High-resolution fault location method for half-wavelength power transmission line

Abstract

The invention relates to a high-resolution fault distance measurement method for a half-wavelength power transmission line, and the method comprises the steps: calculating a fault starting criterion according to the three-phase voltage and current of a transmitting end and the three-phase voltage and current of a receiving end, so as to judge whether a fault occurs or not, and recording a fault starting moment when the fault occurs; taking the three-phase voltage and current of the receiving end in a time window before and after the starting time to synthesize the current fault reverse traveling wave of the sending end; carrying out short-time Fourier transform and second-order transient extraction transform processing on the sending-end current fault reverse traveling wave in sequence, taking the arrival time of a preset frequency band, determining whether to complement the arrival time sequence by using a Lagrange interpolation method according to whether the arrival time is abruptly changed, and then carrying out median filtering; and listing an overdetermined equation set and searching an optimal solution through a gradient descent method. According to the method, accurate fault positioning without double-end synchronous time synchronization is realized, the distance measurement error is controlled to be less than 1km through an STET algorithm, an overdetermined equation and a gradient descent method, and meanwhile, the distance measurement performance is not influenced by transition resistance.

Description

Technical Field

[0001] The invention relates to the field of ultra-high voltage long-distance power transmission, and in particular to a high-resolution fault distance measurement method for a half-wavelength power transmission line. Background Art

[0002] Half-wavelength AC transmission technology is a point-to-point AC transmission method without intermediate substations. Its unit construction cost is much lower than that of traditional AC transmission lines, and it has significant advantages in reactive power self-balancing and large-capacity power transmission. Compared with high-voltage DC transmission, half-wavelength AC transmission is also considered to be more economical and efficient. Studies have shown that the construction investment of half-wavelength AC transmission can be about 30% lower than that of high-voltage DC transmission. Therefore, half-wavelength AC transmission is particularly suitable for countries with vast territories. However, there are currently no actual cases of engineering application of half-wavelength AC transmission because: on the one hand, half-wavelength AC transmission has significantly different operation and fault characteristics from traditional AC transmission, involving technical difficulties in multiple aspects such as system stability and overvoltage; on the other hand, the relay protection and fault location technology adapted to traditional AC transmission will fail on half-wavelength transmission lines, resulting in safety risks for half-wavelength AC transmission.

[0003] In the above background, the relay protection and fault distance measurement technology based on traveling waves has gradually attracted widespread attention from the academic community. Some scholars have used a notch filter with a center frequency of 50Hz and a low-pass filter with a cutoff frequency of 2kHz to identify the peak values ​​of the measured voltage and current, and divide the fault into an internal fault or an external fault based on the polarity comparison to distinguish the fault type. However, this method relies on traveling waves with a frequency lower than 2kHz, so the interference of non-periodic components is very obvious; other scholars have proposed a traveling wave differential protection scheme, and optimized the method considering the dispersion on long-distance lines, effectively avoiding the protection misoperation and ranging error caused by abnormal differential current; some scholars have used high-frequency signals caused by faults, capacitor current compensation and other methods to locate faults. The common problem with the above methods is that the measurement signals at the sending and receiving ends need to be transmitted in real time and synchronized with GPS, so the timing error will seriously affect the accuracy of ranging. In addition, real-time signal transmission will greatly reduce the speed of protection and the real-time performance of ranging: taking a half-wavelength transmission line with a length of 3,000 km as an example, under the condition of a near-field fault, the transmission delay includes 1) the time consumed by the fault traveling wave to reach the opposite side; 2) the time consumed by the protection on the opposite side to identify the fault; 3) the communication delay consumed by the remote trip command of the protection on the opposite side to be transmitted to the local area through the optical fiber. During this period, the bus on this side will feel the existence of low voltage and overcurrent for a long time, which is unbearable for the UHV system. Summary of the invention

[0004] The present invention provides a high-resolution fault location method for half-wavelength transmission lines to solve at least one of the above technical problems.

[0005] The technical solution of the present invention to solve the above technical problem is as follows: a high-resolution fault location method for a half-wavelength transmission line, comprising:

[0006] S1, within a first preset time window before the current moment, the three-phase voltage and three-phase current at the sending end and the receiving end of the half-wavelength transmission line are sampled at a first preset sampling frequency to obtain a first three-phase voltage and current matrix at the sending end and a first three-phase voltage and current matrix at the receiving end; a fault start criterion is calculated according to the first three-phase voltage and current matrix at the sending end and the first three-phase voltage and current matrix at the receiving end; the fault start criterion is compared with a preset fault start threshold to determine whether a fault occurs in the half-wavelength transmission line, if not, S1 is repeatedly executed, if yes, the current moment is recorded as the fault start moment, and S2 to S4 are executed;

[0007] S2, sampling the three-phase voltage and three-phase current at the receiving end at a second preset sampling frequency within a second preset time window before and after the fault initiation moment to obtain a second three-phase voltage and current matrix at the receiving end; synthesizing a line mode reverse traveling wave of the sending end current according to the second three-phase voltage and current matrix at the receiving end;

[0008] S3, performing short-time Fourier transform on the line-mode reverse traveling wave of the sending-end current to obtain the time-frequency distribution of the line-mode reverse traveling wave of the sending-end current; performing second-order transient extraction transformation processing on the time-frequency distribution to obtain a first time-frequency spectrum; intercepting a time-frequency spectrum of a preset frequency band from the first time-frequency spectrum to obtain a second time-frequency spectrum; judging whether there is a sudden change in the arrival time of the second time-frequency spectrum, if so, removing the sudden change in the arrival time of the second time-frequency spectrum, and using the Lagrange interpolation method to fill the removed arrival time in the second time-frequency spectrum to obtain a third time-frequency spectrum, and performing median filtering on the third time-frequency spectrum to obtain a fourth time-frequency spectrum, if not, performing median filtering on the second time-frequency spectrum to obtain a fourth time-frequency spectrum;

[0009] S4, extracting multiple frequency components in the fourth time-frequency spectrum, and finding the time component corresponding to each frequency component; freely combining multiple frequency components and their corresponding time components to obtain multiple pairs of heterofrequency components; writing overdetermined equations according to the wave speed and time of the multiple pairs of heterofrequency components, and using the gradient descent method to find the optimal solution of the overdetermined equation to obtain the fault distance of the half-wavelength transmission line.

[0010] The beneficial effects of the present invention are as follows: a high-resolution fault distance measurement method for a half-wavelength power transmission line of the present invention can realize accurate positioning of the fault position without the need for double-end synchronization; at the same time, a second-order transient extraction transformation algorithm with high time-frequency resolution is used to process the time-frequency distribution of a short-time Fourier transform to obtain an energy-concentrated time-frequency spectrum, which can more accurately obtain the independent wave arrival time of each frequency component of the traveling wave, thereby reducing the ranging error caused by the "uncertainty" principle; and an overdetermined equation and a gradient descent method are used to estimate the fault position, thereby further reducing the random error, and generally speaking, the ranging error can be controlled below 1 km; in addition, the ranging performance of the present invention is not affected by transition resistance. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 A flow chart of a high-resolution fault location method for a half-wavelength transmission line according to the present invention;

[0012] Figure 2 This is a schematic diagram of a half-wavelength transmission line in an embodiment;

[0013] Figure 3 It is a waveform diagram of the sampling points before and after the fault in the embodiment;

[0014] Figure 4 It is a waveform diagram of the start criterion in the embodiment;

[0015] Figure 5 It is a waveform diagram of the reverse traveling wave of the line mode of the sending-end current in the embodiment;

[0016] Figure 6 Schematic diagram of the time-frequency distribution of the line mode reverse traveling wave of the sending-end current in the embodiment;

[0017] Figure 7 is a schematic diagram of a first time spectrum in an embodiment;

[0018] Figure 8 is a schematic diagram of a low frequency band of a fourth time spectrum in the embodiment;

[0019] Fig. 9 FIG. 4 is a schematic diagram of a high frequency band of a fourth time spectrum in the embodiment. DETAILED DESCRIPTION

[0020] The principles and features of the present invention are described below in conjunction with the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

[0021] like Figure 1 As shown, a high-resolution fault location method for a half-wavelength transmission line includes:

[0022] S1, within a first preset time window before the current moment, the three-phase voltage and three-phase current at the sending end and the receiving end of the half-wavelength transmission line are sampled at a first preset sampling frequency to obtain a first three-phase voltage and current matrix at the sending end and a first three-phase voltage and current matrix at the receiving end; a fault start criterion is calculated according to the first three-phase voltage and current matrix at the sending end and the first three-phase voltage and current matrix at the receiving end; the fault start criterion is compared with a preset fault start threshold to determine whether a fault occurs in the half-wavelength transmission line, if not, S1 is repeatedly executed, if yes, the current moment is recorded as the fault start moment, and S2 to S4 are executed;

[0023] S2, sampling the three-phase voltage and three-phase current at the receiving end at a second preset sampling frequency within a second preset time window before and after the fault initiation moment to obtain a second three-phase voltage and current matrix at the receiving end; synthesizing a line mode reverse traveling wave of the sending end current according to the second three-phase voltage and current matrix at the receiving end;

[0024] S3, performing short-time Fourier transform on the line-mode reverse traveling wave of the sending-end current to obtain the time-frequency distribution of the line-mode reverse traveling wave of the sending-end current; performing second-order transient extraction transformation processing on the time-frequency distribution to obtain a first time-frequency spectrum; intercepting a time-frequency spectrum of a preset frequency band from the first time-frequency spectrum to obtain a second time-frequency spectrum; judging whether there is a sudden change in the arrival time of the second time-frequency spectrum, if so, removing the sudden change in the arrival time of the second time-frequency spectrum, and using the Lagrange interpolation method to fill the removed arrival time in the second time-frequency spectrum to obtain a third time-frequency spectrum, and performing median filtering on the third time-frequency spectrum to obtain a fourth time-frequency spectrum, if not, performing median filtering on the second time-frequency spectrum to obtain a fourth time-frequency spectrum;

[0025] S4, extracting multiple frequency components in the fourth time-frequency spectrum, and finding the time component corresponding to each frequency component; freely combining multiple frequency components and their corresponding time components to obtain multiple pairs of heterofrequency components; writing overdetermined equations according to the wave speed and time of the multiple pairs of heterofrequency components, and using the gradient descent method to find the optimal solution of the overdetermined equation to obtain the fault distance of the half-wavelength transmission line.

[0026] S1 to S4 are described in detail below with reference to examples.

[0027] Figure 2 It is a schematic diagram of a half-wavelength transmission line, specifically a half-wavelength AC transmission line. Both ends of the line are connected to the AC system respectively. The measurement points of the three-phase voltage and the three-phase current are at the sending end M and the receiving end N of the half-wavelength transmission line. In this embodiment, a single-phase grounding fault is set to occur at a position 50% of the distance from the sending end M.

[0028] In S1, the three-phase voltage and the three-phase current at the sending end M and the receiving end N are monitored in real time, and the first preset time window [tt s , t], in the first preset time window with the first preset sampling frequency f l The three-phase voltage and three-phase current at the sending end M and the receiving end N are sampled to obtain the first three-phase voltage and current matrix H1 at the sending end and the first three-phase voltage and current matrix H2 at the receiving end; wherein, t s is the first preset time window length; the first three-phase voltage and current matrix H1 at the sending end and the first three-phase voltage and current matrix H2 at the receiving end are respectively expressed as:

[0029]

[0030] Among them, u A 、u B 、u C and i A 、i B 、i C Indicates that within the first preset time window, the first preset sampling frequency f l The three-phase voltage sequence and three-phase current sequence collected at the sending end M; u AA 、u BB 、u CC and i AA 、i BB 、i CC Indicates that within the first preset time window, the first preset sampling frequency f l The three-phase voltage sequence and three-phase current sequence collected at the receiving end N;

[0031] and Indicates tn / f l The three-phase voltage and three-phase current collected at the sending end M at all times; and Indicates tn / f l The three-phase voltage and three-phase current collected at the receiving end N at all times;

[0032] n+1 represents the first preset sampling frequency f l The number of sampling points in the first preset time window, and n = t s f l In this embodiment, the first preset sampling frequency f l Set to 500kHz, the first preset time window length t s It is set to 1 ms, so the number of sampling points n+1 in the first preset time window is 501.

[0033] In S1, a fault initiation criterion is calculated according to the first three-phase voltage and current matrix H1 at the sending end and the first three-phase voltage and current matrix H2 at the receiving end, which specifically includes the following S11 to S13:

[0034] S11, respectively performing phase mode transformation processing on the first three-phase voltage and current matrix H1 at the sending end and the first three-phase voltage and current matrix H2 at the receiving end, and correspondingly obtaining the first three-phase voltage and current phase mode transformation matrix H1′ at the sending end and the first three-phase voltage and current phase mode transformation matrix H2′ at the receiving end;

[0035] Specifically, the formulas for performing phase mode transformation processing on the first three-phase voltage and current matrix H1 at the sending end and the first three-phase voltage and current matrix H2 at the receiving end are respectively:

[0036] H1′=AH1, H2′=AH2; (3)

[0037] Among them, A represents the phase transformation matrix, and its specific expression is:

[0038]

[0039] In addition, the specific representation of the first three-phase voltage and current phase model transformation matrix H1′ at the sending end and the first three-phase voltage and current phase model transformation matrix H2′ at the receiving end is:

[0040]

[0041] Wherein, u1, u2, u0, i1, i2, i0 represent the sending end voltage α modulus component, the sending end voltage β modulus component, the sending end voltage 0 modulus component, the sending end current α modulus component, the sending end current β modulus component, the sending end current 0 modulus component within the first preset time window respectively;

[0042] Respectively represent tn / f l The sending end α mode voltage, sending end β mode voltage, sending end 0 mode voltage, sending end α mode current, sending end β mode current, sending end 0 mode current at the time, that is, at tn / f l The three-phase voltage and current collected at the sending end M at the moment The phase transformation result of

[0043] u 11 、u 22 、u 00 、i 11 、i 22 、i 00 Respectively represent the α-mode component of the receiving-end voltage, the β-mode component of the receiving-end voltage, the 0-mode component of the receiving-end voltage, the α-mode component of the receiving-end current, the β-mode component of the receiving-end current, and the 0-mode component of the receiving-end current within the first preset time window;

[0044] Respectively represent tn / f l The α-mode voltage, β-mode voltage, 0-mode voltage, α-mode current, β-mode current and 0-mode current at the receiving end at the time tn / f are l The three-phase voltage and current collected at the receiving end N at the moment The phase transformation result of .

[0045] S12, summing up all elements of the α modulus component of the sending-end current and all elements of the β modulus component of the sending-end current in the first three-phase voltage and current phase modulus transformation matrix of the sending-end, to obtain the sum of the αβ modulus components of the sending-end current; summing up all elements of the α modulus component of the receiving-end current and all elements of the β modulus component of the receiving-end current in the first three-phase voltage and current phase modulus transformation matrix of the receiving-end, to obtain the sum of the αβ modulus components of the receiving-end current;

[0046] Specifically, extract the sending-end current α modulus component and the sending-end current β modulus component from the sending-end first three-phase voltage and current phase modulus transformation matrix H1′, that is, extract the row vectors of the fourth and fifth rows of the sending-end first three-phase voltage and current phase modulus transformation matrix H1′; and extract the receiving-end current α modulus component and the receiving-end current β modulus component from the receiving-end first three-phase voltage and current phase modulus transformation matrix H2′, that is, extract the row vectors of the fourth and fifth rows of the receiving-end first three-phase voltage and current phase modulus transformation matrix H2′. Combine the extracted sending-end current α modulus component and the sending-end current β modulus component and the receiving-end current α modulus component and the receiving-end current β modulus component to form the sending-end and receiving-end current αβ modulus matrix G; wherein the sending-end and receiving-end current αβ modulus matrix G is expressed as:

[0047]

[0048] Then, the αβ modulus matrix G of the transmitting and receiving end current is transformed according to formula (8) to obtain the first processing matrix G1 of the αβ modulus of the transmitting and receiving end current:

[0049] G1=BG; (8)

[0050] Wherein, B represents the first transformation matrix. The specific representation of the first transformation matrix B and the first processing matrix G1 of the current αβ modulo the transmitting and receiving ends is:

[0051]

[0052] Next, the first processing matrix G1 of the current αβ modulo the transmitting and receiving ends is transformed according to formula (11) to obtain the second processing matrix G2 of the current αβ modulo the transmitting and receiving ends:

[0053] G2=CG1; (11)

[0054] Wherein, C represents the second transformation matrix. The specific representation of the second transformation matrix C and the second processing matrix G2 of the current αβ modulo the transmitting and receiving ends is:

[0055]

[0056] After the above matrix transformation processing, the sum of the αβ modulus components of the sending-end current and the sum of the αβ modulus components of the receiving-end current can be obtained; among which Δg1 and Δg2 represent the sum of the αβ modulus components of the sending-end current and the sum of the αβ modulus components of the receiving-end current, respectively.

[0057] S13, taking the square root of the square difference between the sum of the αβ modulus components of the sending-end current and the sum of the αβ modulus components of the receiving-end current and dividing the square root by 2 to obtain the fault initiation criterion Δg;

[0058] Among them, the calculation formula of the fault start criterion Δg is:

[0059]

[0060] In S1, the fault start criterion is compared with a preset fault start threshold to determine whether a fault occurs in the half-wavelength transmission line, specifically:

[0061] The fault start criterion Δg and the preset fault start threshold Δg set (Δg set 0.5) can be taken for comparison. If the fault start criterion Δg is greater than the preset fault start threshold Δg set , it is determined that the half-wavelength transmission line has a fault, and the current time t is recorded as the fault start time t p , if the fault start criterion Δg is not greater than the preset fault start threshold Δg set , it is determined that the half-wavelength transmission line has no fault.

[0062] In some other embodiments, the first preset sampling frequency f l Set to 500kHz, the first preset time window length t s Set to 2μs, then under this condition, the number of sampling points n+1 in the first preset time window is 1001; under this condition, the waveform formed by collecting 1001 sampling points is as follows Figure 3 As shown; then the fault start criterion Δg is calculated to be 1.2×10 3 >Δg set , and record the current time t as the fault start time t P , it is determined that the half-wavelength transmission line is in an abnormal working state, and then the subsequent steps are carried out; wherein, the schematic diagram of the start judgment criterion is as follows Figure 4 shown.

[0063] In S2, within a second preset time window before and after the fault initiation moment, the three-phase voltage and three-phase current at the receiving end are sampled at a second preset sampling frequency to obtain a second three-phase voltage and current matrix of the receiving end, specifically:

[0064] The fault start time t P As a benchmark, the second preset time window is intercepted as [t p -t q , t p +t q -1 / f h ], where t q is the second preset time window half length; uses the second preset sampling frequency f h The three-phase voltage and current of the sending end and the receiving end within the second preset time window are sampled; the sampling points within the second preset time window are used to form the second three-phase voltage and current matrix M1 of the sending end and the second three-phase voltage and current matrix M2 of the receiving end; the specific representation forms of the second three-phase voltage and current matrix M1 of the sending end and the second three-phase voltage and current matrix M2 of the receiving end are:

[0065]

[0066]

[0067] Among them, u′ A , u′ B , u′ C and i A ′、i′ B , i′ C respectively represent the sampling frequency f in the second preset time window h The three-phase voltage sequence and three-phase current sequence collected at the sending end M; u′ AA , u′ BB , u′ CC and i A ' A , i′ BB , i′ CC respectively represent the sampling frequency f in the second preset time window h The three-phase voltage sequence and three-phase current sequence collected at the receiving end N;

[0068] and Respectively expressed in t p -k / 2f h The three-phase voltage and three-phase current collected at the sending end M at all times; and Respectively expressed in t p -k / 2f hThe three-phase voltage and three-phase current collected at the receiving end N at all times;

[0069] k represents the second preset sampling frequency f h The number of sampling points in the second preset time window, and k = 2t q f h In this embodiment, the second preset sampling frequency f can be set h =1MHz (sampling interval is 1μs), set the second preset time window half length t q is 5 ms, so the number of sampling points in the second preset time window is 10,000.

[0070] The above is a comprehensive description of "sampling the three-phase voltage and three-phase current at the sending end and the receiving end at a second preset sampling frequency within a second preset time window before and after the fault starts, to obtain a second three-phase voltage and current matrix of the sending end and the receiving end". In actual applications, it is only necessary to sample the three-phase voltage and three-phase current at the receiving end at a second preset sampling frequency within the second preset time window before and after the fault starts, to obtain the second three-phase voltage and current matrix of the receiving end.

[0071] In the S2, the sending-end current line mode reverse traveling wave is synthesized according to the receiving-end second three-phase voltage and current matrix, which specifically includes the following S21 to S24:

[0072] S21, performing phase mode transformation processing on the second three-phase voltage and current matrix at the receiving end to obtain a second three-phase voltage and current phase mode transformation matrix at the receiving end.

[0073] Specifically, according to formula (17), the second three-phase voltage and current matrix M1 at the sending end and the second three-phase voltage and current matrix M2 at the receiving end are subjected to phase mode transformation processing, and the second three-phase voltage and current phase mode transformation matrix M1′ at the sending end and the second three-phase voltage and current phase mode transformation matrix M2′ at the receiving end are obtained accordingly:

[0074] M1′=AM1, M2′=AM2; (17)

[0075] Wherein, A represents the phase mode transformation matrix, which is consistent with formula (4).

[0076] The specific representation of the second three-phase voltage and current phase model transformation matrix M1′ at the sending end and the second three-phase voltage and current phase model transformation matrix M2′ at the receiving end is:

[0077]

[0078] Wherein, u′1, u′2, u′0, i′1, i′2, i′0 represent the sending end voltage α modulus component, the sending end voltage β modulus component, the sending end voltage 0 modulus component, the sending end current α modulus component, the sending end current β modulus component, and the sending end current 0 modulus component in the second preset time window respectively; u′ 11 、u' 22 、u' 00 , i′ 11 、i' 22 、i' 00 Respectively represent the α-mode component of the receiving-end voltage, the β-mode component of the receiving-end voltage, the 0-mode component of the receiving-end voltage, the α-mode component of the receiving-end current, the β-mode component of the receiving-end current, and the 0-mode component of the receiving-end current within the second preset time window;

[0079] Respectively represent t p -k / 2f h The sending end α mode voltage, sending end β mode voltage, sending end 0 mode voltage, sending end α mode current, sending end β mode current, sending end 0 mode current at time t p -k / 2f h The three-phase voltage and current collected at the sending end M at the moment The phase transformation result of Respectively represent t p -k / 2f h The α-mode voltage, β-mode voltage, 0-mode voltage, α-mode current, β-mode current, and 0-mode current of the receiving end at the time t p -k / 2f h The three-phase voltage and current collected at the receiving end N at the moment The phase transformation result of .

[0080] S22, respectively subtract the receiving end voltage α mode component, receiving end voltage β mode component, receiving end current α mode component and receiving end current β mode component in the second half time window of the second three-phase voltage and current phase transformation matrix of the receiving end from the receiving end voltage α mode component, receiving end voltage β mode component, receiving end current α mode component and receiving end current β mode component in the first half time window, and obtain the receiving end voltage α mode fault component, receiving end voltage β mode fault component, receiving end current α mode fault component and receiving end current β mode fault component respectively.

[0081] Specifically, extract the row vectors of the first, second, fourth, and fifth rows of the second three-phase voltage and current phase transformation matrix M1′ at the sending end and the second three-phase voltage and current phase transformation matrix M2′ at the receiving end, and then subtract the elements of the first half time window from the elements of the second half time window to obtain eight new row vectors: Δu′1, Δu′2, Δu′ 11 , Δu′22 , Δi1′, Δi′2, Δi1′1, Δi′ 22 ,in:

[0082]

[0083] Among them, Δu′1 and Δi1′ represent the α-mode fault component of the sending-end voltage and the α-mode fault component of the sending-end current, Δu′2 and Δi′2 represent the β-mode fault component of the sending-end voltage and the β-mode fault component of the sending-end current, and Δu′ 11 , Δi1′1 represents the α-mode fault component of the receiving voltage and the α-mode fault component of the receiving current, Δu′ 22 , Δi′ 22 It represents the β-mode fault component of the receiving-end voltage and the β-mode fault component of the receiving-end current.

[0084] S23, correspondingly add each element of the α-mode fault component of the receiving-end voltage with each element of the β-mode fault component of the receiving-end voltage to obtain the line-mode fault component of the receiving-end voltage; correspondingly add each element of the α-mode fault component of the receiving-end current with each element of the β-mode fault component of the receiving-end current to obtain the line-mode fault component of the receiving-end current.

[0085] Specifically, Δu′1 and Δu′2 are combined to obtain a matrix M1″; Δi1′ and Δi′2 are combined to obtain a matrix M2″; Δu′ 11 and Δu′ 22 Combine them to get the matrix M3″; replace Δi1′1 and Δi′ 22 Combine them to get the matrix M4″, where:

[0086]

[0087] The four matrices M1″, M2″, M3″, and M4″ are transformed according to formula (32) to obtain the line mode fault component ΔU1 of the sending end voltage, the line mode fault component ΔI1 of the sending end current, the line mode fault component ΔU2 of the receiving end voltage, and the line mode fault component ΔI2 of the receiving end current. Then, these four row vectors are combined to obtain a new matrix N as shown in formula (33):

[0088]

[0089]

[0090] Wherein, D represents the third transformation matrix, and its specific expression is as follows:

[0091]

[0092] S24, calculating the sending-end current line-mode reverse traveling wave according to the receiving-end voltage line-mode fault component and the receiving-end current line-mode fault component.

[0093] Specifically, the sending-end voltage line mode fault component ΔU1, the sending-end current line mode fault component ΔI1, the receiving-end voltage line mode fault component ΔU2, and the receiving-end current line mode fault component ΔI2 are extracted from the matrix N and the matrix calculation is performed according to formula (35) to obtain the jth element fu in the sending-end voltage line mode reverse traveling wave TU j And the jth element fi in the sending-end current line mode reverse traveling wave TI j Finally, these elements are combined to obtain the sending-end voltage line mode reverse traveling wave TU and the sending-end current line mode reverse traveling wave TI as shown in equations (36) and (37):

[0094]

[0095] Among them, TU represents the line mode reverse wave of the sending end voltage, fu j represents the jth element in the line mode reverse wave TU of the voltage at the sending end; TI represents the line mode reverse wave of the current at the sending end, fi j represents the jth element in the line mode reverse wave TI of the sending-end current; ΔU 1,j represents the jth element in the line mode fault component ΔU1 of the sending voltage, ΔI 1,j represents the jth element in the line mode fault component ΔI1 of the sending-end current; ΔU 2,j represents the jth element in the line mode fault component ΔU2 of the receiving voltage, ΔI 2,j represents the jth element in the line mode fault component ΔI2 of the receiving-end current; Z represents the wave impedance.

[0096] The above S21~S24 is a comprehensive description of the specific steps of obtaining the sending-end voltage line mode reverse wave TU and the sending-end current line mode reverse wave TI; in actual applications, it is only necessary to obtain the sending-end current line mode reverse wave TI, so it is only necessary to collect and process the data required to obtain the sending-end current line mode reverse wave TI.

[0097] In S3, the sending-end current line mode reverse traveling wave is subjected to short-time Fourier transform to obtain the time-frequency distribution of the sending-end current line mode reverse traveling wave, which is specifically:

[0098] Extract the line mode reverse traveling wave TI of the sending end current, and use the line mode reverse traveling wave TI of the sending end current as the target of short-time Fourier transform (STFT); the waveform of the line mode reverse traveling wave TI of the sending end current is as follows: Figure 5 shown.

[0099] Perform short-time Fourier transform on the sending-end current line mode reverse traveling wave TI, that is, decompose the sending-end current line mode reverse traveling wave TI in two dimensions of time and frequency, and obtain the time-frequency distribution tfr(t,ω) of the sending-end current line mode reverse traveling wave TI, which is expressed as:

[0100]

[0101] Among them, TI(t) is the expression of the line mode reverse wave TI of the sending end current in the time domain. ω is the angular frequency, ω(t-τ) is the sliding window function, e -i(t-τ) is a complex exponential function, which transforms TI(t) from the time domain to the frequency domain. The time-frequency distribution of TI(t) after transformation is as follows: Figure 6 shown.

[0102] The time-frequency distribution is subjected to a second-order transient extraction transformation process to obtain a first time-frequency spectrum, specifically:

[0103] The second-order transient-extracting transform (STET) is performed on the time-frequency distribution tfr(t,ω). The second-order transient-extracting transform (STET) is mainly completed in two steps. First, the frequency expression of the current line mode reverse traveling wave is obtained according to equation (39):

[0104]

[0105] A(ω) and is the amplitude and phase of the sending-end current line mode reverse traveling wave TI in the frequency domain;

[0106] Use Dirac function to get the second-order frequency-dependent model Then the second-order frequency-varying model is obtained by short-time Fourier transform. Frequency domain expression G(t,ω):

[0107]

[0108]

[0109] Where σ is the window function in the short-time Fourier transform The elements in .

[0110] The second-order group delay estimate (2D GD) expression is obtained through G(t,ω) right Transform to get a new expression.

[0111]

[0112] Define a new second-order group delay estimate expression For two second-order group delay estimates The partial derivatives are calculated in the frequency and time dimensions, and then the second-order group delay estimate corrected by the second-order model is obtained according to equation (49):

[0113]

[0114] Among them, Re(·) is the real part function.

[0115] Calculated in The short-time Fourier transform pass To correct the amplitude in equation (41), we get the corrected G [2] (t,ω):

[0116]

[0117] combination and G [2] (t,ω) to obtain the second-order transient extraction transform Te [2] (t,ω).

[0118]

[0119] Where δ(t) is the Dirac function. The first time spectrum S1(t,ω) obtained after the STET algorithm transformation is as follows: Figure 7 shown.

[0120] In the S3, the preset frequency band is specifically a low frequency band of 25 to 170 kHz and a high frequency band of 285 to 425 kHz.

[0121] The ridges of the low frequency band of 25 to 170 kHz and the high frequency band of 285 to 425 kHz in the time spectrum S1 (t, ω) are intercepted to obtain the second time spectrum S2 (t, ω), and then the wave arrival times (WATs) of the second time spectrum S2 (t, ω) are obtained by using the different corresponding times in different frequency bands. In this embodiment, the time spectrum S2 (t, ω) consisting of 30 elements in the low frequency band of 25 to 170 kHz and the high frequency band of 285 to 425 kHz is intercepted for analysis. Among them:

[0122] S1(t,ω)=[tω1 tω2...tω j ...tω k tω k+1 ] 1×(k+1) ; (53)

[0123] S2(t,ω)=[tω′1 tω′2 ... tω′ i ... tω 29 ′ tω 30 ′] 1×30 ; (54)

[0124] In the formula, tω j is the jth arrival time in the first time spectrum S1(t,ω), tω i ′ is the i-th arrival time in the second time spectrum S2(t,ω).

[0125] In S3, determining whether there is a sudden change in the arrival time of the second time spectrum specifically includes:

[0126] Extracting corresponding elements from the line-mode reverse traveling wave of the sending-end current according to each wave arrival time of the second time-frequency spectrum to obtain extracted elements;

[0127] Determine whether all the extracted elements are less than or equal to a preset value, if so, determine that there is no sudden change in the arrival time of the second time spectrum, if not, determine that there is a sudden change in the arrival time of the second time spectrum;

[0128] The arrival time corresponding to the extracted element in the second time-frequency spectrum that is greater than the preset value is the sudden arrival time.

[0129] Specifically, this embodiment determines whether there is a sudden change in the arrival time of the second time spectrum by determining whether there is a sudden change in the line mode reverse traveling wave TI of the sending-end current; wherein, the formula for determining whether there is a sudden change in the line mode reverse traveling wave TI of the sending-end current is:

[0130]

[0131] Where b i is the i-th element in the line mode reverse traveling wave TI of the sending-end current, which corresponds to the arrival time of the second time-frequency spectrum; b ref Indicates a preset value. In this embodiment, b can be set ref = 50. When equation (55) is satisfied, it indicates that there is no mutation in the line mode reverse traveling wave TI of the sending-end current, so it can be determined that there is no mutation in the arrival time of the second time spectrum; otherwise, a mutation occurs.

[0132] In S3, a Lagrange interpolation method is used to fill in the arrival time that is removed in the second time spectrum, specifically:

[0133] Extract the time spectrum S2(t,ω), find the part where the mutation occurs according to formula (55), delete this part first, and then calculate the Lagrangian interpolation polynomial. The Lagrangian interpolation polynomial is expressed as:

[0134]

[0135] Where o is L i The independent variable in (o), o i , o j is the horizontal coordinate of the data point and represents the corresponding time in the reverse traveling wave TI of the current line mode at the sending end; j≠i (oo j ) is (o-o0)(o-o1)…(oo k ), that is, except (oo i All except (oo j ), ∏ j≠i (o i -o j ) is (o i -o0)(o i -o1)…(o i -o k ); At the same time, in this embodiment, j≠i (o i -o j ) is set to a constant to ensure that L i (x i )=1 and L i (x j )=0(i≠j).

[0136] The missing part of the Lagrange interpolation polynomial L i (o) and c i Multiply and sum to get the Lagrange interpolation polynomial P of the missing part k (o).

[0137]

[0138] In the formula, c i It is the corresponding frequency in the line mode reverse wave TI of the sending end current.

[0139] The deleted elements are filled by interpolation through equation (57) to obtain the third time-frequency spectrum S3(t,ω):

[0140] S3(t,ω)=[tω1″tω2″...tω e ″tω (e+1) ″...tω 29 ″tω 30 ″] 1×30 ; (58)

[0141] In the formula, tω e ″、tω (e+1) ″ is the element filled in after Lagrange interpolation.

[0142] In S3, median filtering is performed on the second time-frequency spectrum or the third time-frequency spectrum, specifically:

[0143] Set a filter window of size M0, select an element tω(m) in the time spectrum S2(t,ω) or S3(t,ω), and then expand (M0-1) / 2 elements to the left and right with this element as the center to form a filter window U containing M0 elements as shown in formula (59): M0 :

[0144]

[0145] In the formula, is an element of the extension, and the other elements can be obtained similarly.

[0146] Take the filter window U M0 The median of the elements in , and then arrange these M0 elements in order from small to large to get the new filter window U M1 :

[0147]

[0148] Median is for U M0 Take the median value of the M0 elements in; in this embodiment, the value of M0 is 30.

[0149] According to formula (60), the fourth time-frequency spectrum S4(t,ω) is obtained, and S4(t,ω) is used to obtain a more realistic arrival time. Where:

[0150] S4(t,ω)=[tω1(m) tω2(m)…tω i (m)…tω 29 (m) tω 30 (m)] 1×30 ; (61)

[0151] In the formula, tω i (m) is one of the results after median filtering. The schematic diagram of the low frequency band and high frequency band after median filtering in the fourth time spectrum S4(t,ω) is as follows: Figure 8 , Fig. 9 shown.

[0152] In the step S4, multiple frequency components in the fourth time-frequency spectrum are extracted, and the time components corresponding to the respective frequency components are found, which specifically includes the following steps S401 to S405:

[0153] S401, extracting a plurality of initial frequency components from the fourth time-frequency spectrum S4(t,ω).

[0154] In this embodiment, 30 initial frequency components are extracted from the fourth time-frequency spectrum S4 (t, ω).

[0155] S402: sharpen each initial frequency component respectively to obtain a corresponding frequency component.

[0156] Specifically, the corresponding frequency component is obtained according to formula (62);

[0157] f HLx =f hlx -f m ; (62)

[0158] Among them, f HLx represents the xth frequency component, f hlx represents the xth initial frequency component, f m represents the preset fundamental frequency, x=1, 2, ..., a, a represents the total number of initial frequency components extracted from the fourth time-frequency spectrum S4 (t, ω), and also represents the total number of frequency components; in this embodiment, a=30, f m =20kHz. Each frequency component corresponds to a small frequency band.

[0159] Combine all frequency components to form a frequency component matrix M HL , the frequency component matrix M HL It is expressed as:

[0160] M HL =[f HL1 f HL2 ...f HLx ...f HL(a-1) f HLa ] 1×a (63)

[0161] S403, extracting the frequency value of each frequency component respectively to obtain a corresponding small frequency band frequency sequence.

[0162] Specifically, the small frequency band frequency sequence corresponding to the xth frequency component is expressed as:

[0163]

[0164] in, Represents the rth frequency value in the xth frequency component, r = 1, 2, ..., e, and e represents the total number of frequency values ​​in a small frequency band.

[0165] The small-band frequency sequences corresponding to all frequency components are combined to form a small-band frequency matrix M A , the small frequency band frequency matrix M A It is expressed as:

[0166]

[0167] Among them, the small frequency band frequency matrix M A The row vector in is the corresponding small frequency band frequency sequence.

[0168] S404, respectively obtain the small frequency band time sequence corresponding to each small frequency band frequency sequence.

[0169] Specifically, each small frequency band has a frequency value and its corresponding time value. Formula (65) is the frequency value corresponding to each small frequency band. Then the time value corresponding to each small frequency band can be expressed as:

[0170]

[0171] Among them, M a represents the small frequency band time matrix; t HLx represents the x-th small frequency band time series, t HLx With f HLx Corresponding to; t HLxr Represents the rth time value in the xth small frequency band time series; and correspond.

[0172] S405, extracting the maximum time value in each small frequency band time series respectively, to obtain the time component corresponding to each frequency component.

[0173] Specifically, the time component corresponding to each frequency component is expressed as:

[0174]

[0175] in, is the maximum time value in the x-th small frequency band time series, indicating the time component corresponding to the x-th frequency component, that is, the maximum time value in each small frequency band time series is the time component corresponding to the corresponding frequency component.

[0176] Combine the time components corresponding to all frequency components to form a time matrix The time matrix It is expressed as:

[0177]

[0178] In this embodiment, 15 frequencies are selected in the low frequency band and the high frequency band, and the time when each frequency reaches the measurement point (ie, the arrival time) is shown in Table 1.

[0179] Table 1 The time for each frequency of low-frequency and high-frequency components to reach the measurement point

[0180]

[0181] In S4, multiple frequency components and their corresponding time components are freely combined to obtain multiple pairs of different frequency components, that is, multiple frequency components are arbitrarily combined in pairs, and their corresponding time components will also be combined with the frequency component combination; wherein, the free combination expression is as follows:

[0182]

[0183] Wherein, s represents the total logarithm of heterofrequency components, C(·) represents the free combination function, and a represents the total number of frequency components. In this embodiment, a=30.

[0184] In S4, an overdetermined equation is written according to the wave velocities of multiple pairs of heterofrequency components, specifically including S406 to S408:

[0185] S406, according to the time components corresponding to the two frequency components in each pair of hetero-frequency components, the time of each pair of hetero-frequency components is calculated, and the time of all hetero-frequency components is combined to obtain the overdetermined equation time matrix.

[0186] Specifically, any pair of hetero-frequency components is composed of any two frequency components extracted above, and the frequency component with a higher frequency in the hetero-frequency components is defined as a high-frequency component, and the frequency component with a lower frequency in the hetero-frequency components is defined as a low-frequency component. The time matrix T of the overdetermined equation is expressed as:

[0187] T=[t1 t2 ... t s′ ... t s-1 t s ] 1×s ; (70)

[0188] Among them, t s′ is the s′th element in the time matrix T of the overdetermined equation, representing the time of the s′th pair of hetero-frequency components. The time value corresponding to the s′th pair of hetero-frequency components is the difference between the time components corresponding to the two frequency components that make up the s′th pair of hetero-frequency components, that is, t s′ =t ls′ -t hs′ , t hs′ represents the time component corresponding to the high-frequency component in the s′th pair of heterofrequency components, t ls′ represents the time component corresponding to the low-frequency component in the s′th pair of heterofrequency components, t hs′ and t ls′ is an element in formula (68); s′=1,2,…,s.

[0189] S407, according to the wave velocities of the two frequency components in each pair of different frequency components, the wave velocities of each pair of different frequency components are calculated correspondingly, and the wave velocities of all different frequency components are combined to obtain the overdetermined equation wave velocity matrix.

[0190] Specifically, the wave velocity of the frequency component is calculated according to formula (71):

[0191]

[0192] Among them, v x represents the wave velocity of the xth frequency component, L x is the inductance of the half-wavelength transmission line at the xth frequency component, C x is the capacitance value of the half-wavelength transmission line at the xth frequency component.

[0193] In each pair of heterofrequency components, the wave velocity corresponding to the high-frequency component is the high-frequency wave velocity, and the wave velocity corresponding to the low-frequency component is the low-frequency wave velocity. The calculation formula for the wave velocity of the heterofrequency component is:

[0194]

[0195] Specific, vs. ′ represents the wave velocity of the s′th pair of heterofrequency components, v hs′ represents the wave velocity of the high-frequency component in the s′th pair of heterofrequency components, that is, the high-frequency wave velocity, v ls′ It represents the wave velocity of the low-frequency component in the s′th pair of heterofrequency components, that is, the low-frequency wave velocity.

[0196] The wave velocities of all different frequency components are combined to obtain the overdetermined equation wave velocity matrix; the overdetermined equation wave velocity matrix is ​​expressed as:

[0197] v a =[v1 v2 ... v s′ ... v s-1 v s ] 1×s ; (73)

[0198] Among them, v a represents the wave velocity matrix of the overdetermined equation.

[0199] S408: construct an overdetermined equation about the fault distance matrix according to the overdetermined equation time matrix and the overdetermined equation wave velocity matrix. Specifically, the overdetermined equation is expressed as:

[0200] v a d=T; (74)

[0201] d=[d1 d2...d s′ ...d s-1 d s ] 1×s ; (75)

[0202] d represents the fault distance matrix to be determined, d s′represents the s′th element in the fault distance matrix.

[0203] In S4, the gradient descent method is used to find the optimal solution of the overdetermined equation, which specifically includes the following S409 to S412:

[0204] S409, obtaining a fault distance function according to the overdetermined equation; the fault distance function is expressed as:

[0205] f(d)=v a dT. (76)

[0206] S410, setting an initial point d0, performing gradient transformation on the fault distance function, and obtaining a gradient matrix of the initial point d0; wherein the formula for performing gradient transformation on the fault distance function is:

[0207]

[0208] Specifically, is a negative gradient; the gradient matrix of the initial point d0 is expressed as:

[0209] D′=[d′1 d′2 ... d′ s′ ... d′ s-1 d′ s ] 1×s ; (78)

[0210] D′ represents the gradient matrix of the initial point d0, d s ' ′ Represents the s′th element in the gradient matrix of the initial point d0.

[0211] S411, iterating the fault distance function from the initial point d0, and in each iteration, the fault distance function moves a preset step length in the direction of the fastest descent speed, and records the two iteration values ​​before and after the iteration; wherein the relationship between the two iteration values ​​before and after the iteration is:

[0212]

[0213] Specifically, d″ s′ and d″ s′-1 represents two iteration values ​​before and after the iteration, γ represents the preset step size, and in this embodiment, γ=0.0001.

[0214] S412, setting an iteration threshold ε, and stopping the iteration when the absolute value of the difference between the two iteration values ​​before and after the iteration is less than the iteration threshold ε, and the point corresponding to the last iteration is the fault distance of the half-wavelength transmission line. The absolute value of the difference between the two iteration values ​​before and after the iteration is less than the iteration threshold ε is expressed as:

[0215] |d″ s′ -d″ s′-1 |<ε. (80)

[0216] In this embodiment, a=30, and 435 pairs of heterodyne components are obtained according to formula (69). The overdetermined equation is written according to formula (74), and the final fault distance is 1500.428 km, which is 428 m different from the fault distance set in this embodiment. The fault distance of the half-wavelength AC transmission line is calculated very accurately.

[0217] The present invention provides a high-resolution fault distance measurement method for a half-wavelength power transmission line, which can accurately locate the fault position without the need for double-end synchronization. At the same time, a second-order transient extraction transformation algorithm with high time-frequency resolution is used to process the time-frequency distribution of a short-time Fourier transform to obtain an energy-concentrated time-frequency spectrum, which can more accurately obtain the independent arrival time of each frequency component of the traveling wave, thereby reducing the distance measurement error caused by the "uncertainty" principle. The overdetermined equation and the gradient descent method are used to estimate the fault position, thereby further reducing the random error, and generally speaking, the distance measurement error can be controlled below 1 km. In addition, the distance measurement performance of the present invention is not affected by the transition resistance.

[0218] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A high-resolution fault location method for half-wavelength transmission lines, characterized in that: include: S1, within a first preset time window before the current moment, sampling the three-phase voltage and three-phase current at the sending end and the receiving end of the half-wavelength transmission line at a first preset sampling frequency to obtain a first three-phase voltage and current matrix at the sending end and a first three-phase voltage and current matrix at the receiving end; calculating a fault initiation criterion according to the first three-phase voltage and current matrix at the sending end and the first three-phase voltage and current matrix at the receiving end; Compare the fault start criterion with a preset fault start threshold to determine whether the half-wavelength transmission line has a fault. If not, repeat S1. If yes, record the current moment as the fault start moment, and execute S2 to S4. S2, sampling the three-phase voltage and three-phase current at the receiving end at a second preset sampling frequency within a second preset time window before and after the fault initiation moment, to obtain a second three-phase voltage and current matrix at the receiving end; Synthesize a sending-end current line mode reverse traveling wave according to the receiving-end second three-phase voltage and current matrix; S3, performing short-time Fourier transform on the line-mode reverse traveling wave of the sending-end current to obtain the time-frequency distribution of the line-mode reverse traveling wave of the sending-end current; performing second-order transient extraction transformation processing on the time-frequency distribution to obtain a first time-frequency spectrum; intercepting a time-frequency spectrum of a preset frequency band from the first time-frequency spectrum to obtain a second time-frequency spectrum; judging whether there is a sudden change in the arrival time of the second time-frequency spectrum, if so, removing the sudden change in the arrival time of the second time-frequency spectrum, and using the Lagrange interpolation method to fill the removed arrival time in the second time-frequency spectrum to obtain a third time-frequency spectrum, and performing median filtering on the third time-frequency spectrum to obtain a fourth time-frequency spectrum, if not, performing median filtering on the second time-frequency spectrum to obtain a fourth time-frequency spectrum; S4, extracting multiple frequency components in the fourth time-frequency spectrum, and finding the time component corresponding to each frequency component; freely combining multiple frequency components and their corresponding time components to obtain multiple pairs of heterofrequency components; writing overdetermined equations according to the wave speed and time of the multiple pairs of heterofrequency components, and using the gradient descent method to find the optimal solution of the overdetermined equation to obtain the fault distance of the half-wavelength transmission line.

2. The high-resolution fault location method for half-wavelength transmission lines according to claim 1, characterized in that: In S1, a fault start criterion is calculated according to the first three-phase voltage and current matrix of the sending end and the first three-phase voltage and current matrix of the receiving end, which specifically includes: Respectively performing phase-mode transformation processing on the first three-phase voltage and current matrix of the sending end and the first three-phase voltage and current matrix of the receiving end, and correspondingly obtaining the first three-phase voltage and current phase-mode transformation matrix of the sending end and the first three-phase voltage and current phase-mode transformation matrix of the receiving end; Accumulate all elements of the α modulus component of the sending-end current and all elements of the β modulus component of the sending-end current in the first three-phase voltage and current phase modulus transformation matrix of the sending-end to obtain the sum of the αβ modulus components of the sending-end current; accumulate all elements of the α modulus component of the receiving-end current and all elements of the β modulus component of the receiving-end current in the first three-phase voltage and current phase modulus transformation matrix of the receiving-end to obtain the sum of the αβ modulus components of the receiving-end current; The fault start criterion is obtained by taking the square root of the square difference between the sum of the αβ modulus components of the sending-end current and the sum of the αβ modulus components of the receiving-end current and dividing the square root by 2.

3. The high-resolution fault location method for half-wavelength transmission lines according to claim 1, characterized in that: In S1, the fault start criterion is compared with a preset fault start threshold to determine whether a fault occurs in the half-wavelength transmission line, specifically: The fault start criterion is compared with a preset fault start threshold. If the fault start criterion is greater than the preset fault start threshold, it is determined that a fault has occurred in the half-wavelength transmission line. If the fault start criterion is not greater than the preset fault start threshold, it is determined that no fault has occurred in the half-wavelength transmission line.

4. The high-resolution fault location method for half-wavelength transmission lines according to claim 1, characterized in that: In S2, synthesizing a sending-end current line mode reverse traveling wave according to the receiving-end second three-phase voltage and current matrix specifically includes: Performing phase mode transformation processing on the second three-phase voltage and current matrix of the receiving end to obtain a second three-phase voltage and current phase mode transformation matrix of the receiving end; Respectively subtract the receiving end voltage α mode component, receiving end voltage β mode component, receiving end current α mode component and receiving end current β mode component in the second half time window of the receiving end second three-phase voltage and current phase mode transformation matrix from the receiving end voltage α mode component, receiving end voltage β mode component, receiving end current α mode component and receiving end current β mode component in the first half time window to obtain the receiving end voltage α mode fault component, receiving end voltage β mode fault component, receiving end current α mode fault component and receiving end current β mode fault component; Adding correspondingly each element of the receiving-end voltage α-mode fault component to each element of the receiving-end voltage β-mode fault component to obtain the receiving-end voltage line mode fault component; adding correspondingly each element of the receiving-end current α-mode fault component to each element of the receiving-end current β-mode fault component to obtain the receiving-end current line mode fault component; The sending-end current line-mode reverse traveling wave is calculated according to the receiving-end voltage line-mode fault component and the receiving-end current line-mode fault component.

5. The high-resolution fault location method for half-wavelength transmission lines according to claim 4, characterized in that: The formula for calculating the line mode reverse traveling wave of the sending-end current is: Wherein, TI represents the line mode reverse wave of the sending end current, fi j represents the jth element in the line mode reverse wave of the sending-end current, k represents the number of sampling points in the second preset time window, ΔU 2,j represents the jth element in the line mode fault component of the receiving voltage, ΔI 2,j represents the jth element in the line mode fault component of the receiving end current, and Z represents the wave impedance.

6. The high-resolution fault location method for half-wavelength transmission lines according to claim 1, characterized in that: In the S3, the preset frequency band is specifically a low frequency band of 25 to 170 kHz and a high frequency band of 285 to 425 kHz.

7. The high-resolution fault location method for half-wavelength transmission lines according to claim 1, characterized in that: In S3, determining whether there is a sudden change in the arrival time of the second time spectrum specifically includes: Extracting corresponding elements from the line-mode reverse traveling wave of the sending-end current according to each wave arrival time of the second time-frequency spectrum to obtain extracted elements; Determine whether all the extracted elements are less than or equal to a preset value, if so, determine that there is no sudden change in the arrival time of the second time spectrum, if not, determine that there is a sudden change in the arrival time of the second time spectrum; The arrival time corresponding to the extracted element in the second time-frequency spectrum that is greater than the preset value is the sudden arrival time.

8. The high-resolution fault location method for half-wavelength transmission lines according to claim 1, characterized in that: In S4, extracting multiple frequency components in the fourth time-frequency spectrum and finding the time component corresponding to each frequency component specifically includes: Extracting a plurality of initial frequency components from the fourth time spectrum; Sharpen each initial frequency component respectively to obtain the corresponding frequency component; Extract the frequency value of each frequency component respectively to obtain the corresponding small frequency band frequency sequence; Obtain the small frequency band time series corresponding to each small frequency band frequency series respectively; The maximum time value in each small frequency band time series is extracted respectively to obtain the time component corresponding to each frequency component.

9. The high-resolution fault location method for half-wavelength transmission lines according to claim 1, characterized in that: In S4, an overdetermined equation is written according to the wave velocities of multiple pairs of different frequency components, specifically including: According to the time components corresponding to the two frequency components in each pair of hetero-frequency components, the time of each pair of hetero-frequency components is calculated, and the time of all hetero-frequency components is combined to obtain the time matrix of the overdetermined equation; According to the wave velocities of the two frequency components in each pair of hetero-frequency components, the wave velocities of each pair of hetero-frequency components are calculated accordingly, and the wave velocities of all hetero-frequency components are combined to obtain the wave velocity matrix of the overdetermined equation; An overdetermined equation about a fault distance matrix is ​​constructed according to the overdetermined equation time matrix and the overdetermined equation wave velocity matrix; the overdetermined equation is expressed as: v a d=T; Among them, v a represents the wave velocity matrix of the overdetermined equation, T represents the time matrix of the overdetermined equation, and d represents the fault distance matrix to be determined; specifically, v a =[v1 v2 ... v s′ ... in s-1 v s ] 1×s , v s′ represents the wave velocity of the s′th pair of heterofrequency components, v hs′ represents the wave velocity of the high-frequency component in the s′th pair of heterofrequency components, v ls′ represents the wave velocity of the low-frequency component in the s′th pair of hetero-frequency components, and s represents the total number of pairs of hetero-frequency components; T=[t1 t2 ... t s′ ... t s-1 t s ] 1×s ,t s′ =t ls′ -t hs′ ; t s′ represents the time of the s′th pair of heterofrequency components, t hs′ represents the time component corresponding to the high-frequency component in the s′th pair of heterofrequency components, t ls′ represents the time component corresponding to the low-frequency component in the s′th pair of hetero-frequency components; d=[d1 d2...d s′ ...d s-1 d s ] 1×s ; d s′ represents the s′th element in the fault distance matrix.

10. The high-resolution fault location method for half-wavelength transmission lines according to claim 9, characterized in that: In S4, the gradient descent method is used to find the optimal solution of the overdetermined equation, which specifically includes: The fault distance function is obtained according to the overdetermined equation; wherein the fault distance function is expressed as: f(d)=v a d-T; An initial point is set, and the fault distance function is gradient transformed to obtain a gradient matrix of the initial point; wherein the formula for gradient transformation of the fault distance function and the gradient matrix of the initial point are respectively expressed as: D=[d1' d'2 ... d′ s′ ... d s ' -1 d s '] 1×s ; Specifically, is a negative gradient, D′ represents the gradient matrix of the initial point, d′ s′ The s′th element in the gradient matrix representing the initial point; The fault distance function is iterated starting from the initial point, and the fault distance function moves a preset step length in the direction of the fastest descent speed in each iteration, and two iteration values ​​before and after the iteration are recorded; wherein the relationship between the two iteration values ​​before and after the iteration is: Specifically, d″ s′ and d″ s′-1 represents two iteration values ​​before and after the iteration, and γ represents the preset step size; An iteration threshold is set, and the iteration is stopped when the absolute value of the difference between two iteration values ​​before and after the iteration is less than the iteration threshold. The point corresponding to the last iteration is the fault distance of the half-wavelength transmission line.

Images