CN105425111A - Transmission line fault ranging method using transition resistor features - Google Patents

Abstract

The invention relates to a transmission line fault ranging method using transition resistor features. The method comprises the following steps: (1) calculating the complex number of transition resistors by using a power frequency quantity based on resistive features of fault transition resistors; (2) supposing the imaginary part of the complex number is zero and establishing a ranging equation; (3) decoupling three phases of a three-phase transmission line by Karebauer transformation, and giving a corresponding calculation equation; and (4) solving the calculation equation to obtain a fault distance. By adopting the method, accurate fault distance can still be obtained in the presence of large measurement errors and line parameter errors.

Description

A kind of fault positioning method for transmission line utilizing transition resistance feature

Technical field

The invention belongs to transmission line malfunction monitoring technical field, relate to a kind of fault positioning method for transmission line, be specifically related to a kind of fault positioning method for transmission line utilizing transition resistance feature.

Background technology

After electric network fault, be that accelerating system is recovered, reduce power off time, fault localization is a very important job fast and accurately.For meeting the requirement of fault location, various Fault Location Algorithm is carried out.The input data that Fault Location Algorithm needs, two large classes can be divided into: (1) single-ended algorithm, (2) both-end (or multiterminal) algorithm.

Utilize the single-ended method range finding of one end electric parameters, principle needs make some hypothesis with the impact eliminating system impedance and transition resistance, even if Single Terminal Traveling Wave Fault Location, also fully do not reach degree of being practical.When actual conditions and hypothesis are not attached, its range measurement error is larger.And the impact such as transition resistance, system impedance can be eliminated based on the fault localization of Two-Terminal Electrical Quantities in principle.Both-end distance measuring algorithm is divided into needs the algorithm of synchrodata and the algorithm of non-synchronous data.Even if consider and adopt GPS, by mutual inductor phase shift, hardware time delay and sampling delay etc., the location algorithm based on both-end non-synchronous data has larger Practical significance.

Fault Location Algorithm based on unsynchronized two-terminal data introduces the asynchronous time (or asynchronous angle) in principle.The introducing of asynchronous time adds the unknown number of algorithm, adds the complexity of algorithm.To the problem how processing lock in time, a kind of method is that the both-end electric current and voltage before utilizing fault solves asynchronous angle.If faulty line trend is very little, its current precision can not meet requirement, cannot accurately obtain asynchronous angle, and this method is not suitable for the situation of He Zhong Library.Another kind method is the asynchronous angle of cancellation or is solved together as unknown quantity at different angle.These methods mainly utilize sets up range equation from the fault point voltage of both sides calculating is equal, equal or the fault distance of amplitude is utilized to be the features such as real number, by iteration or utilize fault component to set up redundancy equation non-iterative to solve, principle is simple, there is certain practicality, but when voltage and current measurement value or line parameter circuit value error larger time, its error increases thereupon.

Therefore, the high fault positioning method for transmission line of a kind of novel stability is badly in need of now.

Summary of the invention

The object of the invention is to solve the above-mentioned problems in the prior art, utilize a fault positioning method for transmission line for transition resistance feature, the method makes still can obtain fault distance accurately under the larger measuring error of existence and line parameter circuit value error condition.

To achieve these goals, the invention provides following technical scheme: a kind of fault positioning method for transmission line utilizing transition resistance feature, it comprises the following steps:

(1), based on the resistive feature of fault resistance, power frequency gauge is utilized to calculate the plural number of transition resistance;

(2), the imaginary part of described plural number is made to be zero thus to set up range equation;

(3), to three phase line, by the decoupling zero of triumphant human relations Bel transfer pair transmission line of electricity three-phase, corresponding accounting equation is provided;

(4), fault distance is obtained by solving described accounting equation.

Further, wherein, the range equation set up in described step (2) is

$f\left(d\right)=\underset{i=0}{\overset{5}{\Σ}}{a}_i\×d^i=0,$

Wherein, a _ifor the algebraic combination of circuit both sides electric current and voltage power frequency mold component real part and imaginary part after fault, d is fault distance.

Further, wherein, in described step (4), try to achieve initial value by the method ignoring transmission line of electricity admittance parameter over the ground, then iteratively faster solves the solution of described accounting equation.

The fault positioning method for transmission line of transition resistance feature that utilizes of the present invention is these basic characteristics of resistive based on fault resistance, and the imaginary part of transition resistance plural number utilizing power frequency gauge to calculate gained is zero set up range equation.For three phase line, according to different fault types, utilize triumphant human relations Bel phase-model transformation, set up the relation of trouble spot modulus voltage and modulus electric current, solve transition resistance, draw the equation with one unknown quantity of fault distance.Try to achieve initial value by the method ignoring transmission line of electricity admittance parameter over the ground, iteratively faster solves the solution of unitary nonlinear equation.The fast convergence of actual EMTDC simulating, verifying algorithm and accuracy, by carrying out error suseptibility analysis to algorithm, confirm the stability of algorithm under larger measuring error and line parameter circuit value error condition.

Accompanying drawing explanation

Fig. 1 is the schematic flow sheet utilizing the fault positioning method for transmission line of transition resistance feature of the present invention.

Fig. 2 is transmission line of electricity ∏ shape parameter model after fault.

Fig. 3 is singlephase earth fault model.

Fig. 4 is two-phase phase fault model.

Fig. 5 is two-phase short circuit and ground fault model.

Embodiment

Below in conjunction with drawings and Examples, the present invention is further described, and the content of embodiment is not as the restriction to protection scope of the present invention.

Fig. 1 shows the schematic flow sheet utilizing the fault positioning method for transmission line of transition resistance feature of the present invention.As shown in Figure 1, in the present invention, be first the resistive feature based on fault resistance, utilize power frequency gauge to calculate the plural number of transition resistance.Then, the imaginary part of described plural number is made to be zero thus to set up range equation.

Wherein, to simplify the analysis, ∏ type single-phase power transmission line parameter model is as shown in Figure 2 adopted to release Fault Location Algorithm.In figure, U _m, U _n, I _m, I _nbe respectively m side and n side electric current and voltage phasor.I _fm, I _fnbe respectively from m side, n effluent is to the electric current of trouble spot.U _ffor fault point voltage, z, y are respectively line impedance and admittance parameter over the ground.To power frequency amount, if asynchronous angle, circuit both sides is δ, the distance of distance m side, trouble spot and the ratio of line length are d, then the fault point voltage calculated from m side is:

$U_{fm}=U_m+z\×(d^2\frac{y}{2}\×U_m-{\mathrm{dI}}_m)---\left(1\right)$

The fault point voltage calculated from n side is:

$U_{fn}=U_n+z\×\[{(1-d)}^2\frac{y}{2}\×U_n-(1-d)I_n\]---\left(2\right)$

Because trouble spot is same point, then have:

U _f＝U _fm＝U _fn×e ^jδ(3)

From m effluent to the electric current of trouble spot be:

$I_{fm}=I_m-d\frac{y}{2}(U_m+U_{fm})---\left(4\right)$

Mutually in the same time, from n effluent to the electric current of trouble spot be I _fn× e ^{j δ}, wherein:

$I_{fn}=I_n-(1-d)\frac{y}{2}(U_n+U_{fn})---\left(5\right)$

Then trouble spot transition resistance is

$\frac{1}{R_g}=\frac{I_{fm}+I_{fn}\×e^{j\mathrm{\δ}}}{U_f}=\frac{I_{fm}}{U_{fm}}+\frac{I_{fn}\×e^{j\mathrm{\δ}}}{U_{fn}\×e^{j\mathrm{\δ}}}---\left(6\right)$

Therefore formula (6) can cancellation e ^{j δ}.Because transition resistance is purely resistive, then have:

$f\left(d\right)=IM(\frac{I_{fm}}{U_{fm}}+\frac{I_{fn}}{U_{fn}})=0---\left(7\right)$

Wherein IM represents and gets imaginary part to plural number.Solve formula (7) fault distance d.

Then, to three phase line, by the decoupling zero of triumphant human relations Bel transfer pair transmission line of electricity three-phase, corresponding accounting equation is provided.

Particularly, to three phase line, range equation formula (7) is no longer set up each phase.Therefore range equation (7) is applied to the key of three phase line is the transition resistance expression formula of trying to achieve in different faults situation.

Triumphant human relations Bel phase-model transformation is carried out to transmission line of electricity both sides electric current and voltage and line parameter circuit value.Transformation matrix is:

$S=\left[\begin{array}{ccc}1& 1& 1\\ 1& -2& 1\\ 1& 1& -2\end{array}\right],S^{-1}=\frac{1}{3}\left[\begin{array}{ccc}1& 1& 1\\ 1& -1& 0\\ 1& 0& -1\end{array}\right]$

Because the phase-model transformation result of transmission line parameter and selected transformation matrix have nothing to do, therefore, transmission line of electricity zero mould parameter and phase mould parameter are equal with positive order parameter with its zero sequence respectively.To faulty line lumped parameter model as shown in Figure 2.If its modulus parameter matrix Z=diag is (z ₀, z _α, z _β), Y=diag (y ₀, y _α, y _β), m side electric current and voltage modulus is: U _m=[u _m0u _{m α}u _{m β}] ^t, I _m=[I _m0i _{m α}i _{m β}] ^t, n side electric current and voltage modulus is: U _n=[u _n0u _{n α}u _{n β}] ^t, I _n=[i _n0i _{n α}i _{n β}] ^t.Wherein, diag represents with respective element to be the diagonal matrix of diagonal element, and 0, α, β in subscript represents the modulus of corresponding 0, α, β, and T represents the transposition of row vector.

To singlephase earth fault, as shown in Figure 3, wherein U _fma, I _fma, U _fna, I _fnabe respectively the trouble spot a phase voltage calculated from m side and n side and the electric current (as follows) flowing to trouble spot.

$\frac{1}{R_g}=\frac{I_{fma}}{U_{fma}}+\frac{I_{fna}\×e^{j\mathrm{\δ}}}{U_{fna}\×e^{j\mathrm{\δ}}}---\left(8\right)$

Because of I _fma=A × I _fm, I _fna=A × I _fn, U _fna=A × U _fn, U _fma=A × U _fm.Wherein A=[111], U _fm, I _fm, U _fn, I _fncan by U _m, I _m, U _n, I _nand Z, Y are according to formula (1), (2), (4), (5) try to achieve, then:

$\frac{1}{R_g}=\frac{A\×I_{fm}}{A\×U_{fm}}+\frac{A\×I_{fm}}{A\×U_{fn}}---\left(9\right)$

To two-phase phase fault, if fault phase is a phase and b phase, as shown in Figure 4.

$R_f=\frac{(U_{fma}-U_{fnb})}{I_{fma}+I_{fna}}---\left(10\right)$

According to Kirchhoff's current law (KCL), at trouble spot I _fma+ I _fna=-I _fmb-I _fnb, can obtain according to formula (10):

$\frac{2}{R_f}=\frac{I_{fma}-I_{fmb}}{(U_{fma}-U_{fmb})}+\frac{I_{fna}-I_{fnb}}{(U_{fma}-U_{fmb})}---\left(11\right)$

Converted from triumphant human relations Bel, the pass of electric current α modulus and a phase current and b phase current is: voltage relation is also identical, and the trouble spot Aerial mode component voltage calculated because of circuit both sides is equal, then can obtain:

$\frac{1}{R_f}=\frac{I_{fma}}{2U_{fma}}+\frac{I_{fna}}{2U_{fna}}---\left(12\right)$

To two-phase grounding fault, as shown in Figure 5, if fault phase is a phase and b phase.

Because of U _fma-U _fmb=U _fma-U _g-(U _fmb-U _g), i.e. U _fma-U _fmb=(I _fma+ I _fna-I _fmb-I _fmb) × R, then can obtain:

$\frac{1}{R}=\frac{I_{fma}+I_{fna}-I_{fmb}-I_{fnb}}{U_{fma}-U_{fmb}}=\frac{I_{fma}}{U_{fma}}+\frac{I_{fna}}{U_{fna}}---\left(13\right)$

Three characteristics of the middle term short circuit is symmetry short circuit, therefore only calculates with α mold component such as line to line fault:

$\frac{1}{R_{ga}}=\frac{I_{fma}}{U_{fma}}+\frac{I_{fna}}{U_{fna}}---\left(14\right)$

Wherein R _{g α}for the transition resistance calculated by α mold component.

From upper analysis, to employing, triumphant human relations Bel converts the three phase line after decoupling zero, and except singlephase earth fault, its transition resistance computing formula of line to line fault, two-phase grounding fault and three-phase shortcircuit has identical simple form.Whatsoever form, range equation all can be reduced to:

$f\left(d\right)=\underset{i=0}{\overset{5}{\Σ}}{a}_i\×d^i=0---\left(15\right)$

Wherein α _ifor the algebraic combination of circuit both sides electric current and voltage power frequency mold component real part and imaginary part after fault, in view of length no longer launches, formula (15) is take d as the unitary nonlinear equation of unknown number.

Finally, fault distance is obtained by solving described accounting equation.

Be take d as the unitary nonlinear equation of unknown number due to formula (15), therefore, the first step of algorithm is the extraction of power frequency component.Because difference can effectively filtering DC component, after therefore adopting difference, whole wave Fu Liye filtering algorithm extracts the power frequency component of electric current and voltage after fault.For solving formula (15), adopt speed of convergence Newton iteration method faster.Because Newton method only has local convergence, rational initial value is therefore selected to be the key whether algorithm is practical.

Except overlength transmission line of electricity, actual transmission line of electricity over the ground admittance parameter all can be similar to and ignores.For uniline, according to formula (1), (2), (3), (4), (5), ignore parameter y, substitute into the approximate value that formula (7) available analytical method tries to achieve d, with this approximate value for initial value d0:

wherein A ₁, A ₂, A ₃, A ₄, A ₅, A ₆, A ₇, A ₈, A ₉, A ₁₀be respectively plural I _m, U _m, I _n, U _nand the real part of parameter z and imaginary part.

Be that initial value carries out Newton iteration to formula (15) with d0, step is as follows:

1) to f (d) differentiate, derived function is obtained.

$f^{\′}\left(d\right)=\underset{i=1}{\overset{5}{\Σ}}i\×a_i\×d^i$

Separate linear equation: f ' (d _k) × Δ d _k=-f (d _k) obtain Δ d _k.

2) d is made _k+1=d _k+ Δ d _k.

3) as Δ d _kduring < ε (ε is the arithmetic number chosen according to accuracy requirement), iteration terminates, fault distance d.

In order to prove the validity of this distance-finding method, in the present invention, inventors performed EMTDC simulation evaluation.Be emulation tool with PSCAD-EMTDC, set up 220kV transmission line of electricity realistic model, transmission line of electricity both sides electric current and voltage data are all by setting up oscillograph model with the form of failure wave-recording by electrical power system transient data interchange general format record.

Transmission line parameter is as follows: line length 100km, and positive sequence resistance is 3.4676 ohm, and forward-sequence reactance is 42.337 ohm; Zero sequence resistance is 30.002 ohm, and zero-sequence reactance is 114.26 ohm; Positive sequence over the ground conductance is 1*10 ^-5mho, positive sequence over the ground susceptance is 2.726*10 ^-4mho; Zero sequence over the ground conductance is 1*10 ^-5mho, zero sequence over the ground susceptance is 1.936*10 ^-4mho.

First precision simulation has been carried out.

To singlephase earth fault, for A phase ground connection, if asynchronous angle is 45 °, fault localization result (d) under different transition resistance fr (faultresistance) and different faults position fl (faultlocation) condition is as shown in table 1.To alternate (phase fault, two phase ground, three-phase shortcircuit) fault, the fault localization result under different faults type ft (faulttype), different transition resistance and different faults locality condition is as shown in table 2.As can be seen from the results, this algorithm is not subject to the impact of fault resistance and abort situation, all has higher precision.

In algorithm simulating process, invention has been mass data emulation, consider different faults type, various asynchronous angle, different faults distance, range error situation in different transition resistance situation simultaneously, partial simulation result more as shown in table 3.As can be seen from Table 3, this algorithm all has higher precision to different situations, practical demand can be met, through mass data Emulating display, arranging under iteration stopping condition ε is the precision of 0.00001, algorithm the convergence speed is very fast, and iterations is all below 4 times, and the phenomenon do not restrained occurs.

The different transition resistance of table 1 single-phase earthing and position range measurement

The different transition resistance of table 2 phase-to phase fault and position range measurement

Table 3 different faults type and asynchronous angle range measurement

Secondly, error suseptibility analysis has been carried out.

In practicality, current transformer or voltage transformer (VT) all can produce error, and relay protection simultaneously or fault oscillograph measuring unit also can produce error.In order to this algorithm can be used in producing reality, the susceptibility of this algorithm under different error environment also to be studied.

In the process of conducting a research, apply the amplitude error of ± 2% and the angular error of ± 2 ° to voltage and current.Consider worst situation, if line parameter circuit value error is 2%, apply 2% amplitude error in m side, apply-2% amplitude error in n side, partial simulation result is as shown in table 4; Apply 2 ° of angle errors in m side, apply-2 ° of angle errors in n side, partial simulation result is as shown in table 5.Consider the impact by outside environmental elements, transmission line parameter error maximum possible reaches 10%, in order to analytical parameters error is on the impact of range measurement, emulation is under 2% amplitude error, 2% angular error condition, and range error variation tendency when transmission line parameter error is respectively 1%, 5%, 10% is as shown in table 6.Emulation shown in table 4, table 5, table 6 is in 75km place fault, 45 °, asynchronous angle, both sides, the result under fault resistance 10 ohmic conditions.

Range measurement under table 42% amplitude error condition

Range measurement under table 52 ° angle error condition

Range measurement under table 6 different parameters error condition

As can be seen from simulation result, under the electric current and voltage of line parameter circuit value and measurement all exists the condition of error, the error of location algorithm can increase.But as can be seen from relative error size, this location algorithm has good stability concerning line parameter circuit value and measuring error.In the simulation process of mass data, there is not situation about not restraining in algorithm yet.

The present invention, by the calculating formula of transition resistance in transmission line malfunction process under the triumphant human relations Bel conversion condition of research, derives fault localization equation, gives the Simple Solution of equation.Actual emulation the Example Verification accuracy of algorithm and the stability under various error condition.

The above embodiment of the present invention is only for example of the present invention is clearly described, and is not the restriction to embodiments of the present invention.For those of ordinary skill in the field, can also make other changes in different forms on the basis of the above description.Here cannot give exhaustive to all embodiments.Every belong to technical scheme of the present invention the apparent change of extending out or variation be still in the row of protection scope of the present invention.

Claims (3)

1. utilize a fault positioning method for transmission line for transition resistance feature, it comprises the following steps:

(1), based on the resistive feature of fault resistance, power frequency gauge is utilized to calculate the plural number of transition resistance;

(2), the imaginary part of described plural number is made to be zero thus to set up range equation;

(3), to three phase line, by the decoupling zero of triumphant human relations Bel transfer pair transmission line of electricity three-phase, corresponding accounting equation is provided;

(4), fault distance is obtained by solving described accounting equation.

2. the fault positioning method for transmission line utilizing transition resistance feature according to claim 1, wherein, the range equation set up in described step (2) is

$f\left(d\right)=\underset{i=0}{\overset{5}{\&Sigma;}}{a}_i\&times;d^i=0,$

Wherein, a _ifor the algebraic combination of circuit both sides electric current and voltage power frequency mold component real part and imaginary part after fault, d is fault distance.

3. the fault positioning method for transmission line utilizing transition resistance feature according to claim 2, wherein, in described step (4), try to achieve initial value by the method ignoring transmission line of electricity admittance parameter over the ground, then iteratively faster solves the solution of described accounting equation.