Single-ended line fault location method based on complex transient analysis and local frequency spectrum scanning matching and related equipment

Abstract

The application provides a single-ended line fault location method based on complex transient analysis and local frequency spectrum scanning matching and related equipment, and belongs to the technical field of fault location. The method comprises the following steps: converting an actual fault recording time domain signal into a complex domain phasor sequence through numerical Laplace transformation; constructing a complex domain node impedance matrix containing a fault node, and generating an analytical complex domain phasor sequence under a given fault location based on complex transient analysis calculation; scanning in a dynamically moving local frequency spectrum interval, calculating the complex cosine similarity between the actual complex domain phasor subsequence and the analytical complex domain phasor subsequence in each interval, and averaging all local similarities as a matching score; scanning along the fault distance direction, and taking the fault location corresponding to the maximum matching score as the location result. The application does not need to carry out a large number of electromagnetic transient simulation library construction for different fault conditions, effectively solves the time domain waveform feature degradation problem under high resistance and small closing angle conditions, and improves the location accuracy and sensitivity.

Description

Technical Field

[0001] This application relates to the field of power system relay protection and fault location technology, and in particular to a single-ended line fault location method and related equipment based on complex domain transient analysis and local spectrum scanning matching. Background Technology

[0002] Accurate and reliable fault location for transmission lines is a prerequisite for ensuring the safe and stable operation of power systems. Single-end fault location methods, due to their low investment and ease of implementation without requiring multi-end communication synchronization, have significant engineering application value. With the continuous development of modern power grids and the advancement of urbanization, the topology and physical form of AC transmission lines are becoming increasingly complex. Constrained by geographical environment and corridor planning, complex AC transmission corridors exist in the power grid, containing overhead-cable mixed sections, T-junction branches, and other discontinuous wave impedances. Sudden changes in wave impedance in such mixed lines lead to complex refraction and reflection phenomena in the transient traveling wave signal of the fault, making it difficult to reliably identify the subsequent traveling wave front. If a branch structure exists, it becomes even more difficult to accurately determine the fault location.

[0003] Currently, common fault location methods mainly include fault analysis, traveling wave method, and transient analysis method. Fault analysis relies on power frequency or low-frequency transient components to establish steady-state equations, requiring a relatively long data window. Traveling wave method and transient analysis method only require short time windows of data (a few milliseconds), primarily relying on high-frequency transient surge characteristics. Furthermore, existing methods often rely on electromagnetic transient simulation programs to obtain fault traveling wave waveform benchmark libraries, which is time-consuming; and fault transient characteristics are affected by many factors such as fault distance, transition resistance, and fault closing angle, making it difficult to traverse multi-dimensional variables to construct a complete benchmark sample. The fixed network topology further limits its universality. Incorporating all these key fault factors into a high-dimensional space for optimization will face constraints such as high solution difficulty and low efficiency. Summary of the Invention

[0004] The main objective of this application is to propose a single-ended line fault location method, electronic device, storage medium, and program product based on complex domain transient analysis and local spectrum scanning matching, in order to solve the problem of building a large number of electromagnetic transient simulation libraries for different fault conditions in the prior art.

[0005] To achieve the above objectives, one aspect of this application proposes a single-ended line fault location method based on complex domain transient analysis and local spectrum scanning matching, the method comprising: Step S1: Obtain the actual fault waveform time-domain signal sequence at the measurement point of the transmission line, and convert it into an actual complex domain phasor sequence through numerical Laplace transform; Step S2: Construct a complex domain node impedance matrix containing the fault node, and generate an analytical complex domain phasor sequence based on the complex domain transient analytical calculation model for a preset fault location information set; wherein, the fault location information set includes the line segment number where the fault is located and the distance between the fault point and the nearest node of the line segment; Step S3: Based on the actual complex phasor sequence and the analytical complex phasor sequence, a scanning matching is performed using dynamically moving local spectrum intervals. The complex cosine similarity between the actual complex phasor sequence and the analytical complex phasor sequence is calculated in each local spectrum interval. The complex cosine similarity calculated in all local spectrum intervals is averaged and used as the matching score corresponding to the current fault location information set. Step S4: Change the fault location information set along the fault distance direction, repeat steps S2 to S3, and take the fault location information set corresponding to the maximum matching score as the final fault ranging result.

[0006] In some embodiments, the specific method for constructing the complex domain node impedance matrix containing the faulty node in step S2 includes: Based on the geometric parameters and conductor parameters of the transmission line, a vector fitting algorithm is used to obtain the complex domain expressions for the series impedance and parallel admittance per unit length; Based on the long-line equation, a two-port complex domain admittance matrix model of a transmission line is constructed, including a self-admittance submatrix and a mutual admittance submatrix. Port equivalent modeling is performed on the system impedance and transformer to obtain the complex domain admittance matrix of the system impedance and the equivalent complex domain admittance matrix of the transformer. Based on the nodes of the system before the fault, the fault point is taken as a new node. The admittance matrix of the complex domain nodes of the system after the fault is formed according to the rules of admittance matrix construction. Then, the inverse is obtained to obtain the impedance matrix of the complex domain nodes of the system, and the self-impedance order components of the fault node are extracted from it.

[0007] In some embodiments, the specific method for generating the analytic complex phasor sequence in step S2 includes: Based on the fault type and transition resistance, the three-phase complex transient short-circuit current at the fault port is calculated using a composite sequence network. Using the mutual impedance matrix between the measurement point and the fault point in the system complex domain node impedance matrix, and combined with the three-phase complex domain transient short-circuit current, the three-phase complex domain transient voltage and / or three-phase complex domain transient current at the measurement point are calculated as an analytical complex domain phasor sequence.

[0008] In some embodiments, the complex-domain transient analytical computation model in step S2 is represented as an implicit function form containing different input fault influencing factors; the method further includes a step of dimensionality reduction and decoupling processing of the input fault influencing factors before step S2, specifically including: The voltage phasor at the fault point is calculated using the complex domain node impedance matrix at the system power frequency, and the fault closing angle is corrected based on the propagation time of the traveling wave from the fault point to the measurement point. The traveling wave complex domain intensity is defined as the sum of the magnitudes of the complex domain phasor sequence. The transition resistance is estimated based on the difference between the traveling wave complex domain intensity of the actual complex domain phasor sequence and the traveling wave complex domain intensity of the analytical complex domain phasor sequence. By using the corrected and estimated fault closing angle, transition resistance, and fault occurrence time as known input parameters, the complex-domain transient analytical calculation model is reduced to an implicit function with only the fault location information set as a single variable.

[0009] In some embodiments, the propagation time of the traveling wave is calculated as follows: the reciprocal of the propagation time of the traveling wave in each line segment is used as the analog admittance to construct the analog admittance matrix. After deleting the rows and columns corresponding to the observation nodes, the matrix is ​​inverted to obtain the node-like impedance matrix, and its diagonal elements are the traveling wave propagation time of the corresponding node relative to the observation node.

[0010] In some embodiments, the specific method of local spectrum interval scanning matching in step S3 includes: Set the fixed window length and scanning step size for the local spectral range; Starting from the initial data point of the parsed complex domain phasor sequence, slide towards the end of the sequence step by step according to the sliding step size. After each slide, extract the continuous data points in the current window as a local feature subsequence. Within the same local spectral interval, extract the corresponding local subsequence from the actual complex domain phasor sequence; Calculate the complex cosine similarity between two local subsequences within this local spectral interval; After completing the scanning of the entire sequence, the complex cosine similarities calculated from all local spectral intervals are arithmetically averaged to obtain the final matching score of the fault location information set.

[0011] In some embodiments, the step S4 of changing the fault location information set along the fault distance direction includes: firstly, using a first large step size to perform a coarse scan of the entire line to determine the coarse fault interval where the maximum matching score is located, and then using the coarse fault interval as the center to perform a fine scan using a second small step size, wherein the second small step size is smaller than the first large step size.

[0012] In some embodiments, the method is applicable to AC transmission lines containing one or more combinations of overhead line sections, cable line sections, and T-junction branch structures.

[0013] To achieve the above objectives, another aspect of this application provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the method described above.

[0014] To achieve the above objectives, another aspect of the embodiments of this application proposes a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described above.

[0015] To achieve the above objectives, another aspect of the embodiments of this application proposes a computer program product, including a computer program that, when executed by a processor, implements the method described above.

[0016] The embodiments of this application include at least the following beneficial effects: This application replaces the cumbersome electromagnetic transient simulation library construction with complex domain transient analytical calculation, eliminating the need for a large number of electromagnetic transient simulation libraries for different fault conditions. It can adapt to complex transmission corridors such as overhead-cable hybrid and T-junction branches, effectively addressing the problem of time domain waveform feature degradation under high resistance and small closing angle conditions, and significantly improving ranging accuracy and sensitivity. Attached Figure Description

[0017] Figure 1 This is a composite sequence network topology diagram of different fault types in the fault network according to the present invention.

[0018] Figure 2 This is an overall flowchart of the fault location method of the present invention.

[0019] Figure 3 This is a structural diagram of a 110kV AC transmission line system in an embodiment of the present invention.

[0020] Figure 4 This is a comparison diagram of the distribution of complex cosine similarity along the line between the method of this invention and the one-time matching method of the whole sequence under coarse scanning.

[0021] Figure 5 This is a comparison diagram of the distribution of complex cosine similarity along the line between the method of this invention and the one-time matching method of the whole sequence under fine scanning.

[0022] Figure 6 This is a flowchart of a single-ended line fault location method provided in an embodiment of this application, which combines complex-domain transient analysis and local spectrum scanning matching.

[0023] Figure 7 This is a schematic diagram of the hardware structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of this application and are not intended to limit it. In the following description, when referring to the accompanying drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with those of this application; they are merely examples of apparatuses and methods consistent with some aspects of the embodiments of this application as detailed in the appended claims.

[0025] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application.

[0026] Currently, common fault location methods mainly include fault analysis, traveling wave method, and transient analysis method. Fault analysis relies on power frequency or low-frequency transient components to establish steady-state equations; the frequency domain method requires at least 1-2 cycles of data, while the time domain method, although slightly faster, still requires a complete power frequency cycle. In contrast, the traveling wave method and transient analysis method only require short time windows of a few milliseconds, mainly relying on high-frequency transient surge characteristics. The first existing technical solution proposes a fault location method based on a simplified complex domain analytical model. This model only considers the characteristics of the first traveling wave of the fault, deriving a correlation model between the shape of the first traveling wave and the fault distance, and constructing a single-end fault location criterion using waveform similarity. However, under different transition resistance faults, the shape of the first traveling wave is highly similar; relying solely on the shape characteristics of the first traveling wave weakens the feature identification, making it difficult to guarantee fault location accuracy. In addition to the initial traveling wave morphology, the transient characteristics of faults also contain rich waveform morphology and timing features in different sequences within the subsequent milliseconds. Therefore, it is necessary to further explore and utilize the overall transient traveling wave characteristic information of the transient signal to enhance the ranging accuracy and stability of the single-ended transient traveling wave fault ranging method.

[0027] In the mining of fault transient features, existing methods mostly rely on electromagnetic transient simulation programs to obtain a baseline library of fault traveling wave waveforms, extracting time-frequency domain features under various fault conditions for single-end fault localization. On the one hand, building a library using electromagnetic transient simulation programs is time-consuming; moreover, AC system fault transient features are affected by numerous factors such as fault distance, transition resistance, and fault closing angle, resulting in a surge of influence dimensions. This makes it difficult to traverse multiple dimensions to construct a complete baseline sample, and the fixed network topology further limits its universality. On the other hand, existing research has failed to systematically explore the specific influence of changes in key fault factors such as fault distance, transition resistance, and fault closing angle on the proposed feature morphology. Incorporating all these key fault factors into a high-dimensional space for optimization would face constraints such as high solution difficulty and low efficiency. The second existing technical solution establishes a fuzzy correlation function between the fault distance and the recorded waveform based on complex domain analytical calculation, calculates the fault transient traveling wave time-domain waveform online, and establishes a time-domain waveform similarity matching criterion for single-end fault location. This method utilizes the overall morphological characteristics of the traveling wave time-domain waveform based on analytical calculation, which improves the accuracy of single-end traveling wave fault location to a certain extent. However, under small closing angles or high-resistance short circuits, the amplitude of the fault transient component is weak and decays rapidly, and the time-domain waveform characteristics degrade significantly, weakening the discriminative power of the matching criterion. At the same time, it lacks discussion on complex network structures such as branches, and its applicable scenarios are relatively limited.

[0028] In view of this, in order to fully explore the evolution characteristics of the complete fault transient signal to improve the ranging identification, get rid of the constraints of traditional simulation library construction and the computational bottleneck of high-dimensional variable optimization, and effectively overcome the feature degradation problem caused by time-domain waveform attenuation under harsh operating conditions, this application proposes a single-end fault ranging scheme for transmission lines based on complex domain transient analysis and local spectrum interval scanning feature matching. This scheme replaces the cumbersome electromagnetic transient simulation library construction with complex domain transient analytical calculation, fully explores the overall evolution characteristics of the fault transient signal in the complex domain, and innovatively proposes a local spectrum interval scanning feature matching mechanism.

[0029] like Figure 6 As shown, this embodiment provides a single-ended line fault location method based on complex domain transient analysis and local spectrum scanning matching, specifically including the following steps: Step S1: Obtain the actual fault waveform time-domain signal sequence at the measurement point of the transmission line, and convert it into an actual complex domain phasor sequence through numerical Laplace transform; Step S2: Construct a complex domain node impedance matrix containing the fault node, and generate an analytical complex domain phasor sequence based on the complex domain transient analytical calculation model for a preset fault location information set; wherein, the fault location information set includes the line segment number where the fault is located and the distance between the fault point and the nearest node of the line segment; Step S3: Based on the actual complex phasor sequence and the analytical complex phasor sequence, a scanning matching is performed using dynamically moving local spectrum intervals. The complex cosine similarity between the actual complex phasor sequence and the analytical complex phasor sequence is calculated in each local spectrum interval. The complex cosine similarity calculated in all local spectrum intervals is averaged and used as the matching score corresponding to the current fault location information set. Step S4: Change the fault location information set along the fault distance direction, repeat steps S2 to S3, and take the fault location information set corresponding to the maximum matching score as the final fault ranging result.

[0030] The solutions of the embodiments of this application will be described in detail below with reference to the accompanying drawings and specific application examples.

[0031] See Figure 2 This embodiment provides a method for single-end fault location of transmission lines based on complex domain transient analysis and local spectrum interval scanning feature matching, specifically including: Module 1: Transformation of fault recording time-domain signal sequences into complex-domain phasor sequences Actual fault recordings are time-domain signal sequences, which can be transformed into complex-domain phasor sequences using numerical Laplace transform. Taking fault voltage as an example:

[0032] f ( k Δ t U represents the time-domain signal of the fault voltage waveform recorded at the actual measurement point. t ( s ) is the complex domain sequence obtained after the time-domain signal undergoes a numerical Laplace transform.

[0033] Module 2: Generate the complex domain nodal impedance matrix including the faulty node 1) Obtain the frequency response parameters of the transmission line based on the actual tower geometry and related conductor parameters. The methods for obtaining these parameters include, but are not limited to, the following three: a) Obtaining them through the detailed transmission line parameter modeling module of the PSCAD / EMTDC electromagnetic transient simulation program; b) Obtaining the frequency response parameters of the transmission line using an electromagnetic transient program, such as the LINE CONSTANT support subroutine of the ATP / EMTP electromagnetic transient simulation program; c) Obtaining them by writing a parameter calculation program based on the "Theory of Electromagnetic Transient Calculation in Power Systems". It should be noted that obtaining the line frequency response parameters here is a fundamental step in establishing the line complex domain model and does not involve building an electromagnetic transient simulation library for different fault conditions (such as different fault distances, transition resistances, closing angles, etc.). Therefore, it does not affect the core advantage of this method: "no need to build a large number of simulation libraries for different fault conditions". Subsequently, based on descending order matching, a vector fitting algorithm using rational function approximation is used to obtain the unit length series impedance. Z (s) and complex parallel admittance Y Complex representation of (s):

[0034] In the formula, R ( s () represents the resistance per unit length of the line. L ( s () represents the inductance per unit length. G ( s )and C ( s These represent the conductivity and susceptance per unit length, respectively. s This is the Laplace operator. s = c +j ω , c The damping coefficient has a value of [value missing]. c = 2lnN / (N·dt), where j is the imaginary unit of the complex field. ω =(2m+1)π / (Ndt), where N=T / dt, T is the analytical calculation time of this model, dt is the analytical calculation step size, and m=0,1,……N-1.

[0035] 2) Based on the long-line equation, the two-port complex domain admittance matrix model of the transmission line can be further obtained:

[0036] In the formula, I1(s) and I2(s) are the three-phase currents at the beginning and end of the transmission line, respectively, and U1(s) and U2(s) are the three-phase voltages at the beginning and end of the transmission line, respectively. y s (s) andy m (s) represent the self-admittance and mutual admittance matrices of the line, respectively, both with a dimension of 3×3, and the corresponding calculation formulas are as follows:

[0037] In the formula, l This is the length of the transmission line segment. T Here is the Clarke transformation matrix. T and T -1 as follows:

[0038] 3) Perform port equivalent modeling of the system impedance, assuming the system impedance is... Z s The two-port complex domain admittance matrix model of the system impedance is:

[0039] The transformer is equivalently evaluated using a type-P equivalent circuit. Assume nodes... i When connected to a transformer, if the primary side of the transformer uses a star-grounded connection, the equivalent impedance of the load connected to the transformer, referred to the primary side via the transformer, is represented by the three-phase admittance matrix Y, which has positive and negative zero sequences. T,i ( s )for:

[0040] In the formula, S is the symmetric component transformation matrix, S -1 It is the inverse transformation matrix of the symmetric components. Z TL1,i (s), Z TL2,i (s) and Z TL0,i (s) represent the positive, negative, and zero-sequence impedances transferred to the primary side of the transformer, respectively. Z L,i (s) represents the equivalent impedance of the load. Z T,i (s) represents the transformer impedance. k i This represents the transformer's turns ratio.

[0041] If the primary side of the transformer uses a star-connected ungrounded configuration, the transformer does not have an equivalent zero-sequence network. Y TL,i ( s )for:

[0042] 4) Assume the system had n nodes before the failure, and after the failure, the fault point became the new node. Construct a system admittance matrix of dimension 3(n+1)×3(n+1). When a line failure occurs, the location of the fault point needs to be determined by the line segment number. q f and the distance between the fault point and the nearest node of the fault segment d f The decision is made to define it as a fault location information set: F L ={ q f , d f The complex domain self-admittance sub-matrix of each line can be obtained according to the above steps. y s ( s ) and line mutual admittance sub-matrix y m ( s The line self-admittance sub-matrix, mutual admittance sub-matrix, system impedance admittance matrix, and transformer equivalent admittance matrix, according to the rules for constructing admittance matrices, together constitute the complex domain node admittance matrix Y of the system after a fault. all ( s The inverse of this matrix yields the complex domain nodal impedance matrix Z of the system after the fault. all ( s From the system complex domain nodal impedance matrix Z) all ( s In the process, extract the self-impedance Z corresponding to the fault node. ff ( s This can be transformed into an order impedance matrix using symmetric component transformation. In the formula, the operator... a = e j120° , a 2 = e j240° .

[0043]

[0044] In the formula, Z Fff(1) ( s () represents the positive sequence impedance corresponding to the self-impedance of the fault node. Z Fff(2) ( s ) is the negative sequence impedance. Z Fff(0) ( s ) is the zero-sequence impedance.

[0045] Module 3: Calculation of transient voltage and current in complex faults 1) Apply a fault excitation voltage source to the fault node. The time-domain expression of the fault excitation voltage source is as follows:

[0046] In the formula, Δ u f-φ ( t ) indicates the faulty phase φ The fault excitation voltage source U f The instantaneous voltage amplitude at the fault point before the fault occurred. θ f-φ The fault closing angle at the fault point before the fault occurred. α For system power frequency, t 0 represents the time when the fault occurred. ε ( t The given equation represents a unit step signal. Applying a Laplace transform to both sides of the equation above, followed by a symmetric component transform, yields its positive-sequence component Δ. u f(1) ( s ), negative order component Δ u f(2) ( s ) and zero-sequence component Δ u f(0) (s).

[0047] 2) Based on the boundary conditions for different fault types, conditions such as... can be constructed. Figure 1 The composite sequence network shown can be used to calculate the complex short-circuit current under different fault types. Among them, R f This is the transition resistance during a fault.

[0048] 2.1) Single-phase ground fault:

[0049] 2.2) Two-phase ground fault Using the superposition theorem, calculate the positive-sequence component Δ. u f(1) ( s ), negative order component Δ u f(2) ( s ) and zero-sequence component Δ u f(0) The sequence short-circuit currents under the action of (s) are then added together:

[0050]

[0051]

[0052]

[0053] 2.3) Two-phase interphase fault

[0054] 2.4) Three-phase fault

[0055] After obtaining the sequence complex domain short-circuit currents at the fault port, the three-phase complex domain transient short-circuit currents at the fault port can be obtained by inverse transformation of the symmetrical components:

[0056] 3) The system complex domain nodal impedance matrix Z obtained from module 2 all ( s The three-phase complex transient short-circuit current at the fault port obtained from the above formula can be used to obtain the three-phase complex transient voltage at the measurement point using the following formula:

[0057] In the formula, U x1 ( s ) and U x2 ( s Z represents the three-phase complex transient short-circuit voltage at the beginning and end nodes of the line, respectively. fx1 ( s () is the impedance matrix Z from the complex domain nodes all ( s The three mutual impedance matrices between the fault point f and the line head node x1 extracted from the data are Z. fx2 ( s Similarly, the three-phase complex transient current at the beginning of the line can be further obtained from this:

[0058] Module 4: Calculation of different fault influencing factors 1) In this embodiment, the established complex-domain transient analytical calculation model is represented as an implicit function form containing different input fault influencing factors:

[0059] The established model needs to pre-determine the instantaneous voltage amplitude at the fault point based on the actual fault recording. U f The fault closing angle at the fault point before the fault occurs θ f-φ When the fault occurred t 0 and transition resistance R f It becomes a fault location information set F containing only a single variable. L The input variables are implicit functions. Therefore, these input variables need to be calculated in advance.

[0060] 2) The complex domain nodal impedance matrix obtained from module 2 Z all ( s Let be the node impedance matrix under a series of frequency responses. The voltage phasor at the fault point can be obtained using the node impedance matrix at the system's power frequency. The system source can be equivalently represented as an injected current source at this node. Let the voltage at the system node be... The outflow current is The system impedance is Z s ( s If 0), then the equivalent injected current source of the system source is:

[0061] Therefore, the voltage phasor at fault point f is:

[0062] In the formula, Z Sf ( s 0) is the complex domain nodal impedance matrix Z all ( s In ) s for s At time 0, the impedance matrix of this node represents the mutual impedance from the fault point f to the system node S. f 0 represents the system power frequency; however, there is a time delay in the travel wave propagating from the fault point to the measurement point, therefore it is necessary to... φ f Make corrections.

[0063] 3) Calculate the propagation time of the traveling wave to the measurement point, and construct an analog admittance matrix by analogy with the nodal admittance matrix. For a length of... l ab The traveling wave travels at a speed of 0.55 m / s. v ab The propagation time can be obtained. t ab = l ab / v ab Taking a certain node as the observation point, the total propagation time of all other points on the line from the observation point is the sum of the time of the unique path. The reciprocal of the propagation time of the traveling wave for each line segment is used as the analog admittance. Assume the system has n nodes when operating normally. After a line fault occurs, the fault point becomes the new node, and the total number of nodes is n+1. Construct the analog admittance matrix:

[0064] In the formula, the elements of the analog admittance matrix are as follows:

[0065]

[0066] After deleting the rows and columns corresponding to the observed nodes, and then inverting the nodal-like admittance matrix, the nodal-like impedance matrix is ​​obtained as follows:

[0067] Diagonal elements of a nodal impedance matrix T ij | i=j That is, the traveling wave propagation time Δ of the node corresponding to the element relative to the observation node. t .

[0068] If the time when the traveling wave arrives at the observation point is t 1. The actual time of the fault occurrence t 0 is:

[0069] right φ f Make corrections:

[0070] 4) Based on the complex phasor sequence output by the complex domain analytical calculation model and the complex domain phasor sequence obtained by numerical Laplace transform of the fault recording time domain sequence, the complex domain intensity of the traveling wave is defined. E The sum of the moduli of the complex phasor sequence:

[0071] The formula for estimating transition resistance is:

[0072] In the formula, E ( R f0 ,F L ) represents any initial transition resistance value input. R f0 and specific fault location F L At that time, the complex wave complex intensity corresponding to the complex phasor sequence output by the complex domain analytical calculation model is... E rcd The traveling wave complex intensity of the complex phasor sequence under the fault recording corresponding to module 1.

[0073] Module 5: Local Spectral Range Scanning Based on Complex Cosine Similarity 1) Since the complex phasor sequence is a series of complex values ​​that vary with frequency, the complex cosine similarity is used as a matching index to analyze the complex phasor sequence U output by the complex domain analytical calculation. x ( sThe complex domain phasor sequence U derived from fault recordings. t ( s Feature matching is performed, and the formula for calculating complex cosine similarity is as follows:

[0074] In the formula, U x ( s )= [ a 1, a 2, …, a n ], a i = x 1i +j y 1i U t ( s ) = [ b 1, b 2, …, b n ], b i = x 2i +j y 2i . S cos This represents the complex cosine similarity. The closer the complex cosine similarity is to 1, the more similar the two signals are.

[0075] 2) When performing feature matching, this embodiment proposes a local spectral interval scanning mechanism to replace the traditional one-time calculation of the entire sequence. The specific implementation process is as follows: First, assume the complex domain analytic computation phasor sequence to be processed is U. x ( s The algorithm does not take the entire U x ( s Instead of using it as a single computational input, it constructs an observation data window that can dynamically move along discrete numerical points in the sequence, namely the 'local spectral interval'.

[0076] Subsequently, the fixed window length (i.e. the number of consecutive data points contained in the interval) and the scanning sliding step size (i.e. the number of data points that the observation window advances each time) are set.

[0077] In actual scanning calculations, this local spectral range extends from U x ( s Starting from the initial data point of the sequence, the algorithm slides towards the end of the sequence strictly according to the set sliding step size. During each sliding pause, the algorithm only extracts U values ​​within the current data window's coverage area. x (s Continuous data points are extracted into independent local feature subsequences. Within each independent local subsequence, the local complex cosine similarity between the complex domain phasor sequence of the actual fault recording signal and the phasor sequence output by the analytical model is calculated using the formula mentioned in step 1 of this module.

[0078] Finally, the average of all local complex cosine similarities generated after traversing the entire sequence is calculated, and the calculated average is used as the final complex cosine similarity fault ranging criterion for this feature matching. The fault location where the maximum complex cosine similarity is located is the final fault distance result.

[0079] Example explanation: To verify the effectiveness of the single-end fault location method for transmission lines based on complex domain transient analysis and local spectrum interval scanning feature matching proposed in this embodiment, a simulation model was built in PSCAD / EMTDC electromagnetic transient simulation software as follows: Figure 3 The simulation model of the 110kV AC transmission line system is shown. The time window is T=5ms, dt is 10us, and the simulation recording step size is consistent with the analytical calculation, i.e., Δ... t The distance is 10µs. Fault points f are set on lines MK1, K1K2, K2T, TP, and TO. The fault distance is calculated starting from point M (the measurement point). Lines MK1, K2T, TP, and TO are overhead transmission lines, while K1K2 is a cable line. A fault is set at a distance of 49.5km from point M, meaning the fault occurs on line K2T. Characteristic matching is performed using the fault phase voltage. The distance measurement steps are as follows: In the PSCAD simulation software, corresponding faults are set up, and fault voltage waveform signals measured after the actual line fault occurs are obtained, and their complex domain features are extracted. Then, based on the fault voltage waveforms, the suspected fault sections (MK1, K1K2, K2T, TP, TO) are scanned. First, a coarse scan of the entire line is performed with a step size of 1km. For each fault location in the fault location information set, the input of the analytical calculation model other than the fault location information set is determined according to module 4, and the output result of the analytical calculation model under each fault location is generated. Then, according to module 5, feature matching is performed on all complex domain phasor sequences output by the complex domain analytical calculation model and the complex domain phasor sequence obtained by numerical Laplace transform of the fault waveform time domain sequence. To demonstrate the superiority of this application, the results are compared with those of conventional one-time similarity calculation of the entire sequence. The results are as follows. Figure 4 As shown, both methods achieved extreme similarity at 50km, successfully pinpointing the location of the fault on the initial scan. However, the full-sequence calculation curve near the extreme point was flatter than the method proposed in this patent, indicating less sensitivity.

[0080] Subsequently, a fine scan was performed within the range [49.1km, 50.9km], with a center point of 50km and a step size of 0.1km. The results are as follows. Figure 5 As shown, the maximum similarity calculated for the entire sequence occurs at 49.8 km, which has an error of 0.3 km from the actual fault distance of 49.5 km. In contrast, the similarity peak of the local spectral interval scan proposed in this application occurs precisely at 49.5 km.

[0081] To fully illustrate the effectiveness of the ranging method proposed in the embodiments of this application, Tables 1 and 2 provide more verification examples, and the results show that the method proposed in this application can achieve effective fault location.

[0082] Table 1. Fault location results for single-phase ground faults with a fault closing angle of 90° and a transition resistance of 20Ω at different fault distances.

[0083] Table 2. Fault location results for different fault types with a fault closing angle of 45° and a transition resistance of 80Ω.

[0084] In summary, compared with the prior art, the method of this embodiment has at least the following advantages and beneficial effects: 1) Breaking through the bottleneck of traditional simulation database construction, significantly improving the universality and computational efficiency of complex line models: This application proposes a complex domain transient analytical calculation method that can flexibly adapt to complex AC transmission corridors with discontinuous wave impedances, such as overhead-cable mixed sections and T-junction branches. It avoids the lengthy process of traditional time-domain simulation database construction and can restore the fault complex domain phasor sequence at the measurement point according to the specified fault location and fault factors.

[0085] 2) An innovative local spectrum interval scanning mechanism significantly enhances the sensitivity and ranging accuracy of the matching criterion: Addressing the shortcomings of existing full-sequence one-time feature matching, which suffers from a flat curve and poor sensitivity near extreme points, this application proposes constructing a dynamically moving observation data window (i.e., a local spectrum interval). By extracting local feature subsequences, calculating complex cosine similarity, and taking the mean, the extreme peaks of the similarity distribution along the line are effectively sharpened, suppressing the ranging errors easily generated by full-sequence matching, and achieving precise locking of the distance to the actual fault.

[0086] 3) Dimensionality Reduction and Decoupling of High-Dimensional Fault Influencing Factors to Achieve Efficient Optimization Based on a Single Fault Distance Variable: Existing research faces challenges such as high solution difficulty and low efficiency when incorporating key factors like fault distance, transition resistance, and fault closing angle into a high-dimensional space for optimization. This application represents the complex-domain transient analytical calculation model as an implicit function containing different input fault influencing factors. By pre-calculating and correcting the fault occurrence time and fault closing angle, and effectively estimating the transition resistance using the complex-domain intensity of traveling waves, the analytical model is successfully transformed into an implicit function containing only a single variable (the fault location information set). This dimensionality reduction eliminates the computational burden of multi-parameter joint optimization, enabling rapid and accurate line-scan optimization focusing solely on the fault distance dimension.

[0087] 4) Compared with existing methods that use time-domain waveforms for similarity-based fault location, the two-dimensional feature space constructed by the method in this embodiment mainly focuses on the topological rotation trend and morphological evolution of complex-domain feature trajectories on the complex plane. Complex-domain features can simultaneously retain the amplitude and phase information of the signal. The complex-domain characteristics of the signal are mapped to the distribution of point sets in two-dimensional space to characterize the fault features. In essence, it expands the one-dimensional time waveform into a two-dimensional feature space that has both amplitude and phase information. This transformation not only enriches the physical dimension of the features, but also significantly enhances the distinguishability under different fault conditions through the geometric relationship of complex vectors, so that the method can still maintain a very high feature recognition degree when facing weak fault signals.

[0088] This application also provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the above-described method. This electronic device can be any smart terminal, including tablet computers, in-vehicle computers, etc.

[0089] It is understood that the content of the above method embodiments is applicable to this device embodiment. The specific functions implemented by this device embodiment are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0090] Please see Figure 7 , Figure 7 The hardware structure of an electronic device according to another embodiment is illustrated. The electronic device includes: The processor 701 can be implemented using a general-purpose CPU (Central Processing Unit), microprocessor, application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of this application. The memory 702 can be implemented as a read-only memory (ROM), a static storage device, a dynamic storage device, or a random access memory (RAM). The memory 702 can store the operating system and other application programs. When the technical solutions provided in the embodiments of this specification are implemented through software or firmware, the relevant program code is stored in the memory 702 and is called and executed by the processor 701 using the methods described in the embodiments of this application. The input / output interface 703 is used to implement information input and output; The communication interface 704 is used to enable communication and interaction between this device and other devices. Communication can be achieved through wired means (such as USB, Ethernet cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.). Bus 705 transmits information between various components of the device (e.g., processor 701, memory 702, input / output interface 703, and communication interface 704); The processor 701, memory 702, input / output interface 703, and communication interface 704 are connected to each other within the device via bus 705.

[0091] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method.

[0092] It is understood that the content of the above method embodiments is applicable to this storage medium embodiment. The specific functions implemented in this storage medium embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0093] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. Furthermore, memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory may optionally include memory remotely located relative to the processor, and these remote memories can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0094] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method.

[0095] It is understood that the content of the above method embodiments is applicable to the embodiments of this program product. The specific functions implemented in the embodiments of this program product are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments. The executable computer program code or "code" used to perform the various embodiments can be written in high-level programming languages ​​such as C, C++, Python, Smalltalk, Java, JavaScript, Visual Basic, Structured Query Language (e.g., Transact-SQL), Perl, or in various other programming languages.

[0096] The embodiments described in this application are for the purpose of more clearly illustrating the technical solutions of the embodiments of this application, and do not constitute a limitation on the technical solutions provided by the embodiments of this application. As those skilled in the art will know, with the evolution of technology and the emergence of new application scenarios, the technical solutions provided by the embodiments of this application are also applicable to similar technical problems.

[0097] Those skilled in the art will understand that the technical solutions shown in the figures do not constitute a limitation on the embodiments of this application, and may include more or fewer steps than shown, or combine certain steps, or different steps.

[0098] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0099] Those skilled in the art will understand that all or some of the steps in the methods disclosed above, as well as the functional modules / units in the systems and devices, can be implemented as software, firmware, hardware, or suitable combinations thereof.

[0100] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms “comprising” and “having,” and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0101] It should be understood that in this application, "at least one (item)" means one or more, and "more than" means two or more. "And / or" is used to describe the relationship between related objects, indicating that three relationships can exist. For example, "A and / or B" can represent three cases: only A exists, only B exists, and both A and B exist simultaneously, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one (item) of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one (item) of a, b, or c can represent: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, and c can be single or multiple.

[0102] In the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of the units described above is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0103] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0104] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0105] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes multiple instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing programs, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0106] The preferred embodiments of the present application have been described above with reference to the accompanying drawings, but this does not limit the scope of the claims of the present application. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and substance of the embodiments of the present application shall be within the scope of the claims of the present application.

Claims

1. A single-ended line fault location method based on complex-domain transient analysis and local spectrum scanning matching, characterized in that, The method includes the following steps: Step S1: Obtain the actual fault waveform time-domain signal sequence at the measurement point of the transmission line, and convert it into an actual complex domain phasor sequence through numerical Laplace transform; Step S2: Construct a complex domain node impedance matrix containing the fault node, and generate an analytical complex domain phasor sequence based on the complex domain transient analytical calculation model for a preset fault location information set; wherein, the fault location information set includes the line segment number where the fault is located and the distance between the fault point and the nearest node of the line segment; Step S3: Based on the actual complex phasor sequence and the analytical complex phasor sequence, a scanning matching is performed using dynamically moving local spectrum intervals. The complex cosine similarity between the actual complex phasor sequence and the analytical complex phasor sequence is calculated in each local spectrum interval. The complex cosine similarity calculated in all local spectrum intervals is averaged and used as the matching score corresponding to the current fault location information set. Step S4: Change the fault location information set along the fault distance direction, repeat steps S2 to S3, and take the fault location information set corresponding to the maximum matching score as the final fault ranging result.

2. The method according to claim 1, characterized in that, The specific methods for constructing the complex domain nodal impedance matrix containing the faulty node in step S2 include: Based on the geometric parameters and conductor parameters of the transmission line, a vector fitting algorithm is used to obtain the complex domain expressions for the series impedance and parallel admittance per unit length; Based on the long-line equation, a two-port complex domain admittance matrix model of a transmission line is constructed, including a self-admittance submatrix and a mutual admittance submatrix. Port equivalent modeling is performed on the system impedance and transformer to obtain the complex domain admittance matrix of the system impedance and the equivalent complex domain admittance matrix of the transformer. Based on the nodes of the system before the fault, the fault point is taken as a new node. The admittance matrix of the complex domain nodes of the system after the fault is formed according to the rules of admittance matrix construction. Then, the inverse is obtained to obtain the impedance matrix of the complex domain nodes of the system, and the self-impedance order components of the fault node are extracted from it.

3. The method according to claim 1, characterized in that, The specific methods for generating the analytic complex phasor sequence in step S2 include: Based on the fault type and transition resistance, the three-phase complex transient short-circuit current at the fault port is calculated using a composite sequence network. Using the mutual impedance matrix between the measurement point and the fault point in the system complex domain node impedance matrix, and combined with the three-phase complex domain transient short-circuit current, the three-phase complex domain transient voltage and / or three-phase complex domain transient current at the measurement point are calculated as an analytical complex domain phasor sequence.

4. The method according to claim 1, characterized in that, In step S2, the complex-domain transient analytical calculation model is represented as an implicit function form containing different input fault influencing factors; the method also includes a step of dimensionality reduction and decoupling processing of the input fault influencing factors before step S2, specifically including: The voltage phasor at the fault point is calculated using the complex domain node impedance matrix at the system power frequency, and the fault closing angle is corrected based on the propagation time of the traveling wave from the fault point to the measurement point. The traveling wave complex domain intensity is defined as the sum of the magnitudes of the complex domain phasor sequence. The transition resistance is estimated based on the difference between the traveling wave complex domain intensity of the actual complex domain phasor sequence and the traveling wave complex domain intensity of the analytical complex domain phasor sequence. By using the corrected and estimated fault closing angle, transition resistance, and fault occurrence time as known input parameters, the complex-domain transient analytical calculation model is reduced to an implicit function with only the fault location information set as a single variable.

5. The method according to claim 4, characterized in that, The propagation time of the traveling wave is calculated as follows: the reciprocal of the propagation time of the traveling wave in each line segment is used as the analog admittance. An analog admittance matrix is ​​constructed, and the row and column corresponding to the observation node are deleted and then inverted to obtain the node-like impedance matrix. The diagonal elements are the traveling wave propagation time of the corresponding node relative to the observation node.

6. The method according to claim 1, characterized in that, The specific methods for local spectrum interval scanning matching in step S3 include: Set the fixed window length and scanning step size for the local spectral range; Starting from the initial data point of the parsed complex domain phasor sequence, slide towards the end of the sequence step by step according to the sliding step size. After each slide, extract the continuous data points in the current window as a local feature subsequence. Within the same local spectral interval, extract the corresponding local subsequence from the actual complex domain phasor sequence; Calculate the complex cosine similarity between two local subsequences within this local spectral interval; After completing the scanning of the entire sequence, the complex cosine similarities calculated from all local spectral intervals are arithmetically averaged to obtain the final matching score of the fault location information set.

7. The method according to claim 1, characterized in that, The step S4 of changing the fault location information set along the fault distance direction includes: firstly, using a first large step size to perform a coarse scan of the entire line to determine the coarse fault interval where the maximum matching score is located, and then using the coarse fault interval as the center to perform a fine scan using a second small step size, where the second small step size is smaller than the first large step size.

8. The method according to claim 1, characterized in that, The method is applicable to AC transmission lines containing one or more combinations of overhead line sections, cable line sections, and T-junction branch structures.

9. An electronic device, characterized in that, The electronic device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the method according to any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 8.

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