CN114325211A - Fault positioning method for hybrid multi-terminal direct-current transmission line - Google Patents
Fault positioning method for hybrid multi-terminal direct-current transmission line Download PDFInfo
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Abstract
The invention discloses a fault positioning method of a hybrid multi-terminal direct current transmission line, which comprises the following steps: respectively acquiring 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 frequency of the fault traveling wave head 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 wave velocity of the fault traveling wave at each end of the line according to the frequency-dependent characteristic of each end of the line and the frequency of the wave head of the fault traveling wave; determining the fault occurrence time according to the fault traveling wave speed of each end of the line and the arrival time of the fault traveling wave head; determining a fault section identification parameter of each end of the line according to the wave speed of the fault traveling wave of each end of the line and the fault occurrence time; and determining the fault position based on the fault interval identification parameters of each end of the line. By applying the method and the device, the fault of the hybrid multi-terminal direct current transmission line can be accurately positioned.
Description
Technical Field
The invention belongs to the technical field of power electronics, and particularly relates to a fault positioning method of a power system, and more particularly relates to a fault positioning method of a hybrid multi-terminal direct-current transmission line.
Background
The existing high-voltage direct-current transmission system LCC-HVDC (line communated converter based HVDC) based on the line current commutation principle has long transmission distance, large transmission capacity and high transmission efficiency. However, the LCC-HVDC inverter station is prone to phase commutation failure, which in turn leads to transmission reliability problems. The flexible high-voltage direct-current transmission system MMC-HVDC (modular multilevel converter based HVDC) based on the modular multilevel principle has no commutation failure risk and can realize certain power flow control. However, the MMC-HVDC system has smaller transmission capacity and higher construction cost. Therefore, the LCC-MMC-HVDC hybrid direct-current power transmission system adopting the LCC-HVDC principle on the rectification side and the MMC-HVDC principle on the inversion side can simultaneously have the advantages of a traditional high-voltage direct-current power transmission system and a flexible direct-current power transmission system, and is widely applied. In order to obtain higher transmission capacity, a multi-terminal direct current (MTDC) topology structure is adopted on the inversion side, so that an LCC-MMC-MTDC hybrid multi-terminal direct current transmission system is formed.
At present, fault positioning of a hybrid multi-terminal direct-current transmission line is mostly based on fault traveling waves, and positioning accuracy of the fault traveling waves is seriously dependent on wave velocity values of the fault traveling waves. In the existing fault traveling wave positioning method of the hybrid multi-terminal direct current transmission line, a fixed wave speed value is usually adopted to determine the fault position. For the actual transmission line, the traveling wave speed is not a fixed value, so that the fault location is determined by adopting the fixed fault traveling wave speed value, the fault location error is large, the accuracy is low, and the fault maintenance and recovery are influenced.
Chinese patent application publication No. CN112526283A discloses a fault location method for a hvdc transmission line, which determines the wave velocity of a fault traveling wave based on the frequency-dependent characteristics of the traveling wave, and then determines the fault location according to the wave velocity of the fault traveling wave and the arrival time of the wave head of the fault traveling wave, thereby implementing more accurate fault location. However, the two ends of the high-voltage direct-current transmission line aimed at by the chinese patent application have the same structure, and the adopted method is not suitable for being directly applied to fault location of a hybrid multi-end direct-current transmission line. Moreover, the chinese patent application determines the fault position based on the arrival time of the fault traveling wave head, and cannot determine the fault occurrence time or determine the fault position based on the fault occurrence time, so that the fault location still has the disadvantage of being not accurate enough.
Disclosure of Invention
The invention aims to provide a fault positioning method of a hybrid multi-terminal direct-current transmission line.
In order to realize the purpose of the invention, the invention is realized by adopting the following technical scheme:
a fault positioning method for a hybrid multi-terminal direct current transmission line comprises the following steps:
respectively acquiring 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 frequency of the fault traveling wave head 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 wave velocity of the fault traveling wave at each end of the line according to the frequency-dependent characteristic of each end of the line and the frequency of the wave head of the fault traveling wave;
determining the fault occurrence time according to the fault traveling wave speed of each end of the line and the arrival time of the fault traveling wave head;
determining a fault section identification parameter of each end of the line according to the wave speed of the fault traveling wave of each end of the line and the fault occurrence time;
and determining the fault position based on the fault interval identification parameters of each end of the line.
Compared with the prior art, the invention has the advantages and positive effects that: the fault positioning method of the hybrid multi-terminal direct-current transmission line provided by the invention fully utilizes the frequency-dependent characteristic of the traveling wave speed of the line, provides the steps of determining the wave speed of the fault traveling wave according to the frequency-dependent characteristic, determining the fault occurrence time based on the wave speed of the fault traveling wave and the arrival time of the wave head of the fault traveling wave, determining the fault interval identification parameter according to the fault occurrence time and the wave speed of the fault traveling wave, and finally determining the fault position based on the fault difference identification parameter.
Other features and advantages of the present invention will become more apparent from the following detailed description of the invention when taken in conjunction with the accompanying drawings.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
Fig. 1 is a flowchart of an embodiment of a fault location method of a hybrid multi-terminal dc transmission line according to the present invention;
fig. 2 is a schematic diagram of an exemplary hybrid multi-terminal dc transmission system in accordance with an embodiment of the present invention;
fig. 3 is a schematic structural diagram of a typical hybrid multi-terminal dc transmission line according to an embodiment of the present invention;
FIG. 4 is a waveform diagram illustrating a simulation of a traveling wave signal of a three-terminal voltage of a line in an exemplary fault according to an embodiment of the present invention;
fig. 5 is a diagram illustrating a transformation result of a traveling wave signal S of a three-terminal voltage of a line when a typical fault occurs in the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings and examples.
Technical solutions between the embodiments of the present invention may be combined with each other, but it must be based on the realization of those skilled in the art, and when the technical solutions are contradictory or cannot be realized, such a combination should not be considered to exist, and is not within the protection scope of the present invention.
Fig. 1 is a flowchart illustrating a method for locating a fault in a hybrid multi-terminal dc transmission line according to an embodiment of the present invention.
In combination with a schematic diagram of a typical hybrid multi-terminal dc power transmission system shown in fig. 2 and a schematic diagram of a structure of a typical hybrid multi-terminal dc power transmission line shown in fig. 3, the following processes are adopted in this embodiment to implement a fault location method for the hybrid multi-terminal dc power transmission line.
Step 11: and acquiring the time-frequency characteristics of the initial fault traveling wave head at each end of the line.
The typical hybrid multi-terminal dc transmission system shown in fig. 2 is a typical LCC-MMC hybrid three-terminal dc transmission system, wherein the rectifier station side is of an LCC-HVDC structure, the inverter side includes two inverter stations, and each inverter station is of an MMC-HVDC structure. Each end of the line includes one end that is a rectifying station and two ends that are inverting stations. In other embodiments, the inversion stations are not limited to two, but may be more. And the converter station at each end is provided with a traveling wave distance measuring device for acquiring the traveling wave signal at the end and realizing fault positioning.
The time-frequency characteristic of the initial fault traveling wave head can be obtained by adopting the method in the prior art, such as HHT conversion or other frequency extraction methods.
In a preferred embodiment, the time-frequency characteristics of the initial fault traveling wave head at each end are obtained by adopting S transformation. The specific implementation method comprises the following steps:
and (3) performing S conversion on the initial fault traveling wave head:
then, calculating the time-frequency characteristic of the initial fault traveling wave head based on S transformation:
wherein psi is the serial number of the sampling point; t1 is the sampling step size, N1 is the frequency discrimination, which are known values, for example, T1 ═ 1 μ s, N1 ═ 1000; n1 is a sampling frequency number, k1 is a real number, k1 is 0,1, …, N1-1, and X is fourier transform of an original fault signal; f. ofTWFrequency of wave head of traveling wave for initial failure, fsIs a reference frequency, fs＝1/N1T1；τarrThe arrival time of the wave head of the initial fault traveling wave is a known value; e is a natural constant, a known value.
Step 12: and acquiring the arrival time of the fault traveling wave head at each end of the line, and determining 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 according to the time-frequency characteristics of each end of the line.
The arrival time of the fault traveling wave head can be obtained by adopting the prior art. In a preferred embodiment, the arrival time of the fault traveling wave head is determined according to the amplitude of the fault traveling wave. The specific implementation method comprises the following steps:
calculating and determining whether a criterion is satisfied: x (t) > c xmax；
And determining the sampling time corresponding to the first sampling point t meeting the criterion as the arrival time of the fault traveling wave head.
Wherein, x (t) is the fault traveling wave amplitude of the tth sampling point, and is a known value; after the fault traveling wave signal is determined, the corresponding instantaneous value is the amplitude of the fault traveling wave. x is the number ofmaxThe peak value of the amplitude value of the fault traveling wave in the data window is also a known value; c is a known proportionality coefficient, 0 < c < 1. In one specific embodiment, c is 0.5.
The method is adopted to determine the arrival time of the fault traveling wave head at each end of the line, and then the fault traveling wave head frequency corresponding to the arrival time of the fault traveling wave head at each end can be determined according to the time-frequency characteristics of each end.
Step 13: and determining the fault traveling wave speed of each end of the line according to the frequency-dependent characteristic of each end of the line and the frequency of the fault traveling wave head.
The frequency-dependent characteristic of the wave speed is determined according to the structural parameters and the electrical parameters of the high-voltage direct-current transmission line, and the specific determination method can be realized by adopting the prior art.
As a preferred embodiment, the frequency dependent characteristic of the hybrid multi-terminal dc transmission line is determined by the following method:
calculating complex penetration depth
Where ρ is the earth resistivity, μ is the vacuum permeability, both of known values, j is the imaginary unit, and f is the traveling wave frequency. For earth resistivity, different soils, rocks, etc. have different resistivities, which can generally be approximated by a typical value, for example, ρ ═ 100 Ω m. In one embodiment, the vacuum permeability is selected to be 4 π × 10-7H/m。
Calculating the self-impedance coefficient Z of the positive electrode lead1(1)And the self-impedance coefficient Z of the negative electrode lead1(2)：
Wherein R is1(1)And R1(2)Respectively the direct current resistance per unit length of the positive electrode lead and the direct current resistance per unit length of the negative electrode lead, h1(1)And h1(2)The height of the positive wire from the ground and the height of the negative wire from the ground, GMR1(1)And GMR1(2)Respectively the equivalent radius of the positive electrode lead and the equivalent radius of the negative electrode lead, b is splitThe number of splits of a sub-conductor, r the radius of the split sub-conductor, and d the distance between the split sub-conductors, are known values. For R1(1)And R1(2)Determined by the parameters of the line structure and the electrical parameters, such as, in one embodiment, R1(1)0.0286 Ω/km. For h1(1)And h1(2)And the method can be determined after the line is built. As a specific example, the line structure shown in fig. 3, h1(1)＝h 1(2)34 m. For b, r and d, depending on the specific line configuration, it can be determined after the line is constructed. As a specific example, in the line structure shown in fig. 3, b is 4, r is 0.0213m, and d is 0.450 m.
Calculating the mutual impedance coefficient Z between the positive lead and the negative lead2(1-2)、Z2(2-1)：
Wherein d is2(1-2)＝d2(2-1)Is the distance between the positive and negative leads, D2(1-2)Is the distance between the mirror image of the negative conductor and the positive conductor, D2(2-1)Is the spacing between the mirror image of the positive conductor and the negative conductor. These spacings are known values after the wiring is established.
Calculating the self-impedance coefficient Z of the lightning conductor3(1)、Z3(2)：
Wherein Z is3(1)And Z3(2)The self-impedance coefficient of the first and second lightning conductor, R3(1)And R3(2)A direct current resistance per unit length of the first lightning conductor and a direct current resistance per unit length of the second lightning conductor, h3(1)And h3(2)The height of the first lightning conductor from the ground and the height of the second lightning conductor from the ground, GMR, respectively3(1)And GMR3(2)The equivalent radius of the first lightning conductor and the equivalent radius of the second lightning conductor, respectively, and the calculation method of the equivalent radius is described above. After the route is determined, R3(1)、R3(2)、h3(1)、h3(2)And GMR3(1)、GMR3(2)Are all known values.
Calculating the mutual impedance coefficient Z between the conducting wire and the lightning conductor4(1-1)、Z4(1-2)、Z4(2-1)、Z4(2-2)：
Wherein Z is4(1-1)、Z4(1-2)、Z4(2-1)、Z4(2-2)The mutual impedance 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, d4(1-1)、d4(1-2)、d4(2-1)、d4(2-2)Respectively 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, D4(1-1)、D4(1-2)、D4(2-1)、D4(2-2)The distances between the mirror image of the first lightning conductor and the positive electrode lead, between the mirror image of the second lightning conductor and the positive electrode lead, between the mirror image of the first lightning conductor and the negative electrode lead and between the mirror image of the second lightning conductor and the negative electrode lead are respectively set. After the wiring is determined, the distances are known.
Calculating the mutual impedance coefficient Z between the lightning conductor and the lightning conductor5(1-2)、Z5(2-1)：
Wherein d is5(1-2)＝d5(2-1)For the spacing between the first and second conductor, D5(1-2)Is the distance between the mirror image of the second lightning conductor and the first lightning conductor, D5(2-1)Is the spacing between the mirror image of the first lightning conductor and the second lightning conductor. These spacings are known values after the wiring is established.
Determining an impedance coefficient matrix Z:
wherein the content of the first and second substances,
calculating the self-potential coefficient P of the positive and negative leads1(1)And the self-potential coefficient P of the negative electrode lead1(2)：
Wherein ε represents a vacuum dielectric constant and is a known value.
Calculating the mutual potential coefficient P between the positive lead and the negative lead2(1-2)、P2(2-1)：
Calculating the self-potential coefficient P of the lightning conductor3(1)、P3(2)：
Wherein, P3(1)And P3(2)The self-potential systems being the first lightning conductor respectivelyAnd the self-potential coefficient of the second lightning conductor.
Calculating mutual potential coefficient P between the conducting wire and the lightning conductor4(1-1)、P4(1-2)、P4(2-1)、P4(2-2)：
Wherein, P4(1-1)、P4(1-2)、P4(2-1)、P4(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.
Calculating mutual potential coefficient P between the lightning conductor and the lightning conductor5(1-2)、P5(2-1)：
Determining a potential coefficient matrix P:
wherein the content of the first and second substances,
determining a capacitance coefficient matrix Y:
Y＝j2πf×P-1。
then, determining a transmission parameter gamma of the power transmission line according to the impedance coefficient matrix Z and the capacitance coefficient matrix Y:
wherein the content of the first and second substances,
is a phase-mode transformation matrix; alpha is alpha1、β1Are 1-modulus parameters and are real numbers; alpha is alpha0、β0Are 0 modulo parameters and are all real numbers.
And finally, determining the frequency-dependent characteristic according to the transmission parameter gamma of the power transmission line:
wherein v is the wave speed of the 1-mode traveling wave, namely the transmission speed of the 1-mode fault traveling wave on the power transmission line. In the above frequency-dependent characteristic, β1Is a known value, then the corresponding wave speed can be determined after the frequency f is determined.
Specifically, the frequency of the obtained fault traveling wave head at each end of the line is set to be fTWiDetermining the traveling wave speed v of the fault at each end of the linei：
Wherein f isTWiThe wave head frequency of the fault traveling wave at the i-th end converter station side can be obtained by adopting the method in the step 12; v. ofiAnd the wave speed is the fault traveling wave speed of the i-th end converter station side.
Step 14: and determining the fault occurrence time according to the fault traveling wave speed of each end of the line and the arrival time of the fault traveling wave head.
Specifically, the following formula can be used to calculate the time when the fault occurs
Wherein the content of the first and second substances,
at the time of the fault, N is 1,2, …, N is the total number of converter stations, and in the system shown in fig. 2, N is 3; v. ofiIs the wave speed, t, of the fault traveling wave at the i-th converter station sideiIs the arrival time v of the fault traveling wave head at the i-th converter station sidenIs the wave speed, t, of the fault traveling wave at the nth end converter station sidenThe arrival time of the fault traveling wave head at the nth end converter station side is obtained; dnIs the distance between the nth end converter station and the star connection point of the line, DiFor the distance between the i-th end converter station and the star point of the line, after the line has been determined, DnAnd DiAre all known values.
Step 15: and determining a fault section identification parameter of each end of the line according to the wave speed of the fault traveling wave at each end of the line and the fault occurrence time.
Specifically, the fault interval identification parameter at each end of the line can be calculated according to the following formula
Wherein the content of the first and second substances,
and e is a natural constant.
Step 16: and determining the fault position based on the fault interval identification parameters of each end of the line.
Specifically, firstly, the section where the fault is located is determined according to the fault section identification parameters of each end of the line.
As a specific embodiment, e.g. satisfy
The section in which the fault is located is determined to be the section between the i-th end converter station and the star connection point.
The distance between the fault and the converter station in the zone in which it is located is then determined according to the following formula:
wherein the content of the first and second substances,
is the distance between the fault point located between the i-th end converter station and the star connection point and the i-th end converter station. Therefore, the fault can be accurately positioned.
The method for locating the fault of the hybrid multi-terminal direct-current transmission line provided by the embodiment makes full use of the frequency-dependent characteristic of the line traveling wave speed, provides that the fault traveling wave speed is determined according to the frequency-dependent characteristic, the fault occurrence time is determined based on the fault traveling wave speed and the arrival time of the fault traveling wave head, the fault interval identification parameter is determined according to the fault occurrence time and the fault traveling wave speed, and the fault position is determined based on the fault difference identification parameter.
Fig. 4 shows a simulation waveform diagram of a three-terminal voltage traveling wave signal of the hybrid three-terminal direct-current transmission line when a typical fault occurs in the hybrid three-terminal direct-current transmission line. In the figure, ulcc,1、ummc1,1And ummc2,1The fault voltage traveling wave signals are respectively at the LCC rectifying side, the MMC-I inversion side and the MMC-II inversion side. And the arrival time of the fault traveling waves of the LCC rectifying side, the MMC-I inversion side and the MMC-II inversion side is respectively t1＝0.721ms、t21.726ms and t3＝1.726ms。
Fig. 5 is a diagram showing the result of S conversion of a three-terminal voltage traveling wave signal of a line when a typical fault occurs in the hybrid three-terminal dc transmission line according to the present invention. Wherein, (a), (b) and (c) are S change result graphs of voltage traveling wave signals of an LCC rectifying side, an MMC-I inverting side and an MMC-II inverting side respectively.
Through monitoring and calculation, the frequency of the fault traveling wave head on the LCC rectifying side, the MMC-I inverting side and the MMC-II inverting side is respectively f1＝233.603kHz、f2118.885kHz and f3117.957 kHz; the wave speed of fault traveling wave is v1＝299.283km/ms、v2299.109km/ms and v3299.107 km/ms; the time when the fault occurs is
And the fault interval identification parameter values corresponding to the LCC rectifying side, the MMC-I inverting side and the MMC-II inverting side are respectively
And
due to the fact that
It can be determined that the fault is in the interval between the rectifying side of the LCC and the star connection point, as shown by position F in fig. 2. Further, the distance between the fault point and the converter station on the rectification side of the LCC is calculated as
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions.
Claims (8)
1. A fault positioning method for a hybrid multi-terminal direct current transmission line is characterized by comprising the following steps:
respectively acquiring 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 frequency of the fault traveling wave head 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 wave velocity of the fault traveling wave at each end of the line according to the frequency-dependent characteristic of each end of the line and the frequency of the wave head of the fault traveling wave;
determining the fault occurrence time according to the fault traveling wave speed of each end of the line and the arrival time of the fault traveling wave head;
determining a fault section identification parameter of each end of the line according to the wave speed of the fault traveling wave of each end of the line and the fault occurrence time;
and determining the fault position based on the fault interval identification parameters of each end of the line.
2. The method according to claim 1, wherein the determining the fault occurrence time according to the fault traveling wave speed at each end of the line and the arrival time of the fault traveling wave head specifically comprises:
calculating the fault occurrence time according to the following formula
Wherein the content of the first and second substances,
n is 1,2, …, N is the total number of the converter stations, v is the time of the fault occurrenceiIs the wave speed, t, of the fault traveling wave at the i-th converter station sideiIs the arrival time v of the fault traveling wave head at the i-th converter station sidenIs the wave speed, t, of the fault traveling wave at the nth end converter station sidenThe arrival time of the fault traveling wave head at the nth end converter station side, DnFor the nth end converter station and lineDistance between road-star points of connection, DiIs the distance between the i-th end converter station and the star connection point of the line.
3. The method according to claim 2, wherein the determining of the fault interval identification parameters of each end of the line according to the fault traveling wave speed and the fault occurrence time of each end of the line specifically comprises:
calculating fault interval identification parameters of each end of the line according to the following formula
Wherein the content of the first and second substances,
and e is a natural constant.
4. The method according to claim 3, wherein determining the fault location based on the fault interval identification parameters at each end of the line specifically comprises:
determining the interval of the fault according to the fault interval identification parameters at each end of the line;
the distance between the fault and the converter station in the zone in which it is located is determined according to the following formula:
wherein the content of the first and second substances,
to be located at the i-th end converter stationAnd the distance between the fault point of the interval where the star connection point is located and the ith end converter station.
5. The method according to claim 4, wherein the determining of the section where the fault is located according to the fault section identification parameters at each end of the line specifically comprises:
if satisfy
The section in which the fault is located is determined to be the section between the i-th end converter station and the star connection point.
6. The method for fault location of a hybrid multi-terminal direct current transmission line according to any one of claims 1 to 5, wherein the determining of the fault traveling wave velocity at each end of the line according to the frequency-dependent characteristic of each end of the line and the frequency of the fault traveling wave head specifically comprises:
the frequency dependent characteristic is obtained by the following method:
calculating complex penetration depth
Wherein rho is earth resistivity, mu is vacuum magnetic conductivity which are known values, j is an imaginary unit, and f is traveling wave frequency;
calculating the self-impedance coefficient Z of the positive electrode lead1(1)And the self-impedance coefficient Z of the negative electrode lead1(2)：
Wherein R is1(1)And R1(2)Respectively the direct current resistance per unit length of the positive electrode lead and the direct current resistance per unit length of the negative electrode lead, h1(1)And h1(2)The height of the positive wire from the ground and the height of the negative wire from the ground, GMR1(1)And GMR1(2)Respectively the equivalent radius of the positive wire and the equivalent radius of the negative wire, b is the splitting number of the split sub-wire, r is the radius of the split sub-wire, and d is the distance between the split sub-wires;
calculating the mutual impedance coefficient Z between the positive lead and the negative lead2(1-2)、Z2(2-1)：
Wherein d is2(1-2)＝d2(2-1)Is the distance between the positive and negative leads, D2(1-2)Is the distance between the mirror image of the negative conductor and the positive conductor, D2(2-1)The distance between the mirror image of the positive electrode lead and the negative electrode lead is set;
calculating the self-impedance coefficient Z of the lightning conductor3(1)、Z3(2)：
Wherein Z is3(1)And Z3(2)The self-impedance coefficient of the first and second lightning conductor, R3(1)And R3(2)A direct current resistance per unit length of the first lightning conductor and a direct current resistance per unit length of the second lightning conductor, h3(1)And h3(2)Respectively the height of the first lightning conductor from the ground and the height of the second lightning conductor from the ground, GMR3(1)And GMR3(2)Respectively the equivalent radius of the first lightning conductor and the equivalent radius of the second lightning conductor;
calculating the mutual impedance coefficient Z between the conducting wire and the lightning conductor4(1-1)、Z4(1-2)、Z4(2-1)、Z4(2-2)：
Wherein Z is4(1-1)、Z4(1-2)、Z4(2-1)、Z4(2-2)The mutual impedance 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, d4(1-1)、d4(1-2)、d4(2-1)、d4(2-2)Respectively 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, D4(1-1)、D4(1-2)、D4(2-1)、D4(2-2)The distances between the mirror image of the first lightning conductor and the positive electrode lead, between the mirror image of the second lightning conductor and the positive electrode lead, between the mirror image of the first lightning conductor and the negative electrode lead and between the mirror image of the second lightning conductor and the negative electrode lead are respectively set;
calculating the mutual impedance coefficient Z between the lightning conductor and the lightning conductor5(1-2)、Z5(2-1)：
Wherein d is5(1-2)＝d5(2-1)For the spacing between the first and second conductor, D5(1-2)Between the mirror image of the second lightning conductor and the first lightning conductorDistance, D5(2-1)The distance between the mirror image of the first lightning conductor and the second lightning conductor;
determining an impedance coefficient matrix Z:
wherein the content of the first and second substances,
calculating the self-potential coefficient P of the positive electrode wire1(1)And the self-potential coefficient P of the negative electrode lead1(2)：
Wherein ε is a vacuum dielectric constant, which is a known value;
calculating the mutual potential coefficient P between the positive lead and the negative lead2(1-2)、P2(2-1)：
Calculating the self-potential coefficient P of the lightning conductor3(1)、P3(2)：
Wherein, P3(1)And P3(2)The self-potential coefficients are respectively the self-potential coefficient of the first lightning conductor and the self-potential coefficient of the second lightning conductor;
calculating mutual potential coefficient P between the conducting wire and the lightning conductor4(1-1)、P4(1-2)、P4(2-1)、P4(2-2)：
Wherein, P4(1-1)、P4(1-2)、P4(2-1)、P4(2-2)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 are respectively set;
calculating mutual potential coefficient P between the lightning conductor and the lightning conductor5(1-2)、P5(2-1)：
Determining a potential coefficient matrix P:
wherein the content of the first and second substances,
determining a capacitance coefficient matrix Y:
Y＝j2πf×P-1；
determining a transmission parameter gamma of the power transmission line according to the impedance coefficient matrix Z and the capacitance coefficient matrix Y:
wherein the content of the first and second substances,
is a phase mode changeChanging the matrix; alpha is alpha1、β1Are 1-modulus parameters and are real numbers; alpha is alpha0、β0Are 0 modulo parameters and are real numbers;
determining the frequency dependent characteristic according to the transmission parameter gamma of the power transmission line:
wherein v is the wave velocity of 1-mode traveling waves;
obtaining the frequency f of the fault traveling wave head at each end of the lineTWiDetermining the traveling wave profile v of the fault at each end of the linei：
Wherein f isTWiIs the frequency, v, of the fault traveling wave head at the i-th converter station sideiAnd the wave speed is the fault traveling wave speed of the i-th end converter station side.
7. The method for fault location of a hybrid multi-terminal direct current transmission line according to claim 1, wherein the time-frequency characteristics of an initial fault traveling wave head are obtained by the following method:
and (3) performing S conversion on the initial fault traveling wave head:
calculating the time-frequency characteristic of the initial fault traveling wave head based on S transformation:
the method comprises the following steps that psi is a sampling point serial number, T1 is a sampling step length, N1 is a frequency discrimination degree, N1 is a sampling frequency number, k1 is a real number, k1 is 0,1, …, N1-1, and X is Fourier transform of an original fault signal; f. ofTWFrequency of wave head of traveling wave for initial failure, fsIs a reference frequency, fs＝1/N1T1，τarrThe arrival time of the wave head of the initial fault traveling wave is shown.
8. The method for locating the fault of the hybrid multi-terminal direct-current transmission line according to claim 1, wherein the arrival time of the fault traveling wave head at each terminal of the line is obtained by the following method:
calculating and determining whether a criterion is satisfied: x (t) > c xmax；
Determining the sampling time corresponding to the first sampling point t meeting the criterion as the arrival time of the fault traveling wave head;
wherein, x (t) is the fault traveling wave amplitude of the tth sampling point, and is a known value; x is the number ofmaxThe peak value of the amplitude value of the fault traveling wave in the data window is a known value; c is a known proportionality coefficient, 0 < c < 1.
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