CN1976160A - A large electric system vulnerable line identifying method - Google Patents

Abstract

A method for identifying weak line of large-scale power system includes defining line electric inductivity with weighting of the line to be load sum bore on and passed through shortest electric path between power generator and load in system then revising said path by raising electric inductivity index of line in power system to be maximum electric inductivity value of electric inductivity on all lines adjacent to said path.

Description

A kind of method of large electric system vulnerable line identifying

Technical field

The invention belongs to power system security defense technique field, particularly a kind of method of electric system vulnerable line identifying.

Background technology

In recent years, electric power system the taking place frequently of accident of having a power failure on a large scale causes the concern of people to extensive cascading failure and electric system vulnerable.Vulnerability analysis to electric power system is based upon on the basis of differential equation group always, promptly by each element in the system is set up detail mathematic model, with the form of time-domain-simulation system is carried out dynamic analysis.This analytical method is along with the continuous expansion of electric power system scale demonstrates its limitation day by day: 1. too pay attention to the individual dynamic characteristic of each element, and ignore the global behavior of system; 2. detailed Mathematical Modeling need consume a large amount of computing times; 3. the N-X vulnerability analysis runs into the problem of multiple shot array again when large scale electric network.Therefore press for the new systematic analytic method of development and study the fragility of complicated electric power system.

In recent years, the research of complex network is that a new direction has been opened up in the electric system vulnerable analysis.Existing scholar uses Complex Networks Theory that the fragility of electric power networks is analyzed: Meng Zhongwei etc. have verified that two large regional grids of Sino-U.S. all belong to the worldlet network, and qualitative analysis the influence of worldlet network characteristic to chain collapse; Ding Ming etc. have analyzed the influence of electrical network overall structure to chain collapse from topological structure of electric, and the higher contact node of point out the to be situated between number and the number of degrees plays a part to add fuel to the flames to the propagation of fault when guaranteeing the electrical network connectedness.

Pertinent literature: (1) Meng Zhongwei, Lu Zongxiang, Song Jingyan. the worldlet topological model comparative analysis [J] of Sino-U.S.'s electrical network. Automation of Electric Systems, 2004,28 (15): 21-24. (2) fourth is bright, Han Pingping. based on the large-scale power grid vulnerability assessment [J] of worldlet topological model. Proceedings of the CSEE, 2005,25 (supplementary issue): 118-122.

Summary of the invention

The objective of the invention is at the problems referred to above, a kind of method of electric system vulnerable line identifying is provided.

It comprises the steps:

(1) the actual electric network data reduction by electric power networks obtains connection weight matrix { E _IjAnd generator weight matrix { W _i;

(2) according to connection weight matrix { E _Ij, the shortest electrical distance matrix { L of the whole network of employing Floyed algorithm computation _Ij;

(3) the shortest electrical path collection S between use Floyed all generators of algorithm computation and load _L

(4) according to the shortest electrical path collection S _L, calculate every preliminary heavy circuit Jie of cum rights of circuit and count B _LWeighted(m, n);

(5) heavy circuit Jie of cum rights number is revised obtained heavy circuit Jie of final cum rights and count B _LWeighted(m, n) ';

(6) use the ordering of bubbling method, heavy circuit Jie of those cum rights counts B _LWeighted' extra high circuit is vulnerable line.

The step of the actual electric network data reduction method of described electric power networks is as follows:

(1) all circuits the wiring of consideration in power plant and transformer station.Network model among the present invention is used for the vulnerability analysis of real system, therefore requires it that physical system is had higher modeling accuracy;

(2) all nodes are divided into 3 set in the network: generator set of node S _G, load bus collection S _L, the set of node S of transformer station _T

(3) all power circuits all are reduced to the undirected limit of having the right, and the weight definition of circuit is the reactance value of circuit;

(4) power transmission line of merging parallel lines on same tower is disregarded the shunt capacitance branch road, makes model become simple graph;

(5) weights W of generator _iBe defined as the active power output of generator i under current operational mode.

The shortest described electrical path is the path that the shortest electrical path of any point-to-point transmission in the network is defined as circuit weight sum minimum along the line in all paths of point-to-point transmission; The shortest electrical distance is defined as the circuit weight sum the most along the line of short electrical path.

Heavy circuit Jie of described preliminary cum rights counts B _LWeighted(m, computational methods n) are according to following formula:

$B_{\mathrm{LWeighted}}(m,n)=\underset{k\∈S_w}{\mathrm{\Σ}}{W}_k$

S wherein _wExpression is through circuit (m, the set of the generator sequence number of the shortest electrical path n).

Heavy circuit Jie of described final cum rights counts B _LWeighted(m, n) ' modification method is according to following formula:

B _LWeighted(m，n)′＝MAX(B _LWeighted(m，i)，B _LWeighted(j，n))

Wherein (m is i) with (j n) represents the circuit that all and node m link to each other with node n respectively.

The vulnerable line of the present invention in can the identification electric power networks, particularly can identifying those, to bear power few but system's fragility is had the circuit of significant impact because of its specific position in electric network composition.With respect to for the vulnerability analysis method of time-domain-simulation, this method can greatly reduce amount of calculation, accelerates computational speed.

Description of drawings

Fig. 1 is the schematic diagram of existing problem when calculating the shortest electrical path;

Fig. 2 is an example electrical network schematic diagram;

Fig. 3 is the spinner velocity aberration curve of generator 32 when different faults;

Fig. 4 is heavy circuit Jie of cum rights number curve;

Fig. 5 is the key rack schematic diagram of Central China-Chongqing of Sichuan electrical network.

Embodiment

The present invention is from the angle of complex network, uses heavy circuit Jie of cum rights number to make the fragility index and comes vulnerable line in the identification electric power networks.

Thought research electrical network characteristic with complex network at first is reduced to topological model with electrical network, and its principle is:

(1) all circuits the wiring of consideration in power plant and transformer station.Network model among the present invention is used for the vulnerability analysis of real system, therefore requires it that physical system is had higher modeling accuracy.

(2) all nodes are divided into 3 set in the network: generator set of node S _G, load bus collection S _L, the set of node S of transformer station _T, N is arranged respectively _G, N _LAnd N _TIndividual.

(3) all power circuits (power transmission line, transformer branch road) all are reduced to the undirected limit of having the right.The weight definition of circuit is the reactance value of circuit.And the shortest electrical path of any point-to-point transmission is circuit weight along the line and minimum path in all paths of point-to-point transmission in the define grid.The circuit weight the most along the line of short electrical path and be the shortest electrical distance.

(4) power transmission line of merging parallel lines on same tower is disregarded shunt capacitance branch road (eliminating from ring and multiple circuit), makes model become simple graph.

(5) the weight w of generator _iBe defined as the active power output of generator i under current operational mode.

Just become a sparse connected graph that n node and k bar circuit are arranged through simplifying electrical network, by n * n rank connection weight matrix { E _IjAnd n * 1 rank weight matrix { W _iRepresent.

Circuit Jie in the Complex Networks Theory counts B _LBe meant that circuit is by the number of times of shortest path process between all nodes in the network.In the practical power systems except that network topology structure, the distribution of generator and exert oneself and also the stability of a system is had significant impact.Therefore define heavy circuit Jie of cum rights here and counted B _LWeightedIf (m, n) by the shortest electrical path process between generator i and load j, then this circuit need be born the load W that generator i is brought to circuit _i(m, heavy circuit Jie of cum rights n) counts B to the definition circuit _LWeighted(m, n) for its because of by the shortest electrical distance between generator in the network and the load through the load of bearing and, as the formula (1).

$B_{\mathrm{LWeighted}}(m,n)=\underset{k\∈S_w}{\mathrm{\Σ}}{W}_k---\left(1\right)$

S wherein _wExpression is through circuit (m, the set of the generator sequence number of the shortest electrical path n).

This method may be walked around some important line when calculating the shortest electrical distance, as shown in Figure 1.If path (1,3,4) are with respect to path (1,2,4) shorter, then all from node 1 to node 4 the shortest electrical path all can walk through (1,3,4) walk around the road through (1,2,4), heavy circuit Jie of the cum rights number that causes circuit (1,2) and circuit (2,4) is far below circuit (1,3) and circuit (3,4).But the three-phase earth fault of the arbitrary circuit in circuit in real system (1,2) and the circuit (1,3) can make that all a large amount of power inject to the fault point, causes the interruption of passway for transmitting electricity from left to right, that is to say that two kinds of faults are close to the influence of system.Therefore take Jie with circuit in the electric power networks to count index and bring up to all circuit intermediaries that are adjacent before revising and count the way of the highest Jie's numerical value of index and remedy this defective, as the formula (2).

B _LWeighted(m，n)′＝MAX(B _LWeighted(m，i)，B _LWeighted(j，n)) (2)

Wherein (m is i) with (j n) represents the circuit that all and node m link to each other with node n respectively.

Based on above analysis, the implementation step that provides the identification vulnerable line is as follows:

(1) simplifies by the data based simplification principle above of the actual electric network of electric power networks, obtain connection weight matrix { E _IjAnd generator weight matrix { W _i.

(2) according to connection weight matrix { E _Ij, the shortest electrical distance matrix { L of the whole network of use Floyed algorithm computation _Ij.

(3) use Floyed algorithm is sought the shortest electrical path collection S between all generators and load _L

(4) use formula (1) is to the shortest electrical path collection S _LHandle, calculate every preliminary heavy circuit Jie of cum rights of circuit and count B _LWeighted(m, n).

(5) heavy circuit Jie of the cum rights that use formula (2) is obtained step 3 number is revised and is obtained heavy circuit Jie of final cum rights and count B _LWeighted(m, n) '.

(6) use the ordering of bubbling method, heavy circuit Jie of those cum rights counts B _LWeighted' extra high circuit is vulnerable line.

Below by a concrete identification step of simple case explanation.The example electrical network has 4 load buses as shown in Figure 2 in this electrical network, 2 generator nodes, and the weight of all circuits is 1 among the figure, generator G ₁ Weight $W_{G_{}}$ ${{}_1}_{}=20,$ Generator G ₄ Weight $W_{G_{}}$ ${{}_4}_{}=30.$ Concrete computational process sees table 1 for details.

Table 1 identification step example

Step 1	To network modelling	Slightly
			Step 2	Calculate { L ij}	Slightly
Step 3	Seek the shortest path collection S between all generators and load L	1-2-3-6-7-8-9 1-2-3-6-7-8-10 1-2-3-6-11-12 1-2-3-6-11-13 4-5-3-6-7-8-9 4-5-3-6-7-8-10 4-5-3-6-11-12 4-5-3-6-11-13
			Step	Calculate all according to formula (1)	B 1-2＝80 B 7-8＝100 B 2-3＝80 B 8-9＝50 B 3-5＝120 B 8-10＝50

4	Heavy circuit Jie of cum rights number that circuit is preliminary	B 3-6＝200 B 6-11＝100 B 3-7＝0 B 11-12＝50 B 6-7＝100 B 11-13＝50 B 4-5＝120
			Step 5	Revise and obtain heavy circuit Jie of final cum rights number according to formula (2)	B 1-2＝80 B 7-8＝100 B 2-3＝200 B 8-9＝100 B 3-5＝200 B 8-10＝100 B 3-6＝200 B 6-11＝200 B 3-7＝200 B 11-12＝100 B 6-7＝200 B 11-13＝100 B 4-5＝120
Step 6	Press heavy circuit Jie of cum rights and count B LWeighted' fragility ordering, determine that fragility sorts preceding 6 and be vulnerable line	B 2-3＝200 B 7-8＝100 B 3-5＝200 B 8-9＝100 B 3-6＝200 B 8-10＝100 B 3-7＝200 B 11-12＝100 B 6-7＝200 B 11-13＝100 B 6-11＝200 B 1-2＝80 B 4-5＝120

Below by embodiment, further illustrate validity of the present invention and characteristics thereof.

Embodiment 1

Use this method that IEEE 39 examples are carried out the vulnerable line identification, choose heavy circuit Jie of cum rights number and surpass 6000 the vulnerable line that is, have 13.Use PST 2.0 softwares to carry out the time domain checking then.In the time of 0.1 second, three-phase ground short circuit fault is set in the higher bus exit of circuit both end voltage, 0.225 remove fault during second (because IEEE 39 node systematic comparisons are strong, 100ms is little to the stability influence of system with interior fault, so will be extended for 125ms fault time), write down the generator speed aberration curve of all 10 generators in 10 seconds.Except that those and the direct generator coupled of faulty line, if the rotating speed when the generator speed deviation not quite and finally can be got back to system stability judges that this circuit is non-vulnerable line, shown in chain-dotted line in the accompanying drawing 3; If the excessive and rotating speed finally can not get back to system stability time of generator speed deviation is arranged, judges that then this circuit is a vulnerable line, shown in solid line in the accompanying drawing 3.

Checking wherein has 4 circuits to confirm as vulnerable line through time domain, the results are shown in table 2; Heavy circuit Jie of cum rights counts rank 13 later circuits and is non-vulnerable line through the time domain checking.

Vulnerable line in table 2 IEEE 39 node systems

Line name	Heavy circuit Jie of cum rights number	The ordering of heavy circuit Jie of cum rights number	Circuit active power (perunit value)	The ordering of circuit active power
					L 15-16	11200	1	-3.1491	20
L 16-17	11200	2	2.2999	27
					L 2-25	8000	8	-2.3908	26
L 21-22	6800	11	-6.0442	5

Can see and remove circuit L _21-22Outward, the active power that other three-line transmitted belongs to medium in the whole network.The common trait of these vulnerable lines is all to be on the important passway for transmitting electricity, and its fault can directly cause the interruption of passway for transmitting electricity, causes the subregion power shortage, so that system's generation merit angle unstability.Such as circuit L _15-16Perhaps circuit L _16-17Three-phase ground short circuit fault taking place, cause the power of generator 33,34,35,36 to send outside, cause a large amount of power shortages of system's remainder, finally causes system's merit angle unstability.The power that can not only bear according to circuit when therefore analyzing the vulnerable line of electric power networks also need be considered circuit residing position in whole network simultaneously.

Embodiment 2

Central China-Chongqing of Sichuan electrical network is carried out heavy circuit Jie of cum rights number that the vulnerable line identification gets each bar circuit.The size of 3142 circuits according to heavy circuit Jie of cum rights numerical value is arranged in order from left to right, as shown in Figure 4.Curve locates to occur a flex point at heavy circuit Jie of cum rights numerical value about 10000.Increase slowly at heavy circuit Jie of flex point left side cum rights numerical value; And want fast many in the speed that heavy circuit Jie of flex point right side left side cum rights numerical value increases.There is the very high circuit of the heavy circuit Jie's numerical value of a small amount of cum rights in this explanation in network.Conservatively choosing heavy circuit Jie of cum rights number is vulnerable line greater than 10000 circuit, totally 571.

Use PSASP6.2 electric power system analysis-by-synthesis application program to carry out the time domain checking then.In the time of 0.1 second, three-phase ground short circuit fault is set in the higher bus exit of circuit both end voltage, 0.4 remove fault during second (because Central China-Chongqing of Sichuan electrical network is strongr, 100ms is little to the stability influence of system with interior fault, so will be extended for 300ms fault time), write down the rotating speed aberration curve of all 316 generators in 10 seconds.The decision principle embodiment 1 of vulnerable line.

Through the time-domain-simulation checking, in these 571 circuits, have 153 and be vulnerable line; And heavy circuit Jie of cum rights number all is non-vulnerable line less than 10000 circuit empirical tests.

Accompanying drawing 5 is the trunk figure of this large regional grid, and heavy circuit Jie of cum rights counts has 7 to appear among this trunk figure and (all use thick line to indicate in the drawings) in the circuit of rank preceding 10.Node 1 among the figure is a left side, a Three Gorges transformer station, and node 5 is a bamboo hat transformer station, and node 7 is left transformation power station, and node 8 is Jiangling transformer station.See that on the whole these high Jie count circuit and node all is in the Chongqing of Sichuan electrical network on the passage of Central China Power Grid transferring electricity from the west to the east, carry 1520MW under this passage normal condition.If these circuit generation catastrophe failures (three-phase ground short circuit fault) can cause passway for transmitting electricity to interrupt, cause a large amount of power shortages of the inner generation of receiving-end system (Central China Power Grid), finally cause the Central China Power Grid unstability.

Also finding in test has the electric pressure of 30 circuits smaller or equal to 220kV in 153 vulnerable lines.This and common viewpoint are far from each other, because the power that the 220kV circuit is carried is wanted much less for the 500kV circuit.By analyzing, find that the power that these circuits mostly are positioned at generator node close quarters sends outside on the passage, this explanation is when judging the electric power networks vulnerable line, and the power that can not only rely on circuit and transmitted also will be considered circuit residing position in the electrical network overall structure simultaneously.This example illustrates that also this method is can those through-put powers of identification few, but because its specific position in whole electric network composition has the circuit of significant impact to system.

Claims (5)

1. the discrimination method of an electric system vulnerable line is characterized in that, it comprises the steps:

(1) the actual electric network data reduction by electric power networks obtains connection weight matrix { E _IjAnd generator weight matrix { W _i;

(2) according to connection weight matrix { E _Ij, the shortest electrical distance matrix { L of the whole network of employing Floyed algorithm computation _Ij;

(3) the shortest electrical path collection S between use Floyed all generators of algorithm computation and load _L

(4) according to the shortest electrical path collection S _L, calculate every preliminary heavy circuit Jie of cum rights of circuit and count B _LWeighted(m, n);

(5) heavy circuit Jie of cum rights number is revised obtained heavy circuit Jie of final cum rights and count B _LWeighted(m, n) ';

(6) use the ordering of bubbling method, heavy circuit Jie of those cum rights counts B _LWeighted' extra high circuit is vulnerable line.

2, the discrimination method of a kind of electric system vulnerable line according to claim 1 is characterized in that: the step of described electric power networks method for simplifying is as follows:

(1) all circuits the wiring of consideration in power plant and transformer station.Network model among the present invention is used for the vulnerability analysis of real system, therefore requires it that physical system is had higher modeling accuracy;

(2) all nodes are divided into 3 set in the network: generator set of node S _G, load bus collection S _L, the set of node S of transformer station _T

(3) all power circuits all are reduced to the undirected limit of having the right, and the weight definition of circuit is the reactance value of circuit;

(4) power transmission line of merging parallel lines on same tower is disregarded the shunt capacitance branch road, makes model become simple graph;

(5) the weights W i of generator is defined as the active power output of generator i under current operational mode.

3, the discrimination method of a kind of electric system vulnerable line according to claim 1 is characterized in that: the shortest described electrical path is that in any all paths of point-to-point transmission the path of circuit weight sum minimum along the line in the electric power networks; The shortest described electrical distance is the circuit weight sum the most along the line of short electrical path.

4, the discrimination method of a kind of electric system vulnerable line according to claim 1 is characterized in that: heavy circuit Jie of described preliminary cum rights counts B _LWeighted(m n) is to use following formula to calculate:

$B_{\mathrm{LWeighted}}(m,n)=\underset{k\∈S}{\mathrm{\Σ}}{W}_k$

S wherein _wExpression is through circuit (m, the set of the generator sequence number of the shortest electrical path n).

5, the discrimination method of a kind of electric system vulnerable line according to claim 1 is characterized in that: heavy circuit Jie of described final cum rights counts B _LWeighted(m, n) ' be according to following formula correction:

B _LWeighted(m，n)′＝MAX(B _LWeighted(m，i)，B _LWeighted(j，n))

Wherein (m is i) with (j n) represents the circuit that all and node m link to each other with node n respectively.

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