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

Positive sequence on-line testing method for zero sequence parameters of parallel multi-circuit power transmission line

Technical Field

The invention belongs to the field of zero sequence coupling parameter testing of parallel multi-circuit power transmission lines. The invention provides an online test method for zero sequence coupling parameters of parallel multi-circuit power transmission lines, which only needs voltage and current at two ends of a group of parallel multi-circuit power transmission lines in normal operation to measure positive sequence impedance and positive sequence admittance of test circuit lines, calculates the ratio of each impedance and each admittance of the parallel multi-circuit lines under the same environment, establishes the relationship of each corresponding physical quantity, and realizes indirect online test of the zero sequence coupling impedance and the admittance of the parallel multi-circuit power transmission lines. The invention provides a relation that self-impedance and mutual impedance (self-admittance and mutual admittance) are expressed by the ratio of physical quantities among parallel multi-circuit lines under the same environment. For self impedance and mutual impedance (self admittance and mutual admittance)Andis finally estimated inIs present, thus effectively suppressing errors. The testing method provided by the invention specially considers the influence of the soil resistivity on the impedance testing method, and the simulation verifies that when the fluctuation of the soil resistivity reaches +/-50%, the influence on the positive sequence impedance and the zero sequence impedance is very small, wherein the relative deviation of the positive sequence is 0.1%, the relative deviation of the zero sequence is 3%, and the admittance is hardly influenced by the ground conductivity, so that the fault tolerance capability and the anti-interference capability of the method are ensured. The testing method provided by the invention does not need any operation specially generating zero sequence, does not influence the normal operation of the system, is different from the existing zero sequence testing method which needs special equipment and shutdown operation, only needs a group of steady-state voltage and current data at two ends of the system, and even does not need synchronization (the difference is several or even dozens of cycles), so that the testing of the zero sequence coupling parameters of the parallel multi-circuit lines can be realized, the parameter testing method of the parallel multi-circuit transmission lines is greatly simplified, the efficiency of the line parameter testing is greatly improved, the testing method is flexible and convenient, and the method has strong practicability and operability.

Background

With the development of modern power systems, more and more power transmission lines are parallelly erected and provided with multiple loops under the restriction of land and environmental factors, and particularly, multiple power transmission lines are erected and provided with multiple loops on the same tower. The same tower at home and abroad can reach 8 circuit lines at most, and the same tower at home can reach 6 circuit lines. Zero sequence coupling exists between the parallel multi-circuit lines, and the measurement of zero sequence parameters influences the reliability of zero sequence protection of the circuit. The relay protection regulations in China clearly indicate that the zero sequence parameter values of the power transmission line must be obtained through actual measurement. The parameters of the parallel multi-circuit transmission line, especially the zero sequence parameters, are basic parameters of the line and are closely related to the protection setting, the network loss calculation, the state monitoring, the fault diagnosis and the like of the line. Therefore, the research on the parallel multi-circuit line zero-sequence parameter online test method has important theoretical significance and engineering practical value.

The parameters of the power transmission line mainly refer to power frequency parameters of the power transmission line, and the power frequency parameters comprise positive sequence impedance, positive sequence capacitance, zero sequence impedance, capacitance and interphase capacitance. For the multi-loop or the line which is short in distance and long in parallel section and erected on the same tower, coupling capacitance and mutual inductance impedance between all lines exist. For a long time, the test of the zero sequence coupling parameter of the parallel multi-circuit power transmission line is generally regarded by management operators and experts and scholars in the field. And successively providing a perturbation method, an increment method, a differential method, an integral method and other testing methods. Of these, the perturbation method and the incremental method are two main test methods. The perturbation method is used for testing the loop operation, and the increment method needs all parallel loops to operate for a plurality of times synchronously. The existing disturbance method is simple to operate but has low test precision; the existing incremental method has the disadvantages of more measurement quantity, complex operation and large calculation quantity, needs to solve n (n +1)/2 complex equations, and is complex to establish and solve.

The existing multi-loop line synchronous zero sequence testing method can only obtain the overall average equivalent zero sequence coupling parameter, but cannot obtain the actual phase domain parameter, and at least (n-1) times of synchronous zero sequence operations of all parallel loop lines are required, which is difficult to operate in the actual engineering. Under the condition that all parallel loops are in normal operation, the parallel loops are almost impossible to realize. Once all parallel loops (even if only one) are out of sync, a large error is introduced. Under the background, the invention provides a positive sequence online test method for zero sequence parameters of parallel multi-circuit transmission lines, which can obtain coupling parameters (including a mode domain and a phase domain) of a test loop and all loops by extracting a group of steady-state voltage and current data at two ends of the test line in normal operation without any zero sequence operation.

Disclosure of Invention

The invention provides an online testing method for zero sequence coupling parameters of parallel multi-circuit power transmission lines. The method only needs voltage and current data at two ends of a group of parallel multi-circuit power transmission lines in normal operation to measure the positive sequence impedance and the positive sequence admittance of the test circuit, calculates the ratio of each impedance and each admittance of the parallel multi-circuit lines under the same environment, establishes the relationship of each corresponding physical quantity, and realizes the indirect online test of the zero-sequence coupling impedance and the admittance of the parallel multi-circuit power transmission lines.

The positive sequence test method of the zero sequence parameter provided by the invention needs to test the positive sequence parameter (of the test line) first. Therefore, the positive sequence impedance and the positive sequence admittance of the test loop are obtained by utilizing the steady-state operation condition of the power transmission line.

And selecting a single loop at the lower part in the attached drawing 1 as a test loop, and calculating a positive sequence parameter of the line by taking the S end as a coordinate origin. The positive sequence equivalent circuit of the test loop is shown in fig. 2. Wherein,respectively positive sequence voltage and current phasor at the left side and the right side of a tested line. Z₁Is the positive sequence impedance, Y, of the measured loop length per unit length₁Is the positive sequence admittance of the measured loop length per unit length, l is the length of the line (the geographical distance between the two ends of the line, considered as invariant). The following equations may be listed for FIG. 2:

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

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

setting equivalent positive sequence parameters of the unit length of the measured loop as follows: z⁽¹⁾And Y^(1）。

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

Is obtained by the formula (1)

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

Is obtained by the 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) X (4) to obtain

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

(3) Div (4) to

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

Is obtained by the 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 to

Substituting formula (8) for formula (7)

y²-2wy+1＝0 (9)

By the formula (9) to y, by the formula (8)

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

Substituting formula (7) for formula (6)

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

From the formulae (10), (11)

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

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

The positive sequence impedance and the positive sequence admittance of the test loop are obtained by the equations (12) and (13). And (4) solving the zero sequence coupling parameter of the parallel multi-loop on the basis of the positive sequence impedance and the positive sequence admittance of the test loop. Here, equations (12) and (13) are derived by taking a single loop as an example, and are fully applicable to positive sequence parameter tests of double loop and multi loop.

The invention provides a relation that the self-impedance and the mutual impedance (self-admittance and mutual admittance) are expressed by the ratio of physical quantities of parallel multi-loop lines under the same environment. For self impedance and mutual impedance (self admittance and mutual admittance)Andis finally estimated in) Is present, thus effectively suppressing errors. WhileR in_ciAnd α_iAre all derived from the measured values of the measured values,andr in_g(ground resistance) comes from the Karson equation. All these measures ensure the test accuracy and reliability of the method as a whole.

The invention adopts a system of N parallel multi-loop wires (additionally 2 lightning wires) as shown in figure 3 for analyzing and calculating reactance parameters. If the current of N lines returns at a far place and is set as the N +1 th wire, the flux linkage of each wire is obtained by the electromagnetic field theory and the superposition theorem

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

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

.

.

.

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

Wherein r is_i(i ═ 1, 2, 3 … N) is the outer radius of the wire or split wire, D_ijDistance between wire i and wire j, α_i(i-1, 2, 3 … N) are coefficients relating to the ac skin effect and proximity effect, where corresponding to the intrinsic self-inductance and proximity effectThe ratio of (a) to (b).

Taking the return line (the (N +1) th line) as a Karson equivalent conductor by the Karson formula i is 1, 2, 3 … N, j is 1, 2, 3 … N. Where f and gamma are the frequency of the system and the electrical conductivity of the earth, respectively, theni is 1, 2, 3 … N, j is 1, 2, 3 … N. The self-impedance and the mutual impedance per unit length of the conductor are respectively

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

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

Wherein r is_ciIs the resistance per unit length of the wire i, r_gIs the resistance per unit length of the earth along the line. The equivalent self-impedance and mutual impedance of unit length between each parallel conducting wire can be obtained by eliminating the lightning conductor.

If the p-th loop line is an m-split conductor

${\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_i1The internal self-inductance of the split conductor is 1 unit length.

The analysis and calculation of the susceptance parameters of the invention adopts the same-tower multi-circuit transmission line as shown in figure 4. Assuming that the total number of lines is N, and the charge per unit length of each line is τ_k(k 1, 2 … N) and a height h from the ground_k(k-1, 2 … N) and the relative position between the wires is known as D_ij(i-1, 2 … N; j-1, 2 … N). The N overhead transmission lines and the ground form an electrostatic independent system, namelyFig. 5 is a schematic view of the space charge distribution obtained by the mirror image method. By electromagnetic field principle, each wire is integrated with its mirror image, and the electric field generated at any point in the upper space is:

in the formula r_-Is the distance of- τ to P at any point in space, r₊Is the distance of tau to any point P in space. By the law of superposition

.

.

.

Inversion of the above formula

Elimination lightning conductorCan obtain the product

Further, the expression of mutual admittance can be obtained.

If the p-th loop line is an m-split conductor

The invention relates to the AC resistance of the line lightning conductor according to the intersection of the test return wireCorrecting the DC resistance, and calculating the AC resistance of the lightning conductor according to the ratio of the AC resistance to the DC resistance of the test loop as a standard reference value and the ratio of the AC resistance to the DC resistance of the lightning conductor equal to the standard reference value, wherein the correction factor of the internal self-inductance of the lightning conductor is corrected according to the correction factor of the internal self-inductance of the test loop, and the correction factor of the internal self-inductance of the test loop is obtained by measuring the value of the positive sequence reactance and is recorded as α₁The internal self-inductance correction coefficient calculated from the actual internal and external radii of the conductor is recorded as α₂Get α₁And α₂The ratio of the reference value to the reference value is used as a standard reference value so as to correct the lightning conductor to obtain an internal self-inductance correction coefficient.

For the measurement of the impedance parameter, the following equation is given

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

Wherein Z_EEThe parameters of the lightning conductor (self impedance and mutual impedance) are set; z_PEAnd Z_EPFor mutual impedance elements between lightning conductor and other return lines, Z_ppThe parameters of other loops and the mutual elements among other loops. Eliminating lightning conductor

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

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

For the measurement of admittance parameters, the following equation is presented

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

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

For convenient analysis, 2 lightning wires are numbered as N-1 and N, and all phase wires are divided into one group and recorded asτ_pDividing the lightning conductor into another group, denoted asτ_E. Writing into a form of a block matrix

Inversion of the above formula

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

Let β be β_ppEliminate the lightning conductor, then

The voltage and current relationship of each line dx is

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

Y_ii＝g_i+jωβ_ii(34)

Y_ij＝jωβ_ij(i≠j) (35)

The flow of the online positive sequence testing method of the zero sequence coupling parameter provided by the invention is shown in the attached figure 6.

The test method provided by the invention is also obviously superior to other existing test methods in theory. In the practical engineering, transposition of a plurality of parallel power transmission lines is very difficult, and the proportion of non-transposed lines is increased more and more. For a non-transposition line, the transposition line can hardly be diagonalized by a constant matrix, coupling exists among sequences, and a large error is generated even if a zero sequence test is carried out. The invention takes the three circuit lines which are arranged on the same tower in parallel as an example, and the theoretical basis of the proposed testing method is obviously superior to that of other existing testing methods. Without loss of generality, the I-th loop is taken as a test loop, and the test loop equation after the test loop eliminates the lightning conductor is set as

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

The unit length phase domain group reactance matrix is defined as

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

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

Order to

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

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

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

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

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

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

Substituting (38), (39), (40), (41), (42) and (43) into (36) to 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

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

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

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

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

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

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

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

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

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

By the symmetry Z of the loop I itself_IAB＝Z_IBA，Z_IBC＝Z_ICB，Z_ICA＝Z_IACThe equations (45), (46), (47), (48), (49), (50), (51), (52) and (53) can be simplified to

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

It can be seen from the formula (44) that there is coupling between the positive and negative zero three-sequence quantities, and the three-sequence transformation array Q cannot be decoupled generally. Simulation verification is carried out by taking the same tower and frame double-loop and four-loop as an example. It can be seen from tables 45-62 that, in the zero-sequence test method (perturbation method) for parallel multi-circuit transmission lines without transposition, the error of each zero-sequence test result is very large compared with the ATP result, the maximum error of zero-sequence impedance reaches 1506.5%, the maximum error of zero-sequence admittance reaches 4849.98%, the maximum error of conservative estimation zero-sequence impedance also reaches 753%, and the maximum error of conservative estimation zero-sequence admittance also reaches 2425%. The other testing method (incremental method) for synchronously measuring zero sequence voltage and current of the parallel multi-loop line to establish simultaneous equation set solution is reasonable in form, and generation and testing errors of the equation of the line without transposition are uncontrollable in practice, so that the problem is larger. It can be known from the equation (44) of a test loop that the number of the different elements of the modular impedance array reaches more than 8, and if a zero-sequence incremental equation set is forcibly established in a mode of n (n +1)/2 variables, not only is the compatibility of the equations difficult to guarantee, but also the test accuracy is difficult to guarantee, and the error may exceed the error of a single loop zero-sequence test method (perturbation method). Therefore, for the non-transposition line, the existing test method of the main parallel lines, namely the perturbation method and the incremental method, can not guarantee the precision and the reliability of the zero sequence coupling parameter test of the parallel multi-line.

In fact, for parallel multi-circuit transmission lines, cross coupling exists among positive sequence components, negative sequence components and zero sequence components, zero sequence current can generate positive sequence voltage and negative sequence voltage, and positive sequence current and negative sequence current can generate zero voltage; the zero sequence voltage can generate positive and negative sequence current, and the positive and negative sequence voltage can also generate zero current. Therefore, the existing zero sequence test method, whether a disturbance method or an increment method, is not true in theory for the line without transposition. This is also the root cause for the test errors reaching 753% and 2425%, respectively. This is a hard flaw that cannot be eliminated, although they are true for fully transposed lines.

Another equation for the test loop is

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

According to the dual relation, the testing and conclusion of the admittance parameters of the parallel multi-circuit power transmission lines are the same as the impedance parameters, and the existing testing method cannot ensure the testing precision and reliability of the zero sequence admittance parameters.

The positive sequence test method provided by the invention has the advantages that as long as the positive sequence component of the steady state exists, the parallel multi-loop wires are in steady state operation, and two ends of each parallel loop wireThe negative sequence and zero sequence components in the voltage and current are very small, and the positive sequence parameter is exactly equal to the positive sequence parameter of the equivalent balanced array, so that the high test precision is ensured. When r is obtained from the test loop_ci、α_iAnd find outAnd r_gAfter the determination, the rest of the circuits correspond to the function ratio corresponding to the space coordinates of the circuits under the same climatic conditions, so that the test precision and reliability of the method are theoretically ensured to be far higher than those of the existing method. Similarly, the method can also ensure the test accuracy and reliability of the zero sequence admittance parameters of the parallel multi-circuit line.

The testing method of the invention needs to provide the soil resistivity and the spatial position coordinates of the line on site, and the data are available in the electric construction and operation management departments. However, the resistivity of the soil changes to a certain extent along with the climatic seasons, and the invention specially considers the problem. And verified together in the following detailed description. The verification result shows that when the soil resistivity fluctuation reaches +/-50%, the change of the positive sequence impedance and the zero sequence impedance is small, wherein the maximum relative deviation of the positive sequence impedance is 0.1%, the maximum relative deviation of the zero sequence impedance is 3%, and the admittance is hardly influenced by the conductivity of the earth. Due to the earth resistivity gammaOrThe form of (1) affecting the self-impedance and the mutual impedance, pair functionWhen gamma is from 0.05s/m to 10^-4Function when s/m changesFrom 5.112 to 12.255, the functional form of the natural logarithm theoretically ensures the fault tolerance and anti-interference capability of the method.

The invention has self impedance and mutual impedanceAndis finally estimated inIs present, thus effectively suppressing errors. WhileR in_ciAnd α_iAre all derived from the measured values of the measured values,andr in_g(ground resistance) comes from the Karson equation. All these measures ensure the test accuracy and reliability of the method as a whole. The processing method can also be popularized and used for establishing each element and each impedance (in the admittance array)Or(Or) And further measuring all phase domain parameters of the unit length of the parallel multi-circuit line.

Detailed Description

In order to verify the effectiveness and reliability of the method, parallel double-circuit lines and four-circuit lines with different voltage levels (220kV and 110kV) are taken as an example for verification.

The spatial layout of the double-circuit line is shown in fig. 7, wherein reference numeral 0 represents a lightning conductor, reference numerals 1, 2 and 3 represent A, B, C three phases of the first circuit line respectively, reference numerals 4, 5 and 6 represent A, B, C three phases of the second circuit line respectively, and the voltage levels of the double-circuit line are 220 kV. The two-loop simulation model is shown in fig. 8.

According to the invention, the impedance parameter analysis utilizes EMTP-ATP to establish a parallel double-circuit transmission Line model, three different soil resistivities are taken for simulation verification, and the Line-check function of software is utilized to read the self-owned parameters of different circuit wires of the LCC Line module and the mutual-owned parameters among the lines, so that the self-owned parameters and the mutual-owned parameters among the lines are used as standard data. The steady state voltage and current data of the two ends of the circuit (test loop) are extracted, the positive sequence impedance and the positive sequence admittance parameters of the test loop are calculated according to the formula mentioned above, and the zero sequence coupling parameters between different loops are calculated on the basis of the positive sequence impedance and the positive sequence admittance parameters. And comparing standard parameter data given by ATP with the parameter data obtained by calculation by using the method disclosed herein, and verifying the reasonability and effectiveness of the method disclosed herein.

The standard impedance parameters of the parallel-rack double-circuit transmission Line read by using the Line-check function of ATP are shown in tables 1-4.

TABLE 1 Positive sequence standard value of impedance (unit. omega./km) for different soil resistivities

TABLE 2 zero sequence standard values of self and mutual impedance (unit omega/km-soil resistivity 500 omega. m)

TABLE 3 zero sequence standard impedance values (unit omega/km-soil resistivity of 1000 omega. m)

TABLE 4 zero sequence standard impedance values (unit omega/km-soil resistivity 1500 omega. m)

The positive sequence parameters of the transmission line are calculated by using the steady-state voltage and current data at the two ends of the line (test loop), and for the double-loop transmission line, the two loops are connected on the same bus, and the voltage and the current of the two loops are completely consistent. The test data are shown in table 5.

TABLE 5 Positive sequence of self-impedance measurements (in Ω/km) for different soil resistivities

TABLE 6 relative error of module value between positive sequence self-impedance measured value and standard value under different soil resistivity

As can be seen from the above Table 6, the error of the positive sequence measurement is about 2.3%, and the error is within the allowable range.

Aiming at double-circuit transmission lines, the two circuits are connected to the same bus, the circuits are completely symmetrical, so that the electrical quantities of the circuits are completely consistent, and any one of the test circuits can be used. According to the positive sequence parameters obtained by actual measurement, the zero sequence impedance of the line and the zero sequence impedance between lines are calculated by using the space coordinates, and the actual line parameters are obtained according to the ratio relation between the parameter calculation value and the measurement value.

Let r be_g0.05 Ω/km, the lightning conductor was conventionally modified as in other non-test return wiresMethod of

Resistivity p of soil is 500 Ω · m

TABLE 7 zero sequence impedance calculation value (unit omega/km)

TABLE 8 relative error of module value between zero sequence impedance calculated value and standard value

Resistivity of soil rho 1000 Ω · m

TABLE 9 zero sequence impedance calculation value (unit omega/km)

TABLE 10 relative error of module value between zero sequence impedance calculated value and standard value

Resistivity of soil rho 1500 Ω · m

TABLE 11 zero sequence impedance calculation (unit omega/km)

TABLE 12 relative error of module value between zero sequence impedance calculated value and standard value

The standard admittance parameters for parallel-rack duplex transmission lines read using the Line-check function of ATP are shown in tables 13-14.

TABLE 13 Positive sequence admittance Standard value (units us/km)

The real part of the admittance (conductance) in table 13 appears negative and can be attributed to the calculation error, and when the conductance value is negative, the real part of the admittance parameter can be ignored.

Zero sequence standard value of admittance (unit us/km) of table 14

As can be seen from table 14, the real part (conductance) of the admittance parameter has a very small and negligible value.

The invention measures the positive sequence admittance parameters and utilizes the steady-state voltage and current data at two ends of a line (test loop) to calculate the positive sequence parameters of the power transmission line, for a double-loop power transmission line, two loops are connected on the same bus, and the voltage and the current of the two loops are completely consistent. The test data are shown in table 15. Since the line admittance parameters are independent of the earth resistivity, only one set of data is presented for an earth resistivity of 1000 Ω · m.

TABLE 15 Positive sequence admittance measurement (units us/km)

TABLE 16 relative error between the positive sequence admittance measured value and the standard value norm

And testing that the relative error between the zero sequence admittance imaginary part of the true value and the ATP standard value is in an allowable range.

Two loops of the double-loop power transmission line are connected to the same bus, and the lines are completely symmetrical, so that the electrical quantities of the lines are completely consistent, and any one of the test loops can be used. According to the positive sequence parameters obtained by actual measurement, the zero sequence admittance of the line and the zero sequence admittance between the lines are calculated by utilizing the space coordinates, and the calculation of the admittance parameters does not relate to the soil resistivity and the earth resistance, so that the influence of the soil resistivity and the earth resistance does not need to be considered like the impedance calculation, and the problem of correcting the lightning conductor does not need to be considered. The relationship between the zero-sequence admittance and the inter-line transadmittance, which is obtained by using the ratio relationship based on the measured data and the data calculated from the spatial coordinates, is shown in table 17:

TABLE 17 zero sequence own and mutual admittance calculation values (unit us/km)

TABLE 18 relative error between calculated value of zero sequence admittance and norm value

Calculating the real part of the measured value by the zero sequence admittance of the line, and if the real part of the measured value is a negative value, neglecting; the real part of the line-to-line mutual admittance is extremely small and can be ignored.

The structure diagram of the ATP simulation of the parallel-frame four-circuit power transmission line is shown in the attached figure 9. Wherein reference numeral 0 denotes a lightning conductor, reference numerals 1, 2, 3 denote A, B, C three phases of a first loop, reference numerals 4, 5, 6 denote A, B, C three phases of a second loop, reference numerals 7, 8, 9 denote A, B, C three phases of a third loop, and reference numerals 10, 11, 12 denote A, B, C three phases of a fourth loop, respectively. The first and second return lines are 220kV, and the third and fourth return lines are 110 kV. The four-loop simulation model is shown in fig. 10.

According to the invention, an impedance parameter analysis utilizes EMTP-ATP to establish a parallel and parallel four-circuit transmission Line model, three different soil resistivities are taken for simulation verification, and the self-owned parameters of different circuit wires of an LCC Line module and mutual-owned parameters among the lines are read by utilizing the Line-check function of software, so that the self-owned parameters and the mutual-owned parameters among the lines are used as standard data. The steady state voltage and current data of the two ends of the circuit (test loop) are extracted, the positive sequence impedance and the positive sequence admittance parameters of the test loop are calculated according to the formula mentioned above, and the zero sequence coupling parameters between different loops are calculated on the basis of the positive sequence impedance and the positive sequence admittance parameters. And comparing standard parameter data given by ATP with parameter data obtained by calculation by using the method disclosed by the invention, and verifying the reasonability and effectiveness of the method provided by the invention.

The standard impedance parameters of the parallel-rack four-circuit transmission Line read by the Line-check function of ATP of the invention are shown in tables 19-22.

TABLE 19 Positive sequence standard values of self-impedance (unit. omega./km) for different soil resistivities

Table 20 zero sequence impedance standard value (unit omega/km-soil resistivity 500 omega. m)

Table 21 zero sequence impedance standard value (unit omega/km-soil resistivity is 1000 omega. m)

Table 22 zero sequence impedance standard value (unit omega/km-soil resistivity is 1500 omega. m)

The present invention calculates the positive sequence parameters of the transmission line by using the steady-state voltage and current data at the two ends of the line (test loop), and the test data is shown in table 23.

TABLE 23 Positive sequence of self-impedance measurements (in Ω/km) for different soil resistivities

TABLE 24 relative error between the positive sequence self-impedance measured value and the standard value module value under different soil resistivities

As can be seen from the data in the table above, the positive sequence measurement impedance error is around 2%.

For a four-circuit transmission line, the test loop can be an upper two loop or a lower two loop. The invention focuses on zero sequence parameters of a test loop and mutual coupling zero sequence parameters between the test loop and other loops, and zero sequence self parameters of other loops and mutual coupling parameters between other loops are not key focus objects; and calculating the self zero-sequence impedance of the line and the zero-sequence impedance between lines by using the space coordinates according to the positive sequence parameter obtained by actual measurement.

Let r be_gThe lightning conductor adopts the same conventional correction method as other non-test return wires when the lightning conductor is equal to 0.05 omega/km

The test loop is the first and the second loop

Resistivity p of soil is 500 Ω · m

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

TABLE 26 relative error of the module value of the zero sequence impedance calculation value and the standard value (unit omega/km)

Resistivity of soil rho 1000 Ω · m

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

TABLE 28 relative error of the module value of the zero sequence impedance calculation value and the standard value (unit omega/km)

Resistivity of soil rho 1500 Ω · m

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

TABLE 30 relative error of the module value of the zero sequence impedance calculation value and the standard value (unit omega/km)

The test loop is the third and fourth loops below

Resistivity p of soil is 500 Ω · m

Zero sequence impedance calculation value of table 31 (unit omega/km)

TABLE 32 relative error of the module value of the zero sequence impedance calculation value and the standard value (unit omega/km)

Resistivity of soil rho 1000 Ω · m

Zero sequence impedance value of table 33 (unit omega/km)

TABLE 34 relative error of the module value of the zero sequence impedance calculation value and the standard value (unit omega/km)

Resistivity of soil rho 1500 Ω · m

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

TABLE 36 relative error of the module value of the zero sequence impedance calculation value and the standard value (unit omega/km)

The standard admittance parameters for parallel-rack four-circuit transmission lines read using the Line-check function of ATP are shown in tables 37-38. The present invention takes the parameters given by ATP as the standard values (true values).

TABLE 37 Positive sequence admittance Standard value (units us/km)

The real part of the admittance (conductance) in table 37 appears negative and can be attributed to the calculation error, and when the conductance value is negative, the real part of the admittance parameter can be ignored.

Zero sequence of the watch 38 has admittance standard value (unit us/km)

As can be seen from table 38, the real part (conductance) of the admittance parameter has a very small and negligible value.

The invention utilizes the steady state voltage and current data at two ends of a line (test loop) to measure the positive sequence admittance parameters to calculate the positive sequence parameters of the power transmission line, for a four-loop power transmission line, the upper two loops and the lower two loops are respectively connected on the same bus, the voltage and the current of the upper two loops are completely consistent, and the voltage and the current of the lower two loops are completely consistent. The test data are shown in table 39.

TABLE 39 positive sequence admittance measurement (units us/km)

TABLE 40 positive sequence relative error of norm of admittance measured value to standard value

As can be seen from table 40, the relative error between the imaginary part of the zero sequence admittance of the test true value and the ATP standard value is kept around 2%.

Aiming at the four-circuit power transmission line, the upper two-circuit line and the lower two-circuit line are respectively connected to the same bus, the lines are completely symmetrical, so that the electrical quantities are completely consistent, and any one of the test circuits can be used. According to the positive sequence parameters obtained through actual measurement, the zero sequence admittance of the line and the zero sequence admittance between lines are calculated by using the space coordinates, and the calculation of the admittance parameters does not relate to the soil resistivity and the earth resistance, so that the influence of the soil resistivity and the earth resistance does not need to be considered like the impedance calculation, and the problem of correcting the lightning conductor does not need to be considered. The relationship between the zero-sequence admittance and the inter-line transadmittance, which is obtained by using the ratio relationship based on the measured data and the data calculated from the spatial coordinates, is shown in tables 41 and 43.

The test loop is a first loop and a second loop

Zero sequence calculation of susceptance and mutual susceptance (unit us/km) of table 41

TABLE 42 relative error between calculated zero-sequence admittance value and norm value

The third and fourth test loops are taken down from the test loop

TABLE 43 zero sequence own and mutual admittance calculation values (unit us/km)

TABLE 44 relative error between calculated zero-sequence admittance value and norm value

Calculating the real part of the measured value by the zero sequence admittance of the line, and if the real part of the measured value is a negative value, neglecting; the real part of the line-to-line mutual admittance is extremely small and can be ignored.

In an actual power system, the existing high-voltage overhead power transmission line, especially the power transmission line with multiple power transmission lines on the same tower in parallel does not perform transposition or incomplete transposition generally, and if a symmetric component method is used for forced decoupling, coupling still exists between a positive zero sequence and a negative zero sequence, so that the error of the existing zero sequence testing method is large and uncontrollable. For the purpose of analysis and comparison, the parallel multi-circuit line shown in fig. 8 and 10 is artificially generated with the following zero-sequence conditions: 0.1s-0.2 s: phase A load shedding-zero sequence working condition 1; 0.3s-0.4 s: phase B load shedding-zero sequence working condition 2; 0.5s-0.6 s: and C-phase load shedding-zero sequence working condition 3.

And performing difference on every two of the three zero-sequence working conditions to obtain zero-sequence parameters tested by the existing perturbation method. Tables 45-62 list the zero sequence impedances and admittances of fig. 8 and 10 as determined by the prior art zero sequence test method. The defects of the existing zero sequence parameter testing method can be seen by comparing standard data given by ATP.

TABLE 45 double-circuit transmission line (soil resistivity: 500. omega. m)

TABLE 46 relative error analysis of impedance and admittance mode values of double-circuit transmission line (soil resistivity: 500. omega. m)

TABLE 47 double-circuit transmission line (soil resistivity: 1000. omega. m)

TABLE 48 analysis of relative errors of impedance and admittance mode values of double-circuit transmission lines (soil resistivity: 1000. omega. m)

TABLE 49 double-circuit transmission line (soil resistivity: 1500. omega. m)

TABLE 50 analysis of relative errors of impedance and admittance mode values of double-circuit transmission lines (soil resistivity: 1500. omega. m)

TABLE 51 four-circuit transmission line-two-circuit upper (soil resistivity: 500. omega. m)

TABLE 52 four-circuit transmission line-two-circuit impedance, admittance modulus relative error analysis (soil resistivity: 500- Ω. m)

TABLE 53 four-circuit transmission line-two-circuit down (soil resistivity: 500. omega. m)

TABLE 54 four-circuit transmission line-two-circuit impedance, admittance modulus relative error analysis (soil resistivity: 500. omega. m)

TABLE 55 four-circuit transmission line-two-circuit upper (soil resistivity: 1000. OMEGA.m)

TABLE 56 four-circuit transmission line-upper two-circuit impedance, admittance modulus relative error analysis (soil resistivity: 1000. omega. m)

TABLE 57 four-circuit transmission line-two-circuit below (soil resistivity: 1000. omega. m)

TABLE 58 four-circuit transmission line-two-circuit impedance, admittance modulus relative error analysis (soil resistivity: 1000. omega. m)

TABLE 59 four-circuit transmission line-two-circuit upper (soil resistivity: 1500. omega. m)

TABLE 60 four-circuit transmission line-two-circuit impedance, admittance modulus relative error analysis (soil resistivity: 1500. omega. m)

TABLE 61 four-circuit transmission line-two-circuit down (soil resistivity: 1500. omega. m)

TABLE 62 four-circuit transmission line-two-circuit impedance, admittance modulus relative error analysis (soil resistivity: 1500. omega. m)

The invention provides an online testing method for zero sequence coupling parameters of parallel multi-circuit power transmission lines. The method only needs to measure the positive sequence impedance and the positive sequence admittance of the test loop for the voltage and the current at two ends of a group of parallel multi-loop power transmission lines in normal operation, calculates the ratio of each impedance and the ratio of each admittance of the parallel multi-loop power transmission lines under the same environment, establishes the relationship between the corresponding physics, and realizes the indirect online test of the zero-sequence coupling impedance and the admittance of the parallel multi-loop power transmission lines. The specific implementation mode verifies the effectiveness and the reliability of the invention.

The test method provided by the invention has strong practicability and operability. Different from the existing zero sequence test method which needs special equipment and operation stopping, the test method provided by the invention does not need any operation specially generating zero sequence, does not influence the normal operation of the system, can realize the test of the zero sequence coupling parameters of the parallel multi-circuit transmission lines only by a group of steady-state voltage and current data at two ends of the system, greatly simplifies the parameter test method of the parallel multi-circuit transmission lines, greatly improves the efficiency of the line parameter test, is flexible and convenient, and has strong practicability and operability. The method is beneficial to the safe, stable and economic operation of the parallel multi-circuit transmission lines.

Drawings

FIG. 1 is a schematic diagram of parallel three-circuit power transmission lines.

FIG. 2 shows a test loop positive sequence equivalent circuit.

FIG. 3 is a schematic view of a longitudinal section of an N-wire system.

Fig. 4 is a schematic cross-sectional view of a multi-circuit transmission line on the same tower.

FIG. 5 is a schematic view of space charge distribution.

FIG. 6 is a flow chart of a positive sequence testing method of zero sequence coupling parameters of parallel multi-circuit power transmission lines.

FIG. 7 is a schematic diagram of a spatial layout of parallel double-circuit transmission lines.

FIG. 8 shows a simulation model of parallel double-circuit transmission lines.

FIG. 9 is a schematic diagram of a spatial layout of parallel-parallel four-circuit power transmission lines.

FIG. 10 shows a simulation model of parallel-rack four-circuit transmission line.

Claims (9)

1. A positive sequence on-line test method for zero sequence parameters of parallel multi-circuit transmission lines is characterized by comprising the following steps: the positive sequence impedance and the positive sequence admittance of the test loop are measured only by a group of voltage and current data at two ends of the line during normal operation, the ratio of each impedance and the ratio of each admittance of the parallel multi-loop under the same environment are calculated, the relationship of each corresponding physical quantity is established, and the indirect online test of the zero-sequence coupling impedance and the admittance of the parallel multi-loop power transmission line is realized. The relation between the self-impedance and the mutual impedance (self-admittance and mutual admittance) is expressed by the ratio between the physical quantities of the parallel multi-loop lines under the same environment. To pairImpedance of the two (admittance of the two)Andis finally estimated inIs present, thus effectively suppressing errors. WhileR in_ciAnd α_iAre all derived from the measured values of the measured values,andr in_g(ground resistance) comes from the Karson equation. All these measures ensure the test accuracy and reliability of the method as a whole.

2. The method of claim 1, wherein: the original data of the test only needs a group of normal operation steady-state voltage and current data, the positive sequence parameter of the line is calculated according to the group of steady-state voltage and current data of the test loop, and the self-owned parameter and the mutual-owned parameter of the line and the zero sequence between the lines are calculated by using the positive sequence parameter and the coordinates of the space position of the line.

3. The method of claim 1, wherein: the testing method provided by the invention specially considers the influence of the soil resistivity on the impedance testing method, and the simulation verifies that when the fluctuation of the soil resistivity reaches +/-50%, the influence on the positive sequence and the zero sequence impedance is small, wherein the relative deviation of the positive sequence is 0.1%, and the relative deviation of the zero sequence is 0.1%3% difference, while the admittance is hardly affected by the earth's conductivity. Due to the earth resistivity gammaOrThe form of (1) affecting the self-impedance and the mutual impedance, pair functionWhen gamma is from 0.05s/m to 10^-4Function when s/m changesFrom 5.112 to 12.255, the functional form of the natural logarithm theoretically ensures the fault tolerance and anti-interference capability of the method.

4. The method of claim 1, wherein: the line return line (the (N +1) th line) is a Karson equivalent conductor formed by the Karson formular_N+1＝1(m)，i is 1, 2, 3 … N, j is 1, 2, 3 … N. Where f, γ are the frequency of the system and the electrical conductivity of the earth, respectively. Then there isi is 1, 2, 3 … N, j is 1, 2, 3 … N. The self-impedance and the mutual impedance per unit length of the conductor are respectively Wherein r is_ciIs the resistance per unit length of the wire i, r_gIs the resistance per unit length of the earth along the line. The equivalent self-impedance and mutual impedance of unit length between each parallel conducting wire can be obtained by eliminating the lightning conductor.

5. The method of claim 1, wherein: if the p-th loop line is an m-split conductor ${\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_i1The internal self-inductance of the split conductor is 1 unit length. If the p-th loop line is an m-split conductor

6. The method of claim 1, wherein: calculating corresponding elements of an impedance and admittance parameter matrix according to space coordinates of the line by taking impedance and admittance calculation parameters of the line in normal operation as referencesAndand calculating the true values of all elements in the impedance and admittance parameter matrixes according to the ratio relation among all elements of the impedance and admittance parameter matrixes obtained by calculation and the measured values of the line impedance and admittance in a steady state.

7. The method of claim 1, wherein: the positive sequence test method provided by the invention has the advantages that as long as the positive sequence component is stable, the parallel multi-loop wires are in stable operation, the negative sequence component and the zero sequence component in the voltage and the current at the two ends of each parallel loop wire are very small, and the positive sequence parameter is exactly equal to the positive sequence parameter of the equivalent balanced array, so that the high test precision is ensured. When r is obtained from the test loop_ci、α_iAnd find outAnd r_gAfter the determination, the rest of the circuits correspond to the function ratio corresponding to the space coordinates of the circuits under the same climatic conditions, so that the test precision and reliability of the method are theoretically ensured to be far higher than those of the existing method. Similarly, the method can also ensure the test accuracy and reliability of the zero sequence admittance parameters of the parallel multi-circuit line.

8. The method of claim 1, wherein: the test method provided by the invention has strong practicability and operability. Different from the existing zero sequence test method which needs special equipment and operation stopping, the test method provided by the invention can realize the test of the zero sequence coupling parameters of the parallel multi-circuit transmission lines without any special operation for generating the zero sequence and influencing the normal operation of the system, only needs a group of steady-state voltage and current data at two ends of the system, and even does not need synchronization (the difference is several or even dozens of cycles), thereby greatly simplifying the parameter test method of the parallel multi-circuit transmission lines, greatly improving the efficiency of the line parameter test, being flexible and convenient, and having strong practicability and operability.

9. The method of claim 1, wherein: the positive sequence on-line testing method for the zero sequence parameters of the parallel multi-circuit transmission lines is a convenient, practical and efficient zero sequence parameter on-line testing method. Because the signal acquisition is very easy, annual measurement, quarterly measurement, monthly measurement and even daily measurement can be carried out. The method for testing the parallel multi-circuit line parameters at any time not only can greatly simplify the testing of the parallel multi-circuit line zero-sequence coupling parameters, but also can monitor the running state of the parallel multi-circuit line. The positive sequence on-line testing method for the zero sequence parameters of the parallel multi-circuit transmission lines is beneficial to safe, stable and economic operation of the parallel multi-circuit transmission lines.