A fault line selection and positioning method for DG-containing distribution network based on directional traveling wave energy entropy and WMA-VMD-GTKO double-ended traveling wave

Abstract

The application relates to the technical field of power distribution network fault detection, and provides a DG-containing power distribution network fault line selection and positioning method based on directional wave energy entropy and WMA-VMD-GTKO double-end wave, proposes a directional wave energy entropy line selection mechanism, constructs directional waves through Kailunbei transformation, combines wavelet packet decomposition and energy entropy calculation, takes the maximum of reverse wave energy entropy of a fault line as a criterion, and realizes fault line selection of the DG-containing power distribution network; a WMA-VMD-GTKO double-end wave positioning model is constructed: the whale migration algorithm is used to dynamically optimize the mode number and the penalty factor of the variational mode decomposition, and high-frequency features of the wave are adaptively extracted; the time-frequency energy is fused through a generalized energy operator, the wave head features are enhanced, and the arrival time is identified in combination with a dynamic threshold; based on the high-frequency mode center frequency obtained through VMD decomposition, a dynamic correction relationship between the wave speed and the frequency is established, the double-end distance measurement formula is substituted, and the positioning error problem is solved; the application is accurate in line selection, high in positioning precision, and suitable for complex working conditions of the DG-containing power distribution network.

Description

Technical Field

[0001] This invention relates to the field of distribution network fault detection technology, and more specifically, to a fault location method for distribution networks containing DG based on directional traveling wave energy entropy and WMA-VMD-GTKO double-ended traveling wave. Background Technology

[0002] With the rapid development of the new energy industry, distributed generation (DG) power sources such as photovoltaic inverters and energy storage converters have been widely integrated into medium and low voltage distribution networks. This has effectively improved the power supply flexibility and energy utilization efficiency of the distribution network, but it has also changed the traditional radial topology and electrical characteristics of the distribution network, making it a complex network with multiple power sources. However, the integration of DG has brought many challenges to traveling wave-based fault location, and existing fault location and fault location technologies are insufficient to meet the requirements. Specifically: Existing fault location techniques generally employ steady-state component method, transient component method, and single-energy entropy method. Their current status and limitations are as follows: The steady-state component method identifies faulty lines by comparing the amplitude and phase of the zero-sequence and negative-sequence currents of each line, based on the steady-state components of the fault signal. Typical methods include the group amplitude-phase comparison method and the zero-sequence admittance method. However, the integration of distributed generation (DG) alters the positive-sequence network structure of the distribution network, distorting the steady-state current characteristics. In high-resistance grounding scenarios, the difference in zero-sequence current is slight, significantly reducing the accuracy of line selection. Furthermore, the compensation effect of the arc suppression coil further interferes with the discriminative power of the steady-state characteristics. Traditional transient component line selection methods utilize characteristic quantities such as transient traveling waves and first half-waves for line selection, such as the traveling wave method and the transient zero-sequence energy method. However, harmonics generated by power electronic equipment in distributed generation (DG) can severely interfere with the traveling wave characteristics, and the inverter's control strategy can cause distortion in the transient process. This results in a high wavefront identification error rate for traditional methods in DG-containing scenarios, making it impossible to accurately identify faulty lines. The single energy entropy line selection method identifies faulty lines solely by calculating the signal energy entropy value, without considering the directional traveling wave characteristics, which has obvious drawbacks: on the one hand, the energy entropy calculation of noisy signals is easily interfered with, resulting in a high misjudgment rate in low signal-to-noise ratio environments; on the other hand, it cannot distinguish the direction of traveling wave propagation, and the energy entropy distribution is disordered in multi-source DG scenarios, making it difficult to reliably identify faulty lines.

[0003] Existing fault location technologies generally employ traditional traveling wave methods and matrix operation methods. Their current status and limitations are as follows: The traditional traveling wave method relies on the principle that electromagnetic waves, when propagating along a transmission line, are reflected and refracted when they encounter a fault point. It determines the location of the fault by measuring the time difference or amplitude changes of the traveling wave front arriving at different measurement points. However, this method suffers from severe signal attenuation and difficulties in synchronous measurement: distribution networks with distributed generation (DG) typically have multiple branches and short lines, making the traveling wave signal prone to attenuation and distortion during transmission, resulting in a weak received fault traveling wave signal and affecting location accuracy. Furthermore, precise synchronous measurement equipment is needed to ensure accurate measurement of the traveling wave arrival time at each measurement point, but achieving precise synchronization between all measurement points is quite challenging.

[0004] Matrix algorithms primarily construct a network topology model and fault information matrix for the distribution network, using matrix operations to determine faulty sections. Common methods include unified matrix algorithms and novel matrix algorithms. However, these techniques have poor fault tolerance and require high accuracy in fault information. Incorrect or incomplete fault information can easily lead to erroneous location results. Furthermore, some matrix algorithms have limitations in accurately locating faults at the feeder's end.

[0005] In summary, existing fault location methods can no longer meet the fault detection requirements of distribution networks with distributed generation (DG). Therefore, it is necessary to propose an adaptable method with strong anti-interference capabilities, accurate fault selection, and high location accuracy. Summary of the Invention

[0006] The problem addressed by this invention is how to provide a fault location method for distribution networks containing DG, based on directional traveling wave energy entropy and WMA-VMD-GTKO double-ended traveling wave, which has strong anti-interference ability, accurate fault selection, and high positioning accuracy.

[0007] To address the aforementioned issues, this invention provides a fault location method for distribution networks with DG based on directional traveling wave energy entropy and WMA-VMD-GTKO double-ended traveling wave, comprising: signal acquisition, acquiring three-phase voltage and current data of the distribution network, and extracting transient components from the acquired data; For fault line selection, Kelenberg phase-mode transformation is performed on transient components to separate zero-mode current traveling waves and reduce three-phase coupling interference. Then, wavelet packet decomposition and energy entropy calculation are used to quantify the fault characteristic information of each line and determine the fault line based on the criterion of the maximum energy entropy value of the fault line. For fault location, bandpass filtering and noise suppression are applied to the acquired zero-mode current traveling wave. Then, the Whale Migration Algorithm (WMA) is used to dynamically optimize the mode number and penalty factor of Variational Mode Decomposition (VMD), enabling VMD to adaptively decompose the traveling wave signal and extract high-frequency modes containing wavefront features. Next, the generalized energy operator (GTKO) is used to fuse time-domain differential and Wigner-Ville frequency-domain gradient energy to enhance the transient features of the wavefront. The arrival times of the traveling waves at both ends are identified by dynamic thresholding. Finally, based on the time difference between the two ends and the characteristic frequency of the VMD modes, the wave velocity is dynamically corrected and substituted into the two-end ranging formula to calculate the fault distance, achieving high-precision location of fault points in distribution networks containing DG.

[0008] Furthermore, the step of performing Kalenberg phase-mode transformation on the transient components to separate the zero-mode current traveling wave includes: using a Kalenberg transformation matrix to decouple the three-phase currents and separate the zero-mode current traveling wave; and using the decoupled zero-mode current, zero-mode voltage, and line wave impedance to construct a forward traveling wave flowing from the bus to the line and a reverse traveling wave flowing from the line to the bus.

[0009] Furthermore, the quantification of fault characteristic information for each line using wavelet packet decomposition and energy entropy calculation includes: wavelet packet decomposition, using the db3 wavelet to perform 3-level wavelet packet decomposition on the reverse zero-mode current traveling wave, obtaining 8 frequency bands, and selecting the 7.5~8.75kHz frequency band as the fault characteristic frequency band; the energy corresponding to the i-th frequency band of the j-th level is: In the formula The wavelet packet coefficients of the i-th frequency band in the j-th layer reflect the energy distribution of the signal in that frequency band. N is the sampling point number, with a value of 200, corresponding to a time window of 10ms. The total energy of the j-th layer is: ,definition Let be the ratio of the energy of the i-th frequency band of the j-th layer of the signal to the total energy of the signal. ; The energy entropy value T of the fault characteristic frequency band is calculated using the following formula: ; The faulty line is determined by identifying the line with the highest energy entropy value.

[0010] Furthermore, the bandpass filtering and noise suppression of the acquired zero-mode current traveling wave includes: using an 8th-order Butterworth bandpass filter to filter the zero-mode current traveling wave, wherein the passband range of the filter is set to 5~15kHz, and its transfer function is: , where s is the Laplace transform variable, used to describe the characteristics of the system in the complex frequency domain; These are the resonant angular frequencies of each order; The damping coefficient is 0.707.

[0011] Furthermore, the dynamic optimization of the number of modes and penalty factor in variational mode decomposition (VMD) using the whale migration algorithm (WMA) includes: Initialize the whale population, with each individual whale corresponding to a set of VMD modal numbers K and penalty factors α, and the initialization range is K∈[2,10], α∈[200,3500]; Fitness is calculated using the sum of the kurtosis of the decomposed mode functions as the fitness function, as shown in the formula: ,in, Let be the kurtosis of the i-th mode function. The larger the kurtosis, the more significant the signal features and the larger the fitness value, indicating that K and α are better. Whale location updates: When the whale is outside and far from its prey, a spiral update mechanism is used, with the update formula as follows: ,in, b is a constant that controls the shape of the logarithmic spiral, and is usually taken as 1. It is a random number in the range [-1, 1]; when the whale is near or close to its prey, a global random search for prey is performed, and the update formula is: ,in, It randomly selects the position of an individual from the current population, where A is a coefficient vector. ; The termination condition is determined as follows: if the maximum number of iterations (15) is reached or the fitness value changes less than a preset threshold, the iteration stops and the optimal number of modes K and the penalty factor α are output; otherwise, the fitness calculation is restarted.

[0012] Furthermore, the step of enabling VMD adaptive decomposition of the traveling wave signal includes: Constructing and solving the variational model: Taking the zero-mode current traveling wave signal as the object, a variational model is constructed, and the objective function of VMD is: ; in, The decomposed mode set, Here, α represents the center frequency of each mode, and α is the penalty factor. For unit impulse function, " indicates convolution operation; The variational model is solved using an alternating iterative method, with the number of modes K and the penalty factor α set, and the mode functions initialized. Center frequency and Lagrange multipliers For each mode k, solve in the frequency domain ,in, , , These are the frequency domain representations of the signal, mode, and Lagrange multipliers, respectively. The center frequency and Lagrange multipliers are updated sequentially until the convergence condition is met. Stop iteration when threshold Value The formula for updating the center frequency is: The formula for updating the Lagrange multipliers is: ,in, To update the step size, it is usually set to [0.5, 1] ​​to ensure the convergence of the variational model; High-frequency mode screening involves sorting the K decomposed modes from low to high center frequency and selecting high-frequency modes with center frequencies in the range of 8 to 12 kHz.

[0013] Furthermore, the enhancement of wavefront transient characteristics by fusing time-domain differentiation and Wigner-Ville frequency-domain gradient energy through a generalized energy operator includes: The high-frequency modal signal obtained by VMD decomposition is resampled to 100kHz to eliminate wavefront distortion caused by insufficient sampling rate; The first-order differential is calculated using the 5-point central difference method to suppress high-frequency noise, and the time-domain differential energy is also calculated. The formula for calculating the first-order differential is as follows: , Given the sampling interval, the formula for calculating the time-domain differential energy is: ; Apply a 20ms Hanning window to the signal, calculate the time-frequency distribution and frequency gradient, and obtain the frequency gradient energy. The formula for calculating the time-frequency distribution is as follows: , The formula for calculating the frequency domain gradient is: , For frequency resolution, taking a value of 100Hz, the formula for calculating frequency domain gradient energy is: ; Energy fusion weightedly couples the amplitude abrupt change characteristics of the time-domain derivative with the frequency abrupt change characteristics of the frequency-domain gradient. The fusion model is as follows: ; The fused energy sequence is mapped to the [0,1] interval, as expressed by: .

[0014] Furthermore, the step of combining dynamic thresholds to identify the arrival times of the traveling waves at both ends includes: A sliding window with a length of 200, corresponding to a 2ms time window, is used. Perform real-time statistics to calculate the mean and standard deviation within the window: , ; Introducing adaptive coefficients Adjust dynamic threshold Sensitivity: ; ; when First time exceeding And satisfy the rising slope When the wavefront arrives, it is determined to be the time of arrival. .

[0015] Furthermore, the step of calculating the fault distance by substituting the dynamic correction of wave velocity based on the time difference between the two ends, combined with the characteristic frequency of VMD mode, into the two-end ranging formula includes: For the initial fault distance calculation, assuming the measurement points at both ends of the distribution network are P and Q, the total line length is L, and the arrival times of the wavefront at both ends are t1 and t2, the initial calculation formula for the fault distance d is: ,in ; Dynamic correction of wave velocity: Based on the center frequency f of the high-frequency mode obtained by VMD decomposition, a dynamic correction relationship between wave velocity and frequency is established. ,in, The reference frequency; The final fault distance is calculated by substituting the dynamically corrected wave velocity v into the dual-end ranging model. .

[0016] Compared with the prior art, the beneficial effects of the present invention are: The fault line selection accuracy is high. It adopts Karenbell phase mode transformation to separate zero-mode current traveling waves, weakens three-phase coupling interference, and combines db3 wavelet decomposition and energy entropy calculation. It takes advantage of the fact that the energy entropy value of the fault line is the largest to avoid the interference of DG harmonics on the traveling wave characteristics, thus improving the reliability of line selection. The energy entropy of the directional traveling wave is fused with the traveling wave propagation direction characteristics, which can distinguish fault lines in multi-source DG scenarios and significantly reduce the misjudgment rate in low signal-to-noise ratio environments. It boasts high fault location accuracy and anti-interference capability. Utilizing WMA to dynamically optimize VMD parameters, it adaptively decomposes traveling wave signals and extracts high-frequency modes. Combined with the GTKO operator, it fuses time-domain differentiation and frequency-domain gradient energy to enhance wavefront transient characteristics, effectively suppressing DG harmonics and noise interference, thus improving wavefront identification accuracy. Dual-end ranging combined with VMD mode characteristic frequencies dynamically corrects wave velocity, resulting in more accurate fault location for short-line, multi-branch scenarios in DG-containing distribution networks. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the overall principle structure of an embodiment of the present invention. Detailed Implementation

[0018] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0019] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0020] In the description of this specification, references to terms such as "embodiment," "one embodiment," and "one implementation" indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or implementation is included in at least one embodiment or illustrative implementation of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or implementation. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or implementations.

[0021] like Figure 1 As shown, this invention provides a fault location method for distribution networks with distributed generation (DG) based on directional traveling wave energy entropy and WMA-VMD-GTKO double-ended traveling wave. The method includes: signal acquisition, acquiring three-phase voltage and current data of the distribution network, and extracting transient components from the acquired data; fault location, performing Kelvin phase-mode transformation on the transient components to separate the zero-mode current traveling wave and reduce three-phase coupling interference; and then using wavelet packet decomposition and energy entropy calculation to quantify the fault characteristic information of each line, and determining the faulty line based on the criterion of the maximum energy entropy value of the faulty line. For fault location, bandpass filtering and noise suppression are applied to the acquired zero-mode current traveling wave. Then, the Whale Migration Algorithm (WMA) is used to dynamically optimize the mode number and penalty factor of Variational Mode Decomposition (VMD), enabling VMD to adaptively decompose the traveling wave signal and extract high-frequency modes containing wavefront features. Next, the generalized energy operator (GTKO) is used to fuse time-domain differential and Wigner-Ville frequency-domain gradient energy to enhance the transient features of the wavefront. The arrival time of the traveling waves at both ends is identified by dynamic thresholding. Finally, based on the time difference between the two ends and the wave velocity is dynamically corrected by combining the characteristic frequencies of the VMD modes, the fault distance is calculated by substituting it into the two-end ranging formula, thus achieving high-precision location of fault points in distribution networks containing DG.

[0022] In one embodiment of the present invention, the fault line selection method includes: 1. Phase mode transformation and directional traveling wave extraction: To address the electromagnetic coupling problem of three-phase traveling waves in distribution networks containing distributed generation (DG), the Kelvin transform is used to decouple the three-phase currents. The Kelvin transform matrix is: ; This matrix represents the three-phase current. , , Convert to zero-mode current Linear current and : ; The zero-mode component flows only through the ground and is not affected by the positive sequence network of the DG, making it suitable for low-current grounding fault analysis.

[0023] Using the Kelvin transform matrix to obtain the decoupled zero-mode voltage and current, a directional traveling wave can be constructed: ; In the formula, This represents a positive traveling wave flowing from the busbar to the line. This represents the reverse traveling wave flowing from the line to the bus. The zero-mode current traveling wave of the line. The zero-mode voltage traveling wave of the line, This represents the wave impedance of the line. The reverse traveling wave energy of a faulty line is significantly higher than that of a non-faulty line, providing a key characteristic for subsequent line selection.

[0024] 2. Wavelet packet decomposition and energy entropy calculation: Considering that harmonics generated by the distribution grid (such as the 2kHz switching frequency) can interfere with the traveling wave characteristics, the db3 wavelet is used to perform three-level wavelet packet decomposition on the reverse zero-mode current traveling wave, resulting in eight frequency bands: 8.75~10kHz, 7.5~8.75kHz, 6.25~7.5kHz, 5~6.25kHz, 3.75~5kHz, 2.5~3.75kHz, 1.25~2.5kHz, and 0~1.25kHz. The 7.5~8.75kHz band is selected (to avoid the influence of high-frequency interference and the lower-frequency distribution network natural frequency components), as this band contains abundant high-frequency components of the fault traveling wave and is less affected by DG harmonic interference.

[0025] Perform wavelet packet decomposition on the signal, and the energy corresponding to the i-th frequency band of the j-th layer is: ; In the formula represents the wavelet packet coefficients of the j-th layer and the ith frequency band, reflecting the energy distribution of the signal in that frequency band; N is the sampling point number, with a value of 200, corresponding to a time window of 10ms. The total energy of the j-th layer is: ; definition The ratio of the energy of the i-th frequency band of the j-th layer of the signal to the total energy of the signal: ; Then the energy entropy is: ; Energy entropy measures the complexity of signal energy distribution across frequency bands. When energy is concentrated in a few frequency bands, T is small; when the energy distribution is more uniform, T is larger. Because faulty lines contain transient traveling wave changes, energy is concentrated in the high-frequency band, so T is significantly larger than that of non-faulty lines.

[0026] Therefore, the fault diagnosis criterion is: the line with the largest entropy value is the faulty line.

[0027] In one embodiment of the present invention, the fault location method includes: 1. Bandpass filtering and noise suppression: Harmonics generated by inverters in distributed generation (DG) networks (such as a 2kHz switching frequency) and environmental noise can interfere with the traveling wave characteristics. To extract a pure zero-mode current traveling wave signal, an 8th-order Butterworth bandpass filter is used, with a passband range of 5–15kHz. This frequency band avoids the main harmonic frequency band of DG (≤2kHz) while retaining the high-frequency components of the fault traveling wave (typical wavefront frequency 8–12kHz). The transfer function of the bandpass filter is: ; Where s is the Laplace transform variable, used to describe the characteristics of the system in the complex frequency domain; These are the resonant angular frequencies of each order; The damping coefficient (to ensure a flat amplitude-frequency response within the passband) is set to 0.707 here. After filtering, the signal-to-noise ratio of the zero-mode current traveling wave signal is significantly improved, laying the foundation for subsequent wavefront feature extraction.

[0028] 2. WMA dynamically optimizes VMD parameters: ① Overview of the Whale Migration Algorithm (WMA): The whale migration algorithm is a swarm intelligence optimization algorithm inspired by the migratory behavior of whales. In the algorithm, each whale represents a candidate solution, and the whale swarm continuously migrates and searches in the search space, gradually approaching the optimal solution through behaviors such as circling prey and using bubble-web attacks.

[0029] ②VMD parameter optimization process: Variational Mode Decomposition (VMD) is an adaptive signal decomposition method that can decompose complex signals into multiple mode functions. However, its decomposition performance is affected by the number of modes K and the penalty factor α. To determine the optimal K and α, WMA is introduced for dynamic optimization. The steps are as follows: 1) Initialize the whale population: Initialize the whale population position. Each whale corresponds to a set of K and α. The initialization range is K∈[2,10] and α∈[200,3500].

[0030] 2) Fitness Calculation: The fitness function measures the quality of an individual and is defined as the sum of the kurtosis of the decomposed mode functions. The sum of the kurtosis is used as the fitness function. ; in, Let be the kurtosis of the i-th mode function. The larger the kurtosis, the more significant the signal features and the larger the fitness value, indicating that K and α are better.

[0031] 3) Surrounding Prey: When the whale is outside and far from its prey, a spiral update mechanism is executed, where the current individual updates its position using a spiral bubble attack: ; in, b is a constant that controls the shape of the logarithmic spiral, usually taking the value 1, and l is a random number in [-1, 1].

[0032] 4) Bubble Web Attack: When the whale is near or close to its prey, it performs a global random prey search, updating the formula as follows: ; in, It randomly selects the position of an individual from the current population, where A is the coefficient vector. .

[0033] Termination criteria: The maximum number of iterations (15) is reached, or the fitness value changes less than a given threshold. .

[0034] Output optimal parameters: Output the optimal K and α for subsequent VMD decomposition.

[0035] 3. VMD Adaptive Decomposition of Traveling Wave Signals: ①VMD principles and variational models: Variational mode decomposition (VMD) decomposes complex signals into multiple finite-bandwidth modes (IMFs) by constructing and solving a variational model. Each mode corresponds to a center frequency. For zero-mode current traveling wave signals... The objective function of VMD is: ; in, The decomposed mode set, Let α be the center frequency of each mode, and α be the penalty factor (control bandwidth constraint). For unit impulse function, "" indicates convolution operation. This model achieves adaptive decomposition of the signal by minimizing the sum of the bandwidths of each mode.

[0036] ② Solving the variational model (alternating iterative method): 1) Set the number of modes K and the penalty factor α (the optimal K and α after WMA dynamic optimization), and initialize. , and Lagrange multipliers ; 2) For each mode k, solve in the frequency domain: ; in, , , Frequency domain representations of the signal, mode, and Lagrange multipliers, respectively; 3) Update the center frequency using a formula : ; 4) Update the Lagrange multipliers: ; To update the step size, it is usually set to [0.5, 1] ​​to ensure the convergence of the variational model; 5) When satisfied Stop iteration when threshold Value .

[0037] ③ High-frequency mode screening After decomposition, K modes are obtained, ordered by center frequency. Sort and filter the modalities The kHz mode (corresponding to the fault traveling wave characteristic frequency band). This frequency band mode contains complete wavefront information and can be used for subsequent GTKO operator processing.

[0038] 4. GTKO operator enhances wavehead characteristics: ① The high-frequency modal signal (center frequency 8~12kHz) obtained by VMD decomposition is resampled to 100kHz to eliminate wavefront distortion caused by insufficient sampling rate. The resampled high-resolution signal provides accurate time-domain samples for subsequent time-domain differential calculations, avoiding ambiguity of wavefront abrupt changes due to sparse sampling points.

[0039] ② The first-order differential is calculated using the 5-point central difference method to suppress high-frequency noise: ; in, Given the sampling interval, the time-domain differential energy is: ; The time-domain differential energy highlights the instantaneous changes in signal amplitude, but the single time-domain feature is susceptible to high-frequency noise interference caused by DG harmonics, and needs to be combined with frequency domain analysis to further enhance reliability.

[0040] ③ Apply a Hanning window (window length 20ms) to the signal and calculate the time-frequency distribution: ; in Given a conjugate complex number, suppress cross-term interference; calculate the frequency domain gradient: ; in For frequency resolution, the value is 100Hz; Calculate the frequency domain gradient energy: ; Frequency domain gradient energy captures the frequency change trend of characteristic frequency bands, complementing time domain differential energy. The time domain highlights amplitude changes, while the frequency domain suppresses low-frequency noise. The fusion of the two can effectively solve the shortcomings of single-domain analysis.

[0041] ④ The amplitude abrupt change feature of the time-domain derivative is weighted and coupled with the frequency abrupt change feature of the frequency-domain gradient. By integrating the frequency-domain energy enhancement feature continuity, a multi-dimensional enhancement effect on the wavefront is formed, providing a clear energy peak for subsequent threshold identification. The fusion model is as follows: ; Based on experience, The optimal weight is determined by these factors.

[0042] ⑤ Map the energy sequence to the [0,1] interval to facilitate subsequent wavefront time threshold identification: .

[0043] 5. Dynamic threshold wavefront timing identification: ① Use a sliding window with a length of 200, corresponding to a 2ms time window. Perform real-time statistics to calculate the mean and standard deviation within the window: ; ②Dynamic threshold Determined by a linear combination of the mean and standard deviation, an adaptive coefficient is introduced. Dynamically adjust sensitivity: , ; when First time exceeding And satisfy the rising slope When the wavefront arrives, it is determined to be the time of arrival. .

[0044] 6. Dual-end ranging and dynamic wave velocity correction: ① Let the measurement points at both ends of the distribution network be P and Q, the total length of the line be L, and the arrival times of the wavefront at both ends be t1 and t2. Then the initial formula for calculating the fault distance d is: ; in .

[0045] ② High-frequency modes (center frequency) obtained from VMD decomposition Includes the main characteristics of fault traveling waves, wave velocity v and The frequency correction relationship is as follows: ; in The reference frequency; Finally, the dynamically corrected wave velocity v is substituted into the two-end ranging model: .

[0046] While the disclosure is as stated above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of this disclosure, and all such changes and modifications will fall within the protection scope of this invention.

Claims

1. A method for fault location in a distribution network with DG based on directional traveling wave energy entropy and WMA-VMD-GTKO double-ended traveling wave, characterized in that, include: Signal acquisition involves collecting three-phase voltage and current data from the power distribution network and extracting transient components from the collected data. Fault line selection involves performing Kelvin phase-mode transformation on transient components to separate zero-mode current traveling waves and reduce three-phase coupling interference. Then, wavelet packet decomposition and energy entropy calculation are used to quantify the fault characteristic information of each line, and the fault line is determined based on the criterion of the maximum energy entropy value of the fault line. For fault location, bandpass filtering and noise suppression are applied to the acquired zero-mode current traveling wave. Then, the Whale Migration Algorithm (WMA) is used to dynamically optimize the mode number and penalty factor of Variational Mode Decomposition (VMD), enabling VMD to adaptively decompose the traveling wave signal and extract high-frequency modes containing wavefront features. Next, the generalized energy operator (GTKO) is used to fuse time-domain differential and Wigner-Ville frequency-domain gradient energy to enhance the transient features of the wavefront. The arrival time of the traveling waves at both ends is identified by dynamic thresholding. Finally, based on the time difference between the two ends and the wave velocity is dynamically corrected by combining the characteristic frequencies of the VMD modes, the fault distance is calculated by substituting it into the two-end ranging formula, thus achieving high-precision location of fault points in distribution networks containing DG.

2. The fault location method for distribution networks with DG based on directional traveling wave energy entropy and WMA-VMD-GTKO double-ended traveling wave as described in claim 1, is characterized in that, The step of performing a Kalenberg phase-mode transformation on the transient component to separate the zero-mode current traveling wave includes: The three-phase current is decoupled using the Kelvin transform matrix to separate the zero-mode current traveling wave. Using the decoupled zero-mode current, zero-mode voltage and line wave impedance, a forward traveling wave flowing from the bus to the line and a reverse traveling wave flowing from the line to the bus are constructed.

3. The fault location method for distribution networks with DG based on directional traveling wave energy entropy and WMA-VMD-GTKO double-ended traveling wave as described in claim 2, is characterized in that, The method of quantifying the fault characteristic information of each line using wavelet packet decomposition and energy entropy calculation includes: wavelet packet decomposition, using the db3 wavelet to perform 3-level wavelet packet decomposition on the reverse zero-mode current traveling wave, obtaining 8 frequency bands, and selecting the 7.5~8.75kHz frequency band as the fault characteristic frequency band; the energy corresponding to the i-th frequency band of the j-th level is: In the formula The wavelet packet coefficients of the i-th frequency band in the j-th layer reflect the energy distribution of the signal in that frequency band. N is the sampling point number, with a value of 200, corresponding to a time window of 10ms. The total energy of the j-th layer is: ,definition Let be the ratio of the energy of the i-th frequency band of the j-th layer of the signal to the total energy of the signal. ; The energy entropy value T of the fault characteristic frequency band is calculated using the following formula: ; The faulty line is determined by identifying the line with the highest energy entropy value.

4. The fault location method for distribution networks with DG based on directional traveling wave energy entropy and WMA-VMD-GTKO double-ended traveling wave as described in claim 3, is characterized in that, The bandpass filtering and noise suppression of the acquired zero-mode current traveling wave includes: An 8th-order Butterworth bandpass filter is used to filter the zero-mode current traveling wave. The passband range of the filter is set to 5~15kHz, and its transfer function is: , where s is the Laplace transform variable, used to describe the characteristics of the system in the complex frequency domain; These are the resonant angular frequencies of each order; The damping coefficient is 0.

707.

5. The fault location method for distribution networks with DG based on directional traveling wave energy entropy and WMA-VMD-GTKO double-ended traveling wave as described in claim 1, characterized in that, The method of dynamically optimizing the number of modes and penalty factor of variational mode decomposition (VMD) using the whale migration algorithm (WMA) includes: Initialize the whale population, with each individual whale corresponding to a set of VMD modal numbers K and penalty factors α, and the initialization range is K∈[2,10], α∈[200,3500]; Fitness is calculated using the sum of the kurtosis of the decomposed mode functions as the fitness function, as shown in the formula: ,in, Let be the kurtosis of the i-th mode function. The larger the kurtosis, the more significant the signal features and the larger the fitness value, indicating that K and α are better. Whale location updates: When the whale is outside and far from its prey, a spiral update mechanism is used, with the update formula as follows: ,in, b is a constant that controls the shape of the logarithmic spiral, and is usually taken as 1. It is a random number in the range [-1, 1]; when the whale is near or close to its prey, a global random search for prey is performed, and the update formula is: ,in, It randomly selects the position of an individual from the current population, where A is a coefficient vector. ; The termination condition is determined as follows: if the maximum number of iterations (15) is reached or the fitness value changes less than a preset threshold, the iteration stops and the optimal number of modes K and the penalty factor α are output; otherwise, the fitness calculation is restarted.

6. The fault location method for distribution networks with DG based on directional traveling wave energy entropy and WMA-VMD-GTKO double-ended traveling wave as described in claim 5, is characterized in that, The method of enabling VMD adaptive decomposition of traveling wave signals includes: Constructing and solving the variational model: Taking the zero-mode current traveling wave signal as the object, a variational model is constructed, and the objective function of VMD is: ； in, The decomposed mode set, Here, α represents the center frequency of each mode, and α is the penalty factor. For unit impulse function, " indicates convolution operation; The variational model is solved using an alternating iterative method, with the number of modes K and the penalty factor α set, and the mode functions initialized. Center frequency and Lagrange multipliers For each mode k, solve in the frequency domain ,in, , , These are the frequency domain representations of the signal, mode, and Lagrange multipliers, respectively. The center frequency and Lagrange multipliers are updated sequentially until the convergence condition is met. Stop iteration when threshold Value The formula for updating the center frequency is: The formula for updating the Lagrange multipliers is: ,in, To update the step size, it is usually set to [0.5, 1] ​​to ensure the convergence of the variational model; High-frequency mode screening involves sorting the K decomposed modes from low to high center frequency and selecting high-frequency modes with center frequencies in the range of 8 to 12 kHz.

7. The fault location method for distribution networks with DG based on directional traveling wave energy entropy and WMA-VMD-GTKO double-ended traveling wave as described in claim 6, is characterized in that, The method of enhancing wavefront transient characteristics by fusing time-domain differential and Wigner-Ville frequency-domain gradient energy using a generalized energy operator includes: The high-frequency modal signal obtained by VMD decomposition is resampled to 100kHz to eliminate wavefront distortion caused by insufficient sampling rate; The first-order differential is calculated using the 5-point central difference method to suppress high-frequency noise, and the time-domain differential energy is also calculated. The formula for calculating the first-order differential is as follows: , Given the sampling interval, the formula for calculating the time-domain differential energy is: ; Apply a 20ms Hanning window to the signal, calculate the time-frequency distribution and frequency gradient, and obtain the frequency gradient energy. The formula for calculating the time-frequency distribution is as follows: , The formula for calculating the frequency domain gradient is: , For frequency resolution, taking a value of 100Hz, the formula for calculating frequency domain gradient energy is: ; Energy fusion weightedly couples the amplitude abrupt change characteristics of the time-domain derivative with the frequency abrupt change characteristics of the frequency-domain gradient. The fusion model is as follows: ; The fused energy sequence is mapped to the [0,1] interval, as expressed by: .

8. The fault location method for distribution networks with DG based on directional traveling wave energy entropy and WMA-VMD-GTKO double-ended traveling wave as described in claim 1, characterized in that, The method of combining dynamic thresholds to identify the arrival times of the traveling waves at both ends includes: A sliding window with a length of 200, corresponding to a 2ms time window, is used. Perform real-time statistics to calculate the mean and standard deviation within the window: ， ； Introducing adaptive coefficients Adjust dynamic threshold Sensitivity: ； ； when First time exceeding And satisfy the rising slope When the wavefront arrives, it is determined to be the time of arrival. .

9. The fault location method for distribution networks with DG based on directional traveling wave energy entropy and WMA-VMD-GTKO double-ended traveling wave as described in claim 8, is characterized in that, The calculation of fault distance based on the time difference between the two ends, combined with the dynamic correction of wave velocity using VMD modal characteristic frequencies, and substituted into the two-end ranging formula includes: For the initial fault distance calculation, assuming the measurement points at both ends of the distribution network are P and Q, the total line length is L, and the arrival times of the wavefront at both ends are t1 and t2, the initial calculation formula for the fault distance d is: ,in ; Dynamic correction of wave velocity: Based on the center frequency f of the high-frequency mode obtained by VMD decomposition, a dynamic correction relationship between wave velocity and frequency is established. ,in, The reference frequency; The final fault distance is calculated by substituting the dynamically corrected wave velocity v into the dual-end ranging model. .

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, which, when executed by a processor, implements all the steps of the fault location method for distribution networks with DG based on directional traveling wave energy entropy and WMA-VMD-GTKO double-ended traveling wave as described in any one of claims 1-9.

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