CN103792465B - A kind of method of the range finding of the one-phase earthing failure in electric distribution network based on residual voltage - Google Patents

Abstract

A method for one-phase earthing failure in electric distribution network range finding based on residual voltage, belongs to the method that distribution net work earthing fault is found range. This fault distance-finding method is from single-ended radial medium voltage distribution network entirety Zero sequence parameter, while analyzing singlephase earth fault, consider the impact of distributed parameter model, stable state residual voltage value and each feeder line zero-sequence current after measurement bus place and each outlet end fault, find out fault feeder and non-fault feeder residual voltage Variation Features. The present invention is by utilizing a large amount of existing equipment, low to data sampling requirement of real-time, easily realizes; The simulation model analysis of setting up through pressing actual parameter, can realize fault localization, and precision is very high at isolated neutral or neutral by arc extinction coil grounding system. Localization method of the present invention can be applicable in low and medium voltage distribution network.

Description

A kind of method of the range finding of the one-phase earthing failure in electric distribution network based on residual voltage

Technical field:

The present invention relates to a kind of method, particularly a kind of power distribution network based on residual voltage of distribution net work earthing fault range findingThe method of single-phase ground fault distance measuring.

Background technology:

Power distribution network safe operation provides important guarantee to social production life, is difficult to once there is significant trouble economic lossEstimate. Therefore, the fault of quick and precisely finding range, economy, safety and reliability to power system are extremely important. In power distribution networkSinglephase earth fault probability of happening maximum.

Along with the development of distribution network automated technology, on feeder line, install to have and measure and the novel distribution of communication function is openedClose, can obtain a large amount of circuit information about power, then use electrician's network graph theory principle to set up adjacency matrix and the joint of nodeDot information matrix, and then draw fault judgment matrix and to its elementary analysis, can judge fault section. The knowledge of fault sectionCan not realize quick excision fault, but can not realize accurately fault localization, cannot meet follow-up work requirement. For faultRange finding mainly contains two kinds of methods: traveling wave method and impedance method. Wherein traveling wave method has good accuracy, and impedance method has goodStability, the advantage of comprehensive two kinds of methods, and utilize the phase relation of measurement point negative-sequence current and trouble point negative sequence voltage to enterRow range finding. But distribution line complex structure, branch are numerous, circuit distance is short, be difficult to solve identification and the mixed line of fault wave headThe problem that road wave impedance changes. Need many cover row ripple checkout equipments, financial cost is higher simultaneously. Therefore traveling wave method is difficult to be applicable to joinElectrical network. If employing impedance method, not only can overcome a range finding difficult problem for traveling wave method, and can utilize a large amount of existing putting into operation to establishStandby, hardware investment is little, easily realizes. For both-end impedance method, can adopt phase compensation method to eliminate the asynchronous zero sequence collectingError between electric current, voltage is to carry out fault distance calculating. But the impedance method in the past adopting adopts lumped parameter mould mostlyType calculates, and owing to not considering the impact of distribution capacity, error calculated is larger. Based on the fault localization of distributed parameter modelMethod, ignores the drawback that distribution capacity affects while having overcome based on lumped parameter model, can improve range accuracy. Part calculating sideMethod adopts fixing route parameter calculation, the larger error of same existence. China's medium voltage distribution network mostly is single-ended radial electrical network, manySinglephase earth fault occurs, and failure line selection and fault section determine that research aspect has obtained great successes and obtained wellApplication, the fault location difficulty that how to realize medium voltage distribution network is larger. When singlephase earth fault, transient state energy is little, row ripple letterNumber measure difficulty; And traditional ranging technology based on impedance method is used for high-voltage fence, neutral grounding mode and mesolowHow power distribution network difference, consider and consider cannot directly apply to medium voltage distribution network by uniline more from positive order parameter when research.

Summary of the invention

The object of the invention is to provide a kind of method of the range finding of the one-phase earthing failure in electric distribution network based on residual voltage, separateCertainly distribution network line complex structure, branch is numerous, the short feature of circuit distance is brought large the asking of single-phase ground fault distance measuring errorTopic.

The object of the present invention is achieved like this: this fault distance-finding method is from single-ended radial medium voltage distribution network entirety zeroOrder parameter sets out, and considers the impact of distributed parameter model while analyzing singlephase earth fault, measures bus place and the event of each outlet endAfter barrier, stable state residual voltage value and each feeder line zero-sequence current, find out fault feeder and non-fault feeder residual voltage Variation Features.

Concrete steps are as follows:

(1), distributed parameter transmission line model

Power distribution network is carried out to fault localization, utilize distributed parameter model to carry out fault localization; By line parameter circuit value is carried outCalculate, when singlephase earth fault occurs, conduction current is much smaller than capacitance current, therefore can ignore the impact that electricity is led over the ground, zero over the groundOrder equivalent circuit distributed parameter model is reduced to line impedance and direct-to-ground capacitance is evenly distributed along the line;

(2), non-fault line analysis

Feeder line is divided into n minizone, gets wherein arbitrary minizone and be denoted as [x, x+ Δ x], this minizone instituteProduce to earth-current Δ I_C＝I_C.Δx，I_CFor the line mutual-ground capacitor electric current of unit length;

For non-fault line, the electric current Δ I that each minizone produces_CThe scope flowing through on the line by bus to communityBetween the position x at place, then flow to trouble point through ground; If original position corresponding to every minizone is x, the function of current producesVoltage is respectively Δ I_C.X.x the voltage that, each interval function of current over the ground producing produces on circuit: Δ U=ΔI_C.X.x, in formula: X is the resistance value of circuit unit length;

Known according to superposition theorem, the residual voltage at circuit two ends is poor is the result of zero-sequence current effect, above formula both sides withIn time, obtains x integration: ${\∫}_0^{l}d\stackrel{.}{U}={\∫}_0^l\stackrel{.}{I_C}\·X\·x\·\mathrm{dx},$ Calculate: ${\stackrel{.}{U}}_2-\stackrel{.}{U_1}=\frac{1}{2}{I}_C\·X\·l^2\left(1\right),$ L is non-fault line length, Non-fault line first and end residual voltage respectively;

(3), isolated neutral system faulty line is analyzed

For faulty line, trouble point current flowing comprises non-fault capacitive earth current and faulty line direct-to-ground capacitanceElectric current; Voltage, current distributions behind trouble point are identical with non-fault line, and minizone capacitive earth current is flowed to by electric capacityThe earth, then flow back to circuit by trouble point, to the circuit before trouble point without effect, be equivalent to circuit, direct-to-ground capacitance, and faultBetween point, form loop checking installation; Minizone capacitive earth current flows to the earth by direct-to-ground capacitance, then passes through line through trouble pointBus is flowed back on road; Therefore minizone over the ground the function of current produce the scope of voltage be by minizone to trouble point, minizone is to motherLine segment electric current one goes out one and enters to cancel out each other; If fault distance is x, the function of current over the ground producing apart from the minizone of bus x 'Voltage variety Δ the U '=Δ I producing on circuit_C.X. (x-x '); The same, can obtain bus to trouble point line-to-ground electric currentAct on the voltage variety that circuit produces: ${\∫}_0^{x}d\stackrel{.}{U^{\′}}={\∫}_0^x-\stackrel{.}{I_C}\·X\·(x-x^{\′})\·{\mathrm{dx}}^{\′},$ ? $\stackrel{.}{U^{\′}}=-\frac{1}{2}{\stackrel{.}{I}}_C\·X\·x^2;$ Trouble pointAlso comprise non-fault line to earth-current to bus section, busbar section zero-sequence current andIn this interval voltage change producing: $\stackrel{.}{U^{\′\′}}=\stackrel{.}{I_{C_{\mathrm{\Σ}}}}\·X\·x;$ Known according to superposition theorem: $\stackrel{.}{U^{\′}}+\stackrel{.}{U^{\′\′}}=-(\frac{1}{2}{\stackrel{.}{I}}_C\·x-{\stackrel{.}{I}}_{C_{\mathrm{\Σ}}})X\·x={\stackrel{.}{U}}_f-{\stackrel{.}{U}}_1^{\′}$ (2); Trouble point circuitVoltage change is identical with non-fault line situation, therefore, $\frac{1}{2}{\stackrel{.}{I}}_C\·X\·{(l^{\′}-x)}^2={\stackrel{.}{U}}_2^{\′}-{\stackrel{.}{U}}_f$ (3); Wherein: l ' is faulty lineTotal length,Corresponding faulty line first and end residual voltage and fault point voltage respectively; (2), (3) formula is added: ${\stackrel{.}{U}}_2^{\′}-{\stackrel{.}{U}}_1^{\′}=\frac{1}{2}{\stackrel{.}{I}}_C\·X\·(l^{\′2}-{2l}^{\′}\·x)+{\stackrel{.}{I}}_{C_{\mathrm{\Σ}}}\·X\·x---\left(4\right);$

(4), neutral point is analyzed through arc suppression coil faulty line

The non-fault line zero-sequence current of neutral by arc extinction coil grounding system and residual voltage situation of change are with neutralPoint isolated neutral system is identical; And faulty line zero-sequence current situation is equivalent on isolated neutral system faulty line basisFlow through the inductance current of arc suppression coil in trouble point stackAs system works in full compensating coefficient is, trouble point is idle electricityStream is zero, if ignore system watt current, the zero-sequence current recording from fault branch head end is produced by this branch road selfRaw capacitance current, application residual voltage changes and cannot find range; But for avoiding resonance to occur, generally move when arc suppression coil operationAt overcompensation state, also in the time there is single-phase earthing, the zero-sequence current character of fault branch is similar to non-fault branch, due toThe capacitance current that self distributed constant does not produce on year-on-year basis of overcompensation situation is larger, andLarge I adjusted by arc suppression coilGain of parameter when humorous; Residual voltage acts on after the current hysteresis that arc suppression coil produces 90 °, and the leading zero sequence of capacitive earth current90 ° of voltages, thereforeWithSingle spin-echo.The voltage variety producing in fault section:Finally, drawFormula corresponding to compensated distribution network: ${\stackrel{.}{U}}_2^{\′}-{\stackrel{.}{U}}_1^{\′}=\frac{1}{2}{\stackrel{.}{I}}_C\·X\·(l^{\′2}-{2l}^{\′}\·x)+({\stackrel{\·}{I}}_{C_{\mathrm{\Σ}}}-{\stackrel{.}{I}}_L)\·X\·x---\left(5\right).$

Beneficial effect, has adopted such scheme, can utilize a large amount of existing equipment that puts into operation, and realizes simply, has strongerEconomy and preferably practical value; Employing distributed parameter model calculates, overcome in power distribution network tradition Fault Locating Method byIn using lumped parameter model to cause the problem that error is larger; The method is not only applicable to isolated neutral system, is also suitable forIn neutral by arc extinction coil grounding system, and only need obtain each branch road zero-sequence current and branch road end after singlephase earth faultThe tuning situation of residual voltage steady-state value and arc suppression coil can accurately be found range on the basis of correctly selecting fault feeder.

Brief description of the drawings

Fig. 1 zero sequence equivalent circuit distributed parameter model.

Fig. 2 non-fault line zero-sequence current distribution map.

Fig. 3 isolated neutral system faulty line zero-sequence current forms feature.

Fig. 4 neutral point arc suppression coil earthing system faulty line zero-sequence current forms feature.

The method flow diagram of the one-phase earthing failure in electric distribution network range finding of Fig. 5 based on residual voltage.

Fig. 6 PSCAD simulation model.

Detailed description of the invention:

Embodiment 1: this fault distance-finding method is from single-ended radial medium voltage distribution network entirety Zero sequence parameter, analysis listWhen phase earth fault, consider the impact of distributed parameter model, stable state residual voltage value after measurement bus place and each outlet end faultAnd each feeder line zero-sequence current, find out fault feeder and non-fault feeder residual voltage Variation Features.

Concrete steps are as follows:

1, distributed parameter transmission line model

Utilize distributed parameter model to carry out fault localization to power distribution network; By line parameter circuit value is calculated, single-phase earthingWhen fault occurs, conduction current is much smaller than capacitance current over the ground, therefore can ignore the impact that electricity is led over the ground, zero sequence equivalent circuit distributesParameter model is reduced to line impedance and direct-to-ground capacitance is evenly distributed along the line;

2, non-fault line analysis

Feeder line is divided into n minizone, gets wherein arbitrary minizone and be denoted as [x, x+ Δ x], this minizone instituteProduce to earth-current Δ I_C＝I_C.Δx，I_CFor the line mutual-ground capacitor electric current of unit length;

For non-fault line, the electric current Δ I that each minizone produces_CThe scope flowing through on the line by bus to communityBetween the position x at place, then flow to trouble point through ground; If original position corresponding to every minizone is x, the function of current producesVoltage is respectively Δ I_C.X.x the voltage that, each interval function of current over the ground producing produces on circuit: Δ U=ΔI_C.X.x, in formula: X is the resistance value of circuit unit length;

Known according to superposition theorem, the residual voltage at circuit two ends is poor is the result of zero-sequence current effect, above formula both sides withIn time, obtains x integration: ${\∫}_0^{l}d\stackrel{.}{U}={\∫}_0^l\stackrel{.}{I_C}\·X\·x\·\mathrm{dx},$ Calculate: ${\stackrel{.}{U}}_2-\stackrel{.}{U_1}=\frac{1}{2}{I}_C\·X\·l^2\left(1\right),$ L is non-fault line length, Non-fault line first and end residual voltage respectively;

3, isolated neutral system faulty line is analyzed

For faulty line, trouble point current flowing comprises non-fault capacitive earth current and faulty line direct-to-ground capacitanceElectric current; Voltage, current distributions behind trouble point are identical with non-fault line, and minizone capacitive earth current is flowed to by electric capacityThe earth, then flow back to circuit by trouble point, to the circuit before trouble point without effect, be equivalent to circuit, direct-to-ground capacitance, and faultBetween point, form loop checking installation; Minizone capacitive earth current flows to the earth by direct-to-ground capacitance, then passes through line through trouble pointBus is flowed back on road; Therefore minizone over the ground the function of current produce the scope of voltage be by minizone to trouble point, minizone is to motherLine segment electric current one goes out one and enters to cancel out each other; If fault distance is x, the function of current over the ground producing apart from the minizone of bus x 'Voltage variety Δ the U '=Δ I producing on circuit_C.X. (x-x '); The same, can obtain bus to trouble point line-to-ground electric currentAct on the voltage variety that circuit produces: ${\∫}_0^{x}d\stackrel{.}{U^{\′}}={\∫}_0^x-\stackrel{.}{I_C}\·X\·(x-x^{\′})\·{\mathrm{dx}}^{\′},$ ? $\stackrel{.}{U^{\′}}=-\frac{1}{2}{\stackrel{.}{I}}_C\·X\·x^2;$ Trouble pointAlso comprise non-fault line to earth-current to bus section, busbar section zero-sequence current andVoltage variety in this interval generation: $\stackrel{.}{U^{\′\′}}=\stackrel{.}{I_{C_{\mathrm{\Σ}}}}\·X\·x;$ Known according to superposition theorem: $\stackrel{.}{U^{\′}}+\stackrel{.}{U^{\′\′}}=-(\frac{1}{2}{\stackrel{.}{I}}_C\·x-{\stackrel{.}{I}}_{C_{\mathrm{\Σ}}})X\·x={\stackrel{.}{U}}_f-{\stackrel{.}{U}}_1^{\′}$ (2); Trouble point circuitVoltage change is identical with non-fault line situation, therefore,(3); Wherein: l ' is faulty lineTotal length,Corresponding faulty line first and end residual voltage and fault point voltage respectively; (2), (3) formula is added: ${\stackrel{.}{U}}_2^{\′}-{\stackrel{.}{U}}_1^{\′}=\frac{1}{2}{\stackrel{.}{I}}_C\·X\·(l^{\′2}-{2l}^{\′}\·x)+{\stackrel{.}{I}}_{C_{\mathrm{\Σ}}}\·X\·x---\left(4\right);$

4, neutral point is analyzed through arc suppression coil faulty line

The non-fault line zero-sequence current of neutral by arc extinction coil grounding system and residual voltage situation of change are with neutralPoint isolated neutral system is identical; And faulty line zero-sequence current situation is equivalent on isolated neutral system faulty line basisFlow through the inductance current of arc suppression coil in trouble point stackAs system works in full compensating coefficient is, trouble point is idle electricityStream is zero, if ignore system watt current, the zero-sequence current recording from fault branch head end is produced by this branch road selfRaw capacitance current, application residual voltage changes and cannot find range; But for avoiding resonance to occur, generally move when arc suppression coil operationAt overcompensation state, also in the time there is single-phase earthing, the zero-sequence current character of fault branch is similar to non-fault branch, due toThe capacitance current that self distributed constant does not produce on year-on-year basis of overcompensation situation is larger, andLarge I adjusted by arc suppression coilGain of parameter when humorous; Residual voltage acts on after the current hysteresis that arc suppression coil produces 90 °, and the leading zero sequence of capacitive earth current90 ° of voltages, thereforeWithSingle spin-echo.The voltage variety producing in fault section:Finally,Go out the formula corresponding to compensated distribution network: ${\stackrel{.}{U}}_2^{\′}-{\stackrel{.}{U}}_1^{\′}=\frac{1}{2}{\stackrel{.}{I}}_C\·X\·(l^{\′2}-{2l}^{\′}\·x)+({\stackrel{\·}{I}}_{C_{\mathrm{\Σ}}}-{\stackrel{.}{I}}_L)\·X\·x---\left(5\right).$

As shown in Figure 5, specific implementation step is as follows for this method specific implementation flow chart:

From wave recording device, reading flow is crossed arc suppression coil electric current (for neutral by arc extinction coil grounding system), bus electricityHead end zero-sequence current and end residual voltage Wave data after pressure, each feeder fault;

The data that read are carried out to Fast Fourier Transform (FFT) (FFT), obtain the effective value that each signal is corresponding, adoptPower frequency component calculate can harmonic carcellation etc. the error that produces of signal;

On the basis completing in route selection, determine fault branch;

By recording the data substitution formula (1) that non-fault line is corresponding, online calculate fault moment circuit unit lengthZero sequence impedance value X;

Judge system neutral earthing mode;

For isolated neutral system, the circuit unit head that the data that faulty line is recorded and step 4 calculateDegree zero sequence impedance value X substitution formula (4) calculates fault distance; For neutral by arc extinction coil grounding system, substitution formula(5) calculate.

(1) electric current and voltage distribution characteristics after fault

After fault, feeder line capacitive earth current distributes along the line, and first all capacitive earth currents flow to the earth, through trouble pointFlow back to faulty line, finally flow to bus, the circulation of earth-current has been produced to effect to the variation of residual voltage, non-fault lineThe rule that residual voltage virtual value along the line is increased by oblique line to line end gradually by bus distributes, and faulty line residual voltage hasThe rule that effect value is increased by oblique line to bus section gradually by trouble point distributes, trouble point to line end by increasing gradually by oblique lineLong rule distributes, i.e. trouble point place residual voltage virtual value minimum.

(2) Fault Location Algorithm

After fault occurs and malfunction stable after, from wave recording device, read after busbar voltage, each feeder fault firstEnd zero-sequence current and end residual voltage Wave data also need to flow through extinguishing arc line for neutral by arc extinction coil grounding systemThe Wave data of loop current, carries out Fast Fourier Transform (FFT) (FFT) to the data that read, and obtaining the power frequency that each signal is corresponding hasEffect value, adopt power frequency component calculates can harmonic carcellation etc. the error that produces of signal, also basis has been utilizations in, to walk result of calculationThere is ripe variant projects of location to determine faulty line, will record the data substitution formula that non-fault line is correspondingOnline calculate fault moment circuit unit length zero sequence impedance value X, for isolated neutral systemThe circuit unit length zero sequence impedance value X substitution formula that the data that faulty line is recorded and upper step calculateCalculate fault distance, for neutral by arc extinction coil grounding system, substitutionFormula ${\stackrel{.}{U}}_2^{\′}-{\stackrel{.}{U}}_1^{\′}=\frac{1}{2}{\stackrel{.}{I}}_C\·X\·(l^{\′2}-{2l}^{\′}\·x)+{\stackrel{.}{I}}_{C_{\mathrm{\Σ}}}\·X\·x$ Calculate.

The effect assessment of scheme:

The present invention has very high position precision and possesses very high adaptability at Complicated Distribution Network, for different neutralityPoint earthing mode, the present invention all can meet. Now taking a model as example:

Utilize PSCAD/EMTDC Software tool to set up the simulation model of the single-ended radial network system of 35kV, as Fig. 6 instituteShow. Circuit Fault on Secondary Transformer connects arc suppression coil through breaker, can centering point earth-free and compensated distribution network emulation; SystemSystem has three cables, and cable length is got respectively 18km, 16km and 20km, and cable adopts three single-phase cables that are embedded in underground 1m to beDel is placed the system of laying of (axle center spacing is 30mm), and cross-section of cable area is got 240mm2; Bus bar side adopts Y-Δ to connectThe 110kV of method becomes 35kV transformer, and line end adopts the 35kV of Δ-Y connection to become the transformer of 10kV; Load meets 0.35MW+The three-phase balancing load of 0.08MVar.

With isolated neutral system, be that example is calculated there is metallic earthing apart from bus 2km place. Busbar voltageFor 20469.2V, each feeder line head end zero-sequence current is 7.33167A, 6.51593A, 13.8476A, each feeder terminal residual voltage20493.9V, 20488.7V, 20483.4V. Utilize existing variant projects of location, for example ratio phase comparing method can be judged faulty lineCircuit III.

Utilize circuit I unit of account length circuit capacitive earth current I_CAnd unit length zero sequence impedance value X:

$I_C=I_{C1}/l_1=0.407315A/\mathrm{km}.X=\frac{2(U_2-U_1)}{I_C\·l_1}=0.374327\mathrm{\Ω}/\mathrm{km}.$

For isolated neutral system, non-fault line capacitive earth current and equal that faulty line head end measuresZero-sequence current is: $I_{C3}=I_{C1}+I_{C2}=I_{C_{\mathrm{\Σ}}}=13.8476A.$

Above each result of calculation substitution formula (4) is obtained to fault distance x=1.9791km.

Definition measure error is:Error is 0.104%.

For the validity of checking this method, table 1 has provided isolated neutral system singlephase earth fault and has betided differencePosition, range finding result in the time of different transition resistance ground connection.

Table 1 isolated neutral single-phase ground fault distance measuring result

The range finding result of table 1 shows, for isolated neutral system, in different abort situation, transition resistance, maximumRange error all total track length 1% in, in circuit length range, this fault distance-finding method can both be realized accurate surveyDistance.

Table 2 has provided neutral by arc extinction coil grounding system, and when fault, the total capacitive earth current of system is a 64A left sideThe right side, arc suppression coil is operated under overcompensation state, and now de-humorous degree be-4% during with-2% left and right, and singlephase earth fault occurs inDiverse location, range finding result in the time of different transition resistance ground connection.

Table 2 neutral by arc extinction coil grounding single-phase ground fault distance measuring result

This algorithm is equally applicable to neutral by arc extinction coil grounding system as can be seen from Table 2, and for differentDe-humorous degree all has higher ranging accuracy.

Claims (1)

1. a method for the range finding of the one-phase earthing failure in electric distribution network based on residual voltage, is characterized in that: this fault distance-finding methodBe from single-ended radial medium voltage distribution network entirety Zero sequence parameter, while analyzing singlephase earth fault, consider distributed parameter modelImpact, stable state residual voltage value and each feeder line zero-sequence current after measurement bus place and each outlet end fault, find out fault feederAnd non-fault feeder residual voltage Variation Features;

Concrete steps are as follows:

(1), distributed parameter model

Power distribution network is carried out to fault localization, utilize distributed parameter model to carry out fault localization; By line parameter circuit value is calculated,When singlephase earth fault occurs, conduction current is much smaller than capacitance current, therefore can ignore the impact that electricity is led over the ground, zero sequence equivalent over the groundCircuit distributed parameter model is reduced to line impedance and direct-to-ground capacitance is evenly distributed along the line;

(2), non-fault line analysis

Feeder line is divided into n minizone, gets wherein arbitrary minizone and be denoted as [x, x+ Δ x], this minizone producesTo earth-current Δ I_C＝I_C·Δx，I_CFor the line mutual-ground capacitor electric current of unit length;

For non-fault line, the electric current Δ I that each minizone produces_CThe scope flowing through on the line by bus to minizone institutePosition x, then flow to trouble point through ground; If original position corresponding to every minizone is x, the voltage that function of current producesAmount is Δ I_CXx, the voltage that each interval function of current over the ground producing produces on circuit: Δ U=Δ I_CXx, formulaIn: X is the resistance value of circuit unit length;

Known according to superposition theorem, the residual voltage at circuit two ends is poor is the result of zero-sequence current effect, and above formula both sides are simultaneously to xIntegration obtains: ${\∫}_0^{l}d\stackrel{\·}{U}={\∫}_0^l{\stackrel{\·}{I}}_C\·X\·x\·dx,$ Calculate: ${\stackrel{\·}{U}}_2-{\stackrel{\·}{U}}_1=\frac{1}{2}{I}_C\·X\·l^2---\left(1\right),$ L is non-fault line length,Be respectively non-fault line first and end residual voltage;

(3), isolated neutral system faulty line is analyzed

For faulty line, trouble point current flowing comprises non-fault capacitive earth current and faulty line direct-to-ground capacitance electricityStream; Voltage, current distributions behind trouble point are identical with non-fault line, and minizone capacitive earth current is flowed to large by electric capacityGround, then flows back to circuit by trouble point, to the circuit before trouble point without effect, be equivalent to circuit, direct-to-ground capacitance, and trouble pointBetween form loop checking installation; Minizone capacitive earth current flows to the earth by direct-to-ground capacitance, then passes through circuit through trouble pointFlow back to bus; Therefore minizone over the ground the function of current produce the scope of voltage be by minizone to trouble point, bus is arrived in minizoneSection electric current one goes out one and enters to cancel out each other; If fault distance is x, the function of current over the ground producing apart from the minizone of bus x ' inThe voltage variety Δ U '=Δ I producing on circuit_CX (x-x '); The same, can obtain bus to trouble point line-to-ground electric currentAct on the voltage variety that circuit produces: ${\∫}_0^{x}d{\stackrel{\·}{U}}^{\′}={\∫}_0^x-{\stackrel{\·}{I}}_C\·X\·(x-x^{\′})\·{\mathrm{dx}}^{\′},$ ? ${\stackrel{\·}{U}}^{\′}=-\frac{1}{2}{\stackrel{\·}{I}}_C\·X\·x^2;$ Trouble pointAlso comprise non-fault line to earth-current to bus section, busbar section zero-sequence current and Voltage variety in this interval generation: ${\stackrel{\·}{U}}^{\′\′}={\stackrel{\·}{I}}_{C_{\mathrm{\Σ}}}\·X\·x;$ Known according to superposition theorem: ${\stackrel{\·}{U}}^{\′}+{\stackrel{\·}{U}}^{\′\′}=-(\frac{1}{2}{\stackrel{\·}{I}}_C\·x-{\stackrel{\·}{I}}_{C_{\mathrm{\Σ}}})X\·x={\stackrel{\·}{U}}_f-{\stackrel{\·}{U}}_1^{\′}---\left(2\right);$ Fault dotted lineThe voltage change on road is identical with non-fault line situation, therefore,Wherein: l ' is faultTotal line length,Corresponding faulty line first and end residual voltage and fault point voltage respectively; (2), (3) formula phaseAdd: ${\stackrel{\·}{U}}_2^{\′}-{\stackrel{\·}{U}}_1^{\′}=\frac{1}{2}{\stackrel{\·}{I}}_C\·X\·(l^{\′2}-2l^{\′}\·x)+{\stackrel{\·}{I}}_{C_{\mathrm{\Σ}}}\·X\·x---\left(4\right);$

(4), neutral point is analyzed through arc suppression coil faulty line

The non-fault line zero-sequence current of neutral by arc extinction coil grounding system and residual voltage situation of change and neutral point are notEarthed system is identical; And faulty line zero-sequence current situation is equivalent on isolated neutral system faulty line basis in eventThe inductance current of arc suppression coil is flow through in the stack of barrier pointIf system works is when the full compensating coefficient, trouble point reactive current isZero, if ignore system watt current, the zero-sequence current recording from fault branch head end is to be produced by this branch road selfCapacitance current, application residual voltage changes and cannot find range; But for avoiding resonance to occur, generally operated in when arc suppression coil operationCompensating coefficient, also in the time there is single-phase earthing, the zero-sequence current character of fault branch is similar to non-fault branch, mends owing to crossingThe capacitance current that self distributed constant does not produce on year-on-year basis of repaying situation is larger, andLarge I when tuning by arc suppression coilGain of parameter; Residual voltage acts on after the current hysteresis that arc suppression coil produces 90 °, and the leading residual voltage of capacitive earth current90 °, thereforeWithSingle spin-echo;The voltage variety producing in fault section:Finally, draw rightShould be in the formula of compensated distribution network: ${\stackrel{\·}{U}}_2^{\′}-{\stackrel{\·}{U}}_1^{\′}=\frac{1}{2}{\stackrel{\·}{I}}_C\·X\·(l^{\′2}-2l^{\′}\·x)+({\stackrel{\·}{I}}_{C_{\mathrm{\Σ}}}-{\stackrel{\·}{I}}_L)\·X\·x$ $\left(5\right).$