CN105738762A - Fault single-end locating method based on Thompson theory arc model - Google Patents

Abstract

The invention relates to a fault single-end locating method based on a Thompson theory arc model. The algorithm comprises the steps that a Thompson theory model equation is established, the logarithmic relationship between voltage and current in air arc is deduced from the Thompson collision theory, a logarithmic model of fault point voltage uF about zero sequence current i0 is established, the logarithmic model is substituted and final simplifying and solving are performed so that fault single-end locating is performed. Fault single-end locating is enabled to be more accurate by the fault single-end locating method.

Description

A kind of fault method of single end distance measurement based on the inferior theoretical Arc Modelling of soup

Technical field

The present invention relates to a kind of fault method of single end distance measurement, be specifically related to a kind of Arc Modelling based on the inferior theory of soup and derive, and utilize this model to carry out the algorithm of fault single end distance measurement.

Background technology

Statistical analysis according to various faults, in short trouble, the number of times of singlephase earth fault almost accounts for about the 90% of all fault types, and finds from unit faults recorder analysis, and in phase-to phase fault, quite a few is to be developed by single-phase earthing.Particularly by way of the ultra-high-tension power transmission line of mountain area landforms, due to the reason such as insulator arc-over, thunderbolt, often occur because line discharge is caused single-phase high-impedance by branch around, Phyllostachys pubescens Mazei ex H.de Lebaie electric discharge and Huoshaoshan flame by circuit.After single-phase high-impedance occurs, usually due to protection can not correct operation, the long-time abnormal condition of transmission system is run; may result in phase insulation to puncture; it is converted into alternate even three-phase fault, makes fault harm increase, have a strong impact on the safe and stable operation of electrical network.After high resistance earthing fault occurs, there is the high-tension danger of contact when people or domestic animal are near trouble point；High resistance earthing fault occurs mostly with arc phenomenon, it is easy to initiation fire, it is possible to cause the heavy losses of life and property.

High voltage power transmisson system neutral grounding mode is for being directly grounded, if transmission line of electricity generation metallic earthing fault, owing to fault current is big, traditional relay protection device can quickly excise faulty line, it is prevented that fault spreads.But; if there is, at earth point, the transition resistance that numerical value is bigger; the high resistance earthing fault that such as reason such as insulator arc-over, thunderbolt, mountain fire causes; or owing to aerial line limits fault current size through the nonmetal character conducting medium ground connection such as branch, sand ground, may finally causing trouble voltage and current feature inconspicuous and can not be detected by conventional protection devices and excise.

In view of the above-mentioned technological deficiency of prior art, in the urgent need to developing a kind of novel fault method of single end distance measurement.

Summary of the invention

It is an object of the invention to overcome the shortcoming existed in prior art, a kind of fault method of single end distance measurement based on the inferior theoretical Arc Modelling of soup is provided, this fault plan distance-finding method makes singlephase earth fault be prone to be calculated, thus the probability of reduction accident and the extent of damage.

To achieve these goals, the present invention provides following technical scheme: a kind of fault method of single end distance measurement based on the inferior theoretical Arc Modelling of soup, and it comprises the following steps:

(1) model equation of the inferior theory of soup, is set up:

I=I_Se^ad(1)

Wherein: i is arc current, I_sFor the saturation current caused by outer ionization factor, d is arc length, and α is impact ionization coefficient；

Further, impact ionization coefficient α and electric field intensity E in arc space is following direct ratio functional relationship within the scope of certain arc voltage:

α/δ=A E/ δ (2)

Wherein: δ is air relative density, the average electron number produced of α/δ reflection collision every time, E/ δ reflects the energy that electronics is obtained in mean free path by electric field, and A is direct ratio coefficient；

(2), from the inferior collision theory of soup, the logarithmic relationship of voltage and electric current in air arc is derived, specifically:

According to theoretical it can be seen that one can assume that

I=I_Se^ad-I_S=I_Se^AEd-I_S(3)

U=E d (4)

Then

I=I_Se^Au-I_S(5)

U=U_T·ln(i/l_S+1)(6)

Wherein: u is arc voltage, i is arc current, U_T、I_SFor constant；

Through type (6) can derive the logarithmic relationship of voltage and electric current in air arc from the inferior collision theory of soup；

(3), by fault point voltage u_FSet up about zero-sequence current i₀Logarithmic model, specifically: owing to the electric arc logarithmic model under alternating voltage is shown below:

U=sgn (i) U_Tln(|i|I_S+1)(7)

Therefore, fault point voltage u_FSet up about zero-sequence current i₀Logarithmic model be

u_F=sgn (i₀)·U_Tln(|i₀|/I_S+1)(8)

(4), line parameter circuit value in formula (8) is expressed as unit distance line resistance inductance parameters With the product of fault distance l, and by electric arc logarithmic model substitute into, obtain following formula:

Order

Formula (8) is simplified to following formula:

Wherein: a₁And i₀All can calculate measuring end；Undetermined parameterHave: 1 is the fault distance measuring end to trouble point, U_TAnd I_SFor electric arc logarithmic model parameter, R_FThe resistance outside electric arc is removed for fault branch；

(5), known one group of data during fault(i=1,2...n, n > 3), remembers error

$\stackrel{V}{r}\left(\stackrel{V}{x}\right)={\left(r_1\right(\stackrel{V}{x}),L,r_n(\stackrel{V}{x}\left)\right)}^T---\left(12\right)$

Error of fitting is defined asQuadratic sum, then this nonlinear least square method Parameter Estimation Problem is expressed as Optimized model:

Wherein, for ensureing precision, n value requires more than the sampling number of a cycle.

Compared with existing measuring and calculating, the fault method of single end distance measurement based on the inferior theoretical Arc Modelling of soup of the present invention has following Advantageous Effects:

1, this distance-finding method is simple, range finding is accurate.

2, this distance-finding method is prone to find single-phase fault, reduces the infringement of fault.

Accompanying drawing explanation

Fig. 1 is the logic chart of the calculation of fault of the fault method of single end distance measurement based on the inferior theoretical arc fault of soup using the present invention..

Detailed description of the invention

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.

It is arc fault mostly that high resistance earthing fault occurs, and the modeling to fault electric arc waveform is the basis that high resistance earthing fault is studied.

1, arc physics essence describes

The physical essence of fault electric arc is atmospherical discharges phenomenon, uses for reference the inferior theory of soup, and arc phenomenon includes 3 discharge regimes:

(1) ionization outward: near ultra-high-tension power transmission line alternating voltage zero-crossing point, electric arc both end voltage is less can not excite cathode electronics, and electric current density is minimum, and electric arc is in of short duration OFF state.

(2) ionization by collision: along with alternating voltage increases, the electronic kinetic energy existed between air gap increases, and ionization by collision frequently occurs, and electronics and cation between air gap increase, and electric arc conductance increases, and arc current increases.

(3) thermal ionization: when alternating voltage increases to a certain degree, impact ionization process is further strong, raises at electric arc air gap temperature, and gas neutral kinetic energy of particle increases, mutually colliding generation ionization when neutral and form electronics and cation, this phenomenon is called thermal ionization.Thermal ionization makes to be filled with between air gap charged particle, and arc current sharply increases, and the resistance of arc channel levels off to zero.

2: the derivation of model

Due to alternating current arc ionization property, electric arc is relatively big at electric current, the temperature higher moment due to thermal ionization characteristic resistance less, and in the voltage zero-cross moment owing to outer ionization is faint, electric current is minimum, and electric arc is nonlinear distortion characteristic.

In air arc, electronics accelerates under the effect of electric field, because ionization by collision and thermal ionization make free electron number be continuously increased, form electron avalanche, α is called impact ionization coefficient, it is defined as an electronics and passes through the ionization by collision number of times that 1cm length on average occurs along direction of an electric field, if collision only produces a new electronics every time, then α represents the electron number newly ionized out in per stroke.There is equation below in the inferior theory of soup:

I=I_Se^αd(1)

In formula: i arc current；

I_SThe saturation current caused by outer ionization factor；

D arc length.

Following supposition is had when considering Arc Modelling:

(1) electric arc is the gas passage with cylinder, and electronics accelerates in its diametric(al) and ionization by collision occurs；

(2) during electric arc arcing, the electronics directed movement that electric current is mainly produced by ionization by collision determines, ignores the saturation current caused by outer ionization factor；

(3) in impact ionization coefficient α and arc space electric field intensity E within the scope of certain arc voltage shown in proportional functional relationship such as formula (2).

α/δ=A E/ δ (2)

Wherein δ is air relative density (δ=pT₀/(p₀T)), the average electron number produced of α/δ reflection collision every time, E/ δ reflects the energy that electronics is obtained in mean free path by electric field, and A is direct ratio coefficient.

By suppose there is

I=I_Se^αd-I_S=I_Se^AEd-I_S(3)

Arc voltage u is had

U=E d (4)

Then

I=I_Se^Au-I_S(5)

U=U_T·ln(i/I_S+1)(6)

Wherein u is arc voltage, and i is arc current, U_T、I_SFor constant, this formula is deduced in air arc voltage and the logarithmic relationship of electric current from the inferior collision theory of soup, and the electric arc logarithmic model under alternating voltage is shown below:

U=sgn (i) U_Tln(|i|/I_S+1)(7)

3: the derivation of algorithm

Owing to alternating current arc voltage and electric current exist the logarithmic relationship of formula (4), it is possible to by fault point voltage u_FSet up about zero-sequence current i₀Logarithmic model:

u_F=sgn (i₀)·U_Tln(|i₀|/I_S+1)(8)

Line parameter circuit value in formula (5) is expressed as unit distance line resistance inductance parametersWith the product of fault distance l, and by electric arc logarithmic model substitute into, obtain following formula:

Order

Formula (8) is simplified to following formula:

Wherein, a₁And i₀All can calculate measuring end；Undetermined parameterHave: l is the fault distance measuring end to trouble point, U_TAnd I_SFor electric arc logarithmic model parameter, R_FThe resistance outside electric arc is removed for fault branch.

Known one group of data during fault(i=1,2...n, n > 3), remembers error

Error of fitting is defined asQuadratic sum, then this nonlinear least square method Parameter Estimation Problem is expressed as Optimized model:

For ensureing precision, n value requires more than the sampling number of a cycle.

4: algorithm realizes

Due in real process, the fault of transmission line of electricity have metallic earthing and high resistance earthing fault point, therefore when introducing this algorithm, it is necessary to judging, whether this fault is earth fault fault, therefore takes following criterion to make a distinction:

First criterion: the triple-frequency harmonics content of fault point voltage electric current exceedes the 5% of first-harmonic；

Second Criterion: based on traditional fault localization result variance more than 10%.

Specifically, as it is shown in figure 1, after start-up, first it is obtain one-end fault recorder data, and judges whether to meet the first criterion according to acquired one-end fault recorder data, i.e. whether the triple-frequency harmonics content of failure judgement point voltage electric current exceedes the 5% of first-harmonic.If meeting the first criterion, then the fault method of single end distance measurement based on the inferior theoretical Arc Modelling of soup of the present invention is adopted to carry out distance calculation.If being unsatisfactory for the first criterion, then judge whether to meet Second Criterion, i.e. whether judge based on traditional fault localization result variance more than 10%.If meeting Second Criterion, then adopt the fault method of single end distance measurement based on the inferior theoretical Arc Modelling of soup of the present invention.If being unsatisfactory for the second judgement, then tradition distance-finding method is adopted to carry out distance calculation.

The above embodiment of the present invention is only for clearly demonstrating example of the present invention, 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 all of embodiment be given exhaustive.Every belong to apparent change that technical scheme extended out or the variation row still in protection scope of the present invention.

Claims (1)

1., based on a fault method of single end distance measurement for the inferior theoretical Arc Modelling of soup, it comprises the following steps:

(1) model equation of the inferior theory of soup, is set up:

I=I_Se^αd(1)

Wherein: i is arc current, I_SFor the saturation current caused by outer ionization factor, d is arc length, and α is impact ionization coefficient；

Further, impact ionization coefficient α and electric field intensity E in arc space is following direct ratio functional relationship within the scope of certain arc voltage:

α/δ=A E/ δ (2)

Wherein: δ is air relative density, the average electron number produced of α/δ reflection collision every time, E/ δ reflects the energy that electronics is obtained in mean free path by electric field, and A is direct ratio coefficient；

(2), from the inferior collision theory of soup, the logarithmic relationship of voltage and electric current in air arc is derived, specifically:

According to theoretical it can be seen that one can assume that

I=I_Se^αd-I_S=I_Se^AEd-I_S(3)

U=E d (4)

Then

I=I_Se^Au-I_S(5)

U=U_T·ln(i/I_S+1)(6)

Wherein: u is arc voltage, i is arc current, U_T、I_SFor constant；

Through type (6) can derive the logarithmic relationship of voltage and electric current in air arc from the inferior collision theory of soup；

(3), by fault point voltage u_FSet up about zero-sequence current i₀Logarithmic model, specifically:

Owing to the electric arc logarithmic model under alternating voltage is shown below:

U=sgn (i) U_Tln(|i|/I_S+1)(7)

Therefore, fault point voltage u_FSet up about zero-sequence current i₀Logarithmic model be

u_F=sgn (i₀)·U_Tln(|i₀|/I_S+1)(8)

(4), line parameter circuit value in formula (8) is expressed as unit distance line resistance inductance parametersWith the product of fault distance l, and by electric arc logarithmic model substitute into, obtain following formula:

Order

Formula (8) is simplified to following formula:

Wherein: a₁And i₀All can calculate measuring end；Undetermined parameterHave: 1 is the fault distance measuring end to trouble point, U_TAnd I_SFor electric arc logarithmic model parameter, R_FThe resistance outside electric arc is removed for fault branch；

(5), known one group of data during fault(i=1,2...n, n > 3), remembers error

$\stackrel{v}{r}\left(\stackrel{v}{x}\right)={\left(r_1\left(\stackrel{v}{x}\right),L,r_n\left(\stackrel{v}{x}\right)\right)}^T---\left(12\right)$

Error of fitting is defined asQuadratic sum, then this nonlinear least square method Parameter Estimation Problem is expressed as Optimized model:

$\underset{\stackrel{v}{x}}{\min }R$

Wherein, for ensureing precision, n value requires more than the sampling number of a cycle.