Precise Fault Location Method for Complex Power Grids Considering Wave Velocity Attenuation and Time Error

Abstract

The present invention discloses a precise fault location method for complex power grids considering wave velocity attenuation and time error. First, based on the traveling wave transmission law, an equality constraint of wave velocity, time, and distance is established. Secondly, according to the wavefront time error range and wave velocity attenuation law, an average wave velocity variable is introduced to form an inequality constraint. Thirdly, with the goal of minimizing the deviation degree between the wavefront time and the center of the wavefront shape, a shortest path critical flag variable is introduced, a shortest distance function from the fault point to the measurement point is constructed, and a traveling wave fault location model is established. Finally, the optimal solution of the model is solved to obtain the fault distance. The present invention relates to the field of precise fault location for complex power grids. This method can effectively reduce the influence of synchronization error, sampling accuracy, and wave velocity attenuation on the location accuracy, and achieve fast, accurate, and reliable fault location under complex power grids.

Description

Technical Field

[0001] The present invention relates to the field of precise fault location in complex power grids, and specifically to a precise fault location method for complex power grids considering wave velocity attenuation and time error. Background Art

[0002] At present, the traveling wave location methods for transmission power grids mainly include single - end method, double - end method, and wide - area method. Among them, the single - end method and the double - end method mainly focus on the fault location of a single line. With the increasing complexity of the transmission power grid topology and the development of synchronization technology, some scholars have proposed the wide - area traveling wave method. This method comprehensively utilizes the measurement information of the whole network or a part of it, improves the information utilization rate, and realizes relatively precise fault location. At present, the synchronization accuracy and sampling rate of the actual traveling wave measurement equipment can meet the basic requirements of wide - area traveling wave location, but there are still errors at the microsecond level, resulting in deviations between the obtained wave - head time - frequency information and the actual situation, which limits the improvement of the location accuracy. In practical engineering applications, the wide - area synchronous measurement equipment of the transmission power grid with a large range and wide span may experience out - of - step problems of different degrees due to equipment failures, reference time source switching, etc., resulting in abnormal wave - head time information. In addition, the selection of wave velocity is also a major factor affecting the accuracy of the wide - area traveling wave method. If the wave velocity attenuation is not considered in the traveling wave method, the traveling wave data far from the fault point will bring large errors to the location. Most importantly, in the case of a complex network, there are many loop network structures and they show characteristics of mutual coupling and nesting, and the data involving loop networks account for a high proportion, so an effective online loop network processing method needs to be established.

[0003] Facing the above challenges, it is of great significance to study the time - error principle and wave - velocity attenuation law, and propose a method that can effectively reduce the influence of synchronization error, sampling accuracy, and wave - velocity attenuation, and realize fast, accurate, and reliable fault location under complex power grids. Summary of the Invention

[0004] In view of the above situation, to solve the problem that the accuracy of the existing traveling - wave fault location is affected by synchronization error, sampling accuracy, and wave - velocity attenuation, the present invention provides a precise fault location method for complex power grids considering wave - velocity attenuation and time error.

[0005] The present invention provides the following technical solutions: A precise fault location method for complex power grids considering wave - velocity attenuation and time error proposed by the present invention specifically includes the following steps:

[0006] (1) According to the current topology data, use the Dijkstra method to establish the optimal path matrix L, and form the shortest distance difference matrix L of the fault line ifj ;

[0007] (2) Form the upper and lower limit matrices V low 、V up , and define the wave - velocity variable matrix Form a wave velocity constraint;

[0008] (3) According to the wavefront acquisition data, extract the upper and lower limits t es and t se of the wavefront time difference to form a time upper and lower limit matrix T se and T es , define a time difference variable matrix T * , and establish a time constraint;

[0009] (4) Establish a wavefront center time matrix T mij , construct an objective function, and construct a traveling wave fault location model;

[0010] (5) Solve the established model to obtain the fault location result;

[0011] (6) If there is no solution, remove the time constraint from the model and solve it again to obtain the fault location result, thereby realizing fault location.

[0012] Furthermore, the method for establishing the optimal path matrix L in step (1) is as follows:

[0013] Obtain the line lengths of the system topology, label each current node with numbers 1 to N, and establish an adjacency matrix B:

[0014] B = [b ij N×N (1 ≤ i, j ≤ N)

[0015] The elements b ij in the matrix take the following values:

[0016]

[0017] Substitute the adjacency matrix B into the Dijkstra algorithm to solve and obtain the shortest distance matrix L between nodes:

[0018] L = [l ij N×N (1 ≤ i, j ≤ N)

[0019] In the formula, l ij is the shortest distance from node i to node j;

[0020] Form a shortest distance difference matrix L ifj of the fault line: After the fault, identify the fault line according to the breaker status, mark the node numbers at both ends of the fault line as A and B, A > B, set A as the reference node, and set x as the length of the fault point from node A. If it satisfies:

[0021] |l Ai - l Bi | ≥ l AB ​​

[0022] Then the shortest path length \(l\) from the fault point to node \(i\) fi is expressed as:

[0023]

[0024] If not satisfied, then:

[0025]

[0026] In the formula, \(b\) i is the critical point of the shortest distance of the current line relative to node \(i\), \(l\) Abi is the distance between the reference end point \(A\) of the line and the critical point \(b\) i ; \(b\) i is the critical point existing on \(l\) AB , and this critical point makes the position of the fault point \(F\) determine the value of \(l\) fi \((x)\); \(s\) i is the critical flag variable of the shortest path of this line relative to node \(i\), and its value is:

[0027]

[0028] Then generate the set \(L\) of the shortest distance functions from the fault point to all nodes in the network if =\(\{l\) f1 \((x), l\) f2 \((x), \cdots, l\) fN \((x)\}\). Furthermore, generate the shortest distance difference matrix \(L\) ifj :

[0029]

[0030] The value of the element \(l\) ifj \((x)\) is:

[0031] \(l\) ifj \((x)=l\) fi \((x)-l\) fj \((x)\).

[0032] Furthermore, in step (2), the wave speed constraint is established as follows:

[0033]

[0034] In the formula, the matrices \(V\) low and \(V\) up are the wave speed upper limit matrix and the wave speed lower limit matrix respectively. The matrix elements are \(0.936c\) and \(0.987c\) respectively, where \(c\) represents the speed of light, \(c = 3\times10\) 8 m / s. \(V\) * is:

[0035]

[0036] In the formula, the matrix element is the average wave velocity variable between each node.

[0037] Furthermore, in step (3), the time constraint is established as follows:

[0038] Process the first wave head through db6 wavelet transform and extract the detail coefficients of the d1 layer of the wavelet. Set the fluctuation range of the actual wave head arrival time as the range of the entire transient process in this frequency band, and use the morphological center of this transient process as the fluctuation center of the wave head time, which is expressed as:

[0039] t si < t i < t ei

[0040] In the formula, t i is the time when the first wave head arrives at node i. If there is no measurement point at node i, then t i = 0; t si is the transient start time of the first wave head at node i, and t ei is the transient end time of the first wave head at node i. If t i = 0, then t si = 0, t ei = 0; According to the above wave head time fluctuation range, the fluctuation range of the wave head time difference t ij between each node is obtained:

[0041] t si - t ej < t ij < t ei - t sj

[0042] In the formula, t ij takes values as:

[0043]

[0044] Establish a matrix T * of the wave head arrival time difference variables between each node:

[0045]

[0046] In the formula, N is the total number of nodes, and the matrix element t*ij is the wave head arrival time difference to be obtained between each node; similarly, establish an upper time limit matrix T es and a lower time limit matrix T se , matrixize the fluctuation range of the wave head time difference t ij between each node and substitute it into T* to obtain the time constraint:

[0047] T se < T* <T es

[0048] In the formula, the matrix T se 、T es elements are t seij =t si -t ej ,t esij =t ei -t sj ,and the value-taking method is the same as that of t ij 。

[0049] Furthermore, in step (4), the objective function is established as follows:

[0050] Take the average value of the transient start and end times as the corresponding time t of the waveform center mi ,and establish the wavefront time center vector T m {t m1 , t m2 ,…,t mN}。By analogy with T ij ,establish the wavefront time center difference matrix:

[0051] T mij =[t mij N×N (1≤i,j≤N)

[0052] Define the time difference degree matrix E:

[0053] E=T mij -T *

[0054] In the formula, the element e ij in the matrix E is the node time difference degree, which is defined as:

[0055]

[0056] Set the objective function as:

[0057] min||T mij -T * || F

[0058] Furthermore, in step (5), the model is established as follows:

[0059]

[0060] In the formula, T * is the variable matrix in the model, and its physical meaning after solution is the corrected first wavefront arrival time difference data; L ifj is the function matrix containing the variable x, and the fault distance x is obtained after solution.​

[0061] The beneficial effects achieved by the present invention with the above structure are as follows: A precise fault location method for complex power grids considering wave velocity attenuation and time error proposed by the present invention, based on the time error principle and wave velocity attenuation law, provides a precise fault location method for complex power grids considering wave velocity attenuation and time error. This location method can effectively reduce the influence of synchronization error, sampling accuracy, and wave velocity attenuation, and realize a fast, accurate, and reliable fault location method for complex power grids, which is of great significance. Description of the Drawings

[0062] The drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation to the present invention. In the drawings:

[0063] Figure 1 is the overall flowchart of a precise fault location method for complex power grids considering wave velocity attenuation and time error proposed by the present invention;

[0064] Figure 2 is the topological schematic diagram of a power grid line configured with traveling wave measurement points for a precise fault location method for complex power grids considering wave velocity attenuation and time error proposed by the present invention. Detailed Embodiments

[0065] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments; based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0066] It should be noted that the terms "front", "rear", "left", "right", "up" and "down" used in the following description refer to the directions in the drawings, and the terms "inner" and "outer" respectively refer to the directions towards or away from the geometric center of a specific component.

[0067] As Figure 1 、 Figure 2 shown, the technical solutions adopted by the present invention are as follows:

[0068] A typical topological structure of a power grid line configured with traveling wave measurement points is as Figure 2 shown. The present invention proposes a precise fault location method for complex power grids considering wave velocity attenuation and time error. Its overall process is as Figure 1 shown, including the following steps:

[0069] (1) Use the Dijkstra method to establish the optimal path matrix L based on the current topological data:

[0070] Obtain the line length of the system topology, label each current node with numbers from 1 to N, and establish an adjacency matrix B:

[0071] B = [b ij N×N (1 ≤ i, j ≤ N)

[0072] The element b ij in the matrix takes the following values:

[0073]

[0074] Substitute the adjacency matrix B into the Dijkstra algorithm to solve and obtain the shortest distance matrix L between nodes:

[0075] L = [l ij N×N (1 ≤ i, j ≤ N)

[0076] In the formula, l ij is the shortest distance from node i to node j.

[0077] Form the shortest distance difference matrix L ifj of the faulty line: After a fault, identify the faulty line based on the breaker status, mark the node numbers at both ends of the faulty line as A and B, A > B, set A as the reference node, and set x as the length of the fault point from node A; if it satisfies:

[0078] |l Ai - l Bi | ≥ l AB

[0079] Then the shortest path length l fi (x) from the fault point to node i is expressed as:

[0080]

[0081] If not satisfied, then:

[0082]

[0083] In the formula, b i is the shortest distance critical point of the current line relative to node i, l Abi is the distance between the reference end point A of the line and the critical point b i , b i is the critical point existing on l AB such that the position of the fault point F will determine the value of l fi (x); s i is the shortest path critical flag variable of this line relative to node i, and its value is: ​​

[0084]

[0085] Then generate the set L of the shortest distance functions from the fault point to all nodes in the network if ={l f1 (x), l f2 (x), …, l fN (x)}; Furthermore, generate the shortest distance difference matrix L ifj :

[0086]

[0087] The value of the element l ifj (x) in the formula is:

[0088] l ifj (x)=l fi (x)-l fj (x);

[0089] (2) Form the upper and lower limit matrix V low 、V up of the wave velocity value, define the wave velocity variable matrix to form the wave velocity constraint, and V * should satisfy:

[0090]

[0091] In the formula, the matrix V low and V up are the upper and lower limit matrices of the wave velocity respectively, and the matrix elements are 0.936c and 0.987c respectively, where c represents the speed of light, c = 3×10 8 m / s;

[0092]

[0093] In the formula, the matrix element is the average wave velocity variable between each node;

[0094] (3) According to the wave head acquisition data, extract the upper and lower limits t es 、t se of the wave head time difference, form the upper and lower limit matrix T se 、T es , define the time difference variable matrix T * , and establish the time constraint:

[0095] Process the first wave head through db6 wavelet transform and extract the detail coefficients of the d1 layer of the wavelet. Set the fluctuation range of the actual wave head arrival time as the range of the entire transient process in this frequency band, and use the morphological center of this transient process as the fluctuation center of the wave head time, which is expressed as:

[0096] t si <t i <t ei

[0097] In the formula, t i is the time when the first wave head arrives at node i. If there is no measurement point at node i, then t i = 0. t si is the transient start time of the first wave head at node i, and t ei is the transient end time of the first wave head at node i. If t i = 0, then t si = 0, t ei = 0. According to the above wave head time fluctuation range, the wave head time difference t ij of each node is obtained:

[0098] t si - t ej <t ij <t ei - t sj

[0099] In the formula, t ij takes values as:

[0100]

[0101] Establish a variable matrix T * of the arrival time difference of the first wave head at each node:

[0102]

[0103] In the formula, N is the total number of nodes, and the matrix element t*ij is the arrival time difference of the first wave head between each node to be solved. Similarly, establish an upper time limit matrix T es and a lower time limit matrix T se . Matrixize the fluctuation range of the wave head time difference t ij of each node and substitute it into T* to obtain the time constraint:

[0104] T se <T * <T es

[0105] In the formula, the elements of the matrices T se , T es are respectively t seij = t si - t ej , t esij = t ei - t sj , and the value-taking method is the same as that of t ij ;

[0106] (4) Establish the wavefront center time matrix T mij , construct the objective function, and construct the traveling wave fault location model;

[0107] Take the average value of the transient start and end times as the corresponding time t of the morphology center mi , and establish the wavefront time center vector T m {t m1 , t m2 , …, t mN}; By analogy with T ij , establish the wavefront time center difference matrix:

[0108] T mij = [t mij N×N (1 ≤ i, j ≤ N)

[0109] Define the time difference degree matrix E:

[0110] E = T mij - T *

[0111] In the formula, the element e ij in the matrix E is the node time difference degree, which is defined as:

[0112]

[0113] Set the objective function as:

[0114] min||T mij - T * || F

[0115] The model is established as follows:

[0116]

[0117] In the formula, T * is the variable matrix in the model, and its physical meaning after solution is the corrected first wavefront arrival time difference data; L ifj is the function matrix containing the variable x;

[0118] (5) Solve the established model to obtain the fault location result;

[0119] (6) If there is no solution, remove the time constraint from the model and solve it again to obtain the fault location result.

[0120] Simulation verification

[0121] ​To verify the proposed method, taking the IEEE 30-bus transmission network topology as an example, a distributed parameter model of the transmission line of this topology is built in PSCAD / EMTDC. The line lengths are shown in Table A1 of Appendix A, and the sampling frequency is 1 MHz. The configuration scheme of the traveling wave measuring device is shown in Figure 2 . The model is solved by calling Gurobi 9.1.2 in MATLAB. A single-phase grounding fault with a distance of 50 km from the reference node is set on line 10-17, and the grounding resistance is 50 Ω. Through model solving, the positioning result is 49.9851 km, and the error is 14.9 m. To verify the positioning effect of the proposed method at different positions, single-phase grounding faults are set at different positions of the built power topology, with a transition resistance of 50 Ω, and a time error of 1-2 μs is set. In addition, a fault is particularly set near the ring network critical point of 134 km on line 10-17 to verify the influence of the ring network critical point on positioning. The obtained ranging results are as follows:

[0122] Table 1 Ranging results at different fault positions

[0123]

[0124] Table 1 The simulation results show that the method of this paper can achieve the positioning of faults at different distances on different lines, and the positioning error is less than 100 m.

[0125] It should be noted that in this paper, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, material or device including a series of elements not only includes those elements, but also includes other elements not expressly listed, or also includes elements inherent to such process, method, material or device.

[0126] Although the embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A precise fault location method for complex power grids considering wave velocity attenuation and time error, characterized in that: Including steps (1) to (6) executed in sequence: (1)Use the Dijkstra method to establish an optimal path matrix based on the current topology data L to form a shortest distance difference matrix for the faulty line L ifj ; (2) Form the upper and lower limit matrix of wave velocity values V low , V up , define the wave velocity variable matrix , and form the wave velocity constraint; (3) Extract the upper and lower limits of the fluctuation of the wavefront time difference based on the wavefront acquisition data t es , t se to form a time upper and lower limit matrix T se , T es to define a time difference variable matrix T * and establish time constraints; (4)Establish the wavefront center time matrix T mij , construct the objective function, and construct the traveling wave fault location model; (5) Solve the established model to obtain the fault location result; (6) If there is no solution, remove the time constraint from the model and solve it again to obtain the fault location result; In step (2), the wave velocity constraint is established as follows: In the formula, the matrix V low and V up are the upper and lower limit matrices of the wave velocity respectively, and the matrix elements are 0.936 c , 0.987 c , c represents the speed of light, c = 3×10 8 m / s; In step (3), the time constraint is established as follows: Process the first wave head through db6 wavelet transform and extract the detail coefficients of the d1 layer of the wavelet. Set the fluctuation range of the actual wave head arrival time as the range of the entire transient process of the signal frequency band corresponding to the detail coefficients of the d1 layer of the wavelet, and use the morphological center of this transient process as the fluctuation center of the wave head time, expressed as: wherein, t i is the time when the first wave head reaches the node i If there is no measurement point at the node, as i then t i = 0, t si is the transient start time of the first wave head of the node i The transient end time of the first wave head of the node is t ei If i = 0, then t i = 0, according to the above wave head time fluctuation range, the wave head time difference t si = 0, t ei = 0, and the fluctuation range of the wave head time difference of each node is obtained: t ij The fluctuation range is: Establish a variable matrix of the arrival time difference of the first wave heads of each node T * : wherein, N is the total number of nodes, and the matrix element t* ij is the difference in arrival times of the first wavefronts between the nodes to be determined. Similarly, a time upper limit matrix T es and a time lower limit matrix T se are established. The fluctuation range of the node wavefront time difference t ij is matrixed and substituted into T * to obtain a time constraint: In the formula, the matrix T se , T es The elements are respectively t seij =t si -t ej , t esij =t ei -t sj , and the value-taking method is the same as t ij ; In step (4), the objective function is established as follows: Take the average of the transient start and end times as the time corresponding to the morphological center t mi , and establish the wavefront time center vector T m { t m1 , t m2 , …, t mN}, and by analogy T ij , establish the wavefront time center difference matrix: Set the objective function as: 。 2. The precise fault location method for complex power grids considering wave velocity attenuation and time error according to claim 1, characterized in that: In step (1), the optimal path matrix L is established as follows: Obtain the line lengths of the system topology, label each current node from 1 to N , and establish an adjacency matrix B : Elements in the matrix b ij The values are as follows: Substitute the adjacency matrix B into Dijkstra's algorithm to solve for the shortest distance matrix between nodes L : In the formula, l ij is the node i to node j the shortest distance.

3. The precise fault location method for complex power grids considering wave velocity attenuation and time error according to claim 2, characterized in that: In step (1), the shortest distance difference matrix of the faulty line L ifj The establishment method is as follows: After a fault, identify the faulty line based on the breaker status, and mark the node numbers at both ends of the faulty line as A and B , A > B . Let A be the reference node, and let x be the length of the fault point from node A . If it satisfies: The shortest path length from the fault point to node i is l fi ( x ) is expressed as: If not satisfied, then: Wherein, b i is the shortest distance critical point of the current line relative to the node i . l Abi is the distance between the reference end point A of the line and the critical point b i . b i is l AB The critical point existing on makes the position of the fault point F will determine l fi ( x ). s i is the shortest path critical flag variable of the line relative to the node i , thereby generating a set of shortest distance functions of the fault point to all nodes in the network L if ={ l f1 ( x ), l f2 ( x ),…, l fN ( x )}, and then obtaining the shortest distance difference matrix L ifj .

4. The precise fault location method for complex power grids considering wave velocity attenuation and time error according to claim 3, characterized in that: In step (5), the location model is established as follows: In the formula, T * is the variable matrix in the model, and its physical meaning after solution is the corrected first arrival time difference data; L ifj is the function matrix containing the variable x , and the fault distance x is obtained after solution.

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