Method for measuring transition resistance of ac transmission line

Abstract

This invention discloses a method for measuring the transition resistance of AC transmission lines: The method involves acquiring the three-phase electrical signal waveforms at the beginning of the AC transmission line; determining the faulty phase and the arrival time of the first traveling wave of the fault at the measurement point based on the three-phase electrical signal waveforms; calculating the line-mode fault supplementary power supply expression for a designated fault point in the AC transmission line based on the three-phase voltage waveforms and arrival times of the faulty phase at the measurement point; acquiring the first analytical waveform of the time-domain solution corresponding to the first transient voltage equation at the measurement point; comparing the first analytical waveform with the actual measured waveform at the measurement point using cosine similarity to obtain the actual fault distance between the actual fault point and the measurement point; determining the actual line-mode supplementary power supply corresponding to the actual fault occurrence time; and obtaining the transition resistance based on the second analytical waveform of the time-domain solution of the second transient voltage equation corresponding to the measurement point and the actual measured waveform at the measurement point. This method enables accurate calculation of the transition resistance value after a line short-circuit fault.

Description

Technical Field

[0001] This invention relates to the technical field of AC transmission lines, and more particularly to a method for measuring the transition resistance of AC transmission lines. Background Technology

[0002] In AC transmission lines, a transition resistance exists at the short-circuit point during non-metallic short circuits. The value of this transition resistance and the location of the short circuit are random, which can affect power system fault analysis, protection setting calculations, and the reliable operation of protection devices. Current technology typically measures this transition resistance by directly measuring the resistance at the short-circuit point using instruments; or by constructing a measuring circuit using a bridge method, adjusting the proportional or sliding resistors of the bridge to find a balance and thus obtain an accurate value for the transition resistance.

[0003] However, existing methods for measuring transition resistance require direct measurement at the short-circuit point on the line, which increases the cost of the measurement operation. Furthermore, the measurement of transition resistance is affected by various environmental factors (such as temperature, humidity, and electromagnetic interference), resulting in a significant error in the final measured transition resistance value. Summary of the Invention

[0004] This invention provides a method for measuring the transition resistance of AC transmission lines to achieve fault location: quickly finding the fault point, reducing fault investigation time, and improving the accuracy of transition resistance calculation.

[0005] The present invention provides a method for measuring the transition resistance of AC transmission lines, the method comprising:

[0006] Acquire the three-phase electrical signal waveforms at the beginning of the AC transmission line, the three-phase electrical signal waveforms including three-phase voltage waveforms and / or three-phase current waveforms, determine the fault phase and the arrival time of the first traveling wave of the fault at the measurement point based on the three-phase electrical signal waveforms, the measurement point being the beginning of the AC transmission line;

[0007] Based on the three-phase voltage waveforms corresponding to the fault phase at the measurement point and the arrival time, the instantaneous value expression of the line-mode transient voltage at the set fault point in the AC transmission line is calculated, and the instantaneous value expression of the line-mode transient voltage is used as the additional power supply expression for the line-mode fault; wherein, the set fault point is one of the points in the AC transmission circuit; the additional power supply expression for the line-mode fault includes the fault distance variable between the set fault point and the measurement point;

[0008] The first analytical waveform of the time-domain solution corresponding to the first transient voltage equation of the measurement point after the first traveling wave of the fault propagates to the set fault point in the frequency domain is obtained according to the additional power supply expression of the line mode fault.

[0009] The cosine similarity of the first analytical waveform with the actual measured waveform at the measurement point is compared to obtain the actual fault distance between the actual fault point and the measurement point.

[0010] The actual additional power supply of the line model corresponding to the actual fault occurrence time is determined based on the actual fault distance and the line model fault power supply expression. The transition resistance is obtained based on the second analytical waveform of the time-domain solution of the second transient voltage equation corresponding to the measurement point after the fault first traveling wave corresponding to the actual fault point propagates to the actual fault point, and the actual measurement waveform of the measurement point.

[0011] This invention discloses a method for measuring the transition resistance of AC transmission lines, comprising: acquiring the three-phase electrical signal waveforms at the beginning of the AC transmission line; determining the fault phase and the arrival time of the first traveling wave of the fault at the measurement point based on the three-phase electrical signal waveforms; deriving the line-mode fault supplementary power supply expression for a predetermined fault point in the AC transmission line based on the three-phase voltage waveforms and arrival times of the fault phase at the measurement point; acquiring the first analytical waveform of the time-domain solution corresponding to the first transient voltage equation at the measurement point; comparing the first analytical waveform with the actual measured waveform at the measurement point using cosine similarity to obtain the actual fault distance between the actual fault point and the measurement point; determining the actual line-mode supplementary power supply corresponding to the actual fault occurrence time; and obtaining the transition resistance based on the second analytical waveform of the time-domain solution of the second transient voltage equation corresponding to the measurement point and the actual measured waveform at the measurement point. The method disclosed in this invention enables accurate estimation of the transition resistance value after a line short-circuit fault.

[0012] It should be understood that the description in this section is not intended to identify key or essential features of the embodiments of the present invention, nor is it intended to limit the scope of the invention. Other features of the invention will become readily apparent from the following description. Attached Figure Description

[0013] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0014] Figure 1 This is a flowchart of a method for measuring the transition resistance of an AC transmission line provided in an embodiment of the present invention;

[0015] Figure 2 This is a flowchart of another method for measuring the transition resistance of an AC transmission line provided in an embodiment of the present invention;

[0016] Figure 3 It is a waveform diagram of an electrical signal;

[0017] Figure 4 Is for Figure 3 Waveform of the signal extracted after wavelet transform of the electrical signal;

[0018] Figure 5 Is for Figure 4 Waveforms of detailed signals analyzed by wavelet modulus maxima;

[0019] Figure 6 This is a flowchart of another method for measuring the transition resistance of an AC transmission line provided in an embodiment of the present invention;

[0020] Figure 7 This is a schematic diagram of a double-ended overhead transmission line model.

[0021] Figure 8 This is a flowchart of another method for measuring the transition resistance of an AC transmission line provided in an embodiment of the present invention;

[0022] Figure 9 It is a transient equivalent circuit diagram at the fault point;

[0023] Figure 10 This is a flowchart of another method for measuring the transition resistance of an AC transmission line provided in an embodiment of the present invention;

[0024] Figure 11 It is an equivalent circuit diagram of a transmission line transient circuit;

[0025] Figure 12 This is a flowchart of another method for measuring the transition resistance of an AC transmission line provided in an embodiment of the present invention;

[0026] Figure 13 This is a flowchart of another method for measuring the transition resistance of an AC transmission line provided in an embodiment of the present invention;

[0027] Figure 14 This is a flowchart of another method for measuring the transition resistance of an AC transmission line provided in an embodiment of the present invention;

[0028] Figure 15 This is a flowchart of another method for measuring the transition resistance of an AC transmission line provided in an embodiment of the present invention;

[0029] Figure 16 This is a flowchart of another method for measuring the transition resistance of AC transmission lines provided in an embodiment of the present invention. Detailed Implementation

[0030] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0031] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention 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 the invention 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 these processes, methods, products, or apparatuses. It should be understood that steps can be reordered, added, or deleted using the various forms of processes shown above. For example, the steps described in this invention can be performed in parallel, sequentially, or in different orders, as long as the desired results of the technical solution of this invention are achieved, and this is not limited herein.

[0032] Figure 1 This is a flowchart of a method for measuring the transition resistance of an AC transmission line provided in an embodiment of the present invention, as shown below. Figure 1 As shown, the method includes:

[0033] S101: Obtain the three-phase electrical signal waveform at the beginning of the AC transmission line, and determine the fault phase and the arrival time of the first traveling wave of the fault at the measurement point based on the three-phase electrical signal waveform.

[0034] The three-phase electrical signal waveforms include three-phase voltage waveforms and / or three-phase current waveforms, and the measurement point is the beginning of the AC transmission line.

[0035] Specifically, in step S101, the three-phase voltage and / or current waveforms at the head end of the AC transmission line are captured in real time. These waveform data contain instantaneous information at the time of the fault.

[0036] By analyzing the abrupt changes in the three-phase voltage and current waveforms, it is possible to determine which phase or multiple phases have experienced a fault. Optionally, the abrupt changes in the three-phase voltage and current waveforms can be a sudden drop in amplitude or a sudden change in phase; this is not limited to these specific cases.

[0037] Using traveling wave propagation theory, the first traveling wave generated by a fault can be identified, and its precise arrival time at the measurement point can be determined. This first traveling wave contains fault information from the transmission line.

[0038] Optionally, wavelet transform can be used to process the acquired voltage waveform of the fault phase, and the arrival time of the first traveling wave of the fault can be extracted using the wavelet maxima.

[0039] S102, based on the three-phase voltage waveforms and arrival times of the faulty phase at the measurement point, calculate the instantaneous value expression of the line-mode transient voltage at the set fault point in the AC transmission line, and use the instantaneous value expression of the line-mode transient voltage as the additional power supply expression for the line-mode fault.

[0040] The fault point is set to one of the points in the AC transmission circuit; the line-mode fault additional power supply expression includes the fault distance variable between the fault point and the measurement point.

[0041] In step S102, after determining the faulty phase and the arrival time of the first traveling wave, it is necessary to further analyze the voltage waveform of the faulty phase at the measurement point. In step S102, a designated fault point is set for analysis to determine the instantaneous value expression of the line-mode transient voltage at the designated fault point. The instantaneous value expression of the line-mode transient voltage includes the fault distance variable between the fault point and the measurement point to achieve accurate location of the fault point in the line. The instantaneous value expression of the line-mode transient voltage reflects the voltage change caused by the fault at the designated fault point and can be regarded as a transient fault-related power source.

[0042] Optionally, the voltage vector at the designated fault point at a distance d from the measurement point can be represented using the uniform transmission equation; this can then be transformed into a time-domain expression. The arrival time of the first fault traveling wave is then determined as the assumed fault occurrence time to obtain the voltage change at the designated fault point at the fault occurrence time. With the mode-domain boundary conditions related to the fault situation obtained, the instantaneous value expression of the transient voltage of mode 1 at the designated fault point is obtained. This instantaneous value expression of the transient voltage of mode 1 at the designated fault point is the expression for the additional power supply of the line-mode fault.

[0043] S103, based on the additional power supply expression of the line mode fault, obtain the first analytical waveform of the time-domain solution corresponding to the first transient voltage equation of the measurement point after the first traveling wave of the fault propagates to the set fault point in the frequency domain.

[0044] Specifically, the voltage response after the first traveling wave of the fault propagates from the set fault point to the measurement point in the frequency domain will be calculated using the additional power supply expression for line-mode faults and the frequency domain transmission characteristics of transmission lines. Then, the frequency domain solution will be converted into a time domain solution to obtain the time domain waveform corresponding to the first transient voltage equation at the measurement point, which is also the first analytical waveform.

[0045] Optionally, with the value of the fault-addition power supply remaining unchanged, the first-mode frequency domain expression of the fault-addition power supply can be obtained. Then, using the transfer function of the inertial element and the first-mode frequency domain expression of the fault-addition power supply, the frequency domain expression of the equivalent voltage source of the traveling wave at the end of the line is constructed. Finally, the frequency domain expression of the first-mode voltage at the measurement point is obtained. An inverse Laplace transform is then performed on this expression to obtain the time-domain solution of the transient voltage waveform at the measurement point, which is the first analytical waveform.

[0046] S104, compare the cosine similarity between the first analytical waveform and the actual measured waveform at the measurement point to obtain the actual fault distance between the actual fault point and the measurement point.

[0047] The first analytical waveform obtained in steps S101-S103 is calculated under the assumptions of fault occurrence time and fault location. Furthermore, the first analytical waveform is significantly affected by the phase voltage vector corresponding to the assumed fault point. Therefore, in step S104, a cosine similarity comparison is performed between the first analytical waveform and the actual measured waveform at the measurement point to determine the degree of similarity between the two waveforms in terms of vectors. This is achieved by adjusting the parameters in the line-mode fault additional power supply expression. The first analytical waveform with the highest similarity to the actual measured waveform is used to obtain the actual fault distance between the actual fault point and the measurement point.

[0048] S105, determine the actual line-mode auxiliary power supply corresponding to the actual fault occurrence time, and obtain the transition resistance based on the second analytical waveform and the actual measured waveform of the measurement point after the fault first traveling wave corresponding to the actual line-mode auxiliary power supply propagates to the actual fault point.

[0049] Specifically, the actual additional power supply of the line model corresponding to the actual fault occurrence time is determined based on the actual fault distance and the line model fault power supply expression. After obtaining the first analytical waveform with the highest cosine similarity to the actual measured waveform in step S104, the distance between the actual fault point and the measurement point is obtained. The actual fault occurrence time is obtained based on the arrival time of the first traveling wave, the distance between the actual fault point and the measurement point, and the wave velocity of the fault traveling wave.

[0050] Optionally, the obtained parameters can be used to further analyze the line-model auxiliary power supply corresponding to the actual fault occurrence time. This actual line-model auxiliary power supply reflects the true voltage change at the fault point. Using the actual line-model auxiliary power supply and the transmission characteristics of the transmission line, the voltage waveform that the measurement point should receive after the first traveling wave of the fault propagates to the actual fault point is calculated, which is the second analytical waveform.

[0051] By comparing the mean absolute difference between the second analytical waveform and the actual measured waveform, the presence of transition resistance affects the propagation characteristics of the fault traveling wave and the voltage waveform at the measurement point. Therefore, by analyzing these effects, accurate measurement of the transition resistance can be achieved. By comparing the assigned values ​​of the two waveforms, the second analytical waveform with the highest similarity to the mean absolute difference of the actual measured waveform is obtained; the corresponding transition resistance is then the actual transition resistance.

[0052] In the method for measuring the transition resistance of AC transmission lines provided in this invention embodiment, the three-phase electrical signal waveforms at the beginning of the AC transmission line are first acquired. The fault phase and the precise time when the first traveling wave of the fault arrives at the measurement point are determined based on the waveforms. Based on the fault phase voltage waveform and arrival time, the instantaneous value of the line-mode transient voltage at the designated fault point is calculated as the additional power supply for the line-mode fault. Using the additional power supply, the time-domain solution of the first transient voltage equation at the measurement point, i.e., the first analytical waveform, is calculated after the first traveling wave of the fault propagates to the designated fault point. The first analytical waveform is compared with the actual measured waveform using cosine similarity to determine the distance between the actual fault point and the measurement point. Based on the location of the actual fault point and the time of fault occurrence, the actual additional power supply for the line-mode is determined. Based on the actual additional power supply, the second transient voltage waveform at the measurement point, i.e., the second analytical waveform, is calculated after the first traveling wave of the fault propagates to the actual fault point. By comparing the difference between the second analytical waveform and the actual measured waveform, the magnitude of the transition resistance is obtained. This invention embodiment, by comparing the similarity between the first analytical waveform and the actual measured waveform, can determine the location of the actual fault point more accurately. This method is more accurate than traditional fault location methods, helping to quickly find the fault point and reduce troubleshooting time. By comparing the amplitude difference between the second analytical waveform and the actual measured waveform, the magnitude of the transition resistance is determined, improving the accuracy of the transition resistance calculation. In the transition resistance measurement method for AC transmission lines provided by this invention, the measurement point can be set at the beginning of the AC transmission line, allowing the method to be implemented in geographical locations such as power plants or substations, thus providing strong operational convenience.

[0053] Figure 2 This is a flowchart of another method for measuring the transition resistance of an AC transmission line provided in an embodiment of the present invention, as shown below. Figure 2 As shown, based on the above embodiments, the method further includes:

[0054] S201, determine the faulty phase based on the abrupt change in the phase electrical signal difference in the three-phase electrical signal waveform.

[0055] Under normal conditions, the signal differences between phases of an AC transmission line should be relatively small and stable. However, when a short-circuit fault occurs, the current in the faulty phase increases sharply, causing a significant change in the current difference associated with that faulty phase. Therefore, it is necessary to detect whether these current differences have undergone significant abrupt changes. Specifically, when comparing the three-phase electrical signals of the line, the phase with the largest abrupt change in the signal difference compared to the other phases is the faulty phase.

[0056] S202 performs wavelet decomposition on the voltage or current signal of the faulty phase and extracts the arrival time of the first traveling wave of the fault using the wavelet modulus maxima.

[0057] To obtain the arrival time of the first traveling wave of the fault in the faulted phase, wavelet transform can be performed on the electrical signal of the faulted phase, and the arrival time of the first traveling wave can be extracted using the wavelet modulus maxima.

[0058] Optionally, the electrical signal of the fault phase is convolved by performing convolution operations with low-pass and high-pass filters respectively to extract low-frequency and high-frequency components from the signal. The convolution result is then sampled to obtain wavelet coefficients for the approximate and detail parts of the electrical signal. This convolution and sampling process is repeated until the desired number of decomposition layers is obtained.

[0059] Figure 3 It is a waveform diagram of an electrical signal; Figure 4 Is for Figure 3 Waveform of the signal extracted after wavelet transform of the electrical signal; Figure 5 Is for Figure 4 Waveform diagram of wavelet modulus maxima analysis of the detailed signal.

[0060] Specific to Figure 3 The current signal is subjected to wavelet transform to obtain, as shown below. Figure 4 The first detail signal d1, the second detail signal d2, the third detail signal d3, and the approximate signal a3 are shown. For... Figure 4 Wavelet modulus maxima analysis is performed on any one of the multiple detail signals in the dataset. For example, such as... Figure 5 As shown, for Figure 3 The detailed signal d1 is analyzed using wavelet modulus maxima to find signal abrupt change points and obtain information such as the arrival time of the first traveling wave. That is, in Figure 5 In the diagram, the signal abrupt change point is abrupt change point A, which gives us the arrival time of the first traveling wave.

[0061] S203, based on the three-phase voltage waveforms corresponding to the fault phase at the measurement point and the arrival time, calculate the instantaneous value expression of the line mode transient voltage at the set fault point in the AC transmission line, and use the instantaneous value expression of the line mode transient voltage as the additional power supply expression for the line mode fault.

[0062] S204, based on the additional power supply expression of the line mode fault, obtain the first analytical waveform of the time domain solution corresponding to the first transient voltage equation of the measurement point after the first traveling wave of the fault propagates to the set fault point in the frequency domain;

[0063] S205, compare the cosine similarity between the first analytical waveform and the actual measured waveform at the measurement point to obtain the actual fault distance between the actual fault point and the measurement point.

[0064] S206, determine the actual line-mode auxiliary power supply corresponding to the actual fault occurrence time, and obtain the transition resistance based on the second analytical waveform and the actual measured waveform of the measurement point after the fault first traveling wave corresponding to the actual line-mode auxiliary power supply propagates to the actual fault point.

[0065] Figure 6 This is a flowchart of another method for measuring the transition resistance of an AC transmission line provided in an embodiment of the present invention, as shown below. Figure 6 As shown, based on the above embodiments, the method further includes:

[0066] S401: Obtain the three-phase electrical signal waveforms at the beginning of the AC transmission line, and determine the faulty phase and the arrival time of the first traveling wave of the fault at the measurement point based on the three-phase electrical signal waveforms.

[0067] S402, determine the phase voltage vector expression corresponding to the set fault point based on the uniform transmission line equation.

[0068] Specifically, the phasor form of the uniform transmission line equation is formula (1):

[0069]

[0070] In formula (1), The voltage phasor at a certain point on the line; Z is the current phasor at a certain point in the line; c γ is the characteristic impedance of the transmission line; l is the propagation constant of the transmission line; A1 and A2 are specific complex constants that represent two independent components of the voltage and current waveforms on the transmission line, corresponding to waves propagating in the positive and negative directions, respectively.

[0071] Assuming the voltage at the beginning is known and current That is, when l = 0, formula (1) can be transformed into expression (2):

[0072]

[0073] Therefore, the expressions (3) and (4) for A1 and A2 are obtained:

[0074]

[0075] Substituting expressions (3) and (4) into expression (1), we obtain expression (5):

[0076]

[0077] in, For the terminal voltage vector, This is the end current vector.

[0078] Figure 7 This is a schematic diagram of a double-ended overhead transmission line model, such as... Figure 7 As shown, S1 and S2 are the two-terminal power supplies with an internal resistance Z. s =1Ω, the total length of the line is L, the distance between the fault point F and the measurement point M is set as d, and the distance between the fault point F and the measurement terminal N is Ld.

[0079] Therefore, combining the above, the voltage vector at the designated fault point F, which is d away from the measurement point M, is obtained as expression (6):

[0080]

[0081] in, The voltage vector measured at the measurement point. To define the phase voltage vector corresponding to the fault point, The current vector measured at the measurement point. Expression (6) is the expression for the phase voltage vector corresponding to the set fault point.

[0082] S403 converts the phase voltage vector expression into a time-domain equation and determines the arrival time of the first fault traveling wave as the assumed fault occurrence time. Based on the time-domain equation and the assumed fault occurrence time, the voltage change at the set fault point is determined.

[0083] Transform expression (6) into the time-domain equation U f (d,t), and the arrival time of the first traveling wave of the fault is determined as the assumed fault occurrence time t1, then the voltage change at the fault point at the fault time is U. f The expression (7) can be represented as:

[0084]

[0085] Where ω is The corresponding angular frequency, α is The corresponding phase angle. Expression (7) is the voltage surge at the set fault point.

[0086] S404, obtains the additional power supply expression for line mode faults based on voltage mutation.

[0087] For example, after obtaining expression (7), the module boundary conditions are obtained according to the phase domain boundary conditions of the faulty phase and the non-faulty phase, and the instantaneous value expression of the transient voltage of the set fault point 1 is obtained according to the module boundary conditions and expression (7).

[0088] S405, based on the additional power supply expression of the line mode fault, obtain the first analytical waveform of the time-domain solution corresponding to the first transient voltage equation of the measurement point after the first traveling wave of the fault propagates to the set fault point in the frequency domain.

[0089] S406, compare the cosine similarity between the first analytical waveform and the actual measured waveform at the measurement point to obtain the actual fault distance between the actual fault point and the measurement point.

[0090] S407, determine the actual line-mode auxiliary power supply corresponding to the actual fault occurrence time, and obtain the transition resistance based on the second analytical waveform and the actual measured waveform of the measurement point after the fault first traveling wave corresponding to the actual line-mode auxiliary power supply propagates to the actual fault point.

[0091] Figure 8 This is a flowchart of another method for measuring the transition resistance of an AC transmission line provided in an embodiment of the present invention, as shown below. Figure 8 As shown, based on the above embodiments, the method includes:

[0092] S501 acquires the three-phase electrical signal waveforms at the beginning of the AC transmission line, and determines the faulty phase and the arrival time of the first traveling wave of the fault at the measurement point based on the three-phase electrical signal waveforms.

[0093] S502, determine the phase voltage vector expression corresponding to the set fault point based on the uniform transmission line equation.

[0094] S503 converts the phase voltage vector expression into a time-domain equation and determines the arrival time of the first fault traveling wave as the assumed fault occurrence time. Based on the time-domain equation and the assumed fault occurrence time, the voltage change at the set fault point is determined.

[0095] S504. Obtain the module domain boundary conditions based on the phase domain boundary conditions of the faulty phase and the inverse Clarke transform matrix.

[0096] Among them, the phase domain boundary conditions are related to the short-circuit current of each phase, the instantaneous voltage of the fault phase, the transient voltage of the fault phase, and the transition resistance of the fault phase.

[0097] Based on the above, after obtaining expression (7), expression (7) is the voltage change amount at the set fault point.

[0098] When obtaining the phase domain boundary conditions for the faulty phase and the non-faulty phase:

[0099] Assuming a short circuit occurs in phase A of the line, the boundary conditions for the phase domains of the faulted phase and the non-faulted phase are given by expression (8):

[0100]

[0101] In expression (8), U fa U is the transient voltage of phase A at the fault point. f R is the instantaneous value of phase A voltage at the fault point at the time of the fault. f For the transition resistance, I fa I fb and I fc These are the short-circuit currents of phases A, B, and C, respectively.

[0102] The phase mode transformation of expression (8) is performed using the inverse Clarke transform matrix, which is expression (9). The phase mode transformation of expression (9) yields expression (10). After simplifying expression (10), the boundary conditions of the fault phase and non-fault phase mode domains are given by expression (11):

[0103]

[0104] Among them, I f1 I0 is the mode 1 short-circuit current at the set fault point; U0 is the mode 0 short-circuit current at the set fault point; f1 The modulo-1 transient voltage at the fault point is set; U f0 The zero-mode transient voltage is set at the fault point.

[0105] S505, obtain the instantaneous value expression of the transient voltage of the set fault point 1 module according to the boundary conditions of the module domain; determine the instantaneous value expression of the transient voltage of the set fault point 1 module as the additional power supply expression of the line mode fault.

[0106] Figure 9 It is the transient equivalent circuit diagram at the fault point, such as Figure 9 As shown, after obtaining the above expression (11), the transient equivalent circuit diagram at the set fault point can be obtained. Where Z C1 and Z C0 These are the wave impedances for mode 1 and mode 0, respectively.

[0107] Based on the above and Figure 9 The instantaneous values ​​of the 1-mode and 0-mode transient voltages at the set fault point can be expressed as (12):

[0108]

[0109] Among them, Z C1 The impedance of mode 1; Z C0 The impedance is at mode 0. U f1 To define the expression for the instantaneous value of the transient voltage at fault point 1, Uf0 The expression for the instantaneous value of the transient voltage at fault point 0 is set, wherein the expression for the instantaneous value of the transient voltage at fault point 1 is determined as the expression for the additional power supply of the line-mode fault.

[0110] S506, based on the additional power supply expression of the line mode fault, obtain the first analytical waveform of the time-domain solution corresponding to the first transient voltage equation of the measurement point after the first traveling wave of the fault propagates to the set fault point in the frequency domain.

[0111] S507, compare the cosine similarity between the first analytical waveform and the actual measured waveform at the measurement point to obtain the actual fault distance between the actual fault point and the measurement point.

[0112] S508 determines the actual line-mode auxiliary power supply corresponding to the actual fault occurrence time, and obtains the transition resistance based on the second analytical waveform and the actual measured waveform of the measurement point after the fault first traveling wave corresponding to the actual line-mode auxiliary power supply propagates to the actual fault point.

[0113] Figure 10 This is a flowchart of another method for measuring the transition resistance of an AC transmission line provided in an embodiment of the present invention, as shown below. Figure 10 As shown, based on the above embodiments, the method includes:

[0114] S601 acquires the three-phase electrical signal waveforms at the beginning of the AC transmission line, and determines the faulty phase and the arrival time of the first traveling wave of the fault at the measurement point based on the three-phase electrical signal waveforms.

[0115] S602, determine the phase voltage vector expression corresponding to the set fault point based on the uniform transmission line equation.

[0116] S603 converts the phase voltage vector expression into a time-domain equation and determines the arrival time of the first fault traveling wave as the assumed fault occurrence time. Based on the time-domain equation and the assumed fault occurrence time, the voltage change at the set fault point is determined.

[0117] S604. Obtain the module domain boundary conditions based on the phase domain boundary conditions of the faulty phase and the inverse Clarke transform matrix.

[0118] S605, obtain the instantaneous value expression of the transient voltage of the set fault point 1 module according to the boundary conditions of the module domain; determine the instantaneous value expression of the transient voltage of the set fault point 1 module as the additional power supply expression of the line mode fault.

[0119] S606 converts the line mode fault additional power supply expression into a frequency domain expression to obtain the line mode fault additional power supply frequency domain expression.

[0120] Since the amplitude of the additional power supply during a line mode fault remains unchanged, it can be represented by a step signal, and its frequency domain expression is expression (13):

[0121]

[0122] Among them, U f1 (s) is the frequency domain expression of the additional power supply expression for a mode 1 fault, U f0 (s) is the frequency domain expression of the additional power supply expression for a 0-mode fault.

[0123] S607, obtain the frequency domain expression of the equivalent voltage source of the traveling wave at the end of the line based on the frequency domain expression of the additional power supply for line mode faults.

[0124] Among them, the fault traveling wave includes the fault first traveling wave; the frequency domain expression of the equivalent voltage source of the fault traveling wave at the end of the line is related to the first transfer function and the frequency domain expression of the additional power supply of the line mode fault; the first transfer function is the line frequency-varying transfer function constructed by using the inertial element approximation, and the first transfer function is related to the distance from the fault point to the measurement point, the line attenuation coefficient, the line dispersion coefficient, the propagation speed of the fault traveling wave in mode 1, and the time delay caused by the fault traveling wave propagating along the line from the measurement point to the fault point.

[0125] For example, the frequency domain expression of the equivalent voltage source of the line-end fault traveling wave is obtained by using the frequency domain expression of the 1-mode fault additional power supply expression in expression (13).

[0126] Figure 11 It is an equivalent circuit diagram of a transmission line transient circuit, such as... Figure 11 As shown, when the fault traveling wave has propagated to the measurement point and then undergoes reflection, but has not propagated to the fault point, the transient equivalent circuit diagram of the transmission line is as follows. Figure 11 As shown, the first voltage source B... Mf1 The first inductor L is the equivalent voltage source for the traveling wave at measurement point M. Meq Let Z be the equivalent inductance of the transformer at measurement point M, and the first impedance be Z. MS Let Z be the internal resistance of the power supply at measurement point M, and Z be the second impedance. c1 The impedance is a 1-mode wave. The equivalent voltage source of the traveling wave at the end of the line fault, in the frequency domain, is B. Mf1 The expression for (s) is expression (14):

[0127]

[0128] in, The line frequency-varying transfer function is constructed using an inertial element as an approximation, where d is the distance between the fault point and point M; K a1 T represents the line attenuation coefficient, which is related to the line length; a1 represents the line dispersion coefficient, which is related to the line length; v1 is the propagation speed of the traveling wave in mode 1; The delay caused by the traveling wave propagating a distance d along the path.

[0129] S608, obtain the frequency domain expression of the mode voltage at measurement point 1 based on the frequency domain expression of the equivalent voltage source of the traveling wave at the end of the line fault.

[0130] Among them, the frequency domain expression of the mode voltage at measurement point 1 is related to the impedance of the line's equivalent inductance in the complex frequency domain, the impedance of the line's mode 1 wave, and the internal resistance of the equivalent voltage source; the frequency domain expression of the mode voltage at measurement point 1 is the first transient voltage equation of the measurement point.

[0131] Combining the above embodiments and Figure 11 As shown, the frequency domain U of the 1-mode voltage at measurement point M is obtained. Mf1 The expression (s) is expression (15):

[0132]

[0133] Among them, B Mf1 L is the equivalent voltage source of the traveling wave at measurement point M. Meq Z is the equivalent inductance of the transformer at measurement point M. MS Z is the internal resistance of the power supply at measurement point M. c1 It is the impedance of a 1-mode wave.

[0134] The frequency domain expression of the 1-mode voltage at measurement point M in expression (14) is determined as the first transient voltage equation of the measurement point.

[0135] S609, perform an inverse Laplace transform based on the first transient voltage equation at the measurement point to obtain the time-domain solution of the first transient voltage equation at the measurement point as the first analytical waveform.

[0136] Perform an inverse Laplace transform on the first transient voltage equation to obtain the time-domain solution U of the first transient voltage equation at measurement point M. Mf1 The obtained time-domain solution (t) is used as the first analytical waveform.

[0137] S610, compare the cosine similarity between the first analytical waveform and the actual measured waveform at the measurement point to obtain the actual fault distance between the actual fault point and the measurement point.

[0138] S611, determine the actual line-mode auxiliary power supply corresponding to the actual fault occurrence time, and obtain the transition resistance based on the second analytical waveform and the actual measured waveform of the measurement point after the fault first traveling wave corresponding to the actual line-mode auxiliary power supply propagates to the actual fault point.

[0139] Figure 12 This is a flowchart of another method for measuring the transition resistance of an AC transmission line provided in an embodiment of the present invention, as shown below. Figure 12 As shown, based on the above embodiments, the method includes:

[0140] S701 acquires the three-phase electrical signal waveforms at the beginning of the AC transmission line, and determines the faulty phase and the arrival time of the first traveling wave of the fault at the measurement point based on the three-phase electrical signal waveforms.

[0141] S702, based on the three-phase voltage waveforms corresponding to the fault phase at the measurement point and the arrival time, calculates the instantaneous value expression of the line mode transient voltage at the set fault point in the AC transmission line, and uses the instantaneous value expression of the line mode transient voltage as the additional power supply expression for the line mode fault.

[0142] S703, based on the additional power supply expression of the line mode fault, obtains the first analytical waveform of the time-domain solution corresponding to the first transient voltage equation of the measurement point after the first traveling wave of the fault propagates to the set fault point in the frequency domain.

[0143] S704, compare the cosine similarity between the first analytical waveform and the actual measured waveform.

[0144] The cosine similarity of the first analytical waveform and the actual measured waveform is compared, where the expression for the cosine similarity comparison is expression (16):

[0145]

[0146] Among them, u si (t) represents the fault recording of the transient voltage waveform, i.e., the reference signal; u an (t) represents the first analytical waveform, i.e., the signal under test; n represents the number of sampling points within the time window used for similarity evaluation.

[0147] Optionally, the time window can be selected as: t1-10μs—t1+50μs, for a total of 60μs.

[0148] Optionally, a step-by-step search method combined with cosine similarity can be used to compare the similarity between the first analytical waveform and the actual measured waveform: 1. Initialize search parameters: Determine the initial range of the entire search, which is usually the entire length of the transmission line. Choose a large step size (e.g., several hundred meters or several kilometers) to quickly cover the entire search range in the initial stage. Set a similarity threshold or positional accuracy requirement to determine when to stop the search. Optionally, set a maximum number of iterations to prevent infinite loops. 2. Coarse search stage: Over the entire line, at intervals of the initial step size, calculate the cosine similarity between the fault recording waveform and the analytical waveform corresponding to each location point di. Find the location point d with the highest cosine similarity. max . with d max Centered on the similarity curve, a new, smaller search range is determined based on the shape and step size. 3. Fine-tuning search stage: Within the narrowed search range, an even smaller step size is selected for the search. At the new step size, the cosine similarity of each location point is calculated, and the new maximum similarity point d is found. max′。 If d max The point with the highest similarity to the previous one, d max If the difference between the two is greater than the accuracy threshold, or the iteration limit has not been reached, then continue with d. max 4. Stopping Condition: Stop the search when the difference between the maximum similarity points in two consecutive iterations is less than a preset accuracy threshold. Alternatively, stop the search even if the preset maximum number of iterations has been reached, even if the accuracy requirement has not been met. 5. Determine the final position: [The text abruptly ends here, likely due to an incomplete sentence or missing information.] max The distance between the fault point and the fault location is the actual distance at which the fault occurred.

[0149] S705, the distance between the measurement point and the fault point in the analytical waveform that has the highest similarity to the actual measured waveform is the actual fault occurrence distance.

[0150] Cosine similarity comparison measures the degree of similarity between two vectors in direction, without considering their magnitude (i.e., the magnitude of the vectors). Cosine similarity comparison is less affected by amplitude. The distance between the measurement point in the analytical waveform with the highest similarity to the actual measured waveform and the fault point is the actual fault occurrence distance, thus determining the precise time of fault occurrence.

[0151] S706, determine the actual line-mode auxiliary power supply corresponding to the actual fault occurrence time, and obtain the transition resistance based on the second analytical waveform and the actual measured waveform of the measurement point after the fault first traveling wave corresponding to the actual line-mode auxiliary power supply propagates to the actual fault point.

[0152] Figure 13 This is a flowchart of another method for measuring the transition resistance of an AC transmission line provided in an embodiment of the present invention, as shown below. Figure 13 As shown, based on the above embodiments, the method includes:

[0153] S801 acquires the three-phase electrical signal waveforms at the beginning of the AC transmission line, and determines the faulty phase and the arrival time of the first traveling wave of the fault at the measurement point based on the three-phase electrical signal waveforms.

[0154] S802 determines the phase voltage vector expression corresponding to the set fault point based on the uniform transmission line equation.

[0155] S803 converts the phase voltage vector expression into a time-domain equation and determines the arrival time of the first fault traveling wave as the assumed fault occurrence time. Based on the time-domain equation and the assumed fault occurrence time, it determines the voltage change at the set fault point.

[0156] S804 obtains the additional power supply expression for line mode faults based on voltage mutation.

[0157] S805 obtains the first analytical waveform of the time-domain solution of the first transient voltage equation at the measurement point after the first traveling wave of the fault propagates to the set fault point in the frequency domain, based on the additional power supply expression of the line mode fault.

[0158] S806, compare the cosine similarity between the first analytical waveform and the actual measured waveform at the measurement point to obtain the actual fault distance between the actual fault point and the measurement point.

[0159] S807 determines the actual fault occurrence time based on the actual fault distance, arrival time, and the propagation speed of the first traveling wave of the fault.

[0160] After obtaining the actual fault distance d0, the fault occurrence time can be calculated based on the actual fault distance. The specific calculation expression for the fault occurrence time t0 is expression (16):

[0161]

[0162] Where d0 is the actual fault distance; t1 is the arrival time of the first fault traveling wave; and v1 is the wave velocity of the first fault traveling wave.

[0163] S808 corrects the assumed fault occurrence time based on the actual fault occurrence time, and determines the actual additional power supply for the line model fault based on the actual fault distance and the expression for the additional power supply for the line model fault.

[0164] Based on the above, when correcting the assumed fault occurrence time according to the actual fault occurrence time, optionally, the voltage surge at the fault point at the actual fault occurrence time is calculated, and the additional power supply of the actual line-mode fault is calculated, thus obtaining the actual line-mode fault additional power supply U. f11 .

[0165] Optionally, the calculated distance between the actual fault location and the measurement point, as well as the actual fault occurrence time, can be substituted into the expression calculated in the aforementioned steps to obtain the actual modulus 1 fault supplementary power supply.

[0166] S809: Based on the additional power supply of the actual line-mode fault, obtain the frequency domain expression of the second 1-mode voltage at the measurement point after the first traveling wave of the fault propagates to the actual fault point in the frequency domain. The frequency domain expression of the second 1-mode voltage is the second transient voltage equation corresponding to the measurement point; and determine the second analytical waveform of the time domain solution of the second transient voltage equation.

[0167] The actual 1-mode fault supplementary power supply U obtained from the above steps f11 Frequency domain transformation can be performed to obtain the second 1-mode voltage frequency domain expression B. Mf11 (s), the second 1-mode voltage frequency domain expression B Mf11(s) represents the second transient voltage equation corresponding to the measurement point, and the corresponding time-domain solution is obtained. This yields the second analytical waveform. The fault location and fault occurrence time in the second analytical waveform are actual values, not assumed values ​​from the first analytical waveform.

[0168] S810 compares the average absolute difference between the second analytical waveform and the actual measured waveform to obtain the transition resistance.

[0169] After obtaining the second analytical waveform, the transition resistance needs to be determined. The mean absolute difference (MAD) similarity is then compared between the second analytical waveform and the actual measured waveform. The MAD is a method for measuring the difference between two signals; it calculates the average of the absolute values ​​of the differences between corresponding points. Unlike cosine similarity, MAD focuses more on the difference in signal amplitude than on direction or shape.

[0170] In this comparison process, the point where the difference between the second analytical waveform and the actual measured waveform is minimal, i.e., the second analytical waveform with the highest waveform similarity, is found. This point corresponds to a specific transition resistance value, because changes in the transition resistance significantly affect the waveform characteristics of the fault current. Therefore, the corresponding transition resistance value is the required transition resistance.

[0171] Figure 14 This is a flowchart of another method for measuring the transition resistance of an AC transmission line provided in an embodiment of the present invention, as shown below. Figure 14 As shown, based on the above embodiments, the method includes:

[0172] S901 acquires the three-phase electrical signal waveforms at the beginning of the AC transmission line, and determines the faulty phase and the arrival time of the first traveling wave of the fault at the measurement point based on the three-phase electrical signal waveforms.

[0173] S902, determine the phase voltage vector expression corresponding to the set fault point based on the uniform transmission line equation.

[0174] S903 converts the phase voltage vector expression into a time-domain equation and determines the arrival time of the first fault traveling wave as the assumed fault occurrence time. Based on the time-domain equation and the assumed fault occurrence time, the voltage change at the set fault point is determined.

[0175] S904, obtains the additional power supply expression for line mode faults based on voltage mutation.

[0176] S905, based on the additional power supply expression of the line mode fault, obtains the first analytical waveform of the time-domain solution corresponding to the first transient voltage equation of the measurement point after the first traveling wave of the fault propagates to the set fault point in the frequency domain.

[0177] S906, compare the cosine similarity between the first analytical waveform and the actual measured waveform at the measurement point to obtain the actual fault distance between the actual fault point and the measurement point.

[0178] S907 determines the actual fault occurrence time based on the actual fault distance, arrival time, and the propagation speed of the first traveling wave of the fault.

[0179] S908, substitute the actual fault occurrence time and actual fault distance into the line model fault supplementary power supply expression to determine the actual line model fault supplementary power supply.

[0180] Based on the above, after obtaining the actual time of the fault and the actual distance to the fault, these are substituted into the expression for the additional power supply of the line model fault to determine the actual additional power supply of the line model fault.

[0181] Optionally, similar to expression (6), the actual fault occurrence time t0 and the actual fault distance d0 are substituted into the above expression (6) to obtain the voltage vector of the actual fault point at a distance d0 from the measurement point M. The expression (17):

[0182]

[0183] Where d0 is the distance between the actual fault location and the measurement point.

[0184] Similar to expression (7), expression (17) is transformed into the time-domain equation U. f (d0,t), and substituting the actual fault occurrence time t0 into it, we get the actual fault point voltage change U at the actual fault time. f0 The expression (18) can be represented.

[0185]

[0186] Where t0 is the actual time when the fault occurred, and d0 is the distance between the actual fault location and the measurement point.

[0187] Referring to the above embodiment, similar to expression (12), after obtaining the actual fault point voltage change U at the actual fault time... f0 Then, the instantaneous value U of the 1-mode transient voltage at the actual fault point can be obtained. f10 Expression (19):

[0188]

[0189] The instantaneous value expression of the transient voltage at the actual fault point 1 is then determined as the additional power supply expression for the actual line-mode fault.

[0190] S909, based on the additional power supply of the actual line-mode fault, obtain the frequency domain expression of the second 1-mode voltage at the measurement point after the first traveling wave of the fault propagates to the actual fault point in the frequency domain. The frequency domain expression of the second 1-mode voltage is the second transient voltage equation corresponding to the measurement point; and determine the second analytical waveform of the time domain solution of the second transient voltage equation.

[0191] S910 compares the average absolute difference between the second analytical waveform and the actual measured waveform to obtain the transition resistance.

[0192] Figure 15 This is a flowchart of another method for measuring the transition resistance of an AC transmission line provided in an embodiment of the present invention, as shown below. Figure 15 As shown, based on the above embodiments, the method includes:

[0193] S1001: Obtain the three-phase electrical signal waveforms at the beginning of the AC transmission line, and determine the faulty phase and the arrival time of the first traveling wave of the fault at the measurement point based on the three-phase electrical signal waveforms.

[0194] S1002, determine the phase voltage vector expression corresponding to the set fault point according to the uniform transmission line equation.

[0195] S1003 converts the phase voltage vector expression into a time-domain equation and determines the arrival time of the first fault traveling wave as the assumed fault occurrence time. Based on the time-domain equation and the assumed fault occurrence time, the voltage change at the set fault point is determined.

[0196] S1004, obtain the additional power supply expression for line mode fault based on the voltage mutation amount.

[0197] S1005, based on the additional power supply expression of the line mode fault, obtain the first analytical waveform of the time-domain solution corresponding to the first transient voltage equation of the measurement point after the first traveling wave of the fault propagates to the set fault point in the frequency domain.

[0198] S1006, compare the cosine similarity between the first analytical waveform and the actual measured waveform at the measurement point to obtain the actual fault distance between the actual fault point and the measurement point.

[0199] S1007, determine the actual fault occurrence time based on the actual fault distance, arrival time, and the propagation speed of the first traveling wave of the fault.

[0200] S1008, correct the assumed fault occurrence time according to the actual fault occurrence time, and determine the actual line model fault additional power supply according to the actual fault distance and the line model fault additional power supply expression.

[0201] S1009, convert the actual line model fault additional power supply expression into a frequency domain expression to obtain the actual line model fault additional power supply frequency domain expression.

[0202] In the actual expression for the additional power supply of the line mode fault, the expression for the additional power supply of the 1-mode fault is transformed into a frequency domain expression, as shown in the following expression (20):

[0203]

[0204] Among them, U f10 (s) is the frequency domain expression of the additional power supply expression for a mode 1 fault.

[0205] S1010, obtain the frequency domain expression of the equivalent voltage source of the traveling wave at the end of the second line fault based on the frequency domain expression of the additional power supply for the actual line model fault.

[0206] Among them, the frequency domain expression of the equivalent voltage source of the fault traveling wave at the end of the second line is related to the first transfer function and the frequency domain expression of the additional power supply of the actual line mode fault; the first transfer function is the line frequency-varying transfer function constructed by using the inertial element approximation, and the first transfer function is related to the actual distance from the fault point to the measurement point, the line attenuation coefficient, the line dispersion coefficient, the propagation speed of the fault traveling wave in mode 1, and the delay caused by the fault traveling wave propagating along the line from the measurement point to the fault point.

[0207] Frequency Domain B of the Traveling Wave Equivalent Voltage Source for the Fault at the Second Line End Mf10 The expression (s) is expression (21):

[0208]

[0209] in, The line frequency-varying transfer function is constructed using an inertial element as an approximation, where d is the distance between the fault point and point M; K a1 T represents the line attenuation coefficient, which is related to the line length; a1 represents the line dispersion coefficient, which is related to the line length; v1 is the propagation speed of the traveling wave in mode 1; The delay caused by the traveling wave propagating a distance d along the path.

[0210] S1011, obtain the frequency domain expression of the second modulus voltage at the measurement point based on the frequency domain expression of the equivalent voltage source of the traveling wave at the end of the second line fault.

[0211] Among them, the frequency domain expression of the second mode 1 voltage is related to the impedance of the line equivalent inductance in the complex frequency domain, the impedance of the line mode 1 wave, and the internal resistance of the equivalent voltage source; the frequency domain expression of the second mode 1 voltage is the second transient voltage equation.

[0212] Obtain the second 1-mode voltage frequency domain U at measurement point M. Mf10 The expression (s) is expression (22):

[0213]

[0214] Among them, B Mf1 L is the equivalent voltage source of the traveling wave at measurement point M. Meq Z is the equivalent inductance of the transformer at measurement point M. MS Z is the internal resistance of the power supply at measurement point M. c1 It is the impedance of a 1-mode wave.

[0215] The frequency domain expression of the second 1-mode voltage at measurement point M in expression (22) is determined as the second transient voltage equation at measurement point M.

[0216] S1012, perform an inverse Laplace transform based on the second transient voltage equation at the measurement point to obtain the time-domain solution of the second transient voltage equation at the measurement point as the second analytical waveform.

[0217] Performing an inverse Laplace transform on the second transient voltage equation yields the time-domain solution U of the first transient voltage equation at measurement point M. Mf10 The obtained time-domain solution (t) is used as the second analytical waveform.

[0218] S1013: Compare the average absolute difference between the second analytical waveform and the actual measured waveform to obtain the transition resistance.

[0219] Figure 16 This is a flowchart of another method for measuring the transition resistance of an AC transmission line provided in an embodiment of the present invention, as shown below. Figure 16 As shown, based on the above embodiments, the method includes:

[0220] S1101: Obtain the three-phase electrical signal waveform at the beginning of the AC transmission line, and determine the fault phase and the arrival time of the first traveling wave of the fault at the measurement point based on the three-phase electrical signal waveform.

[0221] S1102, determine the phase voltage vector expression corresponding to the set fault point based on the uniform transmission line equation.

[0222] S1103 converts the phase voltage vector expression into a time-domain equation and determines the arrival time of the first fault traveling wave as the assumed fault occurrence time. Based on the time-domain equation and the assumed fault occurrence time, the voltage change at the set fault point is determined.

[0223] S1104, obtain the additional power supply expression for line mode fault based on voltage mutation.

[0224] S1105, based on the additional power supply expression of the line mode fault, obtain the first analytical waveform of the time-domain solution corresponding to the first transient voltage equation of the measurement point after the first traveling wave of the fault propagates to the set fault point in the frequency domain.

[0225] S1106, compare the cosine similarity between the first analytical waveform and the actual measured waveform at the measurement point to obtain the actual fault distance between the actual fault point and the measurement point.

[0226] S1107, determine the actual fault occurrence time based on the actual fault distance, arrival time, and the propagation speed of the first traveling wave of the fault.

[0227] S1108, correct the assumed fault occurrence time according to the actual fault occurrence time, and determine the actual line model fault additional power supply according to the actual fault distance and the line model fault additional power supply expression.

[0228] S1109, based on the actual line-mode fault additional power supply, obtain the second 1-mode voltage frequency domain expression of the measurement point after the first traveling wave of the fault propagates to the actual fault point in the frequency domain. The second 1-mode voltage frequency domain expression is the second transient voltage equation corresponding to the measurement point; and determine the second analytical waveform of the time domain solution of the second transient voltage equation.

[0229] S1110, compare the average absolute difference waveform similarity between the second analytical waveform and the actual measured waveform fault recording, and determine the transition resistance based on the highest waveform similarity point between the second analytical waveform and the actual measured waveform fault recording.

[0230] Specifically, the mean absolute difference waveform similarity is compared between the second analytical waveform and the actual measured waveform fault recording. The expression for the mean absolute difference waveform similarity comparison is expression (23):

[0231]

[0232] Among them, u si (t i ) and the fault record representing the transient voltage waveform, i.e., the reference signal; u an (t i ) represents the second analytical waveform, i.e. the measured signal, and n is the number of sampling points within the selected time window.

[0233] Optionally, a step-by-step search method can be adopted. First, a larger step size is used to find the Ri value where the mean absolute difference is minimized. Then, a smaller step size is used to perform a more precise search within the adjacent intervals of Ri. This process is repeated to improve measurement accuracy. The transition resistance corresponding to the point where the waveform of the fault recording has the highest similarity to the second analytical waveform and the actual measured waveform is the required transition resistance.

[0234] In conjunction with any of the above embodiments, simulation tests were performed on the transmission line model. The specific parameters of the transmission line model are shown in Table 1 below:

[0235]

[0236] Table 1

[0237] For the transmission line model with the above parameters, a phase A ground fault is set at t = 0.286s. Different transition resistances and fault locations are set respectively. The analytical waveform of the mode 1 transient voltage after the first traveling wave reaches point M is compared with the simulated waveform. The time window is t1-10μs—t1+50μs, a total of 60μs.

[0238] The transition resistance value obtained by the transition resistance measurement method of AC transmission lines provided in the above embodiments is compared with the set transition resistance value as shown in Table 2 below.

[0239]

[0240]

[0241] Table 2

[0242] As can be seen from Table 2 above, when measuring the transition resistance of AC transmission lines using the transition resistance measurement method of any of the above embodiments of the present invention, the calculated transition resistance value has a small error relative to the actual transition resistance value when calculating the transition resistance for transmission lines with different fault distances and different actual transition resistances; when using the method provided in any of the above embodiments for fault location, the error is extremely small. Compared with the prior art, the AC transmission line transition resistance measurement method provided in any of the above embodiments of the present invention provides an extremely accurate fault location method, which helps to quickly find the fault point and reduce fault troubleshooting time; it achieves accurate solution for the transition resistance.

[0243] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for measuring the transition resistance of an AC transmission line, characterized in that, include: The three-phase voltage waveform and three-phase current waveform at the beginning of the AC transmission line are obtained. The fault phase and the arrival time of the first traveling wave of the fault at the measurement point are determined based on the three-phase current waveform. The measurement point is the beginning of the AC transmission line. Based on the three-phase voltage waveforms corresponding to the fault phase at the measurement point and the arrival time, the expression for the additional power supply of the line-mode fault in the AC transmission line is calculated. The additional power supply expression for the line mode fault includes: the instantaneous value expression of the transient voltage of mode 1 at the fault point: ;in, To define the expression for the instantaneous value of the transient voltage at fault point 1, Z C1 The wave impedance of mode 1 To set the voltage surge at the fault point at the time of the fault, Z C0 The wave impedance is the zero-mode impedance, R f For transition resistance; The expression for setting the voltage change at the fault point at the fault time includes: ;in, To define the phase voltage vector corresponding to the fault point, for The corresponding angular frequency, for The corresponding phase angle, d is the fault distance variable between the set fault point and the measurement point; Based on the additional power supply expression of the line mode fault, the first transient voltage equation after the first traveling wave of the fault propagates to the measurement point in the frequency domain is obtained, and the time domain solution obtained by numerical inverse Laplace transform is the first analytical waveform. The first analytical waveform is compared with the actual measured waveform at the measurement point using cosine similarity to obtain the actual fault distance between the actual fault point and the measurement point. Based on the actual fault distance and the expression for the additional power supply of the line model fault, the actual additional power supply of the line model corresponding to the actual fault occurrence time is determined. Based on the second analytical waveform of the time-domain solution of the second transient voltage equation corresponding to the measurement point after the fault first traveling wave corresponding to the actual line model additional power supply propagates to the actual fault point, and the actual measured waveform at the measurement point, the transition resistance is obtained. The second transient voltage equation corresponding to the measurement point includes: the second 1-mode voltage frequency domain expression: ; among which, L eq Z is the equivalent inductance of the transformer at measurement point M. MS Z is the internal resistance of the power supply at measurement point M. c1 For a 1-mode wave impedance, The equivalent voltage source of the traveling wave at the end of the second line fault is expressed in the frequency domain as follows: ;in, The line frequency-varying transfer function is constructed by using an inertial element as an approximation; K a1 T represents the line attenuation coefficient, which is related to the line length; a1 represents the line dispersion coefficient, which is related to the line length; v1 is the propagation speed of the traveling wave in mode 1; The delay caused by the traveling wave propagating a distance d along the path.

2. The transition resistance measurement method according to claim 1, characterized in that, The process involves acquiring the three-phase voltage and current waveforms at the beginning of the AC transmission line, determining the fault phase and the arrival time of the first traveling wave of the fault at the measurement point based on the three-phase current waveforms, wherein the measurement point is the beginning of the AC transmission line, including: The faulty phase is determined based on the abrupt change in the current difference between each phase in the three-phase current waveform. Wavelet decomposition is performed on the voltage or current signal of the faulted phase, and the arrival time of the first traveling wave of the fault is extracted using the wavelet modulus maxima.

3. The method for measuring the transition resistance of an AC transmission line according to claim 1, characterized in that, The step of deriving the additional power supply expression for a line-mode fault in the AC transmission line based on the three-phase voltage waveform corresponding to the fault phase at the measurement point and the arrival time includes: The phase voltage vector expression corresponding to the set fault point is determined based on the uniform transmission line equation. The phase voltage vector expression is converted into a time-domain equation, and the arrival time of the first traveling wave of the fault is determined as the assumed fault occurrence time. The voltage change at the set fault point is determined based on the time-domain equation and the assumed fault occurrence time. The additional power supply expression for line mode faults is obtained based on the voltage mutation.

4. The method for measuring the transition resistance of an AC transmission line according to claim 3, characterized in that, The step of obtaining the additional power supply expression for line-mode faults based on the voltage mutation includes: The module domain boundary conditions are obtained based on the phase domain boundary conditions of the faulty phase and the non-faulty phase, as well as the Clark inverse transform matrix; the phase domain boundary conditions are related to the short-circuit current of each phase, the instantaneous voltage value in the faulty phase, the transient voltage of the faulty phase, and the transition resistance of the faulty phase. The instantaneous value expression of the transient voltage of the first mode at the set fault point is obtained based on the boundary conditions of the mode domain; the instantaneous value expression of the transient voltage of the first mode at the set fault point is determined as the additional power supply expression of the line mode fault.

5. The method for measuring the transition resistance of an AC transmission line according to claim 1, characterized in that, The step of comparing the first analytical waveform with the actual measured waveform at the measurement point using cosine similarity to obtain the actual fault distance between the actual fault point and the measurement point includes: Compare the first analytical waveform with the actual measured waveform using cosine similarity. The distance between the measurement point in the analytical waveform that has the highest similarity to the actual measured waveform and the fault point is the actual fault occurrence distance.

6. The method for measuring the transition resistance of an AC transmission line according to claim 3, characterized in that, The step of determining the actual line-mode additional power supply corresponding to the actual fault occurrence time based on the actual fault distance and the line-mode fault additional power supply expression, and obtaining the transition resistance based on the second analytical waveform of the time-domain solution of the second transient voltage equation corresponding to the measurement point and the actual measurement waveform of the measurement point after the fault first traveling wave corresponding to the actual line-mode additional power supply propagates to the actual fault point, includes: The actual fault occurrence time is determined based on the actual fault distance, the arrival time, and the propagation speed of the first traveling wave of the fault. The assumed fault occurrence time is corrected based on the actual fault occurrence time, and the actual line model fault additional power supply is determined based on the actual fault distance and the line model fault additional power supply expression. Based on the actual line-mode fault additional power supply, the second 1-mode voltage frequency domain expression of the measurement point after the first traveling wave of the fault propagates to the actual fault point in the frequency domain is obtained. The second 1-mode voltage frequency domain expression is the second transient voltage equation corresponding to the measurement point. And determine the second analytical waveform of the time-domain solution of the second transient voltage equation; The average absolute difference between the second analytical waveform and the actual measured waveform is compared to obtain the transition resistance.

7. The method for measuring the transition resistance of an AC transmission line according to claim 6, characterized in that, The step of correcting the assumed fault occurrence time based on the actual fault occurrence time, and determining the actual line model fault additional power supply based on the actual fault distance and the line model fault additional power supply expression, includes: Substitute the actual fault occurrence time and the actual fault distance into the expression for the additional power supply of the line model fault to determine the additional power supply of the actual line model fault.

8. The method for measuring the transition resistance of an AC transmission line according to claim 6, characterized in that, The step of obtaining the second 1-mode voltage frequency domain expression of the measurement point after the first traveling wave of the fault propagates to the actual fault point in the frequency domain based on the additional power supply of the actual line-mode fault, and determining the second analytical waveform of the time domain solution of the second 1-mode voltage frequency domain expression, includes: The expression for the additional power supply of the actual line mode fault is transformed into a frequency domain expression to obtain the frequency domain expression for the additional power supply of the actual line mode fault. The frequency domain expression of the equivalent voltage source of the traveling wave at the end of the line fault is obtained based on the frequency domain expression of the additional power supply for the actual line mode fault. The frequency domain expression of the equivalent voltage source of the traveling wave at the end of the line fault is related to the first transfer function and the frequency domain expression of the additional power supply for the actual line mode fault. The first transfer function is a line frequency-varying transfer function constructed using an inertial element approximation. The first transfer function is related to the actual distance from the fault point to the measurement point, the line attenuation coefficient, the line dispersion coefficient, the propagation speed of the fault traveling wave in mode 1, and the delay caused by the fault traveling wave propagating along the line from the measurement point to the fault point. The time-domain solution of the second transient voltage equation at the measurement point is obtained by performing an inverse Laplace transform based on the second transient voltage equation at the measurement point, which is the second analytical waveform.

9. The method for measuring the transition resistance of an AC transmission line according to claim 6, characterized in that, The step of comparing the average absolute difference between the second analytical waveform and the actual measured waveform to obtain the transition resistance includes: The transition resistance is determined by comparing the average absolute difference waveform similarity between the second analytical waveform and the actual measured waveform fault record, and the highest waveform similarity point between the second analytical waveform and the actual measured waveform fault record.

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