CN106919799B - Phase conductor back flash-over rate calculation method on ultra high-tension transmission line staggered tower upward slope position - Google Patents
Phase conductor back flash-over rate calculation method on ultra high-tension transmission line staggered tower upward slope position Download PDFInfo
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Abstract
The invention discloses phase conductor back flash-over rate calculation methods on a kind of ultra high-tension transmission line staggered tower upward slope position, analyze the risk that phase conductor is struck by lightning on staggered tower upward slope position, it is respectively established at left and right sides of the phase hanging point, it proposes that 34 kinds of possible exposed arcs project situation, can comprehensively consider the risk of shielding failure of the phase conductor.The present invention combines modern geography in formation software, can accurately calculate the back flash-over rate of the phase.Mutually larger thunderbolt risk may be faced on staggered tower upward slope position, using the method for the present invention can design to staggered tower and Lighting Protection Measures advise.
Description
Technical field
The present invention relates to ultra high-tension transmission line staggered tower phase conductors to protect field, and in particular to a kind of ultra high-tension transmission line is wrong
Phase conductor back flash-over rate calculation method on layer tower upward slope position.
Background technique
Regular method based on experience, based on semiempirical model electrical geometric method (electro-geometric model,
EGM) and the first inducing defecation by enema and suppository based on thunder and lightning development process is the most common three big methods for calculating thunderbolt trip-out rate.Wherein,
The electric geometry method that Whitehead et al. is proposed, the improvement through the 80s and 90s in last century Eriksson et al. and nearly more than ten
Year development, receive being widely recognized as scholars and standard.Electrical geometric method have passed through continuous improve and perfect, by ring
The factors such as border especially orographic factor, span arc sag, non-normal incidence angle all consider in a model.With modern thunder observation water
The application of flat development and advanced geography in formation software, the tripping rate with lightning strike of shaft tower can be effectively calculated using electrical geometric method.
The basic principle of electric geometry method: the pilot discharge channel head developed to the ground by thunder and lightning reaches and is hit object
Critical striking distance (hit away from) before, it is a little uncertain for hitting, and first reaches hitting away within for which object, i.e., to the object
Body electric discharge.Lightning Stroke Phenomena is studied, draws the electric geometry method of shaft tower, as shown in Figure 1.In figure: point D is lightning conducter extension
Point, point E are middle phase conductor hanging point；Point A is that the vertical line and lightning conducter of horizontal plane are hit away from round intersection point in shaft tower center；Point B is to keep away
Thunder line is hit to be hit with middle phase conductor away from round intersection point away from round；Point C hits for middle phase conductor and hits the intersection point away from straight line away from circle and the earth.M is
CG and y-axis intersection point, MO are the vertical intercept of straight line CG.As seen from the figure, it if thundercloud guide first reaches arc AB, is put to lightning conducter D
Electricity；If thundercloud guide first reaches arc BC, guiding line electric discharge；If thundercloud guide first reaches straight line CG, to ground discharge.
Arc AB is referred to as protection arc, and arc BC is referred to as exposure arc.
By this model, it can be more intuitively laid out according to lightning conducter on shaft tower and lead location, obtain and shielding occurs
Situation.Lightning conducter height needed for calculating will shield the lightning current, considers further that its maximum value and engineered economy, determines
The antenna height of lightning conducter.
The common-tower double-return shaft tower most-often used for supertension line, since middle phase conductor is cross-arm longest in three-phase conducting wire
A phase, and a possibility that descending position is by lightning stroke, is bigger, generally believes that phase conductor in descending position is the phase most vulnerable to lightning stroke.
But in electric system 500kV route actual moving process, it is no lack of upper phase conductor by the case of lightning stroke trip, what the present invention was paid close attention to
Mutually just because of its special cross-arm design on the upward slope position of 500kV common-tower double-return staggered tower, so that traditional symmetrical same tower should be compared
It is mutually more susceptible to be struck by lightning on the upward slope position of double back shaft tower.
There has been no the researchs of Xiang Fasheng thunder shielding in system and the special upward slope position for calculating double back staggered tower at present
And calculation method.On the one hand, operating experience shows that upper phase conductor is not uncommon for by lightning stroke trip；On the other hand, below for double
The case where returning Xiang Fasheng thunder shielding on the upward slope position of staggered tower is analyzed, and illustrates in engineer application it is necessory to consider double back
On the upward slope position of staggered tower the case where Xiang Fasheng thunder shielding.
Staggered tower sketch is as shown in Figure 2.Shaft tower in figure is located at the ground that slope angle is θ, is upward slope position on the left of shaft tower,
Upward slope position is closer from the ground, M, E, K, L point be respectively upward slope position lightning conducter hanging point, upper phase conductor hanging point, middle phase conductor hanging point, under
Phase conductor hanging point；It is descending position on the right side of shaft tower, landform is openr, and D, Q, P, R point are respectively that descending position lightning conducter hanging point, upper phase are led
Line hanging point, middle phase conductor hanging point, lower phase conductor hanging point.Not with the protected situation of phase conductor on conventional symmetric common-tower double-return upward slope position
Together, in terms of the shielding risk of E point is present in following two.The first, the staggered floor design based on landform, may result in D point ratio E's
Height is lower, and D, Q cannot form effective protection to E point；The second, lightning conducter M is limited to the protective effect of E point, M point as shown in the figure
Horizontal position is on the left of E point, and in terms of left side, E point is protected by negative shielding angle, but on the right side of E point, positive shielding angle of the E point by M
Protection, it may appear that exposure arc.If changing pole and tower design, shortens M point horizontal distance, the point horizontal position M is made to be in E point right,
The case where will appear the negative shielding angle in positive shielding angle on the left of E point, right side, it is also possible to exposure arc occur in left side.This shows to go up a slope
Phase conductor E is possible to that shielding occurs on position.
Upward slope position: slope position refers to the upper and lower position of a landform slope profile, and upward slope position is proximate to the position of top of the slope.
Shielding: thunder hits around lightning conducter is known as shielding in conducting wire.
Its size: being associated for a facility using analytical expression appropriate by electric geometry method with lightning current,
It can predict whether thunder hits in shielding harness, the earth and by the geometrical model on protection facility component.
Staggered tower: common-tower double-return shaft tower, using staggered floor Deethanizer design, can be reduced in extreme terrain such as the relatively steep area of side slope
Tower spotting is high, saves 10-15 meters of tower height, has apparent economic benefit.
Tripping rate with lightning strike: per 100 km route, 40 Thunderstorm Days, number is cut-off due to caused by lightning stroke, and (successful reclosing also calculates one
It is secondary), referred to as the tripping rate with lightning strike of the route, abbreviation trip-out rate, trip-out rate are the overall targets for measuring line thunder protection performance quality.
Summary of the invention
Technical problem to be solved by the invention is to provide phase conductor on a kind of ultra high-tension transmission line staggered tower upward slope position around
Trip-out rate calculation method is hit, considers landform and tower-shaped factor comprehensively, can accurately calculate the lightning stroke of phase on staggered tower upward slope position
Trip-out rate.
In order to solve the above technical problems, the technical solution adopted by the present invention is that:
Phase conductor back flash-over rate calculation method on a kind of ultra high-tension transmission line staggered tower upward slope position, comprising the following steps:
Step 1: basic electric geometry method is established according to staggered tower schematic diagram；
Step 2: being based on electric geometry method, E point left and right side shielding risk is modeled and analyzed respectively, comprising: step
It is rapid to calculate left side exposure arc projection, and calculate right side exposure arc projection；Wherein, calculating right side exposure arc projection includes upward slope position
Circular arc does not intersect with descending circle of position arc, and upward slope circle of position arc intersects two classes with descending circle of position arc；
Step 3: calculating risk of shielding failure, the risk of shielding failure P (I) is；
Compared with prior art, the beneficial effects of the invention are as follows
1) present invention proposes under a kind of complicated landform based on electrical geometric method, and phase conductor shielding is jumped on staggered tower upward slope position
The calculation method of lock rate, physical significance is intuitive, and calculating process is simple and efficient, and the modes such as network map are used in combination and are easy to obtain
Shaft tower terrain data, calibrated true result can be obtained.
2) using this method to just having carried out lightning protection in the design scheme of certain 500kV transmission line of electricity staggered tower of design phase
It calculates, more accurate result can be obtained.Calculated result shows that phase may face larger thunderbolt risk on staggered tower upward slope position,
Using context of methods can design to staggered tower and Lighting Protection Measures advise.
Detailed description of the invention
Fig. 1 is electric geometry method schematic diagram.
Fig. 2 is staggered tower sketch.
Fig. 3 is the left side electric geometry method figure that the present invention establishes.
Fig. 4 is the 1st kind of situation schematic diagram of the invention.
Fig. 5 is the 2nd kind of situation schematic diagram of the invention.
Fig. 6 is the 3rd kind of situation schematic diagram of the invention.
Fig. 7 is the 4th kind of situation schematic diagram of the invention.
Fig. 8 is the 5th kind of situation schematic diagram of the invention.
Fig. 9 is the 6th kind of situation schematic diagram of the invention.
Figure 10 is the 7th kind of situation schematic diagram of the invention.
Figure 11 is the 8th kind of situation schematic diagram of the invention.
Figure 12 is the 9th kind of situation schematic diagram of the invention.
Figure 13 is the 10th kind of situation schematic diagram of the invention.
Figure 14 is the 11st kind of situation schematic diagram of the invention.
Figure 15 is the 12nd kind of situation schematic diagram of the invention.
Figure 16 is the 13rd kind of situation schematic diagram of the invention.
Figure 17 is the 14th kind of situation schematic diagram of the invention.
Figure 18 is the 15th kind of situation schematic diagram of the invention.
Figure 19 is the 16th kind of situation schematic diagram of the invention.
Figure 20 is the 17th kind of situation schematic diagram of the invention.
Figure 21 is the 18th kind of situation schematic diagram of the invention.
Figure 22 is the 19th kind of situation schematic diagram of the invention.
Figure 23 is the 20th kind of situation schematic diagram of the invention.
Figure 24 is the 21st kind of situation schematic diagram of the invention.
Figure 25 is the 22nd kind of situation schematic diagram of the invention.
Figure 26 is the 23rd kind of situation schematic diagram of the invention.
Figure 27 is the 24th kind of situation schematic diagram of the invention.
Figure 28 is the 25th kind of situation schematic diagram of the invention.
Figure 29 is the 26th kind of situation schematic diagram of the invention.
Figure 30 is the 27th kind of situation schematic diagram of the invention.
Figure 31 is the 28th kind of situation schematic diagram of the invention.
Figure 32 is the 29th kind of situation schematic diagram of the invention.
Figure 33 is the 30th kind of situation schematic diagram of the invention.
Figure 34 is the 31st kind of situation schematic diagram of the invention.
Figure 35 is the 32nd kind of situation schematic diagram of the invention.
Figure 36 is the 33rd kind of situation schematic diagram of the invention.
Figure 37 is the 34th kind of situation schematic diagram of the invention.
Specific embodiment
The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.Shielding tripping is to threaten to surpass
The most important reason of ultra-high-tension power transmission line safe and stable operation.At present mainly using electrical geometric method to supertension line shielding
Trip-out rate is analyzed；For same tower double back transmission line, in the universal main research longest descending position of cross-arm phase conductor around
Trip-out rate is hit, but practical operating experiences are no lack of upper phase conductor by the case of lightning stroke trip.
The present invention proposes the calculation method of the back flash-over rate of phase left and right side on staggered tower upward slope position.Recommended according to IEEE
Hit away from formula, establish basic electric geometry method, in which:
rc=10I0.65 (1)
Assuming that lightning leader hitting away from equal to lightning conducter and conducting wire, it may be assumed that
rc=rs (3)
rc、rs、rgRespectively thunder and lightning hitting away from unit m to conducting wire, lightning conducter and the earth；Arc sag hc,avFor conducting wire mean height
Degree, unit m；I is lightning current, unit kA.
hc,av=hd-2/3Sd (4)
H in formula (4)dHeight for conducting wire hitch point apart from ground, unit m；SdFor conducting wire sag, unit m.
Based on electric geometry method, E point left and right side shielding risk is modeled and analyzed respectively.The projection of exposure arc
Distance is the sum of the exposure projector distance obtained after E point left and right side calculates separately, the throwing over the ground of uphill, downhill position outermost arc
Shadow overall length is the distance that lightning leader may be hit, and this makes it possible to obtain E point risk of shielding failure, presses lightning stroke conducting wire probability of flashover formula, into
One step calculates back flash-over rate.
1, exposure arc in left side projects calculation method
It is as shown in Figure 3 to establish left side electric geometry method figure.It is hung in figure with upward slope position lightning conducter hanging point (M), upper phase conductor
Point (E), middle phase conductor hanging point (K) are the center of circle, respectively with rs、rc、rcIt launches an attack for radius structure away from circle, hits and be represented by dotted lines away from circle.It keeps away
It is F that thunder line, which protects circle M and upper phase conductor to hit the intersection point away from circle E, and upper phase conductor, which is hit, hits the intersection point away from circle K away from circle E and middle phase conductor
For J, A point is the protection arc and shaft tower central axes intersection point of earth-wire protection circle M, and point N1 is that upper or middle phase conductor is hit away from circle and the earth
Hit the intersection point away from straight line.In Fig. 3, N1 point is determined as hitting with middle phase conductor away from round intersection point, in fact, according to hitting away from round circle
The heart, radius greatly hit distance degree rgDeng difference, greatly hit away from straight line may simultaneously with circle M, circle E, circle K in a circle or
Multiple circle intersections, choosing an intersection point near the left side is N1.
Assuming that thunder and lightning vertical incidence, the calculating of E point left side risk of shielding failure can be according to Fig. 4 to 12 kinds of situations minute shown in figure 15
It does not discuss.In these cases, M1, E1, K1 point are respectively circle M, circle E, the circle leftmost side K point, as expose circular arc or guarantor
The horizontal Far Left border of guard circle arc.When earth-wire protection is round hit with upper phase conductor away from round intersection point F, upper Xiang Yuzhong phase conductor hit away from
When round intersection point J is with the relative position E1 and M1 difference, the projection over the ground of E point exposure arc can change.Concrete analysis is such as 1 institute of table
Show, wherein x*, y* indicate cross, the ordinate of point *.The coordinate origin is O point in Fig. 2, i.e. shaft tower central axes and ground intersection point.
Cross, the ordinate of point M, E, K it is known that the ordinate of M1, E1, K1 it is known that abscissa is the function of lightning current I.Circle
M, the center of circle of circle E, circle K are it is known that radius is to hit away from seeking the coordinate of point F, J and A by corresponding method of geometry.The earth is hit away from straight
The formula y=kx+b of line can geometrical relationship according to Fig.3, find out.Wherein k=-tan θ, b=rg/ cos θ, θ incline for ground
Angle.The earth, which is hit, may have multiple intersection points or without intersection point with circle M, circle E, circle K away from straight line.According to the round intersection formula with straight line,
The coordinate that intersection point can be found out chooses leftmost intersection point as N1 when straight line and three circular arcs have multiple intersection points.
It is different according to the position of intersection point N1 when considering to hit in the presence of the earth has the case where intersection point away from straight line and three circular arcs,
12 kinds of intersection situations can be divided into judge left side exposure arc projected length.As shown in table 1, exposure arc projected length abs (x*1-
x*2) give directions * 1 and * 2 between abscissa absolute value.
If three circular arcs and the earth are hit away from intersection point is not present, that exposure arc projected length is horizontal by exposing segmental arc starting point
Coordinate determines.Right end starting point is earth-wire protection circle leftmost side limit point M1 or earth-wire protection circle M is hit with upper phase conductor away from circle E
Intersection point F point (y-axis coordinate more higher be starting point)；Left end terminal be upper phase conductor hit away from circle the rightmost side E limit point E1 or
Upper, middle phase conductor hits the intersection point J point away from circle E, K (y-axis coordinate is more higher for terminal).
Below according to the height for first comparing F and M1, then it is bigger hit away from straight line and the most left intersection point N1 of each section of circular arc with it is upper
The height of junior between one group analyzes 12 kinds of situations.(1)-(6) kind situation is to be higher than M1 point based on F point to carry out
Analysis, exposure arc starting point generally from the abscissa of F point count；(7)-(12) kind situation is higher than based on M1 point
F point is analyzed, the starting point of exposure arc generally from the abscissa of M1 point count.
(1) is planted in situation, is greatly hit away from sufficiently large, greatly hits higher away from straight line, hands over earth-wire protection circle M in N1, point
N1 highest, thus can Simplified analysis, greatly hit and shield entirely upper phase conductor away from straight line and hit away from circle E, exposure arc projection a length of 0.
(2) are planted in situation, are greatly hit to hit away from straight line and upper phase conductor and are met at N1 away from circle E arc, then upper phase conductor is hit away from circle E
Become exposure arc away from the part on straight line, except earth-wire protection circle M greatly hitting, exposure arc starting point is earth-wire protection circle
M and upper phase conductor hit the intersection point F away from circle E, and terminal is greatly to hit to hit the intersection point N1 away from circle E away from straight line and upper phase conductor.Exposure arc
The absolute value of the difference for projecting the abscissa of a length of point F and point N1, is denoted as abs (xF-xN1)。
(3) plant situation in, it is contemplated that middle phase conductor hit away from circle K and upper phase conductor hit away from justify E intersection point it is higher, exceed phase
Conducting wire is hit away from circle E Far Left border point E1, but not high too greatly hit is hit away from straight line and upper phase conductor away from the intersection point N1 for justifying E, therefore situation
Actually similar with (2), exposure arc starting point is earth-wire protection circle M and upper phase conductor hits the intersection point F away from circle E, and terminal is the earth
It hits and hits the intersection point N1 away from circle E away from straight line and upper phase conductor.Exposure arc projects the absolute value of the difference of the abscissa of a length of point F and point N1
abs(xF-xN1)。
(4) plant situation in, middle phase conductor hit away from circle K and upper phase conductor hit away from circle E intersection point it is higher, height too greatly hit away from straight
Line and upper phase conductor are hit away from circle E intersection point N1, then exposing arc starting point is that earth-wire protection circle M and upper phase conductor hit the intersection point away from circle E
F, terminal are that middle phase conductor hits the intersection point J away from circle K and circle E.Exposure arc projects the absolute of the difference of the abscissa of a length of point F and point J
Value abs (xF-xJ)。
(5) are planted in situation, and phase conductor is hit away from the circle leftmost side E limit point E1 in consideration, are greatly hit and are led away from straight line and upper phase
Line, which is hit, is lower than circle E Far Left border point E1 away from circle E intersection point, and middle phase conductor hits lower with round E intersection point J away from circle K, is greatly hit away from straight
Line shielding, the abscissa absolute value of N1 point is less than E1 point abscissa absolute value at this time, though therefore exposure arc terminus is respectively F, N1,
But exposure arc projects the absolute value of the difference abs (x of the abscissa of a length of point F and point E1F-xE1)。
(6) are planted in situation, are greatly hit and are hit away from circle E intersection point away from straight line and upper phase conductor higher than circle E Far Left border point E1, therefore
Similar with situation (2) at this time, exposure arc starting point is that earth-wire protection circle M and upper phase conductor hit the intersection point F away from circle E, and terminal is big
Ground, which is hit, hits the intersection point N1 away from circle E away from straight line and upper phase conductor.Exposure arc projects the absolute of the difference of the abscissa of a length of point F and point N1
Value abs (xF-xN1)。
In (7) and (8) kind situation, greatly hits and be higher than circle M and upper phase conductor away from straight line and earth-wire protection circle M intersection point N1
It hitting away from circle E intersection point F, i.e., upper phase conductor is hit all to be hit away from straight line and lightning conducter away within circle M protection scope greatly hitting away from circle E,
Therefore no matter N1 is higher than earth-wire protection circle M Far Left border point M1 again below conducting wire is hit not to be exposed away from circle, exposure arc projection
A length of 0.
(9) plant situation in, greatly hit away from straight line and earth-wire protection circle M intersection point N1 be lower than circle M and upper phase conductor hit away from
Circle E intersection point F, upper phase conductor, which is hit, has exposed arc away from circle E, at this time F M leftmost side limit point M1 round lower than earth-wire protection, though therefore it is sudden and violent
Dew arc terminus is respectively F, N1, but exposure arc projects the absolute value of the difference abs (x of the abscissa of a length of point M1 and point N1M1-
xN1)。
(10) are planted in situation, are greatly hit to hit away from straight line and middle phase conductor and are lower than circle K and circle E intersection point J away from circle K intersection point N1,
I.e. lower away from straight line because of greatly hitting, middle phase conductor also produces exposed arc, but not as this case discussion.Upper phase conductor exposure arc
Terminus is respectively F, J, and F projects a length of point M1 and point J lower than the earth-wire protection circle leftmost side M limit point M1, exposure arc at this time
Abscissa absolute value of the difference abs (xM1-xJ)。
(11) are planted in situation, and phase conductor hits to hit away from circle K with upper phase conductor and hit away from circle E intersection point lower than upper phase conductor in consideration
When away from circle leftmost side limit point E1, the circular arc intersection point N1 away from straight line and circle E is greatly hit compared with the height of E1: when N1 is higher than E1
When, upper phase conductor exposure arc starting point is earth-wire protection circle M and upper phase conductor hits the intersection point F away from circle E, but F is protected lower than lightning conducter
Guard circle leftmost side limit point M1；Terminal is that the earth hits the intersection point N1 away from straight line and circle E.Exposure arc projects a length of point M1's and point N1
Absolute value of the difference abs (the x of abscissaM1-xN1)。
(12) plant situation, hit lower than upper phase conductor away from the circle leftmost side when greatly hitting the circular arc intersection point N1 away from straight line and circle K
When the point E1 of limit, upper phase conductor exposure arc starting point is that earth-wire protection circle M and upper phase conductor hit the intersection point F away from circle E, but F is lower than
Earth-wire protection justifies leftmost side limit point M1；Terminal is greatly to hit to hit the intersection point J away from round E away from straight line and upper phase conductor, but J is low
It hits in upper phase conductor away from circle leftmost side limit point E1.Exposure arc projects the absolute value of the difference of the abscissa of a length of point M1 and point E1
abs(xM1-xE1).As N1 ratio J high but when being still below E1, exposure arc projection length is constant.
12 kinds of situations on the left of considerations above when shielding, are summarised in following table.
Exposure arc projected length on the left of 1 E point of table
2, exposure arc in right side projects calculation method
2.1 upward slope circle of position arcs do not intersect with descending circle of position arc
It hits and is determined away from radius by the size of lightning current, the more big then radius of lightning current is bigger, it is possible to can generate upward slope position and keep away
Thunder line, conducting wire are that protection arc, exposure arc etc. that the center of circle is constituted intersect with the circular arc that descending position lightning conducter, conducting wire are center of circle composition,
Keep the analysis to the back flash-over rate of phase on staggered tower upward slope position more complicated.
Assume initially that upward slope circle of position arc does not intersect with descending circle of position arc, possible shielding situation on the right side of analysis E point.Such as Fig. 3
It is shown, H point be earth-wire protection circle M and upper phase conductor to hit intersection point, T point away from circle E be that upper phase conductor is hit away from circle E and middle phase conductor
The intersection point away from circle K is hit, M2 is earth-wire protection circle M rightmost border point, and K2 is that middle phase conductor is hit away from circle K rightmost border point.It is lightning-arrest
The round M of line protection, upper phase conductor hit to hit away from circle K and greatly hit away from circle E and middle phase conductor and hand over away from straight line there may be one or more
Point, selecting abscissa near a right intersection point is N2.According to the relative position of M2, H, E2, T, K2 and N2, can be exposed in the hope of arriving
Arc projected length.The starting point of exposure arc is earth-wire protection circle M and upper phase conductor hits intersection point H or earth-wire protection circle M away from circle E
Rightmost border point M2 (more higher y-axis coordinate is starting point), the terminal of exposure arc are that upper phase conductor is hit away from circle E rightmost border point
E2 or upper, middle phase conductor hit the intersection point T point (y-axis coordinate is more higher for terminal) away from circle E, K, consider further that the earth is hit away from straight line
To the shielding situation of exposure arc.Method for solving is similar to the above-mentioned left side exposure method of arc projected length, and specific relative position is closed
It is that corresponding exposure arc projected length is listed in Table 2 below.
(13)-(24) plant situation, only consider upward slope position earth-wire protection range, middle phase conductor hit away from, greatly hit away from right
The influence of phase conductor on upward slope position.First consider that earth-wire protection circle M and upper phase conductor hit intersection point H and earth-wire protection away from circle E
The height of circle M rightmost border point M2, then compare and wherein hit the height away from straight line Yu circular arc intersection point N2 compared with low spot and the earth.
(13)-(18) are planted in situation, and earth-wire protection circle M and upper phase conductor hit the intersection point H away from circle E and protect higher than lightning conducter
Guard circle M rightmost border point M2；(19)-(24) are planted in situation, and earth-wire protection circle M hits low away from the circle intersection point H of E with upper phase conductor
In earth-wire protection circle M rightmost border point M2.
(13) plant situation, greatly hit away from larger, greatly hit and are higher than lightning conducter away from straight line and earth-wire protection circle M intersection point N2
It protects circle M and upper phase conductor to hit intersection point H and H away from circle E to hit higher than upper phase conductor away from circle E rightmost border point E2, i.e., upper phase conductor
It hits and is shielded away from circle by lightning conducter and the earth, do not expose arc.
(14) plant situation, greatly hit and hit in upper phase conductor away from circle E away from straight line and circular arc intersection point N2, protect lower than lightning conducter
Guard circle M and upper phase conductor hit the intersection point H away from circle E, and H is higher than earth-wire protection circle rightmost side limit point M2, exposure arc starting point at this time
The intersection point H away from circle E is hit for earth-wire protection circle M and upper phase conductor, exposure arc terminal hits for the earth and hits away from straight line and upper phase conductor
Away from circle E intersection point N2, exposure arc projects the absolute value of the difference abs (x of the abscissa of a length of point H and point N2H-xN2)。
(15) and (16) plant situation, it is contemplated that middle phase conductor, which is hit, hits the intersection point T away from circle E away from circle K and upper phase conductor, works as T
When hitting higher than upper phase conductor away from circle E rightmost border point E2, if still having the earth to hit is higher than T, situation away from straight line and circular arc intersection point N2
Similar (14), exposure arc starting point is earth-wire protection circle M and upper phase conductor hits the intersection point H away from circle E, and exposure arc terminal is that the earth is hit
It hits away from straight line and upper phase conductor away from circle E intersection point N2, exposure arc projects the absolute value of the difference abs of the abscissa of a length of point H and point N2
(xH-xN2)；If the earth is hit away from straight line and circular arc intersection point N2 lower than T, N2 is hit in middle phase conductor away from circle K, and exposure arc starting point is
Earth-wire protection circle M and upper phase conductor hit the intersection point H away from circle E, and exposure arc terminal hits for middle phase conductor and hits away from circle K with upper phase conductor
Away from circle E intersection point T, exposure arc projects the absolute value of the difference abs (x of the abscissa of a length of point H and point TH-xT)。
(17) and (18) plant situation, and phase conductor is hit in consideration when hitting lower away from circle E intersection point T away from circle K and upper phase conductor, greatly
Ground, which is hit, hits the height difference away from circle E rightmost border point E2 away from straight line and circular arc intersection point N2 and upper phase conductor.When upper phase conductor hit away from
When circle E rightmost border point E2 higher (when than greatly hitting the circular arc intersection point N2 high away from straight line and circle E), exposure arc starting point is lightning conducter
Circle M and upper phase conductor is protected to hit the intersection point H away from circle E, exposure arc terminal is that the earth is hit away from straight line and circular arc intersection point N2, but N2 is lower than
Upper phase conductor is hit away from circle E rightmost border point E2, and exposure arc projects the absolute value of the difference abs of the abscissa of a length of point H and point E2
(xH-xE2)；When greatly hit be higher than upper phase conductor away from straight line and circular arc intersection point N2 and hit away from circle E rightmost border point E2 when, exposure arc rises
Point is earth-wire protection circle M and upper phase conductor hits the intersection point H away from circle E, and exposure arc terminal is that the earth is hit away from straight line and circular arc intersection point
N2, exposure arc project the absolute value of the difference abs (x of the abscissa of a length of point H and point E2H-xN2)。
(19)-(24) plant situation, consider that earth-wire protection circle M and upper phase conductor hit the intersection point H away from circle E lower than lightning conducter
The case where when protection circle M rightmost border point M2.(19) plant situation, greatly hit and meet at N2 away from straight line and earth-wire protection circle M, high
In earth-wire protection circle M rightmost border point M2, upper phase conductor is hit away from circle without exposure arc.
(20) plant situation, greatly hit and meet at N2 away from straight line and earth-wire protection circle M, though most lower than earth-wire protection circle M
The right border point M2, but be still higher than earth-wire protection circle M and hit the intersection point H away from circle E with upper phase conductor, upper phase conductor is hit away from circle without exposure
Arc.
(21) plant situation, greatly hit to hit away from straight line and upper phase conductor and meet at N2 away from circle E, and N2 is lower than earth-wire protection circle M
The intersection point H away from circle E is hit with upper phase conductor, but is hit higher than middle phase conductor and hits the intersection point T away from circle E away from circle K and upper phase conductor, so when
It is earth-wire protection circle M that upper phase conductor, which is hit away from circle E exposure arc starting point, and upper phase conductor hits the intersection point H away from circle E, and terminal is that the earth is hit
The intersection point N2 away from circle E is hit away from straight line and upper phase conductor, but earth-wire protection circle M rightmost border point M2 abscissa absolute value is greater than and keeps away
Thunder line protects circle M and upper phase conductor to hit the intersection point H away from circle E, and exposure arc projects the exhausted of the difference of the abscissa of a length of point M2 and point N2
To value abs (xM2-xN2)。
(22) plant situation, greatly hit to hit away from straight line and middle phase conductor and meet at N2 away from circle K, and upper phase conductor is hit away from circle E at this time
Exposure arc starting point is earth-wire protection circle M and upper phase conductor hits the intersection point H away from circle E, and terminal is that middle phase conductor is hit away from circle K and upper phase
Conducting wire hit away from circle E intersection point T, but earth-wire protection circle M rightmost border point M2 abscissa absolute value be greater than earth-wire protection circle M with
Upper phase conductor hits the intersection point H away from circle E, and exposure arc projects the absolute value of the difference abs (x of the abscissa of a length of point M2 and point TM2-xT)。
(23) and (24) plant situation, and further phase conductor hits and hits the intersection point T away from circle E away from circle K and upper phase conductor in consideration
The case where when hitting lower than upper phase conductor away from circle E rightmost border point E2.(23) plant situation, when greatly hitting away from straight line and upper phase conductor
It hits and meets at N2 away from circle E, N2 is higher than upper phase conductor and hits away from circle E rightmost border point E2, and upper phase conductor is hit away from circle E exposure arc starting point at this time
The intersection point H away from circle E is hit for earth-wire protection circle M and upper phase conductor, terminal is greatly to hit to hit away from straight line and upper phase conductor away from circle E
Intersection point N2, but earth-wire protection circle M rightmost border point M2 abscissa absolute value be greater than earth-wire protection circle M and upper phase conductor hit away from
The abscissa absolute value of the intersection point H of circle E, exposure arc project the absolute value of the difference abs (x of the abscissa of a length of point M2 and point N2M2-
xN2)。
(24) plant situation, greatly hit to hit away from straight line and upper phase conductor and meet at N2 away from circle E, and N2 is hit lower than upper phase conductor away from circle
E rightmost border point E2, it is earth-wire protection circle M away from circle E exposure arc starting point that upper phase conductor, which is hit, at this time and upper phase conductor is hit away from circle E
Intersection point H, but earth-wire protection circle M rightmost border point M2 abscissa absolute value be greater than earth-wire protection circle M and upper phase conductor hit away from
The intersection point H of circle E；Terminal is that the earth hits and hits the intersection point N2 away from circle E away from straight line and upper phase conductor, but upper phase conductor hit it is most right away from circle E
Marginal point E2 abscissa absolute value, which is greater than greatly to hit, hits the intersection point N2 away from circle E away from straight line and upper phase conductor, and exposure arc projection is a length of
Absolute value of the difference abs (the x of the abscissa of point M2 and point E2M2-xE2)。
Exposure arc projected length on the right side of 2 E point of table
According to the relativeness and formula (3) of M point and E point, it is known that if upward slope circle of position arc does not intersect with descending circle of position arc
In the case where, M point must have side to be positive shielding angle the protection of E point in the left and right sides, and the other side is negative shielding angle.When wherein
Side is negative shielding angle and lightning conducter and conducting wire hit away from it is equal when, exposure arc projection a length of 0 need to only consider the exposure arc of the other side
Projected length.
2.2 upward slope circle of position arcs intersect with descending circle of position arc
Due to staggered tower structure design and positioning landform complexity, the hanging point of descending position lightning conducter could possibly be higher than or
Slightly less than phase conductor hanging point on upward slope position.If hitting for uphill, downhill position can intersect away from circular arc, highest intersection point, it should under being
Slope position lightning conducter, which is hit, to be hit the conducting wire circular arc away from phase on circular arc or upward slope position with the lightning conducter of upward slope position away from circular arc and intersects.
If two lightning conducter circular arcs of uphill, downhill position can intersect, so that it may realize that the right side of phase conductor on upward slope position does not occur
Exposure segmental arc, the complete protection being able to achieve on the right side of E point do not exclusively carry out discussion herein.This section for descending position lightning conducter hit away from
Circular arc hits the case where intersecting away from circular arc with phase conductor on upward slope position and discusses, and is broadly divided into ten kinds of intersection situations.
B point is the intersection point of upward slope position earth-wire protection circle M and descending position earth-wire protection circle D in (25) kind situation,
In the case of this on upward slope position phase conductor hit away from circle E by upward slope position earth-wire protection circle M and descending position earth-wire protection circle D protection,
Do not expose arc, exposure arc projection a length of 0.
(26)-(34) kind situation in B point be on upward slope position phase conductor hit away from circle E and descending position lightning conducter hit away from circle D
Intersection point.The intersection point can be asked by the two round hearts and radial coordinate.First compare upward slope position earth-wire protection circle M rightmost border point M2
The ordinate height that the intersection point H away from circle E is hit with phase conductor on upward slope position earth-wire protection circle M and upward slope position, that is, determine exposure arc
Starting point: (26)-(30) plant situation discussion upward slope position earth-wire protection circle M rightmost border point M2 and are higher than upward slope position earth-wire protection
Circle M and upward slope position on phase conductor hit away from circle E intersection point H when the case where, (31)-(34) plant situation in discuss upward slope position lightning conducter
Protect circle M rightmost border point M2 lower than upward slope position earth-wire protection circle M and upward slope position on phase conductor hit away from circle E intersection point H when
Situation；Compare again phase conductor on upward slope position hit away from circle E and descending position lightning conducter hit away from circle D intersection points B and upward slope position on phase conductor
The ordinate height away from circle E rightmost border point E2 is hit, that is, determines exposure arc terminal.
(26) are planted in situation, are greatly hit and are hit away from circle E under away from straight line and circular arc intersection point N2 lower than phase conductor on upward slope position
Slope position lightning conducter hits the intersection points B away from circle D, i.e., phase conductor is hit away from circle exposure arc on unrelated upward slope position.Upward slope position earth-wire protection justifies M
Rightmost border point M2 is higher than phase conductor on upward slope position earth-wire protection circle M and upward slope position and hits the intersection point H away from circle E, exposure arc starting point
The intersection point H away from circle E is hit for phase conductor on upward slope position earth-wire protection circle M and upward slope position, but upward slope position earth-wire protection circle M is most right
Marginal point M2 abscissa is greater than phase conductor on upward slope position earth-wire protection circle M and upward slope position and hits the intersection point H away from circle E；Exposure arc is whole
Point hits for phase conductor on upward slope position and hits the intersection points B away from circle D away from circle E and descending position lightning conducter, and exposure arc projects a length of point M2 and point B
Abscissa absolute value of the difference abs (xM2-xB)。
(27) and (28) plant situation, greatly hit and hit higher than phase conductor on upward slope position away from circle E away from straight line and circular arc intersection point N2
With descending position lightning conducter hit away from circle D intersection points B, but be still below upward slope position earth-wire protection circle M and upward slope position on phase conductor hit away from
The intersection point H of circle E, exposure arc starting point are that phase conductor hits the intersection point H away from circle E, terminal on upward slope position earth-wire protection circle M and upward slope position
Greatly to hit away from straight line and circular arc intersection point N2.But when calculating exposure arc projection is long, due to upward slope position earth-wire protection circle M rightmost
Border point M2 abscissa is greater than phase conductor on upward slope position earth-wire protection circle M and upward slope position and hits the intersection point H away from circle E, should analyze exposure
Arc terminal N2 and starting point abscissa calculate the abscissa size of point M2.
In (27) kind situation, exposure arc terminal N2 abscissa is greater than the abscissa of exposure arc starting point M2, that is, exposes arc
Projection be that positive direction (right side) under the consideration of situation 27 extends, therefore exposed arc project a length of point M2 and point B abscissa it
Absolute value of the difference abs (xM2-xB)。
In (28) kind situation, exposure arc terminal N2 abscissa is less than exposure arc starting point M2 abscissa, that is, cruelly
Reveal the long positive direction not in situation 28 of arc projection to extend, in other words by starting point M2 institute from thunder and lightning attacking direction (surface)
Upward slope position earth-wire protection round screen cover, so when although have an exposed arc, calculate exposure arc projection it is long when should take 0.
(29) and (30) are planted in situation, and phase conductor, which is hit, on further consideration upward slope position hits away from circle E with descending position lightning conducter
The case where when intersection points B away from circle D is hit lower than phase conductor on upward slope position away from circle E rightmost border point E2.
(29) are planted in situation, greatly hit away from straight line and circular arc intersection point N2 be higher than phase conductor on upward slope position hit it is most right away from E is justified
Marginal point E2, exposure arc starting point are that phase conductor hits the intersection point H away from circle E on upward slope position earth-wire protection circle M and upward slope position, but goes up a slope
Position earth-wire protection circle M rightmost border point M2 abscissa be greater than upward slope position earth-wire protection circle M and upward slope position on phase conductor hit away from
The abscissa of the intersection point H of circle E；Exposure arc terminal is that the earth is hit away from straight line and circular arc intersection point N2.Exposure arc project a length of point M2 with
Absolute value of the difference abs (the x of the abscissa of point N2M2-xN2)。
(30) are planted in situation, greatly hit away from straight line and circular arc intersection point N2 hit lower than phase conductor on upward slope position it is most right away from E is justified
Marginal point E2, exposure arc starting point are that phase conductor hits the intersection point H away from circle E on upward slope position earth-wire protection circle M and upward slope position, but goes up a slope
Position earth-wire protection circle M rightmost border point M2 abscissa be greater than upward slope position earth-wire protection circle M and upward slope position on phase conductor hit away from
The abscissa of the intersection point H of circle E；Exposure arc terminal be the earth hit away from straight line and circular arc intersection point N2, but on upward slope position phase conductor hit away from
Circle E rightmost border point E2 abscissa is greater than the earth and hits away from straight line and circular arc intersection point N2.Exposure arc projects a length of point M2's and point E2
Absolute value of the difference abs (the x of abscissaM2-xE2)。
(31) are planted in situation, and earth-wire protection circle M rightmost border point M2 in upward slope position is lower than upward slope position earth-wire protection circle M
The intersection point H away from circle E is hit with phase conductor on upward slope position, phase conductor, which is hit, on upward slope position hits the friendship away from circle D away from circle E and descending position lightning conducter
Point B is higher than phase conductor on upward slope position and hits away from circle E rightmost border point E2, greatly hits and is higher than on upward slope position away from straight line and circular arc intersection point N2
Phase conductor, which is hit, to be hit the intersection points B away from circle D away from circle E and descending position lightning conducter but is lower than H, and exposure arc starting point is upward slope position earth-wire protection
Circle M hits the intersection point H away from circle E with phase conductor on upward slope position, and terminal is that the earth is hit away from straight line and circular arc intersection point N2, and exposure arc projects length
For the absolute value of the difference abs (x of point H and the abscissa of point N2H-xN2)。
(32) are planted in situation, and earth-wire protection circle M rightmost border point M2 in upward slope position is lower than upward slope position earth-wire protection circle M
The intersection point H away from circle E is hit with phase conductor on upward slope position, phase conductor, which is hit, on upward slope position hits the friendship away from circle D away from circle E and descending position lightning conducter
Point B is higher than phase conductor on upward slope position and hits away from circle E rightmost border point E2, greatly hits lightning-arrest in descending position away from straight line and circular arc intersection point N2
On line protection circle, exposure arc starting point is that phase conductor hits the intersection point H away from circle E, terminal on upward slope position earth-wire protection circle M and upward slope position
It is hit for phase conductor on upward slope position and hits the intersection points B away from circle D away from circle E and descending position lightning conducter, exposure arc projects a length of point H's and point B
Absolute value of the difference abs (the x of abscissaH-xB)。
(33) are planted in situation, and earth-wire protection circle M rightmost border point M2 in upward slope position is lower than upward slope position earth-wire protection circle M
The intersection point H away from circle E is hit with phase conductor on upward slope position, phase conductor, which is hit, on upward slope position hits the friendship away from circle D away from circle E and descending position lightning conducter
Point B is hit lower than phase conductor on upward slope position away from circle E rightmost border point E2, is greatly hit and is higher than on upward slope position away from straight line and circular arc intersection point N2
Phase conductor hit away from circle E rightmost border point E2, exposure arc starting point be upward slope position earth-wire protection circle M and upward slope position on phase conductor hit away from
The intersection point H of circle E, terminal are that the earth is hit away from straight line and circular arc intersection point N2, and exposure arc projects the difference of the abscissa of a length of point H and point N2
Absolute value abs (xH-xN2)。
(34) are planted in situation, and earth-wire protection circle M rightmost border point M2 in upward slope position is lower than upward slope position earth-wire protection circle M
The intersection point H away from circle E is hit with phase conductor on upward slope position, phase conductor, which is hit, on upward slope position hits the friendship away from circle D away from circle E and descending position lightning conducter
Point B is hit lower than phase conductor on upward slope position away from circle E rightmost border point E2, is greatly hit away from straight line and circular arc intersection point N2 lower than on upward slope position
Phase conductor hit away from circle E rightmost border point E2 but be higher than upward slope position on phase conductor hit away from circle E and descending position lightning conducter hit away from circle D friendship
Point B, exposure arc starting point are that phase conductor hits the intersection point H away from circle E on upward slope position earth-wire protection circle M and upward slope position, and terminal is the earth
Hit away from straight line and circular arc intersection point N2, but on upward slope position phase conductor hit away from circle E rightmost border point E2 abscissa be greater than the earth hit away from straight
Line and circular arc intersection point N2, exposure arc project the absolute value of the difference abs (x of the abscissa of a length of point H and point E2H-xE2)。
Exposure arc projected length (circle E and circle D intersection) on the right side of 3 E point of table
3, risk of shielding failure is calculated
According to the coordinates such as shaft tower lightning conducter, conducting wire hanging point M, E, K, D, phase conductor E point on upward slope position can be calculated separately
L is projected in the exposed range of left and right sideleftAnd lright.It, can according to the outermost hanging point of each four hanging points in two sides by formula (3)
Determine outermost circular arc, the overall length of projection over the ground of uphill, downhill position outermost arc is the distance l that lightning leader may be hit.
L=lr+ll (5)
L in formula (5)rAnd llThe respectively outermost circular projection of shaft tower descending position and upward slope position.
Risk of shielding failure P (I) is as shown in formula (8).
Claims (1)
1. phase conductor back flash-over rate calculation method on a kind of ultra high-tension transmission line staggered tower upward slope position, which is characterized in that including
Following steps:
Step 1: basic electric geometry method is established according to staggered tower schematic diagram；The staggered tower schematic diagram are as follows: it is θ that shaft tower, which is located at slope angle,
Ground, be upward slope position on the left of shaft tower, upward slope position is close compared with descending position from the ground, and M, E, K, L point are respectively that upward slope position lightning conducter is hung
Point, upper phase conductor hanging point, middle phase conductor hanging point, lower phase conductor hanging point；It is descending position on the right side of shaft tower, landform is open compared with upward slope position,
D, Q, P, R point are respectively descending position lightning conducter hanging point, upper phase conductor hanging point, middle phase conductor hanging point, lower phase conductor hanging point；
The basic electric geometry method established are as follows:
rc=10I0.65 (1)
Assuming that lightning leader hitting away from equal to lightning conducter and conducting wire, it may be assumed that
rc=rs (3)
rc、rs、rgRespectively thunder and lightning hitting away from unit m to conducting wire, lightning conducter and the earth；Arc sag hc,avIt is single for conducting wire average height
Position m；I is lightning current, unit kA；
hc,av=hd-2/3Sd (4)
H in formula (4)dHeight for conducting wire hitch point apart from ground, unit m；SdFor conducting wire sag, unit m；
Step 2: being based on electric geometry method, E point left and right side shielding risk is modeled and analyzed respectively, comprising:
Step 2.1: calculating left side exposure arc projection
It establishes left side electric geometry method figure: being with upward slope position lightning conducter hanging point M, upper phase conductor hanging point E, middle phase conductor hanging point K
The center of circle, respectively with rs、rc、rcIt launches an attack for radius structure away from circle, corresponding circle and the center of circle are indicated with same symbol；Earth-wire protection justifies M
Hitting the intersection point away from circle E with upper phase conductor is F, and it is J that upper phase conductor, which hits and hits the intersection point away from circle K away from circle E and middle phase conductor, and A point is to keep away
Thunder line protects the protection arc and shaft tower central axes intersection point of circle M, and point N1 hits for upper or middle phase conductor and hits away from circle and the earth away from straight line
Intersection point；
Situation 1: greatly hitting away from sufficiently large, greatly hits higher away from straight line, hands over earth-wire protection circle M in N1, point N1 highest, then bigly
It hits and shields entirely upper phase conductor away from straight line and hit away from circle E, exposure arc projection a length of 0；
Situation 2: greatly hitting to hit away from straight line and upper phase conductor and meet at N1 away from circle E arc, then upper phase conductor, which is hit, is greatly hitting away from circle E away from straight
Part on line, except earth-wire protection circle M becomes exposure arc, and exposure arc starting point is earth-wire protection circle M and upper phase conductor
The intersection point F away from circle E is hit, terminal is greatly to hit to hit the intersection point N1 away from circle E away from straight line and upper phase conductor；Exposure arc projects a length of point F
With the absolute value of the difference of the abscissa of point N1, it is denoted as abs (xF-xN1)；
Situation 3: if middle phase conductor hit away from circle K and upper phase conductor hit away from circle E intersection point it is higher, exceed phase conductor hit away from justify E it is most left
Marginal point E1, but not high too greatly hit hits the intersection point N1 away from circle E away from straight line and upper phase conductor, and exposure arc starting point is earth-wire protection
Circle M and upper phase conductor hit the intersection point F away from circle E, and terminal is greatly to hit to hit the intersection point N1 away from circle E away from straight line and upper phase conductor；Exposure
Arc projects the absolute value of the difference abs (x of the abscissa of a length of point F and point N1F-xN1)；
Situation 4: middle phase conductor hit hit away from circle K and upper phase conductor it is higher away from circle E intersection point, it is high too greatly to hit away from straight line and upper phase conductor
It hits away from circle E intersection point N1, then exposes arc starting point for earth-wire protection circle M and upper phase conductor and hit the intersection point F away from circle E, terminal is middle phase
Conducting wire hits the intersection point J away from circle K and circle E；Exposure arc projects the absolute value of the difference abs (x of the abscissa of a length of point F and point JF-xJ)；
Situation 5: if upper phase conductor is hit away from the circle leftmost side E limit point E1, greatly hit hit away from straight line and upper phase conductor it is low away from E intersection point is justified
In circle E Far Left border point E1, and middle phase conductor hits lower away from circle K and circle E intersection point J, is greatly hit away from straight line shielding, at this time N1 point
Abscissa absolute value be less than E1 point abscissa absolute value, though exposure arc terminus is respectively F, N1, exposure arc projection is a length of
Absolute value of the difference abs (the x of the abscissa of point F and point E1F-xE1)；
Situation 6: it greatly hits and hits away from circle E intersection point away from straight line and upper phase conductor higher than circle E Far Left border point E1, exposure arc starting point is to keep away
Thunder line protects circle M and upper phase conductor to hit the intersection point F away from circle E, and terminal hits for the earth and hits the intersection point away from circle E away from straight line and upper phase conductor
N1；Exposure arc projects the absolute value of the difference abs (x of the abscissa of a length of point F and point N1F-xN1)；
Situation 7: greatly hit away from straight line and earth-wire protection circle M intersection point N1 be higher than circle M and upper phase conductor hit away from circle E intersection point F, i.e., on
Phase conductor hit away from circle E all greatly hit hit away from straight line and lightning conducter away from circle M protection scope within, N1 higher than earth-wire protection justify
M Far Left border point M1, conducting wire is hit not to be exposed away from circle, exposure arc projection a length of 0；
Situation 8: greatly hit away from straight line and earth-wire protection circle M intersection point N1 be higher than circle M and upper phase conductor hit away from circle E intersection point F, i.e., on
Phase conductor hit away from circle E all greatly hit hit away from straight line and lightning conducter away from circle M protection scope within, N1 lower than earth-wire protection justify
M Far Left border point M1, conducting wire is hit not to be exposed away from circle, exposure arc projection a length of 0；
Situation 9: it greatly hits and is hit with upper phase conductor away from circle E intersection point F, upper phase away from straight line and earth-wire protection circle M intersection point N1 lower than circle M
Conducting wire, which is hit, has exposed arc away from circle E, and F is lower than the earth-wire protection circle leftmost side M limit point M1 at this time, though therefore exposure arc terminus difference
For F, N1, but exposure arc projects the absolute value of the difference abs (x of the abscissa of a length of point M1 and point N1M1-xN1)；
Situation 10: it greatly hits and hits away from circle K intersection point N1 away from straight line and middle phase conductor lower than circle K and circle E intersection point J, upper phase conductor exposure
Arc terminus is respectively F, J, and F projects a length of point M1's and point J lower than the earth-wire protection circle leftmost side M limit point M1, exposure arc
Absolute value of the difference abs (the x of abscissaM1-xJ)；
Situation 11: it is hit lower than upper phase conductor away from circle leftmost side limit if middle phase conductor hits to hit away from circle K and upper phase conductor away from circle E intersection point
When point E1, the circular arc intersection point N1 away from straight line and circle E is greatly hit compared with the height of E1: when N1 is higher than E1, upper phase conductor exposure
Arc starting point is earth-wire protection circle M and upper phase conductor hits the intersection point F away from circle E, but F is lower than earth-wire protection circle leftmost side limit point
M1；Terminal is that the earth hits the intersection point N1 away from straight line and circle E；Exposure arc projects the absolute of the difference of the abscissa of a length of point M1 and point N1
Value abs (xM1-xN1)；
Situation 12: when greatly hit away from straight line and circle K circular arc intersection point N1 lower than upper phase conductor hit away from circle the leftmost side limit point E1 when,
Upper phase conductor exposure arc starting point is earth-wire protection circle M and upper phase conductor hits the intersection point F away from circle E, but F is lower than earth-wire protection circle
Leftmost side limit point M1；Terminal is greatly to hit to hit the intersection point J away from round E away from straight line and upper phase conductor, but J is hit lower than upper phase conductor
Away from circle leftmost side limit point E1；Exposure arc projects the absolute value of the difference abs (x of the abscissa of a length of point M1 and point E1M1-xE1)；When
N1 ratio J high but when being still below E1, exposure arc projection length is constant；
Step 2.2: calculate right side exposure arc projection, including upward slope circle of position arc intersect with descending circle of position arc, upward slope circle of position arc and
The intersection of descending circle of position arc
Upward slope circle of position arc does not intersect with descending circle of position arc
Situation 13: it greatly hits away from straight line and earth-wire protection circle M intersection point N2 is higher than earth-wire protection circle M and upper phase conductor is hit away from circle
The intersection point H of E, and H is higher than upper phase conductor and hits away from circle E rightmost border point E2, i.e., upper phase conductor, which is hit, to be shielded away from circle by lightning conducter and the earth
It covers, does not expose arc；
Situation 14: greatly hitting and hit in upper phase conductor away from circle E away from straight line and circular arc intersection point N2, lower than earth-wire protection circle M with it is upper
Phase conductor hits intersection point H, H away from circle E and is higher than earth-wire protection circle rightmost side limit point M2, and exposure arc starting point is earth-wire protection circle
M and upper phase conductor hit the intersection point H away from circle E, and exposure arc terminal is greatly to hit to hit away from circle E intersection point N2, cruelly away from straight line and upper phase conductor
Dew arc projects the absolute value of the difference abs (x of the abscissa of a length of point H and point N2H-xN2)；
Situation 15: exposure arc starting point is earth-wire protection circle M and upper phase conductor hits the intersection point H away from circle E, and exposure arc terminal is the earth
It hits and hits away from straight line and upper phase conductor away from circle E intersection point N2, exposure arc projects the absolute value of the difference of the abscissa of a length of point H and point N2
abs(xH-xN2)；
Situation 16: it is hit in middle phase conductor away from circle K away from straight line and circular arc intersection point N2 lower than T, N2 if the earth is hit, exposes arc starting point
The intersection point H away from circle E is hit for earth-wire protection circle M and upper phase conductor, exposure arc terminal is that middle phase conductor is hit away from circle K and upper phase conductor
It hits away from circle E intersection point T, exposure arc projects the absolute value of the difference abs (x of the abscissa of a length of point H and point TH-xT)；
Situation 17: when upper phase conductor, which is hit, greatly hits the circular arc intersection point N2 high away from straight line and circle E away from circle E rightmost border point E2 ratio,
Exposure arc starting point be earth-wire protection circle M and upper phase conductor hit away from circle E intersection point H, exposure arc terminal be the earth hit away from straight line with
Circular arc intersection point N2, but N2 is hit lower than upper phase conductor away from circle E rightmost border point E2, and exposure arc projects the horizontal seat of a length of point H Yu point E2
Absolute value of the difference abs (the x of markH-xE2)；
Situation 18: when greatly hit be higher than upper phase conductor away from straight line and circular arc intersection point N2 and hit away from circle E rightmost border point E2 when, exposure arc
Starting point is earth-wire protection circle M and upper phase conductor hits the intersection point H away from round E, and exposure arc terminal is that the earth is hit away from straight line and circular arc friendship
Point N2, exposure arc project the absolute value of the difference abs (x of the abscissa of a length of point H and point E2H-xN2)；
Situation 19: greatly hitting and meet at N2 away from straight line and earth-wire protection circle M, is higher than earth-wire protection circle M rightmost border point M2, on
Phase conductor is hit away from circle without exposure arc；
Situation 20: greatly hitting and meet at N2 away from straight line and earth-wire protection circle M, though lower than earth-wire protection circle M rightmost border point M2,
But it is still higher than earth-wire protection circle M and upper phase conductor hits the intersection point H away from circle E, upper phase conductor is hit away from circle without exposure arc；
Situation 21: greatly hitting to hit away from straight line and upper phase conductor and meet at N2 away from circle E, and N2 is lower than earth-wire protection circle M and upper phase conductor
The intersection point H away from circle E is hit, but is hit higher than middle phase conductor and hits the intersection point T away from circle E away from circle K and upper phase conductor, upper phase conductor is hit away from circle E
Exposure arc starting point hits the intersection point H away from circle E for earth-wire protection circle M and upper phase conductor, and terminal is greatly to hit to lead away from straight line and upper phase
Line hit away from circle E intersection point N2, but earth-wire protection circle M rightmost border point M2 abscissa absolute value be greater than earth-wire protection circle M with
Upper phase conductor hits the intersection point H abscissa absolute value away from circle E, and exposure arc projects the absolute of the difference of the abscissa of a length of point M2 and point N2
Value abs (xM2-xN2)；
Situation 22: greatly hitting to hit away from straight line and middle phase conductor and meet at N2 away from circle K, and it is to keep away that upper phase conductor, which is hit away from circle E exposure arc starting point,
Thunder line protects circle M and upper phase conductor to hit the intersection point H away from circle E, and terminal hits for middle phase conductor and hits away from circle K and upper phase conductor away from circle E's
Intersection point T, but earth-wire protection circle M rightmost border point M2 abscissa absolute value be greater than earth-wire protection circle M and upper phase conductor hit away from
The intersection point H abscissa absolute value of circle E, exposure arc project the absolute value of the difference abs (x of the abscissa of a length of point M2 and point TM2-xT)；
Situation 23: N2 is met at away from circle E when greatly hitting to hit away from straight line and upper phase conductor, N2 is higher than upper phase conductor and hits away from circle E rightmost
Border point E2；It is that earth-wire protection circle M and upper phase conductor hit the intersection point H away from circle E, terminal that upper phase conductor, which is hit away from circle E exposure arc starting point,
The intersection point N2 away from circle E is hit away from straight line and upper phase conductor greatly to hit, but earth-wire protection circle M rightmost border point M2 abscissa is absolute
Value is greater than earth-wire protection circle M and upper phase conductor hits the abscissa absolute value of the intersection point H away from circle E, and exposure arc projects a length of point M2
With the absolute value of the difference abs (x of the abscissa of point N2M2-xN2)；
Situation 24: greatly hitting to hit away from straight line and upper phase conductor and meet at N2 away from circle E, and N2 is hit lower than upper phase conductor away from circle E rightmost border
Point E2；It is earth-wire protection circle M away from circle E exposure arc starting point that upper phase conductor, which is hit, and upper phase conductor hits the intersection point H away from circle E, but lightning-arrest
Line protects round M rightmost border point M2 abscissa absolute value to be greater than earth-wire protection circle M and hits the intersection point H cross away from circle E with upper phase conductor
Coordinate absolute value；Terminal is that the earth hits and hits the intersection point N2 away from circle E away from straight line and upper phase conductor, but upper phase conductor hit it is most right away from circle E
Marginal point E2 abscissa absolute value, which is greater than greatly to hit, hits the intersection point N2 away from circle E away from straight line and upper phase conductor, and exposure arc projection is a length of
Absolute value of the difference abs (the x of the abscissa of point M2 and point E2M2-xE2)；
Upward slope circle of position arc intersects with descending circle of position arc
Situation 25:B point is the intersection point of upward slope position earth-wire protection circle M and descending position earth-wire protection circle D, is gone up a slope in the case
Phase conductor is hit away from circle E by upward slope position earth-wire protection circle M and the circle D protection of descending position earth-wire protection on position, does not expose arc, cruelly
Reveal arc projection a length of 0；
Situation 26: greatly hitting the circular arc intersection point N2 away from straight line and circle D, hits lower than phase conductor on upward slope position and keeps away away from circle E with descending position
Thunder line hits the intersection points B away from circle D；Upward slope position earth-wire protection circle M rightmost border point M2 be higher than upward slope position earth-wire protection circle M with it is upper
The upper phase conductor in slope position hits the intersection point H away from circle E, and exposure arc starting point is that upward slope position earth-wire protection circle M is hit with phase conductor on upward slope position
Away from circle E intersection point H, but upward slope position earth-wire protection circle M rightmost border point M2 abscissa be greater than upward slope position earth-wire protection circle M with
Phase conductor hits the intersection point H abscissa away from circle E on upward slope position；Exposure arc terminal is that phase conductor is hit away from circle E and descending position on upward slope position
Lightning conducter hits the intersection points B away from circle D, and exposure arc projects the absolute value of the difference abs (x of the abscissa of a length of point M2 and point BM2-xB)；
Situation 27: exposure arc terminal N2 abscissa is greater than the abscissa of exposure arc starting point M2, that is, the projection for exposing arc is in situation
What the positive direction under 27 considerations extended, therefore exposure arc projects the absolute value of the difference abs (x of the abscissa of a length of point M2 and point BM2-
xB)；
Situation 28: exposure arc terminal N2 abscissa is less than exposure arc starting point M2 abscissa, that is, exposure arc projection length does not have
Positive direction in the present case extends, in other words by the upward slope position earth-wire protection circle where starting point M2 from thunder and lightning attacking direction
Shielding calculates when exposure arc projects long and takes 0；
Situation 29: it greatly hits and is hit higher than phase conductor on upward slope position away from circle E rightmost border point E2, exposure away from straight line and circular arc intersection point N2
Arc starting point is that phase conductor hits the intersection point H away from circle E, but upward slope position earth-wire protection on upward slope position earth-wire protection circle M and upward slope position
Circle M rightmost border point M2 abscissa is greater than phase conductor on upward slope position earth-wire protection circle M and upward slope position and hits the intersection point H's away from circle E
Abscissa；Exposure arc terminal is that the earth is hit away from straight line and circular arc intersection point N2 abscissa；Exposure arc projects a length of point M2's and point N2
Absolute value of the difference abs (the x of abscissaM2-xN2)；
Situation 30: it greatly hits and is hit lower than phase conductor on upward slope position away from circle E rightmost border point E2, exposure away from straight line and circular arc intersection point N2
Arc starting point is that phase conductor hits the intersection point H away from circle E, but upward slope position earth-wire protection on upward slope position earth-wire protection circle M and upward slope position
Circle M rightmost border point M2 abscissa is greater than phase conductor on upward slope position earth-wire protection circle M and upward slope position and hits the intersection point H's away from circle E
Abscissa；Exposure arc terminal is that the earth is hit away from straight line and circular arc intersection point N2, but phase conductor is hit away from circle E rightmost border point on upward slope position
E2 abscissa is greater than the earth and hits away from straight line and circular arc intersection point N2；Exposure arc projects the exhausted of the difference of the abscissa of a length of point M2 and point E2
To value abs (xM2-xE2)；
Situation 31: earth-wire protection circle M rightmost border point M2 in upward slope position is lower than upward slope position earth-wire protection circle M and phase on upward slope position
Conducting wire hits the intersection point H away from round E, and phase conductor, which is hit, on upward slope position hits the intersection points B away from circle D higher than upward slope away from circle E and descending position lightning conducter
Phase conductor is hit away from circle E rightmost border point E2 on position, greatly hit away from straight line and circular arc intersection point N2 be higher than phase conductor on upward slope position hit away from
Circle E and descending position lightning conducter hit the intersection points B away from circle D but lower than H, and exposure arc starting point is upward slope position earth-wire protection circle M and goes up a slope
Phase conductor hits the intersection point H away from circle E on position, and terminal is that the earth is hit away from straight line and circular arc intersection point N2, and exposure arc projects a length of point H and point
Absolute value of the difference abs (the x of the abscissa of N2H-xN2)；
Situation 32: earth-wire protection circle M rightmost border point M2 in upward slope position is lower than upward slope position earth-wire protection circle M and phase on upward slope position
Conducting wire hits the intersection point H away from round E, and phase conductor, which is hit, on upward slope position hits the intersection points B away from circle D higher than upward slope away from circle E and descending position lightning conducter
Phase conductor is hit away from circle E rightmost border point E2 on position, is greatly hit away from straight line and circular arc intersection point N2 on descending position earth-wire protection circle,
Exposure arc starting point is that phase conductor hits the intersection point H away from circle E on upward slope position earth-wire protection circle M and upward slope position, and terminal is on upward slope position
Phase conductor, which is hit, hits the intersection points B away from circle D away from circle E and descending position lightning conducter, and exposure arc projects the difference of the abscissa of a length of point H and point B
Absolute value abs (xH-xB)；
Situation 33: earth-wire protection circle M rightmost border point M2 in upward slope position is lower than upward slope position earth-wire protection circle M and phase on upward slope position
Conducting wire hits the intersection point H away from round E, and phase conductor, which is hit, on upward slope position hits the intersection points B away from circle D lower than upward slope away from circle E and descending position lightning conducter
Phase conductor is hit away from circle E rightmost border point E2 on position, greatly hit away from straight line and circular arc intersection point N2 be higher than phase conductor on upward slope position hit away from
Circle E rightmost border point E2, exposure arc starting point are that phase conductor hits the intersection point away from circle E on upward slope position earth-wire protection circle M and upward slope position
H, terminal are that the earth is hit away from straight line and circular arc intersection point N2, and exposure arc projects the absolute value of the difference of the abscissa of a length of point H and point N2
abs(xH-xN2)；
Situation 34: earth-wire protection circle M rightmost border point M2 in upward slope position is lower than upward slope position earth-wire protection circle M and phase on upward slope position
Conducting wire hits the intersection point H away from round E, and phase conductor, which is hit, on upward slope position hits the intersection points B away from circle D lower than upward slope away from circle E and descending position lightning conducter
Phase conductor is hit away from circle E rightmost border point E2 on position, greatly hit away from straight line and circular arc intersection point N2 lower than phase conductor on upward slope position hit away from
Circle E rightmost border point E2 but be higher than upward slope position on phase conductor hit away from circle E and descending position lightning conducter hit away from circle D intersection points B, exposure arc
Starting point be upward slope position earth-wire protection circle M and upward slope position on phase conductor hit away from circle E intersection point H, terminal be the earth hit away from straight line with
Circular arc intersection point N2, but phase conductor hits to be greater than the earth away from circle E rightmost border point E2 abscissa and hit and hands over away from straight line and circular arc on upward slope position
Point N2 abscissa, exposure arc project the absolute value of the difference abs (x of the abscissa of a length of point H and point E2H-xE2)；
Step 3: calculating risk of shielding failure
According to shaft tower lightning conducter, the coordinate of conducting wire hanging point M, E, K, D, calculate separately on upward slope position phase conductor E point in left side and
The exposed range on right side projects long lleftAnd lright；By formula (3), determined according to the outermost hanging point of each four hanging points in two sides outermost
Side circular arc, the overall length of projection over the ground of uphill, downhill position outermost arc are the distance l that lightning leader may be hit；
L=lr+ll (5)
L in formula (5)rAnd llThe respectively outermost circular projection head of shaft tower descending position and upward slope position；
Risk of shielding failure P (I) is as shown in formula (8)；
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