Transition resistance measuring method of alternating current transmission line

Abstract

The invention discloses a transition resistance measuring method for an alternating-current transmission line. The method comprises the following steps: acquiring a three-phase electric signal waveform at the head end of the alternating-current transmission line, and determining a fault phase and the arrival time of a fault first traveling wave reaching a measuring point according to the three-phase electric signal waveform; according to the corresponding three-phase voltage waveform of the fault phase at the measurement point and the arrival time, calculating a line mode fault additional power supply expression of a set fault point in the AC transmission line; acquiring a first analytic waveform of a time domain solution corresponding to the first transient voltage equation of the measurement point; performing cosine similarity comparison on the first analysis waveform and an actual measurement waveform of the measurement point to obtain an actual fault distance between the actual fault point and the measurement point; and determining an actual line mode additional power supply corresponding to the actual fault occurrence moment, and obtaining the transition resistance based on a second analysis waveform of a time domain solution of a second transient voltage equation corresponding to the measurement point and an actual measurement waveform of the measurement point. According to the method, the value of the transition resistance is accurately calculated after the short circuit fault of the line.

Description

Technical Field

[0001] The invention relates to the technical field of AC transmission lines, and in particular to a method for measuring transition resistance of an AC transmission line. Background Art

[0002] In AC transmission lines, for non-metallic short circuits of the lines, there will be transition resistance at the short circuit point. There is randomness in the value of the transition resistance and the location of the short circuit point, which will affect the power system fault analysis, protection setting calculations, and reliable operation of protection devices. For measuring the value of the transition resistance, the prior art usually uses an instrument to directly measure the transition resistance at the short circuit point; or uses the bridge method to construct a measurement circuit, and finds the balance condition by adjusting the proportional resistance or sliding resistance of the bridge, thereby obtaining the accurate value of the transition resistance.

[0003] However, in the prior art method for measuring transition resistance, it is necessary to measure the short-circuit point directly on the line, which makes the measurement operation costly. Moreover, the measurement of transition resistance is also affected by various factors in the environment (such as temperature, humidity, electromagnetic interference, etc.). The error of the transition resistance value finally measured is large. Summary of the invention

[0004] The present invention provides a method for measuring transition resistance of an AC power transmission line to achieve fault location: quickly find the fault point, reduce the time for troubleshooting, and improve the accuracy of transition resistance solution.

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

[0006] Acquire a three-phase electrical signal waveform at the head end of the AC transmission line, wherein the three-phase electrical signal waveform includes a three-phase voltage waveform and / or a three-phase current waveform, and determine the arrival time of the fault phase and the first fault wave at a measuring point according to the three-phase electrical signal waveform, wherein the measuring point is the head end of the AC transmission line;

[0007] According to the three-phase voltage waveform corresponding to the fault phase at the measuring 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 line mode fault additional power supply expression; wherein the set fault point is one point in the AC transmission circuit; the line mode fault additional power supply expression includes a fault distance variable between the set fault point and the measuring point;

[0008] According to the line mode fault additional power supply expression, a first analytical waveform of a time domain solution corresponding to the first transient voltage equation at the measurement point is obtained after the first fault wave in the frequency domain propagates to the set fault point;

[0009] Performing a cosine similarity comparison between the first analytical waveform and the actual measured waveform of the measuring point to obtain an actual fault distance between the actual fault point and the measuring point;

[0010] The actual line mode additional power supply corresponding to the actual fault occurrence time is determined according to the actual fault distance and the line mode fault power supply expression, and 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 measuring point after the first fault wave corresponding to the actual line mode additional power supply propagates to the actual fault point and the actual measured waveform of the measuring point.

[0011] The present invention discloses a method for measuring the transition resistance of an AC transmission line, including: obtaining a three-phase electrical signal waveform at the head end of the AC transmission line, determining the arrival time of the fault phase and the first fault wave at the measuring point according to the three-phase electrical signal waveform; calculating the line mode fault additional power expression of the set fault point in the AC transmission line according to the three-phase voltage waveform and the arrival time corresponding to the fault phase at the measuring point; obtaining the first analytical waveform of the time domain solution corresponding to the first transient voltage equation at the measuring point; performing cosine similarity comparison between the first analytical waveform and the actual measured waveform at the measuring point to obtain the actual fault distance between the actual fault point and the measuring point; determining the actual line mode additional power 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 measuring point and the actual measured waveform at the measuring point. The method disclosed by the present invention realizes accurate estimation of the value of the transition resistance after a line short circuit fault.

[0012] It should be understood that the contents described in this section are not intended to identify the key or important features of the embodiments of the present invention, nor are they intended to limit the scope of the present invention. Other features of the present invention will become easily understood through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0014] Figure 1 It is a flow chart of a method for measuring transition resistance of an AC transmission line provided by an embodiment of the present invention;

[0015] Figure 2 It is a flow chart of another method for measuring transition resistance of an AC power transmission line provided by 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 diagram of signal extraction after wavelet transform of CEC signal;

[0018] Figure 5 is for Figure 4 Waveform diagram of wavelet modulus maximum analysis of detail signal in;

[0019] Figure 6 It is a flow chart of another method for measuring transition resistance of an AC power transmission line provided by an embodiment of the present invention;

[0020] Figure 7 It is a schematic diagram of a double-terminal overhead transmission line model;

[0021] Figure 8 It is a flow chart of another method for measuring transition resistance of an AC power transmission line provided by an embodiment of the present invention;

[0022] Fig. 9 It is the transient equivalent circuit diagram at the set fault point;

[0023] Fig.10 It is a flow chart of another method for measuring transition resistance of an AC power transmission line provided by an embodiment of the present invention;

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

[0025] Fig.12 It is a flow chart of another method for measuring transition resistance of an AC power transmission line provided by an embodiment of the present invention;

[0026] Fig.13 It is a flow chart of another method for measuring transition resistance of an AC power transmission line provided by an embodiment of the present invention;

[0027] Fig.14 It is a flow chart of another method for measuring transition resistance of an AC power transmission line provided by an embodiment of the present invention;

[0028] Fig.15 It is a flow chart of another method for measuring transition resistance of an AC power transmission line provided by an embodiment of the present invention;

[0029] Fig.16 It is a flow chart of another method for measuring transition resistance of an AC transmission line provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0030] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work 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 and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices. It should be understood that various forms of processes shown above can be used to reorder, add or delete steps. For example, the steps recorded in the present invention can be executed in parallel, can be executed sequentially, or can be executed in different orders, as long as the desired results of the technical solution of the present invention can be achieved, and this document is not limited here.

[0032] Figure 1 is a flow chart of a method for measuring transition resistance of an AC transmission line provided by an embodiment of the present invention, such as Figure 1 As shown, the method includes:

[0033] S101, obtaining a three-phase electrical signal waveform at the head end of an AC transmission line, and determining a fault phase and an arrival time of a first fault wave at a measurement point according to the three-phase electrical signal waveform.

[0034] The three-phase electrical signal waveform includes a three-phase voltage waveform and / or a three-phase current waveform, and the measurement point is the head end 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 when a fault occurs.

[0036] By analyzing the sudden changes in the three-phase voltage and current waveforms, it is possible to determine which phase or phases have a fault. Optionally, the sudden changes in the three-phase voltage and current waveforms may be a sudden drop in amplitude or a sudden change in phase, which is not limited here.

[0037] Using the traveling wave transmission theory, the first traveling wave generated by the fault can be identified and the exact time when it reaches the measurement point can be determined. The first traveling wave of the fault includes the fault information on the transmission line.

[0038] Optionally, the collected voltage waveform of the fault phase is processed using wavelet transform, and the arrival time of the first fault wave is extracted using the wavelet maximum.

[0039] S102, according to the three-phase voltage waveform corresponding to the fault phase at the measuring 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 line mode fault additional power supply expression.

[0040] The fault point is set at one point in the AC transmission circuit; the line mode fault additional power expression includes a fault distance variable between the set fault point and the measurement point;

[0041] In step S102, after determining the arrival time of the fault phase and the first wave, it is necessary to further analyze the voltage waveform of the fault phase at the measuring point. In step S102, a set fault point is set for analysis to determine the instantaneous value expression of the line mode transient voltage at the set fault point. The instantaneous value expression of the line mode transient voltage includes the fault distance variable between the fault point and the measuring point to achieve accurate positioning 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 set fault point, which can be regarded as a transient fault additional power supply.

[0042] Optionally, the voltage vector of the set fault point at a distance d from the measuring point can be expressed according to the uniform transmission equation; and converted into an expression in the time domain, and then the arrival time of the first fault wave is determined as the assumed fault occurrence time to obtain the fault point voltage mutation amount of the set fault point at the time of the fault occurrence. When the mode domain boundary conditions related to the fault situation are obtained, the instantaneous value expression of the transient voltage of the set fault point 1 mode is obtained, and the instantaneous value expression of the transient voltage of the set fault point 1 mode is the line mode fault additional power supply expression.

[0043] S103, obtaining, according to the additional power supply expression of the line mode fault, a first analytical waveform of a time domain solution corresponding to a first transient voltage equation at a measuring point after the first fault wave in the frequency domain propagates to a set fault point.

[0044] Among them, the additional power supply expression of line mode fault and the frequency domain transmission characteristics of the transmission line are used to calculate the voltage response of the first fault wave after it propagates from the set fault point to the measurement point in the frequency domain. Then, the frequency domain solution is converted into a time domain solution to obtain the time domain waveform corresponding to the first transient voltage equation of the measurement point, that is, the first analytical waveform.

[0045] Optionally, when the value of the faulty additional power source remains unchanged, the frequency domain expression of the faulty additional power source under the 1st mode can be obtained. Then, the frequency domain expression of the traveling wave equivalent voltage source at the end of the line is constructed using the inertia link transfer function and the frequency domain expression of the faulty additional power source under the 1st mode. Finally, the frequency domain expression of the 1st mode voltage of the measurement point is obtained. The Laplace inverse transform is performed to obtain the time domain solution of the transient voltage waveform at the measurement point, that is, the first analytical waveform is obtained.

[0046] S104, performing cosine similarity comparison between the first analytical waveform and the actual measured waveform of the measuring point to obtain an actual fault distance between the actual fault point and the measuring point.

[0047] Among them, the first analytical waveform obtained in steps S101-S103 is obtained under the assumption of the fault occurrence time and fault occurrence point. And the first analytical waveform is greatly affected by the phase voltage vector corresponding to the set fault point. Therefore, in step S104, the first analytical waveform is compared with the actual measured waveform of the measuring point by cosine similarity to determine the similarity of the two waveforms in the vector. By adjusting the parameters in the expression of the additional power supply for line mode fault. To compare the cosine similarity of the first analytical waveform with the actual measured waveform, the first analytical waveform with the highest similarity to the actual measured waveform can obtain the actual fault distance between the actual fault point and the measuring point.

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

[0049] The actual line-mode additional power corresponding to the actual fault occurrence time is determined according to the actual fault distance and the line-mode fault power expression, and 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 according to the arrival time of the first traveling wave, the distance between the actual fault point and the measurement point, and the wave speed of the fault traveling wave.

[0050] Optionally, the line-mode additional power supply corresponding to the actual fault occurrence time is further analyzed according to the obtained parameters. This actual line-mode additional power supply reflects the actual voltage change at the fault point. By using the transmission characteristics of the actual line-mode additional power supply and the transmission line, the voltage waveform that the measurement point should receive after the first fault wave propagates to the actual fault point is calculated, that is, the second analytical waveform.

[0051] The second analytical waveform is compared with the actual measured waveform by the mean absolute difference. The existence of transition resistance will affect the propagation characteristics of the fault traveling wave and the voltage waveform at the measurement point. Therefore, by analyzing these effects, the accurate measurement of transition resistance can be achieved. By comparing the assignments of the two, the second analytical waveform with the highest similarity to the mean absolute difference of the actual measured waveform is obtained, and the corresponding transition resistance is the actual transition resistance.

[0052] In the transition resistance measurement method of the AC transmission line provided by the embodiment of the present invention, the three-phase electrical signal waveform at the head end of the AC transmission line is first obtained. The fault phase and the precise time when the first fault wave reaches the measurement point are determined according to the waveform. Based on the fault phase voltage waveform and the arrival time, the instantaneous value of the line mode transient voltage at the set fault point is calculated as the line mode fault additional power supply. The line mode fault additional power supply is used to calculate the time domain solution of the first transient voltage equation at the measurement point after the first fault wave propagates to the set fault point, that is, the first analytical waveform. The first analytical waveform is compared with the actual measured waveform by cosine similarity to determine the distance between the actual fault point and the measurement point. Based on the actual fault point position and the time of fault occurrence, the actual line mode additional power supply is determined. According to the actual line mode additional power supply, the second transient voltage waveform at the measurement point after the first fault wave propagates to the actual fault point, that is, the second analytical waveform, is calculated. By comparing the difference between the second analytical waveform and the actual measured waveform, the magnitude of the transition resistance is obtained. By comparing the similarity between the first analytical waveform and the actual measured waveform, the embodiment of the present invention can more accurately determine the position of the actual fault point. This method is more accurate than the traditional fault location method, helps to quickly find the fault point and reduce the troubleshooting time. By comparing the amplitude difference between the second analytical waveform and the actual measured waveform, the magnitude of the transition resistance is obtained, thereby improving the accuracy of the transition resistance solution. In the transition resistance measurement method of the AC transmission line provided by the present invention, the setting of the measurement point can be selected at the head end of the AC transmission line, so that when the transition resistance is measured, the method of the present invention can be implemented in a geographical location such as a power plant or a substation, so the method provided by the present invention has a strong operational convenience.

[0053] Figure 2 FIG. 1 is a flow chart of another method for measuring transition resistance of an AC transmission line provided by an embodiment of the present invention. Figure 2 As shown, based on the above embodiment, the method further includes:

[0054] S201, determining the fault phase according to the sudden change in the difference of each phase electrical signal in the three-phase electrical signal waveform.

[0055] Under normal conditions of AC transmission lines, the value of the electrical signal difference of each phase should be relatively small and stable. However, when a short circuit occurs in the line, the current of the faulty phase will increase sharply, causing the current difference associated with the faulty phase to change significantly. Therefore, it is necessary to detect whether these current differences have undergone significant mutations. Specifically, when comparing the three-phase electrical signals of the line, the phase with a larger mutation in the electrical signal difference with other phases is the faulty phase.

[0056] S202, performing wavelet decomposition on the voltage signal or current signal of the fault phase, and extracting the arrival time of the first fault wave by using the wavelet modulus maximum.

[0057] In order to obtain the arrival time of the first fault wave in the fault phase, the electrical signal of the fault phase can be transformed by wavelet transform, and the arrival time of the first fault wave can be extracted by using the maximum value of the wavelet modulus.

[0058] Optionally, the electrical signal of the fault phase is convolved, and the electrical signal is convolved with a low-pass filter and a high-pass filter respectively to extract the low-frequency and high-frequency components in the signal. The convolution result is then sampled to obtain the wavelet coefficients of the approximate part and the detail part of the electrical signal. The electrical signal is repeatedly convolved and sampled until the required 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 diagram of signal extraction after wavelet transform of CEC signal; Figure 5 is for Figure 4 Waveform diagram of wavelet modulus maximum analysis of detail signal in the image.

[0060] Specific to Figure 3 The current signal is transformed by wavelet transform to obtain Figure 4 The first detail signal d1, the second detail signal d2, the third detail signal d3 and the approximation signal a3 are shown. Figure 4 For example, any one of the multiple detail signals in the wavelet modulus maximum is analyzed. Figure 5 As shown, Figure 3 The detail signal d1 in the wavelet modulus maximum is analyzed to find the signal mutation point and obtain information such as the arrival time of the first wave. Figure 5 In the figure, the signal mutation point is mutation point A, which also gives the arrival time of the first wave.

[0061] S203, according to the three-phase voltage waveform corresponding to the fault phase at the measuring 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 line mode fault additional power supply expression.

[0062] S204, obtaining, according to the additional power supply expression of the line mode fault, a first analytical waveform of a time domain solution corresponding to a first transient voltage equation at a measuring point after the first fault wave in the frequency domain propagates to a set fault point;

[0063] S205 , performing cosine similarity comparison between the first analytical waveform and the actual measured waveform of the measuring point to obtain an actual fault distance between the actual fault point and the measuring point.

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

[0065] Figure 6 FIG. 1 is a flow chart of another method for measuring transition resistance of an AC transmission line provided by an embodiment of the present invention. Figure 6 As shown, based on the above embodiment, the method further includes:

[0066] S401, obtaining a three-phase electrical signal waveform at the head end of an AC transmission line, and determining a fault phase and an arrival time of a first fault wave at a measurement point according to the three-phase electrical signal waveform.

[0067] S402, determining a phase voltage vector expression corresponding to a set fault point according to a uniform transmission line equation.

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

[0069]

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

[0071] Assume that the voltage at the first end is known and current That is, l = 0, formula (1) can be transformed into expression (2):

[0072]

[0073] Therefore, we can obtain the expressions (3) and (4) of A1 and A2:

[0074]

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

[0076]

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

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

[0079] Then, combined with the above, the voltage vector at the set fault point F with a distance d from the measurement point M is obtained as expression (6):

[0080]

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

[0082] S403, converting the phase voltage vector expression into a time domain equation, and determining the arrival time of the first fault wave as the assumed fault occurrence time, and determining the voltage mutation amount of the set fault point according to the time domain equation and the assumed fault occurrence time.

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

[0084]

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

[0086] S404, obtaining an additional power supply expression for a line mode fault according to the voltage mutation amount.

[0087] Exemplarily, after obtaining expression (7), the mode domain 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 mode transient voltage at the set fault point 1 is obtained according to the mode domain boundary conditions and expression (7).

[0088] S405, obtaining, according to the additional power supply expression of the line mode fault, a first analytical waveform of a time domain solution corresponding to a first transient voltage equation at a measuring point after the first fault wave in the frequency domain propagates to a set fault point.

[0089] S406: Perform a cosine similarity comparison between the first analytical waveform and the actual measured waveform of the measuring point to obtain an actual fault distance between the actual fault point and the measuring point.

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

[0091] Figure 8 FIG. 1 is a flow chart of another method for measuring transition resistance of an AC transmission line provided by an embodiment of the present invention. Figure 8 As shown, based on the above embodiment, the method includes:

[0092] S501, obtaining a three-phase electrical signal waveform at the head end of an AC transmission line, and determining a fault phase and an arrival time of a first fault wave at a measurement point according to the three-phase electrical signal waveform.

[0093] S502, determining a phase voltage vector expression corresponding to a set fault point according to a uniform transmission line equation.

[0094] S503, converting the phase voltage vector expression into a time domain equation, and determining the arrival time of the first fault wave as the assumed fault occurrence time, and determining the voltage mutation amount of the set fault point according to the time domain equation and the assumed fault occurrence time.

[0095] S504, obtaining a mode domain boundary condition according to the phase domain boundary conditions of the faulty phase and the non-faulty phase and the Clarke inverse transformation matrix.

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

[0097] In combination with the above, after obtaining expression (7), expression (7) is the voltage mutation amount of the set fault point.

[0098] When obtaining the phase domain boundary conditions of the fault phase and the non-fault phase:

[0099] Assuming that a short circuit occurs in phase A of the line, the boundary conditions of the fault phase and the non-fault phase domain are as follows:

[0100]

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

[0102] The Clarke inverse transformation matrix is ​​used to transform the expression (8) into a phase mode, where the Clarke inverse transformation matrix is ​​the expression (9). The expression (9) is transformed into a phase mode to obtain the expression (10). After simplifying the expression (10), the boundary conditions of the fault phase and non-fault phase domain are obtained as the expression (11):

[0103]

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

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

[0106] Fig. 9 is the transient equivalent circuit diagram at the set fault point, such as Fig. 9 As shown in the above expression (11), the transient equivalent circuit diagram at the set fault point can be obtained. C1 and Z C0 They are the wave impedances of mode 1 and mode 0 respectively.

[0107] According to the above and Fig. 9 The instantaneous value expressions of the 1-mode and 0-mode transient voltages at the set fault point can be obtained (12):

[0108]

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

[0110] S506, obtaining, according to the additional power supply expression of the line mode fault, a first analytical waveform of a time domain solution corresponding to a first transient voltage equation at a measuring point after the first fault wave in the frequency domain propagates to a set fault point.

[0111] S507: Perform a cosine similarity comparison between the first analytical waveform and the actual measured waveform of the measuring point to obtain an actual fault distance between the actual fault point and the measuring point.

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

[0113] Fig.10 FIG. 1 is a flow chart of another method for measuring transition resistance of an AC transmission line provided by an embodiment of the present invention. Fig.10 As shown, based on the above embodiment, the method includes:

[0114] S601, obtaining a three-phase electrical signal waveform at the head end of an AC transmission line, and determining a fault phase and an arrival time of a first fault wave at a measurement point according to the three-phase electrical signal waveform.

[0115] S602, determining a phase voltage vector expression corresponding to a set fault point according to a uniform transmission line equation.

[0116] S603, converting the phase voltage vector expression into a time domain equation, and determining the arrival time of the first fault wave as the assumed fault occurrence time, and determining the voltage mutation amount of the set fault point according to the time domain equation and the assumed fault occurrence time.

[0117] S604, obtaining a mode domain boundary condition according to the phase domain boundary conditions of the faulty phase and the non-faulty phase and the Clarke inverse transformation matrix.

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

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

[0120] Since the amplitude of the additional power supply for 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 for mode 1 fault, U f0 (s) is the frequency domain expression of the additional power supply expression for 0-mode fault.

[0123] S607, obtaining a frequency domain expression of a traveling wave equivalent voltage source of a line end fault according to a frequency domain expression of an additional power source of a line mode fault.

[0124] Among them, the fault traveling wave includes the first fault 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 line mode fault additional power supply; the first transfer function is a line frequency-variable transfer function constructed by approximating the inertia link, 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 delay caused by the propagation of the fault traveling wave along the line from the measurement point to the fault point.

[0125] Exemplarily, the frequency domain expression of the 1-mode fault additional power supply expression in expression (13) is used to obtain the frequency domain expression of the line end fault traveling wave equivalent voltage source.

[0126] Fig.11 It is a transmission line transient circuit equivalent circuit diagram, such as Fig.11 As shown in Figure 2, when the fault traveling wave has propagated to the measurement point and then refracted and reflected, but has not propagated to the fault point, the transient equivalent circuit diagram of the transmission line is as follows: Fig.11 As shown, where the first voltage source B Mf1 is the traveling wave equivalent voltage source at the measuring point M, the first inductor L Meq is the transformer equivalent inductance at the measuring point M, the first impedance Z MS is the internal impedance of the power supply at the measuring point M, and the second impedance Z c1 is the 1-mode wave impedance. The equivalent voltage source of the traveling wave at the end of the line is in the frequency domain B Mf1 The expression of (s) is expression (14):

[0127]

[0128] in, is the frequency-variable transfer function of the line constructed by using the approximate equivalent of the inertia link, d is the distance between the fault point and point M; K a1 Represents the line attenuation coefficient, which is related to the line length; T 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; is the delay caused by the traveling wave propagating along the line distance d.

[0129] S608, obtaining a frequency domain expression of the mode voltage at the measurement point 1 according to the frequency domain expression of the traveling wave equivalent voltage source at the end of the line fault.

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

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

[0132]

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

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

[0135] S609, performing an inverse Laplace transform according to the first transient voltage equation at the measuring point, and obtaining a time domain solution of the first transient voltage equation at the measuring point as a first analytical waveform.

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

[0137] S610: Perform a cosine similarity comparison between the first analytical waveform and the actual measured waveform of the measuring point to obtain an actual fault distance between the actual fault point and the measuring point.

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

[0139] Fig.12 FIG. 1 is a flow chart of another method for measuring transition resistance of an AC transmission line provided by an embodiment of the present invention. Fig.12 As shown, based on the above embodiment, the method includes:

[0140] S701, obtaining a three-phase electrical signal waveform at the head end of an AC transmission line, and determining a fault phase and an arrival time of a first fault wave at a measurement point according to the three-phase electrical signal waveform.

[0141] S702, according to the three-phase voltage waveform corresponding to the fault phase at the measuring 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 line mode fault additional power supply expression.

[0142] S703, obtaining, according to the additional power supply expression of the line mode fault, a first analytical waveform of a time domain solution corresponding to a first transient voltage equation at a measuring point after the first fault wave in the frequency domain propagates to a set fault point.

[0143] S704: Perform cosine similarity comparison between the first analytical waveform and the actual measured waveform.

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

[0145]

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

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

[0148] Optionally, a step-by-step search method combined with cosine similarity is 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 full length of the transmission line. Select a larger step size (for example, a few hundred meters or a few kilometers) to quickly cover the entire search range in the initial stage. Set a similarity threshold or position accuracy requirement to decide when to stop searching. Optionally, set a maximum number of iterations to prevent infinite loops. 2. Coarse search stage: Within the entire line, calculate the cosine similarity between the fault recording and the analytical waveform corresponding to each location point di at intervals of the initial step size. Find the location point d with the largest cosine similarity. max . max 3. Fine search phase: In the narrowed search range, select a smaller step size for search. Under the new step size, calculate the cosine similarity of each position point and find the new maximum similarity point d max′. If d max ' and the previous maximum similarity point d max If the difference between them is greater than the accuracy threshold, or the iteration limit is not reached, continue with d max ′ as the center to narrow the search range and repeat the above process. 4. Stop condition: When the difference between the maximum similarity points of two consecutive iterations is less than the preset accuracy threshold, stop the search. Or, if the preset maximum number of iterations is reached, stop the search even if the accuracy requirement is not met. 5. Determine the final position: The maximum similarity point d obtained in the last iteration is max The distance between ′ and the fault point is the actual fault occurrence distance.

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

[0150] Cosine similarity comparison measures the degree of similarity between two vectors in direction, regardless of their magnitude (i.e., the modulus of the vector). Cosine similarity comparison is less affected by amplitude, and 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, from which the exact time of the fault can be calculated.

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

[0152] Fig.13 FIG. 1 is a flow chart of another method for measuring transition resistance of an AC transmission line provided by an embodiment of the present invention. Fig.13 As shown, based on the above embodiment, the method includes:

[0153] S801, obtaining a three-phase electrical signal waveform at the head end of an AC transmission line, and determining a fault phase and an arrival time of a first fault wave at a measurement point according to the three-phase electrical signal waveform.

[0154] S802, determining a phase voltage vector expression corresponding to a set fault point according to a uniform transmission line equation.

[0155] S803, converting the phase voltage vector expression into a time domain equation, and determining the arrival time of the first fault wave as the assumed fault occurrence time, and determining the voltage mutation amount of the set fault point according to the time domain equation and the assumed fault occurrence time.

[0156] S804, obtaining an additional power supply expression for a line mode fault according to the voltage mutation amount.

[0157] S805, obtaining, according to the additional power supply expression of the line mode fault, a first analytical waveform of a time domain solution corresponding to a first transient voltage equation at a measuring point after the first fault wave in the frequency domain propagates to a set fault point.

[0158] S806: Perform a cosine similarity comparison between the first analytical waveform and the actual measured waveform of the measuring point to obtain an actual fault distance between the actual fault point and the measuring point.

[0159] S807, determining the actual fault occurrence time according to the actual fault distance, arrival time and the propagation speed of the first fault wave.

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

[0161]

[0162] Wherein, d0 is the actual fault distance; t1 is the arrival time of the first fault wave; v1 is the wave velocity of the first fault wave.

[0163] S808, correcting the assumed fault occurrence time according to the actual fault occurrence time, and determining the actual line mode fault additional power according to the actual fault distance and the line mode fault additional power expression.

[0164] Combined with the above, the assumed fault occurrence time is corrected according to the actual fault occurrence time. Optionally, the voltage mutation amount of the fault point at the actual fault occurrence time is calculated, and the actual line mode fault additional power supply is calculated to obtain the actual 1 mode fault additional power supply U f11 .

[0165] Optionally, the calculated distance between the actual fault occurrence point and the measurement point and the actual fault occurrence time may be substituted into the expression calculated in the above steps to obtain the actual 1-mode fault additional power supply.

[0166] S809, obtaining a second 1-mode voltage frequency domain expression of the measurement point after the first fault wave propagates to the actual fault point in the frequency domain according to the actual line-mode fault additional power supply, the second 1-mode voltage frequency domain expression being a second transient voltage equation corresponding to the measurement point; and determining a second analytical waveform of the time domain solution of the second transient voltage equation.

[0167] For the actual 1-mode fault additional power supply U obtained in the above steps f11 The frequency domain conversion 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) is the second transient voltage equation corresponding to the measurement point, and the corresponding time domain solution is obtained. The second analytical waveform is obtained accordingly. The fault distance and fault occurrence time in the second analytical waveform are actual values ​​rather than the assumed values ​​in the first analytical waveform.

[0168] S810, performing a mean absolute difference comparison between the second analytical waveform and the actually measured waveform to obtain a transition resistance.

[0169] After obtaining the second analytical waveform, the transition resistance needs to be calculated. Perform mean absolute difference similarity comparison between the second analytical waveform and the actual measured waveform. Perform mean absolute difference similarity comparison between the second analytical waveform and the actual measured waveform. Mean absolute difference is a method of measuring the difference between two signals. It calculates the average of the absolute values ​​of the difference between corresponding points. Unlike cosine similarity, mean absolute difference focuses more on the difference in signal amplitude rather than direction or shape.

[0170] In this comparison process, the point with the smallest difference between the second analytical waveform and the actual measured waveform is found, that is, the second analytical waveform with the highest waveform similarity. This point corresponds to a specific transition resistance value, because the change of transition resistance will significantly affect the waveform characteristics of the fault current. The corresponding transition resistance value is the required transition resistance.

[0171] Fig.14 FIG. 1 is a flow chart of another method for measuring transition resistance of an AC transmission line provided by an embodiment of the present invention. Fig.14 As shown, based on the above embodiment, the method includes:

[0172] S901, obtaining a three-phase electrical signal waveform at the head end of an AC transmission line, and determining a fault phase and an arrival time of a first fault wave at a measurement point according to the three-phase electrical signal waveform.

[0173] S902, determining a phase voltage vector expression corresponding to a set fault point according to a uniform transmission line equation.

[0174] S903, converting the phase voltage vector expression into a time domain equation, and determining the arrival time of the first fault wave as the assumed fault occurrence time, and determining the voltage mutation amount of the set fault point according to the time domain equation and the assumed fault occurrence time.

[0175] S904, obtaining an additional power supply expression for a line mode fault according to the voltage mutation amount.

[0176] S905, obtaining, according to the additional power supply expression of the line mode fault, a first analytical waveform of a time domain solution corresponding to a first transient voltage equation at a measuring point after the first fault wave in the frequency domain propagates to a set fault point.

[0177] S906: Perform a cosine similarity comparison between the first analytical waveform and the actual measured waveform of the measurement point to obtain an actual fault distance between the actual fault point and the measurement point.

[0178] S907, determining the actual fault occurrence time according to the actual fault distance, arrival time and the propagation speed of the first fault wave.

[0179] S908, substituting the actual fault occurrence time and the actual fault distance into the expression of the line mode fault additional power supply to determine the actual line mode fault additional power supply.

[0180] In combination with the above, after obtaining the actual fault occurrence time and the actual fault distance, they are substituted into the expression of the line mode fault additional power supply to determine the actual line mode fault additional power supply.

[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 with a distance d0 from the measurement point M: The expression (17) is:

[0182]

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

[0184] Similar to expression (7), expression (17) is transformed into the time domain equation U f (d0, t), and substitute the actual fault occurrence time t0 into it, then the actual fault point voltage mutation amount U f0 The expression (18) can be expressed as

[0185]

[0186] Among them, t0 is the actual fault occurrence time, and d0 is the distance between the actual fault occurrence point and the measurement point.

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

[0188]

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

[0190] S909, obtaining a second 1-mode voltage frequency domain expression of the measurement point after the first fault wave propagates to the actual fault point in the frequency domain according to the actual line-mode fault additional power supply, the second 1-mode voltage frequency domain expression being a second transient voltage equation corresponding to the measurement point; and determining a second analytical waveform of the time domain solution of the second transient voltage equation.

[0191] S910, performing a mean absolute difference comparison between the second analytical waveform and the actually measured waveform to obtain a transition resistance.

[0192] Fig.15 FIG. 1 is a flow chart of another method for measuring transition resistance of an AC transmission line provided by an embodiment of the present invention. Fig.15 As shown, based on the above embodiment, the method includes:

[0193] S1001, obtaining a three-phase electrical signal waveform at the head end of an AC transmission line, and determining a fault phase and an arrival time of a first fault wave at a measurement point according to the three-phase electrical signal waveform.

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

[0195] S1003, converting the phase voltage vector expression into a time domain equation, and determining the arrival time of the first fault wave as the assumed fault occurrence time, and determining the voltage mutation amount of the set fault point according to the time domain equation and the assumed fault occurrence time.

[0196] S1004, obtaining an additional power supply expression for a line mode fault according to the voltage mutation amount.

[0197] S1005, obtaining, according to the additional power supply expression of the line mode fault, a first analytical waveform of a time domain solution corresponding to a first transient voltage equation at a measuring point after the first fault wave in the frequency domain propagates to a set fault point.

[0198] S1006: Perform a cosine similarity comparison between the first analytical waveform and the actual measured waveform of the measuring point to obtain an actual fault distance between the actual fault point and the measuring point.

[0199] S1007, determining the actual fault occurrence time according to the actual fault distance, arrival time and the propagation speed of the first fault wave.

[0200] S1008, correcting the assumed fault occurrence time according to the actual fault occurrence time, and determining the actual line mode fault additional power according to the actual fault distance and the line mode fault additional power expression.

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

[0202] In the actual line mode fault additional power expression, the expression of the 1-mode fault additional power is converted 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 mode 1 fault.

[0205] S1010, obtaining a frequency domain expression of a traveling wave equivalent voltage source of a second line end fault according to a frequency domain expression of an additional power supply of an actual line mode 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 a line frequency-variable transfer function constructed by approximating the inertia link, 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 propagation of the fault traveling wave along the line from the measurement point to the fault point.

[0207] Fault traveling wave equivalent voltage source frequency domain at the end of the second line B Mf10 (s) is expressed as expression (21):

[0208]

[0209] in, is the frequency-variable transfer function of the line constructed by using the approximate equivalent of the inertia link, d is the distance between the fault point and point M; K a1 Represents the line attenuation coefficient, which is related to the line length; T 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; is the delay caused by the traveling wave propagating along the line distance d.

[0210] S1011, obtaining a frequency domain expression of a second 1-mode voltage at a measuring point according to a frequency domain expression of a traveling wave equivalent voltage source at the end of the second line.

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

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

[0213]

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

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

[0216] S1012, performing an inverse Laplace transform on the second transient voltage equation at the measuring point to obtain a time domain solution of the second transient voltage equation at the measuring point as a second analytical waveform.

[0217] Perform inverse Laplace transform on the second transient voltage equation to obtain the time domain solution U of the first transient voltage equation at the measuring point M. Mf10 (t), and the obtained time domain solution is used as the second analytical waveform.

[0218] S1013, performing a mean absolute difference comparison between the second analytical waveform and the actually measured waveform to obtain a transition resistance.

[0219] Fig.16 FIG. 1 is a flow chart of another method for measuring transition resistance of an AC transmission line provided by an embodiment of the present invention. Fig.16 As shown, based on the above embodiment, the method includes:

[0220] S1101, obtaining a three-phase electrical signal waveform at the head end of an AC transmission line, and determining a fault phase and an arrival time of a first fault wave at a measurement point according to the three-phase electrical signal waveform.

[0221] S1102, determining a phase voltage vector expression corresponding to a set fault point according to a uniform transmission line equation.

[0222] S1103, converting the phase voltage vector expression into a time domain equation, and determining the arrival time of the first fault wave as the assumed fault occurrence time, and determining the voltage mutation amount of the set fault point according to the time domain equation and the assumed fault occurrence time.

[0223] S1104, obtaining an additional power supply expression for a line mode fault according to the voltage mutation amount.

[0224] S1105, obtaining, according to the additional power supply expression of the line mode fault, a first analytical waveform of a time domain solution corresponding to a first transient voltage equation at a measuring point after the first fault wave in the frequency domain propagates to a set fault point.

[0225] S1106, performing cosine similarity comparison between the first analytical waveform and the actual measured waveform of the measuring point to obtain an actual fault distance between the actual fault point and the measuring point.

[0226] S1107, determining the actual fault occurrence time according to the actual fault distance, arrival time and the propagation speed of the first fault wave.

[0227] S1108, correcting the assumed fault occurrence time according to the actual fault occurrence time, and determining the actual line mode fault additional power according to the actual fault distance and the line mode fault additional power expression.

[0228] S1109, obtaining a second 1-mode voltage frequency domain expression of the measurement point after the first fault wave propagates to the actual fault point in the frequency domain according to the actual line-mode fault additional power supply, the second 1-mode voltage frequency domain expression being a second transient voltage equation corresponding to the measurement point; and determining a second analytical waveform of the time domain solution of the second transient voltage equation.

[0229] S1110, performing mean absolute difference waveform similarity comparison between the second analytical waveform and the actual measured waveform fault recording, and determining the transition resistance according to the highest point of waveform similarity between the second analytical waveform and the actual measured waveform fault recording.

[0230] Specifically, the second analytical waveform and the actual measured waveform fault recording are compared in terms of mean absolute difference waveform similarity, wherein the expression for the mean absolute difference waveform similarity comparison is expression (23):

[0231]

[0232] Among them, u si (t i ) and the fault recording wave 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 in the taken time window.

[0233] Optionally, a step-by-step search method is used, first using a larger step size to find the Ri value with the smallest mean absolute difference, and then using a smaller step size to perform a more accurate search in the adjacent interval of Ri, and so on, to improve the measurement accuracy. The transition resistance corresponding to the point with the highest waveform similarity between the second analytical waveform and the actual measured waveform fault recording is the required transition resistance.

[0234] In combination with any of the above embodiments, a simulation test is performed on a transmission line model, and specific transmission line model parameters are shown in Table 1 below:

[0235]

[0236] Table 1

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

[0238] The transition resistance value obtained by using the transition resistance measurement method for an AC power transmission line provided by the above embodiment is compared with the set transition resistance value as shown in Table 2 below.

[0239]

[0240]

[0241] Table 2

[0242] It can be seen from Table 2 that when the transition resistance measurement method for an AC transmission line provided by any of the above embodiments of the present invention is used to measure the transition resistance of a transmission line, when calculating the transition resistance for transmission lines with different fault distances and different actual transition resistances, the error of the obtained transition resistance value relative to the actual transition resistance value is small; when the method provided by any of the above embodiments is used to measure the fault distance, the error is extremely small. Compared with the prior art, the transition resistance measurement method for an AC transmission line provided by any of the above embodiments of the present invention is extremely accurate in fault location method, helps to quickly find the fault point, and reduces the troubleshooting time; and realizes the accurate solution of the transition resistance.

[0243] The above specific implementations do not constitute a limitation on the protection scope of the present invention. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modification, equivalent substitution and improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for measuring transition resistance of an AC transmission line, characterized in that: include: Acquire a three-phase electrical signal waveform at the head end of the AC transmission line, wherein the three-phase electrical signal waveform includes a three-phase voltage waveform and / or a three-phase current waveform, and determine the arrival time of the fault phase and the first fault wave at a measuring point according to the three-phase electrical signal waveform, wherein the measuring point is the head end of the AC transmission line; According to the three-phase voltage waveform corresponding to the fault phase at the measuring 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 line mode fault additional power supply expression; wherein the set fault point is one point in the AC transmission circuit; the line mode fault additional power supply expression includes a fault distance variable between the set fault point and the measuring point; According to the line mode fault additional power supply expression, a first analytical waveform of a time domain solution corresponding to the first transient voltage equation at the measurement point is obtained after the first fault wave in the frequency domain propagates to the set fault point; Performing a cosine similarity comparison between the first analytical waveform and the actual measured waveform of the measuring point to obtain an actual fault distance between the actual fault point and the measuring point; The actual line mode additional power supply corresponding to the actual fault occurrence time is determined according to the actual fault distance and the line mode fault power supply expression, and 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 measuring point after the first fault wave corresponding to the actual line mode additional power supply propagates to the actual fault point and the actual measured waveform of the measuring point.

2. The transition resistance measurement method according to claim 1, characterized in that: The method of obtaining a three-phase electrical signal waveform at the head end of the AC transmission line, wherein the three-phase electrical signal waveform includes a three-phase voltage waveform and / or a three-phase current waveform, and determining the arrival time of the fault phase and the first fault wave at a measurement point according to the three-phase electrical signal waveform, wherein the measurement point is the head end of the AC transmission line, comprises: Determine the fault phase according to the sudden change in the difference of each phase electrical signal in the three-phase electrical signal waveform; The voltage signal or current signal of the fault phase is subjected to wavelet decomposition, and the arrival time of the first fault wave is extracted using the wavelet modulus maximum.

3. The method for measuring transition resistance of an AC power transmission line according to claim 1, characterized in that: The method of calculating the instantaneous value expression of the line mode transient voltage at the set fault point in the AC power transmission line according to the three-phase voltage waveform corresponding to the fault phase at the measuring point and the arrival time, and using the instantaneous value expression of the line mode transient voltage as the line mode fault additional power supply expression, comprises: Determine the phase voltage vector expression corresponding to the set fault point according to the uniform transmission line equation; Convert the phase voltage vector expression into a time domain equation, determine the arrival time of the first fault wave as the assumed fault occurrence time, and determine the voltage mutation amount of the set fault point according to the time domain equation and the assumed fault occurrence time; The additional power expression of the line mode fault is obtained according to the voltage mutation amount.

4. The method for measuring transition resistance of an AC power transmission line according to claim 3, characterized in that: The step of obtaining an additional power supply expression for a line mode fault according to the voltage mutation amount includes: Obtaining the mode domain boundary conditions according to the phase domain boundary conditions of the fault phase and the non-fault phase and the Clarke inverse transformation matrix; the phase domain boundary conditions are related to the short-circuit current of each phase, the instantaneous value of the voltage in the fault phase, the transient voltage of the fault phase and the transition resistance of the fault phase; The instantaneous value expression of the transient voltage of mode 1 at the set fault point is obtained according to the boundary conditions of the mode domain; the instantaneous value expression of the transient voltage of mode 1 at the set fault point is determined as the additional power supply expression of the line mode fault.

5. The method for measuring transition resistance of an AC power transmission line according to claim 4, characterized in that: The first analytical waveform of the time domain solution corresponding to the first transient voltage equation at the measurement point after the first fault wave propagates to the set fault point in the frequency domain is obtained according to the line mode fault additional power supply expression, including: Converting the line mode fault additional power supply expression into a frequency domain expression to obtain a line mode fault additional power supply frequency domain expression; According to the frequency domain expression of the additional power supply for the line mode fault, an equivalent voltage source frequency domain expression of the fault traveling wave at the end of the line is obtained; wherein, the fault traveling wave includes the first fault 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 for the line mode fault; the first transfer function is a line frequency-variable transfer function constructed by approximating the inertia link, 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 the 1 mode, and the delay caused by the propagation of the fault traveling wave along the line from the measurement point to the fault point; The frequency domain expression of the mode voltage at the measuring point 1 is obtained according to the frequency domain expression of the traveling wave equivalent voltage source at the end of the line fault; wherein the frequency domain expression of the mode voltage at the measuring point 1 is related to the impedance of the line equivalent inductance in the complex frequency domain, the mode wave impedance of the line 1 and the internal resistance of the equivalent voltage source; the frequency domain expression of the mode voltage at the measuring point 1 is the first transient voltage equation of the measuring point; An inverse Laplace transform is performed on the first transient voltage equation at the measuring point to obtain a time domain solution of the first transient voltage equation at the measuring point as a first analytical waveform.

6. The method for measuring transition resistance of an AC power transmission line according to claim 1, characterized in that: The step of performing cosine similarity comparison between the first analytical waveform and the actual measured waveform of the measuring point to obtain an actual fault distance between the actual fault point and the measuring point includes: Performing cosine similarity comparison between the first analytical waveform and the actual measured waveform; The distance between the measurement point in the analytical waveform having the highest similarity to the actual measurement waveform and the fault point is the actual fault occurrence distance.

7. The method for measuring transition resistance of an AC power transmission line according to claim 3, characterized in that: The method of determining the actual line mode additional power supply corresponding to the actual fault occurrence time according to the actual fault distance and the line mode fault 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 measuring point after the first fault wave corresponding to the actual line mode additional power supply propagates to the actual fault point and the actual measured waveform of the measuring point, comprises: Determine the actual fault occurrence time according to the actual fault distance, the arrival time and the propagation speed of the first fault wave; Correcting the assumed fault occurrence time according to the actual fault occurrence time, and determining the actual line mode fault additional power according to the actual fault distance and the line mode fault additional power expression; According to the actual line mode fault additional power supply, a second 1-mode voltage frequency domain expression of the measurement point after the first fault wave propagates to the actual fault point in the frequency domain is obtained, wherein the second 1-mode voltage frequency domain expression is a second transient voltage equation corresponding to the measurement point; and determining a second analytical waveform of a time domain solution of the second transient voltage equation; The second analytical waveform and the actually measured waveform are compared by average absolute difference to obtain transition resistance.

8. The method for measuring transition resistance of an AC power transmission line according to claim 7, characterized in that: The step of correcting the assumed fault occurrence time according to the actual fault occurrence time, and determining the actual line mode fault additional power supply according to the actual fault distance and the line mode fault additional power supply expression, comprises: The actual fault occurrence time and the actual fault distance are substituted into the expression of the line mode fault additional power supply to determine the actual line mode fault additional power supply.

9. The method for measuring transition resistance of an AC power transmission line according to claim 7, characterized in that: The method of obtaining a second 1-mode voltage frequency domain expression of the measurement point after the first fault wave propagates to the actual fault point in the frequency domain according to the actual line mode fault additional power supply, and determining a second analytical waveform of a time domain solution of the second 1-mode voltage frequency domain expression, includes: Converting the actual line mode fault additional power supply expression into a frequency domain expression to obtain an actual line mode fault additional power supply frequency domain expression; Obtain a frequency domain expression of an equivalent voltage source of a traveling wave at the end of the second line according to the actual frequency domain expression of the additional power supply for the line mode fault; wherein the frequency domain expression of an equivalent voltage source of a traveling wave at the end of the second line fault is related to the first transfer function and the actual frequency domain expression of the additional power supply for the line mode fault; the first transfer function is a line frequency-variable transfer function constructed by approximating the inertia link, 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 the 1 mode, and the delay caused by the propagation of the fault traveling wave along the line from the measurement point to the fault point; Obtain the frequency domain expression of the second mode 1 voltage at the measuring point according to the frequency domain expression of the traveling wave equivalent voltage source at the end of the second line; wherein 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 line mode 1 wave impedance 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; An inverse Laplace transform is performed on the second transient voltage equation at the measuring point to obtain a time domain solution of the second transient voltage equation at the measuring point as a second analytical waveform.

10. The method for measuring transition resistance of an AC power transmission line according to claim 7, characterized in that: The step of comparing the mean absolute difference between the second analytical waveform and the actually measured waveform to obtain the transition resistance includes: The mean absolute difference waveform similarity comparison is performed based on the second analytical waveform and the actual measured waveform fault recording, and the transition resistance is determined based on the highest point of waveform similarity between the second analytical waveform and the actual measured waveform fault recording.

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