CN104408327A - Loop polarity diagnosis method based on relay protection current measurement - Google Patents

Abstract

The invention discloses a loop polarity diagnosis method based on relay protection current measurement, provides a generalized transformation ratio concept for a relay protection measurement loop, and establishes a mathematical model for relay protection current measurement loop polarity diagnosis. According to the method, criterion of current measurement loop polarity faults is provided based on singular value decomposition method, and the relay protection current measurement loop polarity diagnosis method based on the generalized transformation ratio is established. The provided diagnosis method has the advantages that not only can influence of total measuring errors be eliminated, but also the problem about polarity judgment of low-current branch can be solved, and higher sensitivity is provided.

Description

Based on the loop polarity diagnostic method of relay protection current measurement

Technical field

The present invention relates to the method for a kind of loop polarity diagnosis.

Background technology

In current power system, electrical secondary system measuring circuit incorrect polarity problem is difficult to avoid, but detection method is really immature, on-line checkingi cannot be realized, this problem of loop polarity mistake can only be avoided by the method detected respectively every bar branch current, to give up when detecting not only useless respectively power, and cannot on-line checkingi be realized.

Summary of the invention

Object of the present invention is just to provide a kind of loop polarity diagnostic method based on relay protection current measurement, and it can solve the decision problem of small area analysis branch road polarity, highly sensitive.

The object of the invention is by such technical scheme realize, concrete steps are as follows:

1) establish in current measurement circuit and flow to current transformer primary side current i ₁with protect CPU gained secondary current i in current measurement circuit ₂ratio be that current measurement circuit broad sense is than famous value N _g, namely if current measurement circuit broad sense no-load voltage ratio perunit value is wherein N is the nominal transformation ratio value of current transformer;

2) t is gathered _p~ t _qeach branch road each phase secondary current value i in current measurement circuit in time period _2i;

3) to step 2) the data i that collects _2iprocess, filter out m group secondary current value, form matrix A;

4) to step 3) described in matrix A, adopt quick sorting algorithm process, i.e. rank (A);

5) judge whether rank (A) equals n-1, if equal, proceeds to step 6), if be not equal to, proceed to step 3);

6) each branch road each current phasor measurement loop broad sense no-load voltage ratio perunit value n is calculated _gi, make current measurement circuit broad sense no-load voltage ratio perunit value n _gibe multiplied by safety factor r _n, each branch road respectively obtains judgment value p mutually _ngi;

7) by judgment value p _ngirespectively compared with default upper and lower limit threshold values, if within upper and lower limit threshold values numerical value, then represent current measurement circuit i-th branch road a (b, c) phase reverse polarity connection, otherwise then represent that i-th branch road a (b, c) phase polarity is correct.

Further, each branch road each current phasor measurement loop broad sense no-load voltage ratio perunit value n is calculated _giconcrete grammar as follows:

If i ₁₁..., i _1i..., i _1nfor flowing to current transformer each branch road primary side current value in current measurement circuit, record t _p~ t _qcPU each branch road gained secondary current value is protected to be i in time period in current measurement circuit ₂₁..., i _2i..., i _2n;

I can be obtained _1i=N _gii _2i

Utilize Kirchhoff's current law (KCL), namely in office one instantaneous, flow out or flow into the algebraic sum identically vanishing of element current, Σ i can be obtained _1i=0;

By formula i _1i=N _gii _2isubstitute into Σ i _1i=0, both members is simultaneously divided by the nominal transformation ratio value N of current transformer, then any time can obtain:

$\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{n}_{\mathrm{gi}}{i}_{2i}=0$

Wherein, n _gibe i-th branch current measuring circuit broad sense no-load voltage ratio perunit value, be i-th branch current measuring circuit broad sense than famous value N _giwith the ratio of its nominal transformation ratio N;

If be t to the Looking Out Time section of measuring circuit ₁~ t _m, in the current measurement circuit of wherein i-th time period jth bar branch road, protect CPU gained secondary current to be often organize calculated value all should meet then the calculated value of m (m>n) individual period can list following system of equations:

$\left\{\begin{array}{c}{i}_{21}^{\left(1\right)}{n}_{g1}+i_{22}^{\left(1\right)}{n}_{g2}+\·\·\·+i_{2i}^{\left(1\right)}{n}_{\mathrm{gi}}+\·\·\·+i_{2n}^{\left(1\right)}{n}_{\mathrm{gn}}=0\\ i_{21}^{\left(2\right)}{n}_{g1}+i_{22}^{\left(2\right)}{n}_{g2}+\·\·\·+i_{2i}^{\left(2\right)}{n}_{\mathrm{gi}}+\·\·\·+i_{2n}^{\left(2\right)}{n}_{\mathrm{gn}}=0\\ \·\\ \·\\ \·\\ i_{21}^{\left(m\right)}{n}_{g1}+i_{22}^{\left(m\right)}{n}_{g2}+\·\·\·+i_{2i}^{\left(m\right)}{n}_{\mathrm{gi}}+\·\·\·+i_{2n}^{\left(m\right)}{n}_{\mathrm{gn}}=0\end{array}\right.$

Above formula is expressed as matrix form: An _g=0

Wherein

$A=\left[\begin{array}{cccc}{i}_{21}^{\left(1\right)}& i_{22}^{\left(1\right)}& \·\·\·& i_{2n}^{\left(1\right)}\\ i_{21}^{\left(2\right)}& i_{22}^{\left(2\right)}& \·\·\·& i_{2n}^{\left(2\right)}\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ i_{21}^{\left(m\right)}& i_{22}^{\left(m\right)}& \·\·\·& i_{2n}^{\left(m\right)}\end{array}\right],n_g=\left[\begin{array}{c}{n}_{g1}\\ n_{g2}\\ \·\\ \·\\ \·\\ n_{\mathrm{gn}}\end{array}\right]$

Formula An _gin=0, equation number is greater than unknown quantity number, A ∈ R ^{m × n}, A can be decomposed into by Structured Singular Value Theory:

A＝SVD

In formula, S and D is m × m rank and n × n rank orthogonal matrix respectively; V=diag (λ ₁, λ ₂..., λ _n) be diagonal matrix, its diagonal element is the singular value of A, and by descending sort;

Make number of sets of sample m much larger than current measurement circuit number n in calculating, by formula Σ i _1i=0, formula i _1i=N _gii _2ithe column vector of known A is linear correlation, and when m is enough large, can make rank (A)=n-1, now overdetermination homogeneous equation group An _g=0 only has a Basic Solutions, and formula A=SVD is substituted into formula An _g=0 can obtain conversion as follows:

A ^TAn _g＝(SVD) ^T(SVD)n _g

＝D ^T(V ^TV)Dn _g＝0

Wherein unit orthogonal matrix D ^treversible, above formula can abbreviation be:

(V ^TV)Dn _g＝0

In formula,

$V^{T}V=\mathrm{diag}\left(\begin{array}{cccc}{\mathrm{\λ}}_1^2& \·\·\·& {\mathrm{\λ}}_{n-1}^2& 0\end{array}\right)$

D＝[d ₁d ₂…d _n] ^T

Can obtain thus:

Dn _g＝(0,0,…,0,1) ^T

Therefore can solve:

$n_g=d_n^T$

Wherein d _nfor last column of orthogonal matrix D, i.e. A ^tproper vector corresponding to the minimal eigenvalue of A.

Further, described safety factor r _nbe 1.1.

Further, step 7) described in preset upper and lower limit threshold values be respectively-1.23 and-0.83.

Owing to have employed technique scheme, the present invention has following advantage:

The present invention proposes the broad sense no-load voltage ratio concept of relay protection measuring circuit, establish the mathematical model of relay protection current measurement circuit polarity diagnosis.Propose the criterion of current measurement circuit polarity fault based on singular value decomposition method, establish the relay protection current measurement circuit polarity diagnostic method based on broad sense no-load voltage ratio.The diagnostic method proposed not only can get rid of the impact of measuring composition error, and can solve the decision problem of small area analysis branch road polarity, has higher sensitivity.

Other advantages of the present invention, target and feature will be set forth to a certain extent in the following description, and to a certain extent, based on will be apparent to those skilled in the art to investigating hereafter, or can be instructed from the practice of the present invention.Target of the present invention and other advantages can be realized by instructions below and claims and be obtained.

Accompanying drawing explanation

Accompanying drawing of the present invention is described as follows.

Fig. 1 is embodiment electrical block diagram;

Fig. 2 is schematic flow sheet of the present invention.

Embodiment

Below in conjunction with drawings and Examples, the invention will be further described.

Based on the loop polarity diagnostic method of relay protection current measurement, if flow to current transformer primary side current i in current measurement circuit ₁with protect CPU gained secondary current i in current measurement circuit ₂ratio be that current measurement circuit broad sense is than famous value N _g, such as formula (3), i.e. current measurement circuit head end primary system current i ₁cPU gained current sampling data i is protected with end ₂ratio.

$N_g=\frac{i_1}{i_2}---\left(3\right)$

When current measurement circuit is positive polarity connection, N _gfor just; When current measurement circuit is reversed polarity connection, N _gbe negative.Usual nominal transformation ratio N characterizes the relation that CT converts electric current, is defined as the ratio of a rated current and secondary rated current.Be such as the electromagnetic type current transformer of 5A for secondary rated current, when a rated current is 1000A, the nominal transformation ratio of the electromagnetic type current transformer of selection is N=1000/5.Broad sense no-load voltage ratio perunit value can be obtained thus, be the famous value N of broad sense no-load voltage ratio _gratio with its nominal transformation ratio N, is expressed as n _g, shown in (4).

$n_g=\frac{N_g}{N}\frac{i_1/i_2}{N}---\left(4\right)$

Arrange under normal circumstances, when current measurement circuit polarity is correct, N _gsymbol be just, i.e. n _gfor just; When the reverse polarity connection of current measurement circuit, i ₂oppositely, sign change, now N _gsymbol become negative, i.e. n _gbe negative.Therefore, the supervision of current measurement circuit polarity exception can be converted into the mathematical identification to measuring circuit broad sense no-load voltage ratio sign symbol.

According to the definition of broad sense no-load voltage ratio, for detecting current measurement circuit polarity abnormal conditions by solving its identifier, system first and second current value first must be obtained.But, secondary current value can only be collected in engineering reality, therefore will solve the problem solving broad sense no-load voltage ratio when primary current the unknown.

In real system, often overlap the protection of protective device particularly current differential principle, its access current response annexation of primary system.Therefore, according to primary system topological relation, utilize Kirchhoff's current law (KCL), namely in office one instantaneous, flow out or flow into the algebraic sum identically vanishing of certain element current, such as formula (5), wherein i _1ifor flowing through the primary current of element i-th branch road.

In electric power primary system, no matter be connected to the generalized node of each branch current on bus or multiple element compositions of delimiting arbitrarily, meet above-mentioned law all the time.Flowing into certain generalized node electric current in this agreement is just, then it is negative for flowing out.As shown in Figure 1, i ₁₁..., i _1i..., i _1nfor flowing through certain mutually each primary current of generalized node G, be converted to corresponding protection secondary current i through current measurement circuit ₂₁..., i _2i..., i _2n.Formula (6) is defined to obtain, wherein N according to broad sense no-load voltage ratio _giit is the broad sense no-load voltage ratio of i-th branch current measuring circuit.

i _1i＝N _gii _2i(6)

Formula (6) is substituted into formula (5), and both members is simultaneously divided by nominal transformation ratio N, then any time has:

$\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{n}_{\mathrm{gi}}{i}_{2i}=0---\left(7\right)$

Wherein n _gibe the perunit value of i-th branch current measuring circuit broad sense no-load voltage ratio, be the famous value N of i-th branch current measuring circuit broad sense no-load voltage ratio _giwith the ratio of its nominal transformation ratio N.

If be t to the Looking Out Time section of measuring circuit ₁~ t _m, wherein the protection CPU calculated value of i-th time period jth bar branch road is often organize calculated value and all should meet formula (7), then the calculated value of m (m>n) individual period can list following system of equations.

$\left\{\begin{array}{c}{i}_{21}^{\left(1\right)}{n}_{g1}+i_{22}^{\left(1\right)}{n}_{g2}+\·\·\·+i_{2i}^{\left(1\right)}{n}_{\mathrm{gi}}+\·\·\·+i_{2n}^{\left(1\right)}{n}_{\mathrm{gn}}=0\\ i_{21}^{\left(2\right)}{n}_{g1}+i_{22}^{\left(2\right)}{n}_{g2}+\·\·\·+i_{2i}^{\left(2\right)}{n}_{\mathrm{gi}}+\·\·\·+i_{2n}^{\left(2\right)}{n}_{\mathrm{gn}}=0\\ \·\\ \·\\ \·\\ i_{21}^{\left(m\right)}{n}_{g1}+i_{22}^{\left(m\right)}{n}_{g2}+\·\·\·+i_{2i}^{\left(m\right)}{n}_{\mathrm{gi}}+\·\·\·+i_{2n}^{\left(m\right)}{n}_{\mathrm{gn}}=0\end{array}\right.---\left(8\right)$

Above formula is expressed as matrix form:

An _g＝0 (9)

Wherein,

$A=\left[\begin{array}{cccc}{i}_{21}^{\left(1\right)}& i_{22}^{\left(1\right)}& \·\·\·& i_{2n}^{\left(1\right)}\\ i_{21}^{\left(2\right)}& i_{22}^{\left(2\right)}& \·\·\·& i_{2n}^{\left(2\right)}\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ i_{21}^{\left(m\right)}& i_{22}^{\left(m\right)}& \·\·\·& i_{2n}^{\left(m\right)}\end{array}\right],n_g=\left[\begin{array}{c}{n}_{g1}\\ n_{g2}\\ \·\\ \·\\ \·\\ n_{\mathrm{gn}}\end{array}\right]$

In formula (9), equation number is greater than unknown quantity number, A ∈ R ^{m × n}, A can be decomposed into by Structured Singular Value Theory:

A＝SVD (10)

In formula, S and D is m × m rank and n × n rank orthogonal matrix respectively; V=diag (λ ₁, λ ₂..., λ _n) be diagonal matrix, its diagonal element is the singular value of A, and by descending sort.

Make number of sets of sample m much larger than current measurement circuit number n in calculating, linear correlation by the column vector of formula (5), formula (6) known A, and when m is enough large, can make rank (A)=n-1, now overdetermination homogeneous equation group (9) only has a Basic Solutions. ^[30]formula (10) is substituted into formula (9) and conversion as follows can be obtained:

A ^TAn _g＝(SVD) ^T(SVD)n _g

(11)

＝D ^T(V ^TV)Dn _g＝0

Wherein unit orthogonal matrix D ^treversible, above formula can abbreviation be:

(V ^TV)Dn _g＝0 (12)

In formula,

$V^{T}V=\mathrm{diag}\left(\begin{array}{cccc}{\mathrm{\λ}}_1^2& \·\·\·& {\mathrm{\λ}}_{n-1}^2& 0\end{array}\right)$

D＝[d ₁d ₂…d _n] ^T

Can obtain thus:

Dn _g＝(0,0,…,0,1) ^T(13)

Therefore can solve:

$n_g=d_n^T---\left(14\right)$

Wherein d _nfor last column of orthogonal matrix D, i.e. A ^tproper vector corresponding to the minimal eigenvalue of A.

Consider that each link error of relay protection current measurement circuit is on the impact of its polarity fault diagnosis, can be considered in its secondary current sampled value and introduce a composition error item, such as formula (15).

i ₂＝(1+ε)i′ ₂(15)

Wherein i' ₂for the secondary current when measuring circuit is error free, ε is composition error.Formula (15) is substituted into formula (4) can obtain:

$n_g=\frac{i_1}{i_2}=\frac{i_1/i_2^{\′}}{(1+\mathrm{\ϵ})N}---\left(16\right)$

When current measurement circuit polarity is correct, primary current is nominal transformation ratio, i.e. i with the ratio of secondary current ₁/ i' ₂=N.Can be obtained by formula (15):

$n_g=\frac{1}{1+\mathrm{\ϵ}}---\left(17\right)$

When current measurement circuit reverse polarity connection, i' ₂oppositely, sign change, then i ₁/ i' ₂=-N.In like manner can obtain:

$n_g=-\frac{1}{1+\mathrm{\ϵ}}---\left(18\right)$

Under normal operating condition, current measurement circuit composition error absolute value | ε | should 10% be less than, by formula (18) polarity fault time broad sense no-load voltage ratio span n _g∈ (-1.111 ,-0.909).In this case make this method reliability higher, setting safety factor r _n=1.1, polarity failure criterion can be obtained:

p _ng∈(-1.23,-0.83) (19)

According to the span of polarity failure criterion, current measurement circuit a (b, c) mutually each branch road broad sense no-load voltage ratio identifier, relay protection current measurement circuit polarity inline diagnosis flow process as shown in Figure 2.

Be difficult to avoid according to electrical secondary system measuring circuit incorrect polarity problem in current power system, still lack the feature of ripe online test method, the present invention is studied relay protection current measurement circuit method for diagnosing faults, and its main innovate point is as follows:

1) propose the broad sense no-load voltage ratio concept of relay protection measuring circuit, establish the mathematical model of relay protection current measurement circuit polarity diagnosis.

2) propose the criterion of current measurement circuit polarity fault based on singular value decomposition method, establish the relay protection measuring circuit polarity diagnostic method based on broad sense no-load voltage ratio.

3) diagnostic method proposed not only can get rid of the impact of measuring composition error, and can solve the decision problem of small area analysis branch road polarity, has higher sensitivity.

The present invention can realize by means of only software algorithm, is a kind of inline diagnosis method of simple relay protection current measurement circuit polarity fault efficiently.

What finally illustrate is, above embodiment is only in order to illustrate technical scheme of the present invention and unrestricted, although with reference to preferred embodiment to invention has been detailed description, those of ordinary skill in the art is to be understood that, can modify to technical scheme of the present invention or equivalent replacement, and not departing from aim and the scope of the technical program, it all should be encompassed in the middle of right of the present invention.

Claims (4)

1., based on the loop polarity diagnostic method of relay protection current measurement, it is characterized in that, concrete steps are as follows:

1) establish in current measurement circuit and flow to current transformer primary side current i ₁with protect CPU gained secondary current i in current measurement circuit ₂ratio be that current measurement circuit broad sense is than famous value N _g, namely if current measurement circuit broad sense no-load voltage ratio perunit value is wherein N is the nominal transformation ratio value of current transformer;

2) t is gathered _p~ t _qeach branch road each phase secondary current value i in current measurement circuit in time period _2i;

3) to step 2) the data i that collects _2iprocess, filter out m group secondary current value, form matrix A;

4) to step 3) described in matrix A, adopt quick sorting algorithm process, i.e. rank (A);

5) judge whether rank (A) equals n-1, if equal, proceeds to step 6), if be not equal to, proceed to step 3);

6) each branch road each current phasor measurement loop broad sense no-load voltage ratio perunit value n is calculated _gi, make current measurement circuit broad sense no-load voltage ratio perunit value n _gibe multiplied by safety factor r _n, each branch road respectively obtains judgment value p mutually _ngi;

7) by judgment value p _ngirespectively compared with default upper and lower limit threshold values, if within upper and lower limit threshold values numerical value, then represent current measurement circuit i-th branch road a (b, c) phase reverse polarity connection, otherwise then represent that i-th branch road a (b, c) phase polarity is correct.

2., as claimed in claim 1 based on the loop polarity diagnostic method of relay protection current measurement, it is characterized in that, calculate each branch road each current phasor measurement loop broad sense no-load voltage ratio perunit value n _giconcrete grammar as follows:

If i ₁₁..., i _1i..., i _1nfor flowing to current transformer each branch road primary side current value in current measurement circuit, record t _p~ t _qcPU each branch road gained secondary current value is protected to be i in time period in current measurement circuit ₂₁..., i _2i..., i _2n;

I can be obtained _1i=N _gii _2i

Utilize Kirchhoff's current law (KCL), namely in office one instantaneous, flow out or flow into the algebraic sum identically vanishing of element current, Σ i can be obtained _1i=0;

By formula i _1i=N _gii _2isubstitute into Σ i _1i=0, both members is simultaneously divided by the nominal transformation ratio value N of current transformer, then any time can obtain:

$\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{n}_{\mathrm{gi}}{i}_{2i}=0$

Wherein, n _gibe i-th branch current measuring circuit broad sense no-load voltage ratio perunit value, be i-th branch current measuring circuit broad sense than famous value N _giwith the ratio of its nominal transformation ratio N;

If be t to the Looking Out Time section of measuring circuit ₁~ t _m, in the current measurement circuit of wherein i-th time period jth bar branch road, protect CPU gained secondary current to be often organize calculated value all should meet then the calculated value of m (m>n) individual period can list following system of equations:

$\left\{\begin{array}{c}{i}_{21}^{\left(1\right)}{n}_{g1}+i_{22}^{\left(1\right)}{n}_{g2}+...+i_{2i}^{\left(1\right)}{n}_{\mathrm{gi}}+...+i_{2n}^{\left(1\right)}{n}_{\mathrm{gn}}=0\\ i_{21}^{\left(2\right)}{n}_{g1}+i_{22}^{\left(2\right)}{n}_{g2}+...+i_{2i}^{\left(2\right)}{n}_{\mathrm{gi}}+...+i_{2n}^{\left(2\right)}{n}_{\mathrm{gn}}=0\\ .\\ .\\ .\\ i_{21}^{\left(m\right)}{n}_{g1}+i_{22}^{\left(m\right)}{n}_{g2}+...+i_{2i}^{\left(m\right)}{n}_{\mathrm{gi}}+...+i_{2n}^{\left(m\right)}{n}_{\mathrm{gn}}=0\end{array}\right.$

Above formula is expressed as matrix form: An _g=0

Wherein

$A=\left[\begin{array}{cccc}{i}_{21}^{\left(1\right)}& i_{22}^{\left(1\right)}& ...& i_{2n}^{\left(1\right)}\\ i_{21}^{\left(2\right)}& i_{22}^{\left(2\right)}& ...& i_{2n}^{\left(2\right)}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ i_{21}^{\left(m\right)}& i_{22}^{\left(m\right)}& ...& i_{2n}^{\left(m\right)}\end{array}\right],n_g=\left[\begin{array}{c}{n}_{g1}\\ n_{g2}\\ .\\ .\\ .\\ n_{\mathrm{gn}}\end{array}\right]$

Formula An _gin=0, equation number is greater than unknown quantity number, A ∈ R ^{m × n}, A can be decomposed into by Structured Singular Value Theory:

A＝SVD

In formula, S and D is m × m rank and n × n rank orthogonal matrix respectively; V=diag (λ ₁, λ ₂..., λ _n) be diagonal matrix, its diagonal element is the singular value of A, and by descending sort;

Make number of sets of sample m much larger than current measurement circuit number n in calculating, by formula Σ i _1i=0, formula i _1i=N _gii _2ithe column vector of known A is linear correlation, and when m is enough large, can make rank (A)=n-1, now overdetermination homogeneous equation group An _g=0 only has a Basic Solutions, and formula A=SVD is substituted into formula An _g=0 can obtain conversion as follows:

A ^TAn _g＝(SVD) ^T(SVD)n _g＝D ^T(V ^TV)Dn _g＝0

Wherein unit orthogonal matrix D ^treversible, above formula can abbreviation be:

(V ^TV)Dn _g＝0

In formula,

$V^{T}V=\mathrm{diag}\left(\begin{array}{cccc}{\mathrm{\λ}}_1^2& ...& {\mathrm{\λ}}_{n-1}^2& 0\end{array}\right)$

D＝[d ₁d ₂… d _n] ^T

Can obtain thus:

Dn _g＝(0，0，…，0，1) ^T

Therefore can solve:

$n_g=d_n^T$

Wherein d _nfor last column of orthogonal matrix D, i.e. A ^tproper vector corresponding to the minimal eigenvalue of A.

3., as claimed in claim 1 based on the loop polarity diagnostic method of relay protection current measurement, it is characterized in that: described safety factor r _nbe 1.1.

4., as claimed in claim 1 based on the loop polarity diagnostic method of relay protection current measurement, it is characterized in that: step 7) described in preset upper and lower limit threshold values and be respectively-1.23 and-0.83.