CN103093097A - Electrical power system fragile section identification method based on normalized-cut - Google Patents

Abstract

The invention relates to the technical field of electrical power system static status safety analysis and on-line monitoring, and provides a quick method of identifying an electrical power system fragile section. An electrical power system fragile section identification method based on normalized-cut has important guiding significance for the establishment of an effective prevention and control measure and an islanding control strategy. The electrical power system fragile section identification method based on the normalized-cut comprises a first step of establishing a suitable electrical power system graph theory model, a second step of establishing a laplacian matrix and a similarity matrix of the electrical power system graph theory model, a third step of forming corresponding split guiding vectors, searching corresponding sections of the split guiding vectors in a heuristic mode, a forth step of building an objective function regarding to the split guiding vectors based on the normalized-cut mode, calculating the objective function of each of the split guiding vectors, and a fifth step of screening a split guiding vector which enables the objective function to obtain the minimum value, determining the section corresponding to the split guiding vector to be a fragile section. The electrical power system fragile section identification method based on the normalized-cut is mainly applied to the electrical power system static status safety analysis and on-line monitoring.

Description

The electric system vulnerable profile recognition method of cutting based on standard

Technical field

The present invention relates to Contingency Analysis of Power Systems and in-service monitoring technical field, specifically, relate to the electric system vulnerable profile recognition method of cutting based on standard.

Background technology

In order to guarantee the safe and stable operation of electric system, need real-time analysis and monitor some key characters that characterize security of system.Key sections is a kind of important form of characterization system security.Therefore for many years, key sections is one of focus of electrical network analysis and dispatcher's concern always, and its recognition methods has also obtained very large development in the evolution of electrical network.

Recognition methods for key sections in electric system at present mainly comprises following three classes:

1. based on the transmission cross-section recognition methods of interregional interconnection.These class methods are usually according to the regional feature of system, affiliated administrative region, and the interconnection interregional in conjunction with operations staff's experience artificial selection forms transmission cross-section.At the initial stage of Power System Interconnection, the net connection between each zone is weaker, and this moment, electric network composition was still more clear, utilizes the method identification transmission cross-section simple, and fast, practical application is more.But along with the scale of interconnected network increases day by day, interregional contact strengthens gradually, and the method for operation is more flexible and changeable, and the transmission cross-section that this method identifies might be also insufficient and accurate.

2. the transmission cross-section recognition methods of testing based on branch breaking.These class methods are intended to be subjected to the larger line combination of influence on tidal flow to consist of section by cut-offfing the test of overload branch road, filtering out.This class section exists the threat that suffers than the megatrend transfer after the branch road overload trip, have the potential safety hazard that causes the cascading trip fault.But the transmission cross-section that the method identifies depends on the selection of cut-offfing branch road, selects different branch roads to cut-off test, may obtain different transmission cross-sections, has significant limitation.

3. based on the key sections recognition methods of topological structure.These class methods are from the viewpoint of complex network, electric system is converted into the topological model that is formed by point and limit, and then utilize Complex Networks Theory identification by the section that the minority circuit forms, and will make during these line failures that between most of nodes, shortest path becomes large, make system's fragility that becomes.But these class methods only relate to the physical arrangement of system, do not take into account the impact of trend, and along with the variation of power system operating mode and the adjustment of trend on a large scale, the key sections that the method identifies might be also insufficient and accurate.

When said method was applied to the more flexible and changeable interconnected network of the method for operation nowadays, the section that identifies all may be inaccurate.Exist a kind of in electric system and the closely-related fragile section of electrical network Real-time Power Flow distribution, this section is comprised of the weak circuit of contact on physical arrangement, and these circuits trend conveying in system simultaneously is larger.Very easily destroy the passway for transmitting electricity of electrical network when the line failure in this section, cause that in system, trend shifts, the safety and stability problems such as branch road overload easily occur, jeopardize the security of system operation.

Summary of the invention

The present invention is intended to overcome the deficiencies in the prior art, a kind of fast method of identifying the electric system vulnerable section is provided, has great importance to formulating effective prevention and control measure and off-the-line control strategy, for achieving the above object, the technical scheme that the present invention takes is, electric system vulnerable profile recognition method based on standard is cut comprises the steps:

The first step: according to the needs of fragile profile recognition, calculate the electrical network Real-time Power Flow, utilize based on the electric system branch road of electrical distance and trend distribution and compose the power method, set up applicable electric system graph theory model;

Second step: set up this abstract model Laplacian Matrix and degree matrix, and calculate Laplacian Matrix about minimum non-zero eigenwert and the characteristic of correspondence vector thereof of degree matrix;

The 3rd step: the direction that provides according to this proper vector is divided into two groups with the node in system, forms corresponding cutting apart and indicates vector, searches for the section of this vector correspondence heuristicly;

The 4th step: a little less than contact on the circuit physical arrangement in fragile section, and trend is carried larger characteristics in system, builds the objective function of indicating vector about cutting apart based on the standard blanking method, and each is cut apart indication vector calculation target function value;

The 5th step: the screening objective function of sening as an envoy to is obtained the indication vector cut apart of minimum value, and the section of this vector correspondence is exactly fragile section.

The electric system branch road that utilization distributes based on electrical distance and trend is composed the power method and is specially: the graph theory model G=(V that contains n node and m bar limit, E, W), V is vertex set, and the bus in corresponding real system, generator, load, E are the limit collection, the branch road of corresponding connection bus, comprise circuit and transformer, W is weight matrix, weighting matrix elements w _ijBe connected node v _iAnd v _jThe weight on limit; Utilization is composed the power method based on the electric system branch road of electrical distance and trend distribution branch road is composed power:

$w_{\mathrm{ij}}=\frac{y_{\mathrm{ij}}}{\left|P_{\mathrm{ij}}\right|}---\left(1\right)$

y _ijThe line admittance of connected node i and node j, P _ijTo flow to the meritorious trend of ground state of node j from node i.

Calculating Laplacian Matrix is specially about minimum non-zero eigenwert and the characteristic of correspondence vector thereof of spending matrix: the degree of node i is:

$d_i=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}---\left(2\right)$

The degree matrix D is with d ₁, _nBe the diagonal matrix of diagonal element, Laplacian Matrix L is:

L＝D-W (3)

Method for Solving Generalized Eigenproblem:

Lz＝λDz (4)

λ representation feature value, the characteristic of correspondence vector is z, minimum non-zero eigenwert characteristic of correspondence vector v _FExpression.

Cut apart the indication vector:

x＝(x ₁，x ₂，…x _n) ^T∈R ⁿ (5)

$x_i=\left\{\begin{array}{c}1,i\∈A_1\\ -1,i\∈A_2\end{array}\right.---\left(6\right)$

A ₁And A ₂Represent that respectively will scheme G is divided into the node that two subgraphs comprise, and cuts apart the situation of cutting apart that the indication vector x has indicated figure, order

k＝v _F +α (7)

α be one by-∞ to+number that ∞ changes, form the corresponding indication vector x of cutting apart according to the symbol of element of k:

$x_i=\left\{\begin{array}{c}1,k_i\&GreaterEqual;0\\ -1,k_i<0\end{array}\right.---\left(8\right)$

Get rid of the situations that in x, element all equates, be i.e. nonsensical cutting apart, can be formed to many n-1 and cut apart the indication vector x.

The 4th step further was specially:

Fragile section C should satisfy as much as possible:

$\min \underset{l_{\mathrm{ij}}\&Element;C}{\mathrm{\&Sigma;}}{y}_{\mathrm{ij}},\max \underset{l_{\mathrm{ij}}\&Element;C}{\mathrm{\&Sigma;}}\left|P_{\mathrm{ij}}\right|---\left(9\right)$

l _ijThe circuit of expression connected node i and node j, y _ijCircuit l _ijAdmittance, suppose that circuit can't harm, P _ijCircuit l _ijThe meritorious trend of ground state, (9) first of formulas are revised as:

$\min \frac{\underset{l_{\mathrm{ij}}\&Element;C}{\mathrm{\&Sigma;}}{y}_{\mathrm{ij}}}{\underset{i\&Element;A_1,t\&Element;V}{\mathrm{\&Sigma;}}{y}_{\mathrm{it}}\underset{j\&Element;A_2,t\&Element;V}{\mathrm{\&Sigma;}}{y}_{\mathrm{jt}}}\left(10\right)$

Consider on this basis active power, require the meritorious larger of circuit transmission, build about cutting apart the objective function of indication vector:

$\min \frac{\underset{i\&Element;A_1,j\&Element;A_2}{\mathrm{\&Sigma;}}\frac{y_{\mathrm{ij}}}{\left|P_{\mathrm{ij}}\right|}{(x_i-x_j)}^2}{\underset{i\&Element;A_1,t\&Element;V}{\mathrm{\&Sigma;}}\frac{y_{\mathrm{it}}}{\left|P_{\mathrm{ij}}\right|}\underset{j\&Element;A_2,t\&Element;V}{\mathrm{\&Sigma;}}\frac{y_{\mathrm{jt}}}{\left|P_{\mathrm{ij}}\right|}}---\left(11\right)$

With x _iBe relaxed to real number field, according to Rayleigh theorem, x=v _FThe time, formula (11) obtains minimum value; With gained x difference substitution formula (11) calculating target function value in the 3rd step.

Technical characterstic of the present invention and effect:

By method provided by the present invention, utilization is composed the power method based on the electric system branch road of electrical distance and trend distribution, set up and be applicable to the nowadays more flexible and changeable interconnected network electric system graph theory model of the method for operation, and then utilize the standard blanking method to build about cutting apart the objective function of indication vector, rapidly and accurately in recognition system by a little less than contact on physical arrangement, and trend is carried the fragile section that larger circuit forms in system.The attention degree of raising to these sections has great importance to formulating effective prevention and control measure and off-the-line control strategy.

Description of drawings

The electric system vulnerable profile recognition method flow diagram of cutting based on standard that Fig. 1 is proposed by the invention.

Fig. 2 IEEE 30 node system figure and the fragile section that identifies.

Embodiment

The present invention is intended to a kind of approximation method fast, from the fragile section of this class of the whole aspect identification of electrical network.Be the combination of some circuits due to section, identify namely np complete problem of fragile section, simultaneously because actual electric network is huge, the section quantity that comprises is also very large, is difficult to obtain all sections.In recent years, existing proposition utilizes the spectrogram opinion to realize spectral clustering analysis, Grid division, the power transmission network subregion of Voltage Stability Analysis and the determining of key sections of Power grid structure, and these achievements in research show that the spectrogram opinion provides a kind of approximate data of Simple fast for np complete problem.

The purpose of this invention is to provide a kind of fast method of identifying the electric system vulnerable section, set up the graph theory abstract model of electric system in the method, utilize the standard blanking method of spectral graph theory, a little less than contacting from the whole aspect identification of electrical network by physical arrangement, and trend is carried larger circuit in system, consist of the fragile section in electric system, have great importance to formulating effective prevention and control measure and off-the-line control strategy.

The present invention proposes a kind of electric system vulnerable profile recognition method of cutting based on standard, is used for the safe in-service monitoring of power system static, and its step is as follows:

The first step: according to the needs of fragile profile recognition, calculate the electrical network Real-time Power Flow, utilize based on the electric system branch road of electrical distance and trend distribution and compose the power method, set up applicable electric system graph theory model;

Second step: set up this abstract model Laplacian Matrix and degree matrix, and calculate Laplacian Matrix about minimum non-zero eigenwert and the characteristic of correspondence vector thereof of degree matrix;

The 3rd step: the direction that provides according to this proper vector is divided into two groups with the node in system, forms corresponding cutting apart and indicates vector, searches for the section of this vector correspondence heuristicly;

The 4th step: a little less than contact on the circuit physical arrangement in fragile section, and trend is carried larger characteristics in system, builds the objective function of indicating vector about cutting apart based on the standard blanking method, and each is cut apart indication vector calculation target function value;

The 5th step: the screening objective function of sening as an envoy to is obtained the indication vector cut apart of minimum value, and the section of this vector correspondence is exactly fragile section.

The present invention according to the needs of fragile profile recognition, calculates the electric network swim distribution situation in step 1, utilize based on the electric system branch road of electrical distance and trend distribution and compose the power method, sets up applicable electric system graph theory model.

Contain the graph theory model G=(V, E, W) on n node and m bar limit, V is vertex set, and the bus in corresponding real system, generator, load, E are the limit collection, and the branch road of corresponding connection bus comprises circuit and transformer, and W is weight matrix, weighting matrix elements w _ijBe connected node v _iAnd v _jThe weight on limit.Utilization is composed the power method based on the electric system branch road of electrical distance and trend distribution branch road is composed power:

$w_{\mathrm{ij}}=\frac{y_{\mathrm{ij}}}{\left|P_{\mathrm{ij}}\right|}---\left(1\right)$

y _ijThe line admittance of connected node i and node j, P _ijTo flow to the meritorious trend of ground state of node j from node i.Suppose that circuit can't harm.Admittance is less, and the physical connection of circuit is more weak.The meritorious trend absolute value of circuit is larger, and the rear impact on system of breaking down is larger.Therefore, little weight means weak and this circuit important role in trend distributes of internodal physical connection.Weight w _ijVariation with Line Flow changes, and it has reflected the power characteristic of this circuit, and also the variation with the line reactance parameter changes, and has reflected simultaneously the network characteristic of this circuit.

In step 2, set up Laplacian Matrix and the degree matrix of electric system graph theory abstract model, and calculate Laplacian Matrix about minimum non-zero eigenwert and the characteristic of correspondence vector thereof of degree matrix.

The degree of node i is:

$d_i=\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{w}_{\mathrm{ij}}---\left(2\right)$

The degree matrix D is with d ₁... d _nDiagonal matrix for diagonal element.Laplacian matrix of graphs L is:

L＝D-W (3)

Method for Solving Generalized Eigenproblem:

Lz＝λDz (4)

λ representation feature value, the characteristic of correspondence vector is z.Use v _FExpression minimum non-zero eigenwert characteristic of correspondence vector.

In step 3, the direction that provides according to this proper vector is divided into two groups with the node in system, forms corresponding cutting apart and indicates vector, searches for the section of this vector correspondence heuristicly.

Cut apart the indication vector:

x＝(x ₁，x ₂，…x _n) ^T∈R ⁿ (5)

$x_i=\left\{\begin{array}{c}1,i\&Element;A_1\\ -1,i\&Element;A_2\end{array}\right.---\left(6\right)$

A ₁And A ₂Represent that respectively will scheme G is divided into the node that two subgraphs comprise.Cut apart the situation of cutting apart that the indication vector x has indicated figure.Order

k＝v _F+α (7)

α be one by-∞ to+number that ∞ changes.Form the corresponding indication vector x of cutting apart according to the symbol of element of k:

$x_i=\left\{\begin{array}{c}1,k_i\&GreaterEqual;0\\ -1,k_i<0\end{array}\right.---\left(8\right)$

Get rid of the situations that in x, element all equates, be i.e. nonsensical cutting apart, can be formed to many n1 and cut apart the indication vector x.

In step 4, a little less than contact on the circuit physical arrangement in fragile section, and trend is carried larger characteristics in system, builds the objective function of indicating vector about cutting apart based on the standard blanking method, and each is cut apart indication vector calculation target function value.

If interregional grid structure a little less than, and the trend on cut set is very little, multiple failure on this section occurs, the general extensive transfer that can not cause trend, the safety and stability problem be difficult for to occur, otherwise, when carrying the line failure than megatrend in system, very easily cause the extensive transfer of trend, cause the safety and stability problem.Therefore fragile section C should satisfy as much as possible:

$\min \underset{l_{\mathrm{ij}}\&Element;C}{\mathrm{\&Sigma;}}{y}_{\mathrm{ij}},\max \underset{l_{\mathrm{ij}}\&Element;C}{\mathrm{\&Sigma;}}\left|P_{\mathrm{ij}}\right|---\left(9\right)$

l _ijThe circuit of expression connected node i and node j, y _ijCircuit l _ijAdmittance, suppose that circuit can't harm, P _ijCircuit l _ijThe meritorious trend of ground state.Line admittance is less, shows that circuit is longer, and internodal physical connection is more weak, the admittance of cut set and Characterized the connection tightness degree of subsystem.

Larger, show that the meritorious trend of carrying on circuit in cut set is larger, the effect of cut set on trend distributes is more important.Utilize the standard blanking method can fast searching to making two contacts between subgraph weak, and subgraph internal connection cut set closely.According to the objective function of standard blanking method, for the section of avoiding identifying comprises the generator outlet circuit, (9) first of formulas are revised as:

$\min \frac{\underset{l_{\mathrm{ij}}\&Element;C}{\mathrm{\&Sigma;}}{y}_{\mathrm{ij}}}{\underset{i\&Element;A_1,t\&Element;V}{\mathrm{\&Sigma;}}{y}_{\mathrm{it}}\underset{j\&Element;A_2,t\&Element;V}{\mathrm{\&Sigma;}}{y}_{\mathrm{jt}}}\left(10\right)$

Consider on this basis active power, require the meritorious larger of circuit transmission, build about cutting apart the objective function of indication vector:

$\min \frac{\underset{i\&Element;A_1,j\&Element;A_2}{\mathrm{\&Sigma;}}\frac{y_{\mathrm{ij}}}{\left|P_{\mathrm{ij}}\right|}{(x_i-x_j)}^2}{\underset{i\&Element;A_1,t\&Element;V}{\mathrm{\&Sigma;}}\frac{y_{\mathrm{it}}}{\left|P_{\mathrm{ij}}\right|}\underset{j\&Element;A_2,t\&Element;V}{\mathrm{\&Sigma;}}\frac{y_{\mathrm{jt}}}{\left|P_{\mathrm{ij}}\right|}}---\left(11\right)$

With x _iBe relaxed to real number field, according to Rayleigh theorem, x=v _FThe time, formula (11) obtains minimum value.With gained x difference substitution formula (11) calculating target function value in the 3rd step.Be the combination of some circuits due to section, have 2 for the system that m bar branch road is arranged ^m-1 section, and the method that the present invention proposes is according to v _FThe direction of proper vector is searched for section heuristicly, with 2 ^m-1 section is reduced to n-1, greatly reduces computation complexity.

In step 5, the screening objective function of sening as an envoy to is obtained the indication vector cut apart of minimum value, and the section of this vector correspondence is exactly fragile section.

By method provided by the present invention, utilization is composed the power method based on the electric system branch road of electrical distance and trend distribution, set up and be applicable to the nowadays more flexible and changeable interconnected network electric system graph theory model of the method for operation, and then utilize the standard blanking method to build about cutting apart the objective function of indication vector, rapidly and accurately in recognition system by a little less than contact on physical arrangement, and trend is carried the fragile section that larger circuit forms in system.The attention degree of raising to these sections has great importance to formulating effective prevention and control measure and off-the-line control strategy.

Further illustrate the present invention below in conjunction with the drawings and specific embodiments.

The fragile fractograph analysis of embodiment 1:IEEE30 node example system

The first step is calculated the electric network swim distribution situation, utilizes based on the electric system branch road of electrical distance and trend distribution and composes the power method, sets up applicable electric system weighted graph model.Table 1 has been listed the node output power in IEEE 30 node system embodiment, and line parameter circuit value and trend that table 2 has been listed IEEE 30 node systems distribute, and table 3 has been listed the weight of circuit in the graph model.

The node output power of table 1IEEE 30 node systems

Line parameter circuit value and the trend of table 2IEEE 30 node systems distribute

The weight of circuit in table 3IEEE 30 node system graph models

Second step is set up Laplacian Matrix and the degree matrix of electric system graph theory abstract model, and calculates Laplacian Matrix about minimum non-zero eigenwert and the characteristic of correspondence vector thereof of degree matrix.

Laplacian Matrix is about the minimum non-zero eigenvalue λ=0.0415 of degree matrix, characteristic of correspondence vector v _F=[0.0651-0.0630-0.0607-0.0571-0.0623-0.0497-0.0577-0.0497-0.0548-0.0185-0.0572-0.0342-0.0357-0.0298-0.0261-0.0287-0.0248-0.0343-0.0353-0.0336 0.0658 0.11690.0641 0.1210 0.1214 0.1267 0.0979-0.0451 0.1111 0.1121] ^T

The 3rd step, in the direction that minimum non-zero eigenwert characteristic of correspondence vector provides, formation system all nodes corresponding cut apart the indication vector.

At first, make x ⁰Be complete 1 column vector of 30 dimensions, h=1; Then, find out v _FIn the row at the little element of h place, make x ^h-1The element of middle corresponding row is-1, forms x ^h, h=h+1 repeats this step, until h=30 forms altogether 29 and cuts apart the indication vector.For example, find out v _FMiddle least member-0.0651 place behavior 1 makes x ⁰The element of middle corresponding row is-1, forms to cut apart the indication vector x ¹Find out v _FIn the second little element-0.0630 place behavior 2, make x ¹The element of middle corresponding row is-1, forms to cut apart the indication vector x ², until form x ²⁹

The 4th step: build about cutting apart the indication vector x ^hObjective function:

$\min \frac{\underset{i\&Element;A_1,j\&Element;A_2}{\mathrm{\&Sigma;}}\frac{y_{\mathrm{ij}}}{\left|P_{\mathrm{ij}}\right|}{(x_i^h-x_j^h)}^2}{\underset{i\&Element;A_1,t\&Element;V}{\mathrm{\&Sigma;}}\frac{y_{\mathrm{it}}}{\left|P_{\mathrm{ij}}\right|}\underset{j\&Element;A_2,t\&Element;V}{\mathrm{\&Sigma;}}\frac{y_{\mathrm{jt}}}{\left|P_{\mathrm{ij}}\right|}}---\left(11\right)$

And each is cut apart indication vector calculation target function value, as table 4.

The node output power of table 4 IEEE 30 node systems

The 5th step: the screening objective function of sening as an envoy to is obtained the indication vector cut apart of minimum value, and the section of this vector correspondence is exactly fragile section.

The minimum value of objective function is 0.0631, h=21, and the corresponding indication vector of cutting apart is x ²¹=[1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1 111111 1-1 1 1] ^TThe section of this vector correspondence is by 4 circuit 10-21,10-22, and 15-23,28-27 forms, and 9 nodes (21,22,23,24,25,26,27,29,30) and 21 nodes that are left are separated.Dotted line red in Fig. 2 is the fragile section that this method identifies in IEEE 30 node systems.

The mean value of the meritorious absolute value of system line is 8.39MW, analyzes the mean value of active power of gained section take this method as 11.70MW.All the mean value than system line active power absolute value is large for the active power absolute value that transmits on all formation circuits of this section simultaneously, and average reactance is the average reactance 0.2p.u. greater than whole circuits, illustrates that the gained section also forms by connecting weak circuit.Above sample calculation analysis proof this method can effectively identify the fragile section that the heavier circuit of load forms by physical connection is weak.

Claims (5)

1. an electric system vulnerable profile recognition method of cutting based on standard, is characterized in that, comprises the steps:

The first step: according to the needs of fragile profile recognition, calculate the electrical network Real-time Power Flow, utilize based on the electric system branch road of electrical distance and trend distribution and compose the power method, set up applicable electric system graph theory model;

Second step: set up this abstract model Laplacian Matrix and degree matrix, and calculate Laplacian Matrix about minimum non-zero eigenwert and the characteristic of correspondence vector thereof of degree matrix;

The 3rd step: the direction that provides according to this proper vector is divided into two groups with the node in system, forms corresponding cutting apart and indicates vector, searches for the section of this vector correspondence heuristicly;

The 4th step: a little less than contact on the circuit physical arrangement in fragile section, and trend is carried larger characteristics in system, builds the objective function of indicating vector about cutting apart based on the standard blanking method, and each is cut apart indication vector calculation target function value;

The 5th step: the screening objective function of sening as an envoy to is obtained the indication vector cut apart of minimum value, and the section of this vector correspondence is exactly fragile section.

2. electric system vulnerable profile recognition method of cutting based on standard as claimed in claim 1, it is characterized in that, utilize the electric system branch road that distributes based on electrical distance and trend to compose the power method and be specially: the graph theory model G=(V, the E that contain n node and m bar limit, W), V is vertex set, and the bus in corresponding real system, generator, load, E are the limit collection, the branch road of corresponding connection bus, comprise circuit and transformer, W is weight matrix, weighting matrix elements w _ijBe connected node v _iAnd v _jThe weight on limit; Utilization is composed the power method based on the electric system branch road of electrical distance and trend distribution branch road is composed power:

$w_{\mathrm{ij}}=\frac{y_{\mathrm{ij}}}{\left|P_{\mathrm{ij}}\right|}---\left(1\right)$

y _ijThe line admittance of connected node i and node j, P _ijTo flow to the meritorious trend of ground state of node j from node i.

3. electric system vulnerable profile recognition method of cutting based on standard as claimed in claim 1, is characterized in that, calculate Laplacian Matrix and be specially about minimum non-zero eigenwert and the characteristic of correspondence vector thereof of spending matrix: the degree of node i is:

$d_i=\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{w}_{\mathrm{ij}}---\left(2\right)$

The degree matrix D is with d ₁... d _nBe the diagonal matrix of diagonal element, Laplacian Matrix L is:

L＝D-W (3)

Method for Solving Generalized Eigenproblem:

Lz＝λDz (4)

λ representation feature value, the characteristic of correspondence vector is z, minimum non-zero eigenwert characteristic of correspondence vector v _FExpression.

4. electric system vulnerable profile recognition method of cutting based on standard as claimed in claim 1, is characterized in that, cuts apart the indication vector:

Cut apart the indication vector:

x＝(x ₁，x ₂，…x _n) ^T∈R ⁿ (5)

$x_i=\left\{\begin{array}{c}1,i\&Element;A_1\\ -1,i\&Element;A_2\end{array}\right.---\left(6\right)$

A ₁And A ₂Represent that respectively will scheme G is divided into the node that two subgraphs comprise, and cuts apart the situation of cutting apart that the indication vector x has indicated figure, order

k＝v _F+α (7)

α be one by-∞ to+number that ∞ changes, form the corresponding indication vector x of cutting apart according to the symbol of element of k:

$x_i=\left\{\begin{array}{c}1,k_i\&GreaterEqual;0\\ -1,k_i<0\end{array}\right.---\left(8\right)$

Get rid of the situations that in x, element all equates, be i.e. nonsensical cutting apart, can be formed to many n-1 and cut apart the indication vector x.

5. electric system vulnerable profile recognition method of cutting based on standard as claimed in claim 1, is characterized in that, the 4th step further was specially:

Fragile section C should satisfy as much as possible:

$\min \underset{l_{\mathrm{ij}}\&Element;C}{\mathrm{\&Sigma;}}{y}_{\mathrm{ij}},\max \underset{l_{\mathrm{ij}}\&Element;C}{\mathrm{\&Sigma;}}\left|P_{\mathrm{ij}}\right|---\left(9\right)$

l _ijThe circuit of expression connected node i and node j, y _ijCircuit l _ijAdmittance, suppose that circuit can't harm, P _ijCircuit l _ijThe meritorious trend of ground state, (9) first of formulas are revised as:

$\min \frac{\underset{l_{\mathrm{ij}}\&Element;C}{\mathrm{\&Sigma;}}{y}_{\mathrm{ij}}}{\underset{i\&Element;A_1,t\&Element;V}{\mathrm{\&Sigma;}}{y}_{\mathrm{it}}\underset{j\&Element;A_2,t\&Element;V}{\mathrm{\&Sigma;}}{y}_{\mathrm{jt}}}---\left(10\right)$

Consider on this basis active power, require the meritorious larger of circuit transmission, build about cutting apart the objective function of indication vector:

$\min \frac{\underset{i\&Element;A_1,j\&Element;A_2}{\mathrm{\&Sigma;}}\frac{y_{\mathrm{ij}}}{\left|P_{\mathrm{ij}}\right|}{(x_i-x_j)}^2}{\underset{i\&Element;A_1,t\&Element;V}{\mathrm{\&Sigma;}}\frac{y_{\mathrm{it}}}{\left|P_{\mathrm{ij}}\right|}\underset{j\&Element;A_2,t\&Element;V}{\mathrm{\&Sigma;}}\frac{y_{\mathrm{jt}}}{\left|P_{\mathrm{ij}}\right|}}---\left(11\right)$

With x _iBe relaxed to real number field, according to Rayleigh theorem, x=v _FThe time, formula (11) obtains minimum value; With gained x difference substitution formula (11) calculating target function value in the 3rd step.

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