurate fault section according to the weight ratio of the vertex to the previous vertex. According to the method for positioning the single-phase earth fault of the power distribution network, disclosed by the invention, the rapid and accurate positioning of the single-phase earth fault is realized only under the condition that half nodes in a power distribution network model are provided with the D-PMU by utilizing a graph calculation theory and a graph database platform, and a fault section can still be accurately positioned when partial D-PMU loses time synchronism.

Description

Method for positioning single-phase earth fault of power distribution network
Technical Field
The invention belongs to the technical field of fault location in a power grid, and particularly relates to a method for locating a single-phase earth fault of a power distribution network.
Background
The power distribution network in China is characterized by long power supply radius, multiple line branches and incomplete measurement system. Accurately locating the fault section is an important condition for quickly removing the fault of the power distribution network. The single-phase earth fault is the fault which occurs most frequently among all faults and occupies about 80% of all faults. The single-phase earth fault has the characteristics of unobvious fault characteristics, easiness in noise interference and the like, so that the single-phase earth fault is difficult to accurately position when occurring.
At present, the methods for positioning the faults of the power distribution network mainly comprise an impedance method, a traveling wave method, an injection signal method and a wide area measurement information method. The power distribution network fault positioning method based on the impedance method is very sensitive to excessive resistance and fault phase angle of faults, and along with the fact that the network structure of the power distribution network is more and more complex and the line parameters are inaccurate, the accuracy of the impedance method is greatly influenced. The power distribution network fault positioning method based on the traveling wave method is not influenced by a system operation mode and fault resistance, but is easily influenced by power distribution network line branches. The signal injection method, unlike the other three methods, requires locating the location of the fault by injecting a signal into the distribution network, and such methods require additional equipment and additional operations, adding potential risks and costs. With the development of a wide area measurement technology, the volume of a Phasor Measurement Unit (PMU) is gradually reduced, the cost is reduced, the state estimation of a power distribution network is more reliable, more and more students adopt wide area measurement information to carry out a fault positioning method of the power distribution network, and the invention relates to a power distribution network fault power grid method based on a wide area measurement information method.
At present, power distribution network fault location research based on wide area information mostly depends on a large number of high-precision measurement units such as D-PMUs or uPMUs arranged in a power distribution network model. Although the results of such researches can accurately locate the fault section of the power distribution network, two important defects still exist, one is that the cost is greatly increased by arranging a large number of measuring units on a power distribution network model, and the feasibility is not economically provided, and the researches mainly rely on wide-area measurement information and do not fully utilize the topological structure information of the power distribution network. Some students perform power distribution network fault location research only based on the configuration of a D-PMU at the head end and the tail end of a power distribution network model, and the research can locate two-phase short-circuit faults and two-phase short-circuit grounding faults and cannot accurately locate single-phase grounding faults.
Disclosure of Invention
The invention aims to provide a method for positioning a single-phase earth fault of a power distribution network, which can realize the rapid and accurate positioning of the single-phase earth fault under the condition that D-PMU is configured on half nodes in a power distribution network model.
The technical scheme adopted by the invention is that the method for positioning the single-phase earth fault of the power distribution network is implemented according to the following steps:
step 1, establishing a power distribution network model according to a topological structure of a power distribution network, configuring D-PMUs on nodes of the power distribution network model at intervals, and measuring three-phase current, three-phase voltage, zero-sequence current and zero-sequence voltage of corresponding nodes;
step 2, calculating three-phase voltage, three-phase current, zero-sequence current and zero-sequence voltage of a node which is not configured with the D-PMU;
step 3, calculating the fault graph weight S 'of each node in one time window based on the three-phase current of each node' i,k ；
Step 4, establishing a graph model of the power distribution network on a graph database according to the topological structure of the power distribution network, and calculating edge weights formed by two adjacent nodes in the graph model of the power distribution network;
step 5, operating the IPLM on a graph model of the power distribution network to obtain a plurality of communities;
step 6, searching from top to bottom based on the operation result of the IPLM, and determining a vertex M of a first fault section;
and 7, respectively accessing a front vertex L and a rear vertex N of the vertex M, calculating a failure graph weight ratio theta of the front vertex L and the rear vertex N in a time window, and judging another node of the failure section according to the size of the theta so as to locate the failure section.
The invention is also characterized in that:
the specific process of configuring the nodes of the D-PMU on the distribution network model at intervals in the step 1 is as follows: and numbering the model nodes of the power distribution network, wherein the end nodes are not configured with the D-PMU, and only one node in any two connected nodes in the rest nodes is configured with the D-PMU.
The specific process of calculating the three-phase voltage and the three-phase current of the node which is not provided with the D-PMU in the step 2 is as follows:
judging whether the node i is a terminal node, if so, the node i passes through a forward node h and an active load P of the node i i Reactive load Q i Solving the three-phase voltage of the node i:
Figure BDA0003110281000000031
wherein Z hi Represents the line impedance between node h and node i, and J represents an imaginary number;
if the node i is not the tail end node, the node i calculates the three-phase voltage of the node i through a backward node j;
Figure BDA0003110281000000032
wherein Z hi Representing the line impedance between node h and node i
The node i obtains three-phase current through a forward node h;
Figure BDA0003110281000000033
k＝a,b,c；
then the zero sequence current of node i without D-PMU is represented as:
Figure BDA0003110281000000041
then the zero sequence voltage of node i without D-PMU is expressed as:
Figure BDA0003110281000000042
the time window T in step 3 is set to 0.05s.
The specific process of the step 3 is as follows:
step 3.1, extracting a three-phase current sequence of each node in a time window;
step 3.2, calculating the standard deviation S of each phase current sequence of each node i,k I is the node number and k is the mark of the phase;
Figure BDA0003110281000000043
wherein, t 0 F is the frequency of D-PMU, I t,i,k The magnitude of the fault phase current at time t for node i,
Figure BDA0003110281000000044
the average value of the three-phase current amplitude values in a time window T is the node i, and k = a, b, c;
step 3.3, compare S i,a ,S i,b ,S i,c If one value is far larger than the other two values, the phase is a fault phase, and k of all nodes is the phase;
step 3.4, calculating the phase difference delta theta between the zero sequence current and the zero sequence voltage of each node, and processing the delta theta by using an integer function;
Figure BDA0003110281000000045
Figure BDA0003110281000000046
step 3.5, calculating the fault graph weight S 'of each node' i,k Comprises the following steps:
Figure BDA0003110281000000051
the specific process of the step 4 is as follows:
step 4.1, importing the topological structure of the power distribution network into a graph, modeling nodes as vertexes in a graph model, modeling lines as edges in the graph model, and establishing the graph model of the power distribution network;
step 4.2, judging whether the D-PMU loses time synchronism, wherein the judgment formula is as follows:
Figure BDA0003110281000000052
k i =1, where j is a vertex adjacent to i and if the vertex i satisfies the three conditions at the same time, the D-PMU of the vertex i loses time synchronism;
4.3, if the D-PMU of the vertex i loses time synchronism, the failure graph weight of the vertex i is used for taking the average value of the failure graph weights of the adjacent vertexes;
step 4.5, in any two adjacent vertexes in the graph model of the power distribution network, the vertex of the outgoing current is an upstream vertex, the vertex of the incoming current is a downstream vertex, the edge between a certain vertex and the upstream vertex is an upstream edge, all vertexes in the graph model of the power distribution network are accessed, and the standard deviation S of each vertex is calculated j,k Attribute w assigned to upstream edge ij Obtaining an edge weight;
the specific process of the step 5 is as follows:
step 5.1, inputting a graph model of the power distribution network into the IPLM;
step 5.2, accessing all vertexes in the graph model of the power distribution network in parallel, and calculating modularity gain delta Q caused by the fact that all vertexes move to adjacent vertex communities respectively, wherein a modularity gain calculation formula is as follows:
Figure BDA0003110281000000053
therein, sigma tot k i Is the community with vertex c j The sum of all connected edge weights; k is a radical of i,in Is vertex i and community c j The weight of the edges that are connected to each other,
Figure BDA0003110281000000054
step 5.3, changing community attribution of each vertex, moving each vertex into the maximum modularity gain community, if all modularity gains of a certain vertex are negative, keeping the community attribute of each vertex in an original state before changing the community attribution of each vertex, and otherwise, updating the community attribution of the vertex;
step 5.4, judging whether the community attribution of the vertex is updated in the step 5.3, if so, returning to the step 5.2, otherwise, terminating the iteration;
step 5.5, taking communities as a unit, accessing all communities in parallel, calculating modularity gain delta Q of all vertexes of one community moving to adjacent communities respectively, wherein a weight calculation formula of a connection edge between communities is as follows:
Figure BDA0003110281000000061
wherein the content of the first and second substances,
Figure BDA0003110281000000062
is composed of community c i And community c j The weights of the two representative community edges; w is a ij Is a connection community c i And community c j The weight of the edge of the middle vertex;
step 5.6, merging communities when the adjacent communities meet the constraint condition of the following formula:
ΔQ＞0or∑S′ i,k ＝∑|S′ i,k |,v i ∈C i
and 5.7, judging whether community combination exists or not, if so, returning to the step 5.4, and otherwise, finishing the operation of the IPLM.
The specific process of the step 6 is as follows:
step 6.1, according to the direction of the outgoing current, accessing a head end vertex of the power distribution network model, reading a community ID of the head end vertex, and assigning the community ID to a global variable x;
step 6.2, accessing the last vertex with the community ID of x, wherein the last vertex is marked as a vertex M;
6.3, accessing a downstream vertex N connected with the vertex M;
6.4, judging whether the weight of the fault graph of the vertex N is greater than 0;
step 6.5, if S' N,k >0, assigning the ID of the community where the downstream vertex N is located to x, and returning to the step 6.3 until S 'appears' N,k And outputting the ID of the vertex M to determine that the vertex M is one vertex of the fault section.
Step 7.1, judging whether the vertex M is configured with the D-PMU, and if so, directly outputting a fault section between nodes corresponding to the vertex M and the rear vertex N;
7.2, if the vertex M is not configured with the D-PMU, accessing a front vertex L and a rear vertex N of the vertex M, and calculating a failure graph weight ratio theta of the front vertex L and the vertex M;
Figure BDA0003110281000000071
and 7.3, if theta is less than or equal to 0.9, the other vertex of the fault section is N, otherwise, the vertex is L, and nodes corresponding to the two vertexes of the fault section are output.
The invention has the beneficial effects that:
(1) The method for positioning the single-phase earth fault of the power distribution network is not influenced by the fault occurrence position and the fault resistance.
(2) The method combines the topological structure information and the wide area measurement information of the power distribution network, and clusters the graph model by using the IPLM, thereby reducing the retrieval times and improving the calculation speed.
(3) Compared with most power distribution network fault positioning methods, the method has the advantages that the D-PMU is only configured on half of the nodes in the power distribution network model, and the cost is reduced.
(4) The invention has stronger robustness, and can still accurately position the fault under the condition that part of the measurement units in the network fail.
Drawings
FIG. 1 is a diagrammatic representation of a graphical model of a power distribution network employed in an embodiment of the present invention;
FIG. 2 is an initial community distribution of the Luwen algorithm;
FIG. 3 is the first stage of the Luwenn algorithm;
FIG. 4 is the second phase of the Luwenn algorithm;
FIG. 5 is a flow of power distribution network graph model modeling;
FIG. 6 is a modified IEEE 33 node model;
FIG. 7 is a comparison of PLM and IPLM clustering results;
FIG. 8 (a) is a phase current change at the head end node;
FIG. 8 (b) is a phase current change at the end node;
FIG. 9 is a comparison of the number of iterations of the four methods under normal conditions;
fig. 10 is a comparison of the number of iterations of the four methods when the partial D-PMU loses time synchronization.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The power distribution network fault positioning method disclosed by the invention applies graph calculation and an improved luovain algorithm, establishes a graph model of the power distribution network based on a topological structure of the power distribution network, realizes quick and accurate positioning of the single-phase earth fault under the condition that only half nodes in the power distribution network model are required to be configured with the D-PMU, avoids the positioning result from falling into local optimization, has strong robustness, and can still accurately position a fault section when partial D-PMU loses time synchronism.
The invention discloses a method for positioning a single-phase earth fault of a power distribution network, which is implemented according to the following steps:
step 1, establishing a power distribution network model according to a topological structure of a power distribution network, configuring D-PMUs on nodes of the power distribution network model at intervals, and measuring three-phase current, three-phase voltage, zero-sequence current and zero-sequence voltage of corresponding nodes;
the specific process of configuring the nodes of the D-PMU on the distribution network model at intervals in the step 1 is as follows: the nodes of the power distribution network model are numbered, the end nodes are not configured with the D-PMU, and only one node in any two connected nodes in the rest nodes is configured with the D-PMU.
Step 2, calculating three-phase voltage, three-phase current, zero-sequence current and zero-sequence voltage of a node which is not configured with the D-PMU;
the specific process of calculating the three-phase voltage and the three-phase current of the node which is not provided with the D-PMU in the step 2 is as follows:
judging whether the node i is a terminal node, if so, the node i passes through a forward node h and an active load P i Reactive load Q i Solving the three-phase voltage of the node i:
Figure BDA0003110281000000091
wherein Z hi Represents the line impedance between node h and node i, and J represents an imaginary number;
if the node i is not the tail end node, the node i calculates the three-phase voltage of the node i through a backward node j;
Figure BDA0003110281000000092
wherein Z hi Representing the line impedance between node h and node i
The node i obtains three-phase current through a forward node h;
Figure BDA0003110281000000093
k＝a,b,c；
then the zero sequence current of node i without D-PMU is represented as:
Figure BDA0003110281000000094
then the zero sequence voltage of node i without D-PMU is expressed as:
Figure BDA0003110281000000095
step 3, calculating the fault graph weight S 'of each node in a time window based on the three-phase current of each node' i,k (ii) a The time window T is set to 0.05s.
The specific process of the step 3 is as follows:
step 3.1, extracting a three-phase current sequence of each node in a time window;
step 3.2, calculating the standard deviation S of each phase current sequence of each node i,k I is the node number and k is the mark of the phase;
Figure BDA0003110281000000101
wherein, t 0 F is the frequency of D-PMU, I t,i,k The magnitude of the fault phase current at time t for node i,
Figure BDA0003110281000000102
the average value of the three-phase current amplitude values in a time window T is the node i, and k = a, b, c;
step 3.3, compare S i,a ,S i,b ,S i,c If one value is far larger than the other two values, the phase is a fault phase, and k of all nodes is the phase;
step 3.4, calculating the phase difference delta theta between the zero sequence current and the zero sequence voltage of each node, and processing the delta theta by using an integer function;
Figure BDA0003110281000000103
Figure BDA0003110281000000104
step 3.5, calculating the fault graph weight S 'of each node' i,k Comprises the following steps:
S′ i,k ＝S i,k ·σ i (Δθ)。
step 4, establishing a graph model of the power distribution network on a graph database according to the topological structure of the power distribution network, and calculating edge weights formed by two adjacent nodes in the graph model of the power distribution network;
the specific process of the step 4 is as follows:
step 4.1, importing the topological structure of the power distribution network into a graph, modeling nodes as vertexes in a graph model, modeling lines as edges in the graph model, and establishing the graph model of the power distribution network;
step 4.2, judging whether the D-PMU loses time synchronism, wherein the judgment formula is as follows:
Figure BDA0003110281000000111
k i =1, where j is a vertex adjacent to i and if the vertex i satisfies the three conditions at the same time, the D-PMU of the vertex i loses time synchronism;
4.3, if the D-PMU of the vertex i loses time synchronism, the failure graph weight of the vertex i is used for taking the average value of the failure graph weights of the adjacent vertexes;
step 4.5, in any two adjacent vertexes in the graph model of the power distribution network, the vertex of the outgoing current is an upstream vertex, the vertex of the incoming current is a downstream vertex, the edge between a certain vertex and the upstream vertex is an upstream edge, all vertexes in the graph model of the power distribution network are accessed, and the standard deviation S of each vertex is calculated j,k Attribute w assigned to upstream edge ij In (3), an edge weight is obtained.
Step 5, operating the IPLM on a graph model of the power distribution network to obtain a plurality of communities;
the specific process of the step 5 is as follows:
step 5.1, inputting a graph model of the power distribution network into the IPLM;
step 5.2, accessing all vertexes in the graph model of the power distribution network in parallel, and calculating modularity gain delta Q caused by the fact that all vertexes move to adjacent vertex communities respectively, wherein a modularity gain calculation formula is as follows:
Figure BDA0003110281000000112
therein, sigma tot k i Is a company with vertexesRegion c j The sum of all connected edge weights; k is a radical of i,in Is vertex i and community c j The weight of the edges that are connected to each other,
Figure BDA0003110281000000113
step 5.3, changing community attribution of each vertex, moving each vertex into the maximum modularity gain community, if all modularity gains of a certain vertex are negative, keeping the community attribute of each vertex in an original state before changing the community attribution of each vertex, and otherwise, updating the community attribution of the vertex;
step 5.4, judging whether the community attribution of the vertex is updated in the step 5.3, if so, returning to the step 5.2, otherwise, terminating the iteration;
step 5.5, taking communities as a unit, accessing all communities in parallel, calculating modularity gain delta Q of all vertexes of one community moving to adjacent communities respectively, wherein a weight calculation formula of a connection edge between communities is as follows:
Figure BDA0003110281000000121
wherein the content of the first and second substances,
Figure BDA0003110281000000122
is made by community c i And community c j The weights of the two representative community edges; w is a ij Is a connection community c i And community c j The weight of the edge of the middle vertex;
step 5.6, merging communities when the adjacent communities meet the constraint condition of the following formula:
ΔQ＞0or∑S′ i,k ＝∑|S′ i,k |,v i ∈C i
and 5.7, judging whether community combination exists or not, if so, returning to the step 5.4, and otherwise, finishing the operation of the IPLM.
Step 6, searching from top to bottom based on the operation result of the IPLM, and determining the node M of the first fault section;
the specific process of the step 6 is as follows:
6.1, according to the direction of the outgoing current, accessing a head end vertex of the power distribution network model, reading a community ID of the head end vertex, and assigning the community ID to a global variable x;
step 6.2, accessing the last vertex with the community ID of x, wherein the last vertex is marked as a vertex M;
6.3, accessing a downstream vertex N connected with the vertex M;
6.4, judging whether the weight of the fault graph of the vertex N is greater than 0;
step 6.5, if S' N,k >0, assigning the ID of the community where the downstream vertex N is located to x, and returning to the step 6.3 until S 'appears' N,k And outputting the ID of the vertex M to determine that the vertex M is one vertex of the fault section.
The principle of determining vertex M as one vertex of the failed segment is: the vertex before the fault point on the fault branch has a positive fault graph weight, and the fault graph weights of the other vertexes are all smaller than zero. Based on the method, the query is carried out by taking a community as a unit (the query speed is improved), the main purpose is to find the top point with the weight of the last fault graph on the fault branch larger than zero,
and 7, respectively accessing a front vertex L and a rear vertex N of the vertex M, calculating a failure graph weight ratio theta of the front vertex L and the rear vertex N in a time window, and judging another node of the failure section according to the size of the theta so as to locate the failure section.
Step 7, because half of the nodes on the power distribution network model in the present invention are not configured with D-PMU, the three-phase currents of these nodes are calculated from the current-voltage information of the front and rear nodes, if the fault point is located in front of a certain node not configured with D-PMU, the current of this node will also exhibit the characteristic of fault under the influence of the voltage-current value of the upstream node, which enables us to locate the specific section of fault, therefore, further judgment needs to be made on the basis of step 6, and the specific process is:
step 7.1, judging whether the D-PMU is configured on the vertex M, and if so, directly outputting a fault section between nodes corresponding to the vertex M and the rear vertex N;
7.2, if the vertex M is not configured with the D-PMU, accessing a front vertex L and a rear vertex N of the vertex M, and calculating a failure graph weight ratio theta of the front vertex L and the vertex M;
Figure BDA0003110281000000131
and 7.3, if theta is less than or equal to 0.9, the other vertex of the fault section is N, otherwise, the vertex is L, and nodes corresponding to the two vertices of the fault section are output.
The design principle of the positioning method for the single-phase earth fault of the power distribution network is as follows:
the graph data is composed of vertices and edges, and the graph can be represented as G (v, e), which was proposed by Blendel et al, the earliest of the Luwen algorithms, an algorithm specifically designed to process graph data. The algorithm explores community discovery on a graph model based on the gain of modularity, divides the graph into a plurality of communities according to different edge weights, and achieves the maximization of the modularity of the whole network through an objective function. The modularity is a quantity for measuring the strength of the connection between nodes, and is usually represented by the letter Q, and the specific calculation formula is as follows:
Figure BDA0003110281000000141
in the above formula: a. The ij Is the weight of the edge connecting vertex i and vertex j; m is half the sum of the weights of all edges in the network, i.e.
Figure BDA0003110281000000142
k i And k is j Is the sum of all edge weights connected to vertex i and vertex j, respectively, i.e. k i ＝∑ i A ij ，k j ＝∑ j A ij ；c i And c j Respectively, the communities of the vertex i and the vertex j; delta (c) i ,c j ) Is used to judge whether the vertex i and the vertex j are in the same community, if in the same community c i ＝c j Then, delta (c) i ,c j )＝1，Otherwise δ (c) i ,c j )＝0。
As can be seen from the above formula, if all the vertices in the network are independent communities, the modularity of the entire network is 0. To maximize the modularity of the entire network, all within the same community
Figure BDA0003110281000000143
Going to the maximum, if the weight of an edge is considered to be the closeness of the connection between two vertices, then from a spatial perspective this process may be understood as the tendency of each vertex to be assigned to the community in which the vertex most closely connects itself. Based on the process, the core of the Luwen algorithm enables the vertexes with strong links to be in the same community, weakens weak links among the vertexes, and finally achieves clustering on the complex network.
The Luwen algorithm is divided into two stages, the modularity gain generated by vertex movement needs to be repeatedly calculated in each stage, the modularity gain brought by single node movement is calculated in the first stage of the Luwen algorithm, the modularity gain brought by community merging is calculated in the second stage, and the specific calculation formula is as follows:
Figure BDA0003110281000000144
in the formula: Δ Q is the movement from vertex i to community c where vertex j is located j The resulting modularity gain; sigma in Is community c j The sum of the weights of all edges within; sigma tot Is outside and community c j The sum of all connected edge weights; k is a radical of i,in Is vertex i and community c j The weight of the connected edge. The above formula is simplified to obtain a simplified modularity calculation formula, and the specific calculation formula is as follows:
Figure BDA0003110281000000151
assuming a graphical model as shown in fig. 1, the first stage of the venturi algorithm is performed on this graphical model, specifically according to the following steps:
step I, distributing an independent community ID to each vertex in the graph model shown in the figure 1, wherein the distribution result is shown in figure 2, and different colors in the figure 2 represent different communities;
step II, after the step I, each vertex represents an independent community, and modularity gains delta Q generated by moving the vertex with the ID of 1 to an adjacent community are respectively calculated;
step III, after the step II, judging whether the maximum modularity gain delta Q is more than 0, if so, selecting the vertex 1 to move to a community with the maximum modularity gain, and if not, keeping the current situation of the vertex 1;
step IV, after the step III, traversing all the nodes in sequence according to the ID numbers, and executing the step II and the step III on each vertex;
step V, after the step IV, the community attribution of each vertex in the network is changed once, the community information adjacent to each node is also changed, each vertex in the network is repeatedly traversed based on new community distribution, and the complaint operation is repeatedly executed;
step VI, after the step V, when the community attribution of the vertex is unchanged after a certain iteration, the first stage of the Luwen algorithm is finished.
The objective function of the venturi algorithm is to maximize the modularity, so that the modularity gain must be guaranteed to be positive every time the vertex is moved from the original community to other communities, i.e., Δ Q > 0. The traversal operation of the vertices in the first stage of the venturi algorithm is performed sequentially, with the time complexity of each iteration being O (N). If the graph is complex in connection and large in vertex size, not only the time of each iteration is increased, but also the number of iterations is increased, so that the running time of the algorithm is too long. The PLM adopted in the invention is an improvement on the basis of the original Venturi algorithm, and the PLM changes the sequential execution of steps II to IV in the first stage of the Venturi algorithm into parallel execution. This improvement increases the computational speed of the luxin algorithm in each iteration, but may produce negative modularity gains during vertex community attribution changes. This is because all vertices compute their own modularity gains for moving to neighboring communities in parallel, and when a vertex is moved to a neighboring community, the structure of the community may have changed and the actual modularity gains may be negative. The negative modularity gain can be modified by multiple iterations, after which the PLM will obtain a result that approximates the venturi algorithm.
When the community attribution of each vertex does not change after one iteration, which indicates that each vertex has been moved to the optimal community, the task in the first stage of the Luwen algorithm is completed. The computation method of the second stage of the venturi algorithm is the same as that of the first stage, but the computation objects are changed into communities from the vertices in the network, and the computation method is implemented according to the following steps:
step a, as shown in fig. 3, based on the result of the first stage of the luen algorithm, all nodes in each community are regarded as a "supernode";
b, calculating the weight of the edges between the super nodes
Figure BDA0003110281000000161
Figure BDA0003110281000000162
Is made by community c i And community c j The weight of the edge between the two represented "supernodes"; w is a ij Is a connection community c i And community c j The weight of the edge of the middle vertex;
step C, after the step B, executing the first stage of the Luwen algorithm again by taking the super node as a unit;
step D, after step C, when the community structure in the network is unchanged after a certain iteration, the second phase of the Luwen algorithm is completed, as shown in FIG. 4.
As can be seen from the two node steps, the core step of the Luwen algorithm is to calculate the modularity gain brought by the vertex community attribution change. For a complex network, the luxen algorithm needs to perform a large number of iterations to optimize the modularity of the network, and excessive iterations result in too long algorithm running time and reduced real-time performance. In order to avoid that the algorithm runs too long and the number of iterations needs to be limited, previous researches show that the gain of the modularity is not obvious after 10 iterations of each stage, so that the number of iterations of each stage in the PLM is 10 by default.
In order to improve the query speed, the invention improves PLM and proposes IPLM. In the first stage of PLM, a round of community attribution change is performed in a graph model by taking a vertex as a unit, and a preliminary community distribution is formed. In the second stage of PLM, community attribution change is carried out by taking a super node as a unit, compared with the first stage, the second stage has fewer variables, and the result is easier to converge. In the second stage of PLM, the constraint condition of the vertex community attribution is modified, and the constraint condition is changed from delta Q >0 to the following formula:
ΔQ＞0or∑S′ i,k ＝∑|S′ i,k |,v i ∈C i
the invention adds a constraint condition in the second stage of PLM: the sum of the fault graph weights of all the vertexes in the community is equal to the sum of the absolute values of the fault graph weights. The two constraint conditions are in an OR relationship, and any one of the two constraint conditions can fuse two adjacent communities into one community. The improvement obviously increases the size of communities and reduces the number of communities and the iteration times of the fault section query process.
The electric wire netting is a natural picture structure, and fig. 5 is the basic flow of distribution network graph model modeling, and transformer substation, equipment such as generating line in the electric wire netting are modeled as node v, and three-phase current and three-phase voltage are stored in the attribute of node, and the transmission line is modeled as the edge of connected node v, and PLM improved by the wenen algorithm also can realize the clustering to the electric wire netting node. Such as the Schema shown in fig. 5, which contains a class of vertices and a class of edges. Each vertex node comprises six attributes of ID, upstream node, downstream node, failure graph weight, D-PMU state and community ID, and each edge comprises two attributes of NAME and failure graph weight. Among the above attributes, the role of the ID is to ensure uniqueness of each vertex. Upstream node and lowerThe function of the tour node is to determine the location of the vertex on the network topology. The state of the D-PMU is a self-defined two-dimensional array of [ D-PMU configuration, D-PMU synchronism]Two elements of which are 0 or 1 respectively to describe whether the node configures the D-PMU and whether the D-PMU is synchronous, [0,0]And [1,1]Two normal states, no [0,1]State, because a node is not configured with a D-PMU that will not have time synchronization of the D-PMU, [1,0]A state of losing time synchronization for node D-PMU. The NAME of each edge is named as "upstream vertex ID-downstream vertex ID". In the distribution network graph model, any one edge e ij The vertexes i and j at the two ends are determined, and for the power grid, the current flowing on the power transmission line can be approximate to the current of a node at the tail end of the power transmission line, so that the weight of the fault graph of the vertex j can be taken as an edge e ij Weight w of ij 。
Examples
According to the invention, a distribution network graph model of IEEE 33 nodes is established on a graph database TigerGraph as shown in figure 6, green nodes are configured D-PMU nodes, and black nodes are not configured. According to the invention, single-phase earth faults are arranged on 6 lines in an IEEE 33 node model, and fault resistors with the resistance values of 100 omega, 500 omega and 1000 omega are arranged at each fault. Because the faults occur at different positions of the line and the fault current during the fault is different, the single-phase earth fault is respectively arranged at the front 10%, 50% and the rear 10% of the total length of the 6 lines so as to verify the fault positioning accuracy of the algorithm in the whole section of the line.
The fault location method provided by the invention is depth-first traversal (IPLMDF) based on IPLM, and in order to embody the advantages of the invention, a depth-first traversal (DF), a depth-first traversal (PLMDF) based on PLM and a fault location (CS) based on a Cuckoo algorithm are respectively adopted in the embodiment. DF. Both PLMDF and IPLMDF are realized on a graph database Tiger Graph, and are methods for directly positioning fault sections based on network topology. In CS, assuming all of the above fault currents are detectable by the D-PMU, the rounding function is modified to the following equation:
Figure BDA0003110281000000191
the result generated by the above formula is used as the basis for positioning the CS.
Table 1 fault location results when all D-PMUs are working normally;
TABLE 1
Figure BDA0003110281000000192
Figure BDA0003110281000000201
From the results in the above table, it can be seen that the first three map-based calculation fault locations can directly and accurately locate the faults occurring at f1, f2, f3, f4 and f 6. When a fault occurs at the f5 position, the output result of the first three methods is 25,0, and because the 25 nodes are line end vertexes in the power distribution network graph model and no vertexes with the ID of 0 exist in the model, the positioning result is still accurate.
Compared with the first three methods, the CS has the advantages that the output result only has the fault at the f5 position, the other output results comprise the fault section and the normal section, and the positioning range is large. This is because CS relies only on the over-current signal at the test points for fault location, the smallest unit of output being the segment between two test points. Therefore, under the condition of configuring the same number of D-PMUs, the positioning effect of DF, PLMDF and IPLMDF used in the invention is better than that of CS.
To verify that the invention is robust, we work at f 1 -f 6 Set the a phase ground fault with a resistance of 1000 Ω and cause the partial D-PMU in the network to lose time synchronism. The four methods are tested to locate the fault when the partial D-PMU loses time synchronism.
Table 2 positioning results when part of D-PMU loses time synchronization;
TABLE 2
Figure BDA0003110281000000211
In the 13 cases described above, DF and PLMDF can accurately locate the faulty section in the 9 cases above. In the 10 th case, the DF result is not converged, PLMDF falls into local optimum, the iplmddf localization result is inaccurate, CS expands the localization range, and fig. 7 is a comparison of the PLM and IPLM clustering results in the 10 th case. As shown in fig. 8 (a) and 8 (b), since the node 6 is a branch vertex on the graph model and the downstream vertices are 7 and 26, the weight of the fault map of the vertex 7 is less than 0 before the D-PMU of the vertex 7 loses synchronism, and thus erroneous judgment is not caused. After the D-PMU of the vertex 7 does not lose synchronism, the estimated weight of the fault graph is larger than 0, at the moment, the weights of the fault graphs of two vertexes downstream of the vertex 6 are both larger than 0, and the result of DF is not converged. Vertex 6 and vertex 7 are in the same community and vertex 26 is in another community, which results in PLMDF being trapped in local optimality during the query, with the output failing region being 7,8. The size of the community in the IPLMDF is larger, the vertex 6, the vertex 7 and the vertex 26 are merged into the same community, and the output result is the global optimal solution, namely 28,29. In comparison with the first three methods, CS outputs no convergence in the 5 th and 9 th cases, and outputs an erroneous result in the 3 rd case.
When two D-PMUs closest to a fault point lose synchronism, the accurate fault section cannot be positioned by the four methods.
In summary, when part of D-PMU in the network loses time synchronization, the positioning effect of IPLMDF is the best, the positioning effects of DF and PLMDF are the second best, and CS is the worst.
In order to verify that the invention can quickly locate the fault section, the calculation speeds of the above four methods are compared in the embodiment. Since the iteration times of the above four methods are mainly affected by the position of the fault section, the embodiment selects the midpoint of the fault line, and the result of the fault resistance value 1000 Ω as a representative. Fig. 9 is a comparison of the number of iterations of the four methods under normal conditions, and fig. 10 is a comparison of the number of iterations of the four methods when the time synchronization of the portion of the D-PMU is lost. From fig. 9 and 10, it can be concluded that: due to the existence of a random process, the performance of the CS is unstable, and the iteration times are generally more than 10 times; the DF is most sensitive to the topological position of the fault section, the fault section can be quickly positioned when the fault section is close to the power supply node, and the fault section can be positioned by a plurality of iterations when the fault section is close to the tail end of the line; PLMDF is less affected by the topological location of the faulty section than DF, but still requires 5 or more iterations to locate the fault if the faulty section is near the end of the line; the IPLMDF performance is the most stable, and the fault section can be directly and accurately positioned only by 2-3 times of iteration.
Through comparison of the three aspects, the positioning method for the single-phase earth fault of the power distribution network is intuitively found to be superior to other three methods in robustness and calculation speed.
Through the mode, the method for positioning the single-phase earth fault of the power distribution network considers the influence of the fault occurrence position and the fault resistance on the positioning result, and simultaneously reduces the configuration quantity of the D-PMUs in the power distribution network model to a certain extent. Firstly, D-PMUs are configured at intervals from a head end node of a power distribution network model, a three-phase current sequence of nodes which are not configured with the D-PMUs and a standard deviation of fault phase current of each node in a time window when a fault occurs are calculated, then, a power distribution network graph model is built on a graph database according to a power distribution network model topological structure, each edge runs an IPLM after acquiring corresponding weight, finally, a first vertex of a fault section is inquired from top to bottom on the basis of an IPLM running result, and an accurate fault section is determined according to the weight ratio of the vertex to the previous vertex. The method for positioning the single-phase earth fault of the power distribution network is not influenced by the fault occurrence position and the fault resistance, the rapid and accurate positioning of the single-phase earth fault is realized only under the condition that half nodes in a power distribution network model are provided with the D-PMU by utilizing a graph calculation theory and a graph database platform, and the fault section can still be accurately positioned when partial D-PMU loses time synchronism.

Claims (8)

1. A method for positioning a single-phase earth fault of a power distribution network is characterized by comprising the following steps:
step 1, establishing a power distribution network model according to a topological structure of a power distribution network, configuring D-PMUs on nodes of the power distribution network model at intervals, and measuring three-phase current, three-phase voltage, zero-sequence current and zero-sequence voltage of corresponding nodes;
step 2, calculating three-phase voltage, three-phase current, zero-sequence current and zero-sequence voltage of a node which is not configured with the D-PMU;
step 3, calculating the fault graph weight S 'of each node in a time window based on the three-phase current of each node' i,k (ii) a The specific process is as follows:
step 3.1, extracting a three-phase current sequence of each node in a time window;
step 3.2, calculating the standard deviation S of each phase current sequence of each node i,k I is the node number and k is the mark of the phase;
Figure FDA0003988401270000011
wherein, t 0 Is the starting time, i.e. the time of the fault, f is the sampling frequency of the D-PMU, I t,i,k The magnitude of the fault phase current at time t for node i,
Figure FDA0003988401270000012
the average value of the three-phase current amplitude values in a time window T is the node i, and k = a, b, c;
step 3.3, compare S i,a ,S i,b ,S i,c If one value is far larger than the other two values, the phase is a fault phase, and k of all nodes is the phase;
step 3.4, calculating the phase difference delta theta between the zero sequence current and the zero sequence voltage of each node, and processing the delta theta by using an integer function;
Figure FDA0003988401270000013
Figure FDA0003988401270000021
step 3.5, calculating the fault graph weight S 'of each node' i,k Comprises the following steps:
S′ i,k ＝S i,k ·σ i (Δθ)；
step 4, establishing a graph model of the power distribution network on a graph database according to the topological structure of the power distribution network, and calculating edge weights formed by two adjacent nodes in the graph model of the power distribution network;
step 5, running an improved parallel Luwen algorithm on a graph model of the power distribution network to obtain a plurality of communities; in the second stage of the parallel luxen algorithm, the constraint condition when the vertex community attribution is changed is modified, and the constraint condition is changed from delta Q >0 to the following formula:
ΔQ>0 or ∑S′ i,k ＝∑|S′ i,k |,v i ∈C i ；
delta Q represents modularity gain caused by respectively moving vertexes to adjacent vertex communities;
step 6, searching from top to bottom based on the running result of the improved parallel luxen algorithm, and according to the weight S 'of the fault map' i,k Determining a vertex M of a first fault section;
step 7, judging whether the vertex M is configured with the D-PMU, and if so, directly outputting a fault section between nodes corresponding to the vertex M and the rear vertex N; if the vertex M is not configured with the D-PMU, respectively accessing a front vertex L and a rear vertex N of the vertex M, calculating a failure graph weight ratio theta of the front vertex L and the vertex M in a time window, and judging another node of a failure section according to the size of the theta so as to locate the failure section.
2. The method for positioning the single-phase earth fault of the power distribution network according to claim 1, wherein the specific process of configuring the nodes of the D-PMU at intervals on the power distribution network model in step 1 is as follows: and numbering the model nodes of the power distribution network, wherein the end nodes are not configured with the D-PMU, and only one node in any two connected nodes in the rest nodes is configured with the D-PMU.
3. The method for positioning the single-phase earth fault of the power distribution network according to claim 2, wherein the specific process of calculating the three-phase voltage and the three-phase current of the node which is not configured with the D-PMU in the step 2 is as follows:
judging whether the node i is a terminal node or not, if so, passing the active load P of the node h in the forward direction of the node i i Reactive load Q i Solving the three-phase voltage of the node i:
Figure FDA0003988401270000031
wherein Z hi Represents the line impedance between node h and node i, and J represents an imaginary number;
if the node i is not the tail end node, the node i calculates the three-phase voltage of the node i through a backward node j;
Figure FDA0003988401270000032
wherein Z hi Represents the line impedance between node h and node i;
the node i obtains three-phase current through a forward node h;
Figure FDA0003988401270000033
k = a, b, c; wherein k is a label for a phase;
then the zero sequence current of node i without D-PMU is represented as:
Figure FDA0003988401270000034
then the zero sequence voltage of node i without D-PMU is expressed as:
Figure FDA0003988401270000035
4. the method for locating the single-phase ground fault of the power distribution network according to claim 1, wherein the time window T in step 3 is set to 0.05s.
5. The method for positioning the single-phase earth fault of the power distribution network according to claim 1, wherein the specific process of the step 4 is as follows:
step 4.1, importing the topological structure of the power distribution network into a graph, modeling nodes as vertexes in a graph model, modeling lines as edges in the graph model, and establishing the graph model of the power distribution network;
step 4.2, judging whether the D-PMU loses time synchronism, wherein the judgment formula is as follows:
Figure FDA0003988401270000041
k i =1, where j is a vertex adjacent to i and if the vertex i satisfies the three conditions at the same time, the D-PMU of the vertex i loses time synchronism;
4.3, if the D-PMU of the vertex i loses time synchronism, the failure graph weight of the vertex i takes the average value of the failure graph weights of the adjacent vertexes;
step 4.4, defining any two adjacent vertexes in the graph model of the power distribution network, wherein the vertex of the outgoing current is an upstream vertex, the vertex of the incoming current is a downstream vertex, the edge between a certain vertex and the upstream vertex is an upstream edge, accessing all vertexes in the graph model of the power distribution network, and calculating the standard deviation S of each vertex j,k Attribute w assigned to upstream edge ij In (3), an edge weight is obtained.
6. The method for positioning the single-phase earth fault of the power distribution network according to claim 1, wherein the specific process of the step 5 is as follows:
step 5.1, inputting a graph model of the power distribution network into an improved parallel venturi algorithm;
step 5.2, accessing all vertexes in the graph model of the power distribution network in parallel, and calculating modularity gain delta Q caused by the fact that all vertexes move to adjacent vertex communities respectively, wherein a modularity gain calculation formula is as follows:
Figure FDA0003988401270000042
therein, sigma tot k i Is with vertex community c j The sum of all connected edge weights; k is a radical of i,in Is vertex i and community c j The weight of the edges that are connected to each other,
Figure FDA0003988401270000043
step 5.3, changing community attribution of each vertex, moving each vertex into the maximum modularity gain community, if all modularity gains of a certain vertex are negative, keeping the community attribute of each vertex in an original state before changing the community attribution of each vertex, and otherwise, updating the community attribution of the vertex;
step 5.4, judging whether the community attribution of the vertex is updated in the step 5.3, if so, returning to the step 5.2, otherwise, terminating the iteration;
step 5.5, taking communities as a unit, accessing all communities in parallel, calculating modularity gain delta Q of all vertexes of one community moving to adjacent communities respectively, wherein a weight calculation formula of a connection edge between communities is as follows:
Figure FDA0003988401270000051
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003988401270000052
is composed of community c i And community c j The weight of the two representative social interval edges; w is a ij Is a connection community c i And community c j The weight of the edge of the middle vertex;
step 5.6, merging communities when the adjacent communities meet the constraint condition of the following formula:
ΔQ>0 or ∑S′ i,k ＝∑|S′ i,k |,v i ∈C i
and 5.7, judging whether community combination exists or not, if so, returning to the step 5.4, and otherwise, ending the running of the improved parallel venturi algorithm.
7. The method for positioning the single-phase earth fault of the power distribution network according to claim 1, wherein the specific process of the step 6 is as follows:
6.1, according to the direction of the outgoing current, accessing a head end vertex of the power distribution network model, reading a community ID of the head end vertex, and assigning the community ID to a global variable x;
step 6.2, accessing the last vertex with the community ID of x, wherein the last vertex is marked as a vertex M;
6.3, accessing a downstream vertex N connected with the vertex M;
step 6.4, judging whether the weight of the fault graph of the vertex N is larger than 0 or not;
step 6.5, if S' N,k >0, then assign ID of community in which downstream vertex N is located to x, and return to step 6.3 until S 'appears' N,k And outputting the ID of the vertex M to determine that the vertex M is one vertex of the fault section.
8. The method for positioning the single-phase earth fault of the power distribution network according to claim 1, wherein the specific process of the step 7 is as follows:
7.1, accessing a front vertex L and a rear vertex N of the vertex M, and calculating a failure map weight ratio theta of the front vertex L and the vertex M;
Figure FDA0003988401270000061
and 7.2, if theta is less than or equal to 0.9, the other vertex of the fault section is N, otherwise, the vertex is L, and nodes corresponding to the two vertexes of the fault section are output.
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