Multi-band interval cable fault positioning method based on reflection coefficient spectrum

Abstract

The invention discloses a multi-band section cable fault positioning method based on a reflection coefficient spectrum, belongs to the field of cable fault positioning, and aims to solve the problems that an existing cable fault positioning method is low in positioning accuracy, and violent oscillation is easily generated near a positioning peak value. The method comprises the following steps: S1, acquiring a square wave excitation signal as an excitation signal source of a cable fault; s2, obtaining a reflection coefficient spectrum in a fundamental wave frequency band; s3, discretizing the reflection coefficient spectrum, and extending the reflection coefficient spectrum to a required full-band reflection coefficient spectrum; s4, constructing a cable fault positioning function based on a reflection coefficient spectrum; s5, acquiring a positioning function of the intact cable; and S6, the ratio of the results of S4 and S5 is used as a cable fault diagnosis function, and cable fault positioning is realized by searching a sudden change point of a fault diagnosis function curve.

Description

Technical Field

[0001] The invention relates to a cable fault location method based on a multi-frequency band of a reflection coefficient spectrum, and belongs to the field of cable fault location. Background Art

[0002] Cables play a key role in urban distribution networks and new energy transmission systems. The reliability of cables is of great significance to the safety and stability of the power grid. During installation and long-term operation, cables are easily affected by factors such as temperature, humidity, mechanical force, and chemical corrosion, which can cause insulation defects and failures, leading to serious power accidents. Therefore, it is particularly important to diagnose insulation and locate faults on cables.

[0003] The current cable fault location method has the following two defects: (1) The test frequency interval covers a large range, the traveling wave voltage signal attenuation is relatively serious, and the positioning accuracy is low. (2) The existing positioning method is prone to violent oscillation near the positioning peak in the positioning spectrum, which is easy to produce interference peaks in the positioning spectrum. Therefore, it is very necessary to study new cable fault location methods. Summary of the invention

[0004] In view of the problems of low positioning accuracy and strong oscillation near the positioning peak in the current cable fault positioning method, the present invention provides a cable fault positioning method based on a multi-band interval of the reflection coefficient spectrum to locate the cable fault. The positioning algorithm in the present invention can reduce the oscillation interval near the positioning peak and reduce the oscillation peak. Relying on the multi-band interval positioning diagnostic function can effectively block the ripple oscillation generated when the cable fails, improve the positioning accuracy, and realize the precise positioning of the cable fault position.

[0005] The present invention provides a method for locating cable faults in multiple frequency bands based on a reflection coefficient spectrum, the method comprising the following steps:

[0006] Step S1: obtaining a square wave excitation signal as an excitation signal source of a cable fault;

[0007] Step S2: obtaining a reflection coefficient spectrum within the fundamental frequency band under square wave excitation;

[0008] Step S3: discretizing the reflection coefficient spectrum, and extending the reflection coefficient spectrum in the fundamental frequency band to the required reflection coefficient spectrum of the full frequency band according to harmonic decomposition;

[0009] Step S4: constructing a cable fault location function based on the reflection coefficient spectrum;

[0010] Step S5: obtaining the reflection coefficient spectrum of the intact cable and determining the positioning function of the intact cable;

[0011] Step S6: Ratio the multi-band interval positioning function based on the reflection coefficient spectrum obtained in step S4, the positioning function of the intact cable reflection coefficient spectrum obtained in step S5, and the positioning function of the faulty cable reflection coefficient spectrum to obtain a cable fault diagnosis function based on the reflection coefficient spectrum, and realize cable fault positioning by finding the mutation point of the fault diagnosis function curve.

[0012] Preferably, in step S1, a time domain signal of a square wave signal is obtained as an excitation signal source by performing Fourier transform on the non-sinusoidal signal, and the expression is:

[0013]

[0014] Where ω is the angular frequency, τ is the time constant, and U dc is the DC side voltage amplitude, 2n-1 is the number of harmonics, i is the harmonic order, i=1,2,...,2n-1.

[0015] Preferably, the process of obtaining the reflection coefficient spectrum in the fundamental frequency band under square wave excitation in step S2 is:

[0016] The excitation signal source is incident on the cable under test, and the corresponding response signal is obtained in real time. The input impedance of the cable under test is obtained according to the excitation signal and the response signal, and then the reflection coefficient is obtained. The cable reflection coefficient spectrum is obtained according to the continuously collected data.

[0017] Preferably, the process of acquiring the reflection coefficient spectrum of the full frequency band in step S3 is:

[0018] First, the reflection coefficient spectrum obtained at the fundamental frequency is discretized according to the equal frequency method, and the number of discrete frequency points m under the i-th harmonic is obtained:

[0019]

[0020] In the formula, f min is the fundamental frequency sweep start frequency, f max is the fundamental wave sweep end frequency, △f is the fundamental wave frequency interval;

[0021] The expression of the reflection coefficient of the kth discrete point of the fundamental wave is:

[0022]

[0023] In the formula, γ h (k) is the propagation constant of the intact cable at the kth discrete frequency point in the fundamental frequency band, k = 1, 2, ..., m; γ f (k) is the propagation constant of the fault cable at the kth discrete frequency point in the fundamental frequency band, Γ F (k) is the amplitude of the reflection coefficient in the fundamental frequency band, Γ P(k) is the phase of the reflection coefficient in the fundamental frequency band, l is the length of the cable under test;

[0024] The reflection coefficient in the discrete fundamental frequency band is extended at each discrete frequency point according to the harmonic characteristics to obtain the required reflection coefficient spectrum in the full frequency band.

[0025]

[0026] In the formula, Γ F (k,i) is the amplitude of the reflection coefficient of the kth discrete point in the i-th harmonic frequency band; m is the number of discrete points in the i-th harmonic frequency band;

[0027] Γ P (k,i) is the phase of the reflection coefficient of the kth discrete point in the i-th harmonic frequency band;

[0028] is the starting frequency of the frequency sweep in the i-th harmonic frequency band, is the end frequency of the sweep in the i-th harmonic frequency band, Δf i is the frequency interval in the i-th harmonic frequency band.

[0029] Preferably, the cable fault location function based on the reflection coefficient spectrum in step S4 is composed of the reflection coefficient spectrum under the full frequency band From the frequency domain to the spatial domain, we can obtain:

[0030]

[0031] Where x is the coordinate of the fault point, and the distance between the fault point and the incident point of the excitation signal source;

[0032] K(i,k,x) is the core function, and

[0033] In the formula, γ h (i,k) is the propagation constant of the intact cable at the kth discrete frequency point in the i-th harmonic frequency band.

[0034] Preferably, the propagation constant γ of the intact cable at the kth discrete frequency point in the i-th harmonic frequency band is h (i,k) is obtained as follows:

[0035]

[0036] In the formula, R0 is the distributed resistance per unit length, ω is the angular frequency, L0 is the distributed inductance per unit length, G0 is the distributed conductance per unit length, C0 is the distributed capacitance per unit length, The frequency of the k-1th discrete frequency point in the i-th harmonic frequency band.

[0037] Preferably, the method for obtaining the positioning function of the intact cable in step S5 is any one of the following three methods:

[0038] Method 1: Before the new cable is put into use, the reflection coefficient spectrum is measured as the reflection coefficient spectrum of the intact cable;

[0039] Method 2: Obtain the reflection coefficient spectrum of the intact cable by measuring the intact cable of the same type;

[0040] Method 3: Refer to the cable structure size or parameter specifications provided by the manufacturer, pre-calculate the cable's unit length parameters, obtain the cable's propagation coefficient, and then calculate the reflection coefficient spectrum of the intact cable based on the characteristic impedance and propagation coefficient;

[0041] Convert the intact cable reflection coefficient spectrum from the frequency domain to the spatial domain to obtain the positioning function D of the intact cable h (x).

[0042] Preferably, the acquisition process of cable fault location in step S6 is:

[0043] The fault diagnosis function D(x) is obtained as follows:

[0044]

[0045] Find the mutation point of the fault diagnosis function curve as the fault point, and then obtain the position of the fault point to realize cable fault location.

[0046] Preferably, the method further comprises the following steps:

[0047] Step S7: evaluating the positioning accuracy using the positioning error optimization rate;

[0048] The positioning error optimization rate δ is obtained as follows:

[0049]

[0050] In the formula, x T is the traditional IFFT positioning result, x O is the multi-band interval positioning result, x D It is the starting fault position point of the excitation signal input terminal.

[0051] Beneficial effects of the present invention: According to the cable fault location method based on the multi-frequency band of the reflection coefficient spectrum described in the present invention, the positioning algorithm of the present invention is used to reduce the test frequency range, increase the amplitude of the excitation signal, reduce the oscillation range near the positioning peak, and reduce the oscillation peak. Compared with the traditional positioning method, relying on the multi-frequency band positioning diagnostic function can effectively block the ripple oscillation generated when the cable fails, improve the positioning accuracy, and realize the precise positioning of the cable fault position. Therefore, it is of great significance to the operation and maintenance test of the cable and the safe operation of the equipment. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a flow chart of a cable fault location method based on a multi-frequency band of a reflection coefficient spectrum according to the present invention;

[0053] Figure 2 It is a schematic diagram of high-order harmonic impedance spectrum;

[0054] Figure 3 It is a schematic diagram of high-order harmonic impedance spectrum reconstruction;

[0055] Figure 4 It is a comparison chart of fault location chart of copper shield insulation defect;

[0056] Figure 5 It is a comparison chart of aging insulation defect fault location maps. DETAILED DESCRIPTION

[0057] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0058] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0059] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, but they are not intended to limit the present invention.

[0060] Specific implementation method 1: The following is combined Figures 1 to 5 This embodiment describes a cable fault location method based on a multi-frequency band of a reflection coefficient spectrum, and the method comprises the following steps:

[0061] Step S1: obtaining a square wave excitation signal as an excitation signal source of a cable fault;

[0062] Step S2: obtaining a reflection coefficient spectrum within the fundamental frequency band under square wave excitation;

[0063] Step S3: discretizing the reflection coefficient spectrum, and extending the reflection coefficient spectrum in the fundamental frequency band to the required reflection coefficient spectrum of the full frequency band according to harmonic decomposition;

[0064] Step S4: constructing a cable fault location function based on the reflection coefficient spectrum;

[0065] Step S5: obtaining the reflection coefficient spectrum of the intact cable and determining the positioning function of the intact cable;

[0066] Step S6: Ratio the multi-band interval positioning function based on the reflection coefficient spectrum obtained in step S4, the positioning function of the intact cable reflection coefficient spectrum obtained in step S5, and the positioning function of the faulty cable reflection coefficient spectrum to obtain a cable fault diagnosis function based on the reflection coefficient spectrum, and realize cable fault positioning by finding the mutation point of the fault diagnosis function curve.

[0067] In step S1, the non-sinusoidal signal is subjected to Fourier transform to obtain a time domain signal of a square wave signal as an excitation signal source, and the expression is:

[0068]

[0069] Where ω is the angular frequency, τ is the time constant, and U dc is the DC side voltage amplitude, 2n-1 is the number of harmonics, i is the harmonic order, i=1,2,...,2n-1.

[0070] Therefore, the expression of the amplitude of the i-th harmonic excitation is obtained:

[0071]

[0072] The process of obtaining the reflection coefficient spectrum in the fundamental frequency band under square wave excitation in step S2 is:

[0073] The excitation signal source is incident on the cable under test, and the corresponding response signal is obtained in real time. The input impedance of the cable under test is obtained according to the excitation signal and the response signal, and then the reflection coefficient is obtained. The cable reflection coefficient spectrum is obtained according to the continuously collected data (the cable reflection coefficient spectrum is obtained according to the calculation relationship between the input impedance and the reflection coefficient).

[0074] In step S3, according to the harmonic characteristics of the non-sinusoidal (square wave signal) excitation, the reflection coefficient spectrum under the fundamental wave is extended to obtain the required full-band reflection coefficient spectrum. The acquisition process of the full-band reflection coefficient spectrum is:

[0075] First, the reflection coefficient spectrum obtained at the fundamental frequency is discretized according to the equal frequency method, and the number of discrete frequency points m under the i-th harmonic is obtained:

[0076]

[0077] In the formula, f min is the fundamental frequency sweep start frequency, f max is the fundamental wave sweep end frequency, △f is the fundamental wave frequency interval;

[0078] The expression of the reflection coefficient of the kth discrete point of the fundamental wave is:

[0079]

[0080] In the formula, γ h (k) is the propagation constant of the intact cable at the kth discrete frequency point in the fundamental frequency band, k = 1, 2, ..., m; γ f (k) is the propagation constant of the fault cable at the kth discrete frequency point in the fundamental frequency band, Γ F (k) is the amplitude of the reflection coefficient in the fundamental frequency band, Γ P (k) is the phase of the reflection coefficient in the fundamental frequency band, l is the length of the cable under test;

[0081] The reflection coefficient in the discrete fundamental frequency band is extended at each discrete frequency point according to the harmonic characteristics to obtain the required reflection coefficient spectrum in the full frequency band.

[0082]

[0083] In the formula, Γ F (k,i) is the amplitude of the reflection coefficient of the kth discrete point in the i-th harmonic frequency band; m is the number of discrete points in the i-th harmonic frequency band;

[0084] Γ P (k,i) is the phase of the reflection coefficient of the kth discrete point in the i-th harmonic frequency band;

[0085] is the starting frequency of the frequency sweep in the i-th harmonic frequency band, is the end frequency of the sweep in the i-th harmonic frequency band, Δf i is the frequency interval in the i-th harmonic frequency band.

[0086] The positioning method described in step S4 is to construct a multi-band interval positioning function based on harmonic decomposition. The complex function and the kernel function in the reflection coefficient have generalized orthogonality, that is, at the fault point, the integral value of the product of the two is different from other positions (the discrete sequence is the sum of products). Therefore, the cable fault location is achieved by finding the mutation point of the diagnostic function curve.

[0087] In step S4, the cable fault location function based on the reflection coefficient spectrum is obtained by the reflection coefficient spectrum under the full frequency band. From the frequency domain to the spatial domain, we can obtain:

[0088]

[0089] Where x is the coordinate of the fault point, and the distance between the fault point and the incident point of the excitation signal source;

[0090] K(i,k,x) is the core function, the reflection coefficient of the fault cable With operator e -2γ(k)l Based on the orthogonality of its complex variable function, a positioning kernel function K(i,k,x) for multiple frequency bands is constructed:

[0091]

[0092] In the formula, γ h (i,k) is the propagation constant of the intact cable at the kth discrete frequency point in the i-th harmonic frequency band.

[0093] The propagation constant γ of the intact cable at the kth discrete frequency point in the i-th harmonic frequency band h (i,k) is obtained as follows:

[0094]

[0095] In the formula, R0 is the distributed resistance per unit length, ω is the angular frequency, L0 is the distributed inductance per unit length, G0 is the distributed capacitance per unit length, C0 is the distributed conductance per unit length, The frequency of the k-1th discrete frequency point in the i-th harmonic frequency band.

[0096] At high frequencies, ωL0>>R0, ωC0>>G0.

[0097] The method for obtaining the positioning function of the intact cable in step S5 is any one of the following three methods:

[0098] Method 1: Before the new cable is put into use, the reflection coefficient spectrum is measured as the reflection coefficient spectrum of the intact cable;

[0099] Method 2: Obtain the reflection coefficient spectrum of the intact cable by measuring the intact cable of the same type;

[0100] Method 3: Refer to the cable structure size or parameter specifications provided by the manufacturer, pre-calculate the cable's unit length parameters, obtain the cable's propagation coefficient, and then calculate the reflection coefficient spectrum of the intact cable based on the characteristic impedance and propagation coefficient;

[0101] Convert the intact cable reflection coefficient spectrum from the frequency domain to the spatial domain to obtain the positioning function D of the intact cable h (x).

[0102] The acquisition process of cable fault location in step S6 is:

[0103] The fault diagnosis function D(x) is obtained as follows:

[0104]

[0105] Find the mutation point of the fault diagnosis function curve as the fault point, and then obtain the position of the fault point to realize cable fault location.

[0106] The following steps are also included:

[0107] Step S7: evaluating the positioning accuracy using the positioning error optimization rate;

[0108] The diagnostic function is to highlight the fault position in the positioning curve, thereby achieving accurate positioning of the cable fault; and the positioning error is used to evaluate the positioning accuracy.

[0109] The positioning error optimization rate δ is obtained as follows:

[0110]

[0111] In the formula, x T is the traditional IFFT positioning result, x O is the multi-band interval positioning result, x D It is the starting fault position point of the excitation signal input terminal.

[0112] The effects are analyzed below in conjunction with the embodiments.

[0113] In this embodiment, the detection object is a 100m long YJLV 8.7 / 15kV XLPE power cable selected from the laboratory, and a cable insulation defect fault is made at 50m, and the length of the defect section is 10cm. The characteristic impedance is 50.55Ω.

[0114] The method of the present invention is used to locate faults. The positioning error of the improved multi-band positioning method for C-insulation defects is 0.02%, which is 0.4% higher than that of the traditional method; the positioning error of C+ insulation defects is 0.12%, which is 0.54% higher. According to the positioning diagnosis function, the simulation is used to obtain the fault location maps of different types of cables, such as Figure 3 , Figure 4 As shown, the position corresponding to the peak point in the figure is the insulation defect fault point.

[0115] According to the cable fault location method based on multi-frequency bands of reflection coefficient spectrum described in the present invention, the location algorithm of the present invention is used to reduce the test frequency range, increase the amplitude of the excitation signal, reduce the oscillation range near the location peak, and reduce the oscillation peak. Compared with the traditional location method, relying on the multi-frequency band location diagnosis function can effectively block the ripple oscillation generated when the cable fails, improve the positioning accuracy, and realize the accurate location of the cable fault. Therefore, it is of great significance to the operation and maintenance test of the cable and the safe operation of the equipment.

[0116] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the present invention. It should therefore be understood that many modifications may be made to the exemplary embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in a manner different from that described in the original claims. It should also be understood that the features described in conjunction with a single embodiment may be used in other described embodiments.

Claims

1. A cable fault location method based on multi-frequency bands of reflection coefficient spectrum, characterized in that: The method comprises the following steps: Step S1: obtaining a square wave excitation signal as an excitation signal source of a cable fault; Step S2: obtaining a reflection coefficient spectrum within the fundamental frequency band under square wave excitation; Step S3: discretizing the reflection coefficient spectrum, and extending the reflection coefficient spectrum in the fundamental frequency band to the required reflection coefficient spectrum of the full frequency band according to harmonic decomposition; Step S4: constructing a cable fault location function based on the reflection coefficient spectrum; Step S5: obtaining the reflection coefficient spectrum of the intact cable and determining the positioning function of the intact cable; Step S6: Ratio the multi-band interval positioning function based on the reflection coefficient spectrum obtained in step S4, the positioning function of the intact cable reflection coefficient spectrum obtained in step S5, and the positioning function of the faulty cable reflection coefficient spectrum to obtain a cable fault diagnosis function based on the reflection coefficient spectrum, and realize cable fault positioning by finding the mutation point of the fault diagnosis function curve.

2. According to claim 1, a cable fault location method based on multi-frequency intervals of reflection coefficient spectrum is characterized in that: In step S1, the non-sinusoidal signal is subjected to Fourier transform to obtain a time domain signal of a square wave signal as an excitation signal source, and the expression is: Where ω is the angular frequency, τ is the time constant, and U dc is the DC side voltage amplitude, 2n-1 is the number of harmonics, i is the harmonic order, i=1,2,...,2n-1.

3. According to claim 2, a cable fault location method based on a multi-frequency range of a reflection coefficient spectrum, characterized in that: The process of obtaining the reflection coefficient spectrum in the fundamental frequency band under square wave excitation in step S2 is: The excitation signal source is incident on the cable under test, and the corresponding response signal is obtained in real time. The input impedance of the cable under test is obtained according to the excitation signal and the response signal, and then the reflection coefficient is obtained. The cable reflection coefficient spectrum is obtained according to the continuously collected data.

4. According to claim 1, a cable fault location method based on multi-frequency bands of reflection coefficient spectrum, characterized in that: The process of obtaining the reflection coefficient spectrum of the full frequency band in step S3 is as follows: First, the reflection coefficient spectrum obtained at the fundamental frequency is discretized according to the equal frequency method, and the number of discrete frequency points m under the i-th harmonic is obtained: In the formula, f min is the starting frequency of the fundamental frequency sweep, f max is the fundamental wave sweep end frequency, △f is the fundamental wave frequency interval; The expression of the reflection coefficient of the kth discrete point of the fundamental wave is: In the formula, γ h (k) is the propagation constant of the intact cable at the kth discrete frequency point in the fundamental frequency band, k = 1, 2, ..., m; γ f (k) is the propagation constant of the fault cable at the kth discrete frequency point in the fundamental frequency band, Γ F (k) is the amplitude of the reflection coefficient in the fundamental frequency band, Γ P (k) is the phase of the reflection coefficient in the fundamental frequency band, l is the length of the cable under test; The reflection coefficient in the discrete fundamental frequency band is extended at each discrete frequency point according to the harmonic characteristics to obtain the required reflection coefficient spectrum in the full frequency band. In the formula, Γ F (k,i) is the amplitude of the reflection coefficient of the kth discrete point in the i-th harmonic frequency band; m is the number of discrete points in the i-th harmonic frequency band; Γ P (k,i) is the phase of the reflection coefficient of the kth discrete point in the i-th harmonic frequency band; is the starting frequency of the frequency sweep in the i-th harmonic frequency band, is the end frequency of the sweep in the i-th harmonic frequency band, Δf i is the frequency interval in the i-th harmonic frequency band.

5. According to claim 4, a cable fault location method based on multi-frequency intervals of reflection coefficient spectrum is characterized in that: In step S4, the cable fault location function based on the reflection coefficient spectrum is obtained by the reflection coefficient spectrum under the full frequency band. From the frequency domain to the spatial domain, we can obtain: Where x is the coordinate of the fault point, and the distance between the fault point and the incident point of the excitation signal source; K(i,k,x) is the core function, and In the formula, γ h (i,k) is the propagation constant of the intact cable at the kth discrete frequency point in the i-th harmonic frequency band.

6. A cable fault location method based on multi-frequency bands of reflection coefficient spectrum according to claim 5, characterized in that: The propagation constant γ of the intact cable at the kth discrete frequency point in the i-th harmonic frequency band h (i,k) is obtained as follows: In the formula, R0 is the distributed resistance per unit length, ω is the angular frequency, L0 is the distributed inductance per unit length, G0 is the distributed conductance per unit length, C0 is the distributed capacitance per unit length, The frequency of the k-1th discrete frequency point in the i-th harmonic frequency band.

7. A cable fault location method based on multi-frequency bands of reflection coefficient spectrum according to claim 1 or 5, characterized in that: The method for obtaining the positioning function of the intact cable in step S5 is any one of the following three methods: Method 1: Before the new cable is put into use, the reflection coefficient spectrum is measured as the reflection coefficient spectrum of the intact cable; Method 2: Obtain the reflection coefficient spectrum of the intact cable by measuring the intact cable of the same type; Method 3: Refer to the cable structure size or parameter specifications provided by the manufacturer, pre-calculate the cable's unit length parameters, obtain the cable's propagation coefficient, and then calculate the reflection coefficient spectrum of the intact cable based on the characteristic impedance and propagation coefficient; Convert the intact cable reflection coefficient spectrum from the frequency domain to the spatial domain to obtain the positioning function D of the intact cable h (x).

8. The cable fault location method based on multi-frequency bands of reflection coefficient spectrum according to claim 7, characterized in that: The acquisition process of cable fault location in step S6 is: The fault diagnosis function D(x) is obtained as follows: Find the mutation point of the fault diagnosis function curve as the fault point, and then obtain the position of the fault point to realize cable fault location.

9. The cable fault location method based on multi-frequency bands of reflection coefficient spectrum according to claim 1, characterized in that: The following steps are also included: Step S7: evaluating the positioning accuracy using the positioning error optimization rate; The positioning error optimization rate δ is obtained as follows: In the formula, x T is the traditional IFFT positioning result, x O is the multi-band interval positioning result, x D It is the starting fault position point of the excitation signal input terminal.

Images