CN105653760A - Method for designing conductor spatial arrangement-considered line distribution parameter three-dimensional calculation models - Google Patents

Abstract

The invention discloses a method for designing conductor spatial arrangement-considered line distribution parameter three-dimensional calculation models. According to the method, the influences factors such as angles formed by conductors, crossing heights and distances to virtual intersections during the spatial arrangement of the conductors are comprehensively considered, a distribution parameter three-dimensional model general calculation formula of crossed crossing transmission conductors is derived, and general zero-sequence current-voltage equations which are mutually coupled are constructed. Simulation results of a plurality of schemes indicate that the conductor spatial arrangement-considered line parameter three-dimensional general calculation models have effectiveness and practicability and can be further popularized into the parameter calculation of four-circuit transmission lines and more-circuit transmission lines.

Description

Consider the circuit distribution parameter Three-dimensional CAD method of design of conductor spatial arrangement

Technical field

The present invention relates to a kind of circuit distribution parameter three-dimensional universal computer model method of design considering conductor spatial arrangement.

Background technology

Transmitting line parameter is the basis of the every simulation calculation of power system. Along with the development of economy, the dynamic removal expense of corridor land used is day by day expensive, and the continuous increase of transmitting capacity adopts more and more parallel lines on same tower multi circuit transmission lines in engineering reality, and the scene of unavoidable scissors crossing transmitting line gets more and more. In addition, when super, UHV transmission circuit designs, it is possible to the situation crossing over low voltage grade power transmission circuit can be run into. The parameter of the two-dimensional model such as parallel double loop and double-circuit lines on the same pole calculates and applies very ripe, space crossed leap wire belongs to not parallel conductor structure, classical bivariate distribution parameter computation model is no longer applicable, the coupling effect between two loop lines need to be rethought, set up three-dimensional model calculating and solve.

Under new scene, the electromagnetic coupled of scissors crossing transmitting line and static induction make original separate lines parameter there occurs change, be directly connected to Load flow calculation, relaying, the accuracy of fault localization and precision, thus engineering practice is had significance.

Transmitting line flows through electric current can produce heat, and major embodiment is the resistance of circuit, due to the existence of ground resistance, not collinear can be made to produce mutual resistance effect. Circuit flows through the magnetic field that exchange current can produce alternation around wire, thus produces electromotive force on wire itself and adjacent wires, make circuit produce self-inductance and mutual inductance effect. In addition, circuit can produce electric field, induced charge on the earth and adjacent lines, also can ionize part air around, thus and produce ground capacitance between the earth, Leaked Current of Line to Ground lead effect, produce mutual capacity and mutual conductance effect with circuit around.

The principal element affecting line inductance and electric capacity has two, and one is the distance between circuit and the earth and between circuit, and two is the radius of circuit own. When two back transmission line spacings are nearer, between any two-phase conductor on two loop line roads, electromagnetic coupled and static induction are obvious.

For scissors crossing transmission pressure, except distance between centers of tracks from circuit radius, also need to consider to be projected to the at an angle to each other of same plane. In addition, circuit from virtual point of intersection more away from, distance between centers of tracks is from more big, therefore capacitance size changes along the line, is no longer constant.

Uneven transmitting line is carried out certain research by existing method, comprising:

1, the parametric model being deduced a kind of special not parallel transmitting line, becomes parallel circuit by the equivalence of infinitely small transmitting line, calculates the distribution parameter of two wires based on the original physical meaning of distribution parameter circuit.But two wires in model are mutually certain angle in same plane, belongs to two-dimensional model, and the distance between two wires increases along the line, no longer evenly, when �� is 0, circuit is converted into parallel transmitting line.

2, for ultra-high-tension power transmission line and scissors crossing transmitting line, 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. This new scene of scissors crossing transmitting line has been carried out pre-test by this model, is determine that circuit is minimum to ground level and the important evidence delimiting line corridor width, but research spatial arrangement is not on the impact of line parameter circuit value.

Summary of the invention

Based on above-mentioned Problems existing, the present invention provides a kind of circuit distribution parameter Three-dimensional CAD method of design considering conductor spatial arrangement, at an angle to each other, spanning height when this computation model considers conductor spatial arrangement, apart from influence factors such as virtual point of intersection distances, it is to construct the general zero sequence current/voltage equation of mutual coupling. Adopt simulink to emulate many prescriptions case to contrast, demonstrate the exactness of this model.

For achieving the above object, the concrete scheme of the present invention is as follows:

Consider the circuit distribution parameter Three-dimensional CAD method of design of conductor spatial arrangement, it is characterized in that, comprise the following steps:

(1) setting up the transmitting line model of scissors crossing, for calculating explanation clearly, the transmitting line of mark scissors crossing is as follows, and lower section one loop line a, b, c phase is 1,2,3, and top one loop line three-phase label is once 4,5,6;

In the transmitting line model of described scissors crossing, during by the single loop line vertical projection above scissors crossing transmitting line to lower section list loop line, in �� angle between the two-phase of different loop line;

(2) gather the inherent parameters of scissors crossing transmitting line, comprising: wire radius, the single loop line distance floor level h in lower section₁, vertical range �� H between scissors crossing transmitting line �� at an angle to each other and scissors crossing transmitting line;

(3) according to the circuit inherent parameters collected, calculate respectively from impedance factor, with the transimpedance coefficient between loop line and the transimpedance coefficient between different loop line, and obtain each sequence impedance parameter in scissors crossing transmitting line;

(4) the self-potential coefficient of any wire is calculated; The earth is on the impact of wire surrounding electric field distribution to adopt mirror image charge method to consider, according to the radius of wire, wire corresponding thereto distance between the image conductor on ground calculate the mutual potential modulus with any two wires of loop line;

(5) assuming that MN and PQ is the built on stilts wire on different loop line road, ST and PQ is the adjacent wires on same loop line road; Being the projection M'N' of circuit MN in PQ plane, circuit M'N' gives an O' with circuit PQ phase, and some O is the point corresponding with an O' on circuit MN; If the distance of circuit MN upper 1: 2 to some O is x, it is that variable calculates any two wires mutual potential modulus along the line taking x;

(6) the zero sequence mutual capacity being converted between the positive sequence of scissors crossing circuit, negative phase-sequence and zero sequence electric capacity and scissors crossing circuit according to the self-potential coefficient calculated and mutual potential modulus according to phase sequence;

(7) according to the line parameter circuit value of above-mentioned calculating, it is to construct the general sequence currents voltage equation of scissors crossing circuit; Specifically comprise:

When passing through positive sequence or negative phase-sequence electric current when scissors crossing circuit, current/voltage equation is even transmission line equation;

When scissors crossing circuit is by zero sequence electric current, according to the expression formula of the zero sequence voltage increment at distance line end x position place and zero sequence current increment, it is to construct zero sequence current/voltage system of equations.

In described step (3),

In the same circuit, each phase wire is parallel to each other, and to arbitrary two wires i, j between same loop line, transimpedance coefficient is specially:

$Z_{ij}=R_g+j0.145\lg \frac{D_g}{D_{ij}};$

Wherein, R_gFor the equivalent resistance of unit length of big ground circuit,For the equivalent degree of depth of ground medium value wire d, r_si��r_sdIt is respectively wire i and the equivalence radius of equivalent ground wire d, D_idFor the equivalence distance of wire i with equivalently loop line d;

Transimpedance coefficient between different loop line is specially:

$Z_{m^{\′}}=\frac{1}{9}(Z_{14}+Z_{15}+Z_{16}+Z_{24}+Z_{25}+Z_{26}+Z_{34}+Z_{35}+Z_{36})$

Wherein, Z₁₄For the transimpedance between loop line 1 and loop line 4 two-phase wire; Z₁₅��Z₃₆The implication transimpedance that is also respectively between different loop line two-phase wire.

In described step (3), in transmitting line, the impedance parameter of each loop line is specially:

Single loop line positive sequence or negative phase-sequence impedance parameter Z₁=Z₂=Z_s-Z_m, zero-sequence impedance parameter Z₀=Z_s+2Z_m��

Zero sequence mutual impedance Z is only there is between two loop lines_0m=3Z_m';

Wherein, Z_sAverage from impedance factor for each single loop line; Z_mFor the average transimpedance coefficient between phase wire each in same loop line; Z_m'For the zero sequence mutual impedance coefficient between different loop line.

In described step (4), the self-potential coefficient of any wire is specially:

$P_{ii}=41.45\×{10}^6\lg \frac{H_{{\mathrm{ii}}^{\′}}}{r_i}$ Unit is km/F

Wherein, H_ii'For the distance of wire i and its image conductor, r_iFor the radius of wire i.

In described step (4), it is specially with the mutual potential modulus of any two wire i and j of loop line:

$P_{ij}=P_{ji}=41.45\×{10}^6\lg \frac{H_{{\mathrm{ij}}^{\′}}}{D_{ij}}$ Unit is km/F

H in formula_ij'Distance between the image conductor of wire i and wire j, D_ijFor the distance between wire i and wire j.

In described step (5), it is assumed that MN and PQ is two wires on different loop line road, ST and PQ is the adjacent wires on lower loop line road, and at a distance of being s, wire is all parallel to ground; On circuit PQ, point 1 is apart from O' point x, and point 1 and underground mirror point 1' are at a distance of H₁; On circuit MN, point 2 is apart from O point x, point 2 and underground mirror point 2 " at a distance of H₂; On circuit ST, point 3 is apart from the some O corresponding with some O' on circuit PQ " x, point 3 and its underground mirror point 3' are at a distance of H₁; MN is �� H place above PQ circuit, M'N' be under MN vertical direction project, and with PQ copline, meet at virtual point of intersection O', �� at an angle to each other;

Following geometric relationship is there is between circuit PQ and MN:

H₂-H₁=2 �� H

D_1'2=2xsin (��/2)

$H_{{12}^{\′}}=\sqrt{{(H_1+\mathrm{\Δ}H)}^2+{D_{1^{\′}2}}^2}$

$D_{12}=\sqrt{D^2+{\mathrm{\ΔH}}^2}$

Following geometric relationship is there is between circuit ST and MN:

$D_{2^{\′}3}=\sqrt{x^2+(x^2+s^2)-2x\sqrt{x^2+s^2}cos(\mathrm{\θ}+\arctan \frac{s}{x})};$

$H_{2^{\′}3}=\sqrt{{(H_1+\mathrm{\Δ}H)}^2+{D_{2^{\′}3}}^2};$

$D_{23}=\sqrt{{D_{2^{\′}3}}^2+{\mathrm{\ΔH}}^2};$

Wherein, D₁₂For putting the distance that 1 arrives point 2; D_1'2Distance, the H of point 1 is arrived for putting the subpoint 2 ' of 2_12'For distance, the D of the underground mirror image point-to-point 2 of putting 1_2'3Distance, the H of point 3 is arrived for putting the subpoint 2 ' of 2_2'3For distance, the D of the underground mirror image point-to-point 2 of putting 3₂₃For putting the distance that 2 arrive point 3;

Above-mentioned parameter is brought into respectively in step (4) calculation formula of the mutual potential modulus with any two wire i and j of loop line, the mutual potential modulus between any two lines of scissors crossing transmitting line can be tried to achieve.

In described step (6), in two loop lines, the positive sequence of scissors crossing transmitting line, negative phase-sequence and zero sequence electric capacity are specially:

Single loop line positive sequence electric capacityAnother single loop line positive sequence electric capacity

Single loop line negative phase-sequence electric capacityAnother single loop line negative phase-sequence electric capacity

Single loop line zero sequence electric capacityAnother single loop line zero sequence electric capacity

Zero sequence mutual capacity between scissors crossing circuit is:

$C_{0m}\left(x\right)=\frac{1}{3P_{m^{\′}}\left(x\right)}$

Wherein, P_s1��P_s2The average self-potential coefficient being respectively in scissors crossing transmitting line two loop line every phase wire; P_m1��P_m2The average potential modulus mutually being respectively in same loop line between each wire; P_m'X () is average potential modulus mutually between different loop line.

In described step (7), when scissors crossing circuit by zero sequence electric current time, it is to construct zero sequence current/voltage system of equations be specially:

The positive sequence at distance terminal voltage electric current x place or negative sequence voltage electric currentThere is following relation:

$d\stackrel{\·}{V}={\stackrel{\·}{I}}_2{z}_{i}dx;$

$d\stackrel{\·}{I}={\stackrel{\·}{V}}_2{y}_{i}dx$

Its general solution is:

Wherein,For line characteristic impedance,For line propagation coefficient, i=1,2, represents positive sequence or the electric parameter of negative phase-sequence;For terminal voltage electric current positive sequence or negative phase-sequence amount.

To scissors crossing power transmission line zero-sequence network, the voltage-current relationship of the 2nd loop line:

$\frac{{\stackrel{.}{dV}}_1}{dx}={\stackrel{\·}{I}}_1{z}_1+{\stackrel{\·}{I}}_2{z}_m$

$\frac{d{\stackrel{\·}{I}}_1}{dx}={\stackrel{\·}{V}}_1(y_1+y_m(x\left)\right)-{\stackrel{\·}{V}}_2{y}_m\left(x\right)$

The voltage-current relationship of the 2nd loop line:

$\frac{{\stackrel{.}{dV}}_2}{dx}={\stackrel{\·}{I}}_2{z}_2+{\stackrel{\·}{I}}_1{z}_m$

$\frac{d{\stackrel{\·}{I}}_2}{dx}={\stackrel{\·}{V}}_2(y_2+y_m(x\left)\right)-{\stackrel{\·}{V}}_1{y}_m\left(x\right)$

Wherein,It is respectively zero sequence voltage, the electric current at scissors crossing circuit lower and higher loop line distance end x place; z₁For zero sequence impedance, z_mFor zero sequence mutual impedance, y₁For zero sequence admittance, y_mX () is zero sequence transadmittance.

The useful effect of the present invention:

At an angle to each other, spanning height when the present invention considers conductor spatial arrangement, apart from influence factors such as virtual point of intersection distances, derive the distribution parameter three-dimensional model universal calculation equation of scissors crossing transmission pressure, it is to construct the general zero sequence current/voltage equation of mutual coupling. Many prescriptions case emulation result shows, it is contemplated that the three-dimensional universal computer model of the line parameter circuit value of conductor spatial arrangement has validity and practicality, and can be generalized to further in the parameter calculating of four loop lines and even more loop lines.

Accompanying drawing explanation

Fig. 1 is scissors crossing transmission pressure parameter Three-dimensional CAD;

Fig. 2 is scissors crossing transmission pressure space layout vertical view;

Fig. 3 is the transimpedance coefficient between two wires of scissors crossing;

Fig. 4 is magnetic flux schematic diagram;

Fig. 5 is aerial line capacitance parameter figure;

The space multistory figure mono-of two transmission pressures that Fig. 6 (a) is scissors crossing;

The space multistory figure bis-of two transmission pressures that Fig. 6 (b) is scissors crossing;

Fig. 7 is the zero sequence distributed parameter model schematic diagram of coupling mutually;

Fig. 8 (a) is for the zero sequence electric capacity of the higher loop line of scissors crossing circuit is with height change curve;

Fig. 8 (b) is for the positive-negative sequence electric capacity of the higher loop line of scissors crossing circuit is with height change curve;

Fig. 9 (a) is zero-sequence mutual inductance during different angles and the relation of angle between scissors crossing transmitting line;

The relation of angle between zero-sequence mutual inductance and scissors crossing transmitting line when Fig. 9 (b) is 30 degree;

Figure 10 (a) is the relation of vertical height between zero-sequence mutual inductance and scissors crossing transmitting line;

Figure 10 (b) is be highly zero-sequence mutual inductance during 10m and the relation of vertical height between scissors crossing transmitting line;

Figure 11 (a) intersects the relation of �� H between transmitting line for zero sequence mutual tolerance and crossing over;

Figure 11 (b) intersects the relation of �� between transmitting line for zero sequence mutual tolerance and crossing over;

Figure 11 (c) intersects the relation of x between transmitting line for zero sequence mutual tolerance and crossing over;

Figure 12 (a) is single loop line both-end system simulation model during arbitrary loop line generation fault;

Figure 12 (b) is single loop line both-end system simulation model during normal operation;

Figure 13 is Y0m change curve along the line;

Figure 14 is mutually scissors crossing circuit electric current and voltage amplitude along the line, the phase angle change curve of 30 ��;

Figure 15 does not consider the two of coupling single loop line electric current and voltage amplitude along the line, phase angle change curves.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described in detail:

The present invention discloses a kind of circuit distribution parameter Three-dimensional CAD method of design considering conductor spatial arrangement, comprises the following steps:

(1) setting up the transmitting line model of scissors crossing, for calculating explanation clearly, the transmitting line of mark scissors crossing is as follows, and lower section one loop line a, b, c phase is 1,2,3, and top one loop line three-phase label is once 4,5,6;

In the transmitting line model of described scissors crossing, during by the single loop line vertical projection above scissors crossing transmitting line to lower section list loop line, in �� angle between the two-phase of different loop line;

(2) gather the inherent parameters of scissors crossing transmitting line, comprising: wire radius, the single loop line distance floor level h in lower section₁, vertical range �� H between scissors crossing transmitting line �� at an angle to each other and scissors crossing transmitting line;

(3) according to the circuit inherent parameters collected, calculate respectively from impedance factor, with the transimpedance coefficient between loop line and the transimpedance coefficient between different loop line, and obtain each sequence impedance parameter in scissors crossing transmitting line;

(4) the self-potential coefficient of any wire is calculated; The earth is on the impact of wire surrounding electric field distribution to adopt mirror image charge method to consider, according to the radius of wire, wire corresponding thereto distance between the image conductor on ground calculate the mutual potential modulus with any two wires of loop line;

(5) assuming that MN and PQ is the built on stilts wire on different loop line road, ST and PQ is the adjacent wires on same loop line road; Being the projection M'N' of circuit MN in PQ plane, circuit M'N' gives an O' with circuit PQ phase, and some O is the point corresponding with an O' on circuit MN; If the distance of circuit MN upper 1: 2 to some O is x, it is that variable calculates any two wires mutual potential modulus along the line taking x;

(6) the zero sequence mutual capacity being converted between the positive sequence of scissors crossing circuit, negative phase-sequence and zero sequence electric capacity and scissors crossing circuit according to the self-potential coefficient calculated and mutual potential modulus according to phase sequence;

(7) according to the line parameter circuit value of above-mentioned calculating, it is to construct the general sequence currents voltage equation of scissors crossing circuit; Specifically comprise:

When passing through positive sequence or negative phase-sequence electric current when scissors crossing circuit, current/voltage equation is even transmission line equation;

When scissors crossing circuit is by zero sequence electric current, according to the expression formula of the zero sequence voltage increment at distance line end x position place and zero sequence current increment, it is to construct zero sequence current/voltage system of equations.

Below aforesaid method is described in detail.

1. line parameter circuit value is affected theory deduction by conductor spatial arrangement.

Fig. 1, Fig. 2 are respectively scissors crossing transmission pressure parameter Three-dimensional CAD and space layout vertical view. During by the single loop line vertical projection above scissors crossing transmitting line to lower section list loop line, in �� angle between the two-phase of different loop line. When two single loop lines are when nearer, electromagnetic coupled and static induction will be produced so that the parameter of scissors crossing transmission pressure can not calculate according to separate single loop line impedance computation method. The circuit distribution parameter three-dimensional universal computer model that this section will be derived respectively from impedance parameter and capacitance parameter and considered conductor spatial arrangement.

1.1 impedance parameters calculate

(1) from impedance factor with the transimpedance coefficient calculations between loop

Any wire can be written as from the general type of impedance factor:

$Z_{ii}=R_{ii}+j0.145\lg \frac{D_g}{r_{si}}---(2-1)$

R in formula_ii=R_i+R_g��r_siFor the resistance per unit length of wire i, ��/km;

R_gFor the equivalent resistance of unit length of big ground circuit, according to theoretical analysis: R_g=��²��10^-4F=9.869 �� 10^-4F, when frequency f=50Hz, gets R_g=0.05 ��/km;

r_si��r_sdFor being correspondingly the equivalence radius (having counted internal inductance) of wire i and equivalent ground wire d, to the circular solids line of non-ferromagnetic material, r_s=0.779r, r are wire real radius;

For the equivalent degree of depth of ground medium value wire d, byDetermining, wherein �� is soil resistivity, �� m, D_idFor the equivalence distance of wire i with equivalently loop line d.

Adopt complete transposition and get each phase wire radius the same time,

From formula of impedance it is on average

$Z_s=\frac{1}{3}(Z_{11}+Z_{22}+Z_{33})=\frac{1}{3}(Z_{44}+Z_{55}+Z_{66})=R_1+0.05+j0.145\lg \frac{D_g}{r_s}---(2-2)$

The same circuit, each phase wire is parallel to each other, and to arbitrary two wires i, j, the general formula of transimpedance coefficient is:

$Z_{ij}=R_g+j0.145\lg \frac{D_g}{D_{ij}}---(2-3)$

D_ijIt it is the distance between two wires.

Due to D₁₂=D₄₅,D₁₃=D₄₆,D₂₃=D₅₆,

Average transimpedance coefficient between each phase wire is:

$Z_m=\frac{1}{3}(Z_{12}+Z_{23}+Z_{13})=\frac{1}{3}(Z_{45}+Z_{56}+Z_{46})=R_g+j0.145\lg \frac{D_g}{\sqrt[3]{D_{12}{D}_{23}{D}_{13}}}---(2-4)$

(2) transimpedance coefficient calculations between different circuit

First the transimpedance coefficient of any two wires between the different loop line of scissors crossing transmitting line is studied.

As shown in Figure 3, wire aa ' and bb ' different surface beeline each other, meets at O ' point by downward for aa ' vertical projection and wire bb ', and both are �� angle. Wire aa ', at a distance of �� H, will be obtained the wire parallel with wire bb ' with angle, �� projection by two wires.

Knowing by theory of electromagnetic field, in uniform magnetic field as shown in Figure 4, the magnetic flux through area A is ��=BAcos ��, �� is the angle between the direction of area A and B. The N circle coil being then in magnetic field, if the magnetic flux that its each circle passes through is all identical, then the magnetic linkage passing through this coil is ��=N ��.

Z_abAnd Z_bbDifference in size has following 2 points:

One is Z_abIn compare Z_bbLack the resistance R of b wire_b;

Two is Z_abCompare Z_bbThe reactance of a few part, this part reactance is then corresponding with the magnetic linkage between a wire and b wire.

If the impedance being made up of these two portions is Z_bb', then have

$Z_{BB}^{\′}=lcos\mathrm{\θ}(R_{b}lcos\mathrm{\θ}+j0.145\lg \frac{D_{ab}}{r_{sb}})---(2-3)$

$Z_{bb}^{\′}=\frac{Z_{BB}^{\′}}{l}=cos\mathrm{\θ}(R_b+j0.145\lg \frac{D_{ab}}{r_{sb}})---(2-4)$

So, can obtain transimpedance coefficient according to above-mentioned analysis is:

$Z_{ab}=Z_{bb}-Z_{bb}^{\′}=jcos\mathrm{\θ}(R_g+j0.145\lg \frac{D_g}{r_{sb}}-0.145\lg \frac{D_{ab}}{r_{sb}})---(2-5)$

Therefore formula (2-5) is generalized to the transimpedance coefficient Z of different circuit between each wire of different positions₁₄��Z₁₅��Z₁₆Deng, wherein, each conductor spacing D between different circuit₁₄��D₂₄��D₃₄��D₁₅Etc. being �� H.

When circuit complete transposition, the zero sequence mutual impedance coefficient between different loop line is

$Z_{m^{\′}}=\frac{1}{9}(Z_{14}+Z_{15}+Z_{16}+Z_{24}+Z_{25}+Z_{26}+Z_{34}+Z_{35}+Z_{36})---(2-6)$

To scissors crossing circuit, have when complete transposition:

$\left[\begin{array}{c}\stackrel{.}{U_{1a}}\\ \stackrel{.}{U_{1b}}\\ \stackrel{.}{U_{1c}}\\ \stackrel{.}{U_{2a}}\\ \stackrel{.}{U_{2b}}\\ \stackrel{.}{U_{2c}}\end{array}\right]=\left[\begin{array}{ccccc}{Z}_s& Z_m& Z_m{Z}_{m^{\′}}& Z_{m^{\′}}& Z_{m^{\′}}\\ Z_m& Z_s& Z_m{Z}_{m^{\′}}& Z_{m^{\′}}& Z_{m^{\′}}\\ Z_m& Z_m& Z_s{Z}_{m^{\′}}& Z_{m^{\′}}& Z_{m^{\′}}\\ Z_m& Z_m& Z_s{Z}_{m^{\′}}& Z_{m^{\′}}& Z_{m^{\′}}\\ Z_{m^{\′}}& Z_{m^{\′}}& Z_{m^{\′}}{Z}_s& Z_m& Z_m\\ Z_{m^{\′}}& Z_{m^{\′}}& Z_{m^{\′}}{Z}_m& Z_s& Z_m\end{array}\right]\left[\begin{array}{c}\stackrel{.}{I_{1a}}\\ \stackrel{.}{I_{1b}}\\ \stackrel{.}{I_{1c}}\\ \stackrel{.}{I_{2a}}\\ \stackrel{.}{I_{2b}}\\ \stackrel{.}{I_{2c}}\end{array}\right]=\left[\begin{array}{cc}A& B\\ C& D\end{array}\right]\left[\begin{array}{c}\stackrel{.}{I_{1a}}\\ \stackrel{.}{I_{1b}}\\ \stackrel{.}{I_{1c}}\\ \stackrel{.}{I_{2a}}\\ \stackrel{.}{I_{2b}}\\ \stackrel{.}{I_{2c}}\end{array}\right]---(2-7)$

Wherein partitioned matrix $A=D=\left[\begin{array}{ccc}{Z}_s& Z_m& Z_m\\ Z_m& Z_s& Z_m\\ Z_m& Z_m& Z_s\end{array}\right],B=C=\left[\begin{array}{ccc}{Z}_{m^{\′}}& Z_{m^{\′}}& Z_{m^{\′}}\\ Z_{m^{\′}}& Z_{m^{\′}}& Z_{m^{\′}}\\ Z_{m^{\′}}& Z_{m^{\′}}& Z_{m^{\′}}\end{array}\right].$

For obtaining each sequence impedance parameter of aerial line, voltage, electric current are transformed in symmetric component coordinate system and go, can obtain:

U₀₁₂=S^-1Z_abcSI₀₁₂=Z₀₁₂I₀₁₂(2-8)

Wherein, order impedance matrix Z₀₁₂=S^-1Z_abcS. S is phase sequence conversion matrix, specific as follows: $S=\left[\begin{array}{ccc}1& 1& 1\\ 1& a^2& a\\ 1& a& a^2\end{array}\right],$ $S^{-1}=\frac{1}{3}\left[\begin{array}{ccc}1& 1& 1\\ 1& a& a^2\\ 1& a^2& a\end{array}\right].$

Matrix A and D are brought into after formula (2-8) is launched and obtain sequence impedance parameter, wherein single loop line positive sequence (or negative phase-sequence) impedance parameter Z₁=Z₂=Z_s-Z_m, zero-sequence impedance parameter Z₀=Z_s+2Z_m��

B and C carries out symmetric component to be decomposed as follows:

$S^{-1}\left[\begin{array}{ccc}{Z}_{m^{\′}}& Z_{m^{\′}}& Z_{m^{\′}}\\ Z_{m^{\′}}& Z_{m^{\′}}& Z_{m^{\′}}\\ Z_{m^{\′}}& Z_{m^{\′}}& Z_{m^{\′}}\end{array}\right]S=\left[\begin{array}{ccc}3Z_{m^{\′}}& 0& 0\\ 0& 0& 0\\ 0& 0& 0\end{array}\right]---(2-9)$

Namely only there is zero sequence mutual impedance Z between two loop lines_0m=3Z_m'��

1.2 capacitance parameters calculate

When applying voltage of alternating current on transmission line, even if circuit is non-loaded, also No leakage electric current, but still have charge current flows, this is because parallel wire is the two-plate of the electrical condenser of medium taking air just like a centre. The distance of usual circuit is short, and sectional area is little, and distance between centers of tracks is from greatly, therefore capacitance is very little. But for high pressure long-distance transmission line (when length is more than 80km), the impact of electric capacity significantly increases, in many occasions, such as, during transient state process of electric power system calculates, the accommodation of aerial line just must be added in sequence net.

(1) self-potential coefficient and mutual potential modulus calculate

It is illustrated in figure 5 two built on stilts wire a, b, wire is loaded with electric charge respectively(unit is C/m). The earth is on the impact of wire surrounding electric field distribution to adopt mirror image charge method to consider, wire mirror image with electric charge be respectivelyAdopt following hypothesis: ground is the isopotential surface of zero potential; Electric charge on wire evenly distributes, thus for the electrostatic field outside wire, it is possible to being used as is concentrate on the axis of wire; The current potential of wire is constant along the line; Wire is constant apart from the height on ground.

For self-potential coefficient, with P_aaFor example, P_aaRefer to when wire having unit charge and other wires do not have an electric charge due current potential on wire a. When wire b does not have electric charge, between electric charge and above earth potential, there is following relation:

${\stackrel{\·}{U}}_a=P_{aa}{\stackrel{\·}{Q}}_a---(2-11)$

Now wire a and its image conductor a ' form a single phase two-line road, therefore the current potential on wire a can represent according to electric field theory and is:

${\stackrel{\·}{U}}_a=\frac{{\stackrel{\·}{Q}}_a}{2\mathrm{\π}\mathrm{\ζ}}ln\frac{H_{{\mathrm{aa}}^{\′}}}{r_a}---(2-12)$

Thus obtain: $P_{aa}=\frac{1}{2\mathrm{\π}\mathrm{\ζ}}ln\frac{H_{{\mathrm{aa}}^{\′}}}{r_a}---(2-13)$

r_aFor the radius of wire a; H_aa'Distance between wire a and its image conductor; �� is medium coefficient, it is known that the dielectric constant in vacuum is

General expression for the self-potential coefficient of any wire is as follows:

$P_{ii}=\frac{1}{2\mathrm{\π}\mathrm{\ζ}}ln\frac{H_{{\mathrm{ii}}^{\′}}}{r_i}=41.45\×{10}^6\lg \frac{H_{{\mathrm{ii}}^{\′}}}{r_i}km/F---(2-14)$

Mutual potential modulus, with P_ba, due current potential on wire b when being have unit charge on guide line and do not have electric charge on all the other wires.When wire b and c does not have electric charge, define according to mutual potential modulus:

${\stackrel{\·}{U}}_b=P_{ba}{\stackrel{\·}{Q}}_a---(2-15)$

The current potential that wire a and self image conductor a ' produces on wire b, can represent and be

${\stackrel{\·}{U}}_a=\frac{{\stackrel{\·}{Q}}_b}{2\mathrm{\π}\mathrm{\ζ}}ln\frac{H_{{\mathrm{ba}}^{\′}}}{D_{ba}}---(2-16)$

Thus obtain: $P_{ba}=\frac{1}{2\mathrm{\π}\mathrm{\ζ}}ln\frac{H_{{\mathrm{ba}}^{\′}}}{D_{ba}}---(2-17)$

For any two wire i and j, the general expression of mutual potential modulus should be:

$P_{ij}=P_{ji}=\frac{1}{2\mathrm{\π}\mathrm{\ζ}}ln\frac{H_{{\mathrm{ij}}^{\′}}}{D_{ij}}=41.45\×{10}^6\lg \frac{H_{{\mathrm{ij}}^{\′}}}{D_{ij}}km/F---(2-18)$

H in formula_ij'Distance between the image conductor of wire i and wire j, D_ijFor the distance between wire i and wire j.

(2) the phase sequence electric capacity of scissors crossing transmitting line

From mutual potential modulus expression formula (2-18), owing to the distance between scissors crossing transmitting line is in change, the distance to ground mirror image and another loop line of one loop line is also changing, therefore potential modulus changes along the line, parallel double loop is not equally constant for another example, the electric capacity expression formula of scissors crossing circuit of deriving below by variable of place on line x.

The space multistory figure of scissors crossing wire is as shown in Fig. 6 (a) and Fig. 6 (b), and wherein MN and PQ is two built on stilts wires on different loop line road, ST and PQ is the adjacent wires on same loop line road, and at a distance of sm, wire is all parallel to ground. MN is �� H place above PQ circuit, and M ' N ' is the projection under MN vertical direction, and with PQ copline, meet at virtual point of intersection O', �� at an angle to each other. The upper existence point 1 of PQ is apart from O' point xkm, and point 1 and underground mirror point 1' are at a distance of H₁, O point is �� H place above O' point, and point 2 is apart from O point xkm, and point 2 and underground mirror point are at a distance of H₂, some 1' and point 2 are at a distance of H₁₂, 1,2 at a distance of D₁₂, point 1 and the subpoint D apart putting 2_12��, point 2 and the subpoint D apart putting 3_23����

Such as Fig. 6 (a), between circuit PQ and MN, there is following geometric relationship:

H₂-H₁=2 �� H (2-19)

D_1'2=2xsin (��/2) (2-20)

$H_{{12}^{\′}}=\sqrt{{(H_1+\mathrm{\Δ}H)}^2+{D_{1^{\′}2}}^2}---(2-21)$

$D_{12}=\sqrt{D^2+{\mathrm{\ΔH}}^2}---(2-22)$

Such as Fig. 6 (b), between circuit ST and MN, there is following geometric relationship:

$D_{2^{\′}3}=\sqrt{x^2+(x^2+s^2)-2x\sqrt{x^2+s^2}cos(\mathrm{\θ}+\arctan \frac{s}{x})}---(2-23)$

$H_{{12}^{\′}}=\sqrt{{(H_1+\mathrm{\Δ}H)}^2+{D_{2^{\′}3}}^2}---(2-24)$

$D_{23}=\sqrt{{D_{2^{\′}3}}^2+{\mathrm{\ΔH}}^2}---(2-25)$

The geometric relationship of other consecutive position circuits can also similar calculate. Relevant parameter is brought formula (2-14) into and (2-18) can obtain the mutual potential modulus formula between the self-potential coefficient of circuit and any two lines of scissors crossing transmitting line. When changing apart from virtual point of intersection distance x, H₁��H₂Constant, self-potential coefficient and constant with the mutual potential modulus in loop line road; D₁₂Changing, the mutual potential modulus between scissors crossing circuit along the line changes.

Wire is respectively through complete transposition (syllogic), the average self-potential coefficient of scissors crossing transmitting line every phase wire $P_{s1}=\frac{1}{3}(P_{11}+P_{22}+P_{33}),P_{s2}=\frac{1}{3}(P_{44}+P_{55}+P_{66});$ It is respectively with the average potential modulus mutually between each wire of loop line $P_{m1}=\frac{1}{3}(P_{12}+P_{23}+P_{13}),P_{m2}=\frac{1}{3}(P_{45}+P_{46}+P_{56}).$ Between different loop line, average potential modulus mutually is $P_{m^{\′}}\left(x\right)=\frac{1}{9}(P_{14}+P_{15}+P_{16}+P_{24}+P_{25}+P_{26}+P_{34}+P_{35}+P_{36}).$ P₁₁��P₁₂��P₁₄Deng being self-potential coefficient during scissors crossing circuit different positions and mutual potential modulus, circuit label is shown in Fig. 2.

According to Maxwell equation, to the two of scissors crossing single loop lines, current potential and the pass of the contained electric charge of each wire on each line be:

$\left[\begin{array}{c}\stackrel{.}{U_{1a}}\\ \stackrel{.}{U_{1b}}\\ \stackrel{.}{U_{1c}}\\ \stackrel{.}{U_{2a}}\\ \stackrel{.}{U_{2b}}\\ \stackrel{.}{U_{2c}}\end{array}\right]=\left[\begin{array}{ccccc}{P}_{s1}& P_{m1}& P_{m1}{P}_{m^{\′}}& P_{m^{\′}}& P_{m^{\′}}\\ P_{m1}& P_{s1}& P_{m1}{P}_{m^{\′}}& P_{m^{\′}}& P_{m^{\′}}\\ P_{m1}& P_{m1}& P_{s1}{P}_{m^{\′}}& P_{m^{\′}}& P_{m^{\′}}\\ P_{m^{\′}}& P_{m^{\′}}& P_{m^{\′}}{P}_{s2}& P_{m2}& P_{m2}\\ P_{m^{\′}}& P_{m^{\′}}& P_{m^{\′}}{P}_{m2}& P_{s2}& P_{m2}\\ P_{m^{\′}}& P_{m^{\′}}& P_{m^{\′}}{P}_{m2}& P_{m2}& P_{s2}\end{array}\right]\left[\begin{array}{c}\stackrel{.}{Q_{1a}}\\ \stackrel{.}{Q_{1b}}\\ \stackrel{.}{Q_{1c}}\\ \stackrel{.}{Q_{2a}}\\ \stackrel{.}{Q_{2b}}\\ \stackrel{.}{Q_{2c}}\end{array}\right]=\left[\begin{array}{cc}A& B\\ C& D\end{array}\right]\left[\begin{array}{c}\stackrel{.}{Q_{1a}}\\ \stackrel{.}{Q_{1b}}\\ \stackrel{.}{Q_{1c}}\\ \stackrel{.}{Q_{2a}}\\ \stackrel{.}{Q_{2b}}\\ \stackrel{.}{Q_{2c}}\end{array}\right]---(2-26)$

Wherein partitioned matrix $\begin{array}{c}A=\left[\begin{array}{ccc}{P}_{s1}& P_{m1}& P_{m1}\\ P_{m1}& P_{s1}& P_{m1}\\ P_{m1}& P_{m1}& P_{s1}\end{array}\right]\\ D=\left[\begin{array}{ccc}{P}_{s2}& P_{m2}& P_{m2}\\ P_{m2}& P_{s2}& P_{m2}\\ P_{m2}& P_{m2}& P_{s2}\end{array}\right]\end{array},B\left(x\right)=C\left(x\right)=\left[\begin{array}{ccc}{P}_{m^{\′}}\left(x\right)& P_{m^{\′}}\left(x\right)& P_{m^{\′}}\left(x\right)\\ P_{m^{\′}}\left(x\right)& P_{m^{\′}}\left(x\right)& P_{m^{\′}}\left(x\right)\\ P_{m^{\′}}\left(x\right)& P_{m^{\′}}\left(x\right)& P_{m^{\′}}\left(x\right)\end{array}\right]$

Owing to two single loop line heights off the ground are different, therefore current potential matrix A �� D; Due to the distance dependent between mutual potential modulus and two single loop lines, B, C turn into the function of place on line x, change with place on line x and change, and B (x)=C (x).

The sequence potential parameters of single back line is identical with the method for calculation of impedance previously discussed, respectively two systems is carried out decoupling zero by symmetric component method. Voltage, electric current are transformed in symmetric component coordinate system and go, can obtain:

jwU₀₁₂=S^-1PSI₀₁₂=P₀₁₂I₀₁₂Wherein, P₀₁₂=S^-1PS

P₀₁₂For the potential modulus matrix in symmetric component coordinate system, after launching, A and D is separately converted to $\left[\begin{array}{ccc}{P}_{s1}+2P_{m1}& 0& 0\\ 0& P_{s1}-P_{m1}& 0\\ 0& 0& P_{s1}-P_{m1}\end{array}\right]$ With $\left[\begin{array}{ccc}{P}_{s2}+2P_{m2}& 0& 0\\ 0& P_{s2}-P_{m2}& 0\\ 0& 0& P_{s2}-P_{m2}\end{array}\right],$ In matrix, each off-diagonal element is zero, represent positive and negative, between zero sequence without coupling, separate.

B and C carries out symmetric component to be decomposed as follows:

$S^{-1}\left[\begin{array}{ccc}{P}_{m^{\′}}\left(x\right)& P_{m^{\′}}\left(x\right)& P_{m^{\′}}\left(x\right)\\ P_{m^{\′}}\left(x\right)& P_{m^{\′}}\left(x\right)& P_{m^{\′}}\left(x\right)\\ P_{m^{\′}}\left(x\right)& P_{m^{\′}}\left(x\right)& P_{m^{\′}}\left(x\right)\end{array}\right]S=\left[\begin{array}{ccc}3P_{m^{\′}}\left(x\right)& 0& 0\\ 0& 0& 0\\ 0& 0& 0\end{array}\right]---(2-27)$

I.e. coupling capacity between double loop only zero sequence coupling capacity. In sequence potential modulus matrix, the inverse of each element is each sequence electric capacity, when circuit complete transposition, as follows with equation expression:

Single loop line positive sequence electric capacityAnother single loop line positive sequence electric capacity

Single loop line negative phase-sequence electric capacity $C_2=\frac{1}{P_{s1}-P_{m1}}$ Another single loop line negative phase-sequence electric capacity $C_2=\frac{1}{P_{s2}-P_{m2}}---(2-28)$

Single loop line zero sequence electric capacityAnother single loop line zero sequence electric capacity

Zero sequence mutual capacity between scissors crossing circuit

Double-circuit lines on the same pole is as a kind of special case of scissors crossing transmitting line, two loop line angulations are 0, and by optimizing and rationally replace, make same loop line road each phase self-inductance and ground admittance is equal, any two alternate transimpedance are equal with transadmittance, and the transimpedance between any two-phase conductor of different loop line roads is equal with transadmittance. Therefore double-circuit lines on the same pole each sequence electric capacity simplifies as follows by formula (2-27):

Single loop line positive sequence electric capacitySingle loop line negative phase-sequence electric capacity

Single loop line zero sequence electric capacityDouble loop zero sequence coupling capacity

2. the zero sequence current-voltage correlation of coupling mutually

When complete transposition, when two circuits are by positive sequence (or negative phase-sequence) electric current, owing to every loop line tri-phase current sum equals zero, thus the average transimpedance coefficient of positive sequence (or negative phase-sequence) between two loop line roads will be zero. Therefore, the positive sequence impedance of every loop line is completely equal with single loop line zero sequence impedance. At circuit by quite different during zero sequence electric current, because the three-phase zero sequence electric current sum of every loop line is not zero, there is zero sequence mutual impedance between two loop line roads, the formula of a front joint is derived and is demonstrated this point. Also it is like this to zero sequence transadmittance.

The distributed parameter model of positive sequence (or negative phase-sequence) is even Long line transmission equation, the electric current and voltage at distance terminal voltage electric current x placeCan calculate by formula (3-1), corresponding electric current and voltage and Z_c, �� brings positive sequence (or negative phase-sequence) into and measures.

Wherein,For line characteristic impedance,For line propagation coefficient, i=1,2,For terminal voltage electric current positive sequence (or negative phase-sequence) amount.

Scissors crossing transmitting line is discussed containing the zero sequence current-voltage correlation of zero sequence mutual impedance and admittance below. Copying the derivation of even Long line transmission equation, the general zero sequence distributed parameter model schematic diagram that scissors crossing circuit is coupled mutually is as shown in Figure 7.

Distributed parameter model according to Fig. 7, the zero sequence volts lost of the first loop line dx sectionWith zero sequence current incrementCan represent and be:

$\begin{array}{c}d{\stackrel{\·}{V}}_1={\stackrel{\·}{I}}_1{z}_{1}dx+{\stackrel{\·}{I}}_2{z}_{m}dx\\ d{\stackrel{\·}{I}}_1={\stackrel{\·}{V}}_1(y_1+y_m(x\left)\right)dx-{\stackrel{\·}{V}}_2{y}_m\left(x\right)dx\end{array}---(3-2)$

Namely $\begin{array}{c}\frac{{\stackrel{.}{dV}}_1}{dx}={\stackrel{\·}{I}}_1{z}_1+{\stackrel{\·}{I}}_2{z}_m\\ \frac{d{\stackrel{\·}{I}}_1}{dx}={\stackrel{\·}{V}}_1(y_1+y_m(x\left)\right)-{\stackrel{\·}{V}}_2{y}_m\left(x\right)\end{array}---(3-3)$

With reason, the voltage-current relationship of the 2nd loop line is $\begin{array}{c}\frac{{\stackrel{.}{dV}}_2}{dx}={\stackrel{\·}{I}}_2{z}_2+{\stackrel{\·}{I}}_1{z}_m\\ \frac{d{\stackrel{\·}{I}}_2}{dx}={\stackrel{\·}{V}}_2(y_2+y_m(x\left)\right)-{\stackrel{\·}{V}}_1{y}_m\left(x\right)\end{array}---(3-4)$

Wherein, be coupled capacitive reactance y_mX () is the function apart from virtual point of intersection distance x. This differential equation group cannot directly solve shape such as the expression formula of even Long line transmission equation, therefore adopts Runge-Kutta method to separate this first order differential equation system.

To double-circuit lines on the same pole, z₁=z₂, y₁=y₂, y_mFor definite value, V₁=V₂, equation is simplified. When two loop lines are without coupling, z_m��y_mBeing 0, formula (3-3) and (3-4) are simplified, and it is separated as shape is such as formula the even Long line transmission equation of (3-1).

3. calculation result and checking

3.1 spatial arrangement are to the analysis of Influential Factors of line parameter circuit value

Given circuit inherent parameters, comprises wire radius, distance floor level h₁, scissors crossing transmitting line �� at an angle to each other and vertical range �� H etc., according to " Code for planning of urban electric power (GB50293-1999) ", minimum perpendicular distance between 220kV overhead power transmission line road wire and ground, non-residential areas is 6.5m, the horizontal phase spacing of same loop line is 7 12m, arranges concrete parameter as shown in table 1.Use the calculation formula derived can obtain the distribution parameter of transmitting line, comprise single loop line and just (bearing) order parameter R₁��L₁��C₁, single loop line Zero sequence parameter R₀��L₀��C₀, scissors crossing circuit transimpedance parameter R_0m��L_0m��C_0m(x)��

Table 1 sets parameter list

Lower loop line wire real radius r (each phase wire radius is equal)	25mm
		Higher loop line wire real radius r (each phase wire radius is equal)	20mm
Wire average geometric radius r '	R'=0.779r
		The equivalent resistance R of the unit length of big ground circuitg	0.05��/km
A lower loop line distance floor level h1	7m
		Soil resistivity ��	2����m
With loop line phase spacing s (assuming that two loop lines are identical)	7m

The impact of the vertical range �� H that the zero sequence of the higher loop line of scissors crossing circuit and positive-negative sequence electric capacity are subject between scissors crossing two back transmission line, as shown in Fig. 8 (a) and Fig. 8 (b).

Zero sequence mutual resistance between the scissors crossing circuit derived, mutual inductance, mutual tolerance expression formula controlled variable are drawn figure as shown in Fig. 9 (a), Fig. 9 (b) and Figure 10 (a), Figure 10 (b).

As shown in Fig. 9 (a), Fig. 9 (b), when angle is fixing, the zero-sequence mutual inductance between scissors crossing transmitting line reduces with the increase of height. When angle increases to 90 degree, mutual inductance is 0, namely there is not jigger coupling between two loop lines. Shown in Figure 10 (a), Figure 10 (b), when highly fixing, the zero-sequence mutual inductance between scissors crossing transmitting line reduces with the increase of angle, until being 0 when 90 ��.

From Figure 11 (a)-(c) it may be seen that zero sequence mutual tolerance increases with the increase of height between scissors crossing transmitting line, increase with the increase of circuit angulation, increase with the increase of distance intersection. When angle is 90 ��, zero sequence mutual capacity increases speed and speeds, and capacitive reactance reduces rapidly.

3.2 simulating, verifying

Owing to the three-dimensional transmitting line model embodying spatial relation cannot be built by existing simulation software, therefore in simulink, first two groups of list loop parameters are utilized to build two independent single loop line realistic models respectively, wherein can represent for Figure 12 (a) during arbitrary loop line generation fault, can represent for Figure 12 (b) during normal operation, two loop lines all adopt distributed parameter transmission line model, and essential parameter of circuit is as shown in table 1. Wherein, a lower revolving line voltage grade 220kV, phase angle difference is 20 ��, total length 300km, a higher revolving line voltage grade 500kV, and phase angle difference is 20 ��, and both are respectively 1 and 1.05pu, total length 300km at power supply amplitude.

Two separate single loop line system M, N both sides system parameter are:

Z_m1=1.2498+j16.932 ��, Z_m0=6.888+j43.139 ��; Z_n1=1.0415+j14.110 ��, Z_n0=5.74+j35.949 ��.

The lower positive order parameter R of loop line calculated by the 2nd three-dimensional universal former of nodel line road distribution parameter by the initial parameter in table 1₁=0.06 ��/km, L₁=1.226mH/km, C₁=0.009375uF/km; Zero sequence parameter R₀=0.21 ��/km, L₀=2.853mH/km, C₀=0.007048uF/km.

A higher positive order parameter R of loop line₁=0.06 ��/km, L₁=1.271mH/km, C₁=0.008819uF/km; Zero sequence parameter R₀=0.21 ��/km, L₀=2.898mH/km, C₀=0.005307uF/km.

Known double-circuit lines on the same pole single line fault ratio accounts for more than 80%, scissors crossing transmitting line is owing to distance between centers of tracks is from bigger than double-circuit lines on the same pole, and it is more far away apart from point of crossing, the spacing of two loop lines is more big, cross line fault probability is obviously low than double-circuit lines on the same pole, therefore simulating, verifying only considers that the situation of single loop line fault wherein occurs for one time scissors crossing circuit.

Assume that circuit mid point 150km (x=0) place is the virtual point of intersection of scissors crossing circuit. Arranging trouble spot A phase ground fault on a lower loop line road according to left end 150km place, fault interval is [0.04s, 0.08s], and a higher loop line normally runs, and carrys out analog crossover and crosses over the single line fault in circuit. After the fault at circuit left end (x=150km) place measurement obtained, the phase voltage electric current of two cycles is converted into zero sequence electric current and voltage, wherein, and a lower loop line zero sequence voltage U₀=-1.4135+1.3175ikV, I₀=-21.7780-33.6935iA; A higher loop line U₀=0kV, I₀=0A, solves differential equation (3-3), (3-4) as separate single loop line initial value.

Know by 3.1 joints, scissors crossing circuit is more far away apart from virtual point of intersection, more little by zero sequence coupling influence, so time current/voltage value closer to the actual value of two independent single loop lines, owing to the former is relevant with spatial arrangement, the method that there is no at present utilizes software to build model to obtain, therefore has more reasonableness using apart from virtual point of intersection the latter remotely as intersection transmitting line left end current and voltage quantities.

Vertical range �� H between scissors crossing two back transmission line gets 10m. According to different schemes, zero sequence mutual impedance and the anti-parameter of mutual tolerance between the Zero sequence parameter calculated by electric parameter universal computer model and scissors crossing circuit are as shown in table 2.

Table 2 scheme arranges detail

Note: wherein unit impedance parameter unit is ��/km, unit admit parameter unit is 1/ (�� km).

Figure 13 indicates the non-linear ununiformity of scissors crossing transmitting line capacitive reactance parameter, Y_0mThe step-length changed from 1km in virtual point of intersection is increasing, until no longer changing, can be equivalent to segmentation parallel double loop in follow-up study.

Each scheme crossing elimination point zero sequence electric current and voltage is obtained as shown in table 3 by general distributed parameter model.

Scissors crossing voltage of system Current calculation result during a table 3 lower loop line A phase ground connection

Scheme one does not all consider coupling capacity to scheme three, in scheme three, scissors crossing angle is 90 degree, know that zero sequence mutual impedance is 0 by formula (2-5), namely there is not any coupling between circuit, single loop line that the electric parameter of scissors crossing circuit is not considered to be coupled with two is as good as, contrast scheme three and reference scheme, at the zero sequence electric current and voltage at circuit point of crossing place, have confirmed this point, thus have demonstrated the exactness of zero sequence mutual impedance calculation method of parameters in scissors crossing electric transmission line three-dimensional model.

Owing to failure mode and position of fault are numerous, providing the calculation result that the asymmetric fault of several classics occurs 30 �� of scissors crossing circuits below, what obtain with measurement does not consider that be coupled two single loop line systems compare. By table 3 table 7 it will be seen that when loop line a certain in scissors crossing circuit, at different positions along the line, asymmetric fault occurs, mutual resistance, mutually reactance and mutual capacity effect all be can not ignore.

Scissors crossing voltage of system Current calculation result during a table 4 higher loop line A phase ground connection

Scissors crossing voltage of system Current calculation result when the lower loop line BC phase of table 5 is short-circuit

Scissors crossing voltage of system Current calculation result during a table 6 higher loop line BC phase ground short circuit

Get the situation of 30 �� of higher loop line 50km place A phase ground connection of scissors crossing circuit in table 4, calculating the zero sequence electric current and voltage along the line from point of crossing (x=0km) to circuit left end (x=150km) as shown in figure 14, the single loop line zero sequence electric current and voltage along the line of separate two is as shown in figure 15.

Contrast Figure 14,15 is it will be seen that angled scissors crossing circuit, if processed by independent two single loop lines, compared with the current/voltage along the line caused because of actual coupling condition, amplitude, phase angle all exist notable difference. This species diversity along with between scissors crossing circuit height shortening, angle reduction, by increasing. Therefore scissors crossing circuit can not process according to independent single loop line in engineering reality, otherwise likely there is a series of adverse consequences such as false protection, distance accuracy reduction.

The present invention has derived scissors crossing line parameter circuit value universal computer model based on the route parameter calculation formula of classics, analyze angle, relative height, apart from intersection on the impact of circuit coupling parameter, it is to construct general zero sequence current/voltage equation when scissors crossing circuit is coupled mutually. Concerning scissors crossing transmitting line, its zero sequence mutual impedance parameter diminishes with the increase of angle, height, zero sequence mutual capacity parameter becomes big with the increase of angle, height, and change along the line, more far away apart from virtual point of intersection, numerical value is more big, after reaching certain distance, no longer change, the parallel double loop that there is coupling can be equivalent to. Matlab emulation contrast is carried out by many prescriptions case, demonstrate the exactness of the three-dimensional circuits parameter universal computer model considering conductor spatial arrangement, find scissors crossing circuit simultaneously, if processed by independent two single loop lines, difference is there is compared with the current/voltage along the line caused because of actual coupling condition, and difference can not ignore, thus demonstrate the practicality of this model. This mathematical model is the basis of Load flow calculation, relaying, transient state analysis and fault localization, has directive significance in engineering practice.

By reference to the accompanying drawings the specific embodiment of the present invention is described although above-mentioned; but not limiting the scope of the invention; one of ordinary skill in the art should be understood that; on the basis of the technical scheme of the present invention, those skilled in the art do not need to pay various amendment or distortion that creative work can make still within protection scope of the present invention.

Claims (9)

1. consider the circuit distribution parameter Three-dimensional CAD method of design of conductor spatial arrangement, it is characterized in that, comprise the following steps:

(1) setting up the transmitting line model of scissors crossing, the transmitting line model of described scissors crossing comprises lower section one loop line a, b, c three-phase line 1,2,3, and top one loop line a, b, c three-phase line 4,5,6;

In the transmitting line model of described scissors crossing, during by the single loop line vertical projection above scissors crossing transmitting line to lower section list loop line, in �� angle between the two-phase of different loop line;

(2) gather the inherent parameters of scissors crossing transmitting line, comprising: wire radius, the single loop line distance floor level h in lower section₁, vertical range �� H between scissors crossing transmitting line �� at an angle to each other and scissors crossing transmitting line;

(3) according to the circuit inherent parameters collected, calculate respectively from impedance factor, with the transimpedance coefficient between loop line and the transimpedance coefficient between different loop line, and obtain each sequence impedance parameter in scissors crossing transmitting line;

(4) the self-potential coefficient of any wire is calculated; The earth is on the impact of wire surrounding electric field distribution to adopt mirror image charge method to consider, according to the radius of wire, wire corresponding thereto distance between the image conductor on ground calculate the mutual potential modulus with any two wires of loop line;

(5) assuming that MN and PQ is the built on stilts wire on different loop line road, ST and PQ is the adjacent wires on same loop line road;Being the projection M'N' of circuit MN in PQ plane, circuit M'N' gives an O' with circuit PQ phase, and some O is the point corresponding with an O' on circuit MN; If the distance of circuit MN upper 1: 1 to some O is x, it is that variable calculates any two wires mutual potential modulus along the line taking x;

(6) the zero sequence mutual capacity being converted between the positive sequence of scissors crossing circuit, negative phase-sequence and zero sequence electric capacity and scissors crossing circuit according to the self-potential coefficient calculated and mutual potential modulus according to phase sequence;

(7) according to the line parameter circuit value of above-mentioned calculating, it is to construct the general sequence currents voltage equation of scissors crossing circuit; Specifically comprise:

When passing through positive sequence or negative phase-sequence electric current when scissors crossing circuit, current/voltage equation is even transmission line equation;

When scissors crossing circuit is by zero sequence electric current, according to the expression formula of the zero sequence voltage increment at distance line end x position place and zero sequence current increment, it is to construct zero sequence current/voltage system of equations.

2. a kind of circuit distribution parameter Three-dimensional CAD method of design considering conductor spatial arrangement as claimed in claim 1, is characterized in that, in described step (3),

In the same circuit, each phase wire is parallel to each other, and to arbitrary two wires i, j between same loop line, transimpedance coefficient is specially:

$Z_{ij}=R_g+j0.145\lg \frac{D_g}{D_{ij}};$

Wherein, R_gFor the equivalent resistance of unit length of big ground circuit,For the equivalent degree of depth of ground medium value wire d, r_si��r_sdIt is respectively wire i and the equivalence radius of equivalent ground wire d, D_idFor the equivalence distance of wire i with equivalently loop line d;

Transimpedance coefficient between different loop line is specially:

$Z_{m^{\′}}=\frac{1}{9}(Z_{14}+Z_{15}+Z_{16}+Z_{24}+Z_{25}+Z_{26}+Z_{34}+Z_{35}+Z_{36})$

Wherein, Z₁₄For the transimpedance between loop line 1 and loop line 4 two-phase wire; Z₁₅��Z₃₆The implication transimpedance that is also respectively between different loop line two-phase wire.

3. a kind of circuit distribution parameter Three-dimensional CAD method of design considering conductor spatial arrangement as claimed in claim 1, is characterized in that, in described step (3), in transmitting line, the impedance parameter of each loop line is specially:

Single loop line positive sequence or negative phase-sequence impedance parameter Z₁=Z₂=Z_s-Z_m, zero-sequence impedance parameter Z₀=Z_s+2Z_m��

Zero sequence mutual impedance Z is only there is between two loop lines_0m=3Z_m';

Wherein, Z_sAverage from impedance factor for each single loop line; Z_mFor the average transimpedance coefficient between phase wire each in same loop line; Z_m'For the zero sequence mutual impedance coefficient between different loop line.

4. a kind of circuit distribution parameter Three-dimensional CAD method of design considering conductor spatial arrangement as claimed in claim 1, is characterized in that, in described step (4), the self-potential coefficient of any wire is specially:

$P_{ii}=41.45\×{10}^6\lg \frac{H_{{\mathrm{ii}}^{\′}}}{r_i},$ Unit is km/F;

Wherein, H_ii'For the distance of wire i and its image conductor, r_iFor the radius of wire i.

5. a kind of circuit distribution parameter Three-dimensional CAD method of design considering conductor spatial arrangement as claimed in claim 1, is characterized in that, in described step (4), be specially with the mutual potential modulus of any two wire i and j of loop line:

$P_{ij}=P_{ji}=41.45\×{10}^6\lg \frac{H_{{\mathrm{ij}}^{\′}}}{D_{ij}}km/F$

H in formula_ij'Distance between the image conductor of wire i and wire j, D_ijFor the distance between wire i and wire j.

6. a kind of circuit distribution parameter Three-dimensional CAD method of design considering conductor spatial arrangement as claimed in claim 1, is characterized in that, in described step (5), be that the mutual potential modulus of any two wires between the different loop lines of variable is taking x:

In described step (5), it is assumed that MN and PQ is two wires on different loop line road, ST and PQ is the adjacent wires on lower loop line road, and at a distance of being s, wire is all parallel to ground; On circuit PQ, point 1 is apart from O' point x, and point 1 and underground mirror point 1' are at a distance of H₁;On circuit MN, point 2 is apart from O point x, point 2 and underground mirror point 2 " at a distance of H₂; On circuit ST, point 3 is apart from the some O corresponding with some O' on circuit PQ " x, point 3 and its underground mirror point 3' are at a distance of H₁; MN is �� H place above PQ circuit, M'N' be under MN vertical direction project, and with PQ copline, meet at virtual point of intersection O', �� at an angle to each other;

Following geometric relationship is there is between circuit PQ and MN:

H₂-H₁=2 �� H

D_1'2=2xsin (��/2)

$H_{{12}^{\′}}=\sqrt{{(H_1+\mathrm{\Δ}H)}^2+{D_{1^{\′}2}}^2}$

$D_{12}=\sqrt{D^2+{\mathrm{\ΔH}}^2}$

Following geometric relationship is there is between circuit ST and MN:

$D_{2^{\′}3}=\sqrt{x^2+(x^2+s^2)-2x\sqrt{x^2+s^2}cos(\mathrm{\θ}+arctan\frac{s}{x})};$

$H_{2^{\′}3}=\sqrt{{(H_1+\mathrm{\Δ}H)}^2+{D_{2^{\′}3}}^2};$

$D_{23}=\sqrt{{D_{2^{\′}3}}^2+{\mathrm{\ΔH}}^2};$

Wherein, D₁₂For putting the distance that 1 arrives point 2; D_1'2Distance, the H of point 1 is arrived for putting the subpoint 2 ' of 2_12'For distance, the D of the underground mirror image point-to-point 2 of putting 1_2'3Distance, the H of point 3 is arrived for putting the subpoint 2 ' of 2_2'3For distance, the D of the underground mirror image point-to-point 2 of putting 3₂₃For putting the distance that 2 arrive point 3;

Above-mentioned parameter is brought into respectively in step (4) calculation formula of the mutual potential modulus with any two wire i and j of loop line, the mutual potential modulus between any two lines of scissors crossing transmitting line can be tried to achieve.

7. a kind of circuit distribution parameter Three-dimensional CAD method of design considering conductor spatial arrangement as claimed in claim 1, it is characterized in that, in described step (6), in two loop lines, the positive sequence of scissors crossing transmitting line, negative phase-sequence and zero sequence electric capacity are specially:

Single loop line positive sequence electric capacity $C_1=\frac{1}{P_{s1}-P_{m1}};$ Another single loop line positive sequence electric capacity $C_1=\frac{1}{P_{s2}-P_{m2}};$

Single loop line negative phase-sequence electric capacity $C_2=\frac{1}{P_{s1}-P_{m1}};$ Another single loop line negative phase-sequence electric capacity $C_2=\frac{1}{P_{s2}-P_{m2}};$

Single loop line zero sequence electric capacity $C_0=\frac{1}{P_{s1}+2P_{m1}};$ Another single loop line zero sequence electric capacity $C_0=\frac{1}{P_{s2}+2P_{m2}};$

Zero sequence mutual capacity between scissors crossing circuit is:

$C_{0m}\left(x\right)=\frac{1}{3P_{m^{\′}}\left(x\right)}$

Wherein, P_s1��P_s2The average self-potential coefficient being respectively in scissors crossing transmitting line two loop line every phase wire; P_m1��P_m2The average potential modulus mutually being respectively in same loop line between each wire; P_m'X () is average potential modulus mutually between different loop line.

8. a kind of circuit distribution parameter Three-dimensional CAD method of design considering conductor spatial arrangement as claimed in claim 1, it is characterized in that, in described step (7), when scissors crossing circuit by zero sequence electric current time, it is to construct zero sequence current/voltage system of equations be specially:

The positive sequence at distance terminal voltage electric current x place or negative sequence voltage electric currentThere is following relation:

$\begin{array}{c}d\stackrel{\·}{V}={\stackrel{\·}{I}}_2{z}_{i}dx\\ d\stackrel{\·}{I}={\stackrel{\·}{V}}_2{y}_{i}dx\end{array};$

Its general solution is:

Wherein,For line characteristic impedance,For line propagation coefficient, i=1,2, represents positive sequence or the electric parameter of negative phase-sequence;For terminal voltage electric current positive sequence or negative phase-sequence amount.

9. a kind of circuit distribution parameter Three-dimensional CAD method of design considering conductor spatial arrangement as claimed in claim 1, is characterized in that, in described step (7), to scissors crossing power transmission line zero-sequence network, and the voltage-current relationship of the 2nd loop line:

$\frac{{\stackrel{\·}{dV}}_1}{dx}={\stackrel{\·}{I}}_1{z}_1+{\stackrel{\·}{I}}_2{z}_m$

$\frac{d{\stackrel{\·}{I}}_1}{dx}={\stackrel{\·}{V}}_1(y_1+y_m(x\left)\right)-{\stackrel{\·}{V}}_2{y}_m\left(x\right)$

The voltage-current relationship of the 2nd loop line:

$\frac{{\stackrel{\·}{dV}}_2}{dx}={\stackrel{\·}{I}}_2{z}_2+{\stackrel{\·}{I}}_1{z}_m$

$\frac{d{\stackrel{\·}{I}}_2}{dx}={\stackrel{\·}{V}}_2(y_2+y_m(x\left)\right)-{\stackrel{\·}{V}}_1{y}_m\left(x\right)$

Wherein,It is respectively zero sequence voltage, the electric current at scissors crossing circuit lower and higher loop line distance end x place; z₁For zero sequence impedance, z_mFor zero sequence mutual impedance, y₁For zero sequence admittance, y_mX () is zero sequence transadmittance.