CN103904623A - Constant value sensitivity check method applicable to single-return-wire tandem-connection double-return transmission line distance protection - Google Patents

Abstract

The invention discloses a constant value sensitivity check method applicable to single-return-wire tandem-connection double-return transmission line distance protection. According to the working mode, for a single-return-wire interval, a measured impedance calculation expression in fault of the single-return-wire interval is formed on the basis of the characteristic that measured impedance in fault and fault distance are in direct proportion according to a full-line circuit and system impedance parameters; for a double-return-wire interval, according to a grid structure, a circuit and system impedance parameters of a transmission line, circuits and system impedance outside a double return wire are merged to form a typical system layout of power sources at the two ends of the double return wire, then, the calculation mode with which measured impedance changes according to positions of fault points is formed according to the impedance parameters, and different calculation expressions are adopted for one-phase grounding and phase-to-phase faults; all the results are combined, the calculation expression of full-line measured impedance in one-phase grounding and phase-to-phase faults according to the positions of the fault positions is formed, the maximum value of the measured impedance in full-line fault is acquired, and the maximum value is compared with a distance protection element constant value so that the sensitivity of the distance protection element constant value can be checked.

Description

One is applicable to single loop line serial connection double back transmission line distance protection definite value sensitivity check method

Technical field

The present invention relates to a kind of electric grid relay protection constant value Verification Technology, the technology that particularly the Distance Protection Components sensitivity of the particular form of single loop line serial connection double back transmission line is checked.

Background technology

Along with industry and residential electricity consumption demand growing, the rapid growth of electric power system installed capacity, original transmission line transmission capacity approaches the limit, and newly-increased transmission line cost is more and more higher, for utilize existing transmission of electricity corridor as far as possible, there is the middle transmission line new model that seals in double loop of single loop line.

The check method of Distance Protection Components sensitivity at present; normally measure impedance when computational scheme end generation single phase ground fault and phase-to phase fault; this value and distancing element definite value are compared to determine protection action sensitivity, when the basic foundation of which is transmission line malfunction, measure impedance with fault point away from monotone increasing.And the mode of connection of single loop line serial connection double back, due to branch's effect of double loop, has changed the impedance trend of monotone increasing completely of measuring, make existing method of calibration cannot adapt to this special circuit demand, thereby affected the performance of Distance Protection Components.

Summary of the invention

Object of the present invention, is to provide for single loop line serial connection double back transmission line a kind of method of calibration of distance protection definite value, measures impedance and cause with the non-monotonic variation of abort situation the problem that distance protection definite value cannot verification while solving under this system due to fault.

In order to reach above-mentioned purpose, solution of the present invention is:

First, for single back line section, when fault, measure impedance and be directly proportional apart from length, can form and measure impedance according to following formula:

$Z=Z_{\mathrm{PM}}*\frac{L_f}{L_{\mathrm{PM}}}$

In above formula: L _pMfor single time section PM total track length, L _ffor the line length of distance P side relaying protection installation place, fault point, Z _pMfor PM section positive sequence impedance completely;

During for the single loop line generation single-phase earthing in double back transmission line and phase-to phase fault, it measures resistance value and fault distance is not directly proportional, part beyond double loop is carried out to merger, as equivalent system impedance, form typical Double-End Source through double loop power transmission mode by the resistance value after the impedance of the single loop line section in both sides and corresponding system impedance series connection.Be the system configuration after merger as shown in Figure 2, under this line construction when troubles inside the sample space corresponding positive sequence, negative phase-sequence and zero-sequence network respectively as shown in accompanying drawing 3, accompanying drawing 4, accompanying drawing 5, according to this network structure, can calculate double back line segment generation single phase ground fault time, measure impedance and be shown below:

$Z=Z_{\mathrm{PM}}+k_{\mathrm{<figure-callout\; id="1"\; label="B\; Z\; l"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">B</figure-callout>}}{Z}_l{1}_{}\frac{1+(1+{2K}_{\mathrm{set}})D}{2(1+C)+\left({1+3K}_{\mathrm{set}}\right)\mathrm{AD}}+k_B{Z}_{m0}\frac{(A-1)D}{2(1+C)+\left({1+3K}_{\mathrm{set}}\right)\mathrm{AD}}$

Wherein:

$A=\frac{{2Z}_{n0}+\left({1-k}_B\right)(Z_{l0}+Z_{M0})}{Z_{n0}+\left({1-k}_B\right)(Z_{m0}+Z_{l0}+Z_{M0})}$

$B=\frac{{2Z}_{m0}+k_B(Z_{l0}+Z_{M0})}{Z_{m0}+k_B(Z_{n0}+Z_{l0}+Z_{M0})}$

$C=\frac{{\mathrm{<figure-callout\; id="1"\; label="Z\; m"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">Z</figure-callout>}}_m+k_B({\mathrm{<figure-callout\; id="1"\; label="Z\; l"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">Z</figure-callout>}}_l+{\mathrm{<figure-callout\; id="1"\; label="Z\; m"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">Z</figure-callout>}}_m+Z_{n1})}{{\mathrm{<figure-callout\; id="1"\; label="Z\; n"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">Z</figure-callout>}}_n+\left({1-k}_B\right)({\mathrm{<figure-callout\; id="1"\; label="Z\; l"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">Z</figure-callout>}}_l+{\mathrm{<figure-callout\; id="1"\; label="Z\; m"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">Z</figure-callout>}}_m+Z_{m1})}$

$D=\frac{(1-B)(1+C)}{A-B}$

$k_B=\frac{L_f-L_{\mathrm{PM}}}{L_{\mathrm{MN}}}$

Z _m1, Z _n1, Z _m0, Z _n0be respectively m side system positive sequence impedance after merger, n side system positive sequence impedance, m side system zero sequence impedance, n side system zero sequence impedance;

Z _l1, Z _l0, Z _m0be respectively single back line total length positive sequence impedance, zero sequence impedance, zero sequence mutual impedance in double loop;

K _setfor distancing element zero sequence compensation coefficient definite value;

L _mNfor double back section MN total track length.

According to positive sequence network and negative sequence network schematic diagram, can calculate double back line segment generation phase-to phase fault time, measure impedance and be shown below:

$Z={\mathrm{<figure-callout\; id="1"\; label="Z\; l"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">Z</figure-callout>}}_l+\frac{k_{\mathrm{<figure-callout\; id="1"\; label="B\; Z\; l"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">B</figure-callout>}}{Z}_l{1}_{}}{1+k_B-E\left({1-k}_B\right)}$

Wherein:

$E=\frac{\left({1+k}_B\right){\mathrm{<figure-callout\; id="1"\; label="Z\; m"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">Z</figure-callout>}}_m+k_B({\mathrm{<figure-callout\; id="1"\; label="Z\; l"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">Z</figure-callout>}}_l+Z_{n1})}{\left({1-k}_B\right){\mathrm{<figure-callout\; id="1"\; label="Z\; m"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">Z</figure-callout>}}_m+\left({2-k}_B\right){\mathrm{<figure-callout\; id="1"\; label="Z\; n"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">Z</figure-callout>}}_n+\left({1-k}_B\right){\mathrm{<figure-callout\; id="1"\; label="Z\; l"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">Z</figure-callout>}}_l}$

Fault measuring impedance computation formula under comprehensive above-mentioned diverse location, can form measurement impedance computation method completely, while having single phase ground fault, calculates by following:

$Z=\left\{\begin{array}{cc}{Z}_{\mathrm{PM}}*\frac{L_f}{L_{\mathrm{PM}}}& 0\&le;L_f\&le;L_{\mathrm{PM}}\\ Z_{\mathrm{PM}}+k_{\mathrm{<figure-callout\; id="1"\; label="B\; Z\; l"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">B</figure-callout>}}{Z}_l{1}_{}\frac{1+\left({1+3K}_{\mathrm{set}}\right)D}{2(1+C)+\left({1+3K}_{\mathrm{set}}\right)\mathrm{AD}}+k_B{Z}_{m0}\frac{(A-1)D}{2(1+C)+\left({1+3K}_{\mathrm{set}}\right)\mathrm{AD}}& L_{\mathrm{PM}}<L_f\&le;L_{\mathrm{PN}}\\ Z^{\&prime;}+Z_{\mathrm{NQ}}*\frac{L_f-L_{\mathrm{MN}}}{L_{\mathrm{NQ}}}& L_{\mathrm{PN}}<L_f\&le;L_{\mathrm{PQ}}\end{array}\right.$

Wherein:

$Z^{\&prime;}=Z_{\mathrm{PM}}+k_{\mathrm{<figure-callout\; id="1"\; label="B\; Z\; l"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">B</figure-callout>}}{Z}_l{1}_{}\frac{1+\left({1+3K}_{\mathrm{set}}\right)D}{2(1+C)+\left({1+3K}_{\mathrm{set}}\right)\mathrm{AD}}+k_B{Z}_{m0}\frac{(A-1)D}{2(1+C)+\left({1+3K}_{\mathrm{set}}\right)\mathrm{AD}}|L_f=L_{\mathrm{PN}}$

When phase-to phase fault, calculate by following:

$Z=\left\{\begin{array}{cc}{Z}_{\mathrm{PM}}*\frac{L_f}{L_{\mathrm{PM}}}& 0\&le;L_f\&le;L_{\mathrm{PM}}\\ Z_{\mathrm{PM}}+\frac{k_{\mathrm{<figure-callout\; id="1"\; label="B\; Z\; l"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">B</figure-callout>}}{Z}_l{1}_{}}{1+k_B-E\left({1-k}_B\right)}& L_{\mathrm{PM}}<L_f\&le;L_{\mathrm{PN}}\\ Z^{\&prime;\&prime;}+Z_{\mathrm{NQ}}*\frac{L_f-L_{\mathrm{MN}}}{L_{\mathrm{NQ}}}& L_{\mathrm{PN}}<L_f\&le;L_{\mathrm{PQ}}\end{array}\right.$

Wherein:

$Z^{\&prime;}=Z_{\mathrm{PM}}+\frac{k_{\mathrm{<figure-callout\; id="1"\; label="B\; Z\; l"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">B</figure-callout>}}{Z}_l{1}_{}}{1+k_B-E\left({1-k}_B\right)}|L_f=L_{\mathrm{PN}}$

Will be completely according to fixed step size (as 0.01*L _pQ) draw out the track of measuring impedance, can obtain this transmission line and in the time of single phase ground fault, measure impedance maximum Z _{max_p}measure impedance maximum Z with phase-to phase fault _{max_pp}, this maximum and Distance Protection Components definite value are compared, and the sensitivity that can obtain respectively ground distance element and phase spacing element is as follows:

K _{K_p}=Z _{max_p}/Z _{set_p}

K _{K_pp}=Z _{max_pp}/Z _{set_pp}

Single loop line of determining for arbitrary parameter seals in double loop operational system; by above-mentioned steps, can realize the check of protection component sensitivity of adjusting the distance, thereby differentiate the reasonability of this distancing element fixed value adjusting; ensureing when line fault can action message, the fault in excision district.

Brief description of the drawings

Fig. 1 is the schematic network structure of the single loop line serial connection of the typical case that the present invention is directed to double loop;

Fig. 2 is that double loop outside line carries out the system schematic after equivalent merger;

Fig. 3 is system positive sequence network schematic diagram after merger;

Fig. 4 is system negative sequence network schematic diagram after merger;

Fig. 5 is system zero sequence network schematic diagram after merger;

Fig. 6 is three kinds of evolved network structural representations one that the present invention is suitable for;

Fig. 7 is three kinds of evolved network structural representations two that the present invention is suitable for;

Fig. 8 is three kinds of evolved network structural representations three that the present invention is suitable for.

Embodiment

Below with reference to accompanying drawing, technical scheme of the present invention is elaborated.

One is applicable to single loop line serial connection double back transmission line distance protection definite value sensitivity check method, and for single back line interval, impedance computation formula is measured in the formation being directly proportional according to fault measuring impedance and fault distance; To double loop interval, first periphery circuit and system are carried out to merger, while calculating respectively single-phase earthing and phase-to phase fault, double back section is measured the track that impedance changes with position of failure point; Utilize measurement locus of impedance curve completely, obtain and measure impedance maximum, and distance protection definite value is relatively checked its sensitivity;

During for the interval fault of double back, measure the calculating of impedance, part beyond double loop is carried out to merger, as equivalent system impedance, form typical Double-End Source through double loop power transmission mode by the resistance value after the impedance of the single loop line section in both sides and corresponding system impedance series connection;

During for the interval single phase ground fault of double loop, the measurement resistance value of double back section, according to the positive sequence after equivalence, negative phase-sequence and zero-sequence network, forms the relational expression of measuring impedance and abort situation;

The measurement resistance value of double back section during for double loop district phase-to phase fault, according to the positive sequence after equivalence, negative sequence network, forms and measures impedance and abort situation relational expression;

Impedance expression is measured in all fronts that form according to transmission line parameter, can obtain all fronts single-phase earthing and phase-to phase fault and measure the maximum of impedance.

As shown in Figure 1, the present invention, in the time implementing, first can determine that single loop line PM interval measure locus of impedance changes monotone increasing with position of failure point, and measuring impedance can be described according to following formula:

$Z=Z_{\mathrm{PM}}*\frac{L_f}{L_{\mathrm{PM}}}$

In above formula: L _pMfor PM section total track length, L _ffor the line length of distance P side relaying protection installation place, fault point, Z _pMfor PM section positive sequence impedance completely;

Then, while determining in double-circuit line MN section single loop line generation earth fault, measure impedometer formula, the impedance parameter merger of transmission line PM section and NQ section is entered to system impedance, be equivalent to M side and the impedance of N side integrated system, thus, directly formed typical Double-End Source system as shown in Figure 2, according to this grid structure, during for single phase ground fault, the measurement impedance of double back line segment can be described according to following formula:

$Z=Z_{\mathrm{PM}}+k_{\mathrm{<figure-callout\; id="1"\; label="B\; Z\; l"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">B</figure-callout>}}{Z}_l{1}_{}\frac{1+(1+{2K}_{\mathrm{set}})D}{2(1+C)+\left({1+3K}_{\mathrm{set}}\right)\mathrm{AD}}+k_B{Z}_{m0}\frac{(A-1)D}{2(1+C)+\left({1+3K}_{\mathrm{set}}\right)\mathrm{AD}}$

Wherein:

$A=\frac{{2Z}_{n0}+\left({1-k}_B\right)(Z_{l0}+Z_{M0})}{Z_{n0}+\left({1-k}_B\right)(Z_{m0}+Z_{l0}+Z_{M0})}$

$B=\frac{{2Z}_{m0}+k_B(Z_{l0}+Z_{M0})}{Z_{m0}+k_B(Z_{n0}+Z_{l0}+Z_{M0})}$

$C=\frac{{\mathrm{<figure-callout\; id="1"\; label="Z\; m"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">Z</figure-callout>}}_m+k_B({\mathrm{<figure-callout\; id="1"\; label="Z\; l"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">Z</figure-callout>}}_l+{\mathrm{<figure-callout\; id="1"\; label="Z\; m"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">Z</figure-callout>}}_m+Z_{n1})}{{\mathrm{<figure-callout\; id="1"\; label="Z\; n"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">Z</figure-callout>}}_n+\left({1-k}_B\right)({\mathrm{<figure-callout\; id="1"\; label="Z\; l"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">Z</figure-callout>}}_l+{\mathrm{<figure-callout\; id="1"\; label="Z\; m"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">Z</figure-callout>}}_m+Z_{m1})}$

$D=\frac{(1-B)(1+C)}{A-B}$

$k_B=\frac{L_f-L_{\mathrm{PM}}}{L_{\mathrm{MN}}}$

Z _m1, Z _n1, Z _m0, Z _n0be respectively m side system positive sequence impedance after merger, n side system positive sequence impedance, m side system zero sequence impedance, n side system zero sequence impedance;

Z _l1, Z _l0, Z _m0be respectively single back line total length positive sequence impedance, zero sequence impedance, zero sequence mutual impedance in double loop;

K _setfor distancing element zero sequence compensation coefficient definite value;

L _mNfor double back section MN total track length.

For phase-to phase fault, the measurement impedance of double back line segment can be described according to following formula:

$Z={\mathrm{<figure-callout\; id="1"\; label="Z\; l"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">Z</figure-callout>}}_l+\frac{k_{\mathrm{<figure-callout\; id="1"\; label="B\; Z\; l"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">B</figure-callout>}}{Z}_l{1}_{}}{1+k_B-E\left({1-k}_B\right)}$

Wherein:

$E=\frac{\left({1+k}_B\right){\mathrm{<figure-callout\; id="1"\; label="Z\; m"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">Z</figure-callout>}}_m+k_B({\mathrm{<figure-callout\; id="1"\; label="Z\; l"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">Z</figure-callout>}}_l+Z_{n1})}{\left({1-k}_B\right){\mathrm{<figure-callout\; id="1"\; label="Z\; m"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">Z</figure-callout>}}_m+\left({2-k}_B\right){\mathrm{<figure-callout\; id="1"\; label="Z\; n"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">Z</figure-callout>}}_n+\left({1-k}_B\right){\mathrm{<figure-callout\; id="1"\; label="Z\; l"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">Z</figure-callout>}}_l}$

Measurement impedance characteristic while breaking down in comprehensive each section of railroad section, can form following measurement locus of impedance computing formula.

While having single phase ground fault, calculate by following:

$Z=\left\{\begin{array}{cc}{Z}_{\mathrm{PM}}*\frac{L_f}{L_{\mathrm{PM}}}& 0\&le;L_f\&le;L_{\mathrm{PM}}\\ Z_{\mathrm{PM}}+k_{\mathrm{<figure-callout\; id="1"\; label="B\; Z\; l"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">B</figure-callout>}}{Z}_l{1}_{}\frac{1+\left({1+3K}_{\mathrm{set}}\right)D}{2(1+C)+\left({1+3K}_{\mathrm{set}}\right)\mathrm{AD}}+k_B{Z}_{m0}\frac{(A-1)D}{2(1+C)+\left({1+3K}_{\mathrm{set}}\right)\mathrm{AD}}& L_{\mathrm{PM}}<L_f\&le;L_{\mathrm{PN}}\\ Z^{\&prime;}+Z_{\mathrm{NQ}}*\frac{L_f-L_{\mathrm{MN}}}{L_{\mathrm{NQ}}}& L_{\mathrm{PN}}<L_f\&le;L_{\mathrm{PQ}}\end{array}\right.$

Wherein:

$Z^{\&prime;}=Z_{\mathrm{PM}}+k_{\mathrm{<figure-callout\; id="1"\; label="B\; Z\; l"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">B</figure-callout>}}{Z}_l{1}_{}\frac{1+\left({1+3K}_{\mathrm{set}}\right)D}{2(1+C)+\left({1+3K}_{\mathrm{set}}\right)\mathrm{AD}}+k_B{Z}_{m0}\frac{(A-1)D}{2(1+C)+\left({1+3K}_{\mathrm{set}}\right)\mathrm{AD}}|L_f=L_{\mathrm{PN}}$

When phase-to phase fault, calculate by following:

$Z=\left\{\begin{array}{cc}{Z}_{\mathrm{PM}}*\frac{L_f}{L_{\mathrm{PM}}}& 0\&le;L_f\&le;L_{\mathrm{PM}}\\ Z_{\mathrm{PM}}+\frac{k_{\mathrm{<figure-callout\; id="1"\; label="B\; Z\; l"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">B</figure-callout>}}{Z}_l{1}_{}}{1+k_B-E\left({1-k}_B\right)}& L_{\mathrm{PM}}<L_f\&le;L_{\mathrm{PN}}\\ Z^{\&prime;\&prime;}+Z_{\mathrm{NQ}}*\frac{L_f-L_{\mathrm{MN}}}{L_{\mathrm{NQ}}}& L_{\mathrm{PN}}<L_f\&le;L_{\mathrm{PQ}}\end{array}\right.$

Wherein:

$Z^{\&prime;}=Z_{\mathrm{PM}}+\frac{k_{\mathrm{<figure-callout\; id="1"\; label="B\; Z\; l"\; filenames="140312165257.png,140312165302.png"\; state="\{\{state\}\}">B</figure-callout>}}{Z}_l{1}_{}}{1+k_B-E\left({1-k}_B\right)}|L_f=L_{\mathrm{PN}}$

During according to above-mentioned all fronts single-phase earthing and phase-to phase fault, measure the track of impedance, with certain step-length (such as 0.01*L _pQ) measure the size of impedance while calculating completely diverse location fault, obtain accordingly the measurement impedance maximum Z in single-phase earthing and phase-to phase fault situation _{max_p}and Z _{max_pp}.

According to the extreme value of measuring impedance, to calculate according to following formula, the sensitivity that can directly obtain the protection definite value of ground distance element and phase spacing element, can differentiate according to the following formula,

K _{K_p}=Z _{max_p}/Z _{set_p}

K _{K_pp}=Z _{max_pp}/Z _{set_pp}

In addition, check method of the present invention is not only applicable to the canonical system shown in Fig. 1, all can adapt to for three kinds of evolved network shown in Fig. 6～Fig. 8, only needs the length of the corresponding line section in single-phase earthing and phase-to phase fault expression formula to set to 0.

To sum up; the present invention measures impedance computation by the transmission line segmentation that single loop line is sealed in to double loop operation; draw respectively its resistance value in the time of single-phase earthing and phase-to phase fault; thereby the measurement impedance maximum while obtaining all fronts single-phase earthing and phase-to phase fault; in order to compare with distance protection definite value, determine the sensitivity of distance protection definite value.

Claims (1)

1. be applicable to a single loop line serial connection double back transmission line distance protection definite value sensitivity check method, it is characterized in that the method comprises the following steps:

(1) for single back line section, when fault, measure impedance and be directly proportional apart from length, measure formula of impedance as follows:

$Z=Z_{\mathrm{PM}}*\frac{L_f}{L_{\mathrm{PM}}}$

Wherein: L _pMfor single time section PM total track length, L _ffor the line length of distance P side relaying protection installation place, fault point, Z _pMfor PM section positive sequence impedance completely;

(2) during for the single loop line generation single-phase earthing in double back transmission line and phase-to phase fault, it measures resistance value and fault distance is not directly proportional, part beyond double loop is carried out to merger, by the resistance value after the impedance of the single loop line section in both sides and corresponding system impedance series connection as equivalent system impedance, form typical Double-End Source through double loop power transmission mode, while calculating double back line segment generation single phase ground fault, measure formula of impedance as follows:

$Z=Z_{\mathrm{PM}}+k_B{Z}_{l1}\frac{1+(1+{2K}_{\mathrm{set}})D}{2(1+C)+\left({1+3K}_{\mathrm{set}}\right)\mathrm{AD}}+k_B{Z}_{m0}\frac{(A-1)D}{2(1+C)+\left({1+3K}_{\mathrm{set}}\right)\mathrm{AD}}$

Wherein:

$A=\frac{{2Z}_{n0}+\left({1-k}_B\right)(Z_{l0}+Z_{M0})}{Z_{n0}+\left({1-k}_B\right)(Z_{m0}+Z_{l0}+Z_{M0})}$

$B=\frac{{2Z}_{m0}+k_B(Z_{l0}+Z_{M0})}{Z_{m0}+k_B(Z_{n0}+Z_{l0}+Z_{M0})}$

$C=\frac{Z_{m1}+k_B(Z_{l1}+Z_{m1}+Z_{n1})}{Z_{n1}+\left({1-k}_B\right)(Z_{l1}+Z_{m1}+Z_{m1})}$

$D=\frac{(1-B)(1+C)}{A-B}$

$k_B=\frac{L_f-L_{\mathrm{PM}}}{L_{\mathrm{MN}}}$

Z _m1, Z _n1, Z _m0, Z _n0be respectively m side system positive sequence impedance after merger, n side system positive sequence impedance, m side system zero sequence impedance, n side system zero sequence impedance;

Z _l1, Z _l0, Z _m0be respectively single back line total length positive sequence impedance, zero sequence impedance, zero sequence mutual impedance in double loop;

K _setfor distancing element zero sequence compensation coefficient definite value;

L _mNfor double back section MN total track length;

(3), while calculating double back line segment generation phase-to phase fault, measure formula of impedance as follows:

$Z=Z_{l1}+\frac{k_B{Z}_{l1}}{1+k_B-E\left({1-k}_B\right)}$

Wherein:

$E=\frac{\left({1+k}_B\right)Z_{m1}+k_B(Z_{l1}+Z_{n1})}{\left({1-k}_B\right)Z_{m1}+\left({2-k}_B\right)Z_{n1}+\left({1-k}_B\right)Z_{l1}}$

(4) fault measuring impedance computation formula under comprehensive above-mentioned diverse location, can form measurement impedance computation method completely, while having single phase ground fault, calculates by following:

$Z=\left\{\begin{array}{cc}{Z}_{\mathrm{PM}}*\frac{L_f}{L_{\mathrm{PM}}}& 0\&le;L_f\&le;L_{\mathrm{PM}}\\ Z_{\mathrm{PM}}+k_B{Z}_{l1}\frac{1+\left({1+3K}_{\mathrm{set}}\right)D}{2(1+C)+\left({1+3K}_{\mathrm{set}}\right)\mathrm{AD}}+k_B{Z}_{m0}\frac{(A-1)D}{2(1+C)+\left({1+3K}_{\mathrm{set}}\right)\mathrm{AD}}& L_{\mathrm{PM}}<L_f\&le;L_{\mathrm{PN}}\\ Z^{\&prime;}+Z_{\mathrm{NQ}}*\frac{L_f-L_{\mathrm{MN}}}{L_{\mathrm{NQ}}}& L_{\mathrm{PN}}<L_f\&le;L_{\mathrm{PQ}}\end{array}\right.$ Wherein:

$Z^{\&prime;}=Z_{\mathrm{PM}}+k_B{Z}_{l1}\frac{1+\left({1+3K}_{\mathrm{set}}\right)D}{2(1+C)+\left({1+3K}_{\mathrm{set}}\right)\mathrm{AD}}+k_B{Z}_{m0}\frac{(A-1)D}{2(1+C)+\left({1+3K}_{\mathrm{set}}\right)\mathrm{AD}}|L_f=L_{\mathrm{PN}}$

When phase-to phase fault, calculate by following:

$Z=\left\{\begin{array}{cc}{Z}_{\mathrm{PM}}*\frac{L_f}{L_{\mathrm{PM}}}& 0\&le;L_f\&le;L_{\mathrm{PM}}\\ Z_{\mathrm{PM}}+\frac{k_B{Z}_{l1}}{1+k_B-E\left({1-k}_B\right)}& L_{\mathrm{PM}}<L_f\&le;L_{\mathrm{PN}}\\ Z^{\&prime;\&prime;}+Z_{\mathrm{NQ}}*\frac{L_f-L_{\mathrm{MN}}}{L_{\mathrm{NQ}}}& L_{\mathrm{PN}}<L_f\&le;L_{\mathrm{PQ}}\end{array}\right.$

Wherein:

$Z^{\&prime;}=Z_{\mathrm{PM}}+\frac{k_B{Z}_{l1}}{1+k_B-E\left({1-k}_B\right)}|L_f=L_{\mathrm{PN}}$

(5) by drawing out according to fixed step size the track of measuring impedance completely, can obtain this transmission line and in the time of single phase ground fault, measure impedance maximum Z _{max_p}measure impedance maximum Z with phase-to phase fault _{max_pp}, this maximum and Distance Protection Components definite value are compared, and the sensitivity that can obtain respectively ground distance element and phase spacing element is as follows:

K _{K_p}=Z _{max_p}/Z _{set_p}

K _{K_pp}=Z _{max_pp}/Z _{set_pp}

Single loop line of determining for arbitrary parameter seals in double loop operational system; by above-mentioned steps, can realize the check of protection component sensitivity of adjusting the distance, thereby differentiate the reasonability of this distancing element fixed value adjusting; ensureing when line fault can action message, the fault in excision district.

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