CN101907677A - High voltage cable-overhead line hybrid line fault phase ranging method - Google Patents

Abstract

The invention discloses a method for realizing high voltage cable-overhead line hybrid line fault ranging by using the phase characteristic of a positioning function, which belongs to the technical field of relay protection of power systems. The method comprises: firstly, acquiring positive sequence electrical data at two ends of a failed hybrid line system and equaling the entire hybrid line to a line of the same length; secondly, deducing the positioning function by using the positive electrical data at the two ends of the hybrid line system, and determining a minimum fault partition having a fault point according to the size of the phase of the positioning function; and finally, accurately finding the fault range of the hybrid line in the fault partition by using the size of the phase angle of the positioning function. The method can accurately find the position of a fault, reduce troubleshooting time and accelerate power supply restoration and has a great significance for the safe and economic operation of the power system.

Description

High voltage cable-overhead line hybrid line fault phase ranging method

Technical field

The present invention relates to the relay protection of power system technical field, specifically relate to adopt the mapping function phase propetry to realize the method for high voltage cable-overhead line hybrid line fault range finding.

Background technology

Along with the develop rapidly of China's large-and-medium size cities construction and the requirement of city planning, power cable with its take up an area of less, personal safety guarantee, power supply reliability height, maintenance workload are little etc., and advantage has obtained using widely, and further development and application cable-aerial wire mixed line more and more widely on original cable, overhead transmission line basis, for example mountain, small ocean, Shanghai cable-aerial mixed line, railway self-closing perforation cable-aerial circuit and electric railway cable-aerial mixed line.Can precision ranging after high voltage cable-overhead line hybrid line breaks down, can shorten the malfunction elimination time, accelerate to restore electricity, the safety and the economical operation of electric system had very important significance.

Than the independent cable and the fault localization of overhead transmission line, high-tension cable-pole line mixed power transmission line fault localization can face a following new difficult problem: 1. since cable line and overhead transmission line parameter differ greatly, its joint line wave impedance is discontinuous, therefore, for being applied to the impedance method of overhead transmission line fault localization separately, joint line is the non-uniform circuit road, can't directly apply to the fault localization of joint line; 2. the ripple of going can reflect in the junction of cable and overhead transmission line, has increased the identification difficulty of reflection wave; 3. the velocity of propagation in cable and overhead transmission line is obviously inconsistent, is difficult to direct range finding; 4. particularly reflection wave is after propagating through long cable line for capable ripple, and the wave head amplitude attenuation is bigger, is vulnerable to the influence of undesired signal, thereby influences measuring accuracy.Therefore, the traveling wave method that is applied to the fault localization of independent cable and overhead transmission line also can't directly apply to the fault localization of joint line.

Relevant high-tension cable-the fault localization of pole line mixed power transmission line has caused numerous scholars' concern gradually." the cable-aerial wire mixed line failure distance-finding method summary " that people such as Yu Yuze, Qin Jian and Li Gongxin deliver be the fault localization at the cable-aerial circuit propose simultaneously to fault mutually with non-fault injected pulse electric current mutually, by fault relatively mutually and non-fault mutually travelling wave signal judge that earlier tie point and position of failure point go the method for precision ranging again, but the pulse emitter with and the difficult in actual applications realization of synchronism." research of the self-closing perforation circuit of railway fault distance-finding method " that Cai Yumei delivers is carried out the pinpoint method of section at the method that the fault localization problem of the self-closing perforation cable-aerial of railway circuit has proposed a kind of relatively current traveling wave line zero mold component polarity, but does not consider that the influence that lotus root is closed takes place in the trouble spot line zero mold component.Wu Chengen, " method is sought in extra-high-tension cable-overhead line hybrid line fault survey " that spirit of Tai energy and Yu Weiyong deliver utilized this characteristics structure criterion elder generation's differentiation place, trouble spot cable line or overhead transmission line of trouble spot negative sequence voltage amplitude maximum in the additional negative phase-sequence net of fault at the fault localization proposition of extra-high-tension cable-overhead line hybrid line, utilize fault zone first and last terminal voltage then, jump-value of current is extrapolated the trouble spot, but near the joint line junction during high resistant short trouble, the negative sequence voltage amplitude of being extrapolated the tie point place by the both-end electric parameters is basic identical, add the influence of fault transient process, near possible correctly failure judgement section tie point, thus the range finding failure caused." the cable-aerial wire mixed line failure travelling wave ranging new method " that Shu Hongchun and Sun Tao deliver proposes to utilize the big or small failure judgement generation section of the distributed current at the cable trough ceases to be busy tie point place that derives by system's two ends electric parameters under the additional negative sequence network after the fault at the fault localization of cable-aerial circuit, re-use the single-ended traveling wave distance measuring equipment and carry out accurate fault localization, but near the joint line junction during high resistant short trouble, the distributed current size at the cable trough ceases to be busy tie point place that is derived by the two ends electric parameters is equal substantially, add the influence of fault transient process, near tie point, have the range finding dead band, and be not suitable for symmetrical fault.

Summary of the invention

The objective of the invention is to singularity and complicacy at the cable joint line, a kind of distance-finding method that utilizes the mapping function phase propetry to realize the high voltage cable-overhead line hybrid line fault location is provided, it is characterized in that, the positive sequence electrical data at joint line system two ends after the collection fault becomes first-class long transmission line with whole joint line equivalence earlier; Derive mapping function by the positive sequence electrical data at joint line system two ends then, determine to comprise the subregions such as minimum fault of trouble spot according to the size of mapping function phase place; The last phase angle size of utilizing mapping function in subregions such as fault is once more accurately measured the fault distance of joint line, and concrete steps are as follows:

(1) three-phase voltage and the electric current phasor at the m of joint line system, n two ends after the extraction fault,

With Be respectively the three-phase voltage and the electric current phasor of m, n end after the fault, obtain the positive-sequence component of m, n end according to symmetrical component method respectively

With

(2) with the joint line equivalence be a long l of being _MnLong transmission line, the zone that then initially comprises the trouble spot is (l _Begin, l _End)=(0, l _Mn);

(3) zone that will comprise the trouble spot is (l _Begin, l _End) carry out the Num five equilibrium;

(4) electric parameters of utilizing the m of system, n end to measure is derived from joint line system two ends, draws positive sequence voltage, the forward-order current at each Along ent place in (3) determined zone;

(5) derive mapping function by (4), and obtain the phase angle of the mapping function at each Along ent place with this;

(6) size of the mapping function phase angle that is calculated by (5) judges that the Along ent and the position of trouble spot concern:

1) the mapping function phase angle is greater than zero, and the reference position is positioned at the abort situation left side;

2) the mapping function phase angle is less than zero, and the reference position is positioned at the abort situation right side

3) the mapping function phase angle equals zero, and reference position and abort situation are complementary;

Criterion finds two adjacent Along ent k and k+1 thus, and its mapping function phase angle then comprises the zone (l of trouble spot this moment respectively greater than zero and less than zero _Begin, l _End)=(l _k, l _K+1).Set branch zone threshold values Δ l such as a minimum _Set, repeat (3)～(5) until l _End-l _Begin＜Δ l _Set, then can draw the subregion (l such as minimum that comprise the trouble spot _Beginm, l _Endm);

(7) minimum of being calculated by (6) subregion that waits that comprises the trouble spot is determined abort situation:

1) determines step delta l;

2) reference position l _MkFrom l _BeginmBeginning is that step-length is incremented to l with Δ l _Endm, the phase angle of the mapping function at calculating each point place;

3) seek definite optimum reference position l _Mk, it is satisfied at l _Mk-Δ l place mapping function phase angle is greater than zero, at l _MkPlace's mapping function phase angle is less than zero;

Then abort situation f is apart from the fault distance l of m end _Mf=l _Mk-Δ l/2.

In step (5), the mapping function at any point k place is on the high voltage cable-overhead line hybrid line:

$f\left(l_{\mathrm{mk}}\right)=\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{mk}1}-{\stackrel{\&CenterDot;}{U}}_{\mathrm{nk}1}}{{\stackrel{\&CenterDot;}{I}}_{\mathrm{<figure-callout\; id="1"\; label="mk"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">mk</figure-callout>}1}+{\stackrel{\&CenterDot;}{I}}_{\mathrm{<figure-callout\; id="1"\; label="nk"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">nk</figure-callout>}1}}$

Wherein,

With

Be respectively m, n and rectify positive sequence voltage, the forward-order current at k point place on the joint line that the preface electric parameters derives.

Δ l in the step (6) _SetCan require to carry out flexibly the setting of interval size according to realistic accuracy.

Abort situation in the step (7) can be to be positioned at pole line I section, intermediate cable or to be positioned on the pole line II section, and the phase propetry of mapping function all satisfies: work as l _Mf＞l _MkThe time, the mapping function phase angle is greater than zero; Work as l _Mf＜l _MkThe time, the mapping function phase angle is less than zero; And if only if l _Mf=l _MkThe time, the phase angle of mapping function just equals zero.Wherein, l _Mf, l _MkBe respectively abort situation f on the joint line, reference position k distance to pole line I section m end.

Δ l in the step (7) can set flexibly according to actual distance accuracy and actual range finding rate request.

The present invention utilizes the mapping function phase propetry, has realized the fault precision ranging of joint line, mainly has the following advantages:

1. the joint line equivalence is positioned for first-class long transmission line, need not to differentiate in advance fault section can find range.

2. this feature of mapping function zero passage positions during with reference position on the joint line and abort situation coupling, does not have pseudo-root on the principle, has overcome the influence of transition resistance, load current, sample frequency, fault type and position of failure point.

3. required hunting zone is little, has good rapidity.

4. this inventive principle is simple and reliable, the distance accuracy height.

Use and to increase along with cable-aerial mixed line, after cable-aerial mixed line broke down, the abort situation precision ranging can be shortened the malfunction elimination time, accelerated to restore electricity, and the safety and the economical operation of electric system had very important significance.

Description of drawings

Fig. 1 is a Type B joint line syndeton of the present invention;

The positive sequence preface net figure of joint line when Fig. 2 is pole line I segment fault;

The phase propetry of mapping function on joint line when Fig. 3 is pole line I segment fault;

The positive sequence preface net figure of joint line when Fig. 4 is intermediate cable line fault;

The phase propetry of mapping function on joint line when Fig. 5 is intermediate cable line fault;

The positive sequence preface net figure of joint line when Fig. 6 is pole line II section;

The phase propetry of mapping function on joint line when Fig. 7 is pole line II segment fault;

Fig. 8 is the influence to the ABG of 25km place fault localization result on the pole line I section of load current and transition resistance;

Fig. 9 is the influence to AG fault localization result on the middle cable line of transition resistance and abort situation;

Figure 10 is the influence to AG fault localization result on the pole line II section of transition resistance and abort situation;

Figure 11 is the influence to ABCG fault localization result on the joint line of load current and abort situation.

Embodiment

The invention provides a kind of distance-finding method that utilizes the mapping function phase propetry to realize the high voltage cable-overhead line hybrid line fault location.The positive sequence electrical data at joint line system two ends after the collection fault becomes first-class long transmission line with whole joint line equivalence earlier; Derive mapping function by the positive sequence electrical data at joint line system two ends then, determine to comprise the subregions such as minimum fault of trouble spot according to the size of mapping function phase place; The last phase angle size of utilizing mapping function in subregions such as fault is once more accurately measured the fault distance of joint line.Below in conjunction with drawings and Examples the present invention is further specified.

Embodiment 1

Type B joint line type is an example as analysis and simulation object as shown in Figure 1, specifically is as a simple double ended system, and when on the circuit broke down in any point, the utilization symmetrical component method was decomposed into positive and negative, zero-sequence network with fault network; For three-phase symmetrical fault or three-phase title property fault not, all there is positive sequence network, therefore, in the present invention, utilize positive sequence voltage, forward-order current to carry out the mixed line fault range finding.

Suppose to break down on the Type B joint line, position of failure point has 3 kinds of forms: pole line I section, intermediate cable circuit, pole line II section.

One, the mapping function and the phase propetry thereof at any point place on the joint line during pole line I segment fault

The positive sequence preface net figure of joint line when Fig. 2 is pole line I segment fault.Wherein,

With

Be respectively positive sequence voltage, the forward-order current of m, n end; The c node is the tie point of pole line I section and intermediate cable circuit; The t node is the tie point of pole line II section and intermediate cable circuit.The interior k place, any point of pole line I section mapping function expression formula as the formula (1) during pole line I segment fault.

$f\left(l_{\mathrm{mk}}\right)=\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{mk}1}-{\stackrel{\&CenterDot;}{U}}_{\mathrm{nk}1}}{{\stackrel{\&CenterDot;}{I}}_{\mathrm{<figure-callout\; id="1"\; label="mk"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">mk</figure-callout>}1}+{\stackrel{\&CenterDot;}{I}}_{\mathrm{<figure-callout\; id="1"\; label="nk"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">nk</figure-callout>}1}}={\mathrm{<figure-callout\; id="1"\; label="Z\; L"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">Z</figure-callout>}}_L\tanh {\mathrm{\&gamma;}}_{L1}(l_{\mathrm{mf}}-l_{\mathrm{mk}})---\left(1\right)$

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{U}}_{\mathrm{mk}1}={\stackrel{\&CenterDot;}{U}}_{m1}\cosh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{mk}}-{\stackrel{\&CenterDot;}{I}}_{m1}{Z}_{L1}\sin {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{mk}}\\ {\stackrel{\&CenterDot;}{I}}_{\mathrm{mk}1}={\stackrel{\&CenterDot;}{I}}_{m1}\cosh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{mk}}-\frac{{\stackrel{\&CenterDot;}{U}}_{m1}}{Z_{L1}}\sinh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{mk}}\\ {\stackrel{\&CenterDot;}{U}}_{\mathrm{nt}1}={\stackrel{\&CenterDot;}{U}}_{n1}\cosh {\mathrm{\&gamma;}}_{L1}{l}_m-{\stackrel{\&CenterDot;}{I}}_{n1}{Z}_{L1}\sin {\mathrm{h\&gamma;}}_{L1}{l}_{\mathrm{tn}}\\ {\stackrel{\&CenterDot;}{I}}_{\mathrm{nt}1}={\stackrel{\&CenterDot;}{I}}_{n1}\cosh {\mathrm{\&gamma;}}_{L1}{l}_m-{\stackrel{\&CenterDot;}{U}}_{n1}\sinh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{tn}}/Z_{L1}\\ {\stackrel{\&CenterDot;}{U}}_{\mathrm{nc}1}={\stackrel{\&CenterDot;}{U}}_{\mathrm{nt}1}\cosh {\mathrm{\&gamma;}}_{c1}{l}_{\mathrm{ct}}-{\stackrel{\&CenterDot;}{I}}_{\mathrm{nt}1}{Z}_{c1}\sinh {\mathrm{\&gamma;}}_{c1}{l}_{\mathrm{ct}}\\ {\stackrel{\&CenterDot;}{I}}_{\mathrm{nc}1}={\stackrel{\&CenterDot;}{I}}_{\mathrm{nt}1}\cosh {\mathrm{\&gamma;}}_{c1}{l}_{\mathrm{ct}}-{\stackrel{\&CenterDot;}{U}}_{\mathrm{nt}1}\sinh {\mathrm{\&gamma;}}_{c1}{l}_{\mathrm{ct}}/Z_{c1}\\ {\stackrel{\&CenterDot;}{U}}_{\mathrm{nk}1}={\stackrel{\&CenterDot;}{U}}_{\mathrm{nc}1}\cosh {\mathrm{\&gamma;}}_{L1}(l_{\mathrm{mc}}-l_{\mathrm{mk}})-{\stackrel{\&CenterDot;}{I}}_{\mathrm{nc}1}{Z}_{L1}\sinh {\mathrm{\&gamma;}}_{L1}(l_{\mathrm{mc}}-l_{\mathrm{mk}})\\ {\stackrel{\&CenterDot;}{I}}_{\mathrm{nk}1}={\stackrel{\&CenterDot;}{I}}_{\mathrm{nc}1}\cosh {\mathrm{\&gamma;}}_{L1}(l_{\mathrm{mc}}-l_{\mathrm{mk}})-\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{nc}1}}{Z_{L1}}\sinh {\mathrm{\&gamma;}}_{L1}(l_{\mathrm{mc}}-l_{\mathrm{mk}})\end{array}\right.---\left(2\right)$

With

Can calculate by formula (2); Wherein,

With Be respectively m, n and rectify preface electric parameters, positive sequence voltage, the forward-order current at k point place on the pole line I section of deriving; l _Mf, l _MkBe respectively pole line I section internal fault position f, reference position k distance apart from the m end; l _CtBe the intermediate cable Route Length; l _Mc, l _NtThe length of difference pole line I section and pole line II section; Z _L1, r _L1Be respectively wave impedance, the propagation constant of pole line I section and pole line II section; Z _C1, r _C1Be respectively wave impedance, the propagation constant of intermediate cable circuit.

The mapping function that any point is located in the intermediate cable circuit during pole line I segment fault as the formula (3).

$f\left(l_{\mathrm{mk}}\right)=\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{mk}1}-{\stackrel{\&CenterDot;}{U}}_{\mathrm{nk}1}}{{\stackrel{\&CenterDot;}{I}}_{\mathrm{<figure-callout\; id="1"\; label="mk"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">mk</figure-callout>}1}+{\stackrel{\&CenterDot;}{I}}_{\mathrm{<figure-callout\; id="1"\; label="nk"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">nk</figure-callout>}1}}=-\frac{{\mathrm{<figure-callout\; id="1"\; label="Z\; c"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">Z</figure-callout>}}_c^1\sinh {\mathrm{\&gamma;}}_{c1}{l}_{\mathrm{ck}}\cosh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{fc}}+Z_{c1}{\mathrm{<figure-callout\; id="1"\; label="Z\; L"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">Z</figure-callout>}}_L\cosh {\mathrm{\&gamma;}}_{c1}{l}_{\mathrm{ck}}\sin {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{<figure-callout\; id="1"\; label="fc\; Z\; c"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">fc</figure-callout>}}}{Z_c}---\left(3\right)$

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{U}}_{\mathrm{nt}1}={\stackrel{\&CenterDot;}{U}}_{n1}\cosh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{tn}}-{\stackrel{\&CenterDot;}{I}}_{n1}{Z}_{L1}\sin {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{tn}}\\ {\stackrel{\&CenterDot;}{I}}_{\mathrm{nt}1}={\stackrel{\&CenterDot;}{I}}_{n1}\cosh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{tn}}-{\stackrel{\&CenterDot;}{U}}_{n1}\sinh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{tn}}/Z_{L1}\\ {\stackrel{\&CenterDot;}{U}}_{\mathrm{mc}1}={\stackrel{\&CenterDot;}{U}}_{m1}\cosh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{mc}}-{\stackrel{\&CenterDot;}{I}}_{m1}{Z}_{L1}\sin {\mathrm{h\&gamma;}}_{L1}{l}_{\mathrm{mc}}\\ {\stackrel{\&CenterDot;}{I}}_{\mathrm{mc}1}={\stackrel{\&CenterDot;}{I}}_{m1}\cosh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{mc}}-{\stackrel{\&CenterDot;}{U}}_{m1}\sinh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{mc}}/Z_{L1}\\ {\stackrel{\&CenterDot;}{U}}_{\mathrm{mk}1}={\stackrel{\&CenterDot;}{U}}_{\mathrm{mc}1}\cosh {\mathrm{\&gamma;}}_{c1}{(l_{\mathrm{mk}}-l_{\mathrm{mc}})}_{}-{\stackrel{\&CenterDot;}{I}}_{\mathrm{mc}1}{Z}_{c1}\sinh {\mathrm{\&gamma;}}_{c1}(l_{\mathrm{mk}}-l_{\mathrm{mc}})\\ {\stackrel{\&CenterDot;}{I}}_{\mathrm{mk}1}={\stackrel{\&CenterDot;}{I}}_{\mathrm{mc}1}\cosh {\mathrm{\&gamma;}}_{c1}(l_{\mathrm{mk}}-l_{\mathrm{mc}})-\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{mc}1}}{Z_{c1}}\sinh {\mathrm{\&gamma;}}_{c1}(l_{\mathrm{mk}}-l_{\mathrm{mc}})\\ {\stackrel{\&CenterDot;}{U}}_{\mathrm{nk}1}={\stackrel{\&CenterDot;}{U}}_{\mathrm{nc}1}\cosh {\mathrm{\&gamma;}}_{c1}(l_{\mathrm{ct}}+l_{\mathrm{mc}}-l_{\mathrm{mk}})-{\stackrel{\&CenterDot;}{I}}_{\mathrm{nt}1}{Z}_{c1}\sinh {\mathrm{\&gamma;}}_{c1}(l_{\mathrm{ct}}+l_{\mathrm{mc}}-l_{\mathrm{mk}})\\ {\stackrel{\&CenterDot;}{I}}_{\mathrm{nk}1}={\stackrel{\&CenterDot;}{I}}_{\mathrm{nt}1}\cosh {\mathrm{\&gamma;}}_{c1}({l_{\mathrm{ct}}+l}_{\mathrm{mc}}-l_{\mathrm{mk}})-\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{nt}1}}{Z_{c1}}\sinh {\mathrm{\&gamma;}}_{c1}(l_{\mathrm{ct}}+l_{\mathrm{mc}}-l_{\mathrm{mk}})\end{array}\right.---\left(4\right)$

Wherein, l _FcBe the distance of pole line I section internal fault position f apart from the c node; l _Mk, l _CkBe respectively the distance of the interior selected reference position k of intermediate cable circuit apart from m end, c node;

With

Be respectively m, n and rectify positive sequence voltage, the forward-order current at k point place on the intermediate cable circuit that the preface electric parameters derives, and calculate by formula (4).

The mapping function that any point is located in the pole line II section during pole line I segment fault as the formula (5).

$f\left(l_{\mathrm{mk}}\right)=\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{mk}1}-{\stackrel{\&CenterDot;}{U}}_{\mathrm{nk}1}}{{\stackrel{\&CenterDot;}{I}}_{\mathrm{<figure-callout\; id="1"\; label="mk"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">mk</figure-callout>}1}+{\stackrel{\&CenterDot;}{I}}_{\mathrm{<figure-callout\; id="1"\; label="nk"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">nk</figure-callout>}1}}=-\frac{f_1}{f_2}---\left(5\right)$

In the formula

${\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">f</figure-callout>}}_1=Z_{L1}{\mathrm{<figure-callout\; id="1"\; label="Z\; c"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">Z</figure-callout>}}_c^1\sinh {\mathrm{\&gamma;}}_{c1}{l}_{\mathrm{ct}}\cosh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{fc}}\cosh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{tk}}+Z_{c1}{\mathrm{<figure-callout\; id="1"\; label="Z\; L"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">Z</figure-callout>}}_L^1\cosh {\mathrm{\&gamma;}}_{c1}{l}_{\mathrm{ct}}\sin {\mathrm{\&gamma;}}_{L1}(l_{\mathrm{fc}}+l_{\mathrm{tk}})+$

${\mathrm{<figure-callout\; id="1"\; label="Z\; L"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">Z</figure-callout>}}_L^1\sinh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{fc}}\sinh {\mathrm{\&gamma;}}_{c1}{l}_{\mathrm{ct}}\sinh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{tk}}$

$f_2=Z_{L1}{\mathrm{<figure-callout\; id="1"\; label="Z\; c"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">Z</figure-callout>}}_c\cosh {\mathrm{\&gamma;}}_{c1}{l}_{\mathrm{ct}}\cosh {\mathrm{\&gamma;}}_{L1}(l_{\mathrm{fc}}+l_{\mathrm{tk}})+{\mathrm{<figure-callout\; id="1"\; label="Z\; L"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">Z</figure-callout>}}_L^1\sinh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{fc}}\sinh {\mathrm{\&gamma;}}_{c1}{l}_{\mathrm{ct}}\cosh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{tk}}+$

${\mathrm{<figure-callout\; id="1"\; label="Z\; c"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">Z</figure-callout>}}_c^1\sinh {\mathrm{\&gamma;}}_{c1}{l}_{\mathrm{ct}}\cosh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{fc}}\sinh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{tk}}$

Wherein, l _FcBe the distance of pole line I section internal fault position f apart from the c node; l _Mk, l _TkBe respectively the distance of the interior selected reference position k of pole line II section apart from m end, t node; With

Be respectively m, n and rectify positive sequence voltage, the forward-order current at k point place on the pole line II section that the preface electric parameters derives, and calculate by formula (6).

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{U}}_{\mathrm{nk}1}={\stackrel{\&CenterDot;}{U}}_{n1}\cosh {\mathrm{\&gamma;}}_{L1}(l_{\mathrm{mc}}+l_{\mathrm{ct}}+l_{\mathrm{tn}}-l_{\mathrm{mk}})-{\stackrel{\&CenterDot;}{I}}_{n1}{Z}_{L1}\sinh {\mathrm{\&gamma;}}_{L1}(l_{\mathrm{mc}}+l_{\mathrm{ct}}+l_{\mathrm{tn}}-l_{\mathrm{mk}})\\ {\stackrel{\&CenterDot;}{I}}_{\mathrm{nk}1}={\stackrel{\&CenterDot;}{I}}_{n1}\cosh {\mathrm{\&gamma;}}_{L1}(l_{\mathrm{mc}}+l_{\mathrm{ct}}+l_m-l_{\mathrm{mk}})-\frac{{\stackrel{\&CenterDot;}{U}}_{n1}}{Z_{L1}}\sinh {\mathrm{\&gamma;}}_{L1}(l_{\mathrm{mc}}+l_{\mathrm{ct}}+l_{\mathrm{tn}}-l_{\mathrm{mk}})\\ {\stackrel{\&CenterDot;}{U}}_{\mathrm{mc}1}={\stackrel{\&CenterDot;}{U}}_{m1}\cosh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{mc}}-{\stackrel{\&CenterDot;}{I}}_{m1}{Z}_{L1}\sinh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{mc}}\\ {\stackrel{\&CenterDot;}{I}}_{\mathrm{mc}1}={\stackrel{\&CenterDot;}{I}}_{m1}\cosh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{mc}}-{\stackrel{\&CenterDot;}{U}}_{m1}\sinh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{mc}}/Z_{L1}\\ {\stackrel{\&CenterDot;}{U}}_{\mathrm{mt}1}={\stackrel{\&CenterDot;}{U}}_{\mathrm{mc}1}\cosh {\mathrm{\&gamma;}}_{c1}{l}_{\mathrm{ct}}-{\stackrel{\&CenterDot;}{I}}_{\mathrm{mc}1}{Z}_{c1}\sinh {\mathrm{\&gamma;}}_{c1}{l}_{\mathrm{ct}}\\ {\stackrel{\&CenterDot;}{I}}_{\mathrm{mt}1}={\stackrel{\&CenterDot;}{I}}_{\mathrm{mc}1}\cosh {\mathrm{\&gamma;}}_{c1}{l}_{\mathrm{ct}}-\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{mc}1}}{Z_{c1}}\sinh {\mathrm{\&gamma;}}_{c1}{l}_{\mathrm{ct}}\\ {\stackrel{\&CenterDot;}{U}}_{\mathrm{mk}1}={\stackrel{\&CenterDot;}{U}}_{\mathrm{mt}1}\cosh {\mathrm{\&gamma;}}_{L1}(l_{\mathrm{mk}}-l_{\mathrm{ct}}-l_{\mathrm{mc}})-{\stackrel{\&CenterDot;}{I}}_{\mathrm{mt}1}{Z}_{L1}\sinh {\mathrm{\&gamma;}}_{L1}(l_{\mathrm{mk}}-l_{\mathrm{ct}}-l_{\mathrm{mc}})\\ {\stackrel{\&CenterDot;}{I}}_{\mathrm{mk}1}={\stackrel{\&CenterDot;}{I}}_{\mathrm{mt}1}\cosh {\mathrm{\&gamma;}}_{L1}(l_{\mathrm{mk}}-l_{\mathrm{ct}}-l_{\mathrm{mc}})-\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{mt}1}}{Z_{L1}}\sinh {\mathrm{\&gamma;}}_{L1}(l_{\mathrm{mk}}-l_{\mathrm{ct}}-l_{\mathrm{mc}})\end{array}\right.---\left(6\right)$

The mapping function phase propetry is as shown in Figure 3 on the joint line during pole line I segment fault.On joint line, when lmf＞lmk, the mapping function phase angle is greater than zero; Work as l _Mf＞l _MkThe time, the mapping function phase angle is greater than zero; Work as l _Mf＜l _MkThe time, the mapping function phase angle is less than zero; And if only if l _Mf=l _MkThe time, the phase angle of mapping function just equals zero.Wherein, l _Mf, l _MkBe respectively abort situation f on the joint line, reference position k distance to pole line I section m end.

Two, the mapping function and the phase propetry thereof at any point place on the joint line during intermediate cable line fault

The positive sequence preface net figure of joint line when Fig. 4 is intermediate cable line fault.Then place, any point mapping function expression formula is as the formula (7) in the pole line I section during intermediate cable line fault.

$f\left(l_{\mathrm{mk}}\right)=\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{mk}1}-{\stackrel{\&CenterDot;}{U}}_{\mathrm{nk}1}}{{\stackrel{\&CenterDot;}{I}}_{\mathrm{<figure-callout\; id="1"\; label="mk"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">mk</figure-callout>}1}+{\stackrel{\&CenterDot;}{I}}_{\mathrm{<figure-callout\; id="1"\; label="nk"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">nk</figure-callout>}1}}=-\frac{Z_{c1}{\mathrm{<figure-callout\; id="1"\; label="Z\; L"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">Z</figure-callout>}}_L\sinh {\mathrm{\&gamma;}}_{c1}{l}_{\mathrm{cf}}\cosh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{ck}}+{\mathrm{<figure-callout\; id="1"\; label="Z\; L"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">Z</figure-callout>}}_L^1\cosh {\mathrm{\&gamma;}}_{c1}{l}_{\mathrm{cf}}\sinh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{<figure-callout\; id="1"\; label="ck\; Z\; L"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">ck</figure-callout>}}}{Z_L}---\left(7\right)$

Wherein, With Be respectively m, n and rectify positive sequence voltage, the forward-order current at k point place on the pole line I section that the preface electric parameters derives, and calculate by formula (2); l _CfBe the distance of intermediate cable circuit internal fault position f apart from the c node; l _Mk, l _CkBe respectively the distance of the interior selected reference position k of pole line I section apart from m end, c node.

Place, the interior any point of intermediate cable circuit mapping function expression formula as the formula (8) during intermediate cable line fault.

$f\left(l_{\mathrm{mk}}\right)=\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{mk}1}-{\stackrel{\&CenterDot;}{U}}_{\mathrm{nk}1}}{{\stackrel{\&CenterDot;}{I}}_{\mathrm{<figure-callout\; id="1"\; label="mk"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">mk</figure-callout>}1}+{\stackrel{\&CenterDot;}{I}}_{\mathrm{<figure-callout\; id="1"\; label="nk"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">nk</figure-callout>}1}}={\mathrm{<figure-callout\; id="1"\; label="Z\; c"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">Z</figure-callout>}}_c\tanh {\mathrm{\&gamma;}}_{c1}(l_{\mathrm{mf}}-l_{\mathrm{mk}})---\left(8\right)$

Wherein, l _Mf, l _MkBe respectively intermediate cable circuit internal fault position f, selected reference position k distance apart from the m end;

With

Be respectively m, n and rectify positive sequence voltage, the forward-order current at k point place on the intermediate cable circuit that the preface electric parameters derives, and calculate by formula (4).

The mapping function that any point is located in the pole line II section during intermediate cable line fault as the formula (9).

$f\left(l_{\mathrm{mk}}\right)=\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{mk}1}-{\stackrel{\&CenterDot;}{U}}_{\mathrm{nk}1}}{{\stackrel{\&CenterDot;}{I}}_{\mathrm{<figure-callout\; id="1"\; label="mk"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">mk</figure-callout>}1}+{\stackrel{\&CenterDot;}{I}}_{\mathrm{<figure-callout\; id="1"\; label="nk"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">nk</figure-callout>}1}}=-\frac{Z_{c1}{\mathrm{<figure-callout\; id="1"\; label="Z\; L"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">Z</figure-callout>}}_L\sinh {\mathrm{\&gamma;}}_{c1}{l}_{\mathrm{tf}}\cosh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{tk}}+{\mathrm{<figure-callout\; id="1"\; label="Z\; L"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">Z</figure-callout>}}_L^1\cosh {\mathrm{\&gamma;}}_{c1}{l}_{\mathrm{tf}}\sinh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{<figure-callout\; id="1"\; label="tk\; Z\; L"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">tk</figure-callout>}}}{Z_L}---\left(9\right)$

Wherein, l _TfBe the distance of intermediate cable circuit internal fault position f apart from the t node; l _Mk, l _TkBe respectively the distance of the interior selected reference position k of pole line II section apart from m end, t node;

With Be respectively m, n and rectify positive sequence voltage, the forward-order current at k point place on the pole line II section that the preface electric parameters derives, and calculate by formula (6).

The mapping function phase propetry is as shown in Figure 5 on the joint line during intermediate cable line fault.On joint line, work as l _Mf＞l _MkThe time, the mapping function phase angle is greater than zero; Work as l _Mf＜l _MkThe time, the mapping function phase angle is less than zero; Work as l _Mf=l _MkThe time, the phase angle of mapping function just equals zero.Wherein, l _Mf, l _MkBe respectively abort situation f on the joint line, reference position k distance to pole line I section m end.

Three, the mapping function and the phase propetry thereof at joint line any point place during pole line II segment fault

The positive sequence preface net figure of joint line when Fig. 6 is pole line II section.Then place, any point mapping function expression formula is as the formula (10) in the pole line I section during pole line II segment fault.

$f\left(l_{\mathrm{mk}}\right)=\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{mk}1}-{\stackrel{\&CenterDot;}{U}}_{\mathrm{nk}1}}{{\stackrel{\&CenterDot;}{I}}_{\mathrm{<figure-callout\; id="1"\; label="mk"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">mk</figure-callout>}1}+{\stackrel{\&CenterDot;}{I}}_{\mathrm{<figure-callout\; id="1"\; label="nk"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">nk</figure-callout>}1}}=\frac{f_3}{f_4}---\left(10\right)$

$f_3=Z_{L1}{\mathrm{<figure-callout\; id="1"\; label="Z\; c"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">Z</figure-callout>}}_c^1\sinh {\mathrm{\&gamma;}}_{c1}{l}_{\mathrm{ct}}\cosh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{tf}}\cosh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{ck}}+Z_{c1}{\mathrm{<figure-callout\; id="1"\; label="Z\; L"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">Z</figure-callout>}}_L^1\cosh {\mathrm{\&gamma;}}_{c1}{l}_{\mathrm{ct}}\sin {\mathrm{\&gamma;}}_{L1}(l_{\mathrm{tf}}+l_{\mathrm{ck}})$

$+{\mathrm{<figure-callout\; id="1"\; label="Z\; L"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">Z</figure-callout>}}_L^1\sinh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{tf}}\sinh {\mathrm{\&gamma;}}_{c1}{l}_{\mathrm{ct}}\sinh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{ck}}$

$f_4=Z_{L1}{\mathrm{<figure-callout\; id="1"\; label="Z\; c"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">Z</figure-callout>}}_c\cosh {\mathrm{\&gamma;}}_{c1}{l}_{\mathrm{ct}}\cosh {\mathrm{\&gamma;}}_{L1}(l_{\mathrm{tf}}+l_{\mathrm{ck}})+{\mathrm{<figure-callout\; id="1"\; label="Z\; L"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">Z</figure-callout>}}_L^1\sinh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{tf}}\sinh {\mathrm{\&gamma;}}_{c1}{l}_{\mathrm{ct}}\cosh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{ck}}+$

${\mathrm{<figure-callout\; id="1"\; label="Z\; c"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">Z</figure-callout>}}_c^1\sinh {\mathrm{\&gamma;}}_{c1}{l}_{\mathrm{ct}}\cosh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{tf}}\sinh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{ck}}$

Wherein, l _TfBe the distance of pole line II section internal fault position f apart from the t node; l _Mk, l _CkBe respectively the distance of the interior selected reference position k of pole line I section apart from m end, c node;

With

Be respectively m, n and rectify positive sequence voltage, the forward-order current at k point place on the pole line I section that the preface electric parameters derives, and calculate by formula (2);

Place, the interior any point of intermediate cable circuit mapping function expression formula as the formula (11) during pole line II segment fault.

$f\left(l_{\mathrm{mk}}\right)=\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{mk}1}-{\stackrel{\&CenterDot;}{U}}_{\mathrm{nk}1}}{{\stackrel{\&CenterDot;}{I}}_{\mathrm{<figure-callout\; id="1"\; label="mk"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">mk</figure-callout>}1}+{\stackrel{\&CenterDot;}{I}}_{\mathrm{<figure-callout\; id="1"\; label="nk"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">nk</figure-callout>}1}}=-\frac{{\mathrm{<figure-callout\; id="1"\; label="Z\; c"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">Z</figure-callout>}}_c^1\sinh {\mathrm{\&gamma;}}_{c1}{l}_{\mathrm{tk}}\cosh {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{tf}}+Z_{c1}{\mathrm{<figure-callout\; id="1"\; label="Z\; L"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">Z</figure-callout>}}_L\cosh {\mathrm{\&gamma;}}_{c1}{l}_{\mathrm{tf}}\sin {\mathrm{\&gamma;}}_{L1}{l}_{\mathrm{<figure-callout\; id="1"\; label="tk\; Z\; c"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">tk</figure-callout>}}}{Z_c}---\left(11\right)$

Wherein, l _Mk, l _TkBe the distance of selected reference position k in the intermediate cable circuit apart from m end, t node; l _TfBe the distance of pole line II section internal fault position f apart from the t node;

With

Be respectively m, n and rectify positive sequence voltage, the forward-order current at k point place on the intermediate cable circuit that the preface electric parameters derives, and calculate by formula (4).

The mapping function that any point is located in the pole line II section during pole line II segment fault as the formula (12).

$f\left(l_{\mathrm{mk}}\right)=\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{mk}1}-{\stackrel{\&CenterDot;}{U}}_{\mathrm{nk}1}}{{\stackrel{\&CenterDot;}{I}}_{\mathrm{<figure-callout\; id="1"\; label="mk"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">mk</figure-callout>}1}+{\stackrel{\&CenterDot;}{I}}_{\mathrm{<figure-callout\; id="1"\; label="nk"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">nk</figure-callout>}1}}={\mathrm{<figure-callout\; id="1"\; label="Z\; L"\; filenames="HSA00000168437700014.png,HSA00000168437700022.png"\; state="\{\{state\}\}">Z</figure-callout>}}_L\tanh {\mathrm{\&gamma;}}_{L1}(l_{\mathrm{mf}}-l_{\mathrm{mk}})---\left(12\right)$

Wherein, l _Mf, l _MkBe respectively pole line II section internal fault position f, selected reference position k distance apart from the m end;

With Be respectively m, n and rectify positive sequence voltage, the forward-order current at k point place on the pole line II section that the preface electric parameters derives, and calculate by formula (6).

The mapping function phase propetry is as shown in Figure 7 on the joint line during pole line II segment fault.On joint line, work as l _Mf＞l _MkThe time, the mapping function phase angle is greater than zero; Work as l _Mf＜l _MkThe time, the mapping function phase angle is less than zero; And if only if l _Mf=l _MkThe time, the phase angle of mapping function just equals zero.Wherein, lx, l _MkBe respectively abort situation f on the joint line, reference position k distance to pole line I section m end.

Four, algorithm concrete steps

In sum, no matter abort situation is to be positioned at pole line I section or intermediate cable, still is positioned on the pole line II section, and the phase propetry of mapping function all satisfies: work as l _Mf＞l _MkThe time, the mapping function phase angle is greater than zero; Work as l _Mf＜l _MkThe time, the mapping function phase angle is less than zero; Work as l _Mf=l _MkThe time, the phase angle of mapping function equals zero.Mapping function phase angle this feature that equals zero is carried out fault localization when therefore, utilizing on the joint line reference position and abort situation coupling.Concrete location algorithm step is as follows:

(1) three-phase voltage and the electric current phasor of joint line system two ends (m, n end) after the extraction fault,

With

Be respectively the three-phase voltage and the electric current phasor of m, n end after the fault.Obtain the positive-sequence component of m, n end respectively according to symmetrical component method

With

(2) with the joint line equivalence be one and longly be the long transmission line of lx, the zone that then initially comprises the trouble spot is (l _Begin, l _End)=(0, lx);

(3) zone that will comprise the trouble spot is (l _Begin, l _End) carry out the n five equilibrium;

(4) electric parameters of utilizing the m of system, n end to measure is derived from two ends, draws positive sequence voltage, the forward-order current at each Along ent place in (3) determined zone;

(5) derive mapping function by (4), and obtain the phase angle of the mapping function at each Along ent place with this;

(6) size of the mapping function phase angle that is calculated by (5) judges that the Along ent and the position of trouble spot concern:

1) the mapping function phase angle is greater than zero, and the reference position is positioned at the abort situation left side;

2) the mapping function phase angle is less than zero, and the reference position is positioned at the abort situation right side;

3) the mapping function phase angle equals zero, when reference position and abort situation coupling;

Criterion finds two adjacent Along ent k and k+1 thus, and its mapping function phase angle then comprises the zone (l of trouble spot this moment respectively greater than zero and less than zero _Begin, l _End)=(l _k, l _K+1).Set branch zone threshold values Δ l such as a minimum _Set, repeat (3)～(5) until l _End-l _Begin＜Δ l _Set, then can draw the subregion (l such as minimum that comprise the trouble spot _Beginm, l _Endm);

(7) minimum of being calculated by (6) subregion that waits that comprises the trouble spot is determined abort situation:

4) determine step delta l;

5) reference position l _MkFrom l _BeginmBeginning is that step-length is incremented to l with Δ l _Endm, the phase angle of the mapping function at calculating each point place;

6) seek definite optimum reference position l _Mk, it is satisfied at l _Mk-Δ l place mapping function phase angle is greater than zero, at l _MkPlace's mapping function phase angle is less than zero; Then abort situation f is apart from the fault distance l of m end _Mf=l _Mk-Δ l/2.

Hunting zone of the present invention is

(wherein,

Expression is big and immediate integer than χ, l=l _Mc+ l _Ct+ l _Nt), get enough little and Num when rationally getting higher value for improving distance accuracy Δ l,

Very little.

Table 1: sample frequency and abort situation are to AG fault localization result's influence

Five, result of calculation and analysis

Utilize the PSCAD simulation software to build the cable mixture model, different faults point and sample frequency to A mutually metallic earthing fault localization result to influence situation as shown in table 1.

The result shows that under the different sample frequency, this algorithm all can accurately be found range, and the range finding that the present invention is directed to joint line has overcome the influence that abort situation is subjected to sample frequency.

The A result that finds range when high resistance earthing fault is as shown in table 2 near the joint line tie point.

Near table 2: the range finding result of the present invention during high resistive fault joint line tie point

The result shows, during 0.5km place high resistance earthing fault, maximal phase is no more than-1.191% to range error near tie point.Therefore, the present invention does not have the range finding dead band, the range accuracy height.

Load current and transition resistance are to the situation that influences of the AB of 25km place two-phase short-circuit fault range finding result on the pole line I section as shown in Figure 8.Wherein, transition resistance is got 0～60 Ω, and m side system power supply phase angle is got-90 °～90 °, the result shows that range error has very high distance accuracy between-0.4%～0.4% relatively, therefore, the range finding that the present invention is directed to joint line has overcome the influence of load current and transition resistance.

Transition resistance and abort situation to A on the middle cable line mutually the earth fault distance measurement result the situation that influences as shown in Figure 9.Wherein, transition resistance is got 0～60 Ω, and abort situation is got 70～100km, the result shows that range error has very high distance accuracy between-0.6%～1.18% relatively, therefore, the range finding that the present invention is directed to joint line has overcome the influence of transition resistance and abort situation.

Transition resistance and abort situation to A on the pole line II section mutually the earth fault distance measurement result the situation that influences as shown in figure 10.Wherein, transition resistance is got 0～300 Ω, and abort situation is got 100～170km, the result shows that range error has very high distance accuracy between-0.5%～1.3% relatively, therefore, the range finding that the present invention is directed to joint line has overcome the influence of transition resistance and abort situation.

Load current and abort situation are to the situation that influences of ABCG fault localization result on the joint line as shown in figure 11.Wherein, m side system power supply phase angle is got-90 °～90 °, abort situation is got 0～170km, the result shows, the relative range error of the present invention is between-0.3%～0.72%, have very high distance accuracy, therefore, the range finding that the present invention is directed to joint line has overcome the influence of load current and abort situation.To sum up the result shows, this method has very high accuracy and validity at the range finding of joint line.

The above; only for the preferable embodiment of the present invention, but protection scope of the present invention is not limited thereto, and anyly is familiar with those skilled in the art in the technical scope that the present invention discloses; the variation that can expect easily or replacement all should be encompassed within protection scope of the present invention.

Claims (2)

1. one kind is utilized the mapping function phase propetry to realize the distance-finding method that high voltage cable-overhead line hybrid line fault is located, it is characterized in that, the positive sequence electrical data at joint line system two ends after the collection fault becomes first-class long transmission line with whole joint line equivalence earlier; Derive mapping function by the positive sequence electrical data at joint line system two ends then, determine to comprise the subregions such as minimum fault of trouble spot according to the size of mapping function phase place; The last phase angle size of utilizing mapping function in subregions such as fault is once more accurately measured the fault distance of joint line.

2. the distance-finding method that utilizes the mapping function phase propetry to realize the high voltage cable-overhead line hybrid line fault location according to claim 1 is characterized in that concrete steps are as follows:

(1) three-phase voltage and the electric current phasor at the m of joint line system, n two ends after the extraction fault,

With

Be respectively the three-phase voltage and the electric current phasor of m, n end after the fault, obtain the positive-sequence component of m, n end according to symmetrical component method respectively

With

(2) with the joint line equivalence be a long l of being _MnLong transmission line, the zone that initially comprises the trouble spot is (l _Begin, l _End)=(0, l _Mn);

(3) zone that will comprise the trouble spot is (l _Begin, l _End) carry out the Num five equilibrium;

(4) electric parameters of utilizing the m of system, n end to measure is derived from joint line system two ends, draws positive sequence voltage, the forward-order current at each Along ent place in (3) determined zone;

(5) derive mapping function by (4), and obtain the phase angle of the mapping function at each Along ent place with this;

(6) size of the mapping function phase angle that is calculated by (5) judges that the Along ent and the position of trouble spot concern:

1) the mapping function phase angle is greater than zero, and the reference position is positioned at the abort situation left side;

2) the mapping function phase angle is less than zero, and the reference position is positioned at the abort situation right side;

3) the mapping function phase angle equals zero, and reference position and abort situation are complementary;

Criterion finds two adjacent Along ent k and k+1 thus, and its mapping function phase angle then comprises the zone (l of trouble spot this moment respectively greater than zero and less than zero _Begin, l _End)=(l _k, l _K+1), set branch zone threshold values Δ l such as a minimum _Set, repeat (3)～(5) until l _End-l _Begin＜Δ l _Set, then can draw the subregion (l such as minimum that comprise the trouble spot _Beginm, l _Endm);

(7) minimum of being calculated by (6) subregion that waits that comprises the trouble spot is determined abort situation:

1) determines step delta l;

2) reference position l _MkFrom l _BeginmBeginning is that step-length is incremented to l with Δ l _Endm, the phase angle of the mapping function at calculating each point place;

3) seek definite optimum reference position l _Mk, it is satisfied at l _Mk-Δ l place mapping function phase angle is greater than zero, at l _MkPlace's mapping function phase angle is less than zero;

Then abort situation f is apart from the fault distance l of m end _Mf=l _Mk-Δ l/2;

In step (5), the mapping function at any point k place is on the high voltage cable-overhead line hybrid line:

$f\left(l_{\mathrm{mk}}\right)=\frac{{\stackrel{\&CenterDot;}{U}}_{\mathrm{mk}1}-{\stackrel{\&CenterDot;}{U}}_{\mathrm{nk}1}}{{\stackrel{\&CenterDot;}{I}}_{\mathrm{mk}1}+{\stackrel{\&CenterDot;}{I}}_{\mathrm{nk}1}}$

Wherein,

With

Be respectively m, n and rectify positive sequence voltage, the forward-order current at k point place on the joint line that the preface electric parameters derives;

Δ l in the step (6) _SetRequire to carry out flexibly the setting of interval size according to realistic accuracy;

Abort situation in the step (7) can be to be positioned at pole line I section, intermediate cable or to be positioned on the pole line II section, and the phase propetry of mapping function all satisfies: work as l _Mf＞l _MkThe time, the mapping function phase angle is greater than zero; Work as l _Mf＜l _MkThe time, the mapping function phase angle is less than zero; Work as l _Mf=l _MkThe time, the phase angle of mapping function just equals zero; Wherein, l _Mf, l _MkBe respectively abort situation f on the joint line, reference position k distance to pole line I section m end;

Δ l in the step (7) sets flexibly according to actual distance accuracy and actual range finding rate request.

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