A Fault Location Method for Hybrid Multi-Terminal DC Transmission Lines

Abstract

The present invention discloses a method for locating a fault of a hybrid multi-terminal DC transmission line, comprising: respectively obtaining the time-frequency characteristics of the initial fault traveling wave head at each end of the line; respectively obtaining the arrival time of the fault traveling wave head at each end of the line, and determining the fault traveling wave head frequency corresponding to the arrival time of the fault traveling wave head at each end of the line according to the time-frequency characteristics of each end of the line; determining the fault traveling wave velocity at each end of the line according to the frequency-dependent characteristics of each end of the line and the fault traveling wave head frequency; determining the time of occurrence of the fault according to the fault traveling wave velocity at each end of the line and the arrival time of the fault traveling wave head; determining the fault interval identification parameters at each end of the line according to the fault traveling wave velocity at each end of the line and the time of occurrence of the fault; and determining the fault position based on the fault interval identification parameters at each end of the line. The present invention can realize the accurate positioning of the fault of the hybrid multi-terminal DC transmission line.

Description

Technical Field

[0001] The present invention belongs to the technical field of power electronics, and in particular, relates to a fault locating method for a power system, and more particularly, to a fault locating method for a hybrid multi-terminal direct current transmission line. Background Art

[0002] The existing high-voltage direct current transmission system LCC-HVDC (line commutated converter based HVDC) based on the line current commutation principle has a long transmission distance, large transmission capacity and high transmission efficiency. However, the LCC-HVDC inverter station is prone to commutation failure, which leads to transmission reliability problems. The flexible high-voltage direct current transmission system MMC-HVDC (modular multilevel converter based HVDC) based on the modular multi-level principle has no risk of commutation failure and can achieve certain power flow control. However, the MMC-HVDC system has a small transmission capacity and a high construction cost. Therefore, the LCC-MMC-HVDC hybrid direct current transmission system, which adopts the LCC-HVDC principle on the rectifier side and the MMC-HVDC principle on the inverter side, can have the advantages of both the traditional high-voltage direct current transmission system and the flexible direct current transmission system, and has therefore been widely used. In order to obtain higher transmission capacity, the inverter side often adopts a multi-terminal direct current (MTDC) topology, thereby forming an LCC-MMC-MTDC hybrid multi-terminal direct current transmission system.

[0003] At present, the fault location of hybrid multi-terminal DC transmission lines is mostly based on fault traveling waves, and the positioning accuracy of fault traveling waves is seriously dependent on the wave velocity value of the fault traveling waves. In the existing fault traveling wave positioning method of hybrid multi-terminal DC transmission lines, a fixed wave velocity value is usually used to determine the fault location. However, for actual transmission lines, the speed of the traveling wave is not a fixed value. Therefore, the existing method of using a fixed fault traveling wave velocity value to determine the fault location results in large fault location errors and low accuracy, which affects the inspection and recovery of the fault.

[0004] The Chinese patent application with publication number CN112526283A discloses a method for locating faults in high-voltage direct current transmission lines. The method determines the speed of the fault traveling wave based on the frequency-dependent characteristics of the traveling wave, and then determines the fault location based on the speed of the fault traveling wave and the arrival time of the fault traveling wave head, thereby achieving relatively accurate fault location. However, the high-voltage direct current transmission line targeted by the Chinese patent application has the same structure at both ends, and the method adopted is not suitable for direct application in the fault location of hybrid multi-terminal direct current transmission lines. Moreover, the Chinese patent application determines the fault location based on the arrival time of the fault traveling wave head, and cannot determine the time when the fault occurs, nor can it determine the fault location based on the time when the fault occurs. Therefore, the fault location is still not accurate enough. Summary of the invention

[0005] The object of the present invention is to provide a method for locating a fault of a hybrid multi-terminal DC transmission line. The method determines the speed of a fault traveling wave based on the frequency-dependent characteristics of the traveling wave, determines the time of occurrence of the fault based on the speed of the fault traveling wave, and finally locates the fault based on the speed of the fault traveling wave and the time of occurrence of the fault, with high positioning accuracy.

[0006] In order to achieve the above-mentioned purpose, the present invention adopts the following technical solutions:

[0007] A method for locating a fault of a hybrid multi-terminal direct current transmission line, the method comprising:

[0008] Obtain the time-frequency characteristics of the initial fault traveling wave head at each end of the line respectively;

[0009] The arrival time of the fault traveling wave head at each end of the line is obtained respectively, and the frequency of the fault traveling wave head corresponding to the arrival time of the fault traveling wave head at each end of the line is determined according to the time-frequency characteristics of each end of the line;

[0010] Determining the speed of the fault traveling wave at each end of the line according to the frequency-dependent characteristics of each end of the line and the head frequency of the fault traveling wave;

[0011] Determine the fault occurrence time based on the fault traveling wave velocity at each end of the line and the arrival time of the fault traveling wave head;

[0012] Determine the fault interval identification parameters at each end of the line according to the fault traveling wave velocity and fault occurrence time at each end of the line;

[0013] The fault location is determined based on the fault interval identification parameters at each end of the line.

[0014] Compared with the prior art, the advantages and positive effects of the present invention are as follows: the fault location method for a hybrid multi-terminal DC transmission line provided by the present invention makes full use of the frequency-dependent characteristics of the traveling wave velocity of the line, proposes to determine the fault traveling wave velocity according to the frequency-dependent characteristics, and then determine the fault occurrence time based on the fault traveling wave velocity and the arrival time of the fault traveling wave head, and determine the fault interval identification parameter according to the fault occurrence time and the fault traveling wave velocity, and finally determine the fault position based on the fault distinction identification parameter. The method can well adapt to the topological structure of the hybrid multi-terminal DC transmission system and improve the accuracy of fault location of the hybrid multi-terminal DC transmission system.

[0015] After reading the specific embodiments of the present invention in conjunction with the accompanying drawings, other features and advantages of the present invention will become more clear. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] 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 embodiments. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0017] Figure 1 It is a flow chart of an embodiment of a method for locating a fault of a hybrid multi-terminal DC transmission line according to the present invention;

[0018] Figure 2 is a schematic diagram of a typical hybrid multi-terminal direct current transmission system in an embodiment of the present invention;

[0019] Figure 3 is a schematic diagram of a typical hybrid multi-terminal DC transmission line structure in an embodiment of the present invention;

[0020] Figure 4 It is a simulation waveform diagram of the voltage traveling wave signal at three terminals of the line when a typical fault occurs in an embodiment of the present invention;

[0021] Figure 5 This is a diagram showing the transformation results of the voltage traveling wave signal S at the three terminals of the line when a typical fault occurs in an embodiment of the present invention. DETAILED DESCRIPTION

[0022] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0023] The technical solutions between the various embodiments of the present invention can be combined with each other, but it must be based on the fact that ordinary technicians in the field can implement it. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0024] Figure 1 Shown is a flow chart of an embodiment of a method for locating a fault in a hybrid multi-terminal DC transmission line according to the present invention.

[0025] Combination Figure 2 A typical hybrid multi-terminal DC transmission system schematic diagram and Figure 3 A typical hybrid multi-terminal DC transmission line structure schematic diagram is shown. This embodiment uses the following process to implement a hybrid multi-terminal DC transmission line fault location method.

[0026] Step 11: Obtain the time-frequency characteristics of the initial fault traveling wave head at each end of the line.

[0027] Figure 2 The typical hybrid multi-terminal DC transmission system shown is a typical LCC-MMC-MMC hybrid three-terminal DC transmission system, in which the rectifier station side is an LCC-HVDC structure, and the inverter side includes two inverter stations, each of which is an MMC-HVDC structure. Each end of the line includes one end as a rectifier station and two ends as inverter stations. In some other embodiments, the inverter station is not limited to two, but can be more. Moreover, the converter station at each end is provided with a traveling wave ranging device for collecting the traveling wave signal at the end and realizing fault location.

[0028] The time-frequency characteristics of the initial fault traveling wave head can be obtained by using existing methods, such as HHT transformation or other frequency extraction methods.

[0029] In a preferred embodiment, S transform is used to obtain the time-frequency characteristics of the initial fault traveling wave head at each end. The specific implementation method is as follows:

[0030] Perform S-transform on the initial fault traveling wave head:

[0031]

[0032] Then, the time-frequency characteristics of the initial fault traveling wave head are calculated based on the S transform:

[0033]

[0034] Where, ψ is the sampling point number; T1 is the sampling step length, N1 is the frequency discrimination, both of which are known values, for example, T1 = 1 μs, N1 = 1000; n1 is the sampling frequency number, k1 is a real number, k1 = 0, 1, ..., N1-1, X is the Fourier transform of the original fault signal; f TW is the frequency of the initial fault traveling wave head, f s is the reference frequency, f s =1 / N1T1; τ arris the arrival time of the initial fault traveling wave head, which is a known value; e is a natural constant, which is a known value.

[0035] Step 12: Obtain the arrival time of the fault traveling wave head at each end of the line, and determine the fault traveling wave head frequency corresponding to the arrival time of the fault traveling wave head at each end of the line according to the time-frequency characteristics of each end of the line.

[0036] The arrival time of the fault traveling wave head can be obtained by using existing technology. As a preferred implementation, the arrival time of the fault traveling wave head is determined according to the amplitude of the fault traveling wave. The specific implementation method is:

[0037] Calculate and determine whether the criterion is met: x(t)>c×x max ;

[0038] The sampling time corresponding to the first sampling point t that meets the criterion is determined as the arrival time of the fault traveling wave head.

[0039] Among them, x(t) is the fault traveling wave amplitude at the t-th sampling point, which is a known value. After the fault traveling wave signal is determined, its corresponding instantaneous value is the fault traveling wave amplitude. max is the peak value of the fault traveling wave amplitude in the data window, which is also a known value; c is a known proportionality coefficient, 0<c<1. In a specific embodiment, c=0.5.

[0040] The above method is used to determine the arrival time of the fault traveling wave head at each end of the line, and then, based on the time-frequency characteristics of each end, the fault traveling wave head frequency corresponding to the arrival time of the fault traveling wave head at each end can be determined.

[0041] Step 13: Determine the fault traveling wave velocity at each end of the line according to the frequency-dependent characteristics of each end of the line and the fault traveling wave head frequency.

[0042] The frequency-dependent characteristics of the wave velocity are determined according to the structural parameters and electrical parameters of the high-voltage direct current transmission line. The specific determination method can be implemented using existing technologies.

[0043] As a preferred implementation, the following method is used to determine the frequency-dependent characteristics of a hybrid multi-terminal DC transmission line:

[0044] Calculate the complex penetration depth

[0045]

[0046] Where ρ is the earth resistivity, μ is the vacuum permeability, both of which are known values, j is the imaginary unit, and f is the frequency of the traveling wave. Different soils, rocks, etc. have different resistivity. Generally, a typical value can be taken as an approximation, for example, ρ = 100Ωm. In a specific embodiment, the vacuum permeability is μ = 4π×10 -7 H / m.

[0047] Calculate the self-impedance coefficient Z of the positive conductor 1(1) and the self-impedance coefficient Z of the negative conductor 1(2) :

[0048]

[0049] Among them, R 1(1) and R 1(2) are the DC resistance per unit length of the positive wire and the DC resistance per unit length of the negative wire, h 1(1) and h 1(2) are the height of the positive wire from the ground and the height of the negative wire from the ground, GMR 1(1) and GMR 1(2) are the equivalent radius of the positive conductor and the equivalent radius of the negative conductor, b is the number of split sub-conductors, r is the radius of the split sub-conductor, and d is the spacing between the split sub-conductors, all of which are known values. 1(1) and R 1(2) , determined by the circuit structure parameters and electrical parameters. For example, in a specific example, R 1(1) =0.0286Ω / km. For h 1(1) and h 1(2) , which can be determined after the line is built. As a specific embodiment, Figure 3 The circuit structure shown, h 1(1) =h 1(2) =34m. b, r and d depend on the specific line structure and can be determined after the line is built. As a specific example, Figure 3 In the line structure shown, b=4, r=0.0213m, d=0.450m.

[0050] Calculate the mutual impedance coefficient Z between the positive and negative conductors 2(1-2) , Z 2(2-1) :

[0051]

[0052] Among them, d 2(1-2) =d 2(2-1) is the distance between the positive and negative wires, D 2(1-2)is the distance between the mirror image of the negative wire and the positive wire, D 2(2-1) is the distance between the mirror image of the positive conductor and the negative conductor. Once the line is determined, these distances are known values.

[0053] Calculate the self-impedance coefficient Z of the lightning arrester 3(1) , Z 3(2) :

[0054]

[0055] Among them, Z 3(1) and Z 3(2) are the self-impedance coefficients of the first lightning conductor and the second lightning conductor, R 3(1) and R 3(2) are the DC resistance per unit length of the first lightning conductor and the DC resistance per unit length of the second lightning conductor, h 3(1) and h 3(2) The height of the first lightning conductor from the ground is the height of the second lightning conductor from the ground, GMR 3(1) and GMR 3(2) are the equivalent radius of the first lightning conductor and the equivalent radius of the second lightning conductor respectively. The calculation method of the equivalent radius can be found in the above description. 3(1) , R 3(2) 、h 3(1) 、h 3(2) and GMR 3(1) , GMR 3(2) All are known values.

[0056] Calculate the mutual impedance coefficient Z between the conductor and the lightning arrester 4(1-1) , Z 4(1-2) , Z 4(2-1) , Z 4(2-2) :

[0057]

[0058] Among them, Z 4(1-1) , Z 4(1-2) , Z 4(2-1) , Z 4(2-2) The mutual impedance coefficients between the positive conductor and the first lightning conductor, between the positive conductor and the second lightning conductor, between the negative conductor and the first lightning conductor, and between the negative conductor and the second lightning conductor, d 4(1-1) d 4(1-2) d 4(2-1) d 4(2-2)are the distances between the positive wire and the first lightning conductor, between the positive wire and the second lightning conductor, between the negative wire and the first lightning conductor, and between the negative wire and the second lightning conductor, respectively. 4(1-1) , D 4(1-2) , D 4(2-1) , D 4(2-2) They are the distances between the mirror image of the first lightning conductor and the positive conductor, between the mirror image of the second lightning conductor and the positive conductor, between the mirror image of the first lightning conductor and the negative conductor, and between the mirror image of the second lightning conductor and the negative conductor. After the line is determined, the above distances are all known values.

[0059] Calculate the mutual impedance coefficient Z between the lightning conductors 5(1-2) , Z 5(2-1) :

[0060]

[0061] Among them, d 5(1-2) =d 5(2-1) is the distance between the first lightning conductor and the second lightning conductor, D 5(1-2) is the distance between the mirror image of the second lightning conductor and the first lightning conductor, D 5(2-1) is the distance between the mirror image of the first lightning conductor and the second lightning conductor. After the line is determined, these distances are all known values.

[0062] Determine the impedance coefficient matrix Z:

[0063]

[0064] in,

[0065] Calculate the self-potential coefficient P of the positive and negative wires 1(1) , and the self-potential coefficient P of the negative conductor 1(2) :

[0066]

[0067] Where ε is the dielectric constant of vacuum, which is a known value.

[0068] Calculate the mutual potential coefficient P between the positive and negative conductors 2(1-2) , P 2(2-1) :

[0069]

[0070] Calculate the self-potential coefficient P of the lightning conductor 3(1) , P 3(2) :

[0071]

[0072] Among them, P 3(1) and P 3(2) are the self-potential coefficients of the first lightning conductor and the second lightning conductor respectively.

[0073] Calculate the mutual potential coefficient P between the conductor and the lightning arrester 4(1-1) , P 4(1-2) , P 4(2-1) , P 4(2-2) :

[0074]

[0075] Among them, P 4(1-1) , P 4(1-2) , P 4(2-1) , P 4(2-2) They are the mutual potential coefficients between the positive wire and the first lightning conductor, between the positive wire and the second lightning conductor, between the negative wire and the first lightning conductor, and between the negative wire and the second lightning conductor.

[0076] Calculate the mutual potential coefficient P between lightning conductors 5(1-2) , P 5(2-1) :

[0077]

[0078] Determine the potential coefficient matrix P:

[0079]

[0080] in,

[0081] Determine the capacitance coefficient matrix Y:

[0082] Y=j2πf×P -1 .

[0083] Then, the transmission parameter γ of the transmission line is determined according to the impedance coefficient matrix Z and the capacitance coefficient matrix Y:

[0084]

[0085] in, is the phase modulus transformation matrix; α1 and β1 are 1-modulus parameters and are both real numbers; α0 and β0 are 0-modulus parameters and are both real numbers.

[0086] Finally, the frequency-dependent characteristic is determined according to the transmission parameter γ of the transmission line:

[0087]

[0088] Among them, v is the velocity of the 1-mode traveling wave, that is, the transmission speed of the 1-mode fault traveling wave on the transmission line. In the above frequency-dependent characteristics, β1 is a known value, so the corresponding wave velocity can be determined after the frequency f is determined.

[0089] Specifically, the frequency of the fault traveling wave head at each end of the line is set to f TWi , then determine the fault traveling wave velocity v at each end of the line i :

[0090] Among them, f TWi is the frequency of the fault traveling wave head at the i-th converter station side, which can be obtained by the method in step 12; v i is the fault traveling wave velocity at the i-th converter station side.

[0091] Step 14: Determine the fault occurrence time according to the fault traveling wave velocity at each end of the line and the arrival time of the fault traveling wave head.

[0092] Specifically, the following formula can be used to calculate the fault occurrence time:

[0093]

[0094] in, is the time when the fault occurs, n=1,2,…,N, N is the total number of converter stations, Figure 2 In the system shown, N = 3; v i is the fault traveling wave speed at the i-th converter station side, t i is the arrival time of the fault traveling wave head at the i-th converter station side, v n is the fault traveling wave speed at the n-th converter station side, t n is the arrival time of the fault traveling wave head at the n-th converter station side; D n is the distance between the n-th converter station and the line star connection point, D i is the distance between the i-th converter station and the line star connection point. After the line is determined, D n and D i All are known values.

[0095] Step 15: Determine the fault interval identification parameters at each end of the line according to the fault traveling wave velocity and the fault occurrence time at each end of the line.

[0096] Specifically, the fault interval identification parameter at each end of the line can be calculated according to the following formula:

[0097]

[0098] in, is the fault section identification parameter at the i-th converter station side, and e is a natural constant.

[0099] Step 16: Determine the fault location based on the fault interval identification parameters at each end of the line.

[0100] Specifically, firstly, the section where the fault is located is determined according to the fault section identification parameters at each end of the line.

[0101] As a specific implementation method, if The fault section is determined to be the section between the i-th converter station and the star connection point.

[0102] Then, the distance between the fault and the converter station in the section where it is located is determined according to the following formula:

[0103]

[0104] in, is the distance between the fault point located in the section between the i-th end converter station and the star connection point and the i-th end converter station. Thus, the fault can be accurately located.

[0105] The fault location method for the hybrid multi-terminal DC transmission line provided in the above embodiment makes full use of the frequency-dependent characteristics of the line traveling wave velocity, proposes to determine the fault traveling wave velocity according to the frequency-dependent characteristics, and then determine the fault occurrence time based on the fault traveling wave velocity and the arrival time of the fault traveling wave head, and determine the fault interval identification parameter according to the fault occurrence time and the fault traveling wave velocity, and finally determine the fault position based on the fault distinction identification parameter. The method can well adapt to the topological structure of the hybrid multi-terminal DC transmission system and improve the accuracy of fault location of the hybrid multi-terminal DC transmission system.

[0106] Figure 4 The figure shows the simulated waveform of the voltage traveling wave signal at the three terminals of the hybrid three-terminal DC transmission line when a typical fault occurs in the line. lcc,1 、u mmc1,1 and u mmc2,1 They are the fault voltage traveling wave signals of the LCC rectifier side, MMC-I inverter side and MMC-II inverter side. In addition, the arrival times of the fault traveling waves of the LCC rectifier side, MMC-I inverter side and MMC-II inverter side are t1=0.721ms, t2=1.726ms and t3=1.726ms respectively.

[0107] Figure 5 The S transformation result diagram of the voltage traveling wave signal at the three terminals of the hybrid three-terminal DC transmission line of the present invention is shown when a typical fault occurs. Among them, (a), (b) and (c) are the S transformation result diagrams of the voltage traveling wave signal at the LCC rectifier side, the MMC-I inverter side and the MMC-II inverter side respectively.

[0108] After monitoring and calculation, the fault traveling wave head frequencies on the LCC rectifier side, MMC-I inverter side and MMC-II inverter side are f1=233.603kHz, f2=118.885kHz and f3=117.957kHz respectively; the fault traveling wave velocities are v1=299.283km / ms, v2=299.109km / ms and v3=299.107km / ms respectively; the fault occurs at The fault interval identification parameter values ​​corresponding to the LCC rectifier side, MMC-I inverter side and MMC-II inverter side are and because It can be determined that the fault is located between the LCC rectifier side and the star connection point, such as Figure 2 Further, the distance between the fault point and the converter station on the LCC rectifier side is calculated as follows:

[0109] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for a person skilled in the art to modify the technical solutions described in the aforementioned embodiments, or to replace some of the technical features therein by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions claimed to be protected by the present invention.

Claims

1. A method for locating a fault in a hybrid multi-terminal DC transmission line, characterized in that: The method comprises: Obtain the time-frequency characteristics of the initial fault traveling wave head at each end of the line respectively; The arrival time of the fault traveling wave head at each end of the line is obtained respectively, and the frequency of the fault traveling wave head corresponding to the arrival time of the fault traveling wave head at each end of the line is determined according to the time-frequency characteristics of each end of the line; Determining the speed of the fault traveling wave at each end of the line according to the frequency-dependent characteristics of each end of the line and the head frequency of the fault traveling wave; Determine the fault occurrence time based on the fault traveling wave velocity at each end of the line and the arrival time of the fault traveling wave head; Determine the fault interval identification parameters at each end of the line according to the fault traveling wave velocity and fault occurrence time at each end of the line; Determine the fault location based on the fault interval identification parameters at each end of the line; The fault occurrence time is determined based on the fault traveling wave velocity at each end of the line and the arrival time of the fault traveling wave head, including: The fault occurrence time is calculated according to the following formula in, is the time when the fault occurs, n=1,2,…,N, N is the total number of converter stations, v i is the fault traveling wave speed at the i-th converter station side, t i is the arrival time of the fault traveling wave head at the i-th converter station side, v n is the fault traveling wave speed at the n-th converter station side, t n is the arrival time of the fault traveling wave head at the n-th converter station side, D n is the distance between the n-th converter station and the line star connection point, D i is the distance between the i-th converter station and the line star connection point; According to the fault traveling wave velocity and fault occurrence time at each end of the line, the fault interval identification parameters at each end of the line are determined, including: The fault interval identification parameters at each end of the line are calculated according to the following formula: in, is the fault section identification parameter at the i-th converter station side, and e is a natural constant.

2. The fault location method for a hybrid multi-terminal direct current transmission line according to claim 1, characterized in that: Determine the fault location based on the fault interval identification parameters at each end of the line, including: Determine the interval where the fault is located according to the fault interval identification parameters at each end of the line; Determine the distance between the fault and the converter station in the section where it is located according to the following formula: in, is the distance between the fault point located in the section between the i-th converter station and the star connection point and the i-th converter station.

3. The fault location method for a hybrid multi-terminal direct current transmission line according to claim 2, characterized in that: Determining the interval where the fault is located according to the fault interval identification parameters at each end of the line specifically includes: If satisfied The fault section is determined to be the section between the i-th converter station and the star connection point.

4. The method for locating a fault in a hybrid multi-terminal direct current transmission line according to any one of claims 1 to 3, characterized in that: According to the frequency-dependent characteristics of each end of the line and the head frequency of the fault traveling wave, the speed of the fault traveling wave at each end of the line is determined, specifically including: The frequency-dependent characteristics are obtained by the following method: Calculate the complex penetration depth Among them, ρ is the earth resistivity, μ is the vacuum permeability, both of which are known values, j is the imaginary unit, and f is the traveling wave frequency; Calculate the self-impedance coefficient Z of the positive conductor 1(1) and the self-impedance coefficient Z of the negative conductor 1(2) : Among them, R 1(1) and R 1(2) are the DC resistance per unit length of the positive wire and the DC resistance per unit length of the negative wire, h 1(1) and h 1(2) are the height of the positive wire from the ground and the height of the negative wire from the ground, GMR 1(1) and GMR 1(2) are the equivalent radius of the positive conductor and the equivalent radius of the negative conductor, respectively; b is the number of split sub-conductors; r is the radius of the split sub-conductors; and d is the spacing between the split sub-conductors; Calculate the mutual impedance coefficient Z between the positive and negative wires 2(1-2) , Z 2(2-1) : Among them, d 2(1-2) =d 2(2-1) is the distance between the positive and negative wires, D 2(1-2) is the distance between the mirror image of the negative wire and the positive wire, D 2(2-1) is the distance between the mirror image of the positive wire and the negative wire; Calculate the self-impedance coefficient Z of the lightning arrester 3(1) , Z 3(2) : Among them, Z 3(1) and Z 3(2) are the self-impedance coefficients of the first lightning conductor and the second lightning conductor, R 3(1) and R 3(2) are the DC resistance per unit length of the first lightning conductor and the DC resistance per unit length of the second lightning conductor, h 3(1) and h 3(2) The height of the first lightning conductor from the ground is the height of the second lightning conductor from the ground, GMR 3(1) and GMR 3(2) are the equivalent radius of the first lightning conductor and the equivalent radius of the second lightning conductor respectively; Calculate the mutual impedance coefficient Z between the conductor and the lightning arrester 4(1-1) , Z 4(1-2) , Z 4(2-1) , Z 4(2-2) : Among them, Z 4(1-1) , Z 4(1-2) , Z 4(2-1) , Z 4(2-2) The mutual impedance coefficients between the positive conductor and the first lightning conductor, between the positive conductor and the second lightning conductor, between the negative conductor and the first lightning conductor, and between the negative conductor and the second lightning conductor, d 4(1-1) d 4(1-2) d 4(2-1) d 4(2-2) are the distances between the positive wire and the first lightning conductor, between the positive wire and the second lightning conductor, between the negative wire and the first lightning conductor, and between the negative wire and the second lightning conductor, respectively. 4(1-1) , D 4(1-2) , D 4(2-1) , D 4(2-2) are the distances between the mirror image of the first lightning conductor and the positive conductor, between the mirror image of the second lightning conductor and the positive conductor, between the mirror image of the first lightning conductor and the negative conductor, and between the mirror image of the second lightning conductor and the negative conductor; Calculate the mutual impedance coefficient Z between the lightning conductors 5(1-2) , Z 5(2-1) : Among them, d 5(1-2) =d 5(2-1) is the distance between the first lightning conductor and the second lightning conductor, D 5(1-2) is the distance between the mirror image of the second lightning conductor and the first lightning conductor, D 5(2-1) is the distance between the mirror image of the first lightning conductor and the second lightning conductor; Determine the impedance coefficient matrix Z: in, Calculate the self-potential coefficient P of the positive conductor 1(1) , and the self-potential coefficient P of the negative conductor 1(2) : Among them, ε is the dielectric constant of vacuum, which is a known value; Calculate the mutual potential coefficient P between the positive and negative conductors 2(1-2) , P 2(2-1) : Calculate the self-potential coefficient P of the lightning conductor 3(1) , P 3(2) : Among them, P 3(1) and P 3(2) are the self-potential coefficient of the first lightning conductor and the self-potential coefficient of the second lightning conductor respectively; Calculate the mutual potential coefficient P between the conductor and the lightning arrester 4(1-1) , P 4(1-2) , P 4(2-1) , P 4(2-2) : Among them, P 4(1-1) , P 4(1-2) , P 4(2-1) , P 4(2-2) The mutual potential coefficients are respectively between the positive wire and the first lightning conductor, between the positive wire and the second lightning conductor, between the negative wire and the first lightning conductor, and between the negative wire and the second lightning conductor; Calculate the mutual potential coefficient P between lightning conductors 5(1-2) , P 5(2-1) : Determine the potential coefficient matrix P: in, Determine the capacitance coefficient matrix Y: Y=j2πf×P -1 ; Determine the transmission line transmission parameter γ based on the impedance coefficient matrix Z and the capacitance coefficient matrix Y: in, is the phase modulus transformation matrix; α1 and β1 are 1-modulus parameters and are both real numbers; α0 and β0 are 0-modulus parameters and are both real numbers; The frequency-dependent characteristic is determined according to the transmission parameter γ of the transmission line: Where, v is the speed of the 1st mode traveling wave; Get the fault traveling wave head frequency f at each end of the line TWi , determine the fault traveling wave velocity v at each end of the line i : Among them, f TWi is the frequency of the fault traveling wave at the i-th converter station, v i is the fault traveling wave velocity at the i-th converter station side.

5. The fault location method for a hybrid multi-terminal direct current transmission line according to claim 1, characterized in that: The time-frequency characteristics of the initial fault traveling wave head are obtained using the following method: Perform S-transform on the initial fault traveling wave head: The time-frequency characteristics of the initial fault traveling wave head are calculated based on S transform: Where, ψ is the sampling point number, T1 is the sampling step, N1 is the frequency discrimination, n1 is the sampling frequency number, k1 is a real number, k1 = 0, 1, ..., N1-1, X is the Fourier transform of the original fault signal; f TW is the frequency of the initial fault traveling wave head, f s is the reference frequency, f s =1 / N1T1,τ arr is the arrival time of the initial fault traveling wave head.

6. The fault location method for a hybrid multi-terminal direct current transmission line according to claim 1, characterized in that: The following method is used to obtain the arrival time of the fault traveling wave head at each end of the line: Calculate and determine whether the criterion is met: x(t)>c×x max ; The sampling time corresponding to the first sampling point t that meets the criterion is determined as the arrival time of the fault traveling wave head; Where x(t) is the fault wave amplitude at the t-th sampling point, which is a known value; x max is the peak value of the fault wave amplitude in the data window, which is a known value; c is a known proportional coefficient, 0 <c<1。

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