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

Abstract

The invention discloses a positioning method for a single-phase grounding fault in a distribution network. D-PMUs are configured at intervals at the head node of a self-distribution network model, and the three-phase current sequence of nodes without D-PMUs configured and when a fault occurs are calculated The standard deviation of the fault phase current of each node within a time window; the distribution network graph model is established on the graph database according to the topology of the distribution network model, and each edge obtains the corresponding weight before running IPLM. Finally, based on the IPLM operation results The first vertex of the faulty section is queried from top to bottom, and the exact faulty section is determined according to the ratio of the weight of this vertex to the previous vertex. The single-phase ground fault location method of the distribution network of the present invention uses the graph calculation theory and the graph database platform to realize the fast and accurate positioning of the single-phase ground fault only when half of the nodes in the distribution network model are equipped with D-PMUs. When the D‑PMU loses time synchronization, it can still accurately locate the faulty section.

Description

A single-phase-to-earth fault location method in distribution network

technical field

The invention belongs to the technical field of fault location in power grids, and in particular relates to a method for locating single-phase ground faults in distribution networks.

Background technique

The distribution network in my country is characterized by long power supply radius, many line branches, and imperfect measurement system. Accurately locating the fault section is an important condition for quickly troubleshooting the distribution network. Single-phase ground fault is the most frequent fault among all faults, accounting for about 80% of all faults. Single-phase-to-ground faults have the characteristics of indistinct fault characteristics and susceptibility to noise interference, which makes it difficult to accurately locate single-phase-to-ground faults when they occur.

At present, the fault location methods of distribution network mainly include impedance method, traveling wave method, injection signal method and wide-area measurement information method. The distribution network fault location method based on the impedance method is very sensitive to the excessive resistance of the fault and the fault phase angle. As the network structure of the distribution network becomes more and more complex and the line parameters are inaccurate, the accuracy of the impedance method is greatly affected. Influence. The distribution network fault location method based on the traveling wave method is not affected by the system operation mode and fault resistance, but is easily affected by the distribution network line branch. The signal injection method is different from the other three methods. It needs to inject signals into the distribution network to locate the fault location. This type of method requires auxiliary equipment and additional operations, which increases potential risks and costs. With the development of wide-area measurement technology, the volume of phasor measurement unit (PMU) is gradually reduced, and the cost is reduced, which makes the state estimation of distribution network more reliable. More and more scholars use wide-area measurement information for distribution network. The fault location method of the power grid, the present invention is a faulty power grid method of the distribution network based on the wide-area measurement information method.

At present, most researches on distribution network fault location based on wide-area information rely on a large number of high-precision measurement units such as D-PMU or uPMU in the distribution network model. Although the results of this type of research can accurately locate the fault section of the distribution network, there are still two important defects. First, the large number of measurement units arranged on the distribution network model in this type of research greatly increases the cost, which is not economical. It is feasible. Second, this type of research mainly relies on wide-area measurement information, and does not make full use of the topological structure information of the distribution network. Some scholars have conducted research on distribution network fault location based only on the distribution network model with D-PMU at the head end. This type of research can locate two-phase short-circuit faults and two-phase short-circuit ground faults, but cannot accurately locate single-phase ground faults.

Contents of the invention

The purpose of the present invention is to provide a method for locating a single-phase-to-ground fault in a distribution network, which can quickly and accurately locate a single-phase-to-ground fault when D-PMUs are configured on half of the nodes in the distribution network model.

The technical solution adopted in the present invention is a method for locating a single-phase ground fault in a distribution network, which is specifically implemented according to the following steps:

Step 1. Establish a distribution network model based on the topology of the distribution network, configure D-PMUs at intervals on the nodes of the distribution network model, and measure the three-phase current, three-phase voltage, zero-sequence current, and zero-sequence voltage of the corresponding nodes ;

Step 2. Calculate the three-phase voltage, three-phase current, zero-sequence current, and zero-sequence voltage of the unconfigured D-PMU node;

Step 3, calculating the fault map weight S' _i,k of each node within a time window based on the three-phase current of each node;

Step 4. Establish a graph model of the distribution network on the graph database according to the topological structure of the distribution network, and calculate the edge weights formed by two adjacent nodes in the graph model of the distribution network;

Step 5. Run IPLM on the graph model of the distribution network to obtain multiple communities;

Step 6, search from top to bottom based on the running results of IPLM, and determine the vertex M of the first fault section;

Step 7. Visit the front vertex L and the back vertex N of the vertex M respectively, calculate the weight ratio θ of the fault graph between the front vertex L and the back vertex N in a time window, and judge another node in the fault section by the size of θ, so that Locate the faulty section.

The present invention is also characterized in that:

Step 1. The specific process of configuring D-PMU nodes at intervals on the distribution network model is as follows: number the nodes of the distribution network model, no D-PMU is configured on the end nodes, and only one node is configured in any two connected nodes of the remaining nodes D-PMU.

The specific process of calculating the three-phase voltage and three-phase current of the unconfigured D-PMU node in step 2 is as follows:

Judging whether node i is an end node, if so, node i obtains the three-phase voltage of node i through its forward node h and active load P _i and reactive load Q _i :

Where Z _hi represents the line impedance between node h and node i, and J represents an imaginary number;

If node i is not an end node, node i obtains its three-phase voltage through its backward node j;

where Z _hi represents the line impedance between node h and node i

Node i obtains its three-phase current through its forward node h;

k = a, b, c;

Then the zero-sequence current of node i without D-PMU is expressed as:

Then the zero-sequence voltage of the unconfigured D-PMU node i is expressed as:

In step 3, the time window T is set to 0.05s.

The specific process of step 3 is:

Step 3.1, extracting the three-phase current sequence of each node in a time window;

Step 3.2, calculate the standard deviation S _i,k of each phase current sequence of each node, i is the node number, and k is the label of the phase;

为节点i的在一个时间窗T内三相电流幅值的平均值，k＝a,b,c；Among them, t ₀ is the initial moment, that is, the moment when the fault occurs, f is the frequency used by D-PMU, I _t,i,k is the amplitude of the fault phase current of node i at time t,

is the average value of the three-phase current amplitude of node i within a time window T, k=a, b, c;

Step 3.3, compare the three values of S _{i, a} , S _{i, b} , S _{i, c} , if one value is much larger than the other two, then this phase is a faulty phase, and the k of all nodes is selected from this phase;

Step 3.4. Calculate the phase difference △θ between the zero-sequence current and zero-sequence voltage of each node, and use the rounding function to process △θ;

Step 3.5, calculating the fault map weight S' _i,k of each node is:

The specific process of step 4 is:

Step 4.1, import the topological structure of the distribution network into the graph, the nodes are modeled as vertices in the graph model, the lines are modeled as edges in the graph model, and the graph model of the distribution network is established;

Step 4.2. Determine whether any D-PMU loses time synchronization. The formula for judging is as follows:

k _i =1 means that vertex i is equipped with a D-PMU, and j is a vertex adjacent to i. If vertex i satisfies the above three conditions at the same time, the D-PMU of vertex i loses time synchronization;

Step 4.3, if the D-PMU of vertex i loses time synchronization, use the fault graph weight of vertex i to obtain the average value of the fault graph weights of its adjacent vertices;

Step 4.5. Among any two adjacent vertices in the graphical model of the definition distribution network, the vertex of the outflow current is the upstream vertex, the vertex of the inflow current is the downstream vertex, and the edge between a vertex and the upstream vertex is the upstream edge. For all vertices in the graph model of the power grid, assign the standard deviation S _j,k of each vertex to the attribute w _ij of the upstream edge to obtain the edge weight;

The specific process of step 5 is:

Step 5.1, input the graphical model of the distribution network into IPLM;

Step 5.2. Parallel access to all vertices in the graph model of the distribution network, and calculate the modularity gain ΔQ brought about by moving all vertices to the adjacent vertex communities respectively. The modularity gain calculation formula is:

Among them, ∑ _tot k _i is the sum of all edge weights connected to vertex community c _j ; _ki,in is the weight of the edge connected to vertex i and community c _j ,

Step 5.3. Change the community affiliation of each vertex, and move each vertex into the community with the largest modularity gain. If all the modularity gains of a certain vertex are negative, the community attribute of the vertex remains the original state before changing the community affiliation of each vertex, otherwise Update the community affiliation of the vertices;

Step 5.4, judging whether there is a community attribution update of the vertex in step 5.3, if so, return to step 5.2, otherwise, terminate the iteration;

Step 5.5, using the community as the unit, visit all the communities in parallel, and calculate the modularity gain ΔQ of all the vertices of one community moving to the adjacent community respectively. The formula for calculating the weight of the connecting edges between communities is:

是由社区c_i与社区c_j代表的两个社区间边的权重；w_ij是连接社区c_i与社区c_j中顶点的边的权重；in,

is the weight of the edge between two communities represented by community c _i and community c _j ; w _ij is the weight of the edge connecting the vertices in community c _i and community c _j ;

Step 5.6, adjacent communities meet the constraints of the following formula to merge communities:

ΔQ＞0or∑S′ _i,k ＝∑|S′ _i,k |,v _i ∈ C _i

Step 5.7, judge whether there is a community merger, if yes, return to step 5.4, otherwise, the IPLM operation ends.

The specific process of step 6 is:

Step 6.1. According to the direction of the outflow current, access the head-end vertex of the distribution network model, read the community ID of the head-end vertex, and assign the community ID to the global variable x;

Step 6.2, visit the last vertex whose community ID is x, and mark the last vertex as vertex M;

Step 6.3, visit the downstream vertex N connected to the vertex M;

Step 6.4, judging whether the fault graph weight of vertex N is greater than 0;

Step 6.5. If S′ _N,k > 0, assign the ID of the community where the downstream vertex N is located to x, and return to step 6.3 until S′ _N,k ≤ 0, output the ID of vertex M, and determine that vertex M is A vertex of the faulty segment.

Step 7.1. Determine whether the vertex M is configured with a D-PMU. If it is configured, then directly output that the faulty section is between the node corresponding to the vertex M and the subsequent vertex N;

Step 7.2. If the vertex M is not configured with a D-PMU, visit the front vertex L and the back vertex N of the vertex M, and calculate the fault graph weight ratio θ between the front vertex L and the vertex M;

Step 7.3. If θ≤0.9, the other vertex of the faulty section is N, otherwise it is vertex L, and the nodes corresponding to the two vertices of the faulty section are output.

The beneficial effects of the present invention are:

(1) A method for locating a single-phase ground fault in a distribution network according to the present invention is not affected by the location of the fault and the fault resistance.

(2) The present invention combines topological structure information of the distribution network and wide-area measurement information, and uses IPLM to cluster the graph model, which reduces the times of retrieval and improves the calculation speed.

(3) Compared with most distribution network fault location methods, the present invention only configures D-PMUs on half of the nodes in the distribution network model, which reduces the cost.

(4) The present invention has strong robustness, and can still accurately locate faults when some measurement units in the network fail.

Description of drawings

Fig. 1 is the graph model schematic diagram of the distribution network that adopts in the embodiment of the present invention;

Figure 2 is the initial community distribution of the Leuven algorithm;

Figure 3 is the first stage of the Leuven algorithm;

Figure 4 is the second stage of the Leuven algorithm;

Fig. 5 is the flow chart of distribution network graph model modeling;

Fig. 6 is the modified IEEE 33 node model;

Figure 7 is a comparison of PLM and IPLM clustering results;

Figure 8(a) is the phase current change of the head-end node;

Figure 8(b) is the phase current change of the terminal node;

Figure 9 is a comparison of the number of iterations of the four methods under normal circumstances;

Figure 10 is a comparison of the iteration times of the four methods when some D-PMUs lose time synchronization.

Detailed ways

The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

The distribution network fault location method in the present invention applies graph calculation and the improved luovain algorithm, and establishes a graph model of the distribution network based on the topological structure of the distribution network, and only needs to be configured on half of the nodes in the distribution network model In the case of D-PMU, the fast and accurate location of single-phase ground fault is realized, which avoids the location result falling into local optimum, and has strong robustness, and can still accurately locate the fault area when some D-PMUs lose time synchronization part.

A method for locating a single-phase ground fault in a distribution network of the present invention is specifically implemented according to the following steps:

Step 1. Establish a distribution network model based on the topology of the distribution network, configure D-PMUs at intervals on the nodes of the distribution network model, and measure the three-phase current, three-phase voltage, zero-sequence current, and zero-sequence voltage of the corresponding nodes ;

Step 1. The specific process of configuring D-PMU nodes at intervals on the distribution network model is as follows: number the nodes of the distribution network model, no D-PMU is configured on the end nodes, and only one node is configured in any two connected nodes of the remaining nodes D-PMU.

Step 2. Calculate the three-phase voltage, three-phase current, zero-sequence current, and zero-sequence voltage of the unconfigured D-PMU node;

The specific process of calculating the three-phase voltage and three-phase current of the unconfigured D-PMU node in step 2 is as follows:

Judging whether node i is an end node, if so, node i obtains the three-phase voltage of node i through its forward node h and active load P _i and reactive load Q _i :

Where Z _hi represents the line impedance between node h and node i, and J represents an imaginary number;

If node i is not an end node, node i obtains its three-phase voltage through its backward node j;

where Z _hi represents the line impedance between node h and node i

Node i obtains its three-phase current through its forward node h;

k = a, b, c;

Then the zero-sequence current of node i without D-PMU is expressed as:

Then the zero-sequence voltage of the unconfigured D-PMU node i is expressed as:

Step 3. Calculate the fault map weight S′ _i,k of each node within a time window based on the three-phase current of each node; the time window T is set to 0.05s.

The specific process of step 3 is:

Step 3.1, extracting the three-phase current sequence of each node in a time window;

Step 3.2, calculate the standard deviation S _i,k of each phase current sequence of each node, i is the node number, and k is the label of the phase;

为节点i的在一个时间窗T内三相电流幅值的平均值，k＝a,b,c；Among them, t ₀ is the initial moment, that is, the moment when the fault occurs, f is the frequency used by D-PMU, I _t,i,k is the amplitude of the fault phase current of node i at time t,

is the average value of the three-phase current amplitude of node i within a time window T, k=a, b, c;

Step 3.3, compare the three values of S _{i, a} , S _{i, b} , S _{i, c} , if one value is much larger than the other two, then this phase is a faulty phase, and the k of all nodes is selected from this phase;

Step 3.4. Calculate the phase difference △θ between the zero-sequence current and zero-sequence voltage of each node, and use the rounding function to process △θ;

Step 3.5, calculating the fault map weight S' _i,k of each node is:

S' _i,k = S _i,k ·σ _i (Δθ).

Step 4. Establish a graph model of the distribution network on the graph database according to the topological structure of the distribution network, and calculate the edge weights formed by two adjacent nodes in the graph model of the distribution network;

The specific process of step 4 is:

Step 4.1, import the topological structure of the distribution network into the graph, the nodes are modeled as vertices in the graph model, the lines are modeled as edges in the graph model, and the graph model of the distribution network is established;

Step 4.2. Determine whether any D-PMU loses time synchronization. The formula for judging is as follows:

k _i =1 means that vertex i is equipped with a D-PMU, and j is a vertex adjacent to i. If vertex i satisfies the above three conditions at the same time, the D-PMU of vertex i loses time synchronization;

Step 4.3, if the D-PMU of vertex i loses time synchronization, use the fault graph weight of vertex i to obtain the average value of the fault graph weights of its adjacent vertices;

Step 4.5. Among any two adjacent vertices in the graphical model of the definition distribution network, the vertex of the outflow current is the upstream vertex, the vertex of the inflow current is the downstream vertex, and the edge between a vertex and the upstream vertex is the upstream edge. For all vertices in the graph model of the power grid, assign the standard deviation S _j,k of each vertex to the attribute w _ij of the upstream edge to obtain the edge weight.

Step 5. Run IPLM on the graph model of the distribution network to obtain multiple communities;

The specific process of step 5 is:

Step 5.1, input the graphical model of the distribution network into IPLM;

Step 5.2. Parallel access to all vertices in the graph model of the distribution network, and calculate the modularity gain ΔQ brought about by moving all vertices to the adjacent vertex communities respectively. The modularity gain calculation formula is:

Among them, ∑ _tot k _i is the sum of all edge weights connected to vertex community c _j ; _ki,in is the weight of the edge connected to vertex i and community c _j ,

Step 5.3. Change the community affiliation of each vertex, and move each vertex into the community with the largest modularity gain. If all the modularity gains of a certain vertex are negative, the community attribute of the vertex remains the original state before changing the community affiliation of each vertex, otherwise Update the community affiliation of the vertices;

Step 5.4, judging whether there is a community attribution update of the vertex in step 5.3, if so, return to step 5.2, otherwise, terminate the iteration;

Step 5.5, using the community as the unit, visit all the communities in parallel, and calculate the modularity gain ΔQ of all the vertices of one community moving to the adjacent community respectively. The formula for calculating the weight of the connecting edges between communities is:

是由社区c_i与社区c_j代表的两个社区间边的权重；w_ij是连接社区c_i与社区c_j中顶点的边的权重；in,

is the weight of the edge between two communities represented by community c _i and community c _j ; w _ij is the weight of the edge connecting the vertices in community c _i and community c _j ;

Step 5.6, adjacent communities meet the constraints of the following formula to merge communities:

ΔQ＞0or∑S′ _i,k ＝∑|S′ _i,k |,v _i ∈ C _i

Step 5.7, judge whether there is a community merger, if yes, return to step 5.4, otherwise, the IPLM operation ends.

Step 6, search from top to bottom based on the operation result of IPLM, and determine the node M of the first fault section;

The specific process of step 6 is:

Step 6.1. According to the direction of the outflow current, access the head-end vertex of the distribution network model, read the community ID of the head-end vertex, and assign the community ID to the global variable x;

Step 6.2, visit the last vertex whose community ID is x, and mark the last vertex as vertex M;

Step 6.3, visit the downstream vertex N connected to the vertex M;

Step 6.4, judging whether the fault graph weight of vertex N is greater than 0;

Step 6.5. If S′ _N,k > 0, assign the ID of the community where the downstream vertex N is located to x, and return to step 6.3 until S′ _N,k ≤ 0, output the ID of vertex M, and determine that vertex M is A vertex of the faulty segment.

The principle of determining the vertex M as a vertex of the fault section is: the vertices located before the fault point on the fault branch have positive fault graph weights, and the fault graph weights of other vertices are all less than zero. Based on this, the main purpose of querying in units of communities (increasing query speed) is to find the last vertex with a weight greater than zero on the faulty branch,

Step 7. Visit the front vertex L and the back vertex N of the vertex M respectively, calculate the weight ratio θ of the fault graph between the front vertex L and the back vertex N in a time window, and judge another node in the fault section by the size of θ, so that Locate the faulty section.

Step 7 Since half of the nodes in the distribution network model in the present invention are not configured with D-PMUs, the three-phase currents of these nodes are calculated from the current and voltage information of the front and rear nodes. If the fault point is located in an unconfigured D-PMU Before the node of the PMU, the current of this node will also show fault characteristics due to the influence of the voltage and current value of the upstream node, which allows us to locate the specific section of the fault, so we need to make further judgments on the basis of step 6, specifically The process is:

Step 7.1. Determine whether the vertex M is configured with a D-PMU. If it is configured, then directly output that the faulty section is between the node corresponding to the vertex M and the subsequent vertex N;

Step 7.2. If the vertex M is not configured with a D-PMU, visit the front vertex L and the back vertex N of the vertex M, and calculate the fault graph weight ratio θ between the front vertex L and the vertex M;

Step 7.3. If θ≤0.9, the other vertex of the faulty section is N, otherwise it is vertex L, and the nodes corresponding to the two vertices of the faulty section are output.

The design principle of a positioning method for a distribution network single-phase ground fault of the present invention is:

Graph data is composed of vertices and edges. The graph can be expressed as G(v,e). The Leuven algorithm was first proposed by Blondel et al. at the University of Leuven. The Leuven algorithm is an algorithm that specializes in processing graph data. This algorithm explores community discovery on the graph model based on the gain of modularity, divides the graph into several communities according to the difference of edge weight, and its objective function is to maximize the modularity of the entire network. Modularity is a measure of the strength of the connection between nodes, usually represented by the letter Q, and its specific calculation formula is as follows:

k_i与k_j分别是与顶点i和顶点j相连的所有边权重的总和，即k_i＝∑_iA_ij，k_j＝∑_jA_ij；c_i与c_j分别是顶点i和顶点j所在的社区；δ(c_i,c_j)是用来判断顶点i和顶点j是否在同一个社区，若在同一个社区c_i＝c_j，则δ(c_i,c_j)＝1，否则δ(c_i,c_j)＝0。In the above formula: A _ij is the weight of the edge connecting vertex i and vertex j; m is half of the sum of the weights of all edges in the network, namely

k _i and k _j are the sum of the weights of all edges connected to vertex i and vertex j respectively, that is, k _i =∑ _i A _ij , k _j =∑ _j A _ij ; c _i and c _j are vertex i and vertex j respectively community; δ(c _i ,c _j ) is used to judge whether vertex i and vertex j are in the same community, if they are in the same community c _i =c _j , then δ(ci _, c _j )=1, Otherwise δ(c _i ,c _j )=0.

趋于最大，如果边的权重看做两顶点之间联系的紧密程度，那么从空域的角度来看这一过程可以理解为每个顶点都倾向于被分配到和自己联系最紧密的顶点所在的社区。鲁汶算法的核心正是基于这一过程，使具有强联系的顶点处于同一个社区，淡化顶点间的弱联，最终实现对复杂网络的聚类。It is not difficult to see from the above formula that if all vertices in the network are independent communities, the modularity of the entire network is 0. To maximize the modularity of the entire network, it is necessary to make the

Tends to the maximum, if the weight of the edge is regarded as the closeness of the connection between the two vertices, then from the perspective of the airspace, this process can be understood as each vertex tends to be assigned to the vertex that is most closely connected with itself. Community. The core of the Leuven algorithm is based on this process, making the vertices with strong connections in the same community, weakening the weak connections between vertices, and finally realizing the clustering of complex networks.

The Leuven algorithm is divided into two stages. In each stage, the modularity gain generated by vertex movement is repeatedly calculated. In the first stage of the Leuven algorithm, the modularity gain caused by the movement of a single node is calculated. In the second stage, the modularity gain is calculated. is the modularity gain brought by the community merger, and its specific calculation formula is as follows:

In the formula: ΔQ is the modularity gain generated by moving vertex i to the community c _j where vertex j is located; ∑ _in is the sum of all edge weights in community c _j ; ∑ _tot is the sum of all edge weights connected to community c _j outside Sum; ki _,in is the weight of the edge connecting vertex i to community _cj . Simplifying the above formula, the simplified modularity calculation formula can be obtained, and the specific calculation formula is as follows:

Assuming that there is a graph model as shown in Figure 1, the first stage of the Leuven algorithm is executed on this graph model, and the specific implementation is as follows:

Step 1, assign an independent community ID to each vertex in the graph model shown in Figure 1, the distribution result is as shown in Figure 2, and different colors in Figure 2 represent different communities;

Step II. After step I, each vertex represents an independent community, and the modularity gain ΔQ generated by moving the vertex with ID 1 to the adjacent community is calculated respectively;

Step III. After step II, judge whether the maximum modularity gain ΔQ > 0 is established. If it is established, select vertex 1 to move to the community with the largest modularity gain. If not, vertex 1 will maintain the status quo;

Step IV, after step III, traverse all nodes in turn according to the number of ID, and execute step II and step III for each vertex;

Step V. After step IV, the community ownership of each vertex in the network has undergone a round of changes, and the adjacent community information of each node has also changed. Based on the new community distribution, each vertex in the network is traversed repeatedly, repeating perform appeal operations;

After step VI and step V, when the community affiliation of the vertices does not change after a certain round of iterations, the first stage of the Leuven algorithm ends.

The objective function of the Leuven algorithm is to maximize the modularity. Therefore, every time a vertex is moved from the original community to another community, the modularity gain must be positive, that is, ΔQ>0. In the first stage of the Leuven algorithm, the traversal operation on the vertices is executed sequentially, and the time complexity of each iteration is O(N). If the connection of the graph is complex and the scale of vertices is large, not only the time of each iteration will increase, but also the number of iterations will increase, which will cause the algorithm to run for too long. The PLM adopted in the present invention is improved on the basis of the original Leuven algorithm, and the PLM changes step II to step IV in the first stage of the Leuven algorithm from sequential execution to parallel execution. This improvement improves the computational speed of the Leuven algorithm in each iteration, but may produce negative modularity gains during the change of vertex community affiliation. This is because all vertices calculate the modularity gain of moving to the adjacent community in parallel. When the vertex is moved to the adjacent community, the structure of the community may have changed, and the actual modularity gain may be negative. Negative modularity gain can be corrected by multiple iterations, and after multiple iterations, PLM will get a result similar to the Leuven algorithm.

When the community affiliation of each vertex does not change after a round of iterations, it means that each vertex has been moved to the best community at this time, and the task of the first stage of the Leuven algorithm is completed. The calculation method of the second stage of the Leuven algorithm is the same as that of the first stage, but the calculation object is changed from the vertices in the network to the community, and it is implemented according to the following steps:

Step A, as shown in Figure 3, based on the results of the first stage of the Leuven algorithm, all nodes in each community are regarded as a "super node";

Step B. Calculate the weight of the edges between each "super node"

是由社区c_i与社区c_j代表的两个“超级节点”间边的权重；w_ij是连接社区c_i与社区c_j中顶点的边的权重；

is the weight of the edge between two "super nodes" represented by community c _i and community c _j ; w _ij is the weight of the edge connecting the vertices in community c _i and community c _j ;

Step C, after step B, execute the first stage of the Leuven algorithm again in units of "super nodes";

Step D, after step C, when there is no change in the community structure in the network after a certain round of iterations, the second stage of the Leuven algorithm is completed, as shown in Figure 4.

From the above two node steps, it can be seen that the core step of the Leuven algorithm is to calculate the modularity gain brought about by the change of apex community ownership. For complex networks, the Leuven algorithm needs a large number of iterations to optimize the modularity of the network. Excessive iterations will cause the algorithm to run for a long time and reduce real-time performance. In order to prevent the algorithm from running too long, it is necessary to limit the number of iterations. Previous studies have shown that the gain in modularity is not obvious after 10 iterations in each stage, so the default number of iterations in each stage in PLM is 10.

In order to increase the query speed, the present invention improves the PLM and proposes the IPLM. In the first stage of PLM, a round of community affiliation changes have been carried out in units of vertices in the graph model, forming a preliminary community distribution. In the second stage of PLM, the community affiliation is changed in units of "super nodes". Compared with the first stage, the second stage has fewer variables and the result is easier to converge. In this paper, in the second stage of PLM, the constraint conditions when the apex community ownership changes are modified, and the constraint conditions are changed from △Q>0 to the following formula:

ΔQ＞0or∑S′ _i,k ＝∑|S′ _i,k |,v _i ∈ C _i

The present invention adds a constraint condition in the second stage of PLM: the sum of the fault map weights of all vertices in the community is equal to the sum of the absolute value of the fault map weights. Two constraints are "or" relationship, satisfying any one of the two constraints can merge two adjacent communities into one community. This improvement significantly increases the size of the community, reduces the number of communities and the number of iterations of the faulty segment query process.

The power grid is a natural graph structure. Figure 5 shows the basic process of modeling the distribution network graph model. The substations, busbars and other equipment in the power grid are modeled as nodes v, and the three-phase current and three-phase voltage are stored in the attributes of the nodes In , the transmission line is modeled as the edge e connecting the node v, and the PLM improved by the Leuven algorithm can also realize the clustering of the grid nodes. The Schema shown in Figure 5 contains one type of vertex and one type of edge. Each vertex node contains six attributes: ID, upstream node, downstream node, fault graph weight, D-PMU status, and community ID, and each edge contains two attributes: NAME and fault graph weight. Among the above attributes, the role of ID is to ensure the uniqueness of each vertex. The function of the upstream node and the downstream node is to judge the position of the vertex on the network topology. The D-PMU state is a custom two-dimensional array [D-PMU configuration, D-PMU synchronization], the two elements of which are 0 or 1 to describe whether the node is configured with D-PMU and whether D-PMU is synchronized, [0,0] and [1,1] are two normal states, there is no [0,1] state, because the node is not configured with D-PMU and will not have the time synchronization of D-PMU, [1,0] is A state in which the node D-PMU has lost time synchronization. The naming method of each edge is "upstream vertex ID-downstream vertex ID". In the distribution network graph model, the vertex i and vertex j at both ends of any edge e _ij are determined. For the power grid, the current flowing through the transmission line can be approximated as the current of the end node of the line, so the vertex j can be taken as The weight of the fault graph is used as the weight w _ij of the edge e _ij .

Example

The present invention establishes an IEEE 33-node distribution network graph model on the graph database TigerGraph as shown in FIG. 6 , the green nodes are configured D-PMU nodes, and the black nodes are unconfigured nodes. In the present invention, single-phase grounding faults are set on 6 lines in the IEEE 33 node model, and fault resistances with resistance values of 100Ω, 500Ω, and 1000Ω are set for each fault. Since the fault occurs at different positions of the line, the fault current during the fault will be different. Therefore, the present invention respectively sets the single-phase grounding fault at the first 10%, 50% and last 10% of the total length of the above-mentioned 6 lines. , to verify the fault location accuracy of the algorithm in this paper in the whole section of the line.

The fault location method proposed by the present invention is based on the depth-first traversal (IPLMDF) of IPLM. In order to reflect the superiority of the present invention, the depth-first traversal method (DF) and the depth-first traversal method (PLMDF) based on PLM are adopted respectively in the embodiment. And fault localization (CS) based on the cuckoo algorithm. DF, PLMDF, and IPLMDF are all implemented on the graph database TigerGraph, and are methods for directly locating faulty sections based on network topology. In CS, assuming that all the above fault currents can be detected by D-PMU, modify the rounding function to the following formula:

The result generated by the above formula is used as the positioning basis of CS.

Table 1 Fault location results when all D-PMUs work normally;

Table 1

From the results in the above table, it can be seen that the first three fault locations based on graph calculation can directly and accurately locate the faults at f1, f2, f3, f4 and f6. When a fault occurs at f5, the output results of the first three methods are 25,0. Since node 25 is the end vertex of the line in the distribution network graph model, and there is no vertex with ID 0 in the model, the positioning result is still accurate .

Compared with the first three methods, only the fault at f5 is accurate in the output results of CS, and the rest of the output results include both the fault section and the normal section, and the positioning range is larger. This is because CS only relies on the overcurrent signal at the measuring point for fault location, and the smallest unit of output is the section between two measuring points. Therefore, in the case of configuring the same number of D-PMUs, the positioning effect of the present invention using DF, PLMDF, and IPLMDF is better than that of CS.

In order to verify the strong robustness of the present invention, we set a phase A ground fault with a resistance value of 1000Ω at 50% of f ₁ -f ₆ and make some D-PMUs in the network lose time synchronization. The fault location effects of the above four methods are tested when some D-PMUs lose time synchronization.

Table 2 Partial D-PMU positioning results when time synchronization is lost;

Table 2

In the above 13 cases, DF and PLMDF can accurately locate the fault section in the first 9 cases. In the tenth case, the DF result does not converge, the PLMDF falls into a local optimum, the IPLMDF positioning result is inaccurate, and the CS expands the positioning range. Figure 7 shows the comparison of the PLM and IPLM clustering results in the tenth case. As shown in Figure 8(a) and Figure 8(b), since node 6 is a branch vertex on the graph model, its downstream vertices are 7 and 26, before the D-PMU of vertex 7 loses synchronization, the The fault map weight is less than 0, which will not cause misjudgment. After the D-PMU of vertex 7 does not lose synchronization, the estimated fault graph weight is greater than 0. At this time, the fault graph weights of the two vertices downstream of vertex 6 are both greater than 0, and the result of DF does not converge. Vertices 6 and 7 are in the same community, and vertex 26 is in another community, which causes PLMDF to fall into a local optimum during the query process, and the output fault segment is 7,8. The scale of the community in IPLMDF is larger, vertex 6, vertex 7 and vertex 26 are merged into the same community, and the output result is the global optimal solution, namely 28, 29. Compared with the first three methods, CS does not converge in the output results of the fifth and ninth cases, and outputs wrong results in the third case.

When the two D-PMUs closest to the fault point lose synchronization, none of the above four methods can locate the accurate fault section.

To sum up, when some D-PMUs in the network lose time synchronization, IPLMDF has the best positioning effect, followed by DF and PLMDF, and CS is the worst.

In order to verify that the present invention can quickly locate faulty sections, the calculation speeds of the above four methods are compared in the embodiment. Since the number of iterations of the above four methods is mainly affected by the location of the fault section, the embodiment selects the middle point of the fault occurrence line and the result of the fault resistance value of 1000Ω as a representative. Figure 9 is a comparison of the iteration times of the four methods under normal conditions, and Figure 10 is a comparison of the iteration times of the four methods when some D-PMUs lose time synchronization. From Figure 9 and Figure 10, it can be concluded that the performance of CS is unstable due to the existence of random processes, and the number of iterations is generally more than 10; DF is most sensitive to the topological position of the fault section, when the fault section is close to the power node The fault section can be quickly located. If the fault section is close to the end of the line, more iterations are required to locate the fault section. Compared with DF, PLMDF is less affected by the topological position of the fault section, but it can It still needs 5 or more iterations to locate the fault; IPLMDF has the most stable performance, and usually only needs 2-3 iterations to directly and accurately locate the fault section.

Through the comparison of the above three aspects, it can be intuitively found that the method for locating a single-phase-to-ground fault in a distribution network of the present invention is superior to the other three methods in terms of robustness and calculation speed.

Through the above method, the present invention provides a method for locating a single-phase ground fault in a distribution network, which takes into account the influence of the location of the fault and the fault resistance on the locating result, and at the same time reduces the configuration of the D-PMU in the distribution network model to a certain extent quantity. First, the head-end node of the self-distribution network model starts to configure D-PMU at intervals, and calculates the three-phase current sequence of nodes without D-PMU and the standard deviation of the fault phase current of each node within a time window when a fault occurs. Then, in The distribution network graph model is established on the graph database according to the topological structure of the distribution network model, and IPLM is run after each edge obtains the corresponding weight. Finally, the first vertex of the fault section is queried from top to bottom on the basis of the IPLM operation results. , and determine the exact fault segment according to the weight ratio of this vertex to the previous vertex. The single-phase grounding fault location method of the distribution network of the present invention is not affected by the location of the fault and the fault resistance, uses the graph calculation theory and the graph database platform, and is only realized when half of the nodes in the distribution network model are equipped with D-PMUs Fast and accurate positioning of single-phase ground faults is ensured, and when some D-PMUs lose time synchronization, the fault section can still be accurately located.

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;

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,

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;

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:

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;

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;

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:

then the zero sequence voltage of node i without D-PMU is expressed as:

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:

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:

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,

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:

wherein,

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;

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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