CN112649700B - Traveling wave network positioning method based on dynamic virtual fault - Google Patents
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Abstract
The invention discloses a traveling wave network positioning method based on dynamic virtual faults, which comprises the following steps of 1: the arrival time of the initial traveling waves of all the measurement points is differenced pairwise to obtain a time characteristic matrix of the real fault; step 2: obtaining a time characteristic matrix of the virtual fault; and step 3:calculating time information difference e by using time characteristic matrix of real fault and time characteristic matrix of virtual faultt(ii) a And 4, step 4: continuously updating the position of the virtual fault point by using a PSO algorithm, repeating the steps 2-3, and gradually approaching the real fault point; when the iteration number is reached, or the time information difference etIf the value of (1) is less than the preset value, ending the iteration; and taking the current virtual fault point position as a fault point position to realize fault positioning. Simulation results show that the method does not need to analyze the network structure and network disconnection operation, can eliminate the influence of the traveling wave speed to a certain extent, and realizes accurate fault positioning.
Description
Technical Field
The invention relates to a traveling wave network positioning method based on dynamic virtual faults.
Background
As power systems have been developed and the size of power transmission networks has expanded, the length of lines and the transmission capacity have been gradually increased. After the transmission line breaks down, the fault is accurately positioned, effective measures are taken for the fault line, and the method has great significance for ensuring safe and reliable operation of the power system. In recent years, the fault location method mainly includes: impedance methods, fault analysis methods and traveling wave methods. Because the traveling wave method is not influenced by the system operation mode, has the characteristics of high response speed, high positioning accuracy and the like, more and more scholars are put into the study of traveling wave fault positioning.
The traveling wave method is mainly divided into a single-end positioning type and a double-end positioning type. The single-end method fault location has low operation cost, but a fault point reflection traveling wave head needs to be identified; the traditional double-end positioning method only needs to identify the wave head of the initial traveling wave of the fault, the positioning precision is relatively higher, but the method is influenced by time synchronization errors at two ends of a line, and the positioning precision depends on the accuracy of the selected wave velocity value.
Aiming at the problem that the traditional double-end positioning method is easily influenced by the time synchronization error of a measuring point and the accuracy of traveling wave detection, the traveling wave network positioning method becomes a hotspot studied by numerous experts and scholars. There is a document that proposes a network positioning method based on a Folyd algorithm, which can still realize fault positioning when a traveling wave detection device records a time error. The prior document provides a traveling wave positioning algorithm based on a linear fitting principle, and the algorithm establishes a directed tree model of the shortest path of fault traveling wave transmission by utilizing the linear relation between the transmission time and the transmission distance of the fault traveling wave, so that the problems of network data fusion and looped network ring opening of power transmission network fault traveling wave positioning can be solved. The determination of a faulty line by some of the literature methods still relies on breaker status information. According to the algorithm, according to the time information of the whole power grid traveling wave detection device, fault location can be still carried out after a certain wave recording device fails, starts out to be failed or time recording is wrong, and the fault line is determined without depending on the state information of a circuit breaker; but this method lacks efficient handling of wave speed uncertainty. The wave velocity value is a key factor influencing the fault positioning accuracy, is related to line parameters and is easily influenced by factors such as weather and geographic environment, and the wave velocity value is generally 0.936-0.987 times of the light velocity according to experience in engineering; when the calculated wave velocity does not coincide with the actual wave velocity, it will result in an excessive fault location error.
Therefore, it is necessary to design a new method for positioning a traveling wave network based on dynamic virtual faults.
Disclosure of Invention
The invention aims to solve the technical problem of providing a traveling wave network positioning method based on dynamic virtual faults, and the traveling wave network positioning method based on the dynamic virtual faults is easy to implement and high in positioning accuracy.
The technical solution of the invention is as follows:
a traveling wave network positioning method based on dynamic virtual faults is based on the current line construction, and comprises the following steps:
step 1: after the transmission line has a fault, the fault initial traveling wave reaches each transformer substation along the shortest path, the traveling wave detection device records the arrival time of the initial traveling wave, and the arrival times of the initial traveling waves of all measurement points are differenced pairwise to obtain a time characteristic matrix of the real fault;
step 2: randomly selecting a point in the power transmission line as a virtual fault point, and simulating the propagation of a fault initial traveling wave signal at the point according to the shortest path radial measurement point; calculating the time of the initial traveling wave of the virtual fault point reaching each measuring point according to the wave velocity of the virtual fault traveling wave and the length of the propagation path, and further performing difference between every two points to obtain a time characteristic matrix of the virtual fault;
and step 3: calculating time information difference e by using time characteristic matrix of real fault and time characteristic matrix of virtual faultt；
And 4, step 4: continuously updating the position of the virtual fault point by using a PSO algorithm, repeating the steps 2-3, and gradually approaching the real fault point;
when the iteration number is reached, or the time information difference etIf the value of (1) is less than the preset value, ending the iteration; and taking the current virtual fault point position as a fault point position to realize fault positioning.
In step 1, after the transmission line has a fault, the arrival time of the fault initial traveling wave recorded by each measuring point is
T＝(t1,…,ti,…,tm)；
In the formula, m is the number of measuring points in the power transmission network;
making difference between every two arrival times of the initial fault traveling waves to obtain a time characteristic matrix delta T of the real fault;
in the formula,
Δtij＝ti-tj。
in step 2, time characteristic matrix delta T 'of virtual fault'
Wherein, delta t'ij＝ti′-tj′，
dinAnd (6) representing the length of the shortest path from the node i to the virtual fault node, and v calculating the wave speed for the virtual fault traveling wave.
In step 3, according to the time characteristic matrix delta T of the real fault and the time characteristic matrix delta T' of the virtual fault, the time information difference degree of the real fault and the virtual fault is obtained
In the formula, E is a difference matrix;
m representing a matrix1And (4) norm.
The PSO algorithm steps are as follows:
forming a particle community by N particles in the feasible region, wherein the position of each particle represents a feasible solution, and the position of the ith particle after the jth iteration is
In the formula, j represents the current iteration number;
representing the location of the virtual fault point, X and M are in fact equivalent variables in the formula. The difference lies in that: x is a variable in the particle swarm algorithm, representing the particle position (in the present invention, the actual meaning of the particle position is the virtual fault point position); m represents the position of the virtual fault point and is a three-dimensional variable. This equation is equivalent to assigning M to X. Wherein,
a node number indicating the line connection where the virtual fault point is located,
direpresenting virtual fault point-to-node
When j is 0
Indicates the initial position of the particle, this time pair
Assigning a random value;
defining a particle fitness function as
Wherein F is the fitness of the particle and is related to the position of the virtual fault point
A function of (a);
in the iterative search process of each particle, the position with the maximum fitness is used as the individual extreme value of the particle
Taking the maximum fitness of all the individual extreme values of the particles as the group extreme value of the particle swarm
The update of the feasible solution is completed by the movement of the particles, and the motion vector for controlling the movement of the particles is determined by three factors: the original moving direction of the particle individuals, the positions of the individual extrema and the positions of the group extrema;
the movement of the particles is carried out in three steps:
1) self-cognitive vector effects
Under the action of self-cognition vector, the particles move from the current position according to the shortest path radial individual extreme value position vpAs self-cognition vectors
The size of (a) represents the distance length that the particle travels;
vp＝cp·rp·dp；
in the formula, cpIs a self-cognition factor, and is usually taken as 2; r ispIs the interval [0,1]A random number of (c); dpThe length of the shortest path from the particle position to the individual extremum;
2) social cognitive vector effects
Under the action of the social cognition vector, the particles move from the current position according to the position of the shortest radial population extremum, vgAs social cognitive vectors
Represents the distance length of the movement of the particle:
vg＝cg·rg·dg；
in the formula, cgIs a social cognition factor, and is usually taken as 2; r is a radical of hydrogengIs the interval [0,1]A random number of (c); dgThe length of the shortest path from the particle position to the group extreme value;
3) effect of inertia vector
The inertia vector is used to guarantee the randomness of the feasible solution update. The particles move randomly under the effect of the inertial vector,
the magnitude of the inertia vector represents the moving length of the particle under the action of the inertia vector:
wherein j represents the number of iterations, and when j takes 0,
representing the initial value of the inertia vector as a random number; omega is an inertia weight, and the value is adaptively reduced along with the iteration times:
in the formula, ωmaxIs the maximum inertial weight; omegaminIs the minimum inertial weight; j is a function ofmaxThe maximum number of iterations is indicated.
The inertia weight is reduced along with the self-adaption of the iteration times, omegamaxThe value is slightly larger to ensure the global searching capability of the algorithm, but generally not more than 1, such as 0.9; omegaminThe value is generally close to 0, such as 0.01, so as to ensure the convergence of the algorithm at the later iteration stage.
Through the three steps, each particle moves in sequence under the action of the three vectors, the iterative moving process is completed, and the change of the position of the virtual fault point is realized. And each time a new virtual fault point is obtained, calculating the time information difference degree between the point and the real fault point, thereby determining the particle fitness. And according to the fitness of each particle, the particle swarm moves under the moving mechanism, so that the gradual approximation from the virtual fault point to the real fault point is realized. And realizing accurate positioning of the fault through the loop iteration of the algorithm.
The PSO algorithm is an existing algorithm, but the PSO algorithm is improved by the method, and is mainly embodied in the moving process of the particles. The standard PSO algorithm takes the vector sum of three vectors as the final movement vector of the particle, and the improved algorithm redefines the movement rule of the three vectors to the particle, so that the particle moves in sequence under the action of the three vectors.
Has the advantages that:
aiming at the problems that the network resolving process of the traveling wave network positioning method is complicated, the positioning precision is easily influenced by the traveling wave speed and the like, a novel traveling wave network positioning method based on dynamic virtual faults is provided. After the transmission line is in fault, a virtual fault point is randomly assumed in the power grid, the time of the fault initial traveling wave generated by the virtual fault point reaching all the measurement points is calculated according to the characteristic that the fault initial traveling wave is transmitted according to the shortest path, the difference between the virtual fault initial traveling wave reaching time and the real fault initial traveling wave reaching time of all the measurement points in the whole network is simultaneously calculated, and the accuracy of the position of the virtual fault point is measured by using the difference; and continuously correcting the position of the virtual fault point and the traveling wave calculation wave speed by adopting a Particle Swarm Optimization (PSO), reducing the difference between the arrival time of the initial traveling wave of the virtual fault and the actual measurement time, and gradually approaching the virtual fault point to the real fault point until the virtual fault point is coincident with the real fault point, wherein the virtual fault position is the real fault position. Simulation results show that the method does not need to analyze the network structure and network disconnection operation, can eliminate the influence of the traveling wave speed to a certain extent, and realizes accurate fault positioning.
In order to solve the problems of complex network solution and uncertain wave speed of the traveling wave network positioning method, the invention analyzes the arrival time difference characteristics of the initial traveling waves of the faults at different positions in the power grid according to the characteristic that the initial traveling waves of the faults are transmitted according to the shortest path, and provides a fault positioning method based on dynamic virtual faults. And quantizing the time information difference degree of the virtual fault and the real fault by using a time characteristic matrix of the initial traveling wave reaching all the measuring points, and then optimizing the position of the virtual fault point and the traveling wave to calculate the wave speed by adopting a PSO algorithm so as to realize accurate positioning of the fault. Simulation results show that the positioning method can effectively realize accurate positioning of the fault.
Drawings
FIG. 1 is a diagram of a transmission line topology;
FIG. 2 is a modified transmission line topology diagram;
FIG. 3 is a schematic diagram of particle movement;
FIG. 4 is a schematic diagram of a case 1 in which a particle moves under the action of its own cognitive vector;
FIG. 5 is a schematic diagram of case 2 where the particles move under the action of self-cognition vectors;
FIG. 6 is a schematic view of the movement of particles under an inertial vector;
FIG. 7 is a graph of et as a function of ev and ed;
fig. 8 is a 500kV transmission network topology.
Detailed Description
The invention will be described in further detail below with reference to the following figures and specific examples:
example 1:
1 fault traveling wave arrival time difference characteristic analysis
Taking the structure shown in fig. 1 as an example, three lines are connected to the node a. After the transmission line breaks down, the initial traveling wave is respectively transmitted to the three measuring points b, c and d along the shortest path.
Suppose f in line ab1Where a fault occurs, the initial travelling wave of the fault is from f1The time required for propagation to the measurement points b, c, d
Is composed of
In the formula, vb，vc，vdRespectively representing the wave velocity of the initial fault traveling wave transmitted to the measuring points b, c and d;
indicating the length of the line from the point of failure to the point of measurement. The speed of the travelling wave can be generally regarded as a fixed value, so that v can be adjustedb＝vc＝vdV. The time difference of the initial traveling wave of the fault reaching each measuring point is
In the same way, f2After the fault occurs, the time difference delta t of the initial traveling wave reaching each measuring point can be obtainedII. Comparing the time difference value of the two fault initial traveling waves arriving at each measuring point, and defining the time information difference et
In the formula, EijRepresenting the difference degree of the time difference of the initial traveling wave arrival at the i and j measuring points of the two fault points; m is the number of the measuring points;
the time difference of the initial traveling wave of the fault reaching the measurement points i and j after two faults is respectively.
The relationship between the relative position of the two failure points and the degree of difference between the two time information can be obtained from equations (2) to (4) as follows.
1) The two fault points coincide:
et＝0 (5)
2) the two fault points are located on the same line but do not coincide:
in the formula (6), EcdAlthough 0, due to the failure point f1，f2The two-dimensional images are not overlapped with each other,
must not be 0I.e. EbcAnd EbdNot 0, therefore the time information difference etIs not 0.
3) When two fault points are located on different lines:
in the formula (8), Ebc，Ebd，EcdAre all positive numbers, therefore etIs not 0.
From the above analysis, under the condition of not considering the time measurement error, only when the two fault points are completely overlapped, the time difference of the two fault initial traveling waves reaching all the measurement points can be completely consistent, and the time information difference degree is 0. The invention constructs a time characteristic matrix by using the arrival time of the fault initial traveling wave of all the measuring points and the difference between every two. Since the time differences of all the measurement points cannot be all consistent, the time characteristic matrix corresponding to any fault position is unique. The time characteristic matrix quantifies the time information difference degree, and fault points of different positions of the power transmission line can be distinguished.
2 PSO algorithm-based virtual fault traveling wave positioning method
2.1 principle of positioning
The positioning method randomly assumes a virtual fault point in the power transmission line, and calculates the time characteristic matrix of the virtual fault initial traveling wave reaching all the measurement points according to the shortest path propagation characteristic of the fault initial traveling wave. And measuring the position accuracy of the virtual fault point by using the time information difference degree of the virtual fault and the real fault. And continuously updating the position of the virtual fault point in an optimized mode so as to approach the real fault point. The positioning process is as follows:
1) after the transmission line has a fault, the fault initial traveling wave reaches each transformer substation along the shortest path, the traveling wave detection device records the arrival time of the initial traveling wave, and the arrival times of the initial traveling waves of all measurement points are differenced pairwise to obtain a time characteristic matrix of the real fault;
2) and randomly selecting a point in the power transmission line as a virtual fault point, and simulating the propagation of the fault initial traveling wave signal at the point according to the shortest path radial direction of each measurement point. Calculating the time of the initial traveling wave of the virtual fault point reaching each measuring point according to the wave velocity of the virtual fault traveling wave and the length of the propagation path, and further performing difference between every two points to obtain a time characteristic matrix of the virtual fault;
3) the time information difference e is obtained by utilizing the time characteristic matrix of the real fault and the time characteristic matrix of the virtual faultt；
4) And continuously updating the position of the virtual fault point by utilizing a PSO algorithm, and repeating the steps from 2) to 3) to gradually approach the real fault point. When the virtual fault point and the real fault point coincide, the time characteristic matrixes of the virtual fault point and the real fault point have consistency, all elements in the matrixes are completely matched, and the time information difference e istIs 0.
2.2 calculation of time feature matrix and time information difference
2.2.1 time feature matrix of true failure
After the transmission line has a fault, the arrival time of the initial fault traveling wave recorded by each measuring point is
T＝(t1,…,ti,…,tm) (10)
In the formula, m is the number of measurement points in the power transmission network.
And (4) carrying out difference on the arrival time of the initial fault traveling wave pairwise to obtain a time characteristic matrix delta T of the real fault, wherein the lower triangular part is subjected to 0 returning treatment because the delta T is an antisymmetric matrix.
In the formula,
Δtij＝ti-tj (12)
2.2.2 time feature matrix for virtual Fault
And calculating a time characteristic matrix of the initial traveling wave of the virtual fault reaching all the measurement points, wherein the shortest path from the virtual fault point to all the measurement points needs to be obtained. The invention adopts Dijkstra shortest path algorithm to calculate the shortest path from the virtual fault point to all the measuring points.
As shown in fig. 2, assume that f in the power transmission line is a virtual fault point position, and in order to obtain the shortest path from the fault point to other nodes of the network, the fault point is incorporated into the network as a new node. And establishing an n-node adjacency matrix according to the new transmission line topological graph. Regarding the relation between n and m, n-1 is the number of the transformer substation nodes (minus virtual fault points), m is the number of the measurement points, and not all the nodes are provided with detection devices, so m is less than or equal to n-1.
In the formula IijIndicating the length of a line connecting adjacent nodes i and j; b is a mixture ofijRepresents the connection relationship of nodes i and j, wherein binAnd representing the connection relationship between the node i and the virtual fault node.
According to Dijkstra shortest path algorithm, the shortest path distance matrix D of each node is obtained by using the adjacency matrix B
In the formula, dijRepresents the shortest path length between nodes i and j, where dinRepresenting the shortest path length from node i to the virtual failed node.
The time T' for the initial traveling wave of the fault to travel from the faulty node n to the measurement point i along the shortest path is
T'＝(t′1,…,t′i,…,t'm) (16)
In the formula, m is the number of measuring points; v is the calculated wave velocity of the virtual fault traveling wave, and its value is discussed in detail in section 3 of the present invention.
Similarly, the time characteristic matrix delta T 'of the virtual fault is obtained from equation (12)'
2.2.3 time information Difference
According to the time characteristic matrix Delta T of the real fault and the time characteristic matrix Delta T' of the virtual fault, the time information difference degree of the real fault and the virtual fault is obtained
In the formula, m is the number of measuring points; e is a difference degree matrix;
m representing a matrix1And (4) norm.
The positioning algorithm measures the degree of approximation from the virtual fault point to the real fault point by using the time information difference, plays a role in checking the accuracy of the virtual fault point and simultaneously plays a role in feeding back the process of approximation from the virtual fault point to the real fault point.
2.3 approximation of virtual to real failure points
If the position of the virtual fault point is generated purely in a random manner, it is difficult to achieve a high degree of coincidence with the real fault point. In order to ensure the speed and the precision of fault location, the invention takes the minimum time information difference as a target and takes the real fault point position as a solution, and converts the problem into an optimization problem of the solution. The PSO algorithm is used as a heuristic search algorithm, and has high convergence speed and high efficiency. The algorithm starts from a random solution, measures the quality of the solution by using the fitness of particles, and searches the global optimal solution through one iteration. Therefore, the invention adopts the PSO algorithm to realize the approximation from the virtual fault point to the real fault point, and the algorithm process is as follows.
Forming a particle community by N particles in the feasible region, wherein the position of each particle represents a feasible solution, and the position of the ith particle after the jth iteration is
In the formula, j represents the current iteration number;
indicating the position of the virtual fault point, j is 0
Indicates the initial position of the particle, this time pair
A random value is assigned.
In the PSO algorithm, the quality of the solution is measured by the fitness of the particles, and the moving search process of the whole particle group is further influenced. Now define the particle fitness function as
Wherein F is the fitness of the particle and is related to the position of the virtual fault point
As a function of (c). The time information difference e can be uniquely determined by any virtual fault point positiontThe smaller the time information difference is, the greater the adaptability of the particle is, and the greater the influence in the particle population is.
In the iterative search process of each particle, the position with the maximum fitness is used as the individual extreme value of the particle
Taking the maximum fitness of all the individual extreme values of the particles as the group extreme value of the particle swarm
The update of the feasible solution is completed by the movement of the particles, and the motion vector for controlling the movement of the particles is determined by three factors: the original moving direction of the particle individuals, the individual extremum positions and the group extremum positions. Fig. 3 shows the standard PSO algorithm particle movement rules, the vectors of the inertial vector, the self-cognition vector, and the social cognition vector, and the motion vector constituting the particle.
The invention researches a fault positioning method of a power transmission line and determines that a virtual fault point M can only be updated on the power transmission line, but not on the whole plane. Due to the limitations of the feasible fields, the movement process of the particles must be modified. The movement of the particles is carried out in three steps:
1) self-cognitive vector effects
As shown in fig. 4, point M0Is the current position of the particle; point MpIs the individual extremum location. Point M was processed according to the method of section 2.2.20And point MpIncorporating the node into a power grid topological structure as a new node, and solving M by utilizing Dijkstra shortest-circuit algorithm0To point MpThe shortest distance dpAnd a specific path. In the vector
Under the action of the magnetic field, the particles move to a point M along a specific path1. Vector quantity
The size of (d) is given by equation (24), and represents the distance length of movement.
vp＝cp·rp·dp (24)
In the formula, cpIs a self-cognition factor; r ispIs the interval [0,1]The random number of (2).
Due to cpMay be greater than 1 and thus the particle may cross point MpThen, if the node is passed through, any one of the lines is selected to move continuously, as shown in fig. 5, the particle moves to a point M2。
2) Social cognitive vector effects
Social cognitive vector of particles
The movement under action is similar to that of step 1),
is of a size of
vg＝cg·rg·dg (25)
In the formula, cgIs a social cognition factor; r isgIs the interval [0,1]A random number of (c); dgThe shortest path length from the particle position to the population extremum.
3) Effect of inertia vector
In the standard particle swarm algorithm, an inertia vector is defined as a motion vector of a particle in the last iteration process, and represents the original moving direction of the particle. By changing the inertia weight, the randomness of feasible solution updating can be adjusted, and the algorithm is prevented from falling into a local optimal solution. Since the present invention splits the particle velocity into three steps, the inertia vector of the particle is set as an independent variable
The method is used for guaranteeing the randomness of feasible solution updating. The update of the inertia vector is given by equation (26), whose value represents the distance length of the movement. The movement of the particles under the action of the inertial vector is shown in FIG. 6 from point M0Starting at an inertial vector
When the mobile terminal moves to the node 2 under the action of the control signal, a path is randomly selected to continue moving,final arrival point M1Or point M2。
Wherein j represents the number of iterations, and when j takes 0,
representing the initial value of the inertia vector as a random number; omega is an inertia weight, the value is not too large, and is generally in the range of 0-1, so that the convergence of the algorithm is ensured.
Through the three steps, each particle completes the iterative moving process, and the solution is updated (namely the position of the virtual fault point is changed). And each time a new virtual fault point is obtained, calculating the time information difference degree between the point and the real fault point, thereby determining the particle fitness. And according to the fitness of each particle, the particle swarm moves under the moving mechanism, so that the gradual approximation from the virtual fault point to the real fault point is realized. And realizing accurate positioning of the fault through the loop iteration of the algorithm.
2.4 dead time and time error handling
In the actual operation of the power grid, the recording of invalid time at part of the measuring points can be caused due to the failure of a substation detection device and other factors. In order to ensure the accuracy of fault location, the invention adopts an invalid time processing method proposed by the document [ Lizewen, Yao Jiang, Zengjun, Chuxianghui, Denfeng. Power transmission network traveling wave network protection method [ J ]. Power System Automation,2009,33 (06):53-57.Li Zewen, Yao Jianggang, Zeng Xiaoangjun, Chu Xianghui, Deng Feng.tracking wave network protection method for transmission network [ J ]. Power System Automation,2009,33(06) ]: and after the fault, identifying invalid time by analyzing the relation between the recording time of all the adjacent measuring points of the line and the line length and wave speed, and correcting the invalid time by using the valid time.
The positioning method calculates the time information difference degree of the virtual fault and the real fault in real time in the process that the virtual fault point approaches the real fault point. Considering the possible time error of the measuring point, the time information difference degree cannot be completely optimized to 0, so that the virtual fault point position with the minimum time information difference degree is selected as the fault positioning position after the algorithm reaches the maximum iteration times.
Influence and elimination of 3 wave velocity on positioning result
3.1 analysis of the influence of wave velocity on the degree of difference of time information
The positioning method provided by the invention judges the fault points at different positions according to the time information difference, and can realize accurate positioning of the fault only by ensuring the accuracy of the time information difference quantification method. As can be seen from equation (17), the traveling wave velocity calculated in addition to the position of the fault point also affects the magnitude of the time information difference. The invention differentiates the time information into a degree etExpressed as a function of the calculated wave speed v of the travelling wave and the position M of the virtual fault point
et＝f(v,M) (27)
The position of a real fault point and the actual traveling wave speed are given, the wave speed is calculated by changing the position of a virtual fault point and the traveling wave, and the time information difference e can be obtainedtError with wave velocity evError from fault point location edThe function image of the change, as shown in fig. 7. It can be seen that the time information difference is 0 only when the virtual fault point position and the traveling wave calculated wave speed are the same as the real situation.
Therefore, if only the virtual fault point position is changed at the time of fault location, it is difficult to find a fault position that minimizes the degree of time information difference. Only when the wave velocity calculated by the traveling wave approaches to the wave velocity of the real traveling wave, the time information difference degree can be small enough, so that the real fault can be accurately positioned.
3.2 improved method for eliminating wave speed error influence
In order to eliminate the influence of the traveling wave speed error on the positioning result, the positioning method of the invention needs to be improved. And (3) optimizing by using a PSO algorithm by taking the minimum time information difference as an optimization target and the position of the real fault point and the actual traveling wave speed as solutions. On the basis of the method in section 2, the following modifications are made:
the particle position, the particle speed, the particle individual extreme value and the particle group extreme value are defined as two-dimensional variables representing the traveling wave speed and the fault position.
In the formula, v represents the traveling wave calculation wave velocity; m represents a virtual fault point position; i represents a particle individual number; j denotes the number of iterations.
By the correction process, the solved particle fitness reflects the position error of the virtual fault point and the error of the wave velocity value, and the fitness can better balance the quality of the solution.
The updating of the virtual fault point position is carried out by the moving method of the section 2, and the updating of the wave velocity of the traveling wave calculation is carried out according to the standard particle swarm algorithm:
in the formula,
the individual extreme value of the ith particle after the jth iteration is obtained;
is the group extreme value of the ith particle after the jth iteration;
for the position of the ith particle after the jth iteration,
the practical significance of the three is that the traveling wave calculates the wave velocity; omega is the inertia weight of the particle and represents the tendency of the particle to maintain the original direction movement; c. CpAnd cgThe self-cognition factor and the social cognition factor of the particle respectively represent the attraction degree of the individual extremum and the group extremum to the particle; r is a radical of hydrogenpAnd rgIs two [0,1 ]]A random number within a range;
the speed of the jth iteration of the ith particle.
The solution is circularly iterated by using the improved method, and the travelling wave speed calculated by the travelling wave is approximated to the wave speed of the real travelling wave while the virtual fault point is approximated to the position of the real fault point, so that the influence of the wave speed error on the positioning result is eliminated.
4 simulation analysis
4.1 simulation model
The high-voltage power transmission system shown in the figure 8 is built on the PSCAD/EMTDC, red dots in the figure represent substation nodes provided with traveling wave synchronous detection devices, fault traveling waves are detected in real time, and the arrival time of the initial traveling waves is recorded; the sampling frequency was set to 1MHz and the clock accuracy was set to 10 ns.
4.2 different line fault location result and wave velocity optimization analysis
The single-phase earth fault is set in the power grid shown in fig. 8, the length of each line, the fault position and the fault positioning result are shown in table 2, and the figure in the figure is the node serial number. According to the positioning result, the positioning method can accurately position the fault, the maximum positioning error is 89 meters, and the positioning precision is high.
Table 2:
in order to verify the optimization of the algorithm to the wave velocity of the traveling wave calculation, 8 cases of single-phase earth faults are set at different positions of 4-12 lines, and different simulation traveling wave velocities are set by adjusting line parameters. The positioning result is shown in table 3, and the positioning method can calculate the wave velocity of the traveling wave to approach the real wave velocity according to the arrival time of the initial traveling wave of all the measuring points, thereby ensuring the accuracy of fault positioning.
TABLE 3 positioning results of different fault positions of lines 4-12
4.3 positioning algorithm robustness analysis
In order to verify the robustness of the positioning algorithm, simulation is carried out under the influence of a fault initial phase angle, a fault type, transition resistance, a time error and invalid time. The invention mainly works at the positioning part, so the processing of the traveling wave signal and the detection process of the arrival time of the fault initial traveling wave are not discussed in detail.
4.3.1 analysis of the impact of the Fault Primary phase Angle
The amplitude of the fault traveling wave depends on the additional potential of a fault point, when the initial phase angle of the fault voltage is extremely small, the amplitude of the sudden change of the traveling wave is small, and the wave head of the traveling wave is difficult to detect through attenuation in the transmission process of a line. Practical operation shows that the fault initial phase angle is mostly in the range of 30 degrees at the peak. The failure angle of less than 15 ° is rare. Therefore, the A phase grounding fault is arranged at a position 10km away from a 9 node on a 9-10 line, and 9 groups of fault angles from 10 degrees to 90 degrees are arranged. Table 4 shows the positioning results at different initial fault angles, and the results show that the positioning method of the present invention can accurately perform fault positioning at different initial fault angles, the maximum positioning error is 88 meters, and the positioning accuracy is high.
TABLE 4 initial phase angle positioning results of different faults
4.3.2 analysis of the effects of fault type and transition resistance
AG, BC, ACG and ABCG faults are set at the positions 10km, 30km, 50km and 70km away from a 5 node of a 5-10 line respectively, and the transition resistance is 1 omega-300 omega. The positioning result is shown in table 5, and the positioning result shows that the positioning method can accurately position the fault under different fault types and different transition resistances, the maximum positioning error is 97 meters, and the positioning precision is high.
TABLE 5 Fault location results under different parameters of lines 5-10
4.3.3 impact analysis of time error
The accuracy of the fault initial traveling wave arrival time recorded by the measuring point is an important factor influencing the fault positioning result. Due to the influence of factors such as environmental electromagnetic noise, time synchronization and the like, certain errors exist in the time recorded by the measuring points. The invention sets BC fault at the distance of 5-10 lines and 30km from 5 nodes. Adding 0-epsilon based on the arrival time of the initial traveling wave recorded by 9 measuring pointstRandom error of (e)t2, 4, 6, 8 and 10 mus) are respectively taken, and the real data of the arrival time of the fault initial traveling wave and the time error data are shown in a table 6.
TABLE 6 time data under different time errors
Table 7 shows the fault location results under different time errors, and it can be seen from table 7 that the maximum location error of the location method of the present invention is 78m under a time error within 8 μ s, and the location accuracy is slightly reduced when the time error is 10 μ s.
TABLE 7 Fault location results under different time errors
4.3.4 analysis of the effects of dead time
In actual operation of a power grid, due to factors such as faults of substation detection devices, recording of wrong time at partial measurement points may be caused. In order to ensure the accuracy of fault location, the invention adopts an invalid time processing method proposed by the documents [ Lizewen, Yao Jiang, Zengjun, Chuxianghui, Denfeng, Power transmission network traveling wave network protection method [ J ]. Power System Automation,2009,33 (06):53-57.Li Zewen, Yao Jiangan, Zeng Xiaoangjun, Chu Xianghui, Deng Feng.tracking wave network protection method for transmission network [ J ]. Power System Automation,2009,33(06) ]. ABCG faults are set at the position of a line of 5-10 and 70km away from a node of 5, the transition resistance is 100 omega, and four time errors are set respectively and are shown in a table 8. The transmission grid shown in fig. 8 has 5-10 lines, 5, 10 nodes and 5-10 lines between 5 and 10 nodes overhead lines.
TABLE 8 initial traveling wave arrival time error of fault
The positioning results without the invalid time processing are shown in table 9, and the results show that the invalid time has a great influence on the positioning accuracy, and even leads to failure in positioning the fault. According to the invalid time processing method proposed in section 2.4 of the present invention, table 10 gives the positioning result after the invalid time processing. The result shows that when invalid time is recorded at part of the measuring points, the positioning method can accurately position, the maximum positioning error is 78m, and the positioning precision is high.
TABLE 9 Fault location results without dead time handling
TABLE 10 post-invalid time handling Fault location results
4.4 comparison of localization algorithms
In order to verify the superiority of the positioning Method, the Method is compared with a network positioning Method and a traditional double-end positioning Method which are provided by the documents [ Li Zeyan, Tang, Zeng Jun, Xiaoren Ping, Tingzhao, Dijkstra Algorithm-Based Power grid Fault traveling Wave positioning Method [ J ]. Power System Automation,2018,42 (18):162-168.Li Zewen, Tang Ping, Zeng Xiangjun, Xiao Renping, Zha Ting, traveling Wave Location Method Based on Dijkstra Algorithm [ J ]. Power System Automation,2018,42(18):162 and 168 ]. The double-end positioning method directly uses two measuring points closest to a fault point to carry out fault positioning, and a calculation result is only used for comparing positioning accuracy. 4 ABG faults are set in the simulation, and the transition resistance is set to be 100 omega. Failure 1: 3-5 lines are 5km away from 3 nodes; and (3) failure 2: the distance between the 3-5 lines and the 3 nodes is 30 km; failure 3: 7-9 lines are 10km away from 7 nodes; and 4, fault: 4-11 lines 80km from 4 nodes.
The positioning results are shown in Table 11, and it can be seen from Table 11 that: the traditional double-end positioning method is easily influenced by time errors of measuring points, and the positioning error is large; in contrast, the network positioning method comprehensively considers the arrival time of the initial traveling waves of all the measurement points, so that the influence caused by the time error of part of the measurement points is avoided, but when the wave speed value selected by the method is too large different from the real wave speed, the positioning accuracy cannot be guaranteed; the method uses the arrival time of the initial traveling wave of all the measurement points to calculate the time characteristic matrix, optimizes the traveling wave to calculate the wave speed, avoids the influence of the error of the wave speed of the traveling wave, has the maximum positioning absolute error of 75m and has high positioning precision.
TABLE 11 comparison of results of different positioning methods
5 conclusion
The invention provides a novel method for positioning a traveling wave network based on a dynamic virtual fault, which performs simulation calculation according to the characteristics of the initial fault traveling wave propagated according to the shortest path and realizes accurate fault positioning in an optimized mode.
The specific conclusions are as follows:
1) the new method does not need to dissect the network structure, has simple thought and strong implementability;
2) the accuracy of the fault positioning position is measured by using the time information difference during positioning, and the time information of the fault initial traveling wave reaching all the measurement points can be fully excavated, so that the influence of time errors of part of the measurement points is avoided;
3) the PSO algorithm is utilized to optimize the traveling wave calculation wave velocity, so that the influence of the wave velocity uncertain error on the fault positioning result can be eliminated to a certain extent;
4) through a large number of simulation experiments under the influence of different fault lines, different fault types, different fault initial phase angles, different transition resistances, time errors and invalid time, the novel fault positioning method is high in reliability, strong in robustness and high in positioning accuracy.
Claims (5)
1. A traveling wave network positioning method based on dynamic virtual faults is characterized in that based on current line construction, the traveling wave network positioning comprises the following steps:
step 1: after the transmission line has a fault, the fault initial traveling wave reaches each transformer substation along the shortest path, the traveling wave detection device records the arrival time of the initial traveling wave, and the arrival times of the initial traveling waves of all measurement points are differenced pairwise to obtain a time characteristic matrix of the real fault;
step 2: randomly selecting a point in the power transmission line as a virtual fault point, and simulating the propagation of a fault initial traveling wave signal at the point according to the shortest path radial measurement point; calculating the time of the initial traveling wave of the virtual fault point reaching each measuring point according to the wave velocity of the virtual fault traveling wave and the length of the propagation path, and further performing difference between every two points to obtain a time characteristic matrix of the virtual fault;
and step 3: using time of true faultThe time information difference e is obtained by the characteristic matrix and the time characteristic matrix of the virtual faultt；
And 4, step 4: continuously updating the position of the virtual fault point by using a PSO algorithm, repeating the steps 2-3, and gradually approaching the real fault point;
when the iteration number is reached, or the time information difference etIf the value of (2) is less than the preset value, ending the iteration; and taking the current virtual fault point position as a fault point position to realize fault positioning.
2. The traveling wave network positioning method based on dynamic virtual fault as claimed in claim 1, wherein in step 1, after the transmission line is in fault, the arrival time of the fault initial traveling wave recorded by each measurement point is
T＝(t1,···,ti,···,tm)；
In the formula, m is the number of measuring points in the power transmission network;
making difference between every two arrival times of the initial fault traveling waves to obtain a time characteristic matrix delta T of the real fault;
in the formula,
Δtij＝ti-tj。
3. the traveling wave network positioning method based on dynamic virtual faults as claimed in claim 2, wherein in step 2, the time feature matrix Δ T 'of the virtual faults'
Wherein, delta t'ij＝ti′-tj′，
dinAnd (6) representing the length of the shortest path from the node i to the virtual fault node, and v calculating the wave speed for the virtual fault traveling wave.
4. The traveling wave network positioning method based on dynamic virtual fault as claimed in claim 2, wherein in step 3, the difference between the time information of the real fault and the time information of the virtual fault is obtained according to the time characteristic matrix Δ T of the real fault and the time characteristic matrix Δ T' of the virtual fault
In the formula, E is a difference matrix;
m representing a matrix1And (4) norm.
5. The traveling wave network positioning method based on dynamic virtual fault as claimed in claim 2, wherein the PSO algorithm comprises the following steps:
forming a particle community by N particles in the feasible region, wherein the position of each particle represents a feasible solution, and the position of the ith particle after the jth iteration is
In the formula, j represents the current iteration number;
indicating the location of the virtual point of failure, wherein,
a node number indicating the line connection where the virtual fault point is located,
direpresenting virtual fault point-to-node
When j is 0
Indicates the initial position of the particle, this time pair
Assigning a random value;
defining a particle fitness function as
Wherein F is the fitness of the particle and is related to the position of the virtual fault point
A function of (a);
in the iterative search process of each particle, the position with the maximum fitness is used as the individual extreme value of the particle
Taking the maximum fitness of all the individual extreme values of the particles as the group extreme value of the particle swarm
The update of the feasible solution is completed by the movement of the particles, and the motion vector for controlling the movement of the particles is determined by three factors: the original moving direction of the particle individuals, the positions of the individual extrema and the positions of the group extrema;
the movement of the particles is carried out in three steps:
1) self-cognitive vector effects
Under the action of self-cognition vector, the particles move from the current position according to the shortest path radial individual extreme position vpAs self-cognition vectors
The size of (a) represents the distance length that the particle travels;
vp＝cp·rp·dp；
in the formula, cpIs a self-recognition factor; r ispIs the interval [0,1]A random number above; dpThe shortest path length from the particle position to the individual extremum;
2) social cognitive vector effects
Under the action of social cognitive vector, the particles move from the current position according to the position of the shortest radial population extremum, vgAs social cognitive vectors
Represents the distance length of the movement of the particle:
vg＝cg·rg·dg；
in the formula, cgIs a social cognition factor; r isgIs the interval [0,1]A random number of (c); dgThe length of the shortest path from the particle position to the group extreme value;
3) effect of inertia vector
The inertia vector is used for guaranteeing the randomness of feasible solution updating; the particles move randomly under the effect of the inertial vector,
the magnitude of the inertia vector represents the moving length of the particle under the action of the inertia vector:
wherein j represents the number of iterations, and when j takes 0,
representing the initial value of the inertia vector as a random number; omega is an inertia weight, and the value is adaptively reduced along with the iteration times:
in the formula, ωmaxIs the maximum inertial weight; omegaminIs the minimum inertial weight; j is a function ofmaxThe maximum number of iterations is indicated.
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