A method for locating fault sections in distribution networks by combining synthetic magnetic fields with VMD-HHT

Abstract

This invention discloses a method for locating fault sections in distribution networks by combining synthetic magnetic fields with VMD-HHT. The method acquires the horizontal and vertical magnetic induction intensities at each monitoring point and synthesizes the synthetic magnetic field at each monitoring point. After a fault occurs, variational mode decomposition is performed on the synthetic magnetic fields at each monitoring point to obtain high-frequency and low-frequency modes. Hilbert-Huang transform is applied to the high-frequency modes to obtain the instantaneous energy criterion; Hilbert-Huang transform is applied to the low-frequency modes to obtain the instantaneous phase criterion; and the instantaneous polarity criterion is calculated for the low-frequency modes. The final location result is obtained through a voting decision. This invention constructs a comprehensive criterion from three perspectives—instantaneous energy, instantaneous phase, and instantaneous polarity—making the location results more accurate and reliable.

Description

Technical Field

[0001] This invention belongs to the field of power system distribution network relay protection technology, specifically involving a method for locating distribution network fault sections by combining synthetic magnetic field with VMD-HHT. Background Technology

[0002] As the end point of the power system, the distribution network directly reflects the requirements of users in terms of power supply reliability, power quality, safety, and economy. Traditional fault location methods have many drawbacks. Location methods based on steady-state quantities have small steady-state signal values, which can easily lead to misjudgments; the accuracy of impedance methods is highly dependent on knowing accurate line parameters; and because the wave impedance is variable in mixed lines and the traveling wave reflection and refraction are complex, the traveling wave method is difficult to apply widely in large-scale and structurally complex distribution network lines. The section location method based on magnetic field changes is reliable. Magnetic field detection provides a large amount of valid data for analysis, accurately locating the faulty point on the line and identifying and eliminating false fault points. The accuracy of the magnetic field detection method is greatly improved by using both amplitude and phase criteria. The magnetic field detection method has high precision, locating the line fault point within a small area, significantly reducing the time spent by staff in troubleshooting and saving valuable time for maintenance. The magnetic field detection method is economical. Traditional line fault location methods require simultaneous implementation of the line path and time, resulting in high investment and low economic applicability. The magnetic field detection method only needs to measure the current and voltage at both ends of the distribution line. Because it is a non-contact installation and measurement method, the hardware requirements for the equipment are not very high. The magnetic field detection method is applicable; its fault location is not affected by line length, impedance, or current and voltage mutual inductance, making it suitable for both long and short lines. It has broad application prospects.

[0003] CN113341268A discloses a fault section location method that utilizes the magnetic field distribution characteristics under overhead lines in power distribution networks. The method determines the fault section by using the Euclidean metric of the magnetic induction intensity between adjacent monitoring points. However, it uses a single determination method without verification, and its reliability and accuracy need to be improved. Summary of the Invention

[0004] The purpose of this invention is to provide a method for locating fault sections in distribution networks by combining synthetic magnetic fields with VMD-HHT.

[0005] The technical solution adopted in this invention is a method for locating fault sections in a distribution network by combining a synthetic magnetic field with VMD-HHT. This method obtains the horizontal and vertical magnetic induction intensities at each monitoring point and synthesizes the synthetic magnetic field at each monitoring point. After a fault occurs, the synthetic magnetic field at each monitoring point is subjected to variational mode decomposition to obtain high-frequency and low-frequency modes. The high-frequency modes are subjected to Hilbert-Huang Transform (HHT) to obtain their instantaneous energy, which serves as sub-criterion 1. The low-frequency modes are subjected to Hilbert-Huang Transform to obtain their instantaneous phase, which serves as sub-criterion 2. The instantaneous polarity of the low-frequency modes is determined, which serves as sub-criterion 3. The results of the three sub-criterions are used to determine the final fault section location through a voting decision.

[0006] Specifically, if we define the horizontal direction as the x-axis and the vertical direction as the y-axis, then the magnetic induction intensity along the horizontal direction at monitoring point i of the magnetic field sensor is B. x,i The magnetic field strength at monitoring point i along the vertical direction is B. y,i The composite magnetic field at monitoring point i of the magnetic field sensor is: .

[0007] The invention is further characterized by:

[0008] In sub-criterion 1, in order to make full use of the instantaneous energy obtained by Hilbert-Huang Transform (HHT) and to more accurately reflect the high-frequency instantaneous energy differences between different monitoring points, after obtaining the instantaneous energy, the Euclidean distance between the instantaneous energies at both ends of the segment is further calculated.

[0009] In sub-criterion 2, considering that the instantaneous phases of the synthetic magnetic fields at both ends of the healthy section are almost equal, 15° is taken as the threshold. When the instantaneous phase difference Δθ between the synthetic magnetic fields at both ends of the section is greater than 15°, the section is determined to be a faulty section. When Δθ is less than 15°, the section is determined to be a healthy section.

[0010] In sub-criterion 3, the magnetic induction intensity of six consecutive sampling points after the fault occurs at each monitoring point is taken, and the first-order difference is performed to obtain x1~x5. The instantaneous polarity is defined as:

[0011] ;

[0012] ;

[0013] In the formula, P ol x is the instantaneous polarity value. i Let sgn(x) be the value of the first difference. i ) is a symbolic function, defined as follows:

[0014] ;

[0015] After obtaining the sign of the instantaneous polarity, determine whether the instantaneous polarity of adjacent monitoring points is opposite. If the signs are opposite, it is determined to be a faulty section; if the signs are the same, it is a healthy section.

[0016] After defining these three sub-criteria, the final fault location result is determined by voting. If two sub-criteria determine the same segment or all three sub-criteria determine the same segment as the fault segment, then this segment is taken as the final fault location result. If the three sub-criteria result are different, then the calculation is repeated and voting is repeated until the result is correct.

[0017] The beneficial effects of this invention are:

[0018] 1) The Euclidean distance of the instantaneous energy of the high-frequency mode is calculated, making full use of the instantaneous energy obtained through HHT to more accurately reflect the high-frequency energy differences at different monitoring points.

[0019] 2) A comprehensive criterion was constructed from three aspects: instantaneous energy, instantaneous phase, and instantaneous polarity, making the positioning results more accurate and reliable. Attached Figure Description

[0020] Figure 1 This is a flowchart of a method for locating fault sections in a distribution network that combines a synthetic magnetic field with VMD-HHT according to the present invention.

[0021] Figure 2 A schematic diagram for calculating the magnetic field near a current-carrying straight conductor;

[0022] Figure 3 A schematic diagram of the coordinate system of the horizontally arranged three-phase conductors and monitoring points;

[0023] Figure 4 The specific locations of power distribution network towers, three-phase overhead lines, and magnetic field sensors;

[0024] Figure 5 This refers to the 10kV distribution network described in the embodiments of the present invention;

[0025] Figure 6 The composite magnetic field B upstream of the fault point and its decomposed waveform;

[0026] Figure 7 The composite magnetic field B downstream of the fault point and its decomposed waveform;

[0027] Figure 8 The instantaneous energy of the high-frequency component IMF2 upstream of the fault point in the time-frequency domain;

[0028] Figure 9 The instantaneous energy of the high-frequency component IMF2 downstream of the fault point in the time-frequency domain;

[0029] Figure 10The instantaneous phase of the low-frequency component IMF1 upstream and downstream of the fault point. Detailed Implementation

[0030] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0031] This invention discloses a method for locating fault sections in distribution networks by combining synthetic magnetic fields with VMD-HHT, such as... Figure 1 As shown, please follow these steps:

[0032] Step 1, Monitoring Point Numbering: For each tower of the overhead line of the distribution network that requires fault location, set up magnetic field sensor monitoring points and number each monitoring point, i=1,2,3,…,n; n is the number of monitoring points.

[0033] Step 2, Obtaining Magnetic Induction Intensity: Setting the horizontal direction as the x-axis and the vertical direction as the y-axis, the magnetic induction intensity along the horizontal direction at monitoring point i of the magnetic field sensor is B. x,i The magnetic field strength at monitoring point i along the vertical direction is B. y,i Then B x,i and B y,i The calculation formulas are as follows:

[0034] ;

[0035] ;

[0036] in:

[0037] ;

[0038] ;

[0039] ;

[0040] μ0 is the vacuum permeability; B Ai B Bi, B Ci These represent the magnetic induction intensities generated by phases A, B, and C at monitoring point i, respectively; I Ai I Bi I Ci ρ represents the currents of phases A, B, and C at monitoring point i, respectively; A , ρ B , ρ C These represent the distances from the A, B, and C phase conductors at monitoring point i to the sensor measurement point, respectively. The included angle.

[0041] Step 3, Magnetic Field Synthesis: For each monitoring point B... x,i and B y,iThe composite magnetic field of each monitoring point is obtained by synthesis. The composite magnetic field of monitoring point i of magnetic field sensor is:

[0042] ;

[0043] Step 4, Fault Location: After the fault occurs, the synthetic magnetic field of each monitoring point is decomposed into variational modes to obtain high-frequency and low-frequency modes. Hilbert-Huang Transform (HHT) is performed on the high-frequency modes to obtain the instantaneous energy of the high-frequency modes, which is used as sub-criterion 1. Hilbert-Huang Transform is performed on the low-frequency modes to obtain the instantaneous phase of the low-frequency modes, which is used as sub-criterion 2. The instantaneous polarity of the low-frequency modes is calculated as sub-criterion 3. The judgment results of the three sub-criterions are determined by voting to determine the final fault segment location result.

[0044] In sub-criterion 1, in order to make full use of the instantaneous energy obtained by Hilbert-Huang Transform (HHT) and to more accurately reflect the high-frequency instantaneous energy differences between different monitoring points, after obtaining the instantaneous energy, the Euclidean distance between the instantaneous energies at both ends of the segment is further calculated.

[0045] In sub-criterion 2, considering that the instantaneous phases of the synthetic magnetic fields at both ends of the healthy section are almost equal, 15° is taken as the threshold. When the instantaneous phase difference Δθ between the synthetic magnetic fields at both ends of the section is greater than 15°, the section is determined to be a faulty section. When Δθ is less than 15°, the section is determined to be a healthy section.

[0046] In sub-criterion 3, the magnetic induction intensity of six consecutive sampling points after the fault occurs at each monitoring point is taken, and the first-order difference is performed to obtain x1~x5. The instantaneous polarity is defined as:

[0047] ;

[0048] ;

[0049] In the formula, P ol x is the instantaneous polarity value. i Let sgn(x) be the value of the first difference. i ) is a symbolic function, defined as follows:

[0050] ;

[0051] After obtaining the sign of the instantaneous polarity, determine whether the instantaneous polarity of adjacent monitoring points is opposite. If the signs are opposite, it is determined to be a faulty section; if the signs are the same, it is a healthy section.

[0052] After defining these three sub-criteria, the final fault location result is determined by voting. If two sub-criteria determine the same segment or all three sub-criteria determine the same segment as the fault segment, then this segment is taken as the final fault location result. If the three sub-criteria result are different, then the calculation is repeated and voting is repeated until the result is correct.

[0053] The working principle of the distribution network fault section location method of the present invention, which combines synthetic magnetic field with VMD-HHT, is as follows:

[0054] 1. Biot-Savart Law and Magnetic Field Model Analysis of Overhead Lines

[0055] According to the basic theory of electromagnetic fields, a current-carrying conductor generates a magnetic field in the space around it. The magnetic field at a point in this magnetic field can be obtained by superimposing the magnetic inductions generated at that point by all the current elements on the conductor. According to the Biot-Savart law, the magnetic field of a current element on a current-carrying conductor in a static magnetic field... The magnetic induction intensity generated at a point P in a vacuum Size and current element size Proportional to the current element The vector of point P The angle between The value of the sine is directly proportional to the sine value and inversely proportional to the square of the distance r0 from the current element to point P, that is:

[0056] ;

[0057] in, The permeability of free space, , The direction is perpendicular to The plane formed by r0 and along the vector product The direction of , its vector form is:

[0058] ;

[0059] Therefore, the magnetic flux density of the current-carrying conductor at point p can be obtained from the above formula. :

[0060] ;

[0061] Where I is the current flowing through the conductor, the magnetic field strength produced by a straight current-carrying conductor of length L in vacuum at a point P near it can be obtained according to the above formula. The size is:

[0062] ;

[0063] in , like Figure 2 As shown, the unit of B is Tesla (symbol T).

[0064] When the current-carrying straight conductor is infinitely long , Therefore, from the above formula, the magnitude of the magnetic induction intensity B is:

[0065] ;

[0066] The power frequency electromagnetic field around overhead transmission lines, although changing slowly over time, can be ignored due to the negligible electromagnetic induction effect; that is, the power frequency electromagnetic field of overhead lines is a quasi-static electromagnetic field. Assuming the three-phase overhead line consists of three infinitely long straight conductors, the alternating electric field under the overhead line can be considered a quasi-static field, and the power frequency magnetic field is only affected by the current. Therefore, the electric and magnetic fields can be considered separate. Ignoring the magnetic field along the line direction, in practical applications, calculating the magnetic field under the overhead line only requires considering the conductor in space, ignoring its mirror image, which is sufficiently accurate. Ignoring the Earth's magnetic field, the magnetic field generated by the infinitely long straight conductor at the detection point is:

[0067] ;

[0068] Where r is the distance between the conductor and the detection point;

[0069] There are several ways to arrange three-phase overhead lines in a power distribution network, including vertical, delta, and horizontal arrangements. Taking a horizontal three-phase arrangement as an example, a coordinate system is established on a plane perpendicular to the three-phase conductors. The coordinate system between the horizontally arranged three-phase conductors and the detection points is established as follows: Figure 3 As shown, assuming the conductor is infinitely long and parallel to the ground, then:

[0070] ;

[0071] ;

[0072] ;

[0073] Among them, B A B B B C The magnetic induction intensities I generated at point P by phases A, B, and C are respectively. A I B I C These are the three-phase currents, A, B, and C, respectively.

[0074] The components of the magnetic field strength at point P along the x-axis:

[0075] ;

[0076] The component of the magnetic field strength at point P along the y-axis:

[0077] ;

[0078] The closer to the line, the greater the magnetic field strength, which is more conducive to the measurement by the magnetic field sensor.

[0079] At locations 1m and 2m directly below the line, the magnetic field strength exhibits non-stationary variations, easily changing significantly under external interference, which is detrimental to subsequent fault detection. At locations 3m and 5m directly below the line, the magnetic field strength is uniformly distributed and changes smoothly, facilitating measurements by the magnetic field sensor. The specific location distribution diagram of the designed towers, three-phase conductors, and magnetic field sensor is shown below. Figure 4 As shown, JM1, JC1, and JS1 represent three different wire arrangement methods: horizontal, vertical, and triangular arrangement, respectively.

[0080] 2. Variational Mode Decomposition (VMD)

[0081] Variational mode decomposition (VMD) is an adaptive, fully non-recursive method for mode variational signal processing. This technique has the advantage of being able to determine the number of mode decompositions. Its adaptability is manifested in determining the number of mode decompositions for a given sequence based on the actual situation. In the subsequent search and solution process, it can adaptively match the optimal center frequency and finite bandwidth for each mode, and can achieve effective separation of intrinsic mode components (IMFs), frequency domain partitioning of the signal, and thus obtain the effective decomposition components of a given signal, ultimately obtaining the optimal solution to the variational problem. It overcomes the end-point effects and mode component aliasing problems of the EMD method, and has a more solid mathematical theoretical foundation. It can reduce the non-stationarity of time series with high complexity and strong nonlinearity, decomposing them into relatively stationary subsequences containing multiple different frequency scales. It is suitable for non-stationary sequences. The core idea of ​​VMD is to construct and solve variational problems.

[0082] First, construct a variational problem. Assume the original signal f is decomposed into k components, ensuring that the decomposed sequence consists of modal components with finite bandwidth and a center frequency, while minimizing the sum of the estimated bandwidths of each mode. The constraint is that the sum of all modes is equal to the original signal. Then, the corresponding constraint variational expression is:

[0083] ;

[0084] ;

[0085] In the formula: K is the number of modes to be decomposed. These represent the k-th modal component and its center frequency after decomposition, respectively. These represent the sets of modal components and their center frequencies, respectively. is the Dirac function, * is the convolution operator, j is the imaginary sign, and t is time.

[0086] Then, by solving the above equation and introducing the Lagrange multiplier λ, the constrained variational problem is transformed into an unconstrained variational problem, yielding the augmented Lagrange expression:

[0087] ;

[0088] In the formula: α is the quadratic penalty factor, which is used to reduce Gaussian noise interference. The Alternating Directional Multiplier (ADMM) iterative algorithm, combined with Parseval / Plancherel and Fourier isometric transform, is used to optimize each modal component and center frequency, and to search for the saddle point of the augmented Lagrange function. The iteratively optimized u is then used to find the optimal modal components and center frequency. k ω k The expressions for λ are as follows:

[0089] ;

[0090] ;

[0091] ;

[0092] In the formula, γ is the noise tolerance parameter. Indicates the frequency after transformation. This represents the value of the k-th modal component in the (n+1)-th iteration after transformation. The transformed signal, , These represent the values ​​of the i-th modal component after the transformation in the nth and (n+1)th iterations, respectively. , Let these represent the values ​​of the transformed Lagrange multiplication operator at the nth and (n+1)th iterations, respectively. , These represent the values ​​of the k-th center frequency in the nth and (n+1)th iterations, respectively. Generally, when we encounter excessively high noise levels, we can set γ=0 to achieve our desired result.

[0093] The main iterative solution process of VMD is as follows:

[0094] S1: Initialization and maximum number of iterations ;

[0095] S2: Update and ;

[0096] S3: Update .

[0097] 3. Hilbert-Huang Transform (HHT)

[0098] The HHT transform mainly consists of two parts: EMD decomposition and Hilbert transform. EMD decomposition adaptively decomposes a non-stationary signal into approximately single-frequency IMF components. Each IMF component must satisfy two conditions:

[0099] a) The number of extreme points and the number of zero points of a component differ by a maximum of 1;

[0100] b) At any point, the mean of the upper and lower envelopes defined by the maxima and minima is zero.

[0101] Each IMF component is then subjected to Hilbert transform to obtain local signal features with clear physical meaning, including instantaneous frequency, instantaneous amplitude, and instantaneous phase. Furthermore, by plotting the local features of these IMF components into a Hilbert-Huang spectrum, the time-frequency domain distribution characteristics of the entire non-stationary signal can be obtained.

[0102] Given a time series signal x(t), its EMD decomposition process is as follows:

[0103] Step 1: Find all the maxima and minima of the signal x(t), and fit all the maxima and minima using a cubic spline function to obtain the upper and lower envelopes of the signal x(t);

[0104] Step 2: Calculate the average value of the upper and lower envelopes at each point, denoted as m(t). Then calculate the difference between the original signal and the average value, denoted as h(t), and determine whether h(t) satisfies the IMF condition. If h(t) satisfies the IMF condition, then h(t) is taken as the first IMF component of the signal x(t), denoted as C1(t). If h(t) does not satisfy the IMF condition, repeat the above process until the IMF condition is satisfied.

[0105] Step 3: Calculate the difference between x(t) and h(t), denoted as R(t). Then, using R(t) as the original signal, repeat the above steps to obtain all IMF components C1(t), C2(t), ..., C of the signal x(t). j (t), until the decomposition ends.

[0106] For the j-th IMF component (intrinsic mode function) C j The Hilbert transform of (t) is as follows:

[0107] ;

[0108] in, For time delay, For time.

[0109] The j-th IMF component C j (t) and its Hilbert transform Together they form an analytical signal (t):

[0110] ;

[0111] ;

[0112] ;

[0113] In the above formula, A j (t) represents the instantaneous amplitude of the j-th IMF component (intrinsic mode function); The instantaneous phase of the j-th IMF component is represented by i, where i represents an imaginary number.

[0114] Using the calculated instantaneous amplitude and instantaneous phase, the instantaneous frequency of the j-th IMF component can be obtained:

[0115] .

[0116] 4. Euclidean Measurement

[0117] The Euclidean metric is a commonly used definition of distance, referring to the true distance between two points in m-dimensional space, or the natural length of a vector (i.e., the distance from that point to the origin).

[0118] Formula for two-dimensional space:

[0119] ;

[0120] in, The Euclidean metric between points (x2, y2) and (x1, y1);

[0121] Example: Establishing such Figure 5 The 10kV radial distribution network model has three feeders, all of which are overhead lines. Several towers on each feeder are equipped with magnetic field sensor monitoring points. The parameters of the overhead lines are shown in Table 1.

[0122] Table 1 Line Parameters

[0123]

[0124] A ground fault occurs at 100ms, with a grounding resistance of R. f The magnetic field B at each monitoring point is 5Ω. x and B yThe synthesized magnetic field B is then further subjected to variational mode decomposition of the synthesized magnetic fields upstream and downstream of the fault point to obtain low-frequency and high-frequency components, as shown below. Figure 6 and Figure 7 As shown, IMF1 is the low-frequency component and IMF2 is the high-frequency component.

[0125] After the fault occurred, the combined magnetic field increased significantly, due to Figure 6 The high-frequency component of IMF2 is very weak, with an amplitude not exceeding 0.1 μT, while the low-frequency component reaches approximately 30 μT, far exceeding the high-frequency component. Simultaneously, the duration of the high-frequency component is also very short. All of these factors indicate that the high-frequency component accounts for a very small proportion of the original waveform. Therefore, the low-frequency component corresponding to IMF1 is almost identical to the original waveform. Before the fault occurred, the high-frequency component was almost non-existent, approximately zero; at this point, the composite magnetic field only contained a 50 Hz low-frequency component.

[0126] Depend on Figure 7 It can be observed that, compared to the upstream of the fault point, the amplitude of the downstream synthetic magnetic field B also increases, but the increase is significantly lower, with an amplitude of only about 11 μT. The low-frequency and high-frequency components exhibit the same characteristics as the upstream of the fault point, but their amplitudes are relatively small. Further Hilbert-Huang transform of the IMF2 from 99 ms to 101 ms yields the instantaneous energy of the high-frequency components in the time-frequency domain, such as... Figure 8 and Figure 9 As shown.

[0127] Depend on Figure 8 It can be seen that the high-frequency components increase sharply in a short period of time during the initial stage of the fault, with the instantaneous energy amplitude approaching 2×10⁻⁶. -3 As the fault time progresses, the high-frequency energy gradually decreases due to the attenuation of the DC component, eventually returning to zero after a period of time. At this point, only the steady-state component remains in the synthesized magnetic field. The instantaneous energy amplitude of the downstream synthesized magnetic field does not exceed 1×10⁻⁶. -3 The energy amplitude is only about half that of the upstream component. Further calculation of the Euclidean distance between the instantaneous energy of the high-frequency components upstream and downstream of the fault point in the 100ms-101ms range yields a result of 3×10⁻⁶. -3 It can be observed that the instantaneous energy at both ends of the faulty section is significantly different, forming a stark contrast with the healthy section. Therefore, the faulty section can be accurately identified based on the instantaneous energy criterion. After Hilbert-Huang transformation, the instantaneous phase of the low-frequency component IMF1 at each sampling point after the fault occurs can also be obtained, such as... Figure 10 As shown.

[0128] Comparing the instantaneous phase of the lowest frequency component IMF1 upstream and downstream of the fault point at the time of the fault, the upstream phase is -44.2247° and the downstream phase is 7.0287°, with a phase difference Δθ=51°, which is significantly greater than the threshold of 15°. In contrast, the instantaneous phase difference between the two sides of the healthy section is very small. The two types of sections show obvious differences. Therefore, the location method based on instantaneous phase can accurately identify the faulty section.

[0129] The first-order difference was calculated for the six sampling points after the fault, and the five difference values ​​are shown in Table 2. Further calculation of the sign function of the difference values ​​reveals that due to the upstream x... i All values ​​are positive, and the calculated value is 1. The polarity value P ol The value is 5, corresponding to the positive electrode, while the downstream x i All are negative values, and the calculated values ​​are all -1. The polarity value P ol The value is -5, which corresponds to the negative pole. Therefore, the upstream and downstream polarities are exactly opposite, which can be identified as the faulty section.

[0130] Table 2 First-order difference and polarity

[0131]

[0132] In summary, the three sub-criterions of instantaneous energy, instantaneous phase, and instantaneous polarity yielded the same location results, and all correctly located the faulty section. Therefore, even after further voting and decision-making, the fault could still be accurately located.

[0133] Through the above method, the present invention provides a method for locating fault sections in a distribution network by combining a synthetic magnetic field with VMD-HHT. First, the magnetic induction intensity along the horizontal and vertical directions at the location of each monitoring point at the time of the fault is obtained. Second, the magnetic field components along the x-axis and y-axis of each monitoring point are synthesized to obtain a synthetic magnetic field B. Then, variational mode decomposition and Hilbert-Huang transform are performed on the synthetic magnetic field of each monitoring point. The high-frequency components are used to construct instantaneous energy criteria, and the low-frequency components are used to construct instantaneous polarity and instantaneous phase criteria. Finally, the final location result is obtained through voting decision.

Claims

1. A method for locating fault sections in a distribution network using a combination of synthetic magnetic field and VMD-HHT, characterized in that, The horizontal and vertical magnetic induction intensities of each monitoring point are obtained and synthesized to obtain the composite magnetic field of each monitoring point. Variational mode decomposition is performed on the composite magnetic field of each monitoring point after the fault occurs to obtain high-frequency and low-frequency modes. Hilbert-Huang transform is performed on the high-frequency modes to obtain the instantaneous energy of the high-frequency modes, which is used as sub-criterion 1. Hilbert-Huang transform is performed on the low-frequency modes to obtain the instantaneous phase of the low-frequency modes, which is used as sub-criterion 2. The instantaneous polarity of the low-frequency modes is determined as sub-criterion 3. The judgment results of the three sub-criterions are determined by voting to determine the final fault segment location result. In sub-criterion 1, in order to make full use of the instantaneous energy obtained by Hilbert-Huang transform and to more accurately reflect the high-frequency instantaneous energy differences at different monitoring points, after obtaining the instantaneous energy, the Euclidean distance between the instantaneous energies at both ends of the segment is further calculated. In sub-criterion 2, considering that the instantaneous phases of the synthetic magnetic fields at both ends of the healthy section are almost equal, 15° is taken as the threshold. When the instantaneous phase difference Δθ between the synthetic magnetic fields at both ends of the section is greater than 15°, the section is determined to be a faulty section. When Δθ is less than 15°, the section is determined to be a healthy section. In sub-criterion 3, the magnetic induction intensity of six consecutive sampling points after the fault occurs at each monitoring point is taken, and the first-order difference is performed to obtain x1~x5. The instantaneous polarity is defined as: ； ； In the formula, P ol x is the instantaneous polarity value. i Let sgn(x) be the value of the first difference. i ) is a symbolic function, defined as follows: ； After obtaining the sign of the instantaneous polarity, determine whether the instantaneous polarity of adjacent monitoring points is opposite. If the signs are opposite, it is determined to be a faulty section; if the signs are the same, it is a healthy section.

2. The method for locating fault sections in a distribution network by combining a synthetic magnetic field with VMD-HHT according to claim 1, characterized in that, Let the horizontal direction be the x-axis and the vertical direction be the y-axis. Then, the magnetic induction intensity along the horizontal direction at the monitoring point i of the magnetic field sensor is B. x,i The magnetic field strength at monitoring point i along the vertical direction is B. y,i The composite magnetic field at monitoring point i of the magnetic field sensor is: .

3. The method for locating fault sections in a distribution network by combining a synthetic magnetic field with VMD-HHT according to claim 1, characterized in that, After defining the three sub-criteria, the final fault location result is determined by voting. If two sub-criteria determine the same segment or all three sub-criteria determine the same segment as the fault segment, then this segment is taken as the final fault location result. If the three sub-criteria result are different, then the calculation is recalculated and voting is repeated until the result is correct.

4. The method for locating fault sections in a distribution network by combining a synthetic magnetic field with VMD-HHT according to claim 1, characterized in that, The Hilbert-Huang transform consists of two parts: EMD decomposition and Hilbert transform. EMD decomposition adaptively decomposes a non-stationary signal into approximately single-frequency IMF components. Each IMF component must satisfy two conditions: a) The number of extreme points and the number of zero points of a component differ by a maximum of 1; b) At any point, the mean of the upper and lower envelopes defined by the maxima and minima is zero; Each IMF component is then subjected to Hilbert transform to obtain local signal features with clear physical meaning, including instantaneous frequency, instantaneous amplitude, and instantaneous phase. Furthermore, by plotting the local features of these IMF components into a Hilbert-Huang spectrum, the time-frequency domain distribution characteristics of the entire non-stationary signal can be obtained.

5. The method for locating fault sections in a distribution network by combining a synthetic magnetic field with VMD-HHT according to claim 4, characterized in that, Given a time series signal x(t), its EMD decomposition process is as follows: Step 1: Find all the maxima and minima of the signal x(t), and fit all the maxima and minima using a cubic spline function to obtain the upper and lower envelopes of the signal x(t); Step 2: Calculate the average value of the upper and lower envelopes at each point, denoted as m(t). Then calculate the difference between the original signal and the average value, denoted as h(t), and determine whether h(t) satisfies the IMF condition. If h(t) satisfies the IMF condition, then h(t) is taken as the first IMF component of the signal x(t), denoted as C1(t). If h(t) does not satisfy the IMF condition, repeat the above process until the IMF condition is satisfied. Step 3: Calculate the difference between x(t) and h(t), denoted as R(t). Then, using R(t) as the original signal, repeat the above steps to obtain all IMF components C1(t), C2(t), ..., C of the signal x(t). j (t), until the decomposition ends.

6. The method for locating fault sections in a distribution network by combining a synthetic magnetic field with VMD-HHT according to claim 5, characterized in that... For the j-th IMF component C j The Hilbert transform of (t) is as follows: ； in, For time delay, For time; The j-th IMF component C j (t) and its Hilbert transform Together they form an analytical signal (t): ； ； ； In the above formula, A j (t) represents the instantaneous amplitude of the j-th IMF component; The instantaneous phase of the j-th IMF component is represented by i, where i represents an imaginary number. The instantaneous frequency of the j-th IMF component can be obtained from the obtained instantaneous amplitude and instantaneous phase.

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