Power transmission line fault detection method based on improved VMD algorithm

Abstract

The invention relates to a power transmission line fault detection method based on an improved VMD algorithm. Firstly, fault traveling wave signals are collected and analyzed; the fault traveling wave signals are preprocessed, and fault principle analysis is carried out; establishing a power transmission line fault distance measurement model through a double-end traveling wave distance measurement method; a fault position is determined by improving a VMD algorithm and utilizing a double-end traveling wave fault location algorithm. The fault detection success rate is improved, the adaptability of an operation strategy is improved, the system operation efficiency is improved, and important technical guarantee is provided for safe and stable operation of a power grid.

Description

Technical Field

[0001] The present invention belongs to the technical field of power system fault detection, and particularly relates to a transmission line fault detection method based on an improved VMD algorithm. Background Art

[0002] The power industry is an important part of ensuring national security, national economic development and people's livelihood, and is an important pillar industry. The modern power system integrates power generation, transformation, transmission, distribution and power consumption, covers a wide range, has a complex structure and a large number of components. The basic requirements for the operation of the power system are safety, reliability, stability and economy. To conform to the speed and diversification process of human economic and scientific development, the global energy Internet has emerged, which also promotes the power system to gradually develop towards the direction of intelligence and complexity. The grid coverage has been continuously expanded, the transmission distance, transmission capacity and voltage level of transmission lines have been increasing day by day, and the resulting economic and social benefits have become increasingly significant. The healthy and stable operation of the power system has gradually become the premise and key of industrial production and people's daily life.

[0003] Whether the transmission line can operate stably and reliably mainly depends on whether the transmission line can safely transmit electric energy. Therefore, it is very important to accurately judge whether a transmission fault occurs, whether the fault can be removed within a short time, and to improve the sensitivity and reliability of the transmission line. The traditional analysis method uses the steady-state quantities that appear after a fault. With the development of the power grid and the increase in load power consumption, the traditional analysis method gradually reveals its drawbacks, and its deficiencies and shortcomings are more prominent in terms of certainty and reliability. Since the transient values after a transmission line fault contain a large amount of fault information and are less affected by external factors, compared with classical algorithms, they have great advantages in terms of reliability and accuracy. The fault electrical characteristic value data of the transmission line is relatively large, containing uncertainty and disorder. If the original information signal is directly analyzed, a good analysis result may not be obtained. Therefore, to avoid such phenomena, when a fault occurs in the power transmission line, the system must respond quickly and accurately to the fault section to prevent affecting the parallel operation ability of the entire power grid and the stability of local power supply. Summary of the Invention

[0004] The purpose of the present invention is to overcome the deficiencies of the prior art and provide a transmission line fault detection method based on an improved VMD algorithm to solve the problems raised in the background art.

[0005] The technical solution adopted by the present invention is as follows: A transmission line fault detection method based on an improved VMD algorithm includes the following steps:

[0006] S1: Collect and analyze the fault traveling wave signal;

[0007] S2: Preprocess the fault traveling wave signal and perform fault principle analysis;

[0008] S3: Establish a fault location ranging model for the transmission line through the double - end traveling wave ranging method;

[0009] S4: Determine the fault location by improving the VMD algorithm and using the double - end traveling wave ranging algorithm.

[0010] Specifically, in step S1, the acquisition of the fault traveling wave signal is the prerequisite for the completion of the fault traveling wave ranging work. The traveling wave current signal of the transmission line is obtained by the direct method; the direct method is to extract the traveling wave current signal by the induction of the sensor. The sensor has sufficient bandwidth and high sampling frequency, ensuring the accuracy of the acquisition of the fault transient current data and avoiding the distortion of the traveling wave.

[0011] In step S2, when a fault occurs in the transmission line, under the action of the fault voltage, the fault traveling wave at the fault point will propagate along the transmission line to both ends. The transmission line can be regarded as a uniformly distributed parameter loop composed of resistance, inductance, capacitance, and susceptance. The voltage and current continuously change with time and space in the distributed parameter loop, but there is a certain functional relationship between the voltage and current at any point. This functional relationship is called the wave equation:

[0012]

[0013] For further simplification, assume that the line is a lossless line, and substitute R = 0, G = 0 into the above formula, then the wave equation is simplified to:

[0014]

[0015] Solve its d'Alembert solution:

[0016]

[0017] In the formula: is the wave velocity; u + and u - are the forward - traveling wave and backward - traveling wave of the voltage; i + and i - are the forward - traveling wave and backward - traveling wave of the current. The forward - traveling wave propagates in the positive direction of the X - axis, and the backward - traveling wave propagates in the negative direction of the X - axis. There is a certain relationship between the positive and negative traveling waves of the voltage and the positive and negative traveling waves of the current:

[0018]

[0019] In the formula: is the wave impedance. From the expression, it can be known that the wave velocity and wave impedance are only related to the inductance and capacitance per unit length, and have nothing to do with the length of the line.

[0020] In step S3, the double-ended traveling wave ranging method requires installing ranging devices at both ends of the transmission line to record the arrival times of the fault traveling waves at both sides, and calculating the fault distance using the time difference.

[0021] When a fault occurs at point F on transmission lines M and N, the traveling waves generated at the fault point propagate towards measurement ends M and N, and the arrival times at measurement points M and N installed at the busbars are respectively denoted as t M 、t N , and the distances from fault point F to measurement ends M and N are denoted as x MF 、x NF . Through analysis, it can be known that:

[0022]

[0023] Furthermore, the distance formula from fault point F to the two measurement points is obtained as:

[0024]

[0025] It can be seen from the above formula that the double-ended ranging method only needs to process the transient signal through digital signal processing means to calibrate t M and t N . By calculating the difference between t M and t N and combining the traveling wave transmission speed v and the length l of the line, the fault point can be calculated, which not only reduces the ranging difficulty but also effectively reduces the information loss caused by the energy attenuation of the fault traveling wave during transmission.

[0026] In step S4, the function of the VMD algorithm is to decompose the composite signal into multiple sub-modalities according to the frequency bandwidth. The VMD algorithm completes the decomposition of the signal and the acquisition of signal components under the variational framework. By constructing and solving the variational constraint problem, the original signal is adaptively decomposed. In the application of processing fault signals, it can effectively decompose modal components with different center frequencies and bandwidths according to the frequency domain characteristics of the signal and is not easily affected by frequency changes, and has good noise robustness.

[0027] The beneficial effects of the present invention: The present invention proposes a transmission line fault detection method based on improved VMD, collects and analyzes fault traveling wave signals; preprocesses the fault traveling wave signals and conducts fault principle analysis; establishes a transmission line fault ranging model through the double-ended traveling wave ranging method; determines the fault location through the improved VMD algorithm and the double-ended traveling wave ranging algorithm. It improves the success rate of fault detection, enhances the adaptability of operation strategies, improves the system operation efficiency, and provides an important technical guarantee for the safe and stable operation of the power grid. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 Schematic diagram of refraction and reflection of traveling waves of the present invention;

[0029] Figure 2 Principle diagram of double - end ranging in the present invention;

[0030] Figure 3 Schematic diagram of actual power transmission line in the present invention;

[0031] Figure 4 Flow chart of positioning of the new double - end traveling wave ranging algorithm in the present invention. Specific implementation mode

[0032] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts belong to the scope of protection of the present invention. The following will be specifically described in conjunction with the embodiments.

[0033] As Figures 1-4 shown, the present invention includes the following steps:

[0034] S1: Collect and analyze the fault traveling wave signal; the specific process is as follows:

[0035] In step S1, the collection of the fault traveling wave signal is the prerequisite for the completion of fault traveling wave ranging. The traveling wave current signal of the power transmission line is obtained by the direct method; the direct method is to extract the traveling wave current signal by the induction of the sensor. The sensor has sufficient bandwidth and high sampling frequency, ensuring the accuracy of the fault transient current data collection and avoiding the distortion of traveling waves.

[0036] S2: Pre - process the fault traveling wave signal and analyze the fault principle; the specific process is as follows:

[0037] In step S2, when a fault occurs in the power transmission line, under the action of the fault voltage, the fault traveling wave at the fault point will propagate along the power transmission line to both ends. The power transmission line can be regarded as a uniformly distributed parameter circuit composed of resistance, inductance, capacitance and susceptance. The voltage and current change continuously with time and space in the distributed parameter circuit, but there is a certain functional relationship between the voltage and current at any point. This functional relationship is called the wave equation:

[0038]

[0039] For further simplification, assuming that the line is a lossless line and substituting R = 0, G = 0 into equation (1), the wave equation is simplified to:

[0040]

[0041] Solve its d'Alembert solution:

[0042]

[0043] Where: is the wave velocity; u + and u - are the forward and backward traveling waves of voltage; i + and i - are the forward and backward traveling waves of current. The forward traveling wave propagates in the positive direction of the X-axis, and the backward traveling wave propagates in the opposite direction of the X-axis. There is a certain relationship between the forward and backward traveling waves of voltage and the forward and backward traveling waves of current:

[0044]

[0045] Where: is the wave impedance. From the expression, it can be known that the wave velocity and wave impedance are only related to the inductance and capacitance per unit length, and have nothing to do with the length of the line.

[0046] As Figure 1 shown, when the transient traveling wave propagates along the line, refraction and reflection are important parts of the traveling wave theory. Figure 1 is the schematic diagram of traveling wave refraction and reflection. In the figure, A represents the fault point, that is, the point where the wave impedance changes. The wave impedances on both sides of point A are Z1 and Z2. When the transient traveling wave propagating along the line, that is, the incident wave, encounters point A, the traveling wave will undergo refraction and reflection phenomena. The direction of the refracted wave of the traveling wave is the same as that of the incident wave, and the direction of the reflected wave is opposite to that of the incident wave. The existence of refraction and reflection of the traveling wave is to prevent sudden changes in voltage and current at point A.

[0047] There is a certain coefficient relationship between the incident wave, refracted wave and reflected wave of voltage and current at the two sections of the line with wave impedances Z1 and Z2:

[0048]

[0049]

[0050] Where β is the reflection coefficient; γ is the refraction coefficient.

[0051] Combining the above equations, the refraction and reflection coefficients under different wave impedance conditions can be obtained;

[0052] (1) When Z2 = ∞, that is, the line terminal is open, positive total reflection will occur on the line, and there will be no refraction phenomenon. The reflection coefficient: β u = 1, β i = -1, the refraction coefficient: γ u = 2, γ i = 0. This is a process in which all magnetic field energy is converted into electric field energy.

[0053] (2) When Z2 = 0, that is, the line terminal is short-circuited to ground, a negative total reflection will occur on the line, and no refraction phenomenon will appear. The reflection coefficient: β u = -1, β i = 1, the refraction coefficient: γ u = 0, γ i = 2, this is a process in which all electric field energy is converted into magnetic field energy.

[0054] In practice, there are electromagnetic fields in each conductor of the three-phase transmission line, which will affect other conductors. When alternating current flows through the line, the alternating voltage and alternating current in each phase will produce electric field and magnetic field coupling phenomena due to the fluctuation of the alternating current frequency and the influence of electromagnetic effects, resulting in the loss of the fault characteristics of the fault voltage and current traveling waves. Therefore, in the analysis of traveling waves, in order to eliminate the three-phase coupling phenomenon, the transient quantities of the three-phase voltage and current collected need to be subjected to phase-mode transformation to obtain the line-mode components and zero-mode components of the three-phase voltage and current that have eliminated the three-phase coupling and are independent of each other.

[0055] The voltage and current relationships of the three-phase lossless conductors are as follows:

[0056]

[0057]

[0058] Where: L S is the self-inductance of each phase conductor; L m is the mutual inductance of each phase conductor; C0 is the capacitance of each phase conductor to the ground; C m is the capacitance between each phase conductor.

[0059] Since the coefficient matrix in the formula contains non-diagonal elements, it is not easy to solve. The inductance matrix and capacitance matrix in the above formula can be subjected to coordinate transformation to transform the phase space into the mode space, so that the non-diagonal elements of the coefficient matrix become 0. After performing phase-mode transformation on the above two formulas, the matrices are denoted as S and Q respectively, then the voltage and current after transformation can be denoted as:

[0060]

[0061] The decoupled matrix representation of the above formula is:

[0062]

[0063] Performing second partial derivative differentials gives:

[0064]

[0065] The phase components are transformed into a diagonal matrix after decoupling transformation, and each mode is also independent of each other. So far, the key to the solution lies in the S and Q matrices.

[0066] Select the Karen-Bell transform for the phase-mode transformation matrix as follows:

[0067]

[0068] Through the phase-mode transformation, the electromagnetic coupling between the three phases can be eliminated, and the line-mode component and zero-mode component required for further analysis can be obtained.

[0069] S3: Establish a fault location ranging model for the transmission line through the double-terminal traveling wave ranging method; the specific process is as follows:

[0070] In the step S3, the double-terminal traveling wave ranging method is to install ranging devices at both ends of the transmission line to record the moments when the fault traveling wave arrives at both sides, and use the time difference to obtain the fault distance;

[0071] As Figure 2 shown, when a fault occurs at point F on the transmission lines M and N, the traveling wave generated at the fault point propagates towards the two measurement ends M and N, and the moments when it arrives at the measurement points M and N installed at the busbars are respectively recorded as t M 、t N , and the distances from the fault point F to the two measurement ends M and N are recorded as x MF 、x NF , and through analysis, it can be known that:

[0072]

[0073] Furthermore, the distance formula from the fault point F to the two measurement points is obtained as:

[0074]

[0075] It can be seen from Equation (14) that the double-terminal ranging method only needs to process the transient signal through digital signal processing means to calibrate t M and t N , and by calculating the difference between t M and t N , combined with the traveling wave transmission speed v and the length l of the line, the fault point can be calculated, which not only reduces the ranging difficulty but also effectively reduces the information loss caused by the energy attenuation of the fault traveling wave during the transmission process.

[0076] S4: Through the improved VMD algorithm and using the double-terminal traveling wave ranging algorithm, determine the fault location. The specific process is as follows:

[0077] In step S4, the VMD algorithm is used to decompose the composite signal into multiple sub-modalities according to the frequency bandwidth. The VMD algorithm completes the decomposition of the signal and the acquisition of signal components under the variational framework. By constructing and solving the variational constraint problem, the original signal is adaptively decomposed. In the application of processing fault signals, it can effectively decompose modal components with different center frequencies and bandwidths according to the frequency domain characteristics of the signal and is not easily affected by frequency changes, and has good noise robustness.

[0078] The decomposition process of VMD is the process of solving the variational problem, including the construction and solution of the variational problem:

[0079] 1) Construction of the variational problem

[0080] The VMD variational problem is to decompose the analytical signal f into K modal functions u k (t). If each'modality' has a finite bandwidth with a center frequency, then the sum of the estimated bandwidths of each modality is minimized. The bandwidth of each modality is estimated as follows:

[0081] (1) Through the Hilbert transform, calculate the analytical signal of each modal function u k (t) to obtain its single-sided spectrum.

[0082] (2) Modulate the spectrum of each modality to the corresponding base frequency band through the hybrid estimated center frequency e -jωkt .

[0083] (3) Calculate the square L 2 norm of the gradient of the above demodulated signal to estimate the bandwidth of each modal signal.

[0084] Assume that the original signal f is decomposed into K IMF components, then the corresponding constrained variational model expression is:

[0085]

[0086] In the formula, {u k} are the K IMF components obtained by decomposition, {u k} = {u1,... u k}; {ω k} are the frequency centers of each component, {ω k} = {ω1,..., ω K}.

[0087] 2) Solution of the variational problem

[0088] Introduce the quadratic penalty factor α and the Lagrange multiplier operator λ(t) into the above formula, and transform the constrained variational problem into an unconstrained variational problem. The obtained augmented Lagrange expression is:

[0089]

[0090] Equation (16) uses the alternating direction multiplier algorithm to find the saddle point of the above augmented Lagrange function, which is the optimal solution, thus decomposing the original signal f into K narrowband IMF components.

[0091] During the solution process, it is necessary to update and λ n+1 . The problem of the value of

[0092]

[0093] For simplicity, it is considered that Then there is is equivalent to ∑ i≠k u i (t) n+1 ; Using Parseval / Plancherel and Fourier isometric transformation, Equation (17) is transformed into the frequency domain:

[0094]

[0095] Using ω - ω k to replace ω in the first term of Equation (18), there is

[0096]

[0097] Writing Equation (19) in the form of an integral over the non - negative frequency interval

[0098]

[0099] The solution of the frequency can be easily obtained through quadratic optimization

[0100]

[0101] Similarly, when expressed in terms of the center frequency, when the center frequency ω k only appears in the bandwidth expression term of the reconstructed signal, the related problem can be described as

[0102]

[0103] Optimizing as above gives

[0104]

[0105] Solving gives

[0106]

[0107] In the formula, For the current remaining amount Wiener filtering; is the centroid of the current modal function power spectrum. For perform the inverse Fourier transform, and its real part is {u k (t)}.

[0108] The VMD algorithm process is as follows:

[0109] 1) Initialize and n = 0.

[0110] 2) n = n + 1, execute the loop.

[0111] 3) Update u k and ω k according to Equation (21) or Equation (24).

[0112] 4) k = k + 1, repeat step 3) until k = K ends.

[0113] 5) Update λ according to Equation (25).

[0114]

[0115] 6) Repeat steps 2) to 5), if then the iteration ends.

[0116] The VMD algorithm is simple. Each mode is continuously updated in the frequency domain and finally transformed to the time domain through the inverse Fourier transform. As the centroid of the power spectrum of each mode, the center frequency is re-estimated and updated in this cycle. When the fidelity requirement for the decomposition result is low, τ can be set to zero.

[0117] The Teager Energy Operator (TEO) is a non-linear operator with small computational complexity, which can quickly and accurately track the changes of signals and is suitable for real-time detection and processing of signals. Based on this feature, TEO is used to obtain the instantaneous change of signal energy, and the moment corresponding to the first mutation point on the instantaneous frequency spectrum is the moment when the fault initial traveling wave arrives at the detection point. If the signal is s(t), TEO can be defined as

[0118] ψ[s(t)] = s' 2 (t) - s(t)s”(t) (26)

[0119] where s'(t) is the derivative of s(t); ψ is the energy operator.

[0120] For discrete signals, Equation (26) can be approximately expressed as:

[0121] ψ[s(n)] = s 2(n) - s(n + 1)s(n - 1) (27)

[0122] A new type of double - end ranging algorithm corresponds the horizontal distance of the line with the actual position when obtaining line parameters, reduces the error level, and can indirectly improve the accuracy of fault location. The schematic diagram of the actual transmission line erected is as Figure 3 .

[0123] From Figure 3 it can be seen that the actual distance of the line and the theoretical horizontal distance exist with a proportionality coefficient k. And the expansion and contraction of the line within the same time period is uniform, so:

[0124]

[0125] Let the fault occurrence time of the line at point F be recorded as t0, and the actual times when the initial fault traveling - wave head travels along the line to the detection points M and N at both ends are recorded as t M , t N . The actual distance of the transmission line MN is the sum of the actual distance d' MF from the fault point F to the measurement point M and the actual distance d' NF from the fault point F to the measurement point N. The expression is:

[0126] L' = v(t M - t0) + v(t N - t0) (29)

[0127] The actual distance from the fault point F to the measurement point M is:

[0128] d' MF = v(t M - t0) (30)

[0129] From equations (28) and (29), the horizontal theoretical distance d MF from the fault point to the M - end is:

[0130]

[0131] What is calculated through equation (31) is the geographical horizontal distance from the fault point F to the measurement point M without considering the influence of the wire suspension factor. Compared with the traditional ranging method, it avoids the influence brought by the actual length of the line and the traveling - wave velocity. Only by detecting the time when the initial traveling - wave head reaches the measurement point and combining the given length of the transmission line, it can be calculated through equation (31), which greatly improves the working efficiency in practical applications.

[0132] Figure 4It is the location flow chart of a new type of double - ended traveling - wave ranging algorithm. When a fault occurs in a transmission line, fault traveling waves are generated at the fault point and transmitted along the line to both ends. The fault recording devices installed at both ends of the line collect the fault current traveling waves, and the phase - mode transformation is performed on the fault current traveling waves to remove electromagnetic coupling and obtain the required current line - mode components. Then, the VMD decomposition method is used to decompose the current line - mode components to obtain K IMF components with different frequencies and no mode mixing. The IMF component with the highest frequency is selected as the fault transient characteristic signal component for analysis, and its Teager energy value is calculated. The energy value curve is plotted, and the peak point in the curve is the moment when the fault initial traveling wave arrives. Finally, the moments when the fault initial traveling waves arrive at both ends are substituted into formula (31) of the double - ended ranging method that is not affected by the wave velocity to obtain the distance to the fault point.

[0133] For the faults of transmission lines, when a fault occurs in a transmission line, sudden and high - frequency transient traveling waves will be generated at the fault point, and the voltage and current traveling waves carry rich fault information and propagate to both ends of the line. By analyzing the fault system, the generation and reflection and refraction of traveling waves are studied. There is a coupling phenomenon between conductors due to the mutual influence of electric and magnetic fields, so the phase - mode transformation of transient traveling waves is required, and the Karenbauer transform is selected for phase - mode transformation. A fault ranging model for transmission lines is established by the double - ended traveling - wave ranging method. When applying the double - ended traveling - wave ranging method, there is no need to determine the fault point position and the reflected wave head. Only the wave - head information of the fault traveling waves transmitted to both ends needs to be obtained, which is not only easy to identify but also ensures reliability. Based on the traveling - wave wave - head detection method of VMD and TEO, considering the actual situation of the propagation of fault traveling waves in the line, a new double - ended traveling - wave fault ranging algorithm is derived, and the ranging result is not affected by the traveling - wave velocity and the change of the actual length of the line, and the fault location is more reliable.

[0134] For those skilled in the art, it is obvious that the present invention is not limited to the details of the above - mentioned exemplary embodiments, and the present invention can be implemented in other specific forms without departing from the spirit or basic characteristics of the present invention. Therefore, from any point of view, the embodiments should be regarded as exemplary and non - restrictive. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, all changes falling within the meaning and scope of the same elements of the claims are intended to be included in the present invention. Any reference signs in the claims should not be regarded as limiting the claimed rights.

Claims

1. A transmission line fault detection method based on an improved VMD algorithm, characterized in that, It includes the following steps: S1: Collect and analyze the fault traveling wave signal; S2: Preprocess the fault traveling wave signal and conduct fault principle analysis; S3: Establish a fault location ranging model for the transmission line by the double - end traveling wave ranging method; S4: Determine the fault location by improving the VMD algorithm and using the double - end traveling wave ranging algorithm.

2. The method for detecting faults in a transmission line based on an improved VMD algorithm according to claim 1, wherein: In step S1, the collection of the fault traveling wave signal is the premise for the completion of the fault traveling wave ranging work. The traveling wave current signal of the transmission line is obtained by the direct method. The direct method extracts the traveling wave current signal by the induction of the sensor. The sensor has sufficient bandwidth and high sampling frequency, ensuring the accuracy of the fault transient current data collection and avoiding the distortion of the traveling wave.

3. A transmission line fault detection method based on an improved VMD algorithm according to claim 1, characterized in that: In step S2, when a fault occurs in the transmission line, under the action of the fault voltage, the fault traveling wave at the fault point will propagate along the transmission line to both ends. The transmission line can be regarded as a uniformly distributed parameter circuit composed of resistance, inductance, capacitance, and susceptance. The voltage and current continuously change with time and space in the distributed parameter circuit, but there is a certain functional relationship between the voltage and current at any point. This functional relationship is called the wave equation: For further simplification, assume that the line is a lossless line, substitute R = 0, G = 0 into the above formula, then the wave equation is simplified to: Solve its d'Alembert solution: In the formula: is the wave velocity; u + and u - are the forward and backward traveling waves of voltage; i + and i - are the forward and backward traveling waves of current. The forward traveling wave propagates in the positive direction of the X-axis, and the backward traveling wave propagates in the negative direction of the X-axis. There is a certain relationship between the forward and backward traveling waves of voltage and the forward and backward traveling waves of current: Wherein: is the wave impedance. It can be known from the expression that the wave velocity and the wave impedance are only related to the inductance and capacitance per unit length, and have nothing to do with the length of the line.

4. A transmission line fault detection method based on an improved VMD algorithm according to claim 1, characterized in that: In step S3, the double - end traveling wave ranging method is to install ranging devices at both ends of the transmission line to record the moments when the fault traveling wave arrives at both sides, and use the time difference to obtain the fault distance; When a fault occurs at point F on transmission lines M and N, the traveling waves generated at the fault point propagate towards the two measurement ends M and N, and the arrival times at the measurement points M and N installed at the busbar ends are respectively denoted as t M 、t N , and the distances from the fault point F to the two measurement ends M and N are denoted as x MF 、x NF . Through analysis, it can be known that: Furthermore, the distance formulas from the fault point F to the two measurement points are obtained as: It can be seen from the above formula that the double - ended ranging method only needs to process the transient signal through digital signal processing means to calibrate t M and t N . By calculating the difference between t M and t N , combining the traveling - wave transmission speed v and the length l of the line, the fault point can be calculated, which not only reduces the ranging difficulty, but also can effectively reduce the information loss caused by the energy attenuation of the fault traveling wave during the transmission process.

5. A transmission line fault detection method based on an improved VMD algorithm according to claim 1, characterized in that: In step S4, the role of the VMD algorithm is to decompose the composite signal into multiple sub - modes according to the frequency bandwidth. The VMD algorithm completes the decomposition of the signal and the acquisition of the signal components under the variational framework. By constructing and solving the variational constraint problem, the original signal is adaptively decomposed. In the application of processing the fault signal, it can effectively decompose the modal components with different center frequencies and bandwidths according to the frequency domain characteristics of the signal and is not easily affected by frequency changes, having good noise robustness.

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