CN1523366A - Accurate trouble-locating method for electricity transmission lines with SC - Google Patents

Abstract

The invention is a serial-compensated transmission line failure pinpointing method, building a differential equation of transmission line failure according to component characteristic and Kirchhoff's laws, adopting multiple-end voltage and current signal as failure positioning information, and using GPS accurate time system to insure data synchronism, and it can be applied to wide range and pinpoint the transmission line failure.

Description

A kind of accurate Fault Locating Method of the transmission line of electricity of mending with string

Technical field

The present invention relates to a kind of transmission line malfunction accurate positioning method that adopts the band serial compensation capacitance of multiterminal signal, belong to the transmission facility technical field.

Background technology

The transmission line malfunction location is the important measures that guarantee the power grid security economical operation, is that of field of power studies difficult point and focus, and the existing fault localization method divides from principle at present, mainly contains traveling wave method and fault analysis method.

Localization of fault module on the fault wave recording device of Electric Industrial Equipment Co., Ltd.'s production both at home and abroad is to adopt one-sided electric current, voltage signal mostly at present, the mathematical model of using is to describe the algebraic equation of steady-state process, on principle, there is defective, can't eliminate the influence of transition resistance and peer-to-peer system increasing-aid current, the transient state process behavior of electric parameters in the time of can't the accurate description fault, therefore there is the deficiency on the principle in existing fault analyzing and positioning method, is subjected to influence of various factors, and positioning error is bigger.

Along with the continuous rising of transmission line capability and transmission distance, the transmission line of electricity of being with string to mend now is more and more, therefore is necessary the Precision Orientation Algorithm when studying the transmission line of electricity of being with serial compensation capacitance breaks down.

Summary of the invention

Purpose of the present invention is exactly for addressing the above problem, and a kind of accurate Fault Locating Method of the transmission line of electricity of mending with string is provided, and this method is applied widely, can accurately locate the fault that takes place on the transmission line of electricity.

Technical scheme provided by the invention is: a kind of accurate Fault Locating Method of the transmission line of electricity of mending with string, it is characterized in that setting up the differential equation behind the transmission line malfunction by element characteristic and Kirchhoff's law, adopt the information of the voltage and current signal of multiterminal as localization of fault, utilize the accurate time dissemination system of GPS to guarantee the synchronism of data, the fault that takes place on the transmission line of electricity is accurately located.

Aforesaid localization method is characterized in that may further comprise the steps:

(1) utilize GPS to realize voltage, the current signal synchronized sampling of transmission line of electricity multiterminal;

(2) electric parameters before and after record and the exchange trouble is to obtain the localization of fault desired data;

(3) localization of fault is to obtain accuracy position of fault point:

1) failure judgement is separate:

2) accurate localization of fault;

At first, current and voltage quantities and parameter are carried out phase-model transformation; According to pairing fault type, select the line modulus mutually relevant for use with fault; According to Kirchhoff's second law, adopt the multiterminal electric parameters row of this line modulus to write the loop equation, try to achieve the trouble spot;

Concrete performing step is as follows:

(1) row write out differential equation and the starting condition of describing fault front and back process;

(2) current and voltage quantities and parameter are carried out phase-model transformation;

(3), select the line modulus mutually relevant for use with fault according to pairing fault type;

(4a) the supposition fault occurs between a certain side (be designated as the M side, opposite side is designated as the N side) and serial compensation capacitance of transmission line of electricity, positions calculating;

A) utilize the electric current of the serial compensation capacitance of flowing through to calculate the voltage of electric capacity both sides;

B) according to Kirchhoff's second law, adopt the multiterminal electric parameters row of this line modulus to write the loop equation, try to achieve the trouble spot;

When single-phase earthing, line to line fault ground connection, phase fault or three-phase shortcircuit take place on the transmission line of electricity when

Ranging formula is: $p=\frac{u_{\mathrm{mn}}^s+R^s{i}_n^s+L^s\frac{{\mathrm{di}}_n^s}{\mathrm{dt}}+u_{\mathrm{cn}}^s}{R^s{i}_m^s+L^s\frac{{\mathrm{di}}_m^s}{\mathrm{dt}}+R^s{i}_n^s+L^s\frac{{\mathrm{di}}_n^s}{\mathrm{dt}}}$

(4b) the supposition fault occurs between the opposite side (N side) and serial compensation capacitance of transmission line of electricity, positions calculating;

When single-phase earthing, line to line fault ground connection, phase fault or three-phase shortcircuit take place on the transmission line of electricity when

Ranging formula is: $p=\frac{u_{\mathrm{mn}}^s+R^s{i}_n^s+L^s\frac{{\mathrm{di}}_n^s}{\mathrm{dt}}-u_{\mathrm{cn}}^s}{R^s{i}_m^s+L^s\frac{{\mathrm{di}}_m^s}{\mathrm{dt}}+R^s{i}_n^s+L^s\frac{{\mathrm{di}}_n^s}{\mathrm{dt}}}$

In (4a), (4b):

P is the trouble spot apart from the number percent of the distance of transmission line of electricity one side the line is busy road total length;

i _m ^s, i _n ^s(s=α β) is respectively the electric current of s line modulus both sides;

R ^s, L ^s(s=α β) is respectively the resistance and the inductance of s line modulus correspondence;

u _Mn ^s(s=α β) is the voltage difference of s line modulus both sides;

u _Cm ^s(s=α β) is the voltage of s line modulus electric capacity both sides;

(5) utilize the line capacitance current compensation to revise positioning result;

(6) obtain positioning result after, these results are handled with probabilistic method and least square method;

(7) utilize calculate from the circuit both sides the size of difference of fault point voltage differentiate the true and false of root.

Aforesaid localization method is characterized in that the later ranging formula of discretize is:

$p_1\left(k\right)=\frac{u_m^s\left(k\right)+R^s{i}_m^s\left(k\right)+L^s\frac{i_n^s\left(k\right)-i_n^s(k-1)}{\mathrm{\ΔT}}+u_{\mathrm{cn}}^s\left(k\right)}{R^s{i}_m^s\left(k\right)+L^s\frac{i_m^s\left(k\right)-i_m^s(k-1)}{\mathrm{\ΔT}}+R^s{i}_n^s\left(k\right)+L^s\frac{i_n^s\left(k\right)-i_n^s(k-1)}{\mathrm{\ΔT}}}$

$p_2\left(k\right)=\frac{u_{\mathrm{mn}}^s\left(k\right)+R^s{i}_n^s\left(k\right)+L^s\frac{i_n^s\left(k\right)-i_n^s(k-1)}{\mathrm{\ΔT}}-u_{\mathrm{cm}}^s\left(k\right)}{R^s{i}_m^s\left(k\right)+L^s\frac{i_m^s\left(k\right)-i_m^s(k-1)}{\mathrm{\ΔT}}+R^s{i}_n^s\left(k\right)+L^s\frac{i_n^s\left(k\right)-i_n^s(k-1)}{\mathrm{\ΔT}}}$

Wherein:

P (k) is for being tried to achieve the trouble spot apart from the distance of transmission line of electricity one side the line is busy road total length number percent by k-1 and k sampled value;

i _m ^s(k), i _n ^s(k) (s=α β) is respectively the electric current of k sampled point s line modulus both sides;

i _m ^s(k-1), i _n ^s(k-1) (s=α β) is respectively the electric current of k-1 sampled point s line modulus both sides;

R ^s, L ^s(s=α β) is respectively the resistance and the inductance of s line modulus correspondence;

u _Mn ^s(k) (s=α β) is the voltage difference of k sampled point s line modulus both sides;

u _Cn ^s(k) (s=α β) is the voltage of k sampled point s line modulus electric capacity both sides;

Δ T is the sampling period.

This method is set up the differential equation behind the transmission line malfunction by element characteristic and Kirchhoff's law, adopt the information of the voltage and current signal of multiterminal as localization of fault, utilize the accurate time dissemination system of GPS to guarantee the synchronism of data, applied widely, can accurately locate the fault that takes place on the transmission line of electricity, general error is less than 1%.

Concrete embodiment

Implementation step:

One, data acquisition is to obtain the voltage and current signal at detected circuit two ends

1) voltage of transmission line of electricity secondary side, current signal are transformed into the low level that can gather and measure through superpotential, current transducer (TV, TA transmitter), collect the digital signal that computing machine can be handled through digital to analog conversion (A/D or V/F conversion) and sampling card;

2) the GPS OEM plate of this device can be in the pulse per second (PPS) of transmission line of electricity multiterminal output error less than 50ns, every 1 second the high precision crystal oscillator of many sides of transmission line of electricity fault locator is proofreaied and correct once, the pulse signal forward position and the GPS that guarantee crystal oscillator output are synchronous, with control data acquisition separately, realize the synchronized sampling of transmission line of electricity multiterminal, and the electric parameters of being gathered is stamped markers be temporarily stored in the internal memory;

3) electric current, the voltage digital signal that collects according to the sampling card judges whether circuit breaks down, if the circuit non-fault then repeats above process; If break down, the electric parameters that then writes down and preserve the fault front and back arrives hard disk to obtain the localization of fault desired data; The available criterion that has proposed takes place in failure judgement; The criterion whether fault used in the present invention takes place is: the overcurrent starting: utilize current phasor measurement value and phase current setting valve relatively; Negative-sequence current starting: negative-sequence current calculated value and negative-sequence current setting valve relatively, as if the phase current calculated value greater than phase current setting valve or negative-sequence current calculated value greater than the negative-sequence current setting valve, then think and break down;

Two, the electric parameters before and after record and the preservation fault is to obtain the localization of fault desired data

1) line failure then begins to preserve data fault record ripple, and voltage, the current data of circuit in the certain hour before and after the retention fault are stamped markers and are kept in the data file of hard disk recorded data;

2) data are preserved the data that preserve each side transformer station clearing house, back;

Three, separate judgement of fault type and location Calculation:

1) failure judgement zone and separate

The separate criterion of the separate available more existing faults of failure judgement, the separate criterion of the applied fault of the present invention is: locating device is installed in the two ends of circuit, and makes the reference direction of both sides electric current flow to circuit by bus.If the electric current of both sides is zero after by the reference direction addition, show that then circuit normally moves (when circuit normally moves, the electric current of both sides by should be zero after the reference direction addition); If the electric current of both sides is not equal to zero after by the reference direction addition, then show line-internal break down (electric current that both sides record when the line-internal fault is all for flowing to circuit by bus, must be not equal to their results after by the reference direction addition zero).Regard three-phase as three and single-phasely can obtain the result to each processing of carrying out mutually as above respectively: if A phase ground connection, then B is non-fault phase with C mutually mutually, the corresponding respectively addition of the three-phase current of both sides must be that the A phase current is non-vanishing, and B is zero with C electric current mutually mutually; If A is the fault phase with B mutually mutually, after handling with quadrat method, it is non-vanishing to obtain A phase and B phase current, and the electric current of C phase is zero; The three-phase fault conclusion is that the electric current of three-phase is all non-vanishing.

2) accurate localization of fault

At first, row write out the differential equation of describing circuit transient state, and current and voltage quantities and parameter are carried out phase-model transformation; According to pairing fault type, select the line modulus mutually relevant for use with fault; Write the differential equation of outlet modulus,, adopt the both-end electric parameters row of this line modulus to write the loop equation, can try to achieve the trouble spot according to Kirchhoff's second law.

I: earlier the current and voltage quantities and the parameter of circuit are carried out phase-model transformation

Owing to have the coupling of mutual inductance, mutual resistance and mutual capacitance between the loop of three phase line, therefore, before to the three phase line analysis, can carry out decoupling zero earlier.Three-phase or multiphase coupled equation are transformed to a plurality of independent equations find the solution, the phase-model transformation matrix of voltage, electric current is designated as T respectively _u, T _iThe two equates for even transposition circuit, satisfies relational expression for the circuit that do not replace

T _u ^-1＝T _i ^T

V _m＝T _u ^-1V，?I _m＝T _i ^-1I

Through phase-model transformation, modulus resistor matrix R _m=T _u ^-1RT _i=T _i ^TRT _iBe diagonal matrix, in like manner modulus inductance matrix L _m, capacitance matrix C _mBe diagonal matrix, that is to say that the voltage of each pattern, electric current only interrelate by resistance, inductance or the electric capacity of corresponding modes, and irrelevant with the amount of other pattern.This shows that above-mentioned phase-model transformation has been eliminated alternate coupling really, do not have coupling between the modulus that decomposites.

A) choose the Karenbauer conversion as the phase-model transformation matrix

$\left[\begin{array}{c}{i}_0\\ i_{\mathrm{\α}}\\ i_{\mathrm{\β}}\end{array}\right]=\frac{1}{3}\left[\begin{array}{ccc}1& 1& 1\\ 1& -1& 0\\ 1& 0& -1\end{array}\right]\left[\begin{array}{c}{i}_a\\ i_b\\ i_c\end{array}\right]$

This current transformation is A, B, and three phasor currents of C are converted to 0, α, three modulus electric currents of β, the voltage transformation equation is similar.

The resistance and the inductance matrix of phasor are respectively

Then the resistance of modulus and inductance matrix are

R in the formula ₀=R _s+ 2R _m, R _α=R _β=R _s-R _m, L ₀=L _s+ 2L _m, L _α=L _β=L _s-L _m

II: calculate the trouble spot

(1) the supposition fault occurs between a certain side (be designated as the M side, opposite side is designated as the N side) and serial compensation capacitance of transmission line of electricity, positions calculating;

A) utilize the electric current of the serial compensation capacitance of flowing through to calculate the voltage of electric capacity both sides

The computing formula of capacitance voltage is: $u_{\mathrm{cn}}^s\left(t\right)=\frac{1}{C}{\∫}_0^t{i}_n^s\mathrm{dt}+u_{\mathrm{cn}}^s\left(0\right)$

In the application of reality, the later computing formula of discretize is:

$u_{\mathrm{cn}}^s\left(k\right)=\frac{\mathrm{\ΔT}}{C}[\frac{1}{2}{i}_n^s\left(0\right)+\underset{i=1}{\overset{k-1}{\mathrm{\Σ}}}{i}_n^s\left(i\right)+\frac{1}{2}{i}_n^s\left(k\right)]+i_{\mathrm{cn}}^s\left(0\right)$

u _Cn ^sThe voltage of electric capacity both sides when (0) being 0 moment, can utilize following formula to calculate:

$u_{\mathrm{cn}}^s\left(0\right)=u_{\mathrm{mn}}^s\left(0\right)-R^s{i}_n^s\left(0\right)-L^s\frac{i_n^s\left(0\right)-i_n^s(-1)}{2\mathrm{\ΔT}}$

Promptly the serve as reasons computing formula of k sampling instant capacitance voltage after voltage, the current sampling data in a certain initial moment (counting 0 constantly) calculates before the fault of setting of last two formulas.

Wherein:

C is the capacitance of serial compensation capacitance;

R ^s, L ^s(s=α β) is respectively the resistance and the inductance of s line modulus correspondence;

Δ T is the sampling period.

i _n ^s(s=α β) is the electric current of s line modulus N side;

u _Cn ^s(s=α β) is the voltage of s line modulus electric capacity both sides;

i _n ^s(k) (s=α β) is respectively the electric current of k sampled point s line modulus N side;

u _Cn ^s(k) (s=α β) is respectively the voltage of k sampled point s line modulus electric capacity both sides;

i _n ^s(0), i _n ^s(1) (s=α β) is respectively 0 constantly, 0 the electric current of sampled point s line modulus N side in a moment after constantly;

u _Cn ^s(0) (s=α β) is the voltage of the sampled point s line modulus electric capacity both sides in 0 moment;

u _Mn ^s(0) (s=α β) is the voltage difference of the sampled point s line modulus both sides in 0 moment.

B) according to Kirchhoff's second law, adopt the multiterminal electric parameters row of this line modulus to write the loop equation, try to achieve the trouble spot when single-phase earthing, line to line fault ground connection, phase fault or three-phase shortcircuit take place on the transmission line of electricity

Ranging formula is: $p_1=\frac{u_{\mathrm{mn}}^s+R^s{i}_n^s+L^s\frac{{\mathrm{di}}_n^s}{\mathrm{dt}}+u_{\mathrm{cn}}^s}{R^s{i}_m^s+L^s\frac{{\mathrm{di}}_m^s}{\mathrm{dt}}+R^s{i}_n^s+L^s\frac{{\mathrm{di}}_n^s}{\mathrm{dt}}}$

Wherein:

p ₁Be the number percent of trouble spot apart from the distance of transmission line of electricity one side the line is busy road total length;

i _m ^s, i _n ^s(s=α β) is respectively the electric current of s line modulus both sides;

R ^s, L ^s(s=α β) is respectively the resistance and the inductance of s line modulus correspondence;

u _Mn ^s(s=α β) is the voltage difference of s line modulus both sides.

u _Cn ^s(s=α β) is the voltage of s line modulus electric capacity both sides.

In the application of reality, the later ranging formula of discretize is:

$p_1\left(k\right)=\frac{u_{\mathrm{mn}}^s\left(k\right)+R^s{i}_n^s\left(k\right)+L^s\frac{i_n^s\left(k\right)-i_n^s(k-1)}{\mathrm{\ΔT}}+u_{\mathrm{cn}}^s\left(k\right)}{R^s{i}_m^s\left(k\right)+L^s\frac{i_m^s\left(k\right)-i_m^s(k-1)}{\mathrm{\ΔT}}+R^s{i}_n^s\left(k\right)+L^s\frac{i_n^s\left(k\right)-i_n^s(k-1)}{\mathrm{\ΔT}}}$

Wherein:

p ₁(k) for try to achieve the number percent of trouble spot by k-1 and k sampled value apart from the distance of transmission line of electricity one side the line is busy road total length;

i _m ^s(k), i _n ^s(k) (s=α β) is respectively the electric current of k sampled point s line modulus both sides;

i _m ^s(k-1), i _n ^s(k-1) (s=α β) is respectively the electric current of k-1 sampled point s line modulus both sides;

R ^s, L ^s(s=α β) is respectively the resistance and the inductance of s line modulus correspondence;

u _Mn ^s(k) (s=α β) is the voltage difference of k sampled point s line modulus both sides;

u _Cn ^s(k) (s=α β) is the voltage of k sampled point s line modulus electric capacity both sides;

Δ T is the sampling period.

(2) the supposition fault occurs between the opposite side (N side) and serial compensation capacitance of transmission line of electricity, positions calculating

A) utilize the electric current of the serial compensation capacitance of flowing through to calculate the voltage of electric capacity both sides

The computing formula of capacitance voltage is: $u_{\mathrm{cm}}^s\left(t\right)=\frac{1}{C}{\∫}_0^t{i}_n^s\mathrm{dt}+u_{\mathrm{cm}}^s\left(0\right)$

In the application of reality, the later computing formula of discretize is:

$u_{\mathrm{cm}}^s\left(k\right)=\frac{\mathrm{\ΔT}}{C}[\frac{1}{2}{i}_m^s\left(0\right)+\underset{i=1}{\overset{k-1}{\mathrm{\Σ}}}{i}_m^s\left(i\right)+\frac{1}{2}{i}_m^s\left(k\right)]+i_{\mathrm{cm}}^s\left(0\right)$

u _Cm ^sThe voltage of electric capacity both sides when (0) being 0 moment, can utilize following formula to calculate:

$u_{\mathrm{cm}}^s\left(0\right)=u_{\mathrm{mn}}^s\left(0\right)-R^s{i}_m^s\left(0\right)-L^s\frac{i_n^s\left(0\right)-i_m^s(-1)}{2\mathrm{\ΔT}}$

Promptly the serve as reasons computing formula of k sampling instant capacitance voltage after voltage, the current sampling data in a certain initial moment (counting 0 constantly) calculates before the fault of setting of last two formulas.Wherein:

C is the capacitance of serial compensation capacitance;

R ^s, L ^s(s=α β) is respectively the resistance and the inductance of s line modulus correspondence;

Δ T is the sampling period.

i _m ^s(s=α β) is the electric current of s line modulus M side;

u _Cm ^s(s=α β) is the voltage of s line modulus electric capacity both sides;

i _m ^s(k) (s=α β) is respectively the electric current of k sampled point s line modulus M side;

u _Cm ^s(k) (s=α β) is respectively the voltage of k sampled point s line modulus electric capacity both sides;

i _m ^s(0), i _m ^s(1) (s=α β) is respectively 0 constantly, 0 the electric current of sampled point s line modulus M side in a moment after constantly;

u _Cm ^s(0) (s=α β) is the voltage of the sampled point s line modulus electric capacity both sides in 0 moment;

u _Mn ^s(0) (s=α β) is the voltage difference of the sampled point s line modulus both sides in 0 moment.

B) according to Kirchhoff's second law, adopt the multiterminal electric parameters row of this line modulus to write the loop equation, try to achieve the trouble spot when single-phase earthing, line to line fault ground connection, phase fault or three-phase shortcircuit take place on the transmission line of electricity

Ranging formula is: $p_2=\frac{u_{\mathrm{mn}}^s+R^s{i}_n^s+L^s\frac{{\mathrm{di}}_n^s}{\mathrm{dt}}-u_{\mathrm{cm}}^s}{R^s{i}_m^s+L^s\frac{{\mathrm{di}}_m^s}{\mathrm{dt}}+R^s{i}_n^s+L^s\frac{{\mathrm{di}}_n^s}{\mathrm{dt}}}$

Wherein:

P is the trouble spot apart from the number percent of the distance of transmission line of electricity one side the line is busy road total length;

i _m ^s, i _n ^s(s=α β) is respectively the electric current of s line modulus both sides;

R ^s, L ^s(s=α β) is respectively the resistance and the inductance of s line modulus correspondence;

u _Mn ^s(s=α β) is the voltage difference of s line modulus both sides.

u _Cm ^s(s=α β) is the voltage of s line modulus electric capacity both sides.

In the application of reality, the later ranging formula of discretize is:

$p_2\left(k\right)=\frac{u_{\mathrm{mn}}^s\left(k\right)+R^s{i}_n^s\left(k\right)+L^s\frac{i_n^s\left(k\right)-i_n^s(k-1)}{\mathrm{\ΔT}}-u_{\mathrm{cm}}^s\left(k\right)}{R^s{i}_m^s\left(k\right)+L^s\frac{i_m^s\left(k\right)-i_m^s(k-1)}{\mathrm{\ΔT}}+R^s{i}_n^s\left(k\right)+L^s\frac{i_n^s\left(k\right)-i_n^s(k-1)}{\mathrm{\ΔT}}}$

Wherein:

p ₂(k) for try to achieve the number percent of trouble spot by k-1 and k sampled value apart from the distance of transmission line of electricity one side the line is busy road total length;

i _m ^s(k), i _n ^s(k) (s=α β) is respectively the electric current of k sampled point s line modulus both sides;

i _m ^s(k-1), i _n ^s(k-1) (s=α β) is respectively the electric current of k-1 sampled point s line modulus both sides;

R ^s, L ^s(s=α β) is respectively the resistance and the inductance of s line modulus correspondence;

u _Mn ^s(k) (s=α β) is the voltage difference of k sampled point s line modulus both sides;

u _Cm ^s(k) (s=α β) is the voltage of k sampled point s line modulus electric capacity both sides;

Δ T is the sampling period.

(3) utilize the line capacitance current compensation to revise positioning result;

For taking into account capacitance current, positioning result is revised than long transmission line.Modification method is as follows:

If i _Cm ^sAnd i _Cn ^sBe respectively the electric capacity charging s mould electric current of both sides, trouble spot, i _m ^sAnd i _n ^sBe respectively the electric current that the both sides power supply injects circuit, i _Xm ^sAnd i _Xn ^sBe respectively the correcting current that injects circuit behind the consideration capacitance current, promptly

$i_{\mathrm{Xm}}^s=i_m^s-i_{\mathrm{Cm}}^s$

$i_{\mathrm{Xn}}^s=i_n^s-i_{\mathrm{Cn}}^s$

Line current in the above-mentioned ranging formula is replaced with correcting current.Because the shunting of the electric capacity of both sides is relevant with position of failure point, at first calculates a primary fault position with ranging formula, distributes the electric capacity number percent of both sides then according to this primary fault point.

The primary fault point that design is calculated is respectively p apart from the number percent of two lateral extents ₀And 1-p ₀, because the also identical proportional distribution of electric capacity of both sides, so the capacitance current of both sides is respectively:

$i_{\mathrm{Cm}}^s=p_0\frac{C_1}{2}\frac{{\mathrm{du}}_m^s}{\mathrm{dt}}------i_{\mathrm{Cn}}^s=(1-p_0)\frac{C_1}{2}\frac{{\mathrm{du}}_n^s}{\mathrm{dt}}$

The correcting current of both sides is respectively:

$i_{\mathrm{Xm}}^s=i_m^s-i_{\mathrm{Cm}}^s-----i_{\mathrm{Xn}}^s=i_n^s-i_{\mathrm{Cn}}^s$

With the line current in correcting current alternative (1), (2) ranging formula.Can obtain revised ranging formula:

$p_1=\frac{u_{\mathrm{mn}}^s+R^s[i_n^s-(1-p_1)\frac{C_1}{2}\frac{{\mathrm{du}}_n^s}{\mathrm{dt}}]+L^s\frac{d[i_n^s-(1-p_1)\frac{C_1}{2}\frac{{\mathrm{du}}_n^s}{\mathrm{dt}}]}{\mathrm{dt}}+u_{\mathrm{cn}}^s}{R^s(i_m^s-p_1\frac{C_1}{2}\frac{{\mathrm{du}}_s^m}{\mathrm{dt}})+L^s\frac{d(i_m^s-p_1\frac{C_1}{2}\frac{{\mathrm{du}}_m^s}{\mathrm{dt}})}{\mathrm{dt}}+R^s{[i}_n^s-(1-p_1)\frac{C_1}{2}\frac{{\mathrm{du}}_n^s}{\mathrm{dt}}]+L^s\frac{d[i_n^s-(1-p_1)\frac{C_1}{2}\frac{{\mathrm{du}}_n^s}{\mathrm{dt}}]}{\mathrm{dt}}}$

$p_1=\frac{u_{\mathrm{mn}}^s+R^s[i_n^s-(1-p_2)\frac{C_1}{2}\frac{{\mathrm{du}}_n^s}{\mathrm{dt}}]+L^s\frac{d[i_n^s-(1-p_2)\frac{C_1}{2}\frac{{\mathrm{du}}_n^s}{\mathrm{dt}}]}{\mathrm{dt}}-u_{\mathrm{cm}}^s}{R^s(i_m^s-p_2\frac{C_1}{2}\frac{{\mathrm{du}}_s^m}{\mathrm{dt}})+L^s\frac{d(i_m^s-p_2\frac{C_1}{2}\frac{{\mathrm{du}}_m^s}{\mathrm{dt}})}{\mathrm{dt}}+R^s{[i}_n^s-(1-p_2)\frac{C_1}{2}\frac{{\mathrm{du}}_n^s}{\mathrm{dt}}]+L^s\frac{d[i_n^s-(1-p_2)\frac{C_1}{2}\frac{{\mathrm{du}}_n^s}{\mathrm{dt}}]}{\mathrm{dt}}}$

This is the nonlinear equation about p, adopts solution by iterative method, and iteration is till satisfying following condition.

| p (k)-p (k-1) | the error amount of＜ε ε for setting;

(4) the location PRELIMINARY RESULTS that obtains is previously carried out probabilistic method and Least Square in Processing

Theoretically, the differential equation of first order method only needs the sampled value in two moment just can calculate the trouble spot, thereby in whole failure process, can draw many p values, and when practical application, because operating mode complexity, the fault data of sampling may be polluted, and needs positioning result is carried out the pre-service of statistical method.Because the number of discrete back equation is overdetermined equation much larger than the number of unknown number, this method adopts least square method to find the solution.

The treatment step of positioning result:

1. statistic law pre-service

For PRELIMINARY RESULTS, at first must reject invalid data.Account for the percentage of all fronts road total length because positioning result p (k) is trouble spot F to the line length of circuit one side, so 0≤p (k)≤1 is arranged,, should give rejecting so p (k)＞0 or p (k)＜1 are invalid data.And suppose that these results are the center with correct localization of fault result, are normal distribution: by the result that real electric current, voltage signal produced, with higher probability distribution around true value; And by the result that undesired signal produced, then sparsely be distributed in less probability and depart from true value at a distance.According to this thought, the Primary Location result is carried out pre-service, remove bad data.

2. ask the localization of fault result with least square method

The least square solution of P is:

P＝(X ^TX) ^-1X ^TY

Y wherein, X is the matrix representation formula of the sampled value Y (k) and the X (k) of each sampling instant.

P according to following formula calculates obtains X ' with Y as known quantity conversely, makes Z=X ', and Z is auxiliary variable: revised location Calculation result is with auxiliary variable method:

P′＝(Z ^TX) ^-1Z ^TY

(5) utilize calculate from the circuit both sides the size of difference of fault point voltage differentiate the true and false of root

Can calculate two positioning results by above-mentioned steps (3), (4), one of them is true root, and another is pseudo-root, can obtain true root to reject pseudo-root with the true and false that following method is differentiated root:

A) establish by calculate in the step (3) the positioning result that after step (6) is handled, obtains of p (k) be p ₁, p thus then ₁Calculate respectively from the circuit both sides the voltage of trouble spot, with calculate two magnitudes of voltage poor, can obtain the pressure reduction of trouble spot, computing formula is as follows:

${\mathrm{\Δu}}_{f1}^s=u_{\mathrm{mn}}^s+u_{\mathrm{cn}}^s-p_1{R}^s{i}_m^s-p_1{L}^s\frac{{{\mathrm{di}}^s}_m}{\mathrm{dt}}+(1-p_1)R^s{i}_n^s+(1-p_1)L^s\frac{{{\mathrm{di}}^s}_n}{\mathrm{dt}}$

Wherein:

p ₁Be the number percent of trouble spot apart from the distance of transmission line of electricity one side the line is busy road total length;

i _m ^s, i _n ^s(s=α β) is respectively the electric current of s line modulus both sides;

R ^s, L ^s(s=α β) is respectively the resistance and the inductance of s line modulus correspondence;

u _Mn ^s(s=α β) is the voltage difference of s line modulus both sides.

u _Cn ^s(s=α β) is the voltage of s line modulus electric capacity both sides.

Δ u _F1 ^s(s=α, β) be s line modulus by both sides calculate the difference of fault point voltage.

In the application of reality, the later computing formula of discretize is:

${\mathrm{\Δu}}_{f1}^s=u_{\mathrm{mn}}^s+u_{\mathrm{cn}}^s-p_1{R}^s{i}_m^s-p_1{L}^s\frac{i_m^s\left(k\right)-i_m^s(k-1)}{\mathrm{\ΔT}}+(1-p_1)R^s{i}_n^s\left(k\right)+(1-p_1)L^s\frac{i_n^s\left(k\right)-i_n^s(k-1)}{\mathrm{\ΔT}}$

Wherein:

p ₁Be the number percent of trouble spot apart from the distance of transmission line of electricity one side the line is busy road total length;

i _m ^s(k), i _n ^s(k) (s=α β) is respectively the electric current of k sampled point s line modulus both sides;

i _m ^s(k-1), i _n ^s(k-1) (s=α β) is respectively the electric current of k-1 sampled point s line modulus both sides;

R ^s, L ^s(s=α β) is respectively the resistance and the inductance of s line modulus correspondence;

u _Mn ^s(k) (s=α β) is the voltage difference of k sampled point s line modulus both sides;

u _Cn ^s(k) (s=α β) is the voltage of k sampled point s line modulus electric capacity both sides;

Δ T is the sampling period.

Δ u _F1 ^s(k) (s=α, β) be k sampled point s line modulus by both sides calculate the difference of fault point voltage;

B) establish by calculate in the step (4) the positioning result that after step (6) is handled, obtains of p (k) be p ₂, p thus then ₂Calculate respectively from the circuit both sides the voltage of trouble spot, with calculate two magnitudes of voltage poor, can obtain the pressure reduction of trouble spot, computing formula is as follows:

${\mathrm{\Δu}}_{f2}^s=u_{\mathrm{mn}}^s-u_{\mathrm{cm}}^s-p_2{R}^s{i}_m^s-p_2{L}^s\frac{{{\mathrm{di}}^s}_m}{\mathrm{dt}}+(1-p_2)R^s{i}_n^s+(1-p_2)L^s\frac{{{\mathrm{di}}^s}_n}{\mathrm{dt}}$

Wherein:

p ₂Be the number percent of trouble spot apart from the distance of transmission line of electricity one side the line is busy road total length;

i _m ^s, i _n ^s(s=α β) is respectively the electric current of s line modulus both sides;

R ^s, L ^s(s=α β) is respectively the resistance and the inductance of s line modulus correspondence;

u _Mn ^s(s=α β) is the voltage difference of s line modulus both sides.

u _Cm ^s(s=α β) is the voltage of s line modulus electric capacity both sides.

Δ u _F2 ^s(s=α, β) be s line modulus by both sides calculate the difference of fault point voltage.

In the application of reality, the later computing formula of discretize is:

${\mathrm{\Δu}}_{f2}^s=u_{\mathrm{mn}}^s-u_{\mathrm{cm}}^s-p_2{R}^s{i}_m^s-p_2{L}^s\frac{i_m^s\left(k\right)-i_m^s(k-1)}{\mathrm{\ΔT}}+(1-p_2)R^s{i}_n^s\left(k\right)+(1-p_2)L^s\frac{i_n^s\left(k\right)-i_n^s(k-1)}{\mathrm{\ΔT}}$

Wherein:

p ₂Be the number percent of trouble spot apart from the distance of transmission line of electricity one side the line is busy road total length;

i _m ^s(k), i _n ^s(k) (s=α β) is respectively the electric current of k sampled point s line modulus both sides;

i _m ^s(k-1), i _n ^s(k-1) (s=α β) is respectively the electric current of k-1 sampled point s line modulus both sides;

R ^s, L ^s(s=α β) is respectively the resistance and the inductance of s line modulus correspondence;

u _Mn ^s(k) (s=α β) is the voltage difference of k sampled point s line modulus both sides;

u _Cm ^s(k) (s=α β) is the voltage of k sampled point s line modulus electric capacity both sides;

Δ T is the sampling period.

Δ u _F2 ^s(k) (s=α, β) be k sampled point s line modulus by both sides calculate the voltage difference of trouble spot;

C) criterion of the true and false of differentiation root is:

${\mathrm{\ΔU}}_f^s=\mathrm{\Σ}{\mathrm{\Δu}}_f^s{\left(k\right)}^2$

With above-mentioned steps a), b) in the Δ u that tries to achieve _F1 ^s(k) and Δ u _F2 ^s(k) bringing following formula into can obtain:

${\mathrm{\ΔU}}_{f1}^s=\mathrm{\Σ\Δ}{u}_{f1}^s{\left(k\right)}^2$

${\mathrm{\ΔU}}_{f2}^s=\mathrm{\Σ\Δ}{u}_{f2}^s{\left(k\right)}^2$

If ${\mathrm{\ΔU}}_{f1}^s>\mathrm{\Δ}{U}_{f2}^s,$ P then ₁Be pseudo-root, p ₂Be true root; Otherwise, p then ₁Be true root, p ₂Be pseudo-root.

In general, by true root calculate pressure reduction than with pseudo-root calculate little two to three orders of magnitude of pressure reduction, so can differentiate the true and false of root accurately with said method.

Claims (3)

1. transmission line malfunction accurate positioning method of mending with string, it is characterized in that setting up the differential equation behind the transmission line malfunction by element characteristic and Kirchhoff's law, adopt the information of the voltage and current signal of multiterminal as localization of fault, utilize the accurate time dissemination system of GPS to guarantee the synchronism of data, the fault that takes place on the transmission line of electricity is accurately located.

2. localization method according to claim 1 is characterized in that may further comprise the steps:

(1) utilize GPS to realize voltage, the current signal synchronized sampling of transmission line of electricity multiterminal;

(2) electric parameters before and after record and the exchange trouble is to obtain the localization of fault desired data;

(3) localization of fault is to obtain accuracy position of fault point:

1) failure judgement is separate; 2) accurate localization of fault;

At first, current and voltage quantities and parameter are carried out phase-model transformation; According to pairing fault type, select the line modulus mutually relevant for use with fault; According to Kirchhoff's second law, adopt the multiterminal electric parameters row of this line modulus to write the loop equation, try to achieve the trouble spot;

Concrete performing step is as follows:

(1) row write out differential equation and the starting condition of describing fault front and back process;

(2) current and voltage quantities and parameter are carried out phase-model transformation;

(3), select the line modulus mutually relevant for use with fault according to pairing fault type;

(4a) the supposition fault occurs between a certain side (be designated as the M side, opposite side is designated as the N side) and serial compensation capacitance of transmission line of electricity, positions calculating;

A) utilize the electric current of the serial compensation capacitance of flowing through to calculate the voltage of electric capacity both sides;

B) according to Kirchhoff's second law, adopt the multiterminal electric parameters row of this line modulus to write the loop equation, try to achieve the trouble spot; Ranging formula is when single-phase earthing, line to line fault ground connection, phase fault or three-phase shortcircuit take place on the transmission line of electricity: $p=\frac{u_{\mathrm{mn}}^s+R^s{i}_n^s+L^s\frac{d{i}_n^s}{\mathrm{dt}}+u_{\mathrm{cn}}^s}{R^s{i}_m^s+L^s\frac{d{i}_m^s}{\mathrm{dt}}+R^s{i}_n^s+L^s\frac{d{i}_n^s}{\mathrm{dt}}}$

(4b) the supposition fault occurs between the opposite side (N side) and serial compensation capacitance of transmission line of electricity, positions calculating; Ranging formula is when single-phase earthing, line to line fault ground connection, phase fault or three-phase shortcircuit take place on the transmission line of electricity: $p=\frac{u_{\mathrm{mn}}^s+R^s{i}_n^s+L^s\frac{d{i}_n^s}{\mathrm{dt}}-u_{\mathrm{cm}}^s}{R^s{i}_m^s+L^s\frac{d{i}_m^s}{\mathrm{dt}}+R^s{i}_n^s+L^s\frac{d{i}_n^s}{\mathrm{dt}}}$

In (4a), (4b):

P is the trouble spot apart from the number percent of the distance of transmission line of electricity one side the line is busy road total length;

i _m ^s, i _n ^s(s=α β) is respectively the electric current of s line modulus both sides;

R ^s, L ^s(s=α β) is respectively the resistance and the inductance of s line modulus correspondence;

u _Mn ^s(s=α β) is the voltage difference of s line modulus both sides;

u _Cm ^s(s=α β) is the voltage of s line modulus electric capacity both sides;

(5) utilize the line capacitance current compensation to revise positioning result;

(6) obtain positioning result after, these results are handled with probabilistic method and least square method;

(7) utilize calculate from the circuit both sides the size of difference of fault point voltage differentiate the true and false of root.

3. localization method according to claim 2 is characterized in that the later ranging formula of discretize is:

$p_1\left(k\right)=\frac{u_{\mathrm{mn}}^s\left(k\right)+R^s{i}_n^s\left(k\right)+L^s\frac{i_n^s\left(k\right)-i_n^s(k-1)}{\mathrm{\ΔT}}+u_{\mathrm{cn}}^s\left(k\right)}{R^s{i}_m^s\left(k\right)+L^s\frac{i_m^s\left(k\right)-i_m^s(k-1)}{\mathrm{\ΔT}}+R^s{i}_n^s\left(k\right)+L^s\frac{i_n^s\left(k\right)-i_n^s(k-1)}{\mathrm{\ΔT}}}$

$p_2\left(k\right)=\frac{u_{\mathrm{mn}}^s\left(k\right)+R^s{i}_n^s\left(k\right)+L^s\frac{i_n^s\left(k\right)-i_n^s(k-1)}{\mathrm{\ΔT}}-u_{\mathrm{cm}}^s\left(k\right)}{R^s{i}_m^s\left(k\right)+L^s\frac{i_m^s\left(k\right)-i_m^s(k-1)}{\mathrm{\ΔT}}+R^s{i}_n^s\left(k\right)+L^s\frac{i_n^s\left(k\right)-i_n^s(k-1)}{\mathrm{\ΔT}}}$ Wherein:

P (k) is for being tried to achieve the trouble spot apart from the distance of transmission line of electricity one side the line is busy road total length number percent by k-1 and k sampled value;

i _m ^s(k), i _n ^s(k) (s=α β) is respectively the electric current of k sampled point s line modulus both sides;

i _m ^s(k-1), i _n ^s(k-1) (s=α β) is respectively the electric current of k-1 sampled point s line modulus both sides;

R ^s, L ^s(s=α β) is respectively the resistance and the inductance of s line modulus correspondence;

u _Mn ^s(k) (s=α β) is the voltage difference of k sampled point s line modulus both sides;

u _Cn ^s(k) (s=α β) is the voltage of k sampled point s line modulus electric capacity both sides;

Δ T is the sampling period.