A fault location method and system for a multi-terminal hybrid DC power transmission system

Abstract

The application relates to a fault positioning method and system of a multi-terminal hybrid DC power transmission system, which comprises the following steps: calibrating a fault time and improving a Bergeron model; intercepting a theoretical current traveling wave of a preset time window; adopting a time re-distribution multi-synchronous compression transformation method based on wavelet transformation to process waveforms of the intercepted theoretical current traveling wave at low, medium and high frequencies, combining random forests to correct the waveforms, and obtaining a reconstructed current traveling wave; adopting a weighted least square method to fit the reconstructed current traveling wave, and obtaining a fitted current traveling wave; constructing a waveform reference library comprising multiple interval reference current traveling waves according to the fitted current traveling wave; calculating a current traveling wave at any fault position, calculating the similarity between the current traveling wave and each interval reference current traveling wave in the waveform reference library based on a wave arrival time and an amplitude, obtaining a comprehensive similarity, and positioning a fault interval according to the comprehensive similarity.

Description

A fault location method and system for a multi-terminal hybrid DC transmission system Technical Field

[0001] This invention relates to the field of power grid fault location, and specifically to a fault location method and system for a multi-terminal hybrid DC transmission system. Background Technology

[0002] In recent years, multi-terminal hybrid DC transmission systems have emerged, employing large-capacity grid-commutated converters (LCCs) as the centralized power sending end on the rectifier side and multiple modular multilevel converters (MMCs) as the multi-terminal receiving end on the inverter side. These systems combine the flexibility and speed of flexible DC control with the low loss and low cost of conventional DC. Structurally, multiple flexible DC converter stations are connected to the LCCs via DC lines in a branching manner, forming a "one-to-many" tree-like structure. Therefore, multi-terminal hybrid DC transmission systems fully utilize the cost advantages of LCC converter technology and the performance advantages of MMC converter technology, demonstrating broad application prospects. However, there are currently few practical engineering applications of multi-terminal hybrid DC transmission systems because: on the one hand, for such multi-branched multi-terminal hybrid DC transmission systems, since the transmission lines are not directly connected via reactors, the polarity and amplitude characteristics of the fault traveling wave will be more complex; on the other hand, existing technologies need to identify the difficult-to-distinguish second (or even third) real reflected waves and construct well-defined ranging equations, but theoretically reconstructing the fault wave process is quite difficult for both traditional point-to-point DC transmission systems and multi-terminal hybrid DC transmission systems.

[0003] Against this backdrop, relay protection and fault location technology based on traveling waves has attracted widespread attention in academia. Some scholars have constructed time-domain convolutional power, extracted specific frequency bands of traveling waves using wavelet decomposition, and calculated the convolutional power and transient energy of different frequency bands to achieve fault identification and protection. Other scholars have analyzed the refraction / reflection characteristics of fault traveling waves at different line terminals, deducing that the first peak time of the line-mode fault component voltage in intra-zone faults is shorter than that in extra-zone faults and is unaffected by transition resistance and fault type, thus proposing a protection method for ultra-high-speed DC lines. However, in multi-terminal hybrid DC transmission systems, there are multiple transmission lines directly connected without smoothing reactors, making it difficult to quantitatively analyze the fault wave process. Therefore, research can only focus on protection issues, which has certain limitations. Some scholars have also used the arrival times of the first two wavefronts of the line / zero mode for fault location in single-pole grounding faults, and extracted the arrival times of the first three wavefronts of the line-mode traveling wave for fault location in inter-pole short-circuit faults. A common problem with the above methods is that existing technologies face certain difficulties in extracting and distinguishing reflected wavefronts, especially since the complex reflections caused by high-impedance faults significantly interfere with the intrinsic propagation pattern of traveling waves, further contributing to errors. Furthermore, near-field faults, due to their complex reflected wavefronts, significantly reduce the speed of protection and the real-time performance of ranging. Summary of the Invention

[0004] This invention provides a fault location method and system for a multi-terminal hybrid DC transmission system to solve at least one of the above-mentioned technical problems.

[0005] The technical solution of the present invention to solve the above-mentioned technical problems is as follows: A fault location method for a multi-terminal hybrid DC transmission system, comprising:

[0006] S1, detect the real-time current traveling wave of the transmission line in the hybrid DC transmission system, determine whether the transmission line has a fault based on the real-time current traveling wave, and mark the fault time when the transmission line has a fault; and, considering line dispersion, improve the traditional Berylon model to establish an improved Berylon model that considers different fault locations.

[0007] S2, based on the improved Berylon model, obtain the theoretical current traveling wave under different fault conditions, and extract the theoretical current traveling wave of a preset time window according to the fault time.

[0008] S3. The time redistribution multi-synchronization compression transform method based on wavelet transform is used to process the intercepted theoretical current traveling wave at low, medium and high frequencies, and the waveform is corrected by combining random forest to obtain the reconstructed current traveling wave at low, medium and high frequencies.

[0009] S4. Weighted least squares method is used to fit the reconstructed current traveling wave at low, medium and high frequencies to obtain the fitted current traveling wave.

[0010] S5, construct a waveform reference library including multiple interval reference current traveling waves based on the fitted current traveling wave;

[0011] S6. Calculate the current traveling wave at any fault location. Based on the arrival time and amplitude, calculate the similarity between the current traveling wave and the reference current traveling waves in each interval of the waveform reference library to obtain the comprehensive similarity. Then, locate the fault interval based on the comprehensive similarity.

[0012] Based on the above-mentioned fault location method for a multi-terminal hybrid DC transmission system, the present invention also provides a fault location system for a multi-terminal hybrid DC transmission system.

[0013] A fault location system for a multi-terminal hybrid DC transmission system includes:

[0014] The fault detection and modeling module is used to detect the real-time current traveling wave of the transmission line in the hybrid DC transmission system, and to determine whether the transmission line has a fault based on the real-time current traveling wave, and to mark the fault time when the transmission line has a fault; and to improve the traditional Beryllon model by considering line dispersion, so as to establish an improved Beryllon model that considers different fault locations.

[0015] The theoretical calculation module is used to obtain the theoretical current traveling wave under different fault conditions based on the improved Berylone model, and to extract the theoretical current traveling wave of a preset time window according to the fault time.

[0016] The transformation and correction module is used to process the intercepted theoretical current traveling wave at low, medium and high frequencies using a wavelet transform-based time redistribution multi-synchronous compression transform method, and to perform waveform correction in combination with random forest to obtain the reconstructed current traveling wave at low, medium and high frequencies.

[0017] The waveform fitting module is used to perform weighted least squares fitting on the reconstructed current traveling wave at low, medium and high frequencies to obtain the fitted current traveling wave.

[0018] A waveform reference library construction module is used to construct a waveform reference library including multiple interval reference current traveling waves based on the fitted current traveling wave;

[0019] The tracking and ranging module is used to calculate the current traveling wave at any fault location, calculate the similarity between the current traveling wave and the reference current traveling waves in each interval of the waveform reference library based on the wave arrival time and amplitude, obtain the comprehensive similarity, and locate the fault interval based on the comprehensive similarity.

[0020] The beneficial effects of this invention are as follows: The fault location method and system for a multi-terminal hybrid DC transmission system improves upon the traditional Berylon model, enabling it to possess complete distributed parameter line characterization capabilities and theoretical wave process deduction capabilities under hypothetical fault scenarios. This allows it to calculate line dispersion at different frequencies. The time-frequency distribution of wavelet variations is processed using a time-redistribution multi-synchronous compression transform algorithm to obtain the time-frequency spectrum of energy concentration at a fixed frequency, accurately acquiring the arrival time at that frequency. This reduces the errors caused by traditional time-frequency analysis methods such as wavelet transform and Fourier transform when processing strong frequency-varying signals. Furthermore, the accuracy is further improved after random forest correction. Simultaneously, the arrival time group is reconstructed to obtain reconstructed current traveling waves, improving tracking accuracy. The reconstructed current traveling waves at different fault locations are integrated to obtain a reference waveform library. The fault location is estimated using matching and tracking principles. Overall, the ranging error can be controlled below 1 km. Additionally, the ranging performance of this invention is not affected by transition resistance. Attached Figure Description

[0021] Figure 1 is a flowchart of a fault location method for a multi-terminal hybrid DC transmission system according to the present invention.

[0022] Figure 2 is a schematic diagram of an exemplary three-terminal hybrid DC transmission system;

[0023] Figure 3 shows the line in Figure 2. exist ms, A schematic diagram of the concentrated line parameters when a single-pole ground fault occurs.

[0024] Figure 4 shows the line in Figure 2. exist ms, A schematic diagram of the concentrated line parameters when a single-pole ground fault occurs.

[0025] Figure 5. Schematic diagram of theoretical current traveling wave normalization;

[0026] Figure 6 shows the MWT results and its enlarged schematic diagram;

[0027] Figure 7 shows the TSST results and its magnified schematic diagram;

[0028] Figure 8 shows the WTMSST results and its magnified schematic diagram;

[0029] Figure 9 is a schematic diagram of current traveling wave arrival time extraction;

[0030] Figure 10 is a schematic diagram of the reconstructed correction current traveling wave;

[0031] Figure 11 is a schematic diagram of the fitted reconstructed current traveling wave;

[0032] Figure 12 is a structural block diagram of a fault location system for a multi-terminal hybrid DC transmission system according to the present invention. Detailed Implementation

[0033] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0034] As shown in Figure 1, a fault location method for a multi-terminal hybrid DC transmission system includes:

[0035] S1, detect the real-time current traveling wave of the transmission line in the hybrid DC transmission system, determine whether the transmission line has a fault based on the real-time current traveling wave, and mark the fault time when the transmission line has a fault; and, considering line dispersion, improve the traditional Berylon model to establish an improved Berylon model that considers different fault locations.

[0036] S2, based on the improved Berylon model, obtain the theoretical current traveling wave under different fault conditions, and extract the theoretical current traveling wave of a preset time window according to the fault time.

[0037] S3. The time redistribution multi-synchronization compression transform method based on wavelet transform is used to process the intercepted theoretical current traveling wave at low, medium and high frequencies, and the waveform is corrected by combining random forest to obtain the reconstructed current traveling wave at low, medium and high frequencies.

[0038] S4. Weighted least squares method is used to fit the reconstructed current traveling wave at low, medium and high frequencies to obtain the fitted current traveling wave.

[0039] S5, construct a waveform reference library including multiple interval reference current traveling waves based on the fitted current traveling wave;

[0040] S6. Calculate the current traveling wave at any fault location. Based on the arrival time and amplitude, calculate the similarity between the current traveling wave and the reference current traveling waves in each interval of the waveform reference library to obtain the comprehensive similarity. Then, locate the fault interval based on the comprehensive similarity.

[0041] The following is a detailed explanation of the fault location method for a multi-terminal hybrid DC transmission system according to the present invention.

[0042] Figure 2 is a schematic diagram of an exemplary three-terminal hybrid DC transmission system, specifically the Kunliulong ±800 kV three-terminal hybrid DC transmission system, with a transmission line length of 1489 km and equipped with a traveling wave detection device. At the rectifier side of the line, the sampling frequency is... A 1MHz frequency was set for acquiring the positive and negative voltages and currents of the transmission line. Based on Figure 2, the following theoretical analysis is performed:

[0043] I: Traveling Wave Theory

[0044] The voltage-current relationship of a bipolar DC transmission line can be expressed by the following set of first-order partial differential equations:

[0045] ; (1)

[0046] In the formula, These are the positive and negative voltages of the transmission line. These are the positive and negative currents of the transmission line. and Let be the series inductance matrix and parallel capacitance matrix per unit length of the transmission line. Taking the partial derivative of equation (1) yields the wave equation of the transmission line:

[0047] ; (2)

[0048] in, and It can be represented as:

[0049] ; (3)

[0050] In the formula, and For self-inductance, and Mutual inductance, and It is a self-capacitance. and They are mutual capacitances, and in a bipolar circuit, , .

[0051] Because electromagnetic coupling exists between the positive and negative terminals, the following formula is used for decoupling:

[0052] ; (4)

[0053] In the formula, The voltages on the line mode and zero mode are given. For the current in the linear mode and zero mode, Let be the transformation matrix.

[0054] Combining equations (1) and (4), we get:

[0055] ; (5)

[0056] in, and It can be represented as:

[0057] ; (6)

[0058] In the formula, and Let be the unit-length series inductance matrix and parallel capacitance matrix on the line mode and zero mode of the bipolar circuit. Therefore, the traveling wave zero-mode velocity in the bipolar circuit... and linear mode wave speed for:

[0059] ; (7)

[0060] II: Beryllon

[0061] Berylone equivalent circuit:

[0062] The Beryllon method is a technique that uses the concept of mixed waves to analyze the multiple reflections and refractions of waves; its essence remains the solution to the wave equation. Its core principle is to treat distributed parameter elements as equivalent to lumped parameter elements, and then use the numerical values ​​of the lumped parameters to calculate the wave process along the line.

[0063] Capacitor: Lumped parameter capacitor ,exist At that moment, the beginning ( The voltage on the side is , end ( The voltage on the side is The current between the beginning and the end is The voltage across the capacitor and the current flowing through the capacitor The following relationship exists:

[0064] ; (8)

[0065] from arrive Integrating, we get:

[0066] ; (9)

[0067] Approximately:

[0068] ; (10)

[0069] To further simplify the calculation, we can obtain from equation (10):

[0070] ; (11)

[0071] Combining equations (10) and (11), we get:

[0072] ;(12)

[0073] Inductance: Lumped parameter inductance Based on the derivation method of lumped parameter capacitors, the voltage drop across the inductor and the current flowing through it... The following relationship exists:

[0074] ; (13)

[0075] Transmission line (considering line loss): Assuming the transmission line... The wave impedance is , length is .

[0076] According to the propagation law of mixed waves, Side Mixed waves emitted at all times After time Arrived later side( For traveling waves in transmission lines Transmission time in , (for traveling wave speed), therefore in transmission lines In China, according to time The mixed wave on the side can be calculated side The mixed wave at time, i.e. side Voltage at time and current It can be by side Voltage at time and current express; side The mixed wave at time t is represented as:

[0077] ;(14)

[0078] In the formula, for side Mixed waves at time, for side Mixed waves at time, for side Voltage at time, for side Current at any moment for side Voltage at time, for side Current at any given moment; For transmission lines exist The decay coefficient at time;

[0079] For transmission lines exist Decay coefficient at time Performing a complex frequency domain transformation yields the complex frequency domain expression for the attenuation coefficient, which is:

[0080] ; (15)

[0081] In the formula, For transmission lines The attenuation coefficient in the complex frequency domain is represented as follows: , , and Transmission lines The unit resistance, unit inductance, unit conductance, and unit capacitance; s is a complex variable in the complex frequency domain; the exponential function reflects the delay and distortion during the propagation of the traveling wave, while... , , and These are all frequency-varying parameters, resulting in different downlink wave velocities at different frequencies. It cannot be directly expressed mathematically, so approximations are often used.

[0082] Using the exponential function representing delay in the complex frequency domain By transforming the complex frequency domain expression of the attenuation coefficient, we obtain the complex frequency domain expression of the attenuation coefficient based on distortion and attenuation (i.e., using an exponential function in the complex frequency domain). To represent the delay, so as to process equation (15), and the complex frequency domain expression of the attenuation coefficient based on distortion and attenuation is:

[0083] ; (16)

[0084] In the formula, This refers to the distortion and attenuation that occur during the propagation of the fault traveling wave.

[0085] Using step waves to simulate transmission lines Uppropagation preset distance Subsequent distortion and attenuation:

[0086] ; (17)

[0087] In the formula, For a step wave in a transmission line Uppropagation preset distance Subsequent distortion and attenuation This indicates that the attenuation of the fault traveling wave decreases as the propagation distance increases. It represents the distortion of the fault traveling wave; the greater the difference in wave velocity between different frequencies, the smaller its value. For time delay The unit step function.

[0088] For step waves in transmission lines Uppropagation preset distance The subsequent distortion and attenuation are transformed in the complex frequency domain to obtain the step wave in the transmission line. Uppropagation preset distance The subsequent distortion and attenuation are expressed in the complex frequency domain, and the step wave in the transmission line... Uppropagation preset distance The expressions for the subsequent distortion and attenuation in the complex frequency domain are:

[0089] ; (18)

[0090] In the formula, For a step wave in a transmission line Uppropagation preset distance The complex frequency domain representation of subsequent distortion and attenuation. It is a step wave;

[0091] Because in the complex frequency domain, step waves Then, by combining equation (18), the distortion and attenuation of the fault traveling wave during propagation can be calculated. The expression:

[0092] ; (19)

[0093] In the formula, This represents the distortion coefficient of the line. and All are constants.

[0094] Based on the expressions for the distortion and attenuation of the fault traveling wave during propagation, and the complex frequency domain expression for the attenuation coefficient based on distortion and attenuation, the transmission line... The distortion coefficient and attenuation coefficient; that is, by combining equations (16) and (19), the transmission line can be solved. distortion coefficient and attenuation coefficient ,and:

[0095] ; (20)

[0096] In the formula, Let be the angular frequency, and , for The frequency value corresponding to a certain frequency.

[0097] Will side Performing a Laplace transform on the mixed wave at time t, we obtain side The complex frequency domain expression of the mixed wave at time t, and side Substituting the complex frequency domain expression of the mixed wave at time t into the expression for the distortion and attenuation of the fault traveling wave during propagation, we obtain: Side-mixed wave and The relationship expression of the side-mixed wave in the complex frequency domain; that is, first perform Laplace transform on equation (14) to obtain the complex frequency domain expression, and then substitute it into equation (19) to obtain Side-mixed wave and The relationship between the side-mixed wave in the complex frequency domain, and Side-mixed wave and The relationship between the side-mixed wave and the wave in the complex frequency domain is:

[0098] ; (twenty one)

[0099] In the formula, for Complex frequency domain representation of the side-mixed wave, for Complex frequency domain representation of side-mixed waves;

[0100] according to Side-mixed wave and The relational expression of the side-mixed wave in the complex frequency domain is obtained. side Mixed waves at time and side Mixed waves at time The temporal relationship between them; among which, side Mixed waves at time and side Mixed waves at time The temporal relationship between them is expressed as:

[0101] ; (twenty two)

[0102] In the formula, After inverting from the complex frequency domain back to the time domain side Current at any moment for side The current lost in the line at any given moment. For time step.

[0103] according to side Mixed waves at time and side Mixed waves at time and side The time-domain relationship between the mixed waves at different times is used to obtain the transmission line. The equivalent calculation circuit; that is, by combining equations (14) and (22), the transmission line can be obtained. Equivalent calculation circuit; transmission line The equivalent calculation circuit is the improved Beryllon model; transmission line The equivalent calculation circuit is represented as follows:

[0104] ; (twenty three)

[0105] In the formula, for side The transmission line loss equivalent voltage source at time t can be expressed as: , , Three voltage sources connected in series; for side The current lost in the line at any given moment. After inverting from the complex frequency domain back to the time domain side Current at any moment for side Mixed waves at time, for side A mixed wave at any given moment.

[0106] Berylon equivalent network for a three-terminal hybrid HVDC transmission system:

[0107] Using the above derivation method of the Berylon equivalent circuit, the Berylon equivalent network of the three-terminal hybrid HVDC transmission system under different fault locations is obtained.

[0108] Case 1: As shown in Figure 2, when the line exist ms, When a single-pole ground fault occurs, the equivalent current source can be derived from equations (12) and (13), and the equivalent voltage source can be derived from equation (23). Figure 3 shows the situation in Figure 2 when the line... exist ms, A schematic diagram of the concentrated line parameters when a single-pole ground fault occurs; in Figure 3, the concentrated line parameters are selected. , and Explanation:

[0109] ; (twenty four)

[0110] In the formula, for time Equivalent current source on, for Time nodes 3 and 1 (i.e. When a single-pole ground fault occurs at the fault node Equivalent voltage source, for When a single-pole ground fault occurs, the equivalent current source of the capacitor in the DC filter has an initial value of 0 (including the equivalent voltage source and the equivalent current source). =1000 / f s (f s (sampling frequency), , , These represent nodes 3, 4, and 5 in Figure 3, respectively. Voltage at any given moment; , for Length, for Linear mode wave velocity; for Linear mode impedance; for The inductor on, for The current flowing from node 1 to node 3 at time _____ for The current flowing from node 1 to node 3 at time _____ For node 1 at Voltage at time, for The current flowing from node 3 to node 1 at time point 1. for The attenuation coefficient of the traveling wave under fault conditions. for The reciprocal of the distortion coefficient of the traveling wave under fault.

[0111] According to Kirchhoff's current theorem, at any node in a circuit, the algebraic sum of the currents flowing into and out of that node is always equal to zero. Therefore, the current excitation matrix I of each node in the Berylon equivalent network is... s It can be expressed by the following formula:

[0112] ; (25)

[0113] In the formula, Indicates the inflow of the first Current equivalent sources at each node. Indicates the outflow of the first The current equivalent source of each node. Then the voltage of each node can be solved using the following formula:

[0114] ; (26)

[0115] in, , ... and All represent node voltages; there are a total of 22 nodes. The nodal admittance matrix can be derived using the following formula:

[0116] (27)

[0117] In the formula, , ,when Time represents the self-admittance of the node. And if they are directly connected through branches, then it represents a node. and The mutual admittances, these values ​​are usually negative, when and When there is no direct branch connection, .

[0118] By combining equations (25), (26), and (27), the sudden changes in voltage and current at each node during a fault can be solved. Based on these sudden changes, the voltage at the traveling wave detection device can be calculated. Current :

[0119] ; (28)

[0120] In the formula, and The rated voltage and current at the traveling wave detection device. for Wave impedance.

[0121] Case 2: As shown in Figure 2, when the line exist ms, A single-pole ground fault occurs at a certain location. After changing the fault location, the voltage information of each node does not change, therefore the equivalent current source does not change, and the current excitation matrix of each node remains unchanged. The node admittance matrix can be derived from equations (25) and (27). Figure 4 shows the line in Figure 2. exist ms, A schematic diagram of the lumped line parameters for a single-pole ground fault occurs; in Figure 4, lumped line parameters are selected for the changing equivalent voltage source. Demonstration:

[0122] ; (29)

[0123] In the formula, for Time nodes 7 and 1 (i.e. When a single-pole ground fault occurs at the fault node Equivalent voltage source, for The current flowing from node 1 to node 7 at time 1 for The current flowing from node 7 to node 1 at time point 1. For node 7 in Figure 4 Voltage at a given moment.

[0124] According to equation (26), the sudden changes in voltage and current at each node during a fault can be solved, and the voltage and current at the traveling wave detection device can be calculated based on the sudden changes:

[0125] ; (30)

[0126] III: Acquisition and Correction of Transition Point Time of Arrival

[0127] Mutation point acquisition:

[0128] for The frequency domain expression of a signal formed by the superposition of several independent intrinsic mode functions is generally as follows:

[0129] ; (31)

[0130] In the formula, and For the first The amplitude and phase of each component, Group delay. If a signal... wavelet basis is The corresponding wavelet transform is:

[0131] ; (32)

[0132] In the formula, As a scale factor, The translation factor is... To represent complex conjugation, use a window function. Constructing analytic wavelets And by eliminating redundant phase, the modified wavelet transform (MWT) becomes:

[0133] ; (33)

[0134] make Then the frequency domain expression of the window function is:

[0135] ; (34)

[0136] In the formula, According to Parseval's theorem, the frequency domain expression of MWT is:

[0137] ; (35)

[0138] Considering the severe energy diffusion in MWT, in order to improve energy concentration, the WTMSST (Time Redistribution Multi-Synchronous Compression Transform based on Wavelet Transform) fixed-point iterative post-processing method is introduced to repeatedly compress the dispersed time-frequency coefficients to the true group delay estimate, thereby improving the resolution in the time direction.

[0139] According to Plancherel's theorem, the energy spectrum of MWT is as follows:

[0140] ; (36)

[0141] In the formula, for The probability distribution function of the surrounding area. Then the centroid of the signal in the time direction is:

[0142] ; (37)

[0143] In the formula, Indicates taking the real part, , indicating that the window function size is By employing a post-processing strategy along the time direction, the time scale coefficients are transformed from... Transferred to Then WTMSST can be represented as:

[0144] ; (38)

[0145] In the formula, .

[0146] Due to WTSST Unable to accurately estimate the group delay of a strong frequency-varying signal, fixed-point iteration is used to eliminate the error between the two. After accumulating N times, a new expression for the group delay is obtained:

[0147] ; (39)

[0148] The formula for WTMSST at this time is:

[0149] ; (40)

[0150] When N is large enough, that is:

[0151] ; (41)

[0152] At this moment, the new The error between the group delay and the error approach zero, improving the ability to process high-frequency signals.

[0153] Correction of abrupt change point arrival time:

[0154] Due to the Heisenberg uncertainty principle, time and frequency resolutions cannot be simultaneously optimized. The methods described above compress the diffused energy to the true group delay estimate. However, the difference between frequency-varying signals and fixed-frequency signals lies in the fact that multiple frequency components exist at the abrupt change point of the frequency-varying signal. In this case, the wavelet transform coefficients diffuse across multiple scales, and the energy ridge at a certain frequency overlaps with the energy at adjacent scales, leading to errors in extracting the arrival time of the abrupt change point for both frequency-varying and fixed-frequency signals. To eliminate this error, this invention introduces a random forest to learn the mapping relationship between the two, using the prediction result as the final arrival time of the abrupt change point.

[0155] Random forest is an ensemble learning algorithm that combines multiple weak classifiers (decision trees), with the final result obtained through voting or averaging. First, it obtains the mapping relationship between data points by acquiring features such as mean, standard deviation, and time offset. Then, these features are fed into the random forest model for training. Finally, the trained random forest model is used to predict the data, and the prediction result is as follows:

[0156] ; (42)

[0157] In the formula, , representing the characteristic matrix, For the number of trees, Indicates the first The prediction function of a decision tree.

[0158] Based on the above theoretical analysis, the preferred embodiments of each step in the method of the present invention are as follows:

[0159] Preferably, in step S1, the real-time current traveling wave is specifically detected by a traveling wave detection device installed on the rectifier side of the transmission line, and the sampling frequency of the traveling wave detection device is set to be [value missing]. ;

[0160] The criterion for determining whether a transmission line has experienced a fault based on the real-time current traveling wave is as follows:

[0161] ; (43)

[0162] in, The real-time current traveling wave. For time, The preset fault current threshold is used.

[0163] Specifically, when a DC line fault occurs, the traveling wave detection device detects a sudden change in the fault traveling wave. Since CVTs cannot transmit wideband voltage traveling waves, the distortion is severe in the high-frequency range. To ensure that the traveling wave detection device can quickly and accurately acquire fault traveling wave information, this invention selects the current traveling wave as the fault basis. The above fault criterion is simple, highly sensitive, and can quickly and accurately identify the first wave head after a line fault occurs, providing strong support for obtaining fault information.

[0164] Preferably, in S2, Part II above analyzes the Berylon method, transforms the actual transmission line model into a Berylon equivalent network, and obtains the equivalent calculation circuit of the dispersion model by considering transmission line loss and combining it with the Berylon method. Finally, the theoretical fault traveling wave (i.e., the theoretical current traveling wave after a fault occurs) can be derived.

[0165] Specifically, in this embodiment, the arrival time of the first wave head (i.e., the fault time) is obtained using fault criteria, denoted as t. p , extract t p The theoretical current traveling wave within a 2ms time window, 0.05ms before and 1.95ms after the time point.

[0166] Before step S3, the process further includes: normalizing the intercepted theoretical current traveling wave; wherein the formula for normalizing the intercepted theoretical current traveling wave is:

[0167] ;

[0168] in, The normalized theoretical current traveling wave, For the theoretical current traveling wave, The time of the fault, The width of the preset time window.

[0169] Specifically, normalizing the intercepted theoretical current traveling wave aims to reduce the deviation from the actual waveform. Since this embodiment selects the fault time t... p The time window is 2ms, consisting of 0.05ms before and 1.95ms after the specified time. Therefore, in this embodiment... =0.05ms, =1.95ms.

[0170] Preferably, S3 specifically includes:

[0171] S31, the intercepted theoretical current traveling wave is processed by modified wavelet transform at low, medium and high frequencies to obtain the time spectrum at low, medium and high frequencies respectively;

[0172] S32, perform time redistribution synchronous squeezing transformation on the time spectrum at low, medium and high frequencies respectively, and obtain the time redistribution synchronous squeezing transformation post-processing results at low, medium and high frequencies;

[0173] S33, using wavelet transform-based time redistribution multi-synchronization compression transform, performs multiple fixed-point iterations on the post-processing results of time redistribution synchronous compression transform at low, medium, and high frequencies to extract the time points and energy values ​​corresponding to the energy concentration regions at low, medium, and high frequencies.

[0174] S34, calculate the changing trend of the intercepted theoretical current traveling wave to obtain the changing relationship before and after the abrupt change point, and combine the time points and energy values ​​corresponding to the energy concentration areas at low, medium and high frequencies to obtain the time points and energy values ​​related to the changing trend at low, medium and high frequencies.

[0175] S35, using random forest to predict and correct the time points and energy values ​​related to the changing trend at low, medium and high frequencies respectively, to obtain the corrected time points and corrected energy values ​​related to the changing trend at low, medium and high frequencies;

[0176] S36 reconstructs the waveforms of the correction time points and correction energy values ​​related to the changing trends at low, medium, and high frequencies, respectively, to obtain the reconstructed current traveling waves at low, medium, and high frequencies.

[0177] Specifically, since the Barrelon method cannot calculate broadband information when calculating the theoretical current traveling wave, there is a certain deviation from the actual waveform. Therefore, the method of this invention utilizes the characteristic of the WTMSST method in Part III to obtain information of the frequency-varying signal at various frequencies, compressing the actual traveling wave to the same frequency as the theoretical fault traveling wave, and eliminating errors through random forest to obtain the accurate trend of waveform change and reconstruct it. More specifically, the theoretical waveform calculation is the waveform at a fixed frequency. This is equivalent to using TMSST to compress the actual waveform (i.e., the PSCAD waveform, which is a frequency-varying waveform containing many different frequencies) to the same frequency as the theoretical waveform, and analyzing the abrupt change points at the same frequency.

[0178] Since the intercepted theoretical current traveling wave is normalized before step S3 in some embodiments, in step S3, the normalized theoretical current traveling wave is normalized according to the method described in Part III. WTMSST processing is performed to extract mutation point information at a fixed frequency and random forest is used for prediction and correction. However, this method can only obtain the energy value corresponding to the mutation point and cannot reflect the trend of change. Therefore, the following formula (45) is used to obtain the energy value. By observing the changing trends, we can improve the accuracy of the reconstructed waveform.

[0179] ; (45)

[0180] In the formula, when When, it means It shows a downward trend, when When, it means It shows an upward trend.

[0181] Based on the generation and propagation laws of fault traveling waves, the equivalent fault traveling wave in a short transient period (within a few milliseconds) can be approximated as a step wave. The equivalent fault traveling waves superimpose to form the reconstructed current traveling wave during propagation. The equivalent fault traveling wave corresponds one-to-one with the fault traveling wave. Therefore, the reconstructed current traveling wave can be approximated as being composed of multiple step waves superimposed, as shown in the following equation:

[0182] (46)

[0183] In the formula, e(t) represents the unit step function. and These are the first two digits of the reconstructed current traveling wave. The amplitude and arrival delay of each mutation component, This indicates the number of mutation components within the time window.

[0184] According to Part II, the method of the present invention can obtain the distortion and attenuation coefficients of transmission lines at various frequencies. According to Part III, WTMSST can observe information at a fixed frequency. Combining these characteristics, the reconstructed current traveling wave at each frequency can be obtained.

[0185] Considering the different fault information at different frequency components, this invention selects reconstructed current traveling waves at low, medium, and high frequencies. The low-frequency component improves noise immunity, while the medium and high-frequency components are used for ranging and improving ranging accuracy. Then, the three reconstructed current traveling waves are fitted using the weighted least squares method to obtain the fitted current traveling wave. Weighted least squares is a method that assigns weights to data by analyzing biases, as shown in the following formula:

[0186] ; (47)

[0187] in, The fitted current traveling wave, The reconstructed current waveforms are shown at low, medium, and high frequencies. This represents the arithmetic mean of the reconstructed current waveforms at low, medium, and high frequencies. To minimize the value, prevent the denominator from being 0.

[0188] Preferably, S5 specifically includes:

[0189] S51, the transmission line is divided into multiple sub-sections, and a fuzzy interval of preset length is set in each sub-section with the first and last endpoints as the boundary. The fuzzy interval corresponding to the last endpoint of the previous sub-section and the fuzzy interval corresponding to the first endpoint of the next sub-section are defined as a corresponding overlapping interval.

[0190] S52, integrate the fitted current traveling waves at the first and last endpoints of each overlapping interval to obtain the reference current traveling wave for each overlapping interval;

[0191] S53, integrate the fitted current traveling waves at the first end point, the last end point and the midpoint of each sub-interval to obtain the reference current traveling wave for each sub-interval.

[0192] S54, integrate the reference current traveling waves of all overlapping intervals and the reference current traveling waves of all sub-intervals to obtain the waveform reference library.

[0193] Specifically, the transmission lines The length of the equal division is Multiple sub-intervals, total number of sub-intervals Number the sub-intervals and denote them as follows: Then each subinterval It can be represented as Due to the fitted current traveling wave at the boundary of two adjacent sub-intervals. The differences are small, therefore fuzzy intervals are set at the beginning and end of each sub-interval. To improve the distinguishability of boundaries, the corresponding overlapping interval is: , recorded as :

[0194] ; (48)

[0195] in, For the first Overlapping intervals The length of the subinterval, The length of the fuzzy interval, Let be the total number of subintervals, and , This refers to the length of the power transmission line.

[0196] The overlapping intervals are defined, and the fitted current traveling waves at the first and last endpoints of each overlapping interval are integrated according to the endpoint distance obtained by equation (48) to obtain the reference current traveling wave of each overlapping interval. The reference current traveling waves of all overlapping intervals are integrated to obtain the overlapping interval reference waveform library. The fitted current traveling waves at the first endpoint, last endpoint, and midpoint of each sub-interval are integrated to obtain the reference current traveling wave of each sub-interval. The reference current traveling waves of all sub-intervals are integrated to obtain the sub-interval reference waveform library. The overlapping interval reference waveform library and the sub-interval reference waveform library are integrated to obtain the final waveform reference library. Let the reference current traveling wave of the kth sub-interval be denoted as , No. The reference current traveling wave in each overlapping interval is denoted as .

[0197] Preferably, S6 specifically includes:

[0198] S61, calculates the current traveling wave at any fault location;

[0199] S62, based on the arrival time and amplitude, calculate the comprehensive similarity between the current traveling wave and the fitted current traveling wave at the midpoint of each sub-interval in the waveform reference library, obtain the comprehensive similarity at the midpoint of each sub-interval, and mark the three sub-intervals with the highest comprehensive similarity at the midpoint.

[0200] S63, based on the arrival time and amplitude, calculate the comprehensive similarity between the current traveling wave and the fitted current traveling wave at the first endpoint, last endpoint and midpoint of each marked sub-interval, respectively, and obtain the comprehensive similarity at the first endpoint, last endpoint and midpoint of each marked sub-interval. Average the comprehensive similarity at the first endpoint, last endpoint and midpoint of each marked sub-interval, respectively, to obtain the average comprehensive similarity of each marked sub-interval, and select the sub-interval with the highest average comprehensive similarity.

[0201] S64, among the comprehensive similarity at the first endpoint, last endpoint and midpoint of the selected sub-interval, the sub-interval where the point with the largest comprehensive similarity is located is determined as the fault interval, and it is determined whether the fault interval is in the corresponding overlapping interval, and when the fault interval is in the corresponding overlapping interval, S65 is executed.

[0202] S65, based on the arrival time and amplitude, calculate the comprehensive similarity between the current traveling wave and the fitted current traveling wave at the first and last endpoints of the corresponding overlapping interval, obtain the comprehensive similarity at the first and last endpoints of the corresponding overlapping interval, and determine the sub-interval where the point with the higher comprehensive similarity is located as the fault interval.

[0203] Specifically, as can be seen from Part II, the transition resistance will not affect Based on the time of arrival of the waves, this invention proposes a tracking distance method based on multi-feature similarity.

[0204] First, calculate the current traveling wave at any fault location. The traveling wave of the current To reconstruct the current traveling wave, the current traveling wave at the low, medium, and high frequencies at this position is calculated theoretically using equation (28) or equation (30). Then, reconstruction, correction, and fitting are performed to obtain the current traveling wave. .

[0205] in, ,Will The arrival time and amplitude of each waveform in the reference waveform library Comparison, i.e., time similarity And amplitude similarity :

[0206] , ; (49)

[0207] in, The current traveling wave, For the first Reference current traveling wave in each sub-interval; The current traveling wave and the first Time similarity of the reference current traveling wave in each sub-interval The current traveling wave and the first The covariance of the time of arrival of the reference current traveling wave in each sub-interval Let be the standard deviation of the arrival time of the current traveling wave. No. The standard deviation of the arrival time of the reference current traveling wave in each sub-interval; The current traveling wave and the first The amplitude similarity of the reference current traveling waves in each sub-interval. The current traveling wave and the first The covariance of the amplitude of the reference current traveling wave in each sub-interval. Let be the standard deviation of the amplitude of the current traveling wave. No. The standard deviation of the amplitude of the reference current traveling wave in each sub-interval.

[0208] A comprehensive similarity score is obtained by combining time similarity and magnitude similarity with a weighted approach:

[0209] ; (50)

[0210] in, The traveling waves of the current are respectively with the first The overall similarity of the reference current traveling waves in each sub-interval, and All are weighting coefficients, and .

[0211] Next, use equation (50) to modify the waveform reference library. (t) Perform a comprehensive similarity calculation (at this point, the fitted current traveling wave at the midpoint of each sub-interval in the waveform reference library is compared with the current traveling wave to calculate the comprehensive similarity), mark the three sub-intervals with the highest comprehensive similarity to achieve coarse localization, and obtain three similar sub-intervals. Then... (t) A comprehensive similarity calculation is performed with the reference current traveling wave (i.e., the fitted current traveling wave at the first, last, and midpoints of the similar sub-interval) within the similar sub-interval, and the comprehensive similarity is compared to further determine the fault interval. At this point, the interval corresponding to the point with the highest comprehensive similarity among the first, last, and midpoints of the selected sub-intervals is determined as the fault interval. Specifically, if the comprehensive similarity at the midpoint of the selected sub-interval is the highest, then the sub-interval containing the midpoint of the selected sub-interval is determined as the fault interval. If the comprehensive similarity at the first or last endpoint of the selected sub-interval is the highest, then the fault interval is determined to be within the corresponding overlapping interval. Since the overlapping interval is composed of two fuzzy intervals, the fitted current traveling waves of these two fuzzy intervals... The differences are small, so further determination of the fault interval's location is needed. If the fault interval happens to be within the overlapping interval corresponding to the selected sub-interval, the current traveling wave is compared with the reference current traveling wave (i.e., the fitted current traveling wave at the first and last endpoints of the corresponding overlapping interval). The fault interval is further determined based on the interval corresponding to the point with the highest comprehensive similarity. The final complete fault interval determination formula is:

[0212] ; (51)

[0213] Indicates the fault range. This indicates finding the interval corresponding to the maximum overall similarity. Indicates the first The reference current traveling wave in each overlapping region, Indicates overlapping intervals. This indicates that the current traveling wave is respectively related to the first The overall similarity of the reference current traveling waves in the overlapping regions.

[0214] Parameter settings:

[0215] According to Shannon's sampling theorem, to avoid spectral aliasing, the highest frequency that can be accurately observed at a sampling rate of 1 MHz is 500 kHz. Therefore, this invention selects three frequencies—low, medium, and high—within the highest frequency range to improve ranging accuracy and noise immunity. Specifically, the low frequency is 2 kHz, the medium frequency is 10 kHz, and the high frequency is 50 kHz.

[0216] Select and The parameters corresponding to the low, medium, and high frequencies of the two lines are shown in Table 1 and Table 2.

[0217] Table 1. Line-a Frequency Variation Parameters

[0218]

[0219] Table 2 Line-c Frequency Parameters

[0220]

[0221] To ensure that the starting element based on current surge can accurately detect the first wavehead of the current traveling wave after a line fault, and considering the impact of 30dB noise on the surge, based on the PSCAD simulation results of the three-terminal hybrid DC transmission system, the threshold value is set to a single-pole ground fault occurring 1400 km from the end of the line, with a transition resistance of 600 ohms, and the traveling wave detection device detecting I... mThe adjacent values ​​are 3.5487 kA and 3.5497 kA, respectively, with a corresponding current surge of 0.001. To ensure the accuracy of identifying the first wavefront and eliminate interference from ripple, a preset fault threshold K is set to prioritize accuracy at the expense of speed. set =0.0015.

[0222] To ensure the accuracy of distance measurement and improve its precision, the following formula is introduced to calculate the relative error x.

[0223] ; (52)

[0224] In the formula, This represents the actual distance to the fault. To calculate the fault distance theoretically.

[0225] In this invention, it is set According to formula (52), the length of each sub-interval is calculated to be 297.8 m. For ease of calculation, the length of each sub-interval is set to 300 m. For example, the first five sub-intervals are (0,300], (300,600], (600,900], (900,1200], and (1200,1500], with a total of 4964 waveform references. To improve the ability to judge fuzzy intervals, ΔL = 10 m is set. When the fault distance is within the fuzzy interval, the fault interval is further determined by S5.

[0226] The method of the present invention is illustrated below using a single-phase metallic grounding fault as an example:

[0227] Assuming in At 745.5 km ( When a unipolar metallic ground fault occurs, the transition resistance is calculated as the ideal value of 0 ohms. The arrival time of the first wavefront of the PSCAD simulation waveform and the waveform calculated by the Berylon theory are obtained by formula (43). The current traveling wave signal of the 2ms time window is extracted. The result of the obtained signal after normalization by formula (44) is shown in Figure 5. At this time, the frequency resolution corresponding to the time window is 500 Hz, ensuring that the low, medium and high frequencies can be accurately observed. The Morlet wavelet is selected to perform time-frequency transformation on the normalized theoretical current traveling wave. The decomposition scale is 2000. The time spectrum at the 2 kHz frequency is extracted as shown in Figure 6. In Figure 6, the left part is the MWT result diagram and the right part is the enlarged diagram of the MWT result.

[0228] The time spectrum of MWT in Figure 6 was post-processed using TSST (Time Redistribution Synchronous Squeeze Transform Postprocessing), and the result is shown in Figure 7. In Figure 7, the left side is the TSST result image, and the right side is a magnified view of the TSST result. The diffused energy effectively converges near the mutation point, but diffusion still exists, making it impossible to accurately obtain the mutation time corresponding to the mutation point. Then, WTMSST was used for ten fixed-point iterations, as shown in Figure 8. In Figure 8, the left side is the WTMSST result image, and the right side is a magnified view of the WTMSST result. It was found that there is almost no energy diffused along the time direction near the mutation point, and the energy converges significantly, which is consistent with the theory in Part III.

[0229] Repeat the above steps to extract the time points and energy values ​​corresponding to the energy concentration areas of the theoretical waveform and simulated waveform (the simulated waveform is the actual waveform (PSCAD waveform) mentioned earlier) at a frequency of 2 kHz in the WTMSST results, and normalize the energy values. The extracted time points are the arrival times corresponding to the abrupt change points. In order to better reflect the changing trend of the waveform, use equation (45) to obtain the relationship between the changes before and after the abrupt change points, and obtain the time points and energy values ​​related to the changing trend, as shown in Figure 9. In Figure 9, the upper left part is the WTMSST result diagram of the fault traveling wave calculated based on the improved Berylon model, the upper right part is the arrival time extraction diagram of the fault traveling wave calculated based on the improved Berylon model, the lower left part is the WTMSST result diagram of the actual fault traveling wave, and the lower right part is the arrival time extraction diagram of the actual fault traveling wave.

[0230] Due to the influence of group delay on the accuracy of waveform mutation point extraction, there are differences in the time and energy value corresponding to the mutation point. The arrival time is fed into a random forest for prediction correction, and the predicted value is reconstructed using equation (46). The result is shown in Figure 10. In Figure 10, the left part is the random forest prediction, and the right part is the waveform reconstruction. Repeat the above steps to obtain the reconstructed current traveling waves at two other frequencies. The arrival time is fitted by the weighted least squares method (47), and the result is shown in Figure 11. The reconstructed waveform is input into the reference waveform library for tracking search. First, coarse positioning is performed according to equation (49) to determine the approximate fault range. The ranges with high similarity are further compared, and the range with the highest similarity is selected as the fault range. The specific comprehensive similarity is shown in Table 3.

[0231] Table 3: Sub-interval Comprehensive Similarity

[0232]

[0233] At this point, the three sub-intervals with the highest overall similarity are (744.9 km, 745.2 km], (745.2 km, 745.5 km], and (745.5 km, 745.8 km]. The current traveling wave is then compared with the three reference waveforms within these three sub-intervals, and the interval corresponding to the reference waveform with the highest overall similarity is selected as the fault interval. Since the overall similarity is highest and consistent at the endpoint 745.5 km of the two fault intervals (745.2 km, 745.5 km] and (745.5 km, 745.8 km], it is determined that the fault location is within the overlapping interval R(s). Further comparison with the reference waveforms within the overlapping interval R(s) using formula (51) is then used, and the endpoint value corresponding to the reference waveform with the highest overall similarity within the overlapping interval R(s) is selected to determine the final fault interval. At this point, the overall similarity between the current traveling wave and the left endpoint 745.49 km of the overlapping interval is 0.8472, and the similarity with the right endpoint 745.51 km is... The overall similarity of km is 0.8457, which is closer to the fault interval corresponding to the left endpoint. The final fault interval is (745.2 km, 745.5 km], which is consistent with the theoretically set fault interval.

[0234] Based on the above-mentioned fault location method for a multi-terminal hybrid DC transmission system, the present invention also provides a fault location system for a multi-terminal hybrid DC transmission system.

[0235] As shown in Figure 12, a fault location system for a multi-terminal hybrid DC transmission system includes:

[0236] The fault detection module is used to detect the real-time current traveling wave of the transmission line in the hybrid DC transmission system, and to determine whether the transmission line has a fault based on the real-time current traveling wave, and to mark the fault time when the transmission line has a fault; and to improve the traditional Beryllon model by considering line dispersion, so as to establish an improved Beryllon model that considers different fault locations.

[0237] The theoretical calculation module is used to obtain the theoretical current traveling wave under different fault conditions based on the improved Berylone model, and to extract the theoretical current traveling wave of a preset time window according to the fault time.

[0238] The transformation and correction module is used to process the intercepted theoretical current traveling wave at low, medium and high frequencies using a wavelet transform-based time redistribution multi-synchronous compression transform method, and to perform waveform correction in combination with random forest to obtain the reconstructed current traveling wave at low, medium and high frequencies.

[0239] The waveform fitting module is used to perform weighted least squares fitting on the reconstructed current traveling wave at low, medium and high frequencies to obtain the fitted current traveling wave.

[0240] A waveform reference library construction module is used to construct a waveform reference library including multiple interval reference current traveling waves based on the fitted current traveling wave;

[0241] The tracking and ranging module is used to calculate the current traveling wave at any fault location, calculate the similarity between the current traveling wave and the reference current traveling waves in each interval of the waveform reference library based on the wave arrival time and amplitude, obtain the comprehensive similarity, and locate the fault interval based on the comprehensive similarity.

[0242] This invention provides a fault location method and system for multi-terminal hybrid DC transmission systems. It improves upon the traditional Berylon model, enabling it to fully characterize distributed parameter lines and extrapolate theoretical wave processes under hypothetical fault scenarios, thus allowing for the calculation of line dispersion at different frequencies. It utilizes a time-redistribution multi-synchronous compression transform algorithm to process the time-frequency distribution of wavelet variations, obtaining the time-frequency spectrum of energy concentration at a fixed frequency. This accurately acquires the arrival time at a fixed frequency, reducing errors caused by traditional time-frequency analysis methods such as wavelet transform and Fourier transform when processing strong frequency-varying signals. Furthermore, the accuracy is further improved after random forest correction. Simultaneously, the arrival time group is reconstructed to obtain reconstructed current traveling waves, improving tracking accuracy. The reconstructed current traveling waves at different fault locations are integrated to obtain a reference waveform library. The fault location is estimated using matching and tracking principles. Overall, the ranging error can be controlled below 1 km. Additionally, the ranging performance of this invention is unaffected by transition resistance.

[0243] 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 principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A fault location method for a multi-terminal hybrid DC transmission system, characterized in that, include: S1, detect the real-time current traveling wave of the transmission line in the hybrid DC transmission system, determine whether the transmission line has a fault based on the real-time current traveling wave, and mark the fault time when the transmission line has a fault. Furthermore, considering line dispersion, the traditional Beryllon model is improved to establish an improved Beryllon model that considers different fault locations; S2, based on the improved Beryllon model, theoretical current traveling waves under different fault conditions are obtained, and theoretical current traveling waves within a preset time window are extracted according to the fault time; S3, the extracted theoretical current traveling waves are processed at low, medium, and high frequencies using a wavelet transform-based time redistribution multi-synchronization compression transform method, and waveform correction is performed using random forest to obtain reconstructed current traveling waves at low, medium, and high frequencies; S4, the reconstructed current traveling waves at low, medium, and high frequencies are fitted using a weighted least squares method to obtain fitted current traveling waves; S5, a waveform reference library including multiple interval reference current traveling waves is constructed based on the fitted current traveling waves; S6, the current traveling wave is calculated at any fault location, and the similarity between the current traveling wave and the interval reference current traveling waves in the waveform reference library is calculated based on the arrival time and amplitude to obtain a comprehensive similarity, and the fault interval is located based on the comprehensive similarity.

2. The fault location method for a multi-terminal hybrid DC transmission system according to claim 1, characterized in that, In step S1, the real-time current traveling wave is specifically detected by a traveling wave detection device installed on the rectifier side of the transmission line, and the sampling frequency of the traveling wave detection device is set to be [value missing]. The criterion for determining whether a transmission line has experienced a fault based on the real-time current traveling wave is as follows: In the formula, The real-time current traveling wave. For time, The preset fault current threshold is used.

3. The fault location method for a multi-terminal hybrid DC transmission system according to claim 1, characterized in that, Assuming any transmission line include Side and side, Side The mixed wave emitted at any moment passes through time Arrived later On the side; in S1, considering line dispersion, the traditional Beryllon model is improved, specifically including: S101, in the transmission line In China, according to time The mixed wave on the side was calculated. side The mixed wave at time, and side The mixed wave at time t is represented as: In the formula, for side Mixed waves at time, For transmission lines exist The decay coefficient at time, for side Mixed waves at time, for side Voltage at time, for side Current at any moment For transmission lines wave impedance, for side Voltage at time, for side Current at any given moment; S102, for transmission line exist The attenuation coefficient at time t is transformed into the complex frequency domain to obtain the complex frequency domain expression of the attenuation coefficient, which is: In the formula, For transmission lines The attenuation coefficient in the complex frequency domain is represented as follows: For transmission lines Length, 、 、 and Transmission lines The unit resistance, unit inductance, unit conductance, and unit capacitance; S103, using an exponential function representing delay in the complex frequency domain. By transforming the complex frequency domain expression of the attenuation coefficient, we obtain the complex frequency domain expression of the attenuation coefficient based on distortion and attenuation, which is: In the formula, The distortion and attenuation of the fault traveling wave during propagation; S104, using a step wave to simulate a transmission line. Uppropagation preset distance The distortion and attenuation that occur afterward; among them, the transmission line is simulated using a step wave. Uppropagation preset distance The expressions for the subsequent distortion and attenuation are: In the formula, For a step wave in a transmission line Uppropagation preset distance Subsequent distortion and attenuation For the attenuation of the fault traveling wave, The distortion of the fault traveling wave, For time delay The unit step function; S105, for a step wave in a transmission line Uppropagation preset distance The subsequent distortion and attenuation are transformed in the complex frequency domain to obtain the step wave in the transmission line. Uppropagation preset distance The subsequent distortion and attenuation are expressed in the complex frequency domain, and the step wave in the transmission line... Uppropagation preset distance The expressions for the subsequent distortion and attenuation in the complex frequency domain are: In the formula, For a step wave in a transmission line Uppropagation preset distance The complex frequency domain representation of subsequent distortion and attenuation. For a step wave; S106, in the complex frequency domain, based on And combined with step waves in the transmission line Uppropagation preset distance The expressions for the subsequent distortion and attenuation in the complex frequency domain are used to calculate the expressions for the distortion and attenuation of the fault traveling wave during propagation; where the expressions for the distortion and attenuation of the fault traveling wave during propagation are: In the formula, For transmission lines The distortion coefficient; S107, based on the expressions for the distortion and attenuation of the fault traveling wave during propagation and the complex frequency domain expression for the attenuation coefficient based on the distortion and attenuation, the transmission line distortion coefficient is calculated. The distortion coefficient and attenuation coefficient; where, transmission line The distortion coefficient and attenuation coefficient are expressed as follows: In the formula, Let be the angular frequency, and ， for The corresponding frequency value at that frequency; 108, will side Performing a Laplace transform on the mixed wave at time t, we obtain side The complex frequency domain expression of the mixed wave at time t, and side Substituting the complex frequency domain expression of the mixed wave at time t into the expression for the distortion and attenuation of the fault traveling wave during propagation, we obtain: Side-mixed wave and The relationship between the side-mixed wave in the complex frequency domain; where, Side-mixed wave and The relationship between the side-mixed wave and the wave in the complex frequency domain is: In the formula, for Complex frequency domain representation of the side-mixed wave, for Complex frequency domain representation of the side-mixed wave; 109, according to Side-mixed wave and The relational expression of the side-mixed wave in the complex frequency domain is obtained. side Mixed waves at time and side The temporal relationship between the mixed waves at time points; where, side Mixed waves at time and side The time-domain relationship between the mixed waves at time points is expressed as follows: In the formula, After inverting from the complex frequency domain back to the time domain side Current at any moment for side The current lost in the line at any given moment. For time step; S110, according to side Mixed waves at time and side Mixed waves at time and side The time-domain relationship between the mixed waves at different times is used to obtain the transmission line. The equivalent calculation circuit; wherein, the transmission line The equivalent calculation circuit is the improved Beryllon model, and the transmission line The equivalent calculation circuit is represented as follows: In the formula, for side The transmission line loss equivalent voltage source at any given moment. for side The current lost in the line at any given moment. After inverting from the complex frequency domain back to the time domain side Current at any moment for side Mixed waves at time, for side A mixed wave at any given moment.

4. The fault location method for a multi-terminal hybrid DC transmission system according to claim 1, characterized in that, Before step S3, the process further includes: normalizing the intercepted theoretical current traveling wave; wherein the formula for normalizing the intercepted theoretical current traveling wave is: In the formula, The normalized theoretical current traveling wave, For the theoretical current traveling wave, The time of the fault, The preset time window width is defined as follows: S3 specifically involves: S31, performing modified wavelet transform processing on the intercepted theoretical current traveling wave at low, medium, and high frequencies to obtain the time spectrum at low, medium, and high frequencies; S32, performing time redistribution synchronous compression transform post-processing on the time spectrum at low, medium, and high frequencies to obtain the time redistribution synchronous compression transform post-processing results at low, medium, and high frequencies; S33, using wavelet transform-based time redistribution multi-synchronization compression transform, performing multiple fixed-point iteration processing on the time redistribution synchronous compression transform post-processing results at low, medium, and high frequencies to extract the time points and energy corresponding to the energy concentration regions at low, medium, and high frequencies. S34, calculate the changing trend of the intercepted theoretical current traveling wave to obtain the relationship before and after the abrupt change point, and combine it with the time points and energy values ​​corresponding to the energy concentration regions at low, medium and high frequencies to obtain the time points and energy values ​​related to the changing trend at low, medium and high frequencies; S35, use random forest to predict and correct the time points and energy values ​​related to the changing trend at low, medium and high frequencies to obtain the corrected time points and corrected energy values ​​related to the changing trend at low, medium and high frequencies; S36, reconstruct the waveforms of the corrected time points and corrected energy values ​​related to the changing trend at low, medium and high frequencies to obtain the reconstructed current traveling waves at low, medium and high frequencies.

5. The fault location method for a multi-terminal hybrid DC transmission system according to claim 1, characterized in that, In S4, the formula for fitting the reconstructed current traveling waves at low, medium, and high frequencies using the weighted least squares method is as follows: In the formula, The fitted current traveling wave, The reconstructed current traveling waves at low, medium, and high frequencies. This represents the arithmetic mean of the reconstructed current traveling waves at low, medium, and high frequencies. It is a local minimum.

6. The fault location method for a multi-terminal hybrid DC transmission system according to claim 1, characterized in that, S5 specifically involves: S51, dividing the transmission line into multiple sub-sections, and setting a fuzzy interval of a preset length in each sub-section with the first and last endpoints as boundaries, and defining the fuzzy interval corresponding to the last endpoint of the previous sub-section and the fuzzy interval corresponding to the first endpoint of the next sub-section as a corresponding overlapping interval; S52, integrating the fitted current traveling waves at the first and last endpoints of each overlapping interval to obtain the reference current traveling wave for each overlapping interval. S53, integrate the fitted current traveling waves at the first end point, the last end point and the midpoint of each sub-interval to obtain the reference current traveling wave for each sub-interval. S54, integrate the reference current traveling waves of all overlapping intervals and the reference current traveling waves of all sub-intervals to obtain the waveform reference library.

7. The fault location method for a multi-terminal hybrid DC transmission system according to claim 6, characterized in that, In S51, the overlapping interval is represented as: In the formula, For the first Overlapping intervals The length of the subinterval, The length of the fuzzy interval, Let be the total number of subintervals, and ， This refers to the length of the power transmission line.

8. The fault location method for a multi-terminal hybrid DC transmission system according to claim 6, characterized in that, S6 specifically includes: S61, calculating the current traveling wave at any fault location; S62, based on the wave arrival time and amplitude, calculating the comprehensive similarity between the current traveling wave and the fitted current traveling wave at the midpoint of each sub-interval in the waveform reference library, obtaining the comprehensive similarity at the midpoint of each sub-interval, and marking the three sub-intervals with the highest comprehensive similarity at the midpoint. S63, Based on the arrival time and amplitude, calculate the comprehensive similarity between the current traveling wave and the fitted current traveling wave at the first, last, and midpoints of each marked sub-interval, respectively, to obtain the comprehensive similarity at the first, last, and midpoints of each marked sub-interval. Average the comprehensive similarity at the first, last, and midpoints of each marked sub-interval to obtain the average comprehensive similarity of each marked sub-interval, and select the sub-interval with the highest average comprehensive similarity. S64, Among the comprehensive similarities at the first, last, and midpoints of the selected sub-intervals, determine the sub-interval containing the point with the highest comprehensive similarity as the fault interval, and determine whether the fault interval is within the corresponding overlapping interval. If the fault interval is within the corresponding overlapping interval, execute S65. S65, Based on the arrival time and amplitude, calculate the comprehensive similarity between the current traveling wave and the fitted current traveling wave at the first and last endpoints of the corresponding overlapping interval, to obtain the comprehensive similarity at the first and last endpoints of the corresponding overlapping interval, and determine the sub-interval containing the point with the higher comprehensive similarity as the fault interval.

9. The fault location method for a multi-terminal hybrid DC transmission system according to claim 8, characterized in that, The formula for calculating the overall similarity is: In the formula, The current traveling wave, For the first Reference current traveling wave in each sub-interval; For current traveling wave With the Reference current traveling wave in each sub-interval The overall similarity and All are weighting coefficients, and ； For current traveling wave With the Reference current traveling wave in each sub-interval Time similarity, For current traveling wave With the Reference current traveling wave in each sub-interval The amplitude similarity; where: ， In the formula, For current traveling wave With the Reference current traveling wave in each sub-interval The covariance at time of arrival, For current traveling wave The standard deviation of the time of arrival, For the first Reference current traveling wave in each sub-interval The standard deviation of the time of arrival; For current traveling wave With the Reference current traveling wave in each sub-interval The covariance of the amplitude, For current traveling wave The standard deviation of the amplitude, For the first The standard deviation of the reference current traveling wave in each sub-interval; the fault interval determination formula is: In the formula, Indicates the fault range. This indicates finding the interval corresponding to the maximum overall similarity. Indicates the first The reference current traveling wave in each overlapping region, Indicates overlapping intervals. This indicates that the current traveling wave is respectively related to the first The overall similarity of the reference current traveling waves in the overlapping regions.

10. A fault location system for a multi-terminal hybrid DC transmission system, characterized in that, include: The fault detection and modeling module is used to detect the real-time current traveling wave of the transmission line in the hybrid DC transmission system, and to determine whether the transmission line has a fault based on the real-time current traveling wave, and to mark the fault time when the transmission line has a fault. Furthermore, considering line dispersion, the traditional Beryllon model is improved to establish an improved Beryllon model that considers different fault locations. The theoretical calculation module is used to obtain the theoretical current traveling wave under different fault conditions based on the improved Berylon model, and to extract the theoretical current traveling wave within a preset time window according to the fault time. The transformation and correction module is used to perform waveform processing on the extracted theoretical current traveling wave at low, medium and high frequencies using a wavelet transform-based time redistribution multi-synchronization compression transform method, and to perform waveform correction using random forest to obtain the reconstructed current traveling wave at low, medium and high frequencies. The waveform fitting module is used to perform weighted least squares fitting on the reconstructed current traveling wave at low, medium and high frequencies to obtain the fitted current traveling wave. The waveform reference library construction module is used to construct a waveform reference library including multiple interval reference current traveling waves based on the fitted current traveling wave; the tracking and ranging module is used to calculate the current traveling wave at any fault location, calculate the similarity between the current traveling wave and the interval reference current traveling waves in the waveform reference library based on the wave arrival time and amplitude, obtain the comprehensive similarity, and locate the fault interval based on the comprehensive similarity.

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