CN105137289B - Suitable for the traveling wave fault positioning method of high voltage overhead lines-cable hybrid line - Google Patents

Suitable for the traveling wave fault positioning method of high voltage overhead lines-cable hybrid line Download PDF

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CN105137289B
CN105137289B CN201510591223.4A CN201510591223A CN105137289B CN 105137289 B CN105137289 B CN 105137289B CN 201510591223 A CN201510591223 A CN 201510591223A CN 105137289 B CN105137289 B CN 105137289B
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mrow
msub
joint line
tested joint
terminal
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CN105137289A (en
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张健
戴祥慧
王奕
张远
孙闻
盛超
陈迅
安然然
胡玉岚
王俊杰
罗勇
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Electric Power Research Institute of Guangdong Power Grid Co Ltd
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Electric Power Research Institute of Guangdong Power Grid Co Ltd
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Abstract

The invention discloses a kind of traveling wave fault positioning method suitable for high voltage overhead lines cable hybrid line, it by installing traveling wave harvester respectively at the both ends of tested joint line, and gathered respectively using two traveling wave harvesters and calculate the injection traveling wave time difference, the combined floodgate traveling wave time difference, the fault traveling wave time difference, using travelling wave signal in overhead line section or this constant feature of cable sections velocity of wave, whether decision condition is met with each injection traveling wave time difference by the failure judgement traveling wave time difference and meets the order of decision condition come accurate, quickly determine the part of path where the trouble point of tested joint line, the position of failure point of tested joint line is accurately positioned by calculating again.The present invention solve thes problems, such as that current mixed line fault positioning is difficult, velocity of wave need not be adjusted, position error is greatly reduced, has the advantages that fault location speed is fast, localization of fault precision is high, the failure for realizing high voltage overhead lines cable hybrid line is accurately positioned.

Description

Suitable for the traveling wave fault positioning method of high voltage overhead lines-cable hybrid line
Technical field
The present invention relates to a kind of traveling wave fault positioning method suitable for high voltage overhead lines-cable hybrid line.
Background technology
Fault location research both at home and abroad for pure overhead transmission line is more, it is proposed that a variety of online Fault Locating Methods, its Middle both-end traveling wave positioning mode because it has the advantages that the influence from transition resistance, positioning accuracy are high, 220kV and more than It is applied widely in the AC and DC overhead transmission line of voltage class.But since both-end traveling wave positioning mode needs to adjust Traveling wave speed, and cable is different with the traveling wave speed on overhead line, causes both-end traveling wave positioning mode to cannot be used directly for high pressure In the fault location of overhead line-cable hybrid line.Therefore, there is an urgent need to study to be suitable for high voltage overhead lines-cable mixing Line fault new location method, realizes that fault fast positioning shortens the service restoration time, improves power supply reliability.
The content of the invention
The technical problems to be solved by the invention are：A kind of row suitable for high voltage overhead lines-cable hybrid line is provided Ripple Fault Locating Method, with overcome in the prior art high voltage overhead lines-cable hybrid line be difficult to realize fast and accurately failure The problem of positioning.
Above-mentioned technical problem is solved, the technical solution adopted in the present invention is as follows：
A kind of traveling wave fault positioning method suitable for high voltage overhead lines-cable hybrid line, suitable for by least one section Cut cable and the tested joint line that at least one section of overhead line is composed in series, the cut cable and overhead line are in tested joint line In be arranged alternately, set：The cut cable of tested joint line whole and the total quantity of overhead line are n sections, and n >=2, they are by tested M ends to the N-terminal of joint line is represented sequentially as part of path D1,D2,···,Dn, adjacent cable section and frame in tested joint line The tie point of ceases to be busy is represented sequentially as L by M ends to N-terminal1,L2,···,Ln-1, M ends and N-terminal are respectively tested joint line Head end and end or M ends and N-terminal are respectively end and the head end of tested joint line；
The traveling wave fault positioning method includes：
Step 1, traveling wave harvester is installed at the M ends of tested joint line and N-terminal respectively, wherein, which adopts Time synchronization between acquisition means；
Step 2, using travelling wave signal generator respectively in the tie point L of tested joint line1,L2,···,Ln-1Note Enter travelling wave signal so that the travelling wave signal of injection is transmitted from injection phase to the M ends of tested joint line and N-terminal, and utilizes institute State two traveling wave harvesters and record the time that each injection travelling wave signal reaches tested joint line M ends and N-terminal respectively, so that Calculate the tie point L in tested joint line when travelling wave signal generatoriWhen injecting travelling wave signal, injection travelling wave signal difference The injection traveling wave time difference for reaching tested joint line M ends and N-terminal is Δ t1i, i=1 ..., n-1；
Step 3, is carried out combined floodgate power transmission to the M ends breaker of tested joint line, is produced with this in tested joint line Combined floodgate travelling wave signal so that the combined floodgate travelling wave signal is transmitted from the M ends of tested joint line to N-terminal, and utilizes two rows Ripple harvester records the combined floodgate travelling wave signal and reaches the time of tested joint line M ends and N-terminal respectively, so as to calculate the conjunction Lock travelling wave signal respectively reaches the combined floodgate traveling wave time difference Δ t of tested joint line M ends and N-terminal2；
Step 4, calculates travelling wave signal and is located at M ends to tie point L in tested joint line respectivelyiBetween section on Transmission timeAnd calculate travelling wave signal respectively and be located at tie point L in tested joint lineiTo between N-terminal Section on transmission timeWherein, i=1 ..., n-1；
Step 5, when tested joint line breaks down, failed row is recorded with two traveling wave harvesters respectively Ripple signal reaches the time of tested joint line M ends and N-terminal, so that calculating fault traveling wave signal respectively reaches tested blend Road M ends and the fault traveling wave time difference Δ t of N-terminalf；
Step 6, compares Δ t successivelyfWith Δ t11,Δt12,…,Δt1(n-1)Size, if there is meeting Δ tf＜ Δs t1iThe Δ t of decision condition1i, i=1 ..., n-1, then judge that the trouble point of tested joint line is located at part of path DKOn, wherein, Δ t1KFor Δ t11,Δt12,…,Δt1(n-1)Successively with Δ tfSize relatively in meet the injection traveling wave of the decision condition at first Time difference, K are one of value in 1 to n-1；If Δ tfWith Δ t11,Δt12,…,Δt1(n-1)Size be relatively satisfied by Δtf＞ Δs t1i, i=1 ..., n-1, then judge that the trouble point of tested joint line is located at part of path DnOn；
Step 7, calculates the time that travelling wave signal is transferred to circuit M ends from trouble pointCalculate traveling wave letter The time of circuit N-terminal number is transferred to from trouble point
The trouble point for judging tested joint line in step 6 is located at part of path D1When upper, the offline road M ends in trouble point Distance isThe distance of road N-terminal is offline
The trouble point for judging tested joint line in step 6 is located at part of path DkDuring upper and k >=2, the offline road in trouble point The distance at M ends isThe distance of road N-terminal is offline
The trouble point for judging tested joint line in step 6 is located at part of path DnWhen upper, the offline road M ends in trouble point Distance isThe distance of road N-terminal is offline
Wherein liFor part of path DiLength, i=1 ..., n.
Compared with prior art, the invention has the advantages that：
The present invention is adopted by installing traveling wave harvester respectively at the both ends of tested joint line, and using two traveling waves Acquisition means gather and calculate injection traveling wave time difference Δ t respectively1i, i=1 ..., n-1, combined floodgate traveling wave time difference Δ t2, failed row Ripple time difference Δ tf, using travelling wave signal in overhead line section or this constant feature of cable sections velocity of wave, pass through failure judgement The traveling wave time difference comes accurate, fast with the order whether each injection traveling wave time difference meets decision condition and meet decision condition Part of path where the trouble point of the definite tested joint line of speed, then the former of tested joint line is accurately positioned by calculating Barrier point position；
In conclusion the present invention effectively solves the problems, such as that current mixed line fault positioning is difficult, and ripple need not be adjusted Speed, greatly reduces position error, has the advantages that fault location speed is fast, localization of fault precision is high, realizes high-pressure frame The failure of ceases to be busy-cable hybrid line is accurately positioned.
Brief description of the drawings
The present invention is described in further detail with specific embodiment below in conjunction with the accompanying drawings：
Fig. 1 is the conspectus of high voltage overhead lines-cable hybrid line；
Fig. 2 is the FB(flow block) of the traveling wave fault positioning method of the present invention；
Fig. 3 is the principle reference view of the traveling wave fault positioning method of the present invention.
Embodiment
As depicted in figs. 1 and 2, the present invention is suitable for the traveling wave fault positioning method of high voltage overhead lines-cable hybrid line, Suitable for being existed by least one section of cut cable and the tested joint line that at least one section of overhead line is composed in series, cut cable and overhead line It is arranged alternately, sets in tested joint line：The cut cable of tested joint line whole and the total quantity of overhead line are n sections, n >= 2, they are represented sequentially as part of path D by M ends to the N-terminal of tested joint line1,D2,···,Dn, phase in tested joint line The tie point of adjacent cut cable and overhead line is represented sequentially as L by M ends to N-terminal1,L2,···,Ln-1, M ends and N-terminal be respectively by The head end of survey joint line and end or M ends and N-terminal are respectively end and the head end of tested joint line.
The traveling wave fault positioning method of the present invention includes：
Step 1, traveling wave harvester is installed at the M ends of tested joint line and N-terminal respectively, wherein, which adopts Time synchronization between acquisition means.
Step 2, using travelling wave signal generator respectively in the tie point L of tested joint line1,L2,···,Ln-1Note Enter travelling wave signal so that the travelling wave signal of injection is transmitted from injection phase to the M ends of tested joint line and N-terminal, and utilizes two Platform traveling wave harvester records the time that each injection travelling wave signal reaches tested joint line M ends and N-terminal respectively, so as to calculate Go out the tie point L in tested joint line when travelling wave signal generatoriWhen injecting travelling wave signal, injection travelling wave signal respectively reaches The injection traveling wave time difference of tested joint line M ends and N-terminal is Δ t1i, i=1 ..., n-1.
Step 3, is carried out combined floodgate power transmission to the M ends breaker of tested joint line, is produced with this in tested joint line Combined floodgate travelling wave signal so that the combined floodgate travelling wave signal is transmitted from the M ends of tested joint line to N-terminal, and is adopted using two traveling waves Acquisition means record the combined floodgate travelling wave signal and reach the time of tested joint line M ends and N-terminal respectively, so as to calculate the combined floodgate row Ripple signal respectively reaches the combined floodgate traveling wave time difference Δ t of tested joint line M ends and N-terminal2。
Step 4, calculates travelling wave signal and is located at M ends to tie point L in tested joint line respectivelyiBetween section on Transmission timeAnd calculate travelling wave signal respectively and be located at tie point L in tested joint lineiTo between N-terminal Section on transmission timeWherein, i=1 ..., n-1.
Step 5, when tested joint line breaks down, records fault traveling wave with two traveling wave harvesters and believes respectively The time of tested joint line M ends and N-terminal number is reached, so that calculating fault traveling wave signal respectively reaches tested joint line M End and the fault traveling wave time difference Δ t of N-terminalf。
Step 6, compares Δ t successivelyfWith Δ t11,Δt12,…,Δt1(n-1)Size, if there is meeting Δ tf＜ Δs t1iThe Δ t of decision condition1i, i=1 ..., n-1, then judge that the trouble point of tested joint line is located at part of path DKOn, wherein, Δ t1KFor Δ t11,Δt12,…,Δt1(n-1)Successively with Δ tfSize relatively in meet injection traveling wave time of decision condition at first Difference, K are one of value in 1 to n-1；If Δ tfWith Δ t11,Δt12,…,Δt1(n-1)Size be relatively satisfied by Δ tf ＞ Δs t1i, i=1 ..., n-1, then judge that the trouble point of tested joint line is located at part of path DnOn.
Step 7, calculates the time that travelling wave signal is transferred to circuit M ends from trouble pointCalculate traveling wave letter The time of circuit N-terminal number is transferred to from trouble point
The trouble point for judging tested joint line in step 6 is located at part of path D1When upper, the offline road M ends in trouble point Distance isThe distance of road N-terminal is offline
The trouble point for judging tested joint line in step 6 is located at part of path DkDuring upper and k >=2, the offline road in trouble point The distance at M ends isThe distance of road N-terminal is offline
The trouble point for judging tested joint line in step 6 is located at part of path DnWhen upper, the offline road M ends in trouble point Distance isThe distance of road N-terminal is offline
Wherein, liFor part of path DiLength, i=1 ..., n.
Referring to Fig. 3, the principle of traveling wave fault positioning method of the invention is：
Travelling wave signal reaches the time difference at circuit both ends, meter first according to caused by closing a floodgate circuit head end breaker Calculation show that travelling wave signal is transferred to the total time of end from circuit head end, i.e., traveling wave is in all part of path D1,D2,···,DnPass Defeated temporal summation；Travelling wave signal generator is recycled in cable and the junction L of overhead line1,L2,···,Ln-1Injection row Ripple signal, is calculated the injection traveling wave time difference that injection travelling wave signal respectively reaches tested joint line M ends and N-terminal.According to Temporal summation and time difference can be calculated travelling wave signal and be located at M ends to tie point L in tested joint lineiBetween area Transmission time in section and it is located at tie point L in tested joint line in travelling wave signaliTransmission to the section between N-terminal Time.
During line fault, the time at circuit both ends is reached also with travelling wave signal caused by failure, event is calculated Barrier travelling wave signal is transferred to the time of head end from trouble point and the difference of both the time of end is transferred to from trouble point.In conjunction with row Ripple signal is transferred to the total time of end from circuit head end, you can calculates fault traveling wave signal and is transferred to head end from trouble point Time, and fault traveling wave signal are transferred to the time of end from trouble point.
If trouble point is in part of path D1When upper, the time that travelling wave signal travelling wave signal is transferred to circuit M ends from trouble point agrees Surely it is less than travelling wave signal from junction L1The time at circuit M ends is transferred to, and travelling wave signal is transferred to circuit N-terminal from trouble point Time is more than travelling wave signal from junction L certainly1It is transferred to the time of circuit N-terminal.Therefore when trouble point is in part of path D1When upper, Travelling wave signal from trouble point is transferred to the time at M ends and the difference of the time of N-terminal is transferred to from trouble point certainly less than traveling wave from even Meet place L1Be transferred to time at circuit M ends with from junction L1It is transferred to the difference of the time of circuit N-terminal.
If travelling wave signal is transferred to the time at M ends and the difference of the time of N-terminal is transferred to from trouble point from trouble point is more than row Ripple is from junction L1It is transferred to the time at circuit M ends and the difference of the time of circuit N-terminal is transferred to from trouble point, then trouble point does not exist Part of path D1On, and in part of path H1On.At this time similarly, if trouble point is in part of path D2On, then travelling wave signal is transmitted from trouble point Time to circuit M ends is certainly less than travelling wave signal from junction L2It is transferred to the time at circuit M ends, and travelling wave signal is from failure The time that point is transferred to circuit N-terminal is more than travelling wave signal from junction L certainly2It is transferred to the time of circuit N-terminal.Therefore in this feelings Under condition, travelling wave signal is transferred to the time at M ends and the difference of the time of N-terminal is transferred to from trouble point from trouble point is less than traveling wave from even Meet place L2Be transferred to time at circuit M ends with from junction L2It is transferred to the difference of the time of circuit N-terminal.
If trouble point is not still in part of path D2On, then in part of path H2On.Continue to compare where determining trouble point After part of path, you can carry out localization of fault according to traveling wave signal transmission time and transmission range this feature in a linear relationship.
When trouble point is in D1When upper, time and the traveling wave at circuit M ends were transferred to from trouble point using fault traveling wave signal In part of path D1The ratio between time of upper transmission can calculate length of the trouble point away from circuit M ends the line is busy section D1The ratio of length, And then calculate length of the trouble point away from circuit M ends.It is trouble point that total line length, which subtracts length of the trouble point away from circuit M ends, Length away from circuit N-terminal.
When trouble point is in DkWhen, k >=2, junction L is transferred to using fault traveling wave signal from trouble point(k-1)Time with Traveling wave is in part of path DkThe ratio between time of upper transmission can calculate trouble point far from junction L(k-1)Length the line is busy section DkIt is long The ratio of degree, and then trouble point is calculated far from junction L(k-1)Length, plus part of path D1,D2,···,D(k-1)Circuit The sum of length, is the line length of M sections away from circuit of trouble point.Similarly, using fault traveling wave signal company is transferred to from trouble point Meet place LkTime and traveling wave in part of path DkThe ratio between time of upper transmission can calculate trouble point far from junction LkLength account for Part of path DkThe ratio of length, and then trouble point is calculated far from junction LkLength, plus part of path Dk,D(k+1),···, DnThe sum of line length, be N sections away from circuit of trouble point line length.
When trouble point is in DnWhen upper, time and the traveling wave of circuit N-terminal were transferred to from trouble point using fault traveling wave signal In part of path DnThe ratio between time of upper transmission can calculate length of the trouble point away from circuit N-terminal the line is busy section DnThe ratio of length, And then calculate length of the trouble point away from circuit N-terminal.It is trouble point that total line length, which subtracts length of the trouble point away from circuit N-terminal, Length away from circuit M ends.
The present invention is not limited to above-mentioned embodiment, according to the above, according to the ordinary technical knowledge of this area And customary means, under the premise of the above-mentioned basic fundamental thought of the present invention is not departed from, the present invention can also make other diversified forms Equivalent modifications, replacement or change, all fall among protection scope of the present invention.

Claims (1)

  1. A kind of 1. traveling wave fault positioning method suitable for high voltage overhead lines-cable hybrid line, suitable for by least one section of electricity Cable section and the tested joint line that at least one section of overhead line is composed in series, the cut cable and overhead line are in tested joint line It is arranged alternately, sets：The cut cable of tested joint line whole and the total quantity of overhead line are n sections, n >=2, they are by tested mixed M ends to the N-terminal on zygonema road is represented sequentially as part of path D1,D2,···,Dn, in tested joint line adjacent cable section with it is aerial The tie point of line is represented sequentially as L by M ends to N-terminal1,L2,···,Ln-1, M ends and N-terminal are respectively the head of tested joint line End and end or M ends and N-terminal are respectively end and the head end of tested joint line；
    The traveling wave fault positioning method includes：
    Step 1, traveling wave harvester is installed at the M ends of tested joint line and N-terminal respectively, wherein, two traveling wave collection dresses Time synchronization between putting；
    Step 2, using travelling wave signal generator respectively in the tie point L of tested joint line1,L2,···,Ln-1Injection row Ripple signal so that the travelling wave signal of injection is transmitted from injection phase to the M ends of tested joint line and N-terminal, and utilizes described two Platform traveling wave harvester records the time that each injection travelling wave signal reaches tested joint line M ends and N-terminal respectively, so as to calculate Go out the tie point L in tested joint line when travelling wave signal generatoriWhen injecting travelling wave signal, injection travelling wave signal respectively reaches The injection traveling wave time difference of tested joint line M ends and N-terminal is Δ t1i, i=1 ..., n-1；
    Step 3, is carried out combined floodgate power transmission to the M ends breaker of tested joint line, is produced combined floodgate in tested joint line with this Travelling wave signal so that the combined floodgate travelling wave signal is transmitted from the M ends of tested joint line to N-terminal, and is adopted using two traveling waves Acquisition means record the combined floodgate travelling wave signal and reach the time of tested joint line M ends and N-terminal respectively, so as to calculate the combined floodgate row Ripple signal respectively reaches the combined floodgate traveling wave time difference Δ t of tested joint line M ends and N-terminal2；
    Step 4, calculates travelling wave signal and is located at M ends to tie point L in tested joint line respectivelyiBetween section on transmission when BetweenAnd calculate travelling wave signal respectively and be located at tie point L in tested joint lineiTo the section between N-terminal On transmission timeWherein, i=1 ..., n-1；
    Step 5, when tested joint line breaks down, records fault traveling wave with two traveling wave harvesters and believes respectively The time of tested joint line M ends and N-terminal number is reached, so that calculating fault traveling wave signal respectively reaches tested joint line M End and the fault traveling wave time difference Δ t of N-terminalf；
    Step 6, compares Δ t successivelyfWith Δ t11,Δt12,…,Δt1(n-1)Size, if there is meeting Δ tf＜ Δs t1iSentence The Δ t of fixed condition1i, i=1 ..., n-1, then judge that the trouble point of tested joint line is located at part of path DKOn, wherein, Δ t1KFor Δt11,Δt12,…,Δt1(n-1)Successively with Δ tfSize relatively in meet injection traveling wave time of the decision condition at first Difference, K are one of value in 1 to n-1；If Δ tfWith Δ t11,Δt12,…,Δt1(n-1)Size be relatively satisfied by Δ tf ＞ Δs t1i, i=1 ..., n-1, then judge that the trouble point of tested joint line is located at part of path DnOn；
    Step 7, calculates the time that travelling wave signal is transferred to circuit M ends from trouble pointCalculate travelling wave signal from Trouble point is transferred to the time of circuit N-terminal
    The trouble point for judging tested joint line in step 6 is located at part of path D1When upper, the distance at the offline road M ends in trouble point is <mrow> <msub> <mi>l</mi> <mrow> <mi>M</mi> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>t</mi> <mrow> <mi>M</mi> <mi>f</mi> </mrow> </msub> <msub> <mi>t</mi> <mrow> <mi>M</mi> <mn>1</mn> </mrow> </msub> </mfrac> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>,</mo> </mrow> The distance of road N-terminal is offline <mrow> <msub> <mi>l</mi> <mrow> <mi>N</mi> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>t</mi> <mrow> <mi>N</mi> <mi>f</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>t</mi> <mrow> <mi>N</mi> <mn>1</mn> </mrow> </msub> </mrow> <msub> <mi>t</mi> <mrow> <mi>M</mi> <mn>1</mn> </mrow> </msub> </mfrac> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>2</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>l</mi> <mi>i</mi> </msub> <mo>;</mo> </mrow>
    The trouble point for judging tested joint line in step 6 is located at part of path DkDuring upper and k >=2, the offline road M ends in trouble point Distance is that the distance of offline road N-terminal is <mrow> <msub> <mi>l</mi> <mrow> <mi>N</mi> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>t</mi> <mrow> <mi>N</mi> <mi>f</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>t</mi> <mrow> <mi>N</mi> <mi>k</mi> </mrow> </msub> </mrow> <mrow> <msub> <mi>t</mi> <mrow> <mi>N</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </msub> <mo>-</mo> <msub> <mi>t</mi> <mrow> <mi>N</mi> <mi>k</mi> </mrow> </msub> </mrow> </mfrac> <msub> <mi>l</mi> <mi>k</mi> </msub> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>l</mi> <mi>i</mi> </msub> <mo>;</mo> </mrow>
    The trouble point for judging tested joint line in step 6 is located at part of path DnWhen upper, the distance at the offline road M ends in trouble point is <mrow> <msub> <mi>l</mi> <mrow> <mi>M</mi> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>t</mi> <mrow> <mi>M</mi> <mi>f</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>t</mi> <mrow> <mi>M</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </msub> </mrow> <msub> <mi>t</mi> <mrow> <mi>N</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </msub> </mfrac> <msub> <mi>l</mi> <mi>n</mi> </msub> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>l</mi> <mi>i</mi> </msub> <mo>,</mo> </mrow> The distance of road N-terminal is offline <mrow> <msub> <mi>l</mi> <mrow> <mi>N</mi> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>t</mi> <mrow> <mi>N</mi> <mi>f</mi> </mrow> </msub> <msub> <mi>t</mi> <mrow> <mi>N</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </msub> </mfrac> <msub> <mi>l</mi> <mi>n</mi> </msub> <mo>;</mo> </mrow>
    Wherein liFor part of path DiLength, i=1 ..., n.
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