CN105653760B - Consider the route distribution parameter Three-dimensional CAD design method of conductor space arrangement - Google Patents
Consider the route distribution parameter Three-dimensional CAD design method of conductor space arrangement Download PDFInfo
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/30—Circuit design
- G06F30/36—Circuit design at the analogue level
- G06F30/367—Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
Abstract
The invention discloses a kind of route distribution parameter Three-dimensional CAD design methods of consideration conductor space arrangement, this method comprehensively considers at an angle to each other, spanning height when conductor space is arranged, away from influence factors such as virtual point of intersection distances, the distribution parameter threedimensional model universal calculation equation for having derived scissors crossing transmission pressure constructs the general zero-sequence current voltage equation to intercouple.Multiple groups scheme simulation result shows to consider that the line parameter circuit value three-dimensional universal computer model of conductor space arrangement has validity and practicability, and can be further generalized in the parameter calculating of four loop lines or even more loop lines.
Description
Technical field
The present invention relates to a kind of route distribution parameter three-dimensional universal computer model design methods of consideration conductor space arrangement.
Background technique
Transmission line parameter is the basis of electric system items simulation calculation.With the development of economy, corridor land used is dynamic
Removal expense is increasingly expensive, and the continuous increase of transmission line capability, engineering uses more and more parallel lines on same tower multi circuit transmission lines in practice,
And the scene of unavoidable scissors crossing transmission line of electricity is more and more.In addition, when super, UHV transmission line designs, it can
The case where capable of encountering across lower voltage grade power transmission sequence.The two dimensional models such as parallel double loop and double-circuit lines on the same pole
Parameter calculates and application is highly developed, space crossed to belong to not parallel conductor structure, classical Two dimensional Distribution across conducting wire
Parameter computation model is no longer applicable in, and need to rethink the coupling effect between two loop lines, is established threedimensional model and is calculated solution.
Original separate lines parameter has occurred in the electromagnetic coupling of scissors crossing transmission line of electricity and electrostatic induction under new scene
Change, the accuracy and precision of Load flow calculation, relay protection, fault localization is directly related to, to have to engineering practice important
Meaning.
Transmission line of electricity, which flows through electric current, can generate heat, be mainly reflected in the resistance of route, due to the presence of ground resistance, meeting
Make not collinear generation mutual resistance effect.Alternating current is flowed through on route can generate the magnetic field of alternation around conducting wire, thus
Potential is generated on conducting wire itself and adjacent wires, route is made to generate self-inductance and mutual inductance effect.In addition, route can generate electricity
, the charge inducing on the earth and adjacent lines can also ionize the air around a part, to generate between the earth electric over the ground
Appearance, Leaked Current of Line to Ground lead effect, generate mutual capacitance and transconductance effect with route around.
There are two the principal elements for influencing line inductance and capacitor, first is that route between the earth and between route at a distance from, two
It is route radius itself.When being closer between two back transmission lines, between any two phase conductor on two loop line roads electromagnetic coupling and
Electrostatic induction is obvious.
For scissors crossing transmission pressure, in addition to wire spacing and route radius, also need to consider that projection is put down to same
Face it is at an angle to each other.In addition to this, route is remoter from virtual point of intersection, and wire spacing is bigger, therefore changes along capacitance size, no
It is constant again.
Certain research is carried out in existing method to uneven transmission line of electricity, comprising:
1, be deduced a kind of parameter model of special not parallel transmission line of electricity, by infinitesimal transmission line of electricity it is equivalent at
Parallel circuit calculates the distribution parameter of two conducting wires based on the original physical meaning of distributed parameter line.But two in model
Root conducting wire be it is mutually angled in the same plane, belong to two dimensional model, increase along the distance between two conducting wires, no longer
Uniformly, when θ is 0, route is converted into transmission lines in parallel.
2, it is directed to ultra-high-tension power transmission line and scissors crossing transmission line of electricity, is based on Analogue charge method and Biot-savart law,
The 3 D electromagnetic field universal computer model of transmission pressure is established according to catenary equation.The model is to scissors crossing transmission line of electricity
This new scene has carried out pre-test, is the important evidence of determining route minimum distance away the ground and delimitation line corridor width, but simultaneously
Influence of the space layout to line parameter circuit value is not studied.
Summary of the invention
Based on above-mentioned problem, the present invention provides a kind of route distribution parameter of consideration conductor space arrangement is three-dimensional
Computation model design method, the computation model comprehensively consider at an angle to each other, spanning height when conductor space is arranged, away from imaginary intersection
The influence factors such as point distance, construct the general zero-sequence current voltage equation to intercouple.Multiple groups side is emulated using simulink
Case compares, and demonstrates the correctness of the model.
To achieve the above object, concrete scheme of the invention is as follows:
Consider the route distribution parameter Three-dimensional CAD design method of conductor space arrangement, characterized in that including following
Step:
(1) model of power transmission system of scissors crossing is established, the model of power transmission system of the scissors crossing includes: lower section one time
Line three-phase line 1,2,3, one loop line three-phase line 4,5,6 of top；
In the model of power transmission system of the scissors crossing, extremely by the single loop line vertical projection above scissors crossing transmission line of electricity
When the single loop line of lower section, angle o degree between the two-phase of different loop lines；
(2) inherent parameters of scissors crossing transmission line of electricity are acquired, comprising: wire radius, lower section single loop line are apart from ground height
Spend h1, vertical range Δ H between scissors crossing transmission line of electricity θ at an angle to each other and scissors crossing transmission line of electricity；
(3) according to collected route inherent parameters, calculate separately self-impedance coefficient, with the mutual impedance coefficient between loop line with
And the mutual impedance coefficient between different loop lines, and obtain each sequence impedance parameter in scissors crossing transmission line of electricity；
(4) the self-potential coefficient of any one conducting wire is calculated；Consider the earth to conducting wire surrounding electric field using image charge method
The influence of distribution calculates corresponding thereto in the distance between the image conductor on ground according to the radius of conducting wire, conducting wire and appoints with loop line
It anticipates the mutual coefficient of potential of two conducting wires；
(5) assume that MN and PQ is the aerial condutor of different loop line roads, ST and PQ are the adjacent wires with loop line road；Make line
It is opposite with point O' on route MN that road MN the projection M'N' in PQ plane, route M'N', which give point O', point O with route PQ phase,
The point answered；If the distance of route PQ upper 1: 1 to point O is x, the mutual coefficient of potential along any two conducting wires is calculated by variable of x；
(6) scissors crossing route is being converted to just according to phase sequence according to the self-potential coefficient of calculating and the mutual coefficient of potential
Zero sequence mutual capacitance between sequence, negative phase-sequence and zero sequence capacitor and scissors crossing route；
(7) according to the line parameter circuit value of above-mentioned calculating, the general sequence currents voltage equation of scissors crossing route is constructed；Specifically
Include:
When scissors crossing route passes through positive sequence or negative-sequence current, current-voltage equation is uniform transmission line equation；
When scissors crossing route passes through zero-sequence current, according at the x position of distance line end residual voltage increment with
The expression formula of zero-sequence current increment constructs zero-sequence current voltage equation group.
In the step (3),
Each phase conductor is parallel to each other in the same circuit, between arbitrary two conducting wires I, J same loop line, mutual impedance coefficient tool
Body are as follows:
Wherein, RgFor the unit length substitutional resistance of ground return circuit,It is deep for the equivalence of ground medium value conducting wire d
Degree, rsI、rsdThe equivalence radius of respectively conducting wire I and equivalent ground wire d, DIdFor the equivalent distance of conducting wire I and equivalent earthed return d；DIJ
For the distance between two conducting wires；
Mutual impedance coefficient between different loop lines specifically:
Wherein, Z14For the mutual impedance between 4 liang of phase conductors of loop line 1 and loop line；Z15~Z36Meaning also be respectively different loop lines
Mutual impedance between two phase conductors.
In the step (3), the impedance parameter of each loop line in transmission line of electricity specifically:
Single loop line positive sequence impedance parameter Z1=Zs-Zm, single loop line negative sequence impedance parameter Z2=Zs-Zm, zero-sequence impedance parameter Z0
=Zs+2Zm；
Zero sequence mutual impedance Z is only existed between two loop lines0m=3Zm'；
Wherein, ZsFor the average self-impedance coefficient of each single loop line；ZmFor the average mutual resistance between each phase conductor in same loop line
Anti- coefficient；Zm'Zero sequence mutual impedance coefficient between different loop lines.
In the step (4), the self-potential coefficient of any one conducting wire specifically:
Unit is km/F；
Wherein, HII'It is conducting wire I at a distance from its image conductor, rIFor the radius of conducting wire i.
In the step (4), with the mutual coefficient of potential of any two conducting wires I and J of loop line specifically:
Unit is km/F；
H in formulaIJ'The distance between the image conductor of conducting wire I and conducting wire J, DIJFor the distance between conducting wire I and conducting wire J.
In the step (5), it is assumed that MN and PQ is two conducting wires of different loop line roads, and ST and PQ are lower loop line road
Adjacent wires, at a distance of being s, conducting wire is each parallel to ground；Point 1 is away from O' point x on route PQ, and point 1 is with underground mirror point 1' at a distance of H1；
Point 2 is away from O point x on route MN, and point 2 is with underground mirror point 2' at a distance of H2；Point 3 is away from corresponding with point O' on route PQ on route ST
Point O " x, point 3 and its underground mirror point 3' is at a distance of H1；MN above the PQ route at Δ H, M'N' be projected under MN vertical direction, and
It is coplanar with PQ, meet at virtual point of intersection O', θ at an angle to each other；
There are following geometrical relationships between route PQ and MN:
H2-H1=2 Δ H
D1'2=2xsin (θ/2)
There are following geometrical relationships between route ST and MN:
Wherein, D12For point 1 to the distance of point 2；D1'2The distance of point 1, H are arrived for the underground mirror point 2 ' of point 212'For point 1
The distance of underground mirror image point-to-point 2, D2'3The distance of point 3, H are arrived for the underground mirror point 2 ' of point 22'3For the underground mirror point of point 3
Distance, D to point 223For point 2 to the distance of point 3；
Above-mentioned parameter is brought into respectively public with the calculating of the mutual coefficient of potential of any two conducting wires i and j of loop line in step (4)
Formula can acquire the mutual coefficient of potential between any both threads of scissors crossing transmission line of electricity.
In the step (6), in two loop lines, positive sequence, negative phase-sequence and the zero sequence capacitor of scissors crossing transmission line of electricity specifically:
Single loop line positive sequence capacitorAnother single loop line positive sequence capacitor
Single loop line negative phase-sequence capacitorAnother single loop line negative phase-sequence capacitor
Single loop line zero sequence capacitorAnother single loop line zero sequence capacitor
Zero sequence mutual capacitance between scissors crossing route are as follows:
Wherein, Ps1、Ps2The average self-potential coefficient of every phase conductor respectively in two loop line of scissors crossing transmission line of electricity；Pm1、
Pm2Respectively with the average mutual coefficient of potential between conducting wire each in loop line；Pm'(x) the average mutual current potential system between different loop lines
Number.
In the step (7), when scissors crossing route passes through zero-sequence current, the zero-sequence current voltage equation group of construction has
Body are as follows:
Positive sequence or negative sequence voltage electric current at terminal voltage electric current xThere is following relationship:
Its general solution are as follows:
Wherein,For line characteristic impedance,For line propagation coefficient, i=1,2 represent positive sequence or negative
Sequence electric parameter；For terminal voltage electric current positive sequence or negative phase-sequence amount.
In the step (7), to scissors crossing power transmission line zero-sequence network, the voltage-current relationship of the first loop line:
The voltage-current relationship of second loop line:
Wherein,Respectively scissors crossing route is lower electric away from the zero sequence at the x of end with higher loop line
Pressure, electric current；zmFor zero sequence mutual impedance, ymIt (x) is zero sequence transadmittance.
Beneficial effects of the present invention:
The present invention comprehensively considers at an angle to each other, spanning height when conductor space is arranged, influences away from virtual point of intersection distance etc.
Factor has derived the distribution parameter threedimensional model universal calculation equation of scissors crossing transmission pressure, construct intercouple it is logical
With zero-sequence current voltage equation.Multiple groups scheme simulation result shows to consider the three-dimensional general meter of the line parameter circuit value of conductor space arrangement
Calculating model has validity and practicability, and can be further generalized in the parameter calculating of four loop lines or even more loop lines.
Detailed description of the invention
Fig. 1 is scissors crossing transmission pressure parameter Three-dimensional CAD；
Fig. 2 is scissors crossing transmission pressure space layout top view；
Fig. 3 is the mutual impedance coefficient between two conducting wires of scissors crossing；
Fig. 4 is magnetic flux schematic diagram；
Fig. 5 is overhead transmission line capacitance parameter figure；
Fig. 6 (a) is the space diagram one of two transmission pressures of scissors crossing；
Fig. 6 (b) is the space diagram two of two transmission pressures of scissors crossing；
Fig. 7 is the zero sequence distributed parameter model schematic diagram to intercouple；
Fig. 8 (a) is the zero sequence capacitor of the higher loop line of scissors crossing route with height change curve；
Fig. 8 (b) is the positive-negative sequence capacitor of the higher loop line of scissors crossing route with height change curve；
Fig. 9 (a) be different angle when zero-sequence mutual inductance and scissors crossing transmission line of electricity between angle relationship；
Fig. 9 (b) be 30 degree when zero-sequence mutual inductance and scissors crossing transmission line of electricity between angle relationship；
The relationship of Figure 10 (a) vertical height between zero-sequence mutual inductance and scissors crossing transmission line of electricity；
Figure 10 (b) is the relationship of height vertical height between zero-sequence mutual inductance and scissors crossing transmission line of electricity when being 10m；
Figure 11 (a) is the relationship that zero sequence mutual tolerance intersects Δ H between transmission line of electricity with leap；
Figure 11 (b) is the relationship that zero sequence mutual tolerance intersects θ between transmission line of electricity with leap；
Figure 11 (c) is the relationship that zero sequence mutual tolerance intersects x between transmission line of electricity with leap；
Figure 12 (a) is single loop line double ended system simulation model when any loop line breaks down；
Figure 12 (b) is single loop line double ended system simulation model when operating normally；
Figure 13 is change curve along Y0m；
Figure 14 is to be mutually voltage and current amplitude, phase angle change curve along 30 ° of scissors crossing route；
Figure 15 is not consider voltage and current amplitude, phase angle change curve along two single loop lines of coupling.
Specific embodiment:
The present invention is described in detail with reference to the accompanying drawing:
The invention discloses a kind of route distribution parameter Three-dimensional CAD design method of consideration conductor space arrangement, packets
Include following steps:
(1) model of power transmission system of scissors crossing is established, to carry out clearly calculation specifications, marks the transmission of electricity of scissors crossing
Route is as follows, and one loop line a, b, c phase of lower section is 1,2,3, and one loop line three-phase label of top is once 4,5,6；
In the model of power transmission system of the scissors crossing, extremely by the single loop line vertical projection above scissors crossing transmission line of electricity
When the single loop line of lower section, angle o degree between the two-phase of different loop lines；
(2) inherent parameters of scissors crossing transmission line of electricity are acquired, comprising: wire radius, lower section single loop line are apart from ground height
Spend h1, vertical range Δ H between scissors crossing transmission line of electricity θ at an angle to each other and scissors crossing transmission line of electricity；
(3) according to collected route inherent parameters, calculate separately self-impedance coefficient, with the mutual impedance coefficient between loop line with
And the mutual impedance coefficient between different loop lines, and obtain each sequence impedance parameter in scissors crossing transmission line of electricity；
(4) the self-potential coefficient of any one conducting wire is calculated；Consider the earth to conducting wire surrounding electric field using image charge method
The influence of distribution calculates corresponding thereto in the distance between the image conductor on ground according to the radius of conducting wire, conducting wire and appoints with loop line
It anticipates the mutual coefficient of potential of two conducting wires；
(5) assume that MN and PQ is the aerial condutor of different loop line roads, ST and PQ are the adjacent wires with loop line road；Make line
It is opposite with point O' on route MN that road MN the projection M'N' in PQ plane, route M'N', which give point O', point O with route PQ phase,
The point answered；If the distance of route MN upper 1: 2 to point O is x, the mutual coefficient of potential along any two conducting wires is calculated by variable of x；
(6) scissors crossing route is being converted to just according to phase sequence according to the self-potential coefficient of calculating and the mutual coefficient of potential
Zero sequence mutual capacitance between sequence, negative phase-sequence and zero sequence capacitor and scissors crossing route；
(7) according to the line parameter circuit value of above-mentioned calculating, the general sequence currents voltage equation of scissors crossing route is constructed；Specifically
Include:
When scissors crossing route passes through positive sequence or negative-sequence current, current-voltage equation is uniform transmission line equation；
When scissors crossing route passes through zero-sequence current, according at the x position of distance line end residual voltage increment with
The expression formula of zero-sequence current increment constructs zero-sequence current voltage equation group.
The above method is described in detail below.
1. conductor space arrangement influences theory deduction to line parameter circuit value.
Fig. 1, Fig. 2 are respectively scissors crossing transmission pressure parameter Three-dimensional CAD and space layout top view.It will intersect
When single loop line vertical projection to lower section single loop line above span transmission line, angle o degree between the two-phase of different loop lines.When two
Single loop line at a distance of it is closer when, it will generate electromagnetic coupling and electrostatic induction, prevent the parameter of scissors crossing transmission pressure from by
It is calculated according to mutually independent single loop line impedance computation method.This section will derive respectively from impedance parameter and capacitance parameter considers conductor
The route distribution parameter three-dimensional universal computer model of space layout.
1.1 impedance parameters calculate
(1) self-impedance coefficient and between circuit mutual impedance coefficient calculate
The general type of any conducting wire self-impedance coefficient is writeable are as follows:
R in formulaii=Ri+Rg。rsiFor the resistance per unit length of conducting wire i, Ω/km；
RgFor the unit length substitutional resistance of ground return circuit, according to theory analysis: Rg=π2×10-4F=9.869 × 10- 4F takes R in the case where frequency f=50Hzg=0.05 Ω/km；
rsi、rsdFor the equivalence radius (being included in interior inductance) for being correspondingly conducting wire i and equivalent ground wire d, to nonferromagnetic material
Circular solids line, rs=0.779r, r are conducting wire real radius；
For the equivalent depth of ground medium value conducting wire d, byIt determines, wherein ρ is soil
Resistivity, Ω m, DidFor the equivalent distance of conducting wire i and equivalent earthed return d.
When using complete transposition and taking each phase conductor radius the same,
Average self-impedance formula is
The same circuit, each phase conductor are parallel to each other, to arbitrary two conducting wires i, j, the general formulae of mutual impedance coefficient are as follows:
DijFor the distance between two conducting wires.
Due to D12=D45,D13=D46,D23=D56,
Average mutual impedance coefficient between each phase conductor are as follows:
(2) mutual impedance coefficient calculates between different circuit
The mutual impedance coefficient of any two conducting wires first between research scissors crossing transmission line of electricity difference loop line.
As shown in figure 3, conducting wire aa ' and bb ' different surface beeline each other, by aa ', vertical projection and conducting wire bb ' meet at O ' downwards
Point, the angle o degree of the two.Two conducting wires will obtain the conducting wire parallel with conducting wire bb ' at a distance of Δ H, by conducting wire aa ' with angle, θ projection.
Known by Theory of Electromagnetic Field, in uniform magnetic field as shown in Figure 4, the magnetic flux across area A is φ=BAcos θ, and θ is
Angle between the direction and B of area A.A then N circle coil in magnetic field, if the magnetic flux that its each circle passes through is all identical,
It is then ψ=N φ by the magnetic linkage of the coil.
ZabAnd ZbbDifference in size has following two points:
First is that ZabIn compare ZbbThe resistance R of b conducting wire is lackedb；
Second is that ZabCompare ZbbFew a part of reactance, and this magnetic linkage of a part of reactance then between a conducting wire and b conducting wire is opposite
It answers.
If the impedance being made of this two parts is Zb'b, then have
Then, mutual impedance coefficient can be obtained according to above-mentioned analysis are as follows:
Therefore formula (2-5) is generalized to the mutual impedance coefficient Z that different circuit is located between each conducting wire of different location14、Z15、Z16
Deng, wherein each conductor spacing D between different circuit14、D24、D34、D15Etc. being Δ H.
When route complete transposition, the zero sequence mutual impedance coefficient between different loop lines is
To scissors crossing route, have in the case where complete transposition:
Wherein matrix in block form
To obtain each sequence impedance parameter of overhead transmission line, voltage, electric current are transformed into symmetrical components coordinate system, it can
:
U012=S-1ZabcSI012=Z012I012 (2-8)
Wherein, order impedance matrix Z012=S-1ZabcS.S is phase sequence transition matrix, specific as follows:
Sequence impedance parameter is obtained after bringing formula (2-8) expansion into matrix A and D, wherein single loop line positive sequence (or negative phase-sequence) impedance
Parameter Z1=Z2=Zs-Zm, zero-sequence impedance parameter Z0=Zs+2Zm。
It is as follows that symmetrical components decomposition is carried out to B and C:
That is zero sequence mutual impedance Z is only existed between two loop lines0m=3Zm'。
1.2 capacitance parameters calculate
When applying alternating voltage on power transmission line, even if route is non-loaded, also No leakage electric current, but still have charging electricity
Stream flowing, this is because parallel conducting wire is just like a centre using air as the two-plate of the capacitor of medium.Usual route
Apart from short, sectional area is small, and wire spacing is big, therefore capacitance very little.But (the length for high pressure long-distance transmission line
When more than 80km), the influence of capacitor dramatically increases, just must be in many occasions, such as during transient state process of electric power system calculates
The receiving of overhead transmission line is added in sequence net.
(1) self-potential coefficient and the mutual coefficient of potential calculate
Two aerial condutors a, b are illustrated in figure 5, are loaded with charge respectively on conducting wire(unit C/m).It adopts
Influence of the earth to conducting wire surrounding field distribution is considered with image charge method, the charge of conducting wire mirror image institute band is respectivelyUsing following hypothesis: ground is the equipotential surface of zero potential；Charge on conducting wire is evenly distributed, thus to leading
For electrostatic field outside line, it can be considered as concentrating on the axis of conducting wire；It is constant along the current potential of conducting wire；Conducting wire is away from ground
It is highly constant.
For self-potential coefficient, with PaaFor, PaaRefer to when having unit charge on conducting wire and other conducting wires do not have charge
Due current potential on conducting wire a.In the case where conducting wire b does not have charge, there are following relationships between charge and above earth potential:
Conducting wire a and its image conductor a ' forms a single phase two-line road at this time, therefore the current potential on conducting wire a can according to electric field theory
It indicates are as follows:
Thus it obtains:
raFor the radius of conducting wire a；Haa'The distance between conducting wire a and its image conductor；ζ is medium coefficient, it is known that in vacuum
Dielectric constant be
It is as follows for the general of the self-potential coefficient of any one conducting wire:
The mutual coefficient of potential, with PbaFrom the point of view of, it is to have unit charge on guide line and do not have when charge on remaining conducting wire on conducting wire b
Due current potential.In the case where conducting wire b and c do not have charge, defined according to the mutual coefficient of potential:
The current potential that conducting wire a and itself image conductor a ' are generated on conducting wire b, is represented by
Thus it obtains:
For any two conducting wires i and j, the general of the mutual coefficient of potential is answered are as follows:
H in formulaij'The distance between the image conductor of conducting wire i and conducting wire j, DijFor the distance between conducting wire i and conducting wire j.
(2) the phase sequence capacitor of scissors crossing transmission line of electricity
By mutual coefficient of potential expression formula (2-18) it is found that since the distance between scissors crossing transmission line of electricity is becoming, one time
The mirror image over the ground of line is also changing at a distance from another loop line, therefore changes along the coefficient of potential, and parallel double loop is not the same for another example
It is constant, derives scissors crossing route below using place on line x as the capacitor expression formula of variable.
Shown in the space diagram of scissors crossing conducting wire such as Fig. 6 (a) and Fig. 6 (b), wherein MN and PQ is different loop line roads
Two aerial condutors, ST and PQ are the adjacent wires with loop line road, and at a distance of s m, conducting wire is each parallel to ground.MN is in PQ route
At the Δ H of top, M ' N ' is the projection under MN vertical direction, and coplanar with PQ, meets at virtual point of intersection O', θ at an angle to each other.PQ
Upper to there is point 1 away from O' point x km, point 1 is with underground mirror point 1' at a distance of H1, O point above the O' point at Δ H, point 2 away from O point x km,
Point 2 is with underground mirror point at a distance of H2, point 1' and point 2 are at a distance of H12, 1,2 point at a distance of D12, point 1 with point 2 subpoint at a distance of D12’, point
2 with point 3 subpoint at a distance of D23’。
Such as Fig. 6 (a), there are following geometrical relationships between route PQ and MN:
H2-H1=2 Δ H (2-19)
D1'2=2xsin (θ/2) (2-20)
Such as Fig. 6 (b), there are following geometrical relationships between route ST and MN:
The geometrical relationship of other adjacent position routes similar can also be calculated.Bring relevant parameter into formula (2-14)
And the mutual current potential between the self-potential coefficient of route and any both threads of scissors crossing transmission line of electricity can be obtained in (2-18)
Coefficient formula.When away from virtual point of intersection distance x variation, H1、H2It is constant, self-potential coefficient and constant with the mutual coefficient of potential in loop line road；
D12It changes, the mutual coefficient of potential between scissors crossing route changes along the line.
Conducting wire passes through complete transposition (three-stage), and the average self-potential coefficient of the every phase conductor of scissors crossing transmission line of electricity is distinguished
ForWith the average mutual coefficient of potential difference between each conducting wire of loop line
ForThe average mutual coefficient of potential is between different loop linesP11、P12、P14Deng for scissors crossing route difference position
Self-potential coefficient and the mutual coefficient of potential when setting, route label are shown in Fig. 2.
Current potential and the contained charge of each conducting wire according to Maxwell equation, to two single loop lines of scissors crossing, on each line
Relationship are as follows:
Wherein matrix in block form
Since two single loop line heights off the ground are different, therefore current potential matrix A ≠ D；Due between the mutual coefficient of potential and two single loop lines
Distance dependent, B, C become the function of place on line x, changes with place on line x and changes, and B (x)=C (x).
The sequence potential parameters of single back line are identical as the calculation method of impedance previously discussed, right respectively with symmetrical component method
Two systems are decoupled.Voltage, electric current are transformed into symmetrical components coordinate system, can be obtained:
jwU012=S-1PSI012=P012I012Wherein, P012=S-1PS
P012For the coefficient of potential matrix in symmetrical components coordinate system, A and D are separately converted to after being unfoldedWithEach non-diagonal line element in matrix
Element is zero, is indicated between positive and negative, zero sequence without coupling, independently of each other.
It is as follows that symmetrical components decomposition is carried out to B and C:
Coupled capacitor i.e. between double loop only has zero sequence coupled capacitor.The inverse of each element is in sequence coefficient of potential matrix
It is expressed as follows in the case where route complete transposition with formula for each sequence capacitor:
A kind of special case of the double-circuit lines on the same pole as scissors crossing transmission line of electricity, two loop line angulations are 0, and are passed through
Optimization and rationally transposition, so that each phase self-inductance in same loop line road and over the ground admittance are equal, any two alternate mutual impedance and mutual
Admittance is equal, and the mutual impedance and transadmittance between different any two phase conductors in loop line road are equal.Therefore each sequence electricity of double-circuit lines on the same pole
Appearance is simplified as by formula (2-27):
Single loop line positive sequence capacitorSingle loop line negative phase-sequence capacitor
Single loop line zero sequence capacitorDouble loop zero sequence coupled capacitor
2. the zero-sequence current voltage relationship to intercouple
In the case where complete transposition, when two routes pass through positive sequence (or negative phase-sequence) electric current, due to every loop line three-phase current
The sum of be equal to zero, thus the average mutual impedance coefficient of the positive sequence (or negative phase-sequence) between two loop line roads will be zero.Therefore, every loop line
Positive sequence impedance and single loop line zero sequence impedance are essentially equal.It is quite different when route passes through zero-sequence current, because of three phase zeros of every loop line
The sum of sequence electric current is not zero, and zero sequence mutual impedance will be present between two loop line roads, and the derivation of equation of previous section demonstrates this point.It is right
Zero sequence transadmittance is also such.
The distributed parameter model of positive sequence (or negative phase-sequence) is uniform long-line transmission equation, the electricity at terminal voltage electric current x
Current voltageIt can be calculated by formula (3-1), corresponding voltage and current and Zc, Υ bring into positive sequence (or negative phase-sequence) amount.
Wherein,For line characteristic impedance,For line propagation coefficient, i=1,2,For end
Voltage and current positive sequence (or negative phase-sequence) amount.
Zero-sequence current voltage relationship of the scissors crossing transmission line of electricity containing zero sequence mutual impedance and admittance is discussed below.It copies uniformly
The derivation process of long-line transmission equation, general zero sequence distributed parameter model schematic diagram such as Fig. 7 that scissors crossing route intercouples
It is shown.
According to the distributed parameter model of Fig. 7, the residual voltage of the first dx sections of loop line dropsWith zero-sequence current incrementIt can
It indicates are as follows:
I.e.
Similarly, the voltage-current relationship of the second loop line is
Wherein, capacitive reactance y is coupledmIt (x) is the function away from virtual point of intersection distance x.The differential equation group can not be solved directly
Expression formula shaped like uniform long-line transmission equation, therefore the first order differential equation system is solved using Runge-Kutta method.
To double-circuit lines on the same pole, z1=z2, y1=y2, ymFor definite value, V1=V2, equation is simplified.When two loop lines without
When coupling, zm、ymIt is 0, formula (3-3) and (3-4) are simplified, and solution is the uniform long-line transmission equation shaped like formula (3-1).
3. calculated result and verifying
Analysis of Influential Factors of 3.1 space layouts to line parameter circuit value
Given route inherent parameters, including wire radius, apart from ground level h1, scissors crossing transmission line of electricity it is at an angle to each other
θ and vertical range Δ H etc., according to " Code for planning of urban electric power (GB50293-1999) ", 220kV overhead power transmission line line conductor with
Minimum perpendicular distance between ground, non-residential areas 6.5m, the same horizontally arranged phase spacing of loop line are 7-12m, and setting is specific
Parameter is as shown in table 1.With the distribution parameter of the available transmission line of electricity of the calculation formula of derivation, including positive (negative) sequence of single loop line
Parameter R1、L1、C1, single loop line Zero sequence parameter R0、L0、C0, scissors crossing route mutual impedance parameter R0m、L0m、C0m(x)。
1 setup parameter list of table
| Lower loop line conducting wire real radius r (each phase conductor radius is equal) | 25mm |
| Higher loop line conducting wire real radius r (each phase conductor radius is equal) | 20mm |
| Conducting wire is averaged geometric radius r' | R'=0.779r |
| The unit length substitutional resistance R of ground return circuitg | 0.05Ω/km |
| A lower loop line is apart from ground level h1 | 7m |
| Soil resistivity ρ | 2Ω·m |
| With loop line phase spacing s (assuming that two loop lines are identical) | 7m |
The zero sequence and positive-negative sequence capacitor of the higher loop line of scissors crossing route are by between two back transmission line of scissors crossing
Vertical range Δ H influence, as shown in Fig. 8 (a) and Fig. 8 (b).
Zero sequence mutual resistance between the scissors crossing route of derivation, mutual inductance, mutual tolerance expression formula are controlled into variable graphing such as Fig. 9
(a), Fig. 9 (b) and Figure 10 (a), Figure 10 (b) are shown.
As shown in Fig. 9 (a), Fig. 9 (b), when angle is fixed, the zero-sequence mutual inductance between scissors crossing transmission line of electricity is with height
Increase and reduce.When angle increases to 90 degree, inductive coupling is not present between i.e. two loop lines for mutual inductance 0.Figure 10 (a), Figure 10
(b) shown in, when height is fixed, the zero-sequence mutual inductance between scissors crossing transmission line of electricity reduces with the increase of angle, until 90 °
When be 0.
From Figure 11 (a)-(c) as can be seen that zero sequence mutual tolerance increases with the increase of height between scissors crossing transmission line of electricity,
Increase with the increase of route angulation, increases with the increase apart from intersection.When angle is 90 °, zero sequence is mutual
Capacitor, which is increased speed, to be speeded, and capacitive reactance is reduced rapidly.
3.2 simulating, verifying
Since existing simulation software can not build the three-dimensional model of power transmission system of embodiment spatial relationship, therefore in simulink
In, two independent single loop line simulation models are built respectively first with two groups of single loop line parameters, and event occurs for any loop line
It is represented by Figure 12 (a) when barrier, when normal operation is represented by Figure 12 (b), and two loop lines are all made of distributed parameter transmission line model, line
Road basic parameter is as shown in table 1.Wherein, lower revolving line voltage grade 220kV, phase angle difference is 20 °, overall length 300km, higher by one
Revolving line voltage class 5 00kV, phase angle difference are 20 °, and the two power supply amplitude is respectively 1 and 1.05pu, overall length 300km.
Two independent single loop line system M, N two sides system parameters are equal are as follows:
Zm1=1.2498+j16.932 Ω, Zm0=6.888+j43.139 Ω；Zn1=1.0415+j14.110 Ω, Zn0=
5.74+j35.949Ω。
The lower loop line calculated by the initial parameter in table 1 by the second nodel line road distribution parameter three-dimensional universal model is just
Order parameter R1=0.06 Ω/km, L1=1.226mH/km, C1=0.009375uF/km；Zero sequence parameter R0=0.21 Ω/km, L0=
2.853mH/km C0=0.007048uF/km.
The higher positive order parameter R of a loop line1=0.06 Ω/km, L1=1.271mH/km, C1=0.008819uF/km；Zero sequence
Parameter R0=0.21 Ω/km, L0=2.898mH/km, C0=0.005307uF/km.
Known double-circuit lines on the same pole single-line fault ratio accounts for 80% or more, and scissors crossing transmission line of electricity is due to wire spacing
Bigger than double-circuit lines on the same pole and remoter away from crosspoint, distance is bigger between two loop lines, and cross line fault probability obviously compares same bar simultaneously
Frame double loop wants low, therefore simulating, verifying only considers scissors crossing route wherein postback raw single loop line failure the case where.
Assuming that being the virtual point of intersection of scissors crossing route at route midpoint 150km (x=0).In lower loop line road evidence
A phase ground fault in fault point is set at the 150km of left end, fault section is [0.04s, 0.08s], and a higher loop line operates normally,
Carry out the single-line fault in analog crossover span line.Two cycles after the failure at route left end (x=150km) that measurement is obtained
Phase voltage electric current be converted into residual voltage electric current, wherein lower loop line residual voltage U0=-1.4135+1.3175i kV,
I0=-21.7780-33.6935i A；Higher loop line U0=0kV, I0=0A is asked as mutually independent single loop line initial value
Solve differential equation (3-3), (3-4).
Known by 3.1 sections, scissors crossing route is remoter away from virtual point of intersection, smaller by zero sequence coupling influence, so when electricity
The actual value for flowing voltage value closer to two independent single loop lines is not possible at present since the former is related with space layout using soft
Part is built model and is obtained, therefore has more away from the latter of virtual point of intersection remotely as transmission line of electricity left end current and voltage quantities are intersected
Reasonability.
Vertical range Δ H between two back transmission line of scissors crossing takes 10m.According to different schemes, led to by electric parameter
Zero sequence mutual impedance and mutual capacitive reactance parameter such as 2 institute of table between the Zero sequence parameter being calculated with computation model and scissors crossing route
Show.
Detail is arranged in 2 scheme of table
Note: wherein unit impedance parameter unit is Ω/km, and unit admittance parameter unit is 1/ (Ω km).
Figure 13 shows scissors crossing transmission line of electricity capacitive reactance nonlinearity in parameters inhomogeneities, Y0mVirtual point of intersection from
The step-length that change takes place in 1km is increasing, until no longer changing, can be equivalent to piecewise-parallel double back in follow-up study
Line.
It is as shown in table 3 that each scheme crossing elimination point residual voltage electric current is obtained by general distributed parameter model.
Scissors crossing line voltage distribution electric current calculated result when the lower loop line A phase of table 3 is grounded
Scheme one does not consider coupled capacitor to scheme three, and scissors crossing angle is 90 degree in scheme three, is known by formula (2-5)
Zero sequence mutual impedance is 0, i.e., any coupling is not present between route, and the electric parameter of scissors crossing route is coupled with neither consideration
Single loop line is no different, and is compared scheme three and reference scheme in the residual voltage electric current of route intersection, has been confirmed this point, thus
Demonstrate the correctness of zero sequence mutual impedance calculation method of parameters in scissors crossing electric transmission line three-dimensional model.
Since failure mode and abort situation are numerous, 30 ° of scissors crossing routes are given below, several classical asymmetry occur
The calculated result of failure does not consider that two single loop line systems of coupling are compared with what measurement obtained.By 3-table of table 7 it is found that working as
A certain loop line is when unbalanced fault occurs for different location along the line in scissors crossing route, mutual resistance, mutual reactance and mutual capacitance effect
It should can not ignore.
Scissors crossing line voltage distribution electric current calculated result when the higher loop line A phase of table 4 is grounded
Scissors crossing line voltage distribution electric current calculated result when the lower loop line BC phase of table 5 is short-circuit
Scissors crossing line voltage distribution electric current calculated result when 6 higher loop line BC phase ground short circuit of table
The case where A phase is grounded at the higher loop line 50km of 30 ° of scissors crossing routes in table 4 is taken, is calculated from crosspoint
Residual voltage electric current is as shown in figure 14 along (x=0km) to route left end (x=150km), mutually independent two single loop line edge
Line residual voltage electric current is as shown in figure 15.
Comparison diagram 14,15 is it is found that angled scissors crossing route, if handled by independent two single loop line,
Along caused by because of practical coupling condition compared with Current Voltage, there is notable difference in amplitude, phase angle.This species diversity is with friendship
The shortening of height between span line, the reduction of angle are pitched, it will be increasing.Therefore intersects span line and in practice cannot in engineering
It is handled according to independent single loop line, is otherwise likely to occur a series of adverse consequences such as false protection, range accuracy reduction.
The present invention is based on classical route parameter calculation derivation of equation scissors crossing line parameter circuit value universal computer models, divide
Angle, relative altitude, the influence away from intersection to route coupling parameter have been analysed, scissors crossing route has been constructed and intercouples
When general zero-sequence current voltage equation.For scissors crossing transmission line of electricity, zero sequence mutual impedance parameter is with angle, height
Increase and become smaller, zero sequence mutual capacitance parameter with angle, height increase and become larger, and change along the line, it is remoter away from virtual point of intersection,
Numerical value is bigger, after reaching certain distance, no longer changes, and can be equivalent to the parallel double loop in the presence of coupling.It is carried out with multiple groups scheme
Matlab simulation comparison demonstrates the correctness for considering the three-dimensional circuits parameter universal computer model of conductor space arrangement, simultaneously
It was found that scissors crossing route, if handled by independent two single loop line, with because caused by practical coupling condition along line current electricity
Pressure is compared and is had differences, and difference be can not ignore, to demonstrate the practicability of the model.The mathematical model be Load flow calculation,
The basis of relay protection, transient analysis and fault localization has directive significance in engineering practice.
Above-mentioned, although the foregoing specific embodiments of the present invention is described with reference to the accompanying drawings, not protects model to the present invention
The limitation enclosed, those skilled in the art should understand that, based on the technical solutions of the present invention, those skilled in the art are not
Need to make the creative labor the various modifications or changes that can be made still within protection scope of the present invention.
Claims (8)
1. considering the route distribution parameter Three-dimensional CAD design method of conductor space arrangement, characterized in that including following step
It is rapid:
(1) model of power transmission system of scissors crossing is established, the model of power transmission system of the scissors crossing includes: one loop line three of lower section
Phase line 1,2,3, one loop line three-phase line 4,5,6 of top；
In the model of power transmission system of the scissors crossing, by the single loop line vertical projection above scissors crossing transmission line of electricity to lower section
When single loop line, angle o degree between the two-phase of different loop lines；
(2) inherent parameters of scissors crossing transmission line of electricity are acquired, comprising: wire radius, lower section single loop line are apart from ground level h1、
Vertical range Δ H between scissors crossing transmission line of electricity θ at an angle to each other and scissors crossing transmission line of electricity；
(3) according to collected route inherent parameters, self-impedance coefficient is not calculated separately, with the mutual impedance coefficient between loop line and not
With the mutual impedance coefficient between loop line, and obtain each sequence impedance parameter in scissors crossing transmission line of electricity；
(4) the self-potential coefficient of any one conducting wire is calculated；Consider the earth to conducting wire surrounding field distribution using image charge method
Influence, according to the radius of conducting wire, conducting wire corresponding thereto in the distance between the image conductor on ground calculate with loop line any two
The mutual coefficient of potential of root conducting wire；
(5) assume that MN and PQ is the aerial condutor of different loop line roads, ST and PQ are the adjacent wires with loop line road；It is route MN
It is corresponding with point O' on route MN that projection M'N' in PQ plane, route M'N', which give point O', point O with route PQ phase,
Point；If the distance of route PQ upper 1: 1 to point O is x, the mutual coefficient of potential along any two conducting wires is calculated by variable of x；
(6) positive sequence of scissors crossing route is converted to according to phase sequence according to the self-potential coefficient of calculating and the mutual coefficient of potential, is born
Zero sequence mutual capacitance between sequence and zero sequence capacitor and scissors crossing route；
(7) according to the line parameter circuit value of above-mentioned calculating, the general sequence currents voltage equation of scissors crossing route is constructed；Specific packet
It includes:
When scissors crossing route passes through positive sequence or negative-sequence current, current-voltage equation is uniform transmission line equation；
When scissors crossing route passes through zero-sequence current, according to the residual voltage increment and zero sequence at the x position of distance line end
The expression formula of current increment constructs zero-sequence current voltage equation group.
2. the route distribution parameter Three-dimensional CAD design method of conductor space arrangement is considered as described in claim 1,
It is characterized in, in the step (3),
Each phase conductor is parallel to each other in the same circuit, and between arbitrary two conducting wires I, J same loop line, mutual impedance coefficient is specific
Are as follows:
Wherein, RgFor the unit length substitutional resistance of ground return circuit,For the equivalent depth of equivalent earthed return d, rsI、rsd
The equivalence radius of respectively conducting wire I and equivalent earthed return d, DIdFor the equivalent distance of conducting wire I and equivalent earthed return d；DIJIt is two
The distance between conducting wire；
Mutual impedance coefficient between different loop lines specifically:
Wherein, Z14For the mutual impedance between 4 liang of phase conductors of loop line 1 and loop line；Z15~Z36Meaning also be respectively different loop line two-phases
Mutual impedance between conducting wire.
3. the route distribution parameter Three-dimensional CAD design method of conductor space arrangement is considered as described in claim 1,
It is characterized in, in the step (3), the impedance parameter of each loop line in transmission line of electricity specifically:
Single loop line positive sequence impedance parameter Z1=Zs-Zm, single loop line negative sequence impedance parameter Z2=Zs-Zm, zero-sequence impedance parameter Z0=Zs+
2Zm；
Zero sequence mutual impedance Z is only existed between two loop lines0m=3Zm'；
Wherein, ZsFor the average self-impedance coefficient of each single loop line；ZmAverage mutual impedance system between each phase conductor in same loop line
Number；Zm'Zero sequence mutual impedance coefficient between different loop lines.
4. the route distribution parameter Three-dimensional CAD design method of conductor space arrangement is considered as described in claim 1,
It is characterized in, in the step (4), the self-potential coefficient of any one conducting wire specifically:
Unit is km/F；
Wherein, HII'It is conducting wire I at a distance from its image conductor, rIFor the radius of conducting wire I.
5. the route distribution parameter Three-dimensional CAD design method of conductor space arrangement is considered as described in claim 1,
It is characterized in, in the step (4), with the mutual coefficient of potential of any two conducting wires I and J of loop line specifically:
Unit is km/F；
H in formulaIJ'The distance between the image conductor of conducting wire I and conducting wire J, DIJFor the distance between conducting wire I and conducting wire J.
6. the route distribution parameter Three-dimensional CAD design method of conductor space arrangement is considered as described in claim 1,
It is characterized in, in the step (6), in two loop lines, positive sequence, negative phase-sequence and the zero sequence capacitor of scissors crossing transmission line of electricity specifically:
Single loop line positive sequence capacitorAnother single loop line positive sequence capacitor
Single loop line negative phase-sequence capacitorAnother single loop line negative phase-sequence capacitor
Single loop line zero sequence capacitorAnother single loop line zero sequence capacitor
Zero sequence mutual capacitance between scissors crossing route are as follows:
Wherein, Ps1、Ps2The average self-potential coefficient of every phase conductor respectively in two loop line of scissors crossing transmission line of electricity；Pm1、Pm2Point
It Wei not be with the average mutual coefficient of potential between conducting wire each in loop line；Pm'(x) the average mutual coefficient of potential between different loop lines.
7. the route distribution parameter Three-dimensional CAD design method of conductor space arrangement is considered as described in claim 1,
It is characterized in, in the step (7), when scissors crossing route passes through zero-sequence current, the zero-sequence current voltage equation group of construction has
Body are as follows:
Positive sequence or negative sequence voltage electric current at terminal voltage electric current xThere is following relationship:
Its general solution are as follows:
Wherein,For line characteristic impedance,For line propagation coefficient, i=1,2 represent positive sequence or negative phase-sequence
Electric parameter；For terminal voltage electric current positive sequence or negative phase-sequence amount.
8. the route distribution parameter Three-dimensional CAD design method of conductor space arrangement is considered as described in claim 1,
It is characterized in, in the step (7), to scissors crossing power transmission line zero-sequence network, the voltage-current relationship of the first loop line:
The voltage-current relationship of second loop line:
Wherein,Respectively scissors crossing route is lower and higher loop line is away from residual voltage, the electricity at the x of end
Stream；zmFor zero sequence mutual impedance, ymIt (x) is zero sequence transadmittance.
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| CN107632207B (en) * | 2017-08-30 | 2019-08-30 | 国网湖南省电力公司 | A kind of electromagnetic monitoring points distributing method of identical power transmission mode scissors crossing transmission line of electricity |
| CN107908846B (en) * | 2017-11-07 | 2021-10-22 | 武汉大学 | Magnetic field analysis method of magnetic resonance type wireless power supply technology in high-voltage power line monitoring |
| CN107862150A (en) * | 2017-11-20 | 2018-03-30 | 华南理工大学 | A kind of unified modeling method based on tower structure Yu the multiple-loop line transmission line of electricity of wire parameter |
| CN108459206B (en) * | 2018-04-26 | 2020-06-16 | 贵州电网有限责任公司 | Method for calculating spatial line distribution parameter matrix based on complex mirror image |
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