CN106019079A - Novel double end fault location method for double DC circuits on same tower - Google Patents

Abstract

The invention relates to a novel double end fault location method for double DC circuits on same tower and belongs to the technical field of power system relay protection. The method includes steps of obtaining voltage of a measuring end M and a measuring end N and solving a fault component and solving a line mode voltage component by adopting phase mode conversion when the double DC circuits on same tower meets a grounding fault; applying a Bergeron transfer equation and the measuring end line mode voltage component for calculating line-side voltage and current travelling wave variations; cubing a product of the line-side voltage traveling wave variation of the a measuring end M and the line-side current traveling wave variation of the measuring end N and constructing a fault location function through integrating in an observation time window; realizing fault location through combining line-side mutation rules of the fault location function and the polarity of the wavelet transform modulus maxima of fault voltage traveling waves. According to the invention, fault location is performed for the double DC circuits on same tower and the principle is simple. Wave heads of the fault traveling waves do not need to marked and influence caused by fault instantaneity, fault transition resistance variation and the like is eliminated. The fault location result is accurate and reliable.

Description

A kind of common-tower double-return DC line Novel double end fault distance-finding method

Technical field

The present invention relates to a kind of common-tower double-return DC line Novel double end fault distance-finding method, belong to power system relay and protect Protect technical field.

Background technology

DC line is the important component part of one-tower double-circuit DC transmission system, and its electric pressure is high, and transmission distance is remote, During conveying Large Copacity electric energy by way of regional environment badly, easily initiating failure.The trouble point of DC line is carried out Placement technology contributes to determining quickly and accurately abort situation, alleviates line walking blindness, adds quick-recovery power transmission.AC line Road fault location uses row ripple principle mostly.Current travelling wave ranging method be mostly based on fault traveling wave temporal signatures and in time On countershaft, row ripple is observed, portrays and wave head demarcation, and the calculating of fault distance.Wherein, time domain Single Terminal Traveling Wave Fault Location Fixed and the reliability of wave head identification, range finding analysis the automatization's aspect of the wave-wave leader that needs to be expert at makes further research；Time domain is double End travelling wave ranging is owing to utilizing the initial row wave-wave arrival time difference of faulty line both sides, and its initial row ripple demarcates reliability and accuracy It is easy to get to ensure, and does not need trouble point echo is carried out identification, but circuit two ends cycle accurate is synchronized by both-end travelling wave ranging Require higher.

Summary of the invention

The technical problem to be solved in the present invention be overcome the conventional Time-domain travelling wave ranging effective identification of requirement fault traveling wave and The limitation that range finding cycle accurate synchronizes, proposes a kind of common-tower double-return DC line Novel double end fault distance-finding method.

The technical scheme is that a kind of common-tower double-return DC line Novel double end fault distance-finding method, when same tower is double When returning DC line generation earth fault, first, respectively measuring end M and measuring end N is obtained voltage and ask for fault component, and adopt Line mode voltage component is asked for phase-model transformation；Secondly, application Bei Jielong transmission equation and measurement end line mode voltage component calculate edge Line voltage variety；Again ask measuring end M voltage traveling wave along the line and three times of measuring end N current/voltage along the line variable quantity product Side, and be integrated constructing range function in window when observation；Sudden change rule along the line and false voltage in conjunction with range function The wavelet modulus maxima point-polarity of row ripple realizes fault localization.

Concretely comprise the following steps:

The first step, when common-tower double-return DC line generation earth fault, under sample rate 1MHz, to measuring end voltage row Ripple signal is sampled, and the line voltage before deducting fault with measuring end obtained fault line voltage obtains line voltage fault and divides Amount:

$\left\{\begin{array}{c}{u}_{R,IP}^{\′}\left(t\right)=u_{R,IP}\left(t\right)-u_{R,IP\left|0\right|}\\ u_{R,IN}^{\′}\left(t\right)=u_{R,IN}\left(t\right)-u_{R,IN\left|0\right|}\\ u_{R,IIP}^{\′}\left(t\right)=u_{R,IIP}\left(t\right)-u_{R,IIP\left|0\right|}\\ u_{R,IIN}^{\′}\left(t\right)=u_{R,IIN}\left(t\right)-u_{R,IIN\left|0\right|}\end{array}\right.---\left(1\right)$

In formula (1), subscript I P, I N, II P and II N represent I loop line positive pole, I loop line negative pole, II loop line positive pole and II respectively Loop line negative pole；The value of subscript R is M and N, represents rectification side measuring end M and inverter side measuring end N respectively；Subscript | 0 | represents event Before barrier occurs；

Second step, the line voltage Sudden Changing Rate of step (1) is made decoupling conversion, obtains line voltage sudden change modulus:

$\left[\begin{array}{c}{u}_{R,0}^{\′}\left(t\right)\\ u_{R,1}^{\′}\left(t\right)\\ u_{R,2}^{\′}\left(t\right)\\ u_{R,3}^{\′}\left(t\right)\end{array}\right]=S^{-1}\×\left[\begin{array}{c}{u}_{R,IP}^{\′}\left(t\right)\\ u_{R,IN}^{\′}\left(t\right)\\ u_{R,IIP}^{\′}\left(t\right)\\ u_{R,IIN}^{\′}\left(t\right)\end{array}\right]---\left(2\right)$

In formula (2), S^-1For voltage decoupling matrix；u′_R,0T () is zero mode voltage；u′_R,1(t)、u′_R,2(t) and u '_R,3(t) be Three line mode voltages that decoupling change is got in return；

The Aerial mode component voltage that 3rd step, selecting step (2) obtain, and utilize formula (3) to calculate common-tower double-return DC line Voltage traveling wave along the line:

$\begin{array}{c}{u}_R(x,\mathrm{\Δ}t)=\frac{1}{2}\·{\left(\frac{Z_{c,s}+r_{s}x/4}{Z_{c,s}}\right)}^2\·\{\[u_{R,s}^{\′}(t+\frac{x}{v_s})-u_{R,s}^{\′}(t-\mathrm{\Δ}t+\frac{x}{v_s})\]\}\\ +\frac{1}{2}\·{\left(\frac{Z_{c,s}-r_{s}x/4}{Z_{c,s}}\right)}^2\·\{\[u_{R,s}^{\′}(t-\frac{x}{v_s})-u_{R,s}^{\′}(t-\mathrm{\Δ}t-\frac{x}{v_s})\]\}\\ -{\left(\frac{r_{s}x/4}{Z_{c,s}}\right)}^2\·\[u_{R,s}^{\′}\left(t\right)-u_{R,s}^{\′}(t-\mathrm{\Δ}t)\]\end{array}---\left(3\right)$

In formula (3), subscript s represents Aerial mode component, takes s=1,2, or 3；Subscript R represents rectification side measuring end M or inverter side Measuring end N, takes R=M or N；r_s,Z_c,s,v_sIt is respectively resistance, natural impedance and the velocity of wave of s line ripple；X is the distance away from measuring end； u_R(x, Δ t) are the s mould voltage traveling waves along the line at t distance R end x；

4th step, the rectification side voltage traveling wave along the line with inverter side s mould step (3) obtained are multiplied and seek its cube, Last in time window length l/v_sIt is integrated constructing range function:

$f_u\left(x\right)={\∫}_{t_0}^{t_0+L/v_s}{\[u_M(x,\mathrm{\Δ}t)\×u_N(x,\mathrm{\Δ}t)\]}^{3}dt---\left(4\right)$

In formula (4), L is the length of fault polar curve；t₀The moment of measuring end R is arrived for fault initial row ripple；

5th step, the acquisition of abort situation:

To catastrophe point disaggregation x=[x₁,x₂,……x_nIn], find two sudden changes equal to fault line length of the respective distances sum Point, i.e. meets criterion:

x+x^*=l x, x^*∈[x₁,x₂,……x_n] (5)

Meet x and x of formula (6)^*All contain the information of abort situation；

Rectification side measuring end R obtained false voltage row ripple is carried out wavelet transformation, and asks for wavelet modulus maxima, root The 2nd fault traveling wave is determined according to the abort situation that x is corresponding；

If the polarity of second modulus maximum point and the opposite polarity of first modulus maximum point, then failure judgement point is positioned at Within half line length, and fault distance leaves measuring end M:x；

If the polarity of second modulus maximum point is identical with the polarity of first modulus maximum point, then failure judgement point is positioned at Outside half line length, and fault distance leaves measuring end M:l-x.

The invention has the beneficial effects as follows: carry out fault location for common-tower double-return DC line, its principle is simple, does not need mark Determining fault traveling wave wave-wave head, and do not affected by factors such as fault instantaneity, fault resistance changes, range measurement accurately may be used Lean on.

Accompanying drawing explanation

Fig. 1 is the common-tower double-return DC line structure chart of the embodiment of the present invention 1, embodiment 2；

Fig. 2 is measuring end M voltage traveling wave fault component under fault within the embodiment of the present invention 1 half line length；

Fig. 3 is measuring end N voltage traveling wave fault component under fault within the embodiment of the present invention 1 half line length；

Fig. 4 is measuring end M voltage traveling wave mold component under fault within the embodiment of the present invention 1 half line length；

Fig. 5 is measuring end N voltage traveling wave mold component under fault within the embodiment of the present invention 1 half line length；

Fig. 6 is range function f within the embodiment of the present invention 1 half line length_uThe sudden change distribution results of (x)；

Fig. 7 is false voltage row ripple wavelet modulus maxima result within the embodiment of the present invention 1 half line length；

Fig. 8 is measuring end M voltage traveling wave fault component under fault outside the embodiment of the present invention 2 half line length；

Fig. 9 is measuring end N voltage traveling wave fault component under fault outside the embodiment of the present invention 2 half line length；

Figure 10 is measuring end M voltage traveling wave sudden change modulus under fault outside the embodiment of the present invention 2 half line length；

Figure 11 is measuring end N voltage traveling wave mold component under fault outside the embodiment of the present invention 2 half line length；

Figure 12 is range function f outside the embodiment of the present invention 2 half line length_uThe sudden change distribution results of (x)；

Figure 13 is false voltage row ripple wavelet modulus maxima result outside the embodiment of the present invention 2 half line length.

Detailed description of the invention

Below in conjunction with the accompanying drawings and detailed description of the invention, the invention will be further described.

: a kind of common-tower double-return DC line Novel double end fault distance-finding method, when common-tower double-return DC line occurs ground connection During fault, first, respectively measuring end M and measuring end N is obtained voltage and ask for fault component, and use phase-model transformation to ask for line mould Component of voltage；Secondly, application Bei Jielong transmission equation and measurement end line mode voltage component calculate voltage variety along the line；Again ask Measuring end M voltage traveling wave along the line and the cube of measuring end N current/voltage along the line variable quantity product, and carry out in window when observation Integration constructs range function；Sudden change rule along the line and the wavelet modulus maxima of false voltage row ripple in conjunction with range function Point-polarity realizes fault localization.

Concretely comprise the following steps:

The first step, when common-tower double-return DC line generation earth fault, under sample rate 1MHz, to measuring end voltage row Ripple signal is sampled, and the line voltage before deducting fault with measuring end obtained fault line voltage obtains line voltage fault and divides Amount:

$\left\{\begin{array}{c}{u}_{R,IP}^{\′}\left(t\right)=u_{R,IP}\left(t\right)-u_{R,IP\left|0\right|}\\ u_{R,IN}^{\′}\left(t\right)=u_{R,IN}\left(t\right)-u_{R,IN\left|0\right|}\\ u_{R,IIP}^{\′}\left(t\right)=u_{R,IIP}\left(t\right)-u_{R,IIP\left|0\right|}\\ u_{R,IIN}^{\′}\left(t\right)=u_{R,IIN}\left(t\right)-u_{R,IIN\left|0\right|}\end{array}\right.---\left(1\right)$

In formula (1), subscript I P, I N, II P and II N represent I loop line positive pole, I loop line negative pole, II loop line positive pole and II respectively Loop line negative pole；The value of subscript R is M and N, represents rectification side measuring end M and inverter side measuring end N respectively；Subscript | 0 | represents event Before barrier occurs；

Second step, the line voltage Sudden Changing Rate of step (1) is made decoupling conversion, obtains line voltage sudden change modulus:

$\left[\begin{array}{c}{u}_{R,0}^{\′}\left(t\right)\\ u_{R,1}^{\′}\left(t\right)\\ u_{R,2}^{\′}\left(t\right)\\ u_{R,3}^{\′}\left(t\right)\end{array}\right]=S^{-1}\×\left[\begin{array}{c}{u}_{R,IP}^{\′}\left(t\right)\\ u_{R,IN}^{\′}\left(t\right)\\ u_{R,IIP}^{\′}\left(t\right)\\ u_{R,IIN}^{\′}\left(t\right)\end{array}\right]---\left(2\right)$

In formula (2), S^-1For voltage decoupling matrix；u′_R,0T () is zero mode voltage；u′_R,1(t)、u′_R,2(t) and u '_R,3(t) be Three line mode voltages that decoupling change is got in return；

The Aerial mode component voltage that 3rd step, selecting step (2) obtain, and utilize formula (3) to calculate common-tower double-return DC line Voltage traveling wave along the line:

$\begin{array}{c}{u}_R(x,\mathrm{\Δ}t)=\frac{1}{2}\·{\left(\frac{Z_{c,s}+r_{s}x/4}{Z_{c,s}}\right)}^2\·\{\[u_{R,s}^{\′}(t+\frac{x}{v_s})-u_{R,s}^{\′}(t-\mathrm{\Δ}t+\frac{x}{v_s})\]\}\\ +\frac{1}{2}\·{\left(\frac{Z_{c,s}-r_{s}x/4}{Z_{c,s}}\right)}^2\·\{\[u_{R,s}^{\′}(t-\frac{x}{v_s})-u_{R,s}^{\′}(t-\mathrm{\Δ}t-\frac{x}{v_s})\]\}\\ -{\left(\frac{r_{s}x/4}{Z_{c,s}}\right)}^2\·\[u_{R,s}^{\′}\left(t\right)-u_{R,s}^{\′}(t-\mathrm{\Δ}t)\]\end{array}---\left(3\right)$

In formula (3), subscript s represents Aerial mode component, takes s=1,2, or 3；Subscript R represents rectification side measuring end M or inverter side Measuring end N, takes R=M or N；r_s,Z_c,s,v_sIt is respectively resistance, natural impedance and the velocity of wave of s line ripple；X is the distance away from measuring end； u_R(x, Δ t) are the s mould voltage traveling waves along the line at t distance R end x；

4th step, the rectification side voltage traveling wave along the line with inverter side s mould step (3) obtained are multiplied and seek its cube, Last in time window length l/v_sIt is integrated constructing range function:

$f_u\left(x\right)={\∫}_{t_0}^{t_0+L/v_s}{\[u_M(x,\mathrm{\Δ}t)\×u_N(x,\mathrm{\Δ}t)\]}^{3}dt---\left(4\right)$

In formula (4), L is the length of fault polar curve；t₀The moment of measuring end R is arrived for fault initial row ripple；

5th step, the acquisition of abort situation:

To catastrophe point disaggregation x=[x₁,x₂,……x_nIn], find two sudden changes equal to fault line length of the respective distances sum Point, i.e. meets criterion:

x+x^*=l x, x^*∈[x₁,x₂,……x_n] (5)

Meet x and x of formula (6)^*All contain the information of abort situation；

Rectification side measuring end R obtained false voltage row ripple is carried out wavelet transformation, and asks for wavelet modulus maxima, root The 2nd fault traveling wave is determined according to the abort situation that x is corresponding；

If the polarity of second modulus maximum point and the opposite polarity of first modulus maximum point, then failure judgement point is positioned at Within half line length, and fault distance leaves measuring end M:x；

If the polarity of second modulus maximum point is identical with the polarity of first modulus maximum point, then failure judgement point is positioned at Outside half line length, and fault distance leaves measuring end M:l-x.

Embodiment 1: use as shown in Figure 1 ± 500kV one-tower double-circuit DC transmission system.Total track length is 1286km, Using conductors on quad bundled, circuit both sides are equipped with the smoothing reactor of 0.3H, every pole single 12-pulse conveter scheme, specified conveying power For 6400MW, rated current is 3200A.Sample rate is set to 1M.Assume that the electric parameters of rectification side and inverter side all can be surveyed, if I time Metallic earthing fault is there is at distance rectification side measuring end M600km within half line length of line positive pole I P.

According to step one, obtain each line voltage fault component waveform of rectification side measuring end M and N, respectively such as Fig. 2 and Tu Shown in 3；According to step 2, use formula (2) that the line voltage Sudden Changing Rate of measuring end M and measuring end N is carried out voltage decoupling conversion, Obtain the pressure-wire mold component of measuring end M, the most as shown in Figure 4 and Figure 5；According to step 3, formula (3) is used to calculate voltage along the line Variable quantity；According to step 4, use formula (4) structure range function f_uX (), its Energy distribution result along the line is as shown in Figure 6.By scheming 6 understand, catastrophe point disaggregation x=[599 686 1196] that range function is along the line；According to step 5, obtain x₁+x₂=l, it is known that prominent Height x₁And x₂Information containing abort situation.The false voltage row ripple of measuring end M is carried out wavelet modulus maxima analysis, As it is shown in fig. 7, according to x₁=599, obtain the polarity of second modulus maximum point and the opposite polarity of first modulus maximum point, Therefore failure judgement occurs in half line length, and fault distance opens measuring end M599km.

Embodiment 2: use as shown in Figure 1 ± 500kV one-tower double-circuit DC transmission system.Total track length is 1286km, Using conductors on quad bundled, circuit both sides are equipped with the smoothing reactor of 0.3H, every pole single 12-pulse conveter scheme, specified conveying power For 6400MW, rated current is 3200A.Sample rate is set to 1M.Assume that the electric parameters of rectification side and inverter side all can be surveyed, if I time , at 900km, there is metallic earthing fault in distance rectification side measuring end M outside half line length of line positive pole I P.

According to step one, obtain each line voltage fault component waveform of rectification side measuring end M and N, respectively such as Fig. 8 and Tu Shown in 9；According to step 2, use formula (2) that the line voltage Sudden Changing Rate of measuring end M and measuring end N is carried out voltage decoupling conversion, Obtain the pressure-wire mold component of measuring end M, the most as shown in Figure 10 and Figure 11；According to step 3, formula (3) is used to calculate electricity along the line Pressure variable quantity；According to step 4, use formula (4) structure range function f_uX (), its Energy distribution result along the line is as shown in figure 12. As shown in Figure 12, catastrophe point disaggregation x=[386 769 900] that range function is along the line；According to step 5, obtain x₁+x₂=l, can Know catastrophe point x₁And x₃Information containing abort situation.The false voltage row ripple of measuring end M is carried out wavelet modulus maxima divide Analysis, as shown in figure 13, according to x₁=386, obtain the polarity of second modulus maximum point and the polarity of first modulus maximum point Identical, therefore failure judgement occurs outside half line length, and fault distance opens measuring end M:l-x₁=900km.

Above in association with accompanying drawing, the detailed description of the invention of the present invention is explained in detail, but the present invention is not limited to above-mentioned Embodiment, in the ken that those of ordinary skill in the art are possessed, it is also possible to before without departing from present inventive concept Put that various changes can be made.

Claims (2)

1. a common-tower double-return DC line Novel double end fault distance-finding method, it is characterised in that: when common-tower double-return DC line When there is earth fault, first, respectively measuring end M and measuring end N is obtained voltage and ask for fault component, and use phase-model transformation Ask for line mode voltage component；Secondly, application Bei Jielong transmission equation and measurement end line mode voltage component calculate change in voltage along the line Amount；Again ask measuring end M voltage traveling wave along the line and the cube of measuring end N current/voltage along the line variable quantity product, and in observation Time window in be integrated constructing range function；Become in conjunction with the sudden change rule along the line of range function and the small echo of false voltage row ripple Die change maximum point polarity realizes fault localization.

Common-tower double-return DC line Novel double end fault distance-finding method the most according to claim 1, it is characterised in that concrete Step is:

The first step, when common-tower double-return DC line generation earth fault, under sample rate 1MHz, to measuring end voltage traveling wave believe Number sampling, the line voltage before deducting fault with measuring end obtained fault line voltage obtains line voltage fault component:

$\left\{\begin{array}{c}{u}_{R,IP}^{\′}\left(t\right)=u_{R,IP}\left(t\right)-u_{R,IP\left|0\right|}\\ u_{R,IN}^{\′}\left(t\right)=u_{R,IN}\left(t\right)-u_{R,IN\left|0\right|}\\ u_{R,IIP}^{\′}\left(t\right)=u_{R,IIP}\left(t\right)-u_{R,IIP\left|0\right|}\\ u_{R,IIN}^{\′}\left(t\right)=u_{R,IIN}\left(t\right)-u_{R,IIN\left|0\right|}\end{array}\right.---\left(1\right)$

In formula (1), subscript I P, I N, II P and II N represent I loop line positive pole, I loop line negative pole, II loop line positive pole and II loop line respectively Negative pole；The value of subscript R is M and N, represents rectification side measuring end M and inverter side measuring end N respectively；Subscript | 0 | represents that fault is sent out Before death；

Second step, the line voltage Sudden Changing Rate of step (1) is made decoupling conversion, obtains line voltage sudden change modulus:

$\left[\begin{array}{c}{u}_{R,0}^{\′}\left(t\right)\\ u_{R,1}^{\′}\left(t\right)\\ u_{R,2}^{\′}\left(t\right)\\ u_{R,3}^{\′}\left(t\right)\end{array}\right]=S^{-1}\×\left[\begin{array}{c}{u}_{R,IP}^{\′}\left(t\right)\\ u_{R,IN}^{\′}\left(t\right)\\ u_{R,IIP}^{\′}\left(t\right)\\ u_{R,IIN}^{\′}\left(t\right)\end{array}\right]---\left(2\right)$

In formula (2), S^-1For voltage decoupling matrix；u′_R,0T () is zero mode voltage；u′_R,1(t)、u′_R,2(t) and u '_R,3T () is decoupling Three line mode voltages that conversion obtains；

The Aerial mode component voltage that 3rd step, selecting step (2) obtain, and utilize formula (3) to calculate the edge of common-tower double-return DC line Line voltage traveling wave:

$\begin{array}{c}{u}_R\left(x,\mathrm{\Δ}t\right)=\frac{1}{2}\·{\left(\frac{Z_{c,s}+r_{s}x/4}{Z_{c,s}}\right)}^2\·\left\{\[u_{R,s}^{\′}\left(t+\frac{x}{v_s}\right)-u_{R,s}^{\′}\left(t-\mathrm{\Δ}t+\frac{x}{v_s}\right)\]\right\}\\ +\frac{1}{2}\·{\left(\frac{Z_{c,s}-r_{s}x/4}{Z_{c,s}}\right)}^2\·\left\{\[u_{R,s}^{\′}\left(t-\frac{x}{v_s}\right)-u_{R,s}^{\′}\left(t-\mathrm{\Δ}t-\frac{x}{v_s}\right)\]\right\}\end{array}$

$-{\left(\frac{r_{s}x/4}{Z_{c,s}}\right)}^2\·\[u_{R,s}^{\′}\left(t\right)-u_{R,s}^{\′}(t-\mathrm{\Δ}t)\]---\left(3\right)$

In formula (3), subscript s represents Aerial mode component, takes s=1,2, or 3；Subscript R represents that rectification side measuring end M or inverter side measure End N, takes R=M or N；r_s,Z_c,s,v_sIt is respectively resistance, natural impedance and the velocity of wave of s line ripple；X is the distance away from measuring end；u_R (x, Δ t) are the s mould voltage traveling waves along the line at t distance R end x；

4th step, the rectification side voltage traveling wave along the line with inverter side s mould step (3) obtained are multiplied and seek its cube, finally In time window length l/v_sIt is integrated constructing range function:

$f_u\left(x\right)={\∫}_{t_0}^{t_0+L/v_s}{\[u_M(x,\mathrm{\Δ}t)\×u_N(x,\mathrm{\Δ}t)\]}^{3}dt---\left(4\right)$

In formula (4), L is the length of fault polar curve；t₀The moment of measuring end R is arrived for fault initial row ripple；

5th step, the acquisition of abort situation:

To catastrophe point disaggregation x=[x₁,x₂,……x_nIn], find the respective distances sum two catastrophe points equal to fault line length, I.e. meet criterion:

x+x^*=l x, x^*∈[x₁,x₂,……x_n] (5)

Meet x and x of formula (6)^*All contain the information of abort situation；

Rectification side measuring end R obtained false voltage row ripple is carried out wavelet transformation, and asks for wavelet modulus maxima, according to x Corresponding abort situation determines the 2nd fault traveling wave；

If the polarity of second modulus maximum point and the opposite polarity of first modulus maximum point, then failure judgement point is positioned at half line Within length, and fault distance leaves measuring end M:x；

If the polarity of second modulus maximum point is identical with the polarity of first modulus maximum point, then failure judgement point is positioned at half line Outside length, and fault distance leaves measuring end M:l-x.