CN105223468A - Based on the transmission line of electricity one-end fault ranging method of mapping function - Google Patents

Abstract

The invention discloses a kind of transmission line of electricity one-end fault ranging method based on mapping function, comprise the following steps: after 1) transmission line malfunction occurs, in protection installation place, three-phase voltage and three-phase current are sampled, and utilize Fourier algorithm to calculate three-phase voltage vector sum three-phase current vector respectively; 2) by step 1) the three-phase current vector calculation zero-sequence current of gained vector; 3) according to fault type, corresponding mapping function is chosen; 4) adopt search one by one method, search the x making mapping function get minimum value, this x is fault distance.

Description

Based on the transmission line of electricity one-end fault ranging method of mapping function

Technical field

The present invention relates to a kind of transmission line of electricity one-end fault ranging method based on mapping function, belong to Relay Protection Technology in Power System field.

Technical background

Fault localization can promptly and accurately fault point, can not only repair circuit fast, ensure reliable power supply, and play vital effect to the safe and stable operation of electric system.Therefore, fault localization is the study hotspot of protecting electrical power system and control field always.

Fault localization can be divided into double-end distance measurement method and single end distance measurement method from the angle that data use, and double-end distance measurement method uses the electric data at transmission line of electricity two ends to realize fault localization, and single end distance measurement method utilizes local single-end electrical data to carry out fault localization.Double-end distance measurement method can be divided into again dual ended data synchronous range finding method and the asynchronous telemetry of dual ended data, and dual ended data synchronous range finding method is generally higher to communicating requirement, needs circuit two end data absolute synchronization, otherwise will produce error; The asynchronous telemetry of dual ended data does not require circuit two end data stringent synchronization, but still needs to lay data transmission channel, and this can increase fund input; And single end distance measurement method does not need communication channel, economical reliable, simple, therefore, be widely applied in actual transmission line of electricity.

Fault localization can be divided into impedance method and travelling wave ranging method from the angle of principle, impedance method be utilize fault distance to be directly proportional to measurement impedance principle to realize fault localization, travelling wave ranging method determines fault distance by the time of wavefront commute between measured place and fault place.Impedance method affects comparatively large by transition resistance, also do not find the impedance method that can complete and overcome transition resistance so far, and meanwhile, impedance method is also easily subject to the impact of peer-to-peer system impedance and the method for operation; Which kind of method no matter the distance accuracy of travelling wave ranging method generally higher than impedance method, but identifying the reflected traveling wave of trouble spot and having certain difficulty from the generation row ripple of other discontinuous points, therefore, be, be all necessary to carry out more deep research to it.

Summary of the invention

The invention provides a kind of not by the transmission line of electricity one-end fault ranging method based on mapping function that transition resistance affects, there is higher measuring accuracy.

The method comprises the following steps:

1., based on a transmission line of electricity one-end fault ranging method for mapping function, it is characterized in that:

1) after transmission line malfunction occurs, in protection installation place, three-phase voltage and three-phase current are sampled, and calculate three-phase voltage vector sum three-phase current vector respectively;

2) according to step 1) the three-phase current vector calculation zero-sequence current of gained vector;

3) according to fault type, corresponding mapping function is chosen;

4) adopt search one by one method, find the x making mapping function get minimum value, this x is fault distance.

2. the transmission line of electricity one-end fault ranging method based on mapping function according to claim 1; it is characterized in that: the step 1 described) in; hold protection installation place to carry out real time data sampling with the sample frequency of 2000Hz at circuit M, obtain current sequence i _mA(k), i _mB(k), i _mC(k) and contact potential series u _mA(k), u _mB(k), u _mC(k), utilize the three-phase voltage vector sum three-phase current vector of Fourier algorithm difference computing electric power line, specific algorithm is as follows:

Wherein, K=40 is the sampling number of a primitive period, represent current vector and the voltage vector of circuit M end protection installation place respectively.

3. the transmission line of electricity one-end fault ranging method based on mapping function according to claim 1, is characterized in that: the step 2 described) in, according to the three-phase current vector calculation zero-sequence current vector of gained concrete calculating is such as formula shown in (3).

${\stackrel{\·}{I}}_{M0}=\frac{1}{3}({\stackrel{\·}{I}}_{MA}+{\stackrel{\·}{I}}_{MB}+{\stackrel{\·}{I}}_{MC})---\left(3\right)$

4. the transmission line of electricity one-end fault ranging method based on mapping function according to claim 1, is characterized in that: for different fault types, and its corresponding mapping function is provided by formula (4) ~ (12):

Single-phase earthing fault mapping function:

$f_A\left(x\right)=\left|imag\left(\frac{{\stackrel{\·}{U}}_{MA}-({\stackrel{\·}{I}}_{MA}+3\mathrm{\κ}{\stackrel{\·}{I}}_{M0}){\mathrm{xZ}}_{L1}}{{\stackrel{\·}{I}}_{MA}+({\stackrel{\·}{I}}_{MC}-{\stackrel{\·}{I}}_{MB})j\sqrt{3}/3}{C}_1\right(x\left)\right)\right|---\left(4\right)$

$f_B\left(x\right)=\left|imag\left(\frac{{\stackrel{\·}{U}}_{MB}-({\stackrel{\·}{I}}_{MB}+3\mathrm{\κ}{\stackrel{\·}{I}}_{M0}){\mathrm{xZ}}_{L1}}{{\stackrel{\·}{I}}_{MB}+({\stackrel{\·}{I}}_{M4}-{\stackrel{\·}{I}}_{MC})j\sqrt{3}/3}{C}_1\right(x\left)\right)\right|---\left(5\right)$

$f_C\left(x\right)=\left|imag\left(\frac{{\stackrel{\·}{U}}_{MC}-({\stackrel{\·}{I}}_{MC}+3\mathrm{\κ}{\stackrel{\·}{I}}_{M0}){\mathrm{xZ}}_{L1}}{{\stackrel{\·}{I}}_{MC}+({\stackrel{\·}{I}}_{MB}-{\stackrel{\·}{I}}_{MA})j\sqrt{3}/3}{C}_1\right(x\left)\right)\right|---\left(6\right)$

Wherein, f _a(x), f _b(x), f _cx () is respectively the mapping function of A, B, C singlephase earth fault; κ is zero sequence current compensation factor; j is the imaginary part unit of plural number; imag () represents the imaginary numbers getting plural number; || represent and ask mould; x is certain distance a bit and between protection installation place on circuit, and the span of x is zero to total track length, C ₁x () is line current distribution coefficient, be applicable to the mapping function of all fault types, and expression is:

C ₁(x)＝[(L-x)Z _L1+Z _N1]/(Z _M1+LZ _L1+Z _N1)

Wherein, L is total track length, Z _m1, Z _n1be respectively the system positive sequence impedance of circuit M side and N side, Z _l1for unit length circuit positive sequence impedance;

Two-phase phase fault mapping function:

$f_{AB}\left(x\right)=\left|imag\left(\frac{{\stackrel{\·}{U}}_{MA}-{\stackrel{\·}{U}}_{MB}-{\mathrm{xZ}}_{L1}({\stackrel{\·}{I}}_{MA}-{\stackrel{\·}{I}}_{MB})}{{\stackrel{\·}{I}}_{MA}-{\stackrel{\·}{I}}_{MB}+j\sqrt{3}{\stackrel{\·}{I}}_{MC}}{C}_1\right(x\left)\right)\right|---\left(7\right)$

$f_{BC}\left(x\right)=\left|imag\left(\frac{{\stackrel{\·}{U}}_{MB}-{\stackrel{\·}{U}}_{MC}-{\mathrm{xZ}}_{L1}({\stackrel{\·}{I}}_{MB}-{\stackrel{\·}{I}}_{MC})}{{\stackrel{\·}{I}}_{MB}-{\stackrel{\·}{I}}_{MC}+j\sqrt{3}{\stackrel{\·}{I}}_{MA}}{C}_1\right(x\left)\right)\right|---\left(8\right)$

$f_{CA}\left(x\right)=\left|imag\left(\frac{{\stackrel{\·}{U}}_{MC}-{\stackrel{\·}{U}}_{MA}-{\mathrm{xZ}}_{L1}({\stackrel{\·}{I}}_{MC}-{\stackrel{\·}{I}}_{MA})}{{\stackrel{\·}{I}}_{MC}-{\stackrel{\·}{I}}_{MA}+j\sqrt{3}{\stackrel{\·}{I}}_{MB}}{C}_1\right(x\left)\right)\right|---\left(9\right)$

Wherein, f _aB(x), f _bC(x), f _cAx () is respectively AB, BC, CA two-phase phase fault mapping function;

Two-phase short circuit and ground fault mapping function:

$f_{ABG}\left(x\right)=\left|imag\left(\frac{{\stackrel{\·}{U}}_{MA}-{\stackrel{\·}{U}}_{MB}-{\mathrm{xZ}}_{L1}({\stackrel{\·}{I}}_{MA}-{\stackrel{\·}{I}}_{MB})}{{\stackrel{\·}{I}}_{MA}^{\′}-{\stackrel{\·}{I}}_{MB}^{\′}}{C}_1\right(x\left)\right)\right|---\left(10\right)$

Formula (10) is AB Earth design function, ${\stackrel{\·}{I}}_{MA}^{\′}=\[(2-\mathrm{\α}-{\mathrm{c\α}}^2){\stackrel{\·}{I}}_{MA}+({\mathrm{\α}}^2-{\mathrm{c\α}}^2){\stackrel{\·}{I}}_{MB}+(2-{\mathrm{c\α}}^2){\stackrel{\·}{I}}_{MC}\]/3,$ ${\stackrel{\·}{I}}_{MB}^{\′}=\[(-c\mathrm{\α}-2{\mathrm{\α}}^2){\stackrel{\·}{I}}_{MA}+(2-\mathrm{\α}-c\mathrm{\α}){\stackrel{\·}{I}}_{MB}+({\mathrm{\α}}^2-c\mathrm{\α}){\stackrel{\·}{I}}_{MC}\]/3,$ α＝e ^j120°， $c=1-\mathrm{\Δ}{\stackrel{\·}{I}}_{MC}^0/{\stackrel{\·}{I}}_{M0}^0,$ for the difference of fault moment and the C phase current vector in two all after date moment, for the zero-sequence current vector of fault moment;

$f_{BCG}\left(x\right)=\left|imag\left(\frac{{\stackrel{\·}{U}}_{MB}-{\stackrel{\·}{U}}_{MC}-{\mathrm{xZ}}_{L1}({\stackrel{\·}{I}}_{MB}-{\stackrel{\·}{I}}_{MC})}{{\stackrel{\·}{I}}_{MB}^{\′}-{\stackrel{\·}{I}}_{MC}^{\′}}{C}_1\right(x\left)\right)\right|---\left(11\right)$

Formula (11) is BC Earth design function, ${\stackrel{\·}{I}}_{MB}^{\′}=\[(\mathrm{\α}-{\mathrm{c\α}}^2){\stackrel{\·}{I}}_{MA}+(2-{\mathrm{\α}}^2-{\mathrm{c\α}}^2){\stackrel{\·}{I}}_{MB}+(-2\mathrm{\α}-{\mathrm{c\α}}^2){\stackrel{\·}{I}}_{MC}\]/3,$ ${\stackrel{\·}{I}}_{MC}^{\′}=\[({\mathrm{\α}}^2-c\mathrm{\α}){\stackrel{\·}{I}}_{MA}+(-c\mathrm{\α}-2{\mathrm{\α}}^2){\stackrel{\·}{I}}_{MB}+(2-\mathrm{\α}-c\mathrm{\α}){\stackrel{\·}{I}}_{MC}\]/3,$ α＝e ^j120°， $c=1-\mathrm{\Δ}{\stackrel{\·}{I}}_{MA}^0/{\stackrel{\·}{I}}_{M0}^0,$ for the difference of fault moment and the A phase current vector in two all after date moment, for the zero-sequence current vector of fault moment;

$f_{CAG}\left(x\right)=\left|imag\left(\frac{{\stackrel{\·}{U}}_{MC}-{\stackrel{\·}{U}}_{MA}-{\mathrm{xZ}}_{L1}({\stackrel{\·}{I}}_{MC}-{\stackrel{\·}{I}}_{MA})}{{\stackrel{\·}{I}}_{MC}^{\′}-{\stackrel{\·}{I}}_{MA}^{\′}}{C}_1\right(x\left)\right)\right|---\left(12\right)$

Formula (12) is CA Earth design function, ${\stackrel{\·}{I}}_{MC}^{\′}=\[({\mathrm{\α}}^2-{\mathrm{c\α}}^2){\stackrel{\·}{I}}_{MA}+(-2{\mathrm{\α}}^2-{\mathrm{c\α}}^2){\stackrel{\·}{I}}_{MB}+(2-\mathrm{\α}-{\mathrm{c\α}}^2){\stackrel{\·}{I}}_{MC}\]/3,$ ${\stackrel{\·}{I}}_{MA}^{\′}=\[(2-c\mathrm{\α}-{\mathrm{\α}}^2){\stackrel{\·}{I}}_{MA}+(-2\mathrm{\α}-c\mathrm{\α}){\stackrel{\·}{I}}_{MB}+(\mathrm{\α}-c\mathrm{\α}){\stackrel{\·}{I}}_{MC}\]/3,$ α＝e ^j120°， $c=1-\mathrm{\Δ}{\stackrel{\·}{I}}_{MB}^0/{\stackrel{\·}{I}}_{M0}^0,$ for the difference of fault moment and two all after date moment B phase current vectors, for the zero-sequence current vector of fault moment.

5. the transmission line of electricity one-end fault ranging method based on mapping function according to claim 1, it is characterized in that: the initial value getting x is 0km, x is progressively increased to total track length with 0.01km, again each x is all substituted into mapping function to calculate, search out the x that mapping function gets minimum value, this x is fault distance.

The beneficial effect that the present invention reaches is:

The present invention utilizes transition impedance imaginary part to be that the feature of zero is to localization of fault function of deriving, completely not by the impact of transition resistance in principle, simultaneously, the method does not ignore the phase angle of current distribution factor, without any approximate in localization of fault function derivation, there is higher distance accuracy, far above other single-ended impedance location algorithm.The method only needs local measurement voltage and current signal, does not need to arrange special communication channel, has good practical feasibility.

Accompanying drawing explanation

Accompanying drawing 1 is the schematic diagram of the 500kV extra high voltage network model of the embodiment of the present invention.

Accompanying drawing 2 is the transmission line of electricity one-end fault ranging process flow diagrams based on mapping function.

Embodiment

The transmission line of electricity one-end fault ranging method embodiment based on mapping function that the present invention proposes is described in detail as follows:

As shown in Figure 1, the transmission line of electricity schematic diagram of application the inventive method is a 500kV UHV (ultra-high voltage) Double-End Source electric power system, and two side bus are M, N, and total track length L is power phase advanced N side, 200km, M side power supply 20 degree.Need to carry out Fault Phase Selection before application the inventive method, according to phase selection result, choose corresponding mapping function, finally obtain fault localization distance.If phase selection fail result is BC two-phase short circuit and ground fault, fault distance is apart from M end protection installation place 155km, and transition resistance is 100 Ω.

M side, N side system parameter are:

Positive sequence system impedance is: Z _m1=Z _n1=0.9+j19.12888 Ω;

Zero sequence system impedance is: Z _m0=Z _n0=0.7+j15.48962 Ω;

Line parameter circuit value is:

Positive sequence resistance, inductance, electric capacity: r ₁=0.01786 Ω/km, l ₁=0.99962 Ω/km, c ₁=0.01164 μ F/km;

Zero sequence resistance, inductance, electric capacity: r ₁=0.29522 Ω/km, l ₁=3.31178 Ω/km, c ₁=0.00769 μ F/km;

Embodiment concrete steps are as follows:

1), after transmission line malfunction occurs, in protection installation place, three-phase voltage and three-phase current are sampled, and a certain moment three-phase voltage vector sum three-phase current vector after utilizing Fourier algorithm to calculate fault respectively:

${\stackrel{\·}{U}}_{MA}=-308.27+j60.192kV$

${\stackrel{\·}{U}}_{MB}=214.90+j224.27kV$

${\stackrel{\·}{U}}_{MC}=86.030-j292.99kV$

${\stackrel{\·}{I}}_{MA}=-1.1075+j0.2496kA$

${\stackrel{\·}{I}}_{MB}=1.4823+j1.3009kA$

${\stackrel{\·}{I}}_{MC}=0.1850-j1.9985kA$

2) by three-phase current vector calculating zero-sequence current vector

${\stackrel{\·}{I}}_{M0}=\frac{1}{3}({\stackrel{\·}{I}}_{MA}+{\stackrel{\·}{I}}_{MB}+{\stackrel{\·}{I}}_{MC})=0.1850-j1.9985kA$

3) be BC double earthfault according to phase selection gained fault type, choosing localization of fault function is:

$f_{BCG}\left(x\right)=\frac{\stackrel{\·}{U}-{\stackrel{\·}{U}}_{MC}-{\mathrm{xZ}}_{L1}({\stackrel{\·}{I}}_{MB}-{\stackrel{\·}{I}}_{MC})}{{\stackrel{\·}{I}}_{MB}^{\′}-{\stackrel{\·}{I}}_{MC}^{\′}}{C}_1\left(x\right)$

Above formula is BC Earth design function, ${\stackrel{\·}{I}}_{MB}^{\′}=\[(\mathrm{\α}-{\mathrm{c\α}}^2){\stackrel{\·}{I}}_{MA}+(2-{\mathrm{\α}}^2-{\mathrm{c\α}}^2){\stackrel{\·}{I}}_{MB}+(-2\mathrm{\α}-{\mathrm{c\α}}^2){\stackrel{\·}{I}}_{MC}\]/3,$ ${\stackrel{\·}{I}}_{MC}^{\′}=\[({\mathrm{\α}}^2-c\mathrm{\α}){\stackrel{\·}{I}}_{MA}+(-c\mathrm{\α}-2{\mathrm{\α}}^2){\stackrel{\·}{I}}_{MB}+(2-\mathrm{\α}-c\mathrm{\α}){\stackrel{\·}{I}}_{MC}\]/3,$ α＝e ^j120°， $c=1-\mathrm{\Δ}{\stackrel{\·}{I}}_{MA}^0/{\stackrel{\·}{I}}_{M0}^0,$ for the difference of fault moment and the A phase current vector in two all after date moment, for the zero-sequence current vector value of fault moment;

Wherein, corresponding vector calculation result is as follows:

c＝1.2709-j0.0301

I′ _MB＝0.7753+j0.4835kA

I′ _MC＝-0.1695-j0.9775kA

4) initial value getting x is 0km, x is increased gradually to total track length with step-length 0.01km, again the numerical value of each x is all substituted into mapping function to calculate, search out the x that mapping function gets minimum value, this x is fault distance, and searching the mapping function as x=157.48km has minimum value, and namely fault distance is 157.48km, error is 1.24%, and concrete error calculation formula is E _rror=| L _actual-L _computed|/L × 100%, wherein, L _actual, L _computedbe respectively physical fault Distance geometry measurement fault distance of the present invention, L is total track length.Table 1 ~ 3 give the measurement fault distance that metallicity single-phase earthing, two-phase phase fault and two-phase short circuit and ground fault occur diverse location respectively.

There is the measurement fault distance of A, B, C Single Phase Metal earth fault respectively in table 1 diverse location

There is the measurement fault distance of AB, BC, CA two-phase metallic earthing short trouble respectively in table 2 diverse location

There is the measurement fault distance of AB, BC, CA two-phase metallicity phase fault respectively in table 3 diverse location

Table 4 ~ 6 give diverse location and single-phase earthing, two-phase phase fault and the two-phase short circuit and ground fault measurement fault distance through 100 Ω transition resistances occur respectively.

There is the measurement fault distance of A, B, C singlephase earth fault through 100 Ω transition resistances respectively in table 4 diverse location

There is the measurement fault distance of AB, BC, CA two-phase short circuit and ground fault through 100 Ω transition resistances respectively in table 5 diverse location

There is the measurement fault distance of AB, BC, CA two-phase phase fault through 100 Ω transition resistances respectively in table 6 diverse location

Claims (5)

1., based on a transmission line of electricity one-end fault ranging method for mapping function, it is characterized in that, comprise the following steps:

1) after transmission line malfunction occurs, in protection installation place, three-phase voltage and three-phase current are sampled, and utilize Fourier algorithm to calculate three-phase voltage vector sum three-phase current vector respectively;

2) according to step 1) the three-phase current vector calculation zero-sequence current of gained vector;

3) according to fault type, corresponding mapping function is chosen;

4) adopt search one by one method, find the x making mapping function get minimum value, this x is fault distance.

2. the transmission line of electricity one-end fault ranging method based on mapping function according to claim 1; it is characterized in that: the step 1 described) in; hold protection installation place to carry out real time data sampling with the sample frequency of 2000Hz at circuit M, obtain current sequence i _mA(k), i _mB(k), i _mC(k) and contact potential series u _mA(k), u _mB(k), u _mC(k), utilize the three-phase voltage vector sum three-phase current vector of Fourier algorithm difference computing electric power line, specific algorithm is as follows:

Wherein, K=40 is the sampling number of a primitive period, represent current vector and the voltage vector of circuit M end protection installation place respectively.

3. the transmission line of electricity one-end fault ranging method based on mapping function according to claim 1, is characterized in that: the step 2 at described A) in, according to the three-phase current vector calculation zero-sequence current vector of gained concrete calculating is such as formula shown in (3).

${\stackrel{\·}{I}}_{M0}=\frac{1}{3}({\stackrel{\·}{I}}_{MA}+{\stackrel{\·}{I}}_{MB}+{\stackrel{\·}{I}}_{MC})---\left(3\right)$

4. the transmission line of electricity one-end fault ranging method based on mapping function according to claim 1, is characterized in that: for different fault types, and its corresponding mapping function is provided by formula (4) ~ (12):

Single-phase earthing fault mapping function:

$f_A\left(x\right)=\left|imag\left(\frac{{\stackrel{\·}{U}}_{MA}-({\stackrel{\·}{I}}_{MA}+3\mathrm{\κ}{\stackrel{\·}{I}}_{M0}){\mathrm{xZ}}_{L1}}{{\stackrel{\·}{I}}_{MA}+({\stackrel{\·}{I}}_{MC}-{\stackrel{\·}{I}}_{MB})j\sqrt{3}/3}{C}_1\right(x\left)\right)\right|---\left(4\right)$

$f_B\left(x\right)=\left|imag\left(\frac{{\stackrel{\·}{U}}_{MB}-({\stackrel{\·}{I}}_{MB}+3\mathrm{\κ}{\stackrel{\·}{I}}_{M0}){\mathrm{xZ}}_{L1}}{{\stackrel{\·}{I}}_{MB}+({\stackrel{\·}{I}}_{M4}-{\stackrel{\·}{I}}_{MC})j\sqrt{3}/3}{C}_1\right(x)\right)|---\left(5\right)$

$f_C\left(x\right)=\left|imag\left(\frac{{\stackrel{\·}{U}}_{MC}-({\stackrel{\·}{I}}_{MC}+3\mathrm{\κ}{\stackrel{\·}{I}}_{M0}){\mathrm{xZ}}_{L1}}{{\stackrel{\·}{I}}_{MC}+({\stackrel{\·}{I}}_{MB}-{\stackrel{\·}{I}}_{MA})j\sqrt{3}/3}{C}_1\right(x)\right)|---\left(6\right)$

Wherein, f _a(x), f _b(x), f _cx () is respectively the mapping function of A, B, C singlephase earth fault; κ is zero sequence current compensation factor; j is the imaginary part unit of plural number; imag () represents the imaginary numbers getting plural number; || represent and ask mould; x is the distance on circuit between certain any and protection installation place, and the span of x is zero to total track length, C ₁x () is line current distribution coefficient, be applicable to the mapping function of all fault types, and expression is:

C ₁(x)＝[(L-x)Z _L1+Z _N1]/(Z _M1+LZ _L1+Z _N1)

Wherein, L is total track length, Z _m1, Z _n1be respectively the system positive sequence impedance of circuit M side and N side, Z _l1for unit length circuit positive sequence impedance;

Two-phase phase fault mapping function:

$f_{AB}\left(x\right)=\left|imag\left(\frac{{\stackrel{\·}{U}}_{MA}-{\stackrel{\·}{U}}_{MB}-{\mathrm{xZ}}_{L1}({\stackrel{\·}{I}}_{MA}-{\stackrel{\·}{I}}_{MB})}{{\stackrel{\·}{I}}_{MA}-{\stackrel{\·}{I}}_{MB}+j\sqrt{3}{\stackrel{\·}{I}}_{MC}}{C}_1\right(x)\right)|---\left(7\right)$

$f_{BC}\left(x\right)=\left|imag\left(\frac{{\stackrel{\·}{U}}_{MB}-{\stackrel{\·}{U}}_{MC}-{\mathrm{xZ}}_{L1}({\stackrel{\·}{I}}_{MB}-{\stackrel{\·}{I}}_{MC})}{{\stackrel{\·}{I}}_{MB}-{\stackrel{\·}{I}}_{MC}+j\sqrt{3}{\stackrel{\·}{I}}_{MA}}{C}_1\right(x)\right)|---\left(8\right)$

$f_{CA}\left(x\right)=\left|imag\left(\frac{{\stackrel{\·}{U}}_{MC}-{\stackrel{\·}{U}}_{MA}-{\mathrm{xZ}}_{L1}({\stackrel{\·}{I}}_{MC}-{\stackrel{\·}{I}}_{MA})}{{\stackrel{\·}{I}}_{MC}-{\stackrel{\·}{I}}_{MA}+j\sqrt{3}{\stackrel{\·}{I}}_{MB}}{C}_1\right(x)\right)|---\left(9\right)$

Wherein, f _aB(x), f _bC(x), f _cAx () is respectively AB, BC, CA two-phase phase fault mapping function;

Two-phase short circuit and ground fault mapping function:

$f_{ABG}\left(x\right)=\left|imag\left(\frac{{\stackrel{\·}{U}}_{MA}-{\stackrel{\·}{U}}_{MB}-{\mathrm{xZ}}_{L1}({\stackrel{\·}{I}}_{MA}-{\stackrel{\·}{I}}_{MB})}{{\stackrel{\·}{I}}_{MA}^{\′}-{\stackrel{\·}{I}}_{MB}^{\′}}{C}_1\right(x)\right)|---\left(10\right)$

Formula (10) is AB Earth design function, ${\stackrel{\·}{I}}_{MA}^{\′}=\[(2-\mathrm{\α}-{\mathrm{c\α}}^2){\stackrel{\·}{I}}_{MA}+({\mathrm{\α}}^2-{\mathrm{c\α}}^2){\stackrel{\·}{I}}_{MB}+(2-{\mathrm{c\α}}^2){\stackrel{\·}{I}}_{MC}\]/3,$ ${\stackrel{\·}{I}}_{MB}^{\′}=\[(-c\mathrm{\α}-2{\mathrm{\α}}^2){\stackrel{\·}{I}}_{MA}+(2-\mathrm{\α}-c\mathrm{\α}){\stackrel{\·}{I}}_{MB}+({\mathrm{\α}}^2-c\mathrm{\α}){\stackrel{\·}{I}}_{MC}\]/3,$ α＝e ^j120°， $c=1-\mathrm{\Δ}{\stackrel{\·}{I}}_{MC}^0/{\stackrel{\·}{I}}_{M0}^0,$ for the difference of fault moment and the C phase current vector in two all after date moment, for the zero-sequence current vector of fault moment;

$f_{BCG}\left(x\right)=\left|imag\left(\frac{{\stackrel{\·}{U}}_{MB}-{\stackrel{\·}{U}}_{MC}-{\mathrm{xZ}}_{L1}({\stackrel{\·}{I}}_{MB}-{\stackrel{\·}{I}}_{MC})}{{\stackrel{\·}{I}}_{MB}^{\′}-{\stackrel{\·}{I}}_{MC}^{\′}}{C}_1\right(x)\right)|---\left(11\right)$

Formula (11) is BC Earth design function, ${\stackrel{\·}{I}}_{\mathrm{\ω}}^{\′}=\[(\mathrm{\α}-{\mathrm{c\α}}^2){\stackrel{\·}{I}}_{MA}+(2-{\mathrm{\α}}^2-{\mathrm{c\α}}^2){\stackrel{\·}{I}}_{MB}+(-2\mathrm{\α}-{\mathrm{c\α}}^2){\stackrel{\·}{I}}_{MC}\]/3,$ ${\stackrel{\·}{I}}_{MC}^{\′}=\[({\mathrm{\α}}^2-c\mathrm{\α}){\stackrel{\·}{I}}_{MA}+(-c\mathrm{\α}-2{\mathrm{\α}}^2){\stackrel{\·}{I}}_{MB}+(2-\mathrm{\α}-c\mathrm{\α}){\stackrel{\·}{I}}_{MC}\]/3,$ α＝e ^j120°， $c=1-\mathrm{\Δ}{\stackrel{\·}{I}}_{MA}^0/{\stackrel{\·}{I}}_{M0}^0,$ for the difference of fault moment and the A phase current vector in two all after date moment, for the zero-sequence current vector of fault moment;

$f_{CAG}\left(x\right)=\left|imag\left(\frac{{\stackrel{\·}{U}}_{MC}-{\stackrel{\·}{U}}_{MA}-{\mathrm{xZ}}_{L1}({\stackrel{\·}{I}}_{MC}-{\stackrel{\·}{I}}_{MA})}{{\stackrel{\·}{I}}_{MC}^{\′}-{\stackrel{\·}{I}}_{MA}^{\′}}{C}_1\right(x)\right)|---\left(12\right)$

Formula (12) is CA Earth design function, ${\stackrel{\·}{I}}_{MC}^{\′}=\[({\mathrm{\α}}^2-{\mathrm{c\α}}^2){\stackrel{\·}{I}}_{MA}+(-2{\mathrm{\α}}^2-{\mathrm{c\α}}^2){\stackrel{\·}{I}}_{MB}+(2-\mathrm{\α}-{\mathrm{c\α}}^2){\stackrel{\·}{I}}_{MC}\]/3,$ ${\stackrel{\·}{I}}_{MA}^{\′}=\[(2-c\mathrm{\α}-{\mathrm{\α}}^2){\stackrel{\·}{I}}_{MA}+(-2\mathrm{\α}-c\mathrm{\α}){\stackrel{\·}{I}}_{MB}+(\mathrm{\α}-c\mathrm{\α}){\stackrel{\·}{I}}_{MC}\]/3,$ α＝e ^j120°， $c=1-\mathrm{\Δ}{\stackrel{\·}{I}}_{MB}^0/{\stackrel{\·}{I}}_{M0}^0,$ for the difference of fault moment and two all after date moment B phase current vectors, for the zero-sequence current vector of fault moment.

5. the transmission line of electricity one-end fault ranging method based on mapping function according to claim 1, it is characterized in that: the initial value getting x is 0, x is progressively increased to total track length with 0.01km, again each x is all substituted into mapping function to calculate, search out the x that mapping function gets minimum value, this x is fault distance.