1. A traveling wave fault positioning method based on a directed tree model and linear fitting comprises the following steps:

1) judging a line MN with a fault in the power transmission network, analyzing a transmission path of a fault traveling wave in the power transmission network, and solving the shortest transmission path of the fault traveling wave in the power transmission network, namely the transmission path of a fault initial traveling wave, by combining the analysis of a graph theory;

2) in the graph theory, a tree is a finite set of n (n is more than or equal to 0) nodes, a power transmission network with a fault is defined as a directed tree model, a fault point f is defined as a root node of the tree, two end points M, N of a fault line where the fault point f is located are root nodes of subtrees, and a path L of fault initial traveling waves obtained in the step 1) is transmitted to other end points on the left side and the right side of the power transmission network from M, N_M，L_N；

3) Selecting a subtree root node M as a distance base point, defining the fault initial traveling wave transmitted to the root node f direction along the distance base point M as a positive direction traveling wave, the wave velocity is positive, the passing end point is a positive direction end point, the distance from the node M to the root node is positive, otherwise, the fault initial traveling wave is a negative direction traveling wave, the wave velocity is negative, the passing end point is a negative direction end point, and the distance from the node M to the root node is negative, so that the transmission distances from the positive direction end point and the negative direction end point to the root node are respectively L₊＝L_N+l_MN，L_-＝-L_MWherein l is_MNM, N, defining the endpoint of the transmission path of the fault initial traveling wave in the power transmission network, which is not matched with the transmission time, as a virtual point;

4) according to a double-end traveling wave positioning formula and a linear fitting principle, two sets of positive and negative data points which are formed by the transmission distance obtained in the step 3) and the arrival time of the fault initial traveling wave detected by each end point can be respectively fitted to form two fitting straight lines which are intersected with each other and have mutually opposite slopes in a rectangular coordinate system with the time as an X axis and the distance as a Y axis;

5) judging whether each positive and negative data point meets the correction criterion 1, if so, executing the step 6), otherwise, returning to the step 4), and simultaneously eliminating virtual data points possibly generated in the step 3);

6) judging whether the slopes of the two fitting straight lines meet the correction criterion 2, if so, executing the step 7), otherwise, returning to the step 4);

7) and finally, obtaining the vertical coordinate of the intersection point of the two fitting straight lines, namely the distance from the fault point f to the base point M, finishing the positioning process and realizing the accurate positioning of the fault position.

2. The traveling wave fault location method based on the directed tree model and the linear fitting as claimed in claim 1, wherein the linear fitting correction criterion 1 is characterized in that: in the step 5), the correction criterion 1 is: | t_k'-t_kLess than or equal to 1 mu s; in the formula t_k' fitting time value, t, for calculation_kIs the actual time value recorded. Fitting value t of fault traveling wave arrival time of each power station one by one_k' following the actual recorded value t_kAnd carrying out error correction. According to the existing high-precision synchronous second clock based on the digital phase locking principle, the time synchronization error can be 1 mu s. Fitting value t of each power station_k' with the actual recorded value t_kThe difference of (a) is less than 1 mus, i.e. all forward and reverse stations have to meet the correction criterion 1.

3. The traveling wave fault location method based on the directed tree model and linear fitting of claim 1, wherein the linear fitting correction criterion 2 is characterized in that: in step 6) shown, the correction criterion 2 is:where a is the slope of the fitted line, v_lightIs the speed of light. According to the traveling wave transmission principle, the wave speed of the traveling wave is close to the speed of light. Although the traveling wave has certain dispersion characteristics, and traveling wave components with different frequencies have different propagation speeds when being transmitted on the transmission line, the deviation amount of the traveling wave speed relative to the light speed is small. Based on the above analysis, the slope of the fitting straight line showing the fault traveling wave characteristic must satisfy the correction criterion 2.

Background

With the rapid development of smart grids, the capacity and grid area of a power system are continuously enlarged, so that the operation management of the power grid becomes more and more complex. If the fault position can be quickly and accurately determined after the transmission line has a fault, the burden of line patrol and line maintenance of workers can be reduced, and the loss of the whole economy caused by power failure can be reduced. Therefore, high-precision grid fault location is of great significance to safe, stable and economic operation of the power system.

The position of the fault point of the high-voltage transmission line is usually calculated by using an impedance method, but the measurement accuracy of the impedance method is greatly influenced by factors such as fault resistance, transformer error, asymmetry of a line structure, uneven distribution of zero-sequence parameters along the line and the like, so that the actual application effect of the impedance method is not ideal. With the continuous development of computer communication and measurement technology, scholars at home and abroad propose various power transmission network fault positioning methods. Among them, many fault location methods based on the traveling wave principle are widely used in power transmission networks because they can be applied to power transmission lines having various structures, different transition resistances, and different parameters. The method based on the traditional single-ended traveling wave positioning principle is easy to implement and high in reliability during fault positioning, but the method is interfered by a complex ring network structure in a power transmission network, and the reflected traveling wave for positioning is difficult to accurately identify. Compared with a single-ended method, the method based on the double-ended traveling wave positioning principle is not influenced by various reflected waves and refracted waves, and only the initial fault traveling wave heads reaching the two ends of the power transmission line need to be captured. However, in some existing double-end traveling wave positioning methods, only fault information on one side or two sides of a line is generally considered for positioning, fault information of the whole network is not fully utilized, and accuracy and reliability of fault positioning need to be improved.

In addition, based on the traveling wave fault location of a single line, when the locating device fails, has a fault or the time record of the locating device has an error, the locating reliability is not ensured, and the requirement of the operation of the power grid cannot be met.

In summary, a fault traveling wave positioning method for eliminating recording clock errors is urgently needed at home and abroad.

Disclosure of Invention

The invention provides a traveling wave fault positioning method based on a directed tree model and linear fitting, which solves the problem that fault positioning fails under the abnormal conditions of fault, starting failure or time recording error and the like of a certain positioning device in a power transmission network, solves the problem that some existing positioning methods cannot comprehensively utilize the fault positioning information of the whole power transmission network, simultaneously eliminates the influence of traveling wave speed uncertainty and fault traveling wave time recording error on positioning precision, can realize automatic loop-opening of a power transmission network ring network, and improves the reliability and accuracy of fault positioning. The invention comprises the following steps:

1) judging a line MN with a fault in the power transmission network, analyzing a transmission path of a fault traveling wave in the power transmission network, and solving the shortest transmission path of the fault traveling wave in the power transmission network, namely the transmission path of a fault initial traveling wave, by combining the analysis of a graph theory;

2) in the graph theory, a tree is a finite set of n (n is more than or equal to 0) nodes, a power transmission network with a fault is defined as a directed tree model, a fault point f is defined as a root node of the tree, two end points M, N of a fault line where the fault point f is located are root nodes of subtrees, and a path L of fault initial traveling waves obtained in the step 1) is transmitted to other end points on the left side and the right side of the power transmission network from M, N_M，L_N；

3) Selecting a subtree root node M as a distance base point, defining the fault initial traveling wave transmitted to the root node f direction along the distance base point M as a positive direction traveling wave, the wave velocity is positive, the passing end point is a positive direction end point, the distance from the node M to the root node is positive, otherwise, the fault initial traveling wave is a negative direction traveling wave, the wave velocity is negative, the passing end point is a negative direction end point, and the distance from the node M to the root node is negative, so that the transmission distances from the positive direction end point and the negative direction end point to the root node are respectively L₊＝L_N+l_MN，L_-＝-L_MWherein l is_MNM, N, defining the endpoint of the transmission path of the fault initial traveling wave in the power transmission network, which is not matched with the transmission time, as a virtual point;

4) according to a double-end traveling wave positioning formula and a linear fitting principle, two sets of positive and negative data points consisting of the transmission distance obtained in the step 3) and the arrival time of the initial fault traveling wave detected by each end point can be respectively fitted to form two fitting straight lines which are intersected and have mutually opposite slopes in a rectangular coordinate system with the time as an X axis and the distance as a Y axis;

5) judging whether each positive and negative data point meets the correction criterion 1, if so, executing the step 6), otherwise, returning to the step 4), and simultaneously eliminating virtual data points possibly generated in the step 3);

6) judging whether the slopes of the two fitting straight lines meet the correction criterion 2, if so, executing the step 7), otherwise, returning to the step 4);

7) and finally, obtaining the vertical coordinate of the intersection point of the two fitting straight lines, namely the distance from the fault point f to the distance base point M, finishing the positioning process and realizing the accurate positioning of the fault position.

In the power transmission network fault traveling wave positioning method, in the step 5), the correction criterion 1 is as follows: | t_k'-t_kLess than or equal to 1 mu s; in the formula t_k' fitting time value, t, for calculation_kIs the actual time value recorded. In the step 6), the correction criterion 2 is:where a is the slope of the fitted line, v_lightIs the speed of light.

The invention has the beneficial effects that:

1) according to the method, the relationship that the arrival time of the traveling wave head recorded by the positioning device is in direct proportion to the shortest path distance between each transformer substation is utilized, the related data can be subjected to linear fitting, the fault distance can be calculated, and the influence of uncertainty of the wave speed on the positioning result in most double-end traveling wave based fault positioning methods is eliminated.

2) The method has high fault tolerance reliability, all recorded data are drawn in the rectangular coordinate system, and even if the arrival time of the fault traveling wave of a positioning device in the power network is not recorded or the recording is wrong, the time recording error point can be automatically eliminated through linear fitting, and accurate fault positioning can be still realized.

3) The method is based on the directed tree model, comprehensively utilizes the fault information of the whole power transmission network in fault positioning, and compared with the conventional method for processing the fault information by using a weighted average method, the method avoids the weighted imbalance of weight representative data, eliminates the artificial error caused by weighting, and has a more convenient and reasonable data processing mode.

4) The method can ensure that the shortest path obtained passes through the fault line through the shortest path, eliminates the non-shortest path of fault traveling wave, saves the loop disconnection of network loop, reduces the data required by the criterion and makes the fault location easier.

Drawings

Fig. 1 is a diagram of a traveling wave transmission network topology.

Fig. 2 is a diagram of a fault initial traveling wave directed tree model.

Fig. 3 is a diagram of a transmission grid shortest path topology.

Fig. 4 is a fault traveling wave linear fit graph.

Fig. 5 is a schematic diagram of a fault location method.

FIG. 6 is a 500kV transmission network simulation topological model diagram.

FIG. 7 shows a fault f₁Positioning schematic diagram.

FIG. 8 shows a fault f₂Positioning schematic diagram.

FIG. 9 shows a fault f₃Positioning schematic diagram.

FIG. 10 shows a fault f₄Positioning schematic diagram.

Detailed Description

In order to make the technical scheme and the implemented functions of the present invention clearer, the present invention is further described below with reference to the accompanying drawings and embodiments.

The fault initial traveling wave is transmitted in the shortest path in the whole power grid to form a fault initial traveling wave transmission network, as shown in FIG. 1As shown. The invention adopts a graph theory method to analyze the network and provides a directed tree model constructed by the shortest path directed tree. The directed tree model is shown in fig. 2, and a failure point f is defined as a root node of the tree. M, N is a subtree root node, the shortest path of traveling wave transmission from the fault point f is equal to the shortest path of transmission to the left and right ends of M, N, the shortest path from the subtree root node to each transformer substation is the shortest path of traveling wave transmission, the invention calculates the shortest path of two subtree root nodes according to the shortest path algorithm: l is_M， L_N. Selecting any subtree node M as a distance base point, defining that the initial traveling wave is positive traveling wave when propagating to the root node (fault point) along the base point, the wave velocity is positive, the initial traveling wave is negative traveling wave when propagating to the base point along the fault point, the wave velocity is negative, the transformer substation through which the positive traveling wave passes is a positive transformer substation, the distance between the positive traveling wave and the base point is positive, otherwise, the distance between the positive traveling wave and the base point is negative, and each detection distance is the distance between the detection distance and the coordinate base point. Obviously, the transmission distance of the forward transformer substation to the base point is L₊＝L_N+l_MNThe transmission distance of the transformer substation in the negative direction to the base point is L_-＝-L_M。

As shown in fig. 1, the power transmission network has a ring network MND and an EFH. When a failure occurs in the ring network, the traveling wave of the failure may reach the point D (f → M → D) from the failure point via M or reach the point D (f → N → D) via N, and therefore, it is necessary to determine the transmission path of the initial traveling wave. The non-shortest path interference circuit in the judging process is defined as a virtual tree, so that a shortest path directed tree model suitable for ring network fault location is established. The method comprises the following specific steps:

step 1: d and H, the looped network is unfastened, and subtree nodes D 'and H' are added;

step 2: establishing a shortest path directed tree model;

and step 3: and judging the point D and the point H, and excluding the wrong virtual tree.

Since the H point is fixed and unique based on the shortest path algorithm when finding the shortest path, there is no virtual tree at the H point and the H' F path should be eliminated in the directed tree model. Point D cannot determine the shortest path for traveling wave transmission, so MD and ND' can be defined as virtual trees. The method provided by the invention can automatically release the ring network, and the incorrect virtual tree can be automatically eliminated by utilizing the self-adaptability of the algorithm in the process of determining the transmission path.

Line M in shortest path topology of power transmission network when fault occurs₁N₁As shown in fig. 3. With a substation M₁For a distance base point, all substations in the transmission network are defined as k, i.e.:

for any substation k to the left of the fault point f, there must be:

l_M1k＝v(t_k-t_M1)＝vt_k-vt_M1 (2)

where v is the propagation velocity of the traveling wave; m₁k is from M₁Shortest path to any substation k; t is t_M1Is a detection point M₁The initial traveling wave arrival time is recorded. t is t_kIs the initial traveling wave arrival time recorded at any detection point k. Likewise, for any substation k to the right of the fault point f, there must be:

in the formula t_N1Is a detection point N₁Recording the arrival time of the initial traveling wave; l_M1N1Is a point M₁And point N₁The shortest distance between them via the fault point f.

By observing equations (2) and (3), it was found that they can be linearly fitted using the principle of unary linear regression. Let Y equal to l_M1k，X＝t_k. In the formula (2), let a₁＝v，b₁＝-vt_M1I.e. Y ═ a₁X+b₁. In formula (3), let a₂＝v，b₂＝-vt_N1+l_M1N1I.e. Y ═ a₂X+b₂. According to the above analysis, a₁And a₂Are both v, should be of theoretically equal magnitude, but from a linear fitting point of view the slopes of the two lines fitted through the two different sets of data will be somewhat different, so they will only be approximately equal. According to the principle of unary linear regression, using a₁、a₂、b₁And b₂The parameters calculate the minimum value of equation (4).

Wherein k (i) ═ M_i(i＝1,2,…,m)，k(j)＝N_j(j ═ 1,2, …, n). Based on the minimum value, a₁、a₂、 b₁And b₂The parameters should satisfy equations (5) and (6):

the formulas (5) and (6) are simplified to obtain a₁、a₂、b₁And b₂The parameter values are as follows:

a fitted straight line 1(Y ═ a) can be obtained according to equation (7)₁X+b₁) A fitted straight line 2(Y ═ a) can be obtained according to equation (8)₂X+b₂) As shown in fig. 4.

According to directionDefinition of the Tree model, M₁Are arranged as distance base points as shown in fig. 3. The traveling wave traveling rightward from the failure point f is a forward traveling wave, the wave speed is positive, and N₁，N₂，...，N_nIs a forward substation with a positive distance from the base point. Conversely, the traveling wave traveling leftward from the failure point f is a negative traveling wave, the wave speed is negative, and M₁，M₂，...，M_mIs a negative direction substation with a negative distance from the base point. At this time, all the substations in fig. 3 still satisfy equations (2) and (3), but the wave velocity is changed from scalar to vector.

From the above definitions and analysis, there is then a change in the slope of the fitted straight line 1 of FIG. 4 from + v to-v (i.e., a)₁Is changed into-a₁) Intercept of-vt_M1Becomes + vt_M1(i.e. b)₁Is changed to-b₁) As shown in fig. 5. At the moment, the two fitting straight lines have a unique intersection point f, and the figure shows that the fault traveling wave characteristic of the point f simultaneously accords with the traveling wave transmission characteristics of the forward transformer substation and the reverse transformer substation, namely the transmission direction of the traveling wave is positive and negative. According to the traveling wave transmission principle, the f point is necessary to be a fault point, and the ordinate of the f point represents the distance from the fault point to the base point M₁Fault distance l of_M1f. The intersection ordinate can be obtained from the system of equations (9) for two fitted straight lines in parallel:

compared with the traditional traveling wave positioning method, the method establishes a rectangular coordinate system representing the transmission characteristics of the fault traveling wave, and comprehensively utilizes the fault information of the whole power transmission network. In the rectangular coordinate system, the influence of the wave speed as the slope of the fitting straight line on fault positioning can be automatically eliminated, and accurate fault positioning can be realized according to the intersection point of the positive fitting straight line and the negative fitting straight line. The algorithm is simple and easy to implement, and does not need a complex solving process, so that the algorithm is easy to apply to an actual power system.

Although the positioning algorithm based on the intersection point of the fitting straight line can automatically eliminate the recording time of the interference fault traveling wave, the positioning algorithm is not influenced by the fault of equipment at a certain point or the error of the synchronization time. However, in order to improve the positioning accuracy of the algorithm, the invention provides two correction criteria of the fitting straight line to ensure the high accuracy of the fitting straight line and realize the undifferentiated description of the transmission characteristics of the fault traveling wave.

Correction criterion 1: fitting value t of fault traveling wave arrival time of each power station one by one_k' following the actual recorded value t_kAnd carrying out error correction. According to the existing high-precision synchronous second clock based on the digital phase locking principle, the time synchronization error can be 1 mu s. Fitting value t of each power station_k' with the actual recorded value t_kIs less than 1 mus, i.e. all forward and reverse stations have to satisfy formula (11):

|t_k'-t_k|≤1μs (11)

correction criterion 2: according to the traveling wave transmission principle, the wave speed of the traveling wave is close to the speed of light. Although the traveling wave has certain dispersion characteristics, and traveling wave components with different frequencies have different propagation speeds when being transmitted on the transmission line, the deviation amount of the traveling wave speed relative to the light speed is small. Based on the above analysis, the slope of the fitting straight line showing the traveling fault wave characteristic must satisfy equation (12):

in order to verify the feasibility of the invention, a 500kV power transmission network simulation model shown in FIG. 6 is constructed by using PSCAD, the model consists of 10 substations and 14 power transmission lines, each substation is provided with a traveling wave positioning device, the parameters of the power transmission lines are shown in Table 1, and the length of each power transmission line is marked in FIG. 6 and is km. In the simulation model, an A-phase grounding fault f with a transition resistance of 50 omega is set on a line CD at a distance of 26.95km from a point C₁(ii) a Over the line EFBC phase grounding fault f with transition resistance of 100 omega is arranged 39.53km away from the E point₂(ii) a Setting BC phase-to-phase fault f with transition resistance of 200 omega at distance of 68.74km from point I on line IG₃(ii) a A C-phase grounding fault f with the transition resistance of 400 omega is arranged on the line AJ at a distance of 85.31km from the point A₄。

The traveling waves generated by the above 4 faults are processed by phase-mode transformation and wavelet transformation, and the time of arrival of the wave head at each substation is obtained as shown in table 2.

In order to verify that the fault can still be accurately positioned under the condition that a traveling wave positioning device of a certain transformer substation in a power transmission network fails or the time record is incorrect, different fault situations are respectively set in 4 faults: suppose when fault f₁When the fault happens, the time record of the traveling wave positioning device of the transformer substation G is 926.8 mu s; when fault f₂When the fault happens, the traveling wave positioning device of the transformer substation H fails, and the time record of the traveling wave positioning device of the transformer substation C has the fault of 913.9 mu s; when fault f₃When the fault occurs, the traveling wave positioning device of the transformer substation C fails; when fault f₃When the fault occurs, the time recording errors of the traveling wave positioning devices of the substations D and G are 1008.8 mus and 538.6 mus respectively.

Positioning schematic diagrams of 4 faults obtained under different fault conditions according to the directed tree model and the linear fitting principle are respectively shown in fig. 7-10, and positioning results are shown in table 3. The method provided by the invention has the advantages of high precision and small error, the fault location can be realized only by the intersection point coordinates of two fitting straight lines, the fault location thought is simple, convenient and feasible, and the fault location error of any position and type in the power transmission network is less than 0.01%. Even if a certain positioning device in the power transmission network fails or time recording is wrong, the error point of positioning can be effectively eliminated through the correction criterion in the method, and a highly accurate and reliable fault positioning result can still be obtained.

Table 1500 kV transmission line simulation parameters

TABLE 2 time of arrival of initial traveling wave at each substation

TABLE 3 Fault location results