CN106199192A - The positive sequence on-line testing method of parallel many back transmission lines Zero sequence parameter - Google Patents

Abstract

The positive sequence on-line testing method of parallel many back transmission lines Zero sequence parameter, belongs to parallel multi circuit transmission lines coupling parameter field tests.The method utilizes steady state data to measure the positive sequence impedance of tested loop line, admittance, calculate ratio and the ratio of each admittance of the parallel each impedance of many loop lines under equivalent environment, set up the relation of each corresponding physical quantity, to own impedance and mutual impedance (own admittance and mutual admittance)WithEstimation, finally withForm occur, restrained effectively error, it is achieved the zero sequence coupled impedance of parallel many back transmission lines, the indirect on-line testing of admittance.The method of testing that the present invention proposes need not produce zero sequence operation specially, do not affect the properly functioning of system, and consider the soil resistivity impact on impedance detecting method specially, ensure that fault-tolerant ability and the capacity of resisting disturbance of context of methods, simplify the parameter test method of parallel many back transmission lines, improve efficiency, motility and the operability of test.

Description

The positive sequence on-line testing method of parallel many back transmission lines Zero sequence parameter

Technical field

The invention belongs to parallel many back transmission lines zero sequence coupling parameter field tests.The present invention proposes a kind of parallel many The on-line testing method of back transmission line zero sequence coupling parameter, when the method only needs parallel many back transmission lines one group properly functioning Both end voltage, electric current, measure positive sequence impedance and the positive sequence admittance of test loop, calculate parallel many loop lines under equivalent environment and respectively hinder Anti-ratio and the ratio of each admittance, set up the relation of each corresponding physical quantity, it is achieved the zero sequence coupling of parallel many back transmission lines Impedance and the indirect on-line testing of admittance.The present invention proposes and represents with the ratio of physical quantity between many loop lines parallel under equivalent environment Own impedance and the relation of mutual impedance (own admittance and mutual admittance).To own impedance and mutual impedance (own admittance and Mutual admittance)WithEstimation, finally withForm occur, thus restrained effectively error.The present invention proposes Method of testing consider the soil resistivity impact on impedance detecting method specially, the fluctuation of simulating, verifying soil resistivity reaches During to ± 50%, the impact on positive sequence and zero sequence impedance is the least, wherein the relative deviation 0.1% of positive sequence, the relative deviation of zero sequence 3%, and admittance is little affected by the impact of earth conductivity, it is ensured that the fault-tolerant ability of the inventive method and capacity of resisting disturbance.This The method of testing that invention proposes need not produce specially any operation of zero sequence, does not affect the properly functioning of system, with existing zero It is different with operation of stopping transport that sequence method of testing needs special equipment, only needs the steady state voltage at group system two ends, current data, even Need not synchronize (differing several even tens cycles), the survey of parallel multi circuit transmission lines zero sequence coupling parameter can be realized Examination, enormously simplify the parameter test method of parallel many back transmission lines, substantially increases the efficiency of line parameter circuit value test, flexibly Convenient, there is the strongest practicality and operability.

Background technology

Along with the development of modern power systems, being restricted by soil and environmental factors, the many back transmission lines of parallel and frame are more Come the most, particularly the many loop lines of parallel erected on same tower.Abroad the most having reached 8 loop lines with tower, domestic same tower has reached 6 loop lines.Parallel many times There is zero sequence coupling between line, and the measurement of Zero sequence parameter affects the reliability of circuit zero-sequenceprotection.China's relay protection code is bright Really pointing out, the Zero sequence parameter value of transmission line of electricity must be obtained by actual measurement.The parameter of the many back transmission lines of parallel and frame, particularly Zero sequence parameter, is the underlying parameter of circuit, close with the protection seting of circuit, line losses management, condition monitoring and fault diagnosis etc. Relevant.Therefore study parallel multi circuit transmission lines Zero sequence parameter on-line testing method and there is important theory significance and Practical valency Value.

The parameter of transmission line of electricity is primarily referred to as its power frequency parameter, and it includes positive sequence impedance, positive sequence electric capacity, zero sequence impedance, electricity Appearance, capacitive coupling.For the multiloop or close together of wiring on the same tower, the circuit that parallel-segment is longer, there is also each bar circuit it Between coupling electric capacity and mutual inductive impedance.For a long time, the test of parallel many back transmission lines zero sequence coupling parameter, by this field Management operating personnel and the most attention of experts and scholars.Successively propose the tests such as method of perturbation, method of addition, differentiation and integration method Method.Wherein method of perturbation and method of addition are two kinds of main method of testings.The test of method of perturbation is to operate at test loop, increment Rule needs all parallel loop lines to synchronize multi-pass operation.Existing method of perturbation is simple to operate but measuring accuracy is the highest；Existing increment Method measurement amount is many, operation complexity, computationally intensive, needs to solve n (n+1)/2 complex number equation, no matter the foundation of equation with solve The most complicated.

Existing many loop lines synchronize zero sequence method of testing and can only obtain the equivalent zero sequence coupling parameter of population mean, and cannot Obtaining the phase field parameter of reality, it needs the synchronization zero sequence operation of at least (n-1) secondary all parallel loop lines, and this is in engineering reality It is difficult to operation.Under all parallel loop line normal operation, almost cannot realize.Whole parallel loop lines (even if Once) the most asynchronous, also bring along bigger error.In this context, the present invention proposes a kind of without carrying out any zero sequence Operation, one group of steady state voltage, current data at measurement circuit two ends when only need to extract properly functioning, i.e. can get test loop and The positive sequence on-line testing side of parallel many back transmission lines Zero sequence parameter of the coupling parameter (including modular field and phase region) of all loop lines Method.

Summary of the invention

The present invention proposes a kind of on-line testing method of parallel many back transmission lines zero sequence coupling parameter.The method only needs Both end voltage when parallel many back transmission lines one group are properly functioning, current data, measure the positive sequence impedance and just of test loop Sequence admittance, calculates ratio and the ratio of each admittance of the parallel each impedance of many loop lines under equivalent environment, sets up each corresponding physical quantity Relation, it is achieved the zero sequence coupled impedance of parallel many back transmission lines and the indirect on-line testing of admittance.

The positive sequence method of testing of the Zero sequence parameter that the present invention proposes needs first to measure (measurement circuit) positive order parameter.Therefore it is first Steady-state operation situation first with transmission line of electricity obtains positive sequence impedance and the positive sequence admittance of test loop.

Choosing the single loop line in lower section in accompanying drawing 1 is test loop, with S end as zero, calculates the positive order parameter of circuit.Survey The positive sequence equivalent circuit of examination loop line is as shown in Figure 2.Wherein,It is respectively the test line left and right sides Positive sequence voltage and electric current phasor.Z₁It is the positive sequence impedance of tested loop line unit length, Y₁It is the positive sequence of tested loop line unit length Admittance, l is the length (geographic distance of circuit go-and-retum, be considered as invariant) of circuit.Accompanying drawing 2 can be listed following equations:

${\stackrel{\·}{U}}_1^{\left(1\right)}={\stackrel{\·}{U}}_2^{\left(1\right)}{\mathrm{cosh\γ}}^{\left(1\right)}l+Z_c^{\left(1\right)}{\stackrel{\·}{I}}_2^{\left(1\right)}{\mathrm{sinh\γ}}^{\left(1\right)}l---\left(1\right)$

${\stackrel{\·}{I}}_1^{\left(1\right)}=\frac{{\stackrel{\·}{U}}_2^{\left(1\right)}}{Z_c^{\left(1\right)}}{\mathrm{sinh\γ}}^{\left(1\right)}l+{\stackrel{\·}{I}}_2^{\left(1\right)}{\mathrm{cosh\γ}}^{\left(1\right)}l---\left(2\right)$

If the positive order parameter of the equivalence of tested loop line unit length is respectively as follows: Z⁽¹⁾And Y⁽¹⁾。

${\mathrm{\γ}}^{\left(1\right)}=\sqrt{Z^{\left(1\right)}\×Y^{\left(1\right)}},Z_c^{\left(1\right)}=\sqrt{\frac{Z^{\left(1\right)}}{Y^{\left(1\right)}}}$

Obtained by formula (1)

${\stackrel{\·}{U}}_1^{\left(1\right)}-{\stackrel{\·}{U}}_2^{\left(1\right)}{\mathrm{cosh\γ}}^{\left(1\right)}l=Z_c^{\left(1\right)}{\stackrel{\·}{I}}_2^{\left(1\right)}{\mathrm{sinh\γ}}^{\left(1\right)}l---\left(3\right)$

Obtained by formula (2)

${\stackrel{\·}{I}}_1^{\left(1\right)}-{\stackrel{\·}{I}}_2^{\left(1\right)}{\mathrm{cosh\γ}}^{\left(1\right)}l=\frac{{\stackrel{\·}{U}}_2^{\left(1\right)}}{Z_c^{\left(1\right)}}{\mathrm{sinh\γ}}^{\left(1\right)}l---\left(4\right)$

(3) × (4)

$({\stackrel{\·}{U}}_1^{\left(1\right)}-{\stackrel{\·}{U}}_2^{\left(1\right)}{\mathrm{cosh\γ}}^{\left(1\right)}l)\×({\stackrel{\·}{I}}_1^{\left(1\right)}-{\stackrel{\·}{I}}_2^{\left(1\right)}{\mathrm{cosh\γ}}^{\left(1\right)}l)={\stackrel{\·}{U}}_2^{\left(1\right)}{\stackrel{\·}{I}}_2^{\left(1\right)}{\sinh }^2{\mathrm{\γ}}^{\left(1\right)}l---\left(5\right)$

(3) ÷ (4) obtains

$\frac{{\stackrel{\·}{U}}_1^{\left(1\right)}-{\stackrel{\·}{U}}_2^{\left(1\right)}{\mathrm{cosh\γ}}^{\left(1\right)}l}{{\stackrel{\·}{I}}_1^{\left(1\right)}-{\stackrel{\·}{I}}_2^{\left(1\right)}{\mathrm{cosh\γ}}^{\left(1\right)}l}=\frac{{\stackrel{\·}{I}}_2^{\left(1\right)}}{{\stackrel{\·}{U}}_2^{\left(1\right)}}{\left(Z_c^{\left(1\right)}\right)}^2---\left(6\right)$

Obtained by formula (5)

${\mathrm{cosh\γ}}^{\left(1\right)}l=\frac{{\stackrel{\·}{U}}_1^{\left(1\right)}{\stackrel{\·}{I}}_1^{\left(1\right)}+{\stackrel{\·}{U}}_2^{\left(1\right)}{\stackrel{\·}{I}}_2^{\left(1\right)}}{{\stackrel{\·}{U}}_1^{\left(1\right)}{\stackrel{\·}{I}}_2^{\left(1\right)}+{\stackrel{\·}{U}}_2^{\left(1\right)}{\stackrel{\·}{I}}_1^{\left(1\right)}}\stackrel{\mathrm{\Δ}}{=}W---\left(7\right)$

Order

Wushu (8) substitutes into formula (7) and obtains

y²-2wy+1=0 (9)

Solved y by formula (9), substitute into formula (8) and obtain

${\mathrm{\γ}}^{\left(1\right)}=\frac{\ln \left|y\right|+i\arg \left(y\right)}{l}---\left(10\right)$

Wushu (7) substitutes into formula (6) and obtains

$Z_c^{\left(1\right)}=\sqrt{\frac{{\stackrel{\·}{U}}_2^{\left(1\right)}}{{\stackrel{\·}{I}}_2^{\left(1\right)}}\·\frac{{\stackrel{\·}{U}}_1^{\left(1\right)}-{\stackrel{\·}{U}}_2^{\left(1\right)}W}{{\stackrel{\·}{I}}_1^{\left(1\right)}-{\stackrel{\·}{I}}_2^{\left(1\right)}W}}---\left(11\right)$

Can be obtained by formula (10), (11)

${\mathrm{\γ}}^{\left(1\right)}{Z}_c^{\left(1\right)}=Z^{\left(1\right)}---\left(12\right)$

$\frac{{\mathrm{\γ}}^{\left(1\right)}}{Z_c^{\left(1\right)}}=Y^{\left(1\right)}---\left(13\right)$

Positive sequence impedance and the positive sequence admittance of test loop is tried to achieve by (12), (13) formula.With the positive sequence impedance of test loop and Based on positive sequence admittance, and then obtain the zero sequence coupling parameter of parallel many loop lines.Here it is the formula released as a example by single loop line (12), (13), be suitable for the positive sequence parameter testing of double loop and many loop lines completely.

The present invention proposes the ratio of the physical quantity with many loop lines parallel under equivalent environment and represents own impedance and mutual resistance The relation of anti-(own admittance and mutual admittance).To own impedance and mutual impedance (own admittance and mutual admittance)With's Estimate, finally with) form occur, thus restrained effectively error.AndIn r_ciAnd α_iIt is all from measured value,WithIn r_g(ground resistance) is from Carlson, Evans Fordyce formula.All these measures, ensure that the survey of context of methods on the whole Examination accuracy and reliability.

The analytical calculation of reactance parameter is used N root parallel many loop lines wire as shown in Figure 3 (separately to add 2 to keep away by the present invention Thunder line) system.If the electric current of N bar circuit returns at far place, be set to N+1 root wire, then fixed by Theory of Electromagnetic Field and superposition Manage the magnetic linkage of each wire is

${\mathrm{\ψ}}_1=(\frac{{\mathrm{\μ}}_0{\mathrm{\α}}_1}{2\mathrm{\π}}{i}_1+\frac{{\mathrm{\μ}}_0{i}_1}{2\mathrm{\π}}ln\frac{D_{1N+1}-r_1}{r_1}\frac{D_{1N+1}-r_{N+1}}{r_{N+1}})+\frac{{\mathrm{\μ}}_0{i}_2}{2\mathrm{\π}}ln\frac{D_{2N+1}(D_{1N+1}-r_1)}{D_{21}{r}_{N+1}}+...+\frac{{\mathrm{\μ}}_0{i}_N}{2\mathrm{\π}}ln\frac{D_{NN+1}(D_{1N+1}-r_1)}{D_{N1}{r}_{N+1}}---\left(14\right)$

${\mathrm{\ψ}}_2=\frac{{\mathrm{\μ}}_0{i}_1}{2\mathrm{\π}}ln\frac{D_{1N+1}(D_{2N+1}-r_1)}{D_{12}{r}_{N+1}}+(\frac{{\mathrm{\μ}}_0{\mathrm{\α}}_2}{2\mathrm{\π}}{i}_2+\frac{{\mathrm{\μ}}_0{i}_2}{2\mathrm{\π}}ln\frac{D_{2N+I}-r_{N+1}}{r_2}\frac{D_{2N+1}-r_2}{r_{N+1}})+...+\frac{{\mathrm{\μ}}_0{i}_N}{2\mathrm{\π}}ln\frac{D_{NN+1}(D_{2N+1}-r_2)}{D_{N2}{r}_{N+1}}---\left(15\right)$

.

.

.

${\mathrm{\ψ}}_N=\frac{{\mathrm{\μ}}_0{i}_1}{2\mathrm{\π}}\ln \frac{D_{1N+1}(D_{NN+1}-r_N)}{D_{1N}{r}_{N+1}}+\frac{{\mathrm{\μ}}_0{i}_2}{2\mathrm{\π}}\ln \frac{D_{2N+1}(D_{NN+1}-r_N)}{D_{2N}{r}_{N+1}}+...+(\frac{{\mathrm{\μ}}_0{\mathrm{\α}}_N}{2\mathrm{\π}}{i}_N+\frac{{\mathrm{\μ}}_0{i}_N}{2\mathrm{\π}}ln\frac{D_{NN+1}-r_{N+1}}{r_N}\frac{D_{NN+1}-r_N}{r_{N+1}})---\left(16\right)$

Wherein r_i(i=1,2,3 ... N) is the outer radius of wire or split conductor, D_ijFor between wire i and wire j away from From, α_i(i=1,2,3 ... N) is and exchange Kelvin effect and the relevant coefficient of kindred effect, corresponding here in self-induction withRatio Value.

Taking return line (N+1 root) is Carlson, Evans Fordyce equivalence wire, by Carlson, Evans Fordyce formula I=1,2,3 ... N, j=1,2,3 ... N.Wherein f, γ are respectively frequency and the electrical conductivity of the earth of system, then haveI=1,2,3 ... N, j=1,2,3 ... N.Then every conductor unit length self-impedance It is respectively with mutual impedance

$Z_{ii}=r_{ci}+r_g+j\mathrm{\ω}\frac{{\mathrm{\μ}}_0}{2\mathrm{\π}}ln\frac{e^{{\mathrm{\α}}_i}{D}_g}{r_i}---\left(17\right)$

$Z_{ij}=r_g+j\mathrm{\ω}\frac{{\mathrm{\μ}}_0}{2\mathrm{\π}}ln\frac{D_g}{D_{ij}}---\left(18\right)$

Wherein r_ciFor the resistance of the unit length of wire i, r_gFor greatly along the resistance of line direction unit length.Cancellation keeps away Thunder line can obtain equivalent self-impedance and the mutual impedance of unit length between each parallel wire.

If pth return lead is m split conductor, then

${\mathrm{\ψ}}_p=\frac{{\mathrm{\μ}}_0{i}_p}{2\mathrm{\π}}ln\frac{e^{\frac{{\mathrm{\α}}_i}{m}}{D}_g}{\sqrt[m\×m]{r_1^m{\[(D_{12}{D}_{13}\·\·\·D_{1m})\·\·\·(D_{23}{D}_{24}\·\·\·D_{2m})\·\·\·\left(D_{(m-1)m}\right)\]}^2}}---\left(19\right)$

L_i1Interior self-induction for 1 unit length of split conductor.

The present invention uses multiple-loop line transmission line of electricity as shown in Figure 4 to the analytical calculation of susceptance parameter.If circuit is total For N bar, if the electric charge of every circuit unit length is τ_k(k=1,2 ... N), the height on distance ground is h_k(k=1,2 ... N), line Between relative position be known D_ij(i=1,2 ... N；J=1,2 ... N).Then this N bar overhead transmission line and the earth composition electrostatic are only Erection system, i.e.Accompanying drawing 5 is the distribution of space charge schematic diagram obtained by image method.By electromagnetic field principle, lead for every Line is an entirety with its mirror image, and the electric field that any point, space produces up is:

R in formula_-For the distance of the P of-τ to space any point, r₊Distance for τ to space any point P.Obtained by superposition theorem

.

.

.

Above formula is inverted

Eliminate lightning conducterCan obtain

It is available from the expression formula of mutual admittance further.

If pth return lead is m split conductor, then

The AC resistance of circuit lightning conducter is gone to revise, with test loop by the present invention according to the alternating current-direct current resistance of test loop The ratio of AC resistance and D.C. resistance be standard reference value, the AC resistance of lightning conducter is equal to the ratio of its D.C. resistance This standard reference value, asks for lightning conducter with this and obtains AC resistance；It addition, the interior self-induction correction factor of lightning conducter also will be according to test The interior self-induction correction factor of loop line goes to revise, forward-sequence reactance measured value obtain the interior self-induction correction factor of test loop, be designated as α₁, According to the interior self-induction correction factor of radius calculation inside and outside conductor reality, it is designated as α₂, take α₁With α₂Ratio as standard reference value, Revise lightning conducter with this and obtain interior self-induction correction factor.

For the measurement of impedance parameter, there is equation below

$-\frac{d}{dx}\left[\begin{array}{c}{\stackrel{\·}{U}}_P\\ 0\end{array}\right]=\left[\begin{array}{cc}{Z}_{PP}& Z_{PE}\\ Z_{EP}& Z_{EE}\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{I}}_P\\ {\stackrel{\·}{I}}_E\end{array}\right]---\left(24\right)$

Wherein Z_EEFor lightning conducter inherent parameters element (own impedance and mutual impedance)；Z_PEAnd Z_EPFor lightning conducter and other Mutual impedance element between loop line, Z_ppFor the mutual element between other loop line inherent parameters elements and other each loop lines.Eliminate Lightning conducter obtains

$-\frac{d{\stackrel{\·}{U}}_P}{dx}=Z_P{\stackrel{\·}{I}}_P---\left(25\right)$

$Z_P=Z_{PP}-Z_{PE}{Z}_{EE}^{-1}{Z}_{EP}---\left(26\right)$

For the measurement of admittance parameter, there is equation below

${\mathrm{\α}}_{ii}=\frac{1}{2{\mathrm{\π\ϵ}}_0}ln\frac{2h_1-r_i}{r_i}---\left(28\right)$

${\mathrm{\α}}_{ij}=\frac{1}{2{\mathrm{\π\ϵ}}_0}ln\frac{D_{i^{\′}j}-r_j}{D_{ij}-r_j}(i\≠j)---\left(29\right)$

For easy analysis, 2 lightning conducters numbered N-1, N, all phase conductors are divided into one group, are designated asτ_p, keeping away Thunder line is divided into another set, is designated asτ_E.Write as the form of matrix in block form

Above formula is inverted

$\left[\begin{array}{c}{\mathrm{\τ}}_P\\ {\mathrm{\τ}}_E\end{array}\right]=\left[\begin{array}{cc}{\mathrm{\β}}_{PP}& {\mathrm{\β}}_{PE}\\ {\mathrm{\β}}_{EP}& {\mathrm{\β}}_{EE}\end{array}\right]\left[\begin{array}{c}{\mathrm{\φ}}_P\\ {\mathrm{\φ}}_E\end{array}\right]---\left(31\right)$

Make β=β_pp, eliminate lightning conducter, then

Voltage, current relationship on every circuit dx are

$-\frac{d{\stackrel{\·}{I}}_P}{dx}=Y{\stackrel{\·}{U}}_P---\left(33\right)$

Y_ii=g_i+jωβ_ii (34)

Y_ij=j ω β_ij(i≠j) (35)

The online positive sequence method of testing flow process of zero sequence coupling parameter proposed by the invention is as shown in Figure 6.

The method of testing that the present invention proposes is also significantly better than other method of testing existing in theory.Actual in engineering In, the transposition of parallel many back transmission lines is the most difficult, and the proportion shared by circuit that do not replaces is increasing.And to the circuit that do not replaces Almost cannot there is coupling between each sequence with constant constant matrix by its diagonalization, also can produce very even if carrying out zero sequence test Big error.The present invention, as a example by parallel erected on same tower three loop line, discusses the method for testing proposed and is substantially better than other test existing Theoretical method basis.Without loss of generality, with I loop line as test loop, if the test loop after test loop cancellation lightning conducter Equation is

$-\frac{d}{dx}\left[\begin{array}{c}{\stackrel{\·}{U}}_{IA}\\ {\stackrel{\·}{U}}_{IB}\\ {\stackrel{\·}{U}}_{IC}\end{array}\right]=\left[\begin{array}{ccc}{Z}_{IAA}& Z_{IAB}& Z_{IAC}\\ Z_{IBA}& Z_{IBB}& Z_{IBC}\\ Z_{ICA}& Z_{ICB}& Z_{ICC}\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{I}}_{IA}\\ {\stackrel{\·}{I}}_{IB}\\ {\stackrel{\·}{I}}_{IC}\end{array}\right]+\left[\begin{array}{ccc}{Z}_{IAIIA}& Z_{IAIIB}& Z_{IAIIC}\\ Z_{IBIIA}& Z_{IBIIB}& Z_{IBIIC}\\ Z_{ICIIA}& Z_{ICIIB}& Z_{ICIIC}\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{I}}_{IIA}\\ {\stackrel{\·}{I}}_{IIB}\\ {\stackrel{\·}{I}}_{IIC}\end{array}\right]+\left[\begin{array}{ccc}{Z}_{IAIIIA}& Z_{IAIIIB}& Z_{IAIIIC}\\ Z_{IBIIIA}& Z_{IBIIIB}& Z_{IBIIIC}\\ Z_{ICIIIA}& Z_{ICIIIB}& Z_{ICIIIC}\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{I}}_{IIIA}\\ {\stackrel{\·}{I}}_{IIIB}\\ {\stackrel{\·}{I}}_{IIIC}\end{array}\right]---\left(36\right)$

The anti-battle array of unit length phase region group is defined as

$Z_{ABC}=\left[\begin{array}{ccc}{Z}_{IAA}& Z_{IAB}& Z_{IAC}\\ Z_{IBA}& Z_{IBB}& Z_{IBC}\\ Z_{ICA}& Z_{ICB}& Z_{ICC}\end{array}\right]+\left[\begin{array}{ccc}{Z}_{IAIIA}& Z_{IAIIB}& Z_{IAIIC}\\ Z_{IBIIA}& Z_{IBIIB}& Z_{IBIIC}\\ Z_{ICIIA}& Z_{ICIIB}& Z_{ICIIC}\end{array}\right]+\left[\begin{array}{ccc}{Z}_{IAIIIA}& Z_{IAIIIB}& Z_{IAIIIC}\\ Z_{IBIIIA}& Z_{IBIIIB}& Z_{IBIIIC}\\ Z_{ICIIIA}& Z_{ICIIIB}& Z_{ICIIIC}\end{array}\right]---\left(37\right)$

Take $Q=\left[\begin{array}{ccc}1& 1& 1\\ 1& a^2& a\\ 1& a& a^2\end{array}\right],$ $Q^{-1}=\frac{1}{3}\left[\begin{array}{ccc}1& 1& 1\\ 1& a& a^2\\ 1& a^2& a\end{array}\right],$ $a=e^{j\frac{2\mathrm{\π}}{3}}=-\frac{1}{2}+j\frac{\sqrt{3}}{2}$

Order

$\left[\begin{array}{c}{\stackrel{\·}{U}}_{IA}\\ {\stackrel{\·}{U}}_{IB}\\ {\stackrel{\·}{U}}_{IC}\end{array}\right]=Q\left[\begin{array}{c}{\stackrel{\·}{U}}_I^{\left(0\right)}\\ {\stackrel{\·}{U}}_I^{\left(1\right)}\\ {\stackrel{\·}{U}}_I^{\left(2\right)}\end{array}\right]---\left(38\right)$

$\left[\begin{array}{c}{\stackrel{\·}{I}}_{IA}\\ {\stackrel{\·}{I}}_{IB}\\ {\stackrel{\·}{I}}_{IC}\end{array}\right]=Q\left[\begin{array}{c}{\stackrel{\·}{I}}_I^{\left(0\right)}\\ {\stackrel{\·}{I}}_I^{\left(1\right)}\\ {\stackrel{\·}{I}}_I^{\left(2\right)}\end{array}\right]---\left(39\right)$

$\left[\begin{array}{c}{\stackrel{\·}{U}}_{IIA}\\ {\stackrel{\·}{U}}_{IIB}\\ {\stackrel{\·}{U}}_{IIC}\end{array}\right]=Q\left[\begin{array}{c}{\stackrel{\·}{U}}_{II}^{\left(0\right)}\\ {\stackrel{\·}{U}}_{II}^{\left(1\right)}\\ {\stackrel{\·}{U}}_{II}^{\left(2\right)}\end{array}\right]---\left(40\right)$

$\left[\begin{array}{c}{\stackrel{\·}{I}}_{IIA}\\ {\stackrel{\·}{I}}_{IIB}\\ {\stackrel{\·}{I}}_{IIC}\end{array}\right]=Q\left[\begin{array}{c}{\stackrel{\·}{I}}_{II}^{\left(0\right)}\\ {\stackrel{\·}{I}}_{II}^{\left(1\right)}\\ {\stackrel{\·}{I}}_{II}^{\left(2\right)}\end{array}\right]---\left(41\right)$

$\left[\begin{array}{c}{\stackrel{\·}{U}}_{IIIA}\\ {\stackrel{\·}{U}}_{IIIB}\\ {\stackrel{\·}{U}}_{IIIC}\end{array}\right]=Q\left[\begin{array}{c}{\stackrel{\·}{U}}_{III}^{\left(0\right)}\\ {\stackrel{\·}{U}}_{III}^{\left(1\right)}\\ {\stackrel{\·}{U}}_{III}^{\left(2\right)}\end{array}\right]---\left(42\right)$

$\left[\begin{array}{c}{\stackrel{\·}{I}}_{IIIA}\\ {\stackrel{\·}{I}}_{IIIB}\\ {\stackrel{\·}{I}}_{IIIC}\end{array}\right]=Q\left[\begin{array}{c}{\stackrel{\·}{I}}_{III}^{\left(0\right)}\\ {\stackrel{\·}{I}}_{III}^{\left(1\right)}\\ {\stackrel{\·}{I}}_{III}^{\left(2\right)}\end{array}\right]---\left(43\right)$

(38), (39), (40), (41), (42), (43) are substituted into (36) formula and obtain

$-\frac{d}{dx}\left[\begin{array}{c}{\stackrel{\·}{U}}_I^{\left(0\right)}\\ {\stackrel{\·}{U}}_I^{\left(1\right)}\\ {\stackrel{\·}{U}}_I^{\left(2\right)}\end{array}\right]=\left[\begin{array}{ccc}{Z}_1& Z_2& Z_3\\ Z_4& Z_5& Z_6\\ Z_7& Z_8& Z_9\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{I}}_I^{\left(0\right)}\\ {\stackrel{\·}{I}}_I^{\left(1\right)}\\ {\stackrel{\·}{I}}_I^{\left(2\right)}\end{array}\right]+\left[\begin{array}{ccc}{Z}_{10}& Z_{11}& Z_{12}\\ Z_{13}& Z_{14}& Z_{15}\\ Z_{16}& Z_{17}& Z_{18}\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{I}}_{II}^{\left(0\right)}\\ {\stackrel{\·}{I}}_{II}^{\left(1\right)}\\ {\stackrel{\·}{I}}_{II}^{\left(2\right)}\end{array}\right]+\left[\begin{array}{ccc}{Z}_{19}& Z_{20}& Z_{21}\\ Z_{22}& Z_{23}& Z_{24}\\ Z_{25}& Z_{26}& Z_{27}\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{I}}_{III}^{\left(0\right)}\\ {\stackrel{\·}{I}}_{III}^{\left(1\right)}\\ {\stackrel{\·}{I}}_{III}^{\left(2\right)}\end{array}\right]---\left(44\right)$

Wherein

$Z_1=\frac{Z_{IAA}+Z_{IAB}+Z_{IAC}+Z_{IBA}+Z_{IBB}+Z_{IBC}+Z_{ICA}+Z_{ICB}+Z_{ICC}}{3}---\left(45\right)$

$Z_2=\frac{Z_{IAA}+Z_{IBA}+Z_{ICA}+a^2(Z_{IAB}+Z_{IBB}+Z_{ICB})+a(Z_{IAC}+Z_{IBC}+Z_{ICC})}{3}---\left(46\right)$

$Z_3=\frac{Z_{IAA}+Z_{IBA}+Z_{ICA}+a(Z_{IAB}+Z_{IBB}+Z_{ICB})+a^2(Z_{IAC}+Z_{IBC}+Z_{ICC})}{3}---\left(47\right)$

$Z_4=\frac{Z_{IAA}+Z_{IAB}+Z_{IAC}+a(Z_{IBA}+Z_{IBB}+Z_{IBC})+a^2(Z_{ICA}+Z_{ICB}+Z_{ICC})}{3}---\left(48\right)$

$Z_5=\frac{Z_{IAA}+a^2{Z}_{IAB}+{\mathrm{aZ}}_{IAC}+{\mathrm{aZ}}_{IBA}+Z_{IBB}+a^2{Z}_{IBC}+a^2{Z}_{ICA}+{\mathrm{aZ}}_{ICB}+Z_{ICC}}{3}---\left(49\right)$

$Z_6=\frac{Z_{IAA}+{\mathrm{aZ}}_{IAB}+a^2{Z}_{IAC}+{\mathrm{aZ}}_{IBA}+a^2{Z}_{IBB}+Z_{IBC}+a^2{Z}_{ICA}+Z_{ICB}+{\mathrm{aZ}}_{ICC}}{3}---\left(50\right)$

$Z_7=\frac{Z_{IAA}+Z_{IAB}+z_{IAC}+a^2(Z_{IBA}+Z_{IBB}+Z_{IBC})+a(Z_{ICA}+Z_{ICB}+Z_{ICC})}{3}---\left(51\right)$

$Z_8=\frac{Z_{IAA}+a^2{Z}_{IAB}+{\mathrm{aZ}}_{IAC}+a^2{Z}_{IBA}+{\mathrm{aZ}}_{IBB}+Z_{IBC}+{\mathrm{aZ}}_{ICA}+Z_{ICB}+a^2{Z}_{ICC}}{3}---\left(52\right)$

$Z_9=\frac{Z_{IAA}+{\mathrm{aZ}}_{IAB}+a^2{Z}_{IAC}+a^2{Z}_{IBA}+Z_{IBB}+{\mathrm{aZ}}_{IBC}+{\mathrm{aZ}}_{ICA}+a^2{Z}_{ICB}+Z_{ICC}}{3}---\left(53\right)$

Symmetry Z by I loop line self_IAB=Z_IBA, Z_IBC=Z_ICB, Z_ICA=Z_IACFormula (45), (46), (47), (48) (49), (50), (51), (52), (53) can abbreviation be

$Z_1=\frac{Z_{IAA}+Z_{IBB}+Z_{ICC}+2(Z_{IAB}+Z_{IBC}+Z_{ICA})}{3}---\left(54\right)$

$Z_2=\frac{Z_{IAA}+a^2{Z}_{IBB}+{\mathrm{aZ}}_{ICC}-{\mathrm{aZ}}_{IAB}-Z_{IBC}-a^2{Z}_{ICA})}{3}---\left(55\right)$

$Z_3=\frac{Z_{IAA}+{\mathrm{aZ}}_{IBB}+a^2{Z}_{ICC}-a^2{Z}_{IAB}-Z_{IBC}-{\mathrm{aZ}}_{ICA})}{3}---\left(56\right)$

$Z_4=\frac{Z_{IAA}+{\mathrm{aZ}}_{IBB}+a^2{Z}_{ICC}-a^2{Z}_{IAB}-{\mathrm{aZ}}_{ICA}-Z_{IBC}}{3}---\left(57\right)$

$Z_5=\frac{Z_{IAA}+Z_{IBB}+Z_{ICC}-(Z_{IAB}+Z_{IBC}+Z_{IAC})}{3}---\left(58\right)$

$Z_6=\frac{Z_{IAA}++a^2{Z}_{IBB}+{\mathrm{aZ}}_{ICC}+2{\mathrm{aZ}}_{IAB}+2Z_{IBC}+2a^2{Z}_{ICA}}{3}---\left(59\right)$

$Z_7=\frac{Z_{IAA}+a^2{Z}_{IAB}+{\mathrm{aZ}}_{ICC}-{\mathrm{aZ}}_{IAB}-Z_{IBC}-a^2{Z}_{ICA}}{3}---\left(60\right)$

$Z_8=\frac{Z_{IAA}+{\mathrm{aZ}}_{IBB}+a^2{Z}_{ICC}+2a^2{Z}_{IAB}+2Z_{IBC}++{\mathrm{aZ}}_{ICA}}{3}---\left(61\right)$

$Z_9=\frac{Z_{IAA}+Z_{IBB}+Z_{ICC}-(Z_{IAB}+Z_{IBC}+Z_{ICA})}{3}---\left(62\right)$

$Z_{10}=\frac{Z_{IAIIA}+Z_{IAIIB}+Z_{IAIIC}+Z_{IBIIA}+Z{IBIIB}_{}+Z_{IBIIC}+Z_{ICIIA}+Z_{ICIIB}+Z_{ICIIC}}{3}---\left(63\right)$

$Z_{11}=\frac{Z_{IAIIA}+Z_{IBIIA}+Z_{ICIIA}+a^2(Z_{IAIIB}+Z_{IBIIB}+Z_{ICIIB})+a(Z_{IAIIC}+Z_{IBIIC}+Z_{ICIIC})}{3}---\left(64\right)$

$Z_{12}=\frac{Z_{IAIIA}+Z_{IBIIA}+Z_{ICIIA}+a(Z_{IAIIB}+Z_{IBIIB}+Z_{ICIIB})+a^2(Z_{IAIIC}+Z_{IBIIC}+Z_{ICIIC})}{3}---\left(65\right)$

$Z_{13}=\frac{Z_{IAIIA}+Z_{IAIIB}+Z_{IAIIC}+a(Z_{IBIIA}+Z_{IBIIB}+Z_{IBIIC})+a^2(Z_{ICIIA}+Z_{ICIIB}+Z_{ICIIC})}{3}---\left(66\right)$

$Z_{14}=\frac{Z_{IAIIA}+a^2{Z}_{IAIIB}+{\mathrm{aZ}}_{IAIIC}+{\mathrm{aZ}}_{IBIIA}+Z_{IBIIB}+a^2{Z}_{IBIIC}+a^2{Z}_{ICIIA}+{\mathrm{aZ}}_{ICIIB}+Z_{ICIIC}}{3}---\left(67\right)$

$Z_{15}=\frac{Z_{IAIIA}+{\mathrm{aZ}}_{IAIIB}+a^2{Z}_{IAIIC}+{\mathrm{aZ}}_{IBIIA}+a^2{Z}_{IBIIB}+Z_{IBIIC}+a^2{Z}_{ICIIA}+Z_{ICIIB}+{\mathrm{aZ}}_{ICIIC}}{3}---\left(68\right)$

$Z_{16}=\frac{Z_{IAIIA}+Z_{IAIIB}+Z_{IAIIC}+a^2(A_{IBIIA}+Z_{IBIIB}+Z_{IBIIC})+a(Z_{ICIIA}+Z_{ICIIB}+Z_{ICIIC})}{3}---\left(69\right)$

$Z_{17}=\frac{Z_{IAIIA}+a^2{Z}_{IAIIB}+{\mathrm{aZ}}_{IAIIC}+a^2{Z}_{IBIIA}+{\mathrm{aZ}}_{IBIIB}+Z_{IBIIC}+{\mathrm{aZ}}_{ICIIA}+Z_{ICIIB}+a^2{Z}_{ICIIC}}{3}---\left(70\right)$

$Z_{18}=\frac{Z_{IAIIA}+{\mathrm{aZ}}_{IAIIB}+a^2{Z}_{IAIIC}+a^2{Z}_{IBIIA}+Z_{IBIIB}+{\mathrm{aZ}}_{IBIIC}+{\mathrm{aZ}}_{ICIIA}+a^2{Z}_{ICIIB}+Z_{ICIIC}}{3}---\left(71\right)$

$Z_{19}=\frac{Z_{IAIIIA}+Z_{IAIIIB}+Z_{IAIIIC}+z_{IBIIIA}+Z_{IBIIIB}+Z_{IBIIIC}+Z_{ICIIIA}+Z_{ICIIIB}+Z_{ICIIIC}}{3}---\left(72\right)$

$Z_{20}=\frac{Z_{IAIIIA}+Z_{IBIIIA}+Z_{ICIIIA}+a^2(Z_{IAIIIB}+Z_{IBIIIB}+Z_{ICIIIB})+a(Z_{IAIIIC}+Z_{IBIIIC}+Z_{ICIIIC})}{3}---\left(73\right)$

$Z_{21}=\frac{Z_{IAIIIA}+Z_{IBIIIA}+Z_{ICIIIA}+a(Z_{IAIIIB}+Z_{IBIIIB}+Z_{ICIIIB})+a^2(Z_{IAIIIC}+Z_{IBIIIC}+Z_{ICIIIC})}{3}---\left(74\right)$

$Z_{22}=\frac{Z_{IAIIIA}+Z_{IAIIIB}+Z_{IAIIIC}+a(Z_{IBIIIA}+Z_{IBIIIB}+Z_{IBIIIC})+a^2(Z_{ICIIIA}+Z_{ICIIIB}+Z_{ICIIIC})}{3}---\left(75\right)$

$Z_{23}=\frac{Z_{IAIIIA}+a^2{Z}_{IAIIIB}+{\mathrm{aZ}}_{IAIIIC}+{\mathrm{aZ}}_{IBIIIA}+Z_{IBIIIB}+a^2{Z}_{IBIIIC}+a^2{Z}_{ICIIIA}+{\mathrm{aZ}}_{ICIIIB}+Z_{ICIIIC}}{3}---\left(76\right)$

$Z_{24}=\frac{Z_{IAIIIA}+{\mathrm{aZ}}_{IAIIIB}+a^2{Z}_{IAIIIC}+{\mathrm{aZ}}_{IBIIIA}+a^2{Z}_{IBIIIB}+Z_{IBIIIC}+a^2{Z}_{ICIIIA}+Z_{ICIIIB}+{\mathrm{aZ}}_{ICIIIC}}{3}---\left(77\right)$

$Z_{25}=\frac{Z_{IAIIIA}+Z_{IAIIIB}+Z_{IAIIIC}+a^2(Z_{IBIIIA}+Z_{IBIIIB}+Z_{IBIIIC})+a(Z_{ICIIIA}+Z_{ICIIIB}+Z_{ICIIIC})}{3}---\left(78\right)$

$Z_{26}=\frac{Z_{IAIIIA}+a^2{Z}_{IAIIIB}+{\mathrm{aZ}}_{IAIIIC}+a^2{Z}_{IBIIIA}+{\mathrm{aZ}}_{IBIIIB}+Z_{IBIIIC}+{\mathrm{aZ}}_{ICIIIA}+Z_{ICIIIB}+a^2{Z}_{ICIIIC}}{3}---\left(79\right)$

From formula (44) it can be seen that there is coupling between positive negative zero three sequence amount, general three sequence transformation matrix Q cannot decouple.This Literary composition has carried out simulating, verifying as a example by parallel erected on same tower double back, four loop lines.From table 45-table 62, in the case of not replacing, parallel The zero sequence method of testing (method of perturbation) of many back transmission lines, the test result of each zero sequence and ATP result phase ratio error are very big, and zero Sequence impedance maximum error reaches 1506.5%, and the maximum error of zero sequence admittance reaches 4849.98%, and conservative estimation zero sequence impedance maximum is by mistake Difference also reaches 753%, and conservative estimation zero sequence admittance maximum error also reaches 2425%.And another kind synchro measure parallel many loop lines zero sequence Voltage, electric current set up the method for testing (method of addition) that Simultaneous Equations solves, and formally see it is rational, actually to not changing Generation and the test error of its equation of bit line are the most uncontrollable, and problem is bigger.Knowable to the equation (44) of a test loop, its The number of modular field Impedance Matrix differential element just reaches more than 8, if setting up zero sequence by the mode of n (n+1)/2 variable by force Incremental Equation group, not only equation the compatibility it is difficult to ensure that, and its measuring accuracy also be difficult to ensure, its error may exceed The error of single loop line zero sequence method of testing (method of perturbation).Visible to the circuit that do not replaces, the method for testing of existing major parallel loop line Method of perturbation and method of addition, the most just cannot ensure precision and reliability that parallel many loop lines zero sequence coupling parameter tests.

In fact to parallel many back transmission lines, between positive sequence, negative phase-sequence and zero-sequence component, there is cross-couplings, zero-sequence current Can produce positive and negative sequence voltage, positive and negative sequence electric current can produce no-voltage；Residual voltage can produce positive and negative sequence electric current, just, Negative sequence voltage can also produce zero current.The most existing zero sequence method of testing, either method of perturbation or method of addition, to not replacing Circuit, is invalid in theory.This is also the basic reason that its test error respectively reaches 753% and 2425%.This is Hard defects, it is impossible to eliminating, complete transposition circuit is still set up by they certainly.

Another equation of test loop is

$-\frac{d}{dx}\left[\begin{array}{c}{\stackrel{\·}{I}}_{IA}\\ {\stackrel{\·}{I}}_{IB}\\ {\stackrel{\·}{I}}_{IC}\end{array}\right]=\left[\begin{array}{ccc}{Y}_{IAA}& Y_{IAB}& Y_{IAC}\\ Y_{IBA}& Y_{IBB}& Y_{IBC}\\ Y_{ICA}& Y_{ICB}& Y_{ICC}\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{U}}_{IA}\\ {\stackrel{\·}{U}}_{IB}\\ {\stackrel{\·}{U}}_{IC}\end{array}\right]+\left[\begin{array}{ccc}{Y}_{IAIIA}& Y_{IAIIB}& Y_{IAIIC}\\ Y_{IBIIA}& Y_{IBIIB}& Y_{IBIIC}\\ Y_{ICIIA}& Y_{ICIIB}& Y_{ICIIC}\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{U}}_{IIA}\\ {\stackrel{\·}{U}}_{IIB}\\ {\stackrel{\·}{U}}_{IIC}\end{array}\right]+\left[\begin{array}{ccc}{Y}_{IAIIIA}& Y_{IAIIIB}& Y_{IAIIIC}\\ Y_{IBIIIA}& Y_{IBIIIB}& Y_{IBIIIC}\\ Y_{ICIIIA}& Y_{ICIIIB}& Y_{ICIIIC}\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{U}}_{IIIA}\\ {\stackrel{\·}{U}}_{IIIB}\\ {\stackrel{\·}{U}}_{IIIC}\end{array}\right]---\left(81\right)$

From duality relation, test and the conclusion of parallel many back transmission lines admittance parameter are identical with impedance parameter, existing There is method of testing also cannot ensure measuring accuracy and the reliability of zero sequence admittance parameter.

The positive sequence method of testing that the present invention proposes, as long as the positive-sequence component of stable state, the most parallel many loop lines are in steady-state operation, In each parallel loop line both end voltage and electric current, negative phase-sequence and zero-sequence component are the least, and positive order parameter is just being exactly equal to active balance battle array Order parameter, hereby it is ensured that the highest measuring accuracy.As the r obtained by test loop_ci、α_iAnd obtainAnd r_gDetermine Afterwards, the function ratio that under remaining the most corresponding same weather conditions, the space coordinates of circuit is corresponding, this ensure that the most theoretically The measuring accuracy of context of methods and reliability are far above existing method.In like manner context of methods also can ensure parallel multi circuit transmission lines zero sequence The test accuracy of admittance parameter and reliability.

The method of testing of the present invention needs scene to provide soil resistivity and the locus coordinate of circuit, these data electricity Found a capital and operating management department has.But soil resistivity has certain change with climatic season, the present invention considers this specially Problem.Detailed description of the invention below is verified together.The result shows, when soil resistivity fluctuation reaches ± 50% Time, varying less of its positive sequence and zero sequence impedance, the wherein maximum relative deviation 0.1% of positive sequence impedance, zero sequence maximum is the most inclined Differ from 3%, and admittance is little affected by the impact of earth conductivity.Due to ground resistivity γ withOrForm The own impedance of impact and mutual impedance, to functionWhen γ is from 0.05s/m to 10^-4During s/m change, functionOnly from 5.112 change to 12.255, the functional form of this natural logrithm, ensure that the fault-tolerant ability of context of methods and anti-dry theoretically Disturb ability.

The present invention is to own impedance and mutual impedanceWithEstimation, finally withForm occur, thus effectively Inhibit error.AndIn r_ciAnd α_iIt is all from measured value,WithIn r_g(ground resistance) is from Carlson, Evans Fordyce formula. All these measures, ensure that test accuracy and the reliability of context of methods on the whole.This processing method herein is also Can promote set up each impedance (in admittance battle array) each element withOr(Or) relation, and then record parallel multi circuit transmission lines All phase field parameters of unit length.

Detailed description of the invention

In order to verify effectiveness and the reliability of the inventive method, parallel with certain different electric pressure (220kV, 110kV) Verify as a example by double loop and four loop lines.

As shown in Figure 7, wherein label 0 represents that lightning conducter, label 1,2,3 represent first respectively to the space layout of double loop A, B, C three-phase of loop line, A, B, C three-phase of label 4,5,6 second loop line respectively, double loop electric pressure is 220kV.Double back Line phantom is as shown in Figure 8.

The impedance parameter analysis and utilization EMTP-ATP of the present invention sets up parallel and frame double back transmission line model, takes three not Same soil resistivity carries out simulating, verifying, and the Line-check function utilizing software to carry reads LCC line module difference and returns Mutual parameter between the own parameter of line and line, in this, as normal data.Extract the stable state at circuit (test loop) two ends Voltage x current data, calculate positive sequence impedance and the positive sequence admittance parameter of test loop, as base according to formula mentioned above Plinth calculates the zero sequence coupling parameter between different loop line.Canonical parameter data that relatively ATP is given and utilize context of methods to calculate The supplemental characteristic obtained, checking set forth herein the reasonability of method, effectiveness.

The present invention utilizes the normal impedance parameter of the parallel and frame double back transmission line that the Line-check function of ATP reads As shown in table 1-table 4.

Under table 1 different soils resistivity, positive sequence has impedance standard value (unit Ω/km) by oneself

Table 2 zero sequence is own, mutual impedance standard value (unit Ω/km-soil resistivity is 500 Ω m)

Table 3 zero sequence is own, mutual impedance standard value (unit Ω/km-soil resistivity is 1000 Ω m)

Table 4 zero sequence is own, mutual impedance standard value (unit Ω/km-soil resistivity is 1500 Ω m)

Utilize the positive order parameter of the steady state voltage current data computing electric power line at circuit (test loop) two ends, for double Back transmission line, two loop lines are connected on same bus, and the voltage x current of two loop lines is completely the same.Test data are as shown in table 5.

Under table 5 different soils resistivity, positive sequence has impedance measurements (unit Ω/km) by oneself

Under table 6 different soils resistivity, positive sequence has the modulus value relative error of impedance measurements and standard value by oneself

Being found out by upper table 6, positive sequence measurement error is about 2.3%, and error is in allowed band.

For double back transmission line, receiving on same bus of two loop line roads, circuit is full symmetric, therefore its electric parameters is complete Unanimously, test loop takes any of which one.The positive order parameter obtained according to actual measurement, utilizes spatial coordinates calculation circuit certainly Mutual zero sequence impedance between body zero sequence impedance and line, obtains ratio relation according to parameter value of calculation and measured value and asks for the circuit of reality Parameter.

Make r_g=0.05 Ω/km, lightning conducter uses the conventional correction procedure the same with other non-test loop lines

Soil resistivity ρ=500 Ω m

Table 7 zero sequence impedance value of calculation (unit Ω/km)

Table 8 zero sequence impedance value of calculation and the modulus value relative error of standard value

Soil resistivity ρ=1000 Ω m

Table 9 zero sequence impedance value of calculation (unit Ω/km)

Table 10 zero sequence impedance value of calculation and the modulus value relative error of standard value

Soil resistivity ρ=1500 Ω m

Table 11 zero sequence impedance value of calculation (unit Ω/km)

Table 12 zero sequence impedance value of calculation and the modulus value relative error of standard value

Utilize the standard admittance parameter such as table of the parallel and frame double back transmission line that the Line-check function of ATP reads Shown in 13-table 14.

Table 13 positive sequence has admittance standard value (unit us/km) by oneself

There is negative value in real part (conductance) part of admittance in table 13, can be attributed to calculating error, when conductance numerical value is for bearing, The real part of negligible admittance parameter.

Table 14 zero sequence is own, mutual admittance standard value (unit us/km)

As can be seen from Table 14, real part (conductance) part of admittance parameter, numerical value is minimum, is negligible.

The present invention utilizes the steady state voltage current data meter at circuit (test loop) two ends to the measurement of positive sequence admittance parameter Calculating the positive order parameter of transmission line of electricity, for double back transmission line, two loop lines are connected on same bus, and the voltage x current of two loop lines is complete Complete consistent.Test data are as shown in Table 15.Because line admittance parameter is unrelated with ground resistivity, the most only list the earth electricity Resistance rate is one group of data of 1000 Ω m.

Table 15 positive sequence has admittance measurement value (unit us/km) by oneself

Table 16 positive sequence has admittance measurement value and standard value modulus value relative error by oneself

Relative error between zero sequence admittance imaginary part and the ATP standard value of test true value is in allowed limits.

Two loop lines of double back transmission line are connected to same bus, and circuit is full symmetric, therefore its electric parameters is completely the same, test Loop takes any of which one.The positive order parameter obtained according to actual measurement, the present invention utilizes spatial coordinates calculation circuit self Mutual zero sequence admittance between zero sequence admittance and line, the calculating of admittance parameter is not related to soil resistivity and ground resistance, therefore without The impact of soil resistivity and ground resistance need to be considered, without considering that lightning conducter must revise problem as impedance computation.With Measurement data and according to the data of spatial coordinates calculation based on, utilize transadmittance between the zero sequence admittance and line that ratio relation tries to achieve Relation as shown in table 17:

Table 17 zero sequence is own, mutual admittance value of calculation (unit us/km)

Table 18 zero sequence admittance value of calculation and standard value modulus value relative error

The zero sequence admittance value of calculation of circuit self obtains real part and takes the real part of measured value, if measured value real part is negative value, then Ignore；Between line, transadmittance real part is minimum, is negligible.

The present invention is to parallel and frame four back transmission line ATP simulation architecture figure as shown in Figure 9.Wherein label 0 expression keeps away Thunder line, label 1,2,3 represents A, B, C three-phase of the first loop line respectively, A, B, C three-phase of label 4,5,6 second loop line respectively, mark A, B, C three-phase of numbers 7,8,9 third circuits respectively, A, B, C three-phase of label 10,11,12 the 4th loop line respectively.First, second Loop line road electric pressure is 220kV, and the three, the 4th revolving line voltage grades are 110kV.Four loop line phantoms such as accompanying drawing 10 institute Show.

The impedance parameter analysis and utilization EMTP-ATP of the present invention sets up parallel and frame four back transmission line model, takes three not Same soil resistivity carries out simulating, verifying, and the Line-check function utilizing software to carry reads LCC line module difference and returns Mutual parameter between the own parameter of line and line, in this, as normal data.Extract the stable state at circuit (test loop) two ends Voltage x current data, calculate positive sequence impedance and the positive sequence admittance parameter of test loop, as base according to formula mentioned above Plinth calculates the zero sequence coupling parameter between different loop line.Canonical parameter data that relatively ATP is given and utilize context of methods to calculate The supplemental characteristic obtained, the checking present invention proposes the reasonability of method, effectiveness.

The present invention utilizes the parallel and normal impedance parameter of frame four back transmission line that the Line-check function of ATP reads As shown in table 19-table 22.

Under table 19 different soils resistivity, positive sequence has impedance standard value (unit Ω/km) by oneself

Table 20 zero sequence is own, mutual impedance standard value (unit Ω/km-soil resistivity is 500 Ω m)

Table 21 zero sequence is own, mutual impedance standard value (unit Ω/km-soil resistivity is 1000 Ω m)

Table 22 zero sequence is own, mutual impedance standard value (unit Ω/km-soil resistivity is 1500 Ω m)

The present invention utilizes the positive order parameter of the steady state voltage current data computing electric power line at circuit (test loop) two ends, Test data are as shown in table 23.

Under table 23 different soils resistivity, positive sequence has impedance measurements (unit Ω/km) by oneself

Under table 24 different soils resistivity, positive sequence has impedance measurements and standard value modulus value relative error by oneself

By upper table data it can be seen that positive sequence measures impedance error about 2%.

For four back transmission lines, test loop can take top two loop lines, it is also possible to the side of taking off two loop line.The present invention is closed Note be test loop self Zero sequence parameter and test loop with other loop lines between mutual couple Zero sequence parameter, as The zero sequence of other loop lines have by oneself the zero sequence mutual coupling parameter between parameter and other loop lines be not we pay close attention to object； The positive order parameter obtained according to actual measurement, utilizes mutual zero sequence impedance between self zero sequence impedance of spatial coordinates calculation circuit and line.

Make r_g=0.05 Ω/km, lightning conducter uses the conventional correction procedure the same with other non-test loop lines

Test loop is top first, second loop line

Soil resistivity ρ=500 Ω m

Table 25 zero sequence impedance value of calculation (unit Ω/km)

Table 26 zero sequence impedance value of calculation and the modulus value relative error (unit Ω/km) of standard value

Soil resistivity ρ=1000 Ω m

Table 27 zero sequence impedance value of calculation (unit Ω/km)

Table 28 zero sequence impedance value of calculation and the modulus value relative error (unit Ω/km) of standard value

Soil resistivity ρ=1500 Ω m

Table 29 zero sequence impedance value of calculation (unit Ω/km)

Table 30 zero sequence impedance value of calculation and the modulus value relative error (unit Ω/km) of standard value

Test loop is lower section the three, the 4th loop line

Soil resistivity ρ=500 Ω m

Table 31 zero sequence impedance value of calculation (unit Ω/km)

Table 32 zero sequence impedance value of calculation and the modulus value relative error (unit Ω/km) of standard value

Soil resistivity ρ=1000 Ω m

Table 33 zero sequence impedance value of calculation (unit Ω/km)

Table 34 zero sequence impedance value of calculation and the modulus value relative error (unit Ω/km) of standard value

Soil resistivity ρ=1500 Ω m

Table 35 zero sequence impedance value of calculation (unit Ω/km)

Table 36 zero sequence impedance value of calculation and the modulus value relative error (unit Ω/km) of standard value

The standard admittance parameter such as table of parallel and frame four back transmission line that the Line-check function utilizing ATP reads Shown in 37-table 38.The parameter that the present invention is given using ATP is as standard value (true value).

Table 37 positive sequence has admittance standard value (unit us/km) by oneself

There is negative value in real part (conductance) part of admittance in table 37, can be attributed to calculating error, when conductance numerical value is for bearing, The real part of negligible admittance parameter.

Table 38 zero sequence is own, mutual admittance standard value (unit us/km)

As can be seen from Table 38, real part (conductance) part of admittance parameter, numerical value is minimum, is negligible.

The present invention utilizes the steady state voltage current data meter at circuit (test loop) two ends to the measurement of positive sequence admittance parameter Calculate the positive order parameter of transmission line of electricity, same bus is connected on respectively for four back transmission lines, top two loop line and lower section two loop line On, the voltage x current of top two loop line is completely the same, and the voltage x current of lower section two loop line is completely the same.Test data such as table 39 institute Show.

Table 39 positive sequence has admittance measurement value (unit us/km) by oneself

Table 40 positive sequence has the modulus value relative error of admittance measurement value and standard value by oneself

Being found out by table 40, it is left that the relative error between zero sequence admittance imaginary part and the ATP standard value of test true value is maintained at 2% Right.

For four back transmission lines, twice, top and loop line road, lower section two are coupled with on same bus, and circuit is the most right Claiming, therefore its electric parameters is completely the same, test loop takes any of which one.The positive order parameter obtained according to actual measurement, utilizes Mutual zero sequence admittance between self zero sequence admittance of spatial coordinates calculation circuit and line, the calculating of admittance parameter is not related to electric resistance of soil Rate and ground resistance, therefore without considering the impact of soil resistivity and ground resistance as impedance computation, without consideration Lightning conducter must revise problem.By measurement data and according to the data of spatial coordinates calculation based on, utilize ratio relation to try to achieve Between zero sequence admittance and line, the relation of transadmittance is as shown in table 41, table 43.

Test loop takes top first, second loop line

Table 41 zero sequence is own, mutual susceptance value of calculation (unit us/km)

Table 42 zero sequence admittance value of calculation and standard value modulus value relative error

The test loop side of taking off the three, the 4th loop line

Table 43 zero sequence is own, mutual admittance value of calculation (unit us/km)

Table 44 zero sequence admittance value of calculation and standard value modulus value relative error

The zero sequence admittance value of calculation of circuit self obtains real part and takes the real part of measured value, if measured value real part is negative value, then Ignore；Between line, transadmittance real part is minimum, is negligible.

In practical power systems, the many back transmission lines of existing high pressure overhead power line especially parallel erected on same tower are general not Transposition or non-complete transposition, if using symmetrical component method to decouple by force, yet suffer from coupling between positive negative zero three sequence, this just makes The error having become existing zero sequence method of testing is big and uncontrollable.In order to be analyzed contrast, the present invention is to Fig. 8 and Figure 10 Shown parallel multi circuit transmission lines, creates following zero sequence operating mode artificially: 0.1s-0.2s:A phase removal of load-zero sequence operating mode 1； 0.3s-0.4s:B phase removal of load-zero sequence operating mode 2；0.5s-0.6s:C phase removal of load-zero sequence operating mode 3.

Three kinds of zero sequence operating modes do difference two-by-two, obtain the Zero sequence parameter of existing method of perturbation test.Table 45-table 62 lists existing The zero sequence impedance of Fig. 8 and Figure 10 that zero sequence method of testing is obtained and admittance.The normal data that contrast ATP is given, it can be seen that existing The drawback of some Zero sequence parameter method of testings.

Table 45 double back transmission line (soil resistivity: 500 Ω m)

Table 46 double back transmission line impedance, admittance modulus value relative error analysis (soil resistivity: 500 Ω m)

Table 47 double back transmission line (soil resistivity: 1000 Ω m)

Table 48 double back transmission line impedance, admittance modulus value relative error analysis (soil resistivity: 1000 Ω m)

Table 49 double back transmission line (soil resistivity: 1500 Ω m)

Table 50 double back transmission line impedance, admittance modulus value relative error analysis (soil resistivity: 1500 Ω m)

Twice, table 51 4 back transmission lines-top (soil resistivity: 500 Ω m)

Twice impedances in table 52 4 back transmission lines-top, admittance modulus value relative error analysis (soil resistivity: 500- Ω·m)

Twice, table 53 4 back transmission lines-lower section (soil resistivity: 500 Ω m)

Twice impedances in table 54 4 back transmission lines-lower section, admittance modulus value relative error analysis (soil resistivity: 500 Ω·m)

Twice, table 55 4 back transmission lines-top (soil resistivity: 1000 Ω m)

Twice impedances in table 56 4 back transmission lines-top, admittance modulus value relative error analysis (soil resistivity: 1000 Ω·m)

Twice, table 57 4 back transmission lines-lower section (soil resistivity: 1000 Ω m)

Twice impedances in table 58 4 back transmission lines-lower section, admittance modulus value relative error analysis (soil resistivity: 1000 Ω·m)

Twice, table 59 4 back transmission lines-top (soil resistivity: 1500 Ω m)

Twice impedances in table 60 4 back transmission lines-top, admittance modulus value relative error analysis (soil resistivity: 1500 Ω·m)

Twice, table 61 4 back transmission lines-lower section (soil resistivity: 1500 Ω m)

Twice impedances in table 62 4 back transmission lines-lower section, admittance modulus value relative error analysis (soil resistivity: 1500 Ω·m)

The present invention proposes a kind of on-line testing method of parallel many back transmission lines zero sequence coupling parameter.The method only needs To the parallel many back transmission lines one group both end voltage time properly functioning, electric current, measure positive sequence impedance and the positive sequence of test loop Admittance, calculates ratio and the ratio of each admittance of the parallel each impedance of many loop lines under equivalent environment, sets up the pass between each corresponding physics System, it is achieved the zero sequence coupled impedance of parallel many back transmission lines and the indirect on-line testing of admittance.Detailed description of the invention demonstrates Effectiveness of the invention, reliability.

The method of testing practicality and workable that the present invention proposes.Special equipment is needed with existing zero sequence method of testing Operation is different with stopping transport, method of testing in this paper, it is not necessary to the special any operation producing zero sequence, is not just affecting system Often run, only need the steady state voltage at group system two ends, current data, parallel multi circuit transmission lines zero sequence coupling parameter can be realized Test, enormously simplify the parameter test method of parallel many back transmission lines, substantially increases the efficiency of line parameter circuit value test, spirit Live convenient, there is the strongest practicality and operability.Be conducive to safety and stability and the economical operation of parallel many back transmission lines.

Accompanying drawing explanation

Fig. 1. parallel and frame three back transmission line schematic diagram.

Fig. 2. test loop positive sequence equivalent circuit.

Fig. 3 .N wiring system longitudinal section structural representation.

Fig. 4. multiple-loop line transmission line of electricity cross sectional representation.

Fig. 5. distribution of space charge schematic diagram.

Fig. 6. the positive sequence method of testing FB(flow block) of parallel many back transmission lines zero sequence coupling parameter.

Fig. 7. parallel and frame double back transmission line space layout schematic diagram.

Fig. 8. parallel and frame double back transmission line phantom.

Fig. 9. parallel and frame four back transmission line space layout schematic diagram.

Figure 10. parallel and frame four back transmission line phantom.

Claims (9)

1. the positive sequence on-line testing method of parallel many back transmission lines Zero sequence parameter, it is characterised in that: only need one group of circuit Both end voltage time properly functioning, current data, measure positive sequence impedance and the positive sequence admittance of test loop, calculates under equivalent environment The ratio of the parallel each impedance of many loop lines and the ratio of each admittance, set up the relation of each corresponding physical quantity, it is achieved feed back electricity parallel more The zero sequence coupled impedance of circuit and the indirect on-line testing of admittance.With the ratio between the physical quantity of many loop lines parallel under equivalent environment Represent own impedance and the relation of mutual impedance (own admittance and mutual admittance).Own impedance and mutual impedance (are had by oneself and led Receive and mutual admittance)WithEstimation, finally withForm occur, thus restrained effectively error.AndIn r_ciAnd α_iIt is all from measured value,WithIn r_g(ground resistance) is from Carlson, Evans Fordyce formula.All these measures, Ensure that test accuracy and the reliability of context of methods on the whole.

Method the most according to claim 1, it is characterised in that: the initial data of test only needs one group of properly functioning stable state electricity Pressure, current data, according to one group of steady state voltage, the positive order parameter of current data calculating circuit of test loop, utilize this positive sequence The zero sequence that the coordinate of the locus of parameter and circuit calculates between circuit self and circuit has parameter and mutual parameter by oneself.

Method the most according to claim 1, it is characterised in that: the method for testing that the present invention proposes considers soil electricity specially The resistance rate impact on impedance detecting method, the fluctuation of simulating, verifying soil resistivity reaches ± 50% time, positive sequence and zero sequence are hindered Anti-impact is the least, the wherein relative deviation 0.1% of positive sequence, the relative deviation 3% of zero sequence, and admittance is little affected by the earth conductance The impact of rate.Due to ground resistivity γ withOrThe form own impedance of impact and mutual impedance, to functionWhen γ is from 0.05s/m to 10^-4During s/m change, functionOnly change to 12.255 from 5.112, this natural logrithm Functional form, ensure that fault-tolerant ability and the capacity of resisting disturbance of context of methods theoretically.

Method the most according to claim 1, it is characterised in that: the circuit line of return (N+1 root) is Carlson, Evans Fordyce equivalence wire, By Carlson, Evans Fordyce formular_N+1=1 (m),I=1,2,3 ... N, j=1,2,3 ... N.Wherein f, γ The frequency of the system of being respectively and the electrical conductivity of the earth.Then haveI=1,2,3 ... N, j=1,2,3 ... N.Then every conductor unit length self-impedance and mutual impedance are respectively Wherein r_ciFor the resistance of the unit length of wire i, r_gFor greatly along the electricity of line direction unit length Resistance.Eliminate lightning conducter and can obtain equivalent self-impedance and the mutual impedance of unit length between each parallel wire.

Method the most according to claim 1, it is characterised in that: if pth return lead is m split conductor, then ${\mathrm{\ψ}}_p=\frac{{\mathrm{\μ}}_0}{2\mathrm{\π}}\ln \frac{e\frac{{\mathrm{\α}}_i}{m}{D}_g}{\sqrt[m\×m]{r_1^m{\[(D_{12}{D}_{13}...D_{1m})...(D_{23}{D}_{24}...D_{2m})...\left(D_{(m-1)m}\right)\]}^2}},{\mathrm{\α}}_1=L_{i1}/\left(\frac{{\mathrm{\μ}}_0}{2\mathrm{\π}}\right),$ L_i1For 1 unit length of split conductor Interior self-induction.If pth return lead is m split conductor, then

Method the most according to claim 1, it is characterised in that: calculate parameter with the impedance of circuit time properly functioning, admittance On the basis of, according to spatial coordinates calculation impedance, the respective element of admittance parameter matrix of circuitWithAccording to being calculated Impedance, ratio relation between each element of admittance parameter matrix and stable state time line impedance, the measured value of admittance, calculate resistance The actual value of each element in anti-, admittance parameter matrix.

Method the most according to claim 1, it is characterised in that: the positive sequence method of testing that the present invention proposes, as long as stable state is just Order components, the most parallel many loop lines are in steady-state operation, and in each parallel loop line both end voltage and electric current, negative phase-sequence and zero-sequence component are very Little, and positive order parameter is exactly equal to the positive order parameter of active balance battle array, hereby it is ensured that the highest measuring accuracy.When by testing back The r that line obtains_ci、α_iAnd obtainAnd r_gAfter determining, the space coordinates of circuit under remaining the most corresponding same weather conditions Corresponding function ratio, this measuring accuracy that ensure that context of methods the most theoretically and reliability are far above existing method.With Reason context of methods also can ensure test accuracy and the reliability of parallel multi circuit transmission lines zero sequence admittance parameter.

Method the most according to claim 1, it is characterised in that: the method for testing practicality of present invention proposition and operability By force.Need special equipment and operation of stopping transport different from existing zero sequence method of testing, method of testing in this paper, it is not necessary to special Produce any operation of zero sequence, do not affect the properly functioning of system, only need the steady state voltage at group system two ends, current data, Even without synchronizing (differing several even tens cycles), parallel multi circuit transmission lines zero sequence coupling parameter can be realized Test, enormously simplify the parameter test method of parallel many back transmission lines, substantially increases the efficiency of line parameter circuit value test, spirit Live convenient, there is the strongest practicality and operability.

Method the most according to claim 1, it is characterised in that: parallel and frame many back transmission lines zero sequence that the present invention proposes The positive sequence on-line testing method of parameter, is a kind of Zero sequence parameter online test method convenient, practical, efficient.Owing to signal obtains It is very easy to take, and can survey, season in season surveys every year, surveys month in and month out, surveys the most everyday.This can test parallel many loop parameters at any time Method, be possible not only to be greatly simplified the test of parallel many loop lines zero sequence coupling parameter, and parallel multi circuit transmission lines can be monitored Running status.The in this paper parallel and positive sequence on-line testing method of frame many back transmission lines Zero sequence parameter, is conducive to flat The safety and stability of the many back transmission lines of row and economical operation.