CN105699856A - Cable fault locating system and method based on intelligent acquisition and analysis - Google Patents

Abstract

The invention relates to a cable fault locating system and method based on intelligent acquisition and analysis. A cable is formed by connecting a plurality of sections of cables with different lengths and cross-sectional areas through insulation joints. The cable fault locating system comprises a fault cable, a reference cable, a shorting wire (6), a grounding switch, a data acquisition unit, a cable resistor detection unit and a processor unit (5), wherein one end of the fault cable and one end of the reference cable are reference ends, the other ends are testing ends, the fault cable and the reference cable are connected through the shorting wire (6), the reference end of the fault cable is grounded through the grounding switch, the cable resistor detection unit is respectively connected with the testing ends of the fault cable and the reference cable, and the data acquisition unit and the cable resistor detection unit are connected to the processor unit (5). Compared with the prior art, the system and method are convenient for testing, high in automation degree and accurate in fault locating result.

Description

A kind of cable fault positioning system based on intelligent acquisition and analysis and method

Technical field

The present invention relates to a kind of cable fault positioning system and method, especially relate to a kind of cable fault positioning system based on intelligent acquisition with analysis and method。

Background technology

The advantages such as high tension cable takes up an area less with it, lays convenience, personal safety guarantee, power supply reliability is high, maintenance workload lacks are widely applied in high voltage power transmission and transforming network。Cable in network, is also a complicated system, it is possible to containing GIS terminal；It is likely to containing T joint or Y-shaped connector；It is likely long transmission line, comprises multiple cross interconnected section。Cable once occur insulation breakdown, often several days cannot fault point, delay power-on time, reduce power supply reliability。

In the market Murray bridge method and traveling wave bounce technique two kinds are mainly utilized for cable fault location in high-voltage and ultra-high power transmission and transformation network。

Murray bridge method is the classical way to breakdown point location, such as Fig. 1, A phase is connected with B by shorting stub, but electric bridge can only obtain permillage P ‰, artificial calculates trouble point distance, the i.e. x terminal distance L from trouble point F in Fig. 1₁, computing formula is as follows:

L₁=(2L+L '_d) × P ‰,

$L_d^{\′}=L_d\×\frac{S}{S_d},$

Wherein, L is the overall length of every phase cable, L_dFor shorting stub length, S is the sectional area of cable, S_dFor the sectional area of shorting stub, owing to shorting stub participates in bridge balance, it is therefore desirable to being converted into and the prismatic length of cable participate in calculating, shorting stub generally adopts the shorting stub that sectional area is less, thus the shorting stub sectional area S recorded_dError is relatively big, causes L '_dError is also very big, has had a strong impact on positioning precision。Assuming that cable length is L is 1000m, sectional area S is 1000mm², shorting stub length L_dFor 10m, sectional area S_dFor 16mm²(actual cross-section is amassed as 12mm²), after bridge balance, permillage reading is 30 ‰。Table 1 is test result contrast table, it can be seen that test value is little 63m than theoretical value, has bigger error。

Table 1 test result contrast table

	Cable total length L=2L+L 'd	Trouble point distance L1=(2L+L 'd)×P‰
			Theoretical value	2833m	L1=850m
Test value	2625m	L1=787m

Additionally going back under some scene, Murray bridge method also cannot position, and is respectively as follows:

(1) close on the load current running cable and produce power frequency magnetic field, become to can exceed that the power-frequency voltage of 200V at galvanometric 2 end M, X-shaped, and the DC potential difference only millivolt level for positioning。Therefore, galvanometer is easily damaged, or can not balance, or because exchange participates in bridge balance, localization ratio error is very big；

(2) cable run is long, and every section of cable conductor sectional area is different, and conductor material has copper core or aluminum core, it is necessary to manually tested cable being converted into the identical material of same uiform section with relief cable, the big error of workload is also big。

Traveling wave bounce technique is mainly secondary pulse process, three subpulse method and pulse current methods。But because high tension cable has cross interconnected, T joint, natural impedance produces sudden change, makes location echo sufficiently complex, it is difficult to location, and high-voltage pulse also has energy loss at this point, it is difficult to arrive at a distance。

Summary of the invention

Defect that the purpose of the present invention is contemplated to overcome above-mentioned prior art to exist and a kind of complicated cable fault positioning system based on intelligent acquisition with analysis and method are provided。

The purpose of the present invention can be achieved through the following technical solutions:

A kind of cable fault positioning system based on intelligent acquisition Yu analysis, the cable that described cable is all differed by multiple lengths and cross-sectional area is formed by connecting by insulating joint, described cable fault positioning system includes failure cable, reference cable, shorting stub, earthed switch, data acquisition unit, cable resistance detection unit and processor unit, described failure cable and reference cable one end are reference edge, the other end is test lead, failure cable and reference cable reference edge are connected by shorting stub, failure cable reference edge is also by ground switch earthing, described cable resistance detection unit connects the test lead of failure cable and reference cable respectively, described data acquisition unit and cable resistance detection unit are connected to processor unit；

Data acquisition unit gathers the cable information of each section of cable in failure cable and carries out unitized obtaining the unitized total length L of cable, when earthed switch is opened, cable resistance detection unit detection voltage x current information also sends to processor unit, and processor unit acquisition failure cable test lead is to the cable resistance R between trouble point₁, during earthed switch Guan Bi, cable resistance detection unit detection voltage x current information also sends to processor unit, and processor unit obtains the faulty cable test lead cable resistance R to reference edge₂, processor unit is according to L_x=L × (R₁/R₂) obtain the failure cable test lead unitized distance L to trouble point_x, and then processor unit is according to L_xThe failure cable test lead actual range L to trouble point is conversed with the cable information of each section of cable_x′。

Described data acquisition unit includes the digit manipulation knob being manually entered cable information, and described digit manipulation knob connects processor unit。

Described cable information includes length of cable, cable cross-sections amasss and cable resistance rate。

Described cable resistance detection unit includes high-voltage constant current source, sampling resistor, current collector and voltage collector, described high-voltage constant current source connects failure cable test lead by sampling resistor, described current collector is connected to sampling resistor two ends, and described voltage collector is parallel between failure cable test lead and reference cable test lead；

When earthed switch is opened, it is I that current collector gathers electric current₁, it is U that voltage collector gathers voltage₁, thus obtaining cable resistance R₁=U₁/I₁；During earthed switch Guan Bi, it is I that current collector gathers electric current₂, voltage collector gather voltage be U₂, thus obtaining cable resistance R₂=U₂/I₂。

This cable fault positioning system also includes display unit, and described display unit connects processor unit。

A kind of cable fault localization method based on intelligent acquisition Yu analysis, the method comprises the steps:

(1) each section of cable in failure cable is numbered successively D from test lead_i, wherein i=1,2 ... n, n are the total hop count of cable of composition failure cable, and processor unit gathers i-th section of cable D in failure cable_iCable information and send to processor unit, wherein i-th section of cable D_iCable information to include length of cable be L_i, sectional area be S_iIt is ρ with cable resistance rate_i；

(2) processor unit is with first paragraph cable for reference wire, and second segment cable to n-th section cable is unitized, and calculates the second segment cable unitized length to n-th section of cable according to following formula:

${L_j}^{\′}=L_j\×\frac{S_1}{S_j}\×\frac{{\mathrm{\ρ}}_j}{{\mathrm{\ρ}}_1},$

Wherein j=2,3 ... n；

(3) processor unit obtains the unitized total length L of faulty cable:

$L=L_1+\underset{j=2}{\overset{n}{\Σ}}{L_i}^{\′};$

(4) opening earthed switch, cable resistance detection unit obtains failure cable test lead to the cable resistance R between trouble point₁；

(5) closing earthed switch, cable resistance detection unit obtains faulty cable test lead to the cable resistance R between reference edge₂；

(6) according to L_x=L × (R₁/R₂) calculate obtain the failure cable test lead unitized distance L to trouble point_x；

(7) the failure cable test lead actual range L to trouble point is conversed according to following formula_x':

${L_x}^{\&prime;}=\left\{\begin{array}{cc}{L}_x& L_x\&le;L_1\\ L_1+(L_x-L_1)\&times;\frac{S_2}{S_1}\&times;\frac{{\mathrm{\&rho;}}_1}{{\mathrm{\&rho;}}_2}& L_1<L_x\&le;L_1+{L_2}^{\&prime;}\\ \underset{k=1}{\overset{j}{\&Sigma;}}{L}_k+(L_x-L_1-\underset{p=2}{\overset{j}{\&Sigma;}}{L_p}^{\&prime;})\&times;\frac{S_{j+1}}{S_1}\&times;\frac{{\mathrm{\&rho;}}_1}{{\mathrm{\&rho;}}_{j+1}}& L_1+{L_2}^{\&prime;}+...+{L_j}^{\&prime;}<L_x\&le;L_1+{L_2}^{\&prime;}+...+{L_j}^{\&prime;}+{L_{j+1}}^{\&prime;},j=2,3...n\end{array}\right..$

Compared with prior art, present invention have the advantage that

(1) data acquisition unit of the present invention gathers the cable information of each section of cable in failure cable and carries out unitized obtaining the unitized total length L of cable, different materials different cross-sectional cable in failure cable is converted into the equivalent cable length of same cross-sectional same conductor material, whole process by processor unit from row operation, automaticity is high, utilize the resistive voltage ratio of cable resistance detection unit detection simultaneously, the distance of trouble point and test lead in anti-release failure cable, test result precision is high；

(2) Fault Locating Method of the present invention can be effectively improved cable fault search efficiency, shortens power off time, improves power supply reliability, has good market using value。

Accompanying drawing explanation

Fig. 1 is Murray bridge method fault location principle schematic；

Fig. 2 is threephase cable system line figure；

Fig. 3 is threephase cable system failure assignment test first step functional arrangement figure；

Fig. 4 is threephase cable system failure assignment test second step functional arrangement figure。

In figure, 1 is high-voltage constant current source, and 2 is sampling resistor, and 3 is current collector, and 4 is voltage collector, and 5 is processor unit, and 6 is shorting stub, and J1 is the first conductive clamp, and J2 is the second conductive clamp, and J3 is the 3rd conductive clamp, and J4 is the 4th conductive clamp。

Detailed description of the invention

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail。

Embodiment

A kind of cable fault positioning system based on intelligent acquisition Yu analysis, the cable that cable is all differed by multiple lengths and cross-sectional area is formed by connecting by insulating joint, cable fault positioning system includes failure cable, reference cable, shorting stub 6, earthed switch, data acquisition unit, cable resistance detection unit and processor unit 5, failure cable and reference cable one end are reference edge, the other end is test lead, failure cable and reference cable reference edge are connected by shorting stub 6, shorting stub 6 adopts thin shorting stub, failure cable reference edge is also by ground switch earthing, cable resistance detection unit connects the test lead of failure cable and reference cable respectively, data acquisition unit and cable resistance detection unit are connected to processor unit 5；Data acquisition unit gathers the cable information of each section of cable in failure cable and carries out unitized obtaining the unitized total length L of cable, when earthed switch is opened, cable resistance detection unit detection voltage x current information transmission are to processor unit 5, and processor unit 5 obtains failure cable test lead to the cable resistance R between trouble point₁, during earthed switch Guan Bi, cable resistance detection unit detection voltage x current information also sends to processor unit 5, and processor unit 5 obtains the faulty cable test lead cable resistance R to reference edge₂, processor unit 5 is according to L_x=L × (R₁/R₂) obtain the failure cable test lead unitized distance L to trouble point_x, and then processor unit 5 is according to L_xThe failure cable test lead actual range L to trouble point is conversed with the cable information of each section of cable_x′。

Data acquisition unit includes the digit manipulation knob being manually entered cable information, and digit manipulation knob connects processor unit 5, is equivalent to computer keyboard, it is possible to provide this alignment system is carried out parameter setting and is operated alignment system controlling by user。Cable information includes length of cable, cable cross-sections amasss and cable resistance rate。Cable resistance detection unit includes high-voltage constant current source 1, sampling resistor 2, current collector 3 and voltage collector 4, high-voltage constant current source 1 connects failure cable test lead by sampling resistor 2, current collector 3 is connected to sampling resistor 2 two ends, and voltage collector 4 is parallel between failure cable test lead and reference cable test lead；When earthed switch is opened, it is I that current collector 3 gathers electric current₁, it is U that voltage collector 4 gathers voltage₁, thus obtaining cable resistance R₁=U₁/I₁；During earthed switch Guan Bi, it is I that current collector 3 gathers electric current₂, to gather voltage be U to voltage collector 4₂, thus obtaining cable resistance R₂=U₂/I₂。This cable fault positioning system also includes display unit, and display unit connects processor unit 5。

A kind of cable fault localization method based on intelligent acquisition Yu analysis, the method comprises the steps:

(1) each section of cable in failure cable is numbered successively D from test lead_i, wherein i=1,2 ... n, n are the total hop count of cable of composition failure cable, and processor unit 5 gathers i-th section of cable D in failure cable_iCable information and send to processor unit 5, wherein i-th section of cable D_iCable information to include length of cable be L_i, sectional area be S_iIt is ρ with cable resistance rate_i；

(2) processor unit 5 is with first paragraph cable for reference wire, and second segment cable to n-th section cable is unitized, and calculates the second segment cable unitized length to n-th section of cable according to following formula:

${L_j}^{\&prime;}=L_j\&times;\frac{S_1}{S_j}\&times;\frac{{\mathrm{\&rho;}}_j}{{\mathrm{\&rho;}}_1},$

Wherein j=2,3 ... n；

(3) processor unit 5 obtains the unitized total length L of faulty cable:

$L=L_1+\underset{j=2}{\overset{n}{\&Sigma;}}{L_i}^{\&prime;};$

(4) opening earthed switch, cable resistance detection unit obtains failure cable test lead to the cable resistance R between trouble point₁；

(5) closing earthed switch, cable resistance detection unit obtains faulty cable test lead to the cable resistance R between reference edge₂；

(6) according to L_x=L × (R₁/R₂) calculate obtain the failure cable test lead unitized distance L to trouble point_x；

(7) the failure cable test lead actual range L to trouble point is conversed according to following formula_x':

${L_x}^{\&prime;}=\left\{\begin{array}{cc}{L}_x& L_x\&le;L_1\\ L_1+(L_x-L_1)\&times;\frac{S_2}{S_1}\&times;\frac{{\mathrm{\&rho;}}_1}{{\mathrm{\&rho;}}_2}& L_1<L_x\&le;L_1+{L_2}^{\&prime;}\\ \underset{k=1}{\overset{j}{\&Sigma;}}{L}_k+(L_x-L_1-\underset{p=2}{\overset{j}{\&Sigma;}}{L_p}^{\&prime;})\&times;\frac{S_{j+1}}{S_1}\&times;\frac{{\mathrm{\&rho;}}_1}{{\mathrm{\&rho;}}_{j+1}}& L_1+{L_2}^{\&prime;}+...+{L_j}^{\&prime;}<L_x\&le;L_1+{L_2}^{\&prime;}+...+{L_j}^{\&prime;}+{L_{j+1}}^{\&prime;},j=2,3...n\end{array}\right..$

For threephase cable system line, above-mentioned cable fault positioning system and method is adopted to carry out fault potential。It is illustrated in figure 2 threephase cable system line figure, containing A, B, C three-phase, one end is outdoor terminal, in figure, A, B, C three-phase outdoor terminal corresponds to AN1, BN1 and CN1, the other end is gas insulated terminal (GIS), in figure, the three-phase, gas insulated terminal of A, B, C corresponds to AG1, BG1 and CG1, the cable that threephase cable all differs each through three segment length and cross-sectional area is formed by connecting by insulating joint, insulating joint respectively AIJ1, AIJ2, BIJ1, BIJ2, CIJ1 and CIJ2 in figure, trouble point is at C phase F place, and RF is fault resstance。

As shown in Figure 3, Figure 4, C phase fault cable, choosing A phase cable is reference cable, failure cable and reference cable gas-insulated end are reference edge, outdoor terminal is test lead, failure cable and reference cable reference edge are connected by shorting stub 6, failure cable reference edge is also by ground switch earthing, in figure, earthed switch is K3, shorting stub 6 one end connects reference cable reference edge by the 3rd conductive clamp J3, the other end connects failure cable reference edge by the 4th conductive clamp J4, and earthed switch connects the 4th conductive clamp J4。Cable resistance detection unit includes high-voltage constant current source 1, sampling resistor 2, current collector 3 and voltage collector 4, high-voltage constant current source 1 connects failure cable test lead by sampling resistor 2, figure is connected with the second conductive clamp J2 on faulty cable by second switch K2, sampling resistor 2 connects the first conductive clamp J1 on reference cable also by the first switch K2 simultaneously, current collector 3 is connected to sampling resistor 2 two ends, voltage collector 4 two ends connect the first conductive clamp J1 respectively and the second conductive clamp J2, current collector 3 and voltage collector 4 are connected to processor unit 5。

Before test, first to the cable information of three sections of cables in processor unit 5 input fault cable, including length of cable L₁、L₂、L₃, sectional area is S₁、S₂、S₃With cable resistance rate ρ₁、ρ₂、ρ₃。Processor unit 5 processes automatically, can calculate each section of cable insulated joint positional information, namely calculates the percentage ratio accounting for total track length of each insulated cable joint, and can be displayed in display unit by tabular form。

Then passing through two step methods of testing and position test, the first step, as it is shown on figure 3, the first switch K1 opens in figure, second switch K2 closes, and earthed switch K3 opens, and it is I that current collector 3 records electric current₁, it is U that voltage collector 4 gathers voltage₁Owing to earthed switch K3 opens, therefore, now reference cable test lead, reference cable reference edge, failure cable reference edge are identical with trouble point current potential, electric current flows out from high-voltage constant current source 1 and flows through faulty cable test lead through sampling resistor 2, and flow back to the earth by fault resstance RF, form current loop, the electric current I therefore recorded₁For the size of current between faulty cable test lead to trouble point, voltage U₁For the voltage swing between faulty cable test lead to trouble point。Second step, as shown in Figure 4, the first switch K1 opens, and second switch K2 closes, and earthed switch K3 closes, and it is I that current collector 3 records electric current₂, it is U that voltage collector 4 gathers voltage₂, due to earthed switch K3 ground connection, now electric current flows out from high-voltage constant current source 1 and flows through faulty cable test lead through sampling resistor 2, and is flowed directly to failure cable reference edge and flow to the earth, forms current loop, the electric current I therefore recorded₂For the size of current between faulty cable test lead to reference edge, voltage U₂For the voltage swing between faulty cable test lead to reference edge。

The small DC voltage U gathered₁、U₂With electric current I₁、I₂Sending to processor unit 5, processor unit 5 carries out Intelligent Calculation, filters further, rejects garbage, is analyzed data calculating, thus obtaining the positional information of Method of Cable Trouble Point。Second segment cable and the 3rd section of cable, with first paragraph cable for reference wire, are unitized, calculate the unitized length of the 3rd section of cable of second segment cable according to following formula by concrete processor unit 5:

${L_2}^{\&prime;}=L_2\&times;\frac{S_1}{S_2}\&times;\frac{{\mathrm{\&rho;}}_2}{{\mathrm{\&rho;}}_1},{L_3}^{\&prime;}=L_3\&times;\frac{S_1}{S_3}\&times;\frac{{\mathrm{\&rho;}}_3}{{\mathrm{\&rho;}}_1};$

And then obtain the unitized total length L of faulty cable:

L=L₁+L₂′+L₃'；

Obtain faulty cable test lead to the cable resistance R between trouble point₁=U₁/I₁, obtain faulty cable test lead to the cable resistance R between reference edge₂=U₂/I₂, according to L_x=L × (R₁/R₂) calculate obtain the failure cable test lead unitized distance L to trouble point_x。Then amassing at the cable cross-sections according to each section of cable and unitize with resistivity is counter, the cable information obtaining each section of cable converses the failure cable test lead actual range L to trouble point_x', particularly as follows:

${L_x}^{\&prime;}=\left\{\begin{array}{cc}{L}_x& L_x\&le;L_1\\ L_1+(L_x-L_1)\&times;\frac{S_2}{S_1}\&times;\frac{{\mathrm{\&rho;}}_1}{{\mathrm{\&rho;}}_2}& L_1<L_x\&le;L_1+{L_2}^{\&prime;}\\ L_1+L_2+(L_x-L_1-{L_2}^{\&prime;})\&times;\frac{S_3}{S_1}\&times;\frac{{\mathrm{\&rho;}}_1}{{\mathrm{\&rho;}}_3}& L_x>L_1+{L_2}^{\&prime;}\end{array}\right..$

The result finally recorded can be displayed by display unit。

Claims (6)

1. the cable fault positioning system based on intelligent acquisition Yu analysis, the cable that described cable is all differed by multiple lengths and cross-sectional area is formed by connecting by insulating joint, it is characterized in that, described cable fault positioning system includes failure cable, reference cable, shorting stub (6), earthed switch, data acquisition unit, cable resistance detection unit and processor unit (5), described failure cable and reference cable one end are reference edge, the other end is test lead, failure cable and reference cable reference edge are connected by shorting stub (6), failure cable reference edge is also by ground switch earthing, described cable resistance detection unit connects the test lead of failure cable and reference cable respectively, described data acquisition unit and cable resistance detection unit are connected to processor unit (5)；

Data acquisition unit gathers the cable information of each section of cable in failure cable and carries out unitized obtaining the unitized total length L of cable, when earthed switch is opened, cable resistance detection unit detection voltage x current information also sends to processor unit (5), and processor unit (5) acquisition failure cable test lead is to the cable resistance R between trouble point₁, during earthed switch Guan Bi, cable resistance detection unit detection voltage x current information also sends to processor unit (5), and processor unit (5) obtains the faulty cable test lead cable resistance R to reference edge₂, processor unit (5) is according to L_x=L × (R₁/R₂) obtain the failure cable test lead unitized distance L to trouble point_x, and then processor unit (5) is according to L_xThe failure cable test lead actual range L to trouble point is conversed with the cable information of each section of cable_x′。

2. a kind of cable fault positioning system based on intelligent acquisition Yu analysis according to claim 1, it is characterized in that, described data acquisition unit includes the digit manipulation knob being manually entered cable information, and described digit manipulation knob connects processor unit (5)。

3. a kind of cable fault positioning system based on intelligent acquisition Yu analysis according to claim 1 or 2 any one, it is characterised in that described cable information includes length of cable, cable cross-sections amasss and cable resistance rate。

4. a kind of cable fault positioning system based on intelligent acquisition Yu analysis according to claim 1, it is characterized in that, described cable resistance detection unit includes high-voltage constant current source (1), sampling resistor (2), current collector (3) and voltage collector (4), described high-voltage constant current source (1) connects failure cable test lead by sampling resistor (2), described current collector (3) is connected to sampling resistor (2) two ends, described voltage collector (4) is parallel between failure cable test lead and reference cable test lead；

When earthed switch is opened, it is I that current collector (3) gathers electric current₁, it is U that voltage collector (4) gathers voltage₁, thus obtaining cable resistance R₁=U₁/I₁；During earthed switch Guan Bi, it is I that current collector (3) gathers electric current₂, voltage collector (4) gather voltage be U₂, thus obtaining cable resistance R₂=U₂/I₂。

5. a kind of cable fault positioning system based on intelligent acquisition Yu analysis according to claim 1, it is characterised in that this cable fault positioning system also includes display unit, and described display unit connects processor unit (5)。

6. one kind adopts the method based on intelligent acquisition Yu the cable fault positioning system of analysis as claimed in claim 1, it is characterised in that the method comprises the steps:

(1) each section of cable in failure cable is numbered successively D from test lead_i, wherein i=1,2 ... n, n are the total hop count of cable of composition failure cable, and processor unit (5) gathers i-th section of cable D in failure cable_iCable information and send to processor unit (5), wherein i-th section of cable D_iCable information to include length of cable be L_i, sectional area be S_iIt is ρ with cable resistance rate_i；

(2) processor unit (5) is with first paragraph cable for reference wire, and second segment cable to n-th section cable is unitized, and calculates the second segment cable unitized length to n-th section of cable according to following formula:

${L_j}^{\&prime;}=L_j\&times;\frac{S_1}{S_j}\&times;\frac{{\mathrm{\&rho;}}_j}{{\mathrm{\&rho;}}_1},$

Wherein j=2,3 ... n；

(3) processor unit (5) obtains the unitized total length L of faulty cable:

$L=L_1+\underset{j=2}{\overset{n}{\&Sigma;}}{L_i}^{\&prime;};$

(4) opening earthed switch, cable resistance detection unit obtains failure cable test lead to the cable resistance R between trouble point₁；

(5) closing earthed switch, cable resistance detection unit obtains faulty cable test lead to the cable resistance R between reference edge₂；

(6) according to L_x=L × (R₁/R₂) calculate obtain the failure cable test lead unitized distance L to trouble point_x；

(7) the failure cable test lead actual range L to trouble point is conversed according to following formula_x':

${L_x}^{\&prime;}=\left\{\begin{array}{cc}{L}_x& L_x\&le;L_1\\ L_1+(L_x-L_1)\&times;\frac{S_2}{S_1}\&times;\frac{{\mathrm{\&rho;}}_1}{{\mathrm{\&rho;}}_2}& L_1<L_x\&le;L_1+{L_2}^{\&prime;}\\ \underset{k=1}{\overset{j}{\&Sigma;}}{L}_k+\left(L_x-L_1-\underset{p=2}{\overset{j}{\&Sigma;}}{L_p}^{\&prime;}\right)\&times;\frac{S_{j+1}}{S_1}\&times;\frac{{\mathrm{\&rho;}}_1}{{\mathrm{\&rho;}}_{j+1}}& L_1+{L_2}^{\&prime;}+\mathrm{...}+{L_j}^{\&prime;}<L_x\&le;L_1+{L_2}^{\&prime;}+\mathrm{...}+{L_j}^{\&prime;}+{L_{j+1}}^{\&prime;},j=2,\mathrm{3...}n\end{array}\right..$