CN102684191A - Matrix network topology analysis method - Google Patents

Abstract

The invention discloses a matrix network topology analysis method which comprises the following steps: compiling a node switch association table, a node branch association table, a node information table and a bus information table of a network to be analyzed; determining a connected graph module by invoking a matrix local multiplication to obtain all buses in the current voltage grade; determining the connected graph module by invoking the matrix local multiplication to obtain all electric islands; and directly forming two arrays of an adjacent matrix , i.e. an array AR and an array AC stored according to a sparse matrix when the connected graph module is determined by the matrix local multiplication. The matrix network topology analysis method has the benefits that the initial value I of a connected matrix (adjacent matrix) is not required to be formed according to the prior art, so that the internal memory is remarkably saved, and the network topology analysis speed is improved; and the initial value I of the connected matrix is not required to be stored through a two-dimensional array, the sparsely-stored arrays AR and AC of the adjacent matrix are one-dimensional arrays, and when procedures are designed, the cohesion of each module and the data encapsulation of data are improved, and the readability and the transplantability of the procedures are improved.

Description

A kind of matrix method network topology analytical method

Technical field

The present invention relates to a kind of power system network topology analyzing method, particularly a kind of matrix method network topology analytical method.

Background technology

The power system network topological analysis is a very important basic module in EMS and the distribution management system, and its effect is to be converted into the Mathematical Modeling that network analysis needs to the physical model of electric power system.Network topology analytical method comprises bus analysis and electric island analysis two parts, though this two parts effective object is different, method is identical, is connected graph problem analysis in the graph theory.

In the graph theory, the annexation of the node of a figure can be represented with adjacency matrix A.Adjacency matrix is the square formation (n is the node number) of a n * n, the incidence relation of its expression between each node, and when node i and node j are associated, matrix element a _Ij Be 1; When node i and node j are unconnected, a _IjBe 0.Internodal one-level connected relation in the adjacency matrix presentation graphs.

If adjacency matrix involution then obtain connection matrix T, I and II connected relation between node in the presentation graphs is called 2 grades and is communicated with matrixes.Connection matrix multiply by adjacency matrix again and then obtains 3 grades of connection matrixes.Repeat this process, can obtain the n-1 cascade at most for the figure of n node and be open to the custom and be.If certain grade of all connected relations between node among the figure that have been communicated with matrix description then are called the full-mesh matrix.In the full-mesh matrix, the node that connects together belongs to a connected graph, can comprise several connected graphs among the figure in the graph theory.

Network topology mainly contains search method and matrix method as the connected graph analytical method.Simple, the understanding easily of search method principle, but it is loaded down with trivial details to programme; Matrix method is asked for the full-mesh matrix through matrix multiple and carried out topological analysis, and is relatively more directly perceived, but memory demand and amount of calculation are all very big.In existing matrix method, the matrix multiple number of times is n – 2 times when adopting the matrix involution to demand perfection connection matrix, and the matrix multiple number of times is log when adopting quadratic method to demand perfection connection matrix ₂(n – 1), computing time is all very long.Disclosed a kind of sparse matrix method power system network topology analyzing method among the Chinese patent ZL 201010509562.0, analysis speed has had large increase, but still the leeway of further raising is arranged.

The principle of matrix method network topology analytical method is following:

The demand perfection matrix method formula of connection matrix of adjacency matrix involution does

T ^(k+1)＝T ^(k)·A （1）

In the formula: subscript (k) representes that this connection matrix is communicated with matrix for the k level.Adjacency matrix is represented the one-level connected relation, thereby 1 grade of connection matrix is exactly an adjacency matrix.

When employing formula (1) was demanded perfection connection matrix, the computing formula of connection matrix element did

$t_{\mathrm{ij}}^{(k+1)}=\underset{m=1}{\overset{n}{\mathrm{\Σ}}}{t}_{\mathrm{im}}^{\left(k\right)}{a}_{\mathrm{mj}}---\left(2\right)$

In the formula: n is the node number.

Symmetry according to adjacency matrix has a _Mj=a _Jm, then formula (2) can be rewritten as:

$t_{\mathrm{ij}}^{(k+1)}=\underset{m=1}{\overset{n}{\mathrm{\Σ}}}{t}_{\mathrm{im}}^{\left(k\right)}{a}_{\mathrm{jm}}---\left(3\right)$

Chinese patent ZL 201010509562.0 proposition methods are following:

Connection matrix reflects internodal annexation, is communicated with matrix for a m level, and whether what need care is to be communicated with between two nodes, need not know between two nodes it is what connection.Therefore whenever obtain an element; Can upgrade matrix element with it at once; Can be reflected in two nodes early in the connection matrix through the indirect annexation of plurality of nodes, help obtaining quickly the full-mesh matrix, also save the memory space of preserving new connection matrix.This pattern (3) is revised as:

$t_{\mathrm{ij}}=\underset{m=1}{\overset{n}{\mathrm{\Σ}}}{t}_{\mathrm{im}}{a}_{\mathrm{jm}}---\left(4\right)$

Formula (4) is no longer distinguished t _IjBe the element of which rank of connection matrix, can represent whether related getting final product of node i and node j.

Adjacency matrix and connection matrix all are symmetrical matrixes, when calculating connection matrix, only calculate the last triangle element of connection matrix, and following triangle element can obtain according to symmetry:

$t_{\mathrm{ij}}=\underset{m=1}{\overset{n}{\mathrm{\Σ}}}{t}_{\mathrm{im}}{a}_{\mathrm{jm}}$ j=i+1,…,n （5）

Connection matrix is a dense matrix, and adjacency matrix is a sparse matrix, during calculating formula (5), adopts sparse matrix technology:

To the storage of adjacency matrix, can use following two arrays:

(a) array AC is used for writing down the row number of each nonzero element;

(b) array AR is used for writing down the position of first nonzero element of every row in array AC, total n+1 element, wherein AR _N+1Be used for confirming the final position of capable last nonzero element of n.

Application number is that 201110249362.0 invention application has disclosed a kind of matrix method network topology analytical method; On the basis of ZL 201010509562.0, improve; Make its analysis speed that large increase arranged; Memory demand also greatly reduces (only using a n rank square formation), but memory demand is still big, analysis process more complicated still.

Summary of the invention

For solving the problems referred to above that prior art exists, the present invention will design a kind of fast operation, littler, the simpler matrix method network topology analytical method of analysis process of memory demand.

For realizing above-mentioned purpose, technical scheme of the present invention is following: a kind of matrix method network topology analytical method may further comprise the steps:

Steps A 1: node switch contingency table, node branch road contingency table, informational table of nodes, the bus information table of the establishment electrical network of analyzing;

Steps A 2: the current electric pressure sign KV=1 that will carry out the bus analysis is set, the analysis of beginning bus;

Steps A 3: connect the close switch number according to each node and carry out the node optimization numbering by order from big to small;

Steps A 4: form the adjacency matrix of reflection node through the close switch annexation;

Steps A 5: call the local multiplication of matrix and confirm the connected graph module, obtain all buses in the current electric pressure;

Steps A 6: electric pressure sign KV=KV+1 is set, prepares to analyze next electric pressure;

Steps A 7: judge whether KV counts KVS greater than total electric pressure, if KV is greater than KVS then enter into the electric island of steps A 8 beginning and analyze; If KV is not more than KVS, then turn back to steps A 3, proceed the bus analysis of new electric pressure;

Steps A 8: form bus branch road contingency table according to branch road two end nodes;

Steps A 9: carry out bus optimization numbering by order from big to small according to each bus institute chord way;

Steps A 10: form the adjacency matrix of reflection bus through the branch road annexation;

Steps A 11: call the local multiplication of matrix and confirm the connected graph module, obtain all electric islands;

Steps A 5 confirms that with the local multiplication of steps A 11 described matrixes the step of connected graph module is following:

Step B1: two array AR that form that adjacency matrix press that sparse matrix stores and array AC;

Step B2: be communicated with the array Group zero clearing of figure number under the expression node;

Step B3: connection figure number k=0 is set, current line i=1 is set;

Step B4: judge that whether Group [i] is 0, if be not 0, then goes to step B20;

Step B5: it is capable to utilize array AR and AC to form the i of initial connection matrix;

Step B6: connection figure number k=k+1 is set;

Step B7: make Group [i]=k;

Step B8: the sign change=0 of connection matrix element variation is set, is provided with as prostatitis j=i+1;

Step B9: judge whether j counts n greater than node, if j greater than n, then goes to step B19;

Step B10: judgment matrix element t _IjWhether be 0, if t _IjBe not 0, then go to step B16;

Step B11: make l=AR _j

Step B12: judge that whether l is less than AR _J+1If l is not less than AR _J+1, then go to step B16;

Step B13: make m=AC _l

Step B14: judge t _ImWhether be 1, if t _ImBe not 1, then make l=l+1, go to step B12;

Step B15: make t _Ij=1, change=1;

Step B16: judgment matrix element t _IjWhether be 1, if t _IjBe not 1, then go to step B18;

Step B17: make Group [j]=k;

Step B18: make j=j+1, go to step B9;

Step B19: judge whether change equals 1,, then forward step B8 to if change equals 1;

Step B20: make i=i+1;

Step B21: judge whether i counts n greater than node,, then go to step B4 if i is not more than n; Otherwise, finish.

Compared with prior art, the present invention has following beneficial effect:

1, prior art need form connection matrix initial value T (adjacency matrix) and the sparse storage array of adjacency matrix AR, AC, and the present invention no longer need form connection matrix initial value T (adjacency matrix), has saved internal memory significantly.

2, the present invention is directly generated the initial value of the connection matrix element of this delegation by array AR, AC when needs are handled certain delegation (algorithm need not handled all row) of connection matrix, leaves in the interim array.

3, the present invention need not generate connection matrix initial value T (adjacency matrix), and the network topology analysis speed increases.

4, the present invention need be with 2 dimension groups storage connection matrix initial value T (adjacency matrix); The sparse storage array of adjacency matrix AR, AC are 1 dimension groups; During programming, improve " cohesion " and the encapsulation property of data of each module, improved the readable and portable of program.

Description of drawings

3 in the total accompanying drawing of the present invention, wherein:

Fig. 1 is the flow chart that the local multiplication of matrix of the present invention is confirmed the connected graph module.

Fig. 2 is the network diagram of the inventive method embodiment.

Fig. 3 is the topological diagram of the inventive method embodiment.

Among Fig. 2,1, the electric pressure KV1 at factory station one, 2, the electric pressure KV2 at factory station two, 3, first electric pressure KV3 at factory station three, 4, second electric pressure KV4 at factory station three.Switch has the closure state that is of black filling among the figure, and packless is off-state.

Embodiment

Below in conjunction with accompanying drawing the present invention is described further.Accompanying drawing 2 is physical models of a simple electric power networks; Comprise 3 factory's 4 electric pressures in station; Wherein the electric pressure KV1 at factory station one has the electric pressure KV2 at 8 nodes, factory station two to have first electric pressure KV3 at 4 nodes, factory station three to have second electric pressure KV4 at 2 nodes, factory station 3 that 6 nodes are arranged; Node has omitted isolating switch by the electric pressure numbering among the figure.In the electric pressure KV1 of simple network shown in Figure 2, carry out the bus analysis according to the inventive method flow process shown in Figure 1, the data that need when adopting algorithm of the present invention comprise:

Node switch contingency table, node branch road contingency table, informational table of nodes, bus information table.Wherein branch road comprises circuit, transformer, reactor, capacitor.

In the electric pressure KV1 of simple network shown in Figure 2, carry out step that bus analyzes (in order to reduce the complexity of elaboration, it is technological that the node optimization numbering is not introduced in following introduction, does the understanding that does not influence the inventive method like this) as follows:

Step 1: form adjacency matrix.The adjacency matrix of this example electric pressure KV1 is following:

$A=\left[\begin{array}{cccccccc}1& 0& 1& 0& 1& 0& 0& 0\\ 0& 1& 1& 0& 0& 0& 0& 0\\ 1& 1& 1& 0& 0& 0& 0& 0\\ 0& 0& 0& 1& 0& 0& 0& 1\\ 1& 0& 0& 0& 1& 0& 1& 0\\ 0& 0& 0& 0& 0& 1& 0& 1\\ 0& 0& 0& 0& 1& 0& 1& 0\\ 0& 0& 0& 1& 0& 1& 0& 1\end{array}\right]$

It is following that the present invention only need store above-mentioned adjacency matrix by sparse matrix technology:

The data of array AC are: 1,3,5,2,3,1,2,3,4,8,1,5,7,6,8,5,7,4,6,8;

The data of array AR are: 1,4,6,9,11,14,16,18,21.

Step 2: be communicated with the array Group zero clearing of figure number under the expression node.

Step 3: connection figure number k=0 is set, current line i=1 is set.

Step 4: judge that whether Group [i] is 0, if be not 0, then goes to step 20.

Since Group [1]=0, execution in step 5.

Step 5: it is capable following to utilize array AR and AC to form the i of initial connection matrix:

T=[1?0?1?0?1?0?0?0]

Step 6: connection figure number k=k+1 is set.k＝0+1=1。

Step 7: make Group [i]=k.Group[1]＝1。

Step 8: the sign change=0 of connection matrix element variation is set, is provided with as prostatitis j=i+1.

Make change=0, j=1+1=2, the 1st row the 2nd column element of generation connection matrix.

Step 9: judge whether j counts n greater than node, if j greater than n, then goes to step 19.

N=8, j=2 is not more than n, execution in step 10.

Step 10: judgment matrix element t _IjWhether be 0, if t _IjBe not 0, then go to step 16.

Because t ₁₂=0, execution in step 11.

Step 11: make l=AR _jl＝AR ₂＝4

Step 12: judge that whether l is less than AR _J+1If l is not less than AR _J+1, then go to step 16.

AR ₃=6, l=4 is less than AR ₃, execution in step 13.

Step 13: make m=AC _lm＝AC ₄＝2。

Step 14: judge t _ImWhether be 1, if t _ImBe not 1, then make l=l+1, go to step 12.

Because t ₁₂=0, make l=4+1=5, go to step 12.

Step 12: judge that whether l is less than AR _J+1If l is not less than AR _J+1, then go to step 16.

AR ₃=6, l=5 is less than AR ₃, execution in step 13.

Step 13: make m=AC _lm＝AC ₅＝3。

Step 14: judge t _ImWhether be 1, if t _ImBe not 1, then make l=l+1, go to step 12.

Because t ₁₃=1, execution in step 15.

Step 15: make t _Ij=1, change=1.

Make t ₁₂=1, change=1.

Step 16: judgment matrix element t _IjWhether be 1, if t _IjBe not 1, then go to step 18.

Because t ₁₂=1, execution in step 17.

Step 17: make Group [j]=k.Group[2]＝1。

Step 18: make j=j+1, go to step 9.

Make j=2+1=3, go to step 9, generate the 1st row the 3rd column element of connection matrix.

Step 9: judge whether j counts n greater than node, if j greater than n, then goes to step 19.

N=8, j=3 is not more than n, execution in step 10.

Step 10: judgment matrix element t _IjWhether be 0, if t _IjBe not 0, then go to step 16.

Because t ₁₃=1, be not 0, go to step 16.

Step 16: judgment matrix element t _IjWhether be 1, if t _IjBe not 1, then go to step 18.

Because t ₁₃=1, execution in step 17.

Step 17: make Group [j]=k.Group[3]=1。

Step 18: make j=j+1, go to step 9.

Make j=3+1=4, go to step 9, generate the 1st row the 4th column element of connection matrix.

Step 9: judge whether j counts n greater than node, if j greater than n, then goes to step 19.

N=8, j=4 is not more than n, execution in step 10.

Step 10: judgment matrix element t _IjWhether be 0, if t _IjBe not 0, then go to step 16.

Because t ₁₄=0, execution in step 11.

Step 11: make l=AR _jl＝AR ₄＝9。

Step 12: judge that whether l is less than AR _J+1If l is not less than AR _J+1, then go to step 16.

AR ₅=11, l=9 is less than AR ₅, execution in step 13.

Step 13: make m=AC _lm＝AC ₉＝4。

Step 14: judge t _ImWhether be 1, if t _ImBe not 1, then make l=l+1, go to step 12.

Because t ₁₄=0, make l=9+1=10, go to step 12.

Step 12: judge that whether l is less than AR _J+1If l is not less than AR _J+1, then go to step 16.

AR ₅=11, l=10 is less than AR ₅, execution in step 13.

Step 13: make m=AC _lm＝AC ₁₀＝8。

Step 14: judge t _ImWhether be 1, if t _ImBe not 1, then make l=l+1, go to step 12.

Because t ₁₈=0, make l=10+1=11, go to step 12.

Step 12: judge that whether l is less than AR _J+1If l is not less than AR _J+1, then go to step 16.

AR ₅=11, l=11 is not less than AR ₅, then go to step 16.

Step 16: judgment matrix element t _IjWhether be 1, if t _IjBe not 1, then go to step 18.

Because t ₁₄=0, then go to step 18.

Step 18: make j=j+1, go to step 9.

Make j=4+1=5, go to step 9, generate the 1st row the 5th column element of connection matrix.

Step 9: judge whether j counts n greater than node, if j greater than n, then goes to step 19.

N=8, j=5 is not more than n, execution in step 10.

Step 10: judgment matrix element t _IjWhether be 0, if t _IjBe not 0, then go to step 16.

Because t ₁₅=1, be not 0, go to step 16.

Step 16: judgment matrix element t _IjWhether be 1, if t _IjBe not 1, then go to step 18.

Because t ₁₅=1, execution in step 17.

Step 17: make Group [j]=k.Group[5]=1。

Step 18: make j=j+1, go to step 9.

Make j=5+1=6, go to step 9, generate the 1st row the 6th column element of connection matrix.

Step 9: judge whether j counts n greater than node, if j greater than n, then goes to step 19.

N=8, j=6 is not more than n, execution in step 10.

Step 10: judgment matrix element t _IjWhether be 0, if t _IjBe not 0, then go to step 16.

Because t ₁₆=0, execution in step 11.

Step 11: make l=AR _jl＝AR ₆＝14。

Step 12: judge that whether l is less than AR _J+1If l is not less than AR _J+1, then go to step 16.

AR ₇=16, l=14 is less than AR ₇, execution in step 13.

Step 13: make m=AC _lm＝AC ₁₄＝6。

Step 14: judge t _ImWhether be 1, if t _ImBe not 1, then make l=l+1, go to step 12.

Because t ₁₆=0, make l=14+1=15, go to step 12.

Step 12: judge that whether l is less than AR _J+1If l is not less than AR _J+1, then go to step 16.

AR ₇=16, l=15 is less than AR ₇, execution in step 13.

Step 13: make m=AC _lm＝AC ₁₅＝8。

Step 14: judge t _ImWhether be 1, if t _ImBe not 1, then make l=l+1, go to step 12.

Because t ₁₈=0, make l=15+1=16, go to step 12.

Step 12: judge that whether l is less than AR _J+1If l is not less than AR _J+1, then go to step 16.

AR ₇=16, l=16 is not less than AR ₇, then go to step 16.

Step 16: judgment matrix element t _IjWhether be 1, if t _IjBe not 1, then go to step 18.

Because t ₁₆=0, then go to step 18.

Step 18: make j=j+1, go to step 9.

Make j=6+1=7, go to step 9, generate the 1st row the 7th column element of connection matrix.

Step 9: judge whether j counts n greater than node, if j greater than n, then goes to step 19.

N=8, j=7 is not more than n, execution in step 10.

Step 10: judgment matrix element t _IjWhether be 0, if t _IjBe not 0, then go to step 16.

Because t ₁₇=0, execution in step 11.

Step 11: make l=AR _jMake l=AR ₇=16.

Step 12: judge that whether l is less than AR _J+1If l is not less than AR _J+1, then go to step 16.

AR ₈=18, l=16 is less than AR ₈, execution in step 13.

Step 13: make m=AC _lm＝AC ₁₆＝5。

Step 14: judge t _ImWhether be 1, if t _ImBe not 1, then make l=l+1, go to step 12.

Because t ₁₅=1, execution in step 15.

Step 15: make t _Ij=1, change=1.

Make t ₁₇=1, change=1.

Step 16: judgment matrix element t _IjWhether be 1, if t _IjBe not 1, then go to step 18.

Because t ₁₇=1, execution in step 17.

Step 17: make Group [j]=k.Group[7]=1。

Step 18: make j=j+1, go to step 9.

Make j=7+1=8, go to step 9, generate the 1st row the 8th column element of connection matrix.

Step 9: judge whether j counts n greater than node, if j greater than n, then goes to step 19.

N=8, j=8 is not more than n, execution in step 10.

Step 10: judgment matrix element t _IjWhether be 0, if t _IjBe not 0, then go to step 16.

Because t ₁₈=0, execution in step 11.

Step 11: make l=AR _jMake l=AR ₈=18.

Step 12: judge that whether l is less than AR _J+1If l is not less than AR _J+1, then go to step 16.

AR ₉=21, l=18 is less than AR ₉, execution in step 13.

Step 13: make m=AC _lm＝AC ₁₈＝4。

Step 14: judge t _ImWhether be 1, if t _ImBe not 1, then make l=l+1, go to step 12.

Because t ₁₄=0 is not 1, makes l=l+1=18+1=19, goes to step 12.

Step 12: judge that whether l is less than AR _J+1If l is not less than AR _J+1, then go to step 16.

AR ₉=21, l=19 is less than AR ₉, execution in step 13.

Step 13: make m=AC _lm＝AC ₁₉＝6。

Step 14: judge t _ImWhether be 1, if t _ImBe not 1, then make l=l+1, go to step 12.

Because t ₁₆=0 is not 1, makes l=l+1=19+1=20, goes to step 12.

Step 12: judge that whether l is less than AR _J+1If l is not less than AR _J+1, then go to step 16.

AR ₉=21, l=20 is less than AR ₉, execution in step 13.

Step 13: make m=AC _lm＝AC ₂₀＝8。

Step 14: judge t _ImWhether be 1, if t _ImBe not 1, then make l=l+1, go to step 12.

Because t ₁₈=0 is not 1, makes l=l+1=20+1=21, goes to step 12.

Step 12: judge that whether l is less than AR _J+1If l is not less than AR _J+1, then go to step 16.

AR ₉=21, l=21 is not less than AR ₉, then go to step 16.

Step 16: judgment matrix element t _IjWhether be 1, if t _IjBe not 1, then go to step 18.

Because t ₁₈=0 is not 1, then goes to step 18.

Step 18: make j=j+1, go to step 9.

J=8+1=9 goes to step 9.

Step 9: judge whether j counts n greater than node, if j greater than n, then goes to step 19.

N=8, j=9 go to step 19 greater than n.

Step 19: judge whether change equals 1,, then forward step 8 to if change equals 1;

Because change=1 goes to step 8, recomputates the 1st row matrix element.Final connection matrix the 1st row element of accomplishing is following:

T=[1?1?1?0?1?0?1?0]

Array Group is:

Group=[1?1?1?0?1?0?1?0]

The situation that the 2nd of calculating connection matrix walks to the 4th row matrix element is following:

After the 1st row element calculated and accomplishes, this row element no longer changed, change=0, execution in step 20.

Step 20: make i=i+1.i＝1+1=2。

Step 21: judge whether i counts n greater than node,, then go to step 4 if i is not more than n.Otherwise, finish.

N=8, i=2 is not more than n, execution in step 4.

Step 4: judge that whether Group [i] is 0, if be not 0, then goes to step 20.

Group [2]=1 is not 0, then goes to step 20.

Step 20: make i=i+1.i＝2+1=3。

Step 21: judge whether i counts n greater than node,, then go to step 4 if i is not more than n.Otherwise, finish.

N=8, i=3 is not more than n, execution in step 4.

Step 4: judge that whether Group [i] is 0, if be not 0, then goes to step 20.

Group [3]=1 is not 0, then goes to step 20.

Step 20: make i=i+1.i＝3+1=4。

Step 21: judge whether i counts n greater than node,, then go to step 4 if i is not more than n.Otherwise, finish.

N=8, i=4 is not more than n, execution in step 4.

Step 4: judge that whether Group [i] is 0, if be not 0, then goes to step 20.

Group [4]=0, execution in step 5 forms the 4th of initial connection matrix and goes, and carries out the 4th row matrix element and calculates, and step is with the 1st row matrix element calculated case.

The 4th of connection matrix after the calculating is gone as follows:

T=[0?0?0?1?0?1?0?1]

Array Group is:

Group=[1?1?1?2?1?2?1?2]

The value of the 5th～8 element of array Group is not 0 at this moment, shows that the 5th～8 row element does not need to calculate, and the bus analysis in the electric pressure KV1 finishes.

Can be known by array Group: node 1.1, node 1.2, node 1.3, node 1.5, node 1.7 belong to same connected graph; Their female wire size all is 1, and promptly bus 1 comprises node 1.1, node 1.2, node 1.3, node 1.5, node 1.7 totally 5 nodes; Node 1.4, node 1.6, node 1.8 belong to a connected graph, and its female wire size is 2, and expression bus 2 comprises node 1.4, node 1.6, node 1.8 totally 3 nodes.

The bus analysis of other electric pressure is identical with the bus analytical method of electric pressure KV1, repeats no more.Bus analysis result embodiment illustrated in fig. 2 is seen table 1.

The bus analysis result of table 1 Fig. 2 embodiment

Embodiment illustrated in fig. 2ly obtain network shown in Figure 3 through the bus analysis, it is carried out electric island analyze, analytical method is identical with the method that bus is analyzed, and the result sees table 2, totally 2 electric islands, and wherein electric island A comprises power supply, is the work island; Electric island B does not comprise power supply, is dead island.

The electric island analysis result of table 2 Fig. 3 embodiment

An alternative embodiment of the invention is that the Hangzhou electrical network to a certain period carries out topological analysis:

The Hangzhou electrical network is a large-scale power grid, and scale was at that time: 187 at factory station, 715 of physics bus section, busbar sections; 7329 on switch, 318 of transmission lines, 250 in transformer; Wherein two winding transformer is 127,123 of three-winding transformers, 11 of series reactor branch roads; 232 of reactive power compensation electric capacity, 27 of reactive power compensation reactance.Several 7097 of node, branch road comprise totally 825 of transmission line, transformer (three-winding transformer is 3 branch roads) and series reactor branch roads.

Topological analysis forms 957 of buses, 49 on electric island (wherein 1 is the island of living).The bus number on island alive is 704, and 48 dead islands comprise 122 buses altogether, and remaining is isolated bus.

Computing environment is the PC of the Intel Pentium of dominant frequency 1.10GHz.Relatively see table 3 computing time of the present invention and patent applied for (number of applying for a patent is ZL201110249362.0), visible the inventive method and existing matrix method compare, and computational speed significantly improves.

Table 3 the present invention and existing method result of calculation are relatively

When this example formed electric island, non-isolated bus number was 826, and the adjacency matrix nonzero element is 2438.When adjacency matrix adopted sparse storage, the size of AC array was 2438, and the size of AR array is 827, then needs 3265 integers of storage altogether; When adopting full battle array to store is one 826 rank square formation, totally 682276 Boolean type numbers.General programming language integers accounts for 4B (byte) internal memory; Boolean type accounts for the 1B internal memory.The Boolean type of some system such as Visual C++4.2 version accounts for the 4B internal memory.The memory demand of the different storage modes of adjacency matrix is seen table 4.

The memory demand of table 4 adjacency matrix

The inventive method only need be stored adjacency matrix by sparse mode, re-uses a size in addition and be the interim array of 826 Boolean type; The adjacency matrix of ZL201110249362.0 method adopt simultaneously sparse mode store and expire the battle array mode (as the initial value of connection matrix) storage.If Boolean type accounts for the 1B internal memory, total memory demand of the inventive method is 13060+826=13886B.Total memory demand of ZL201110249362.0 method is 13060+682276=695336B.The memory demand of the adjacency matrix of the inventive method is merely 1/50 of ZL201110249362.0 method.If Boolean type accounts for the 4B internal memory, total memory demand of the inventive method is 13060+826 * 4=16364B.Total memory demand of ZL201110249362.0 method is 13060+2729104=2742164B.The memory demand of the adjacency matrix of the inventive method is merely 1/168 of ZL201110249362.0 method.It is thus clear that the inventive method and existing algorithm are relatively, memory requirements obviously reduces.

The adjacency matrix of ZL201110249362.0 method adopt simultaneously sparse mode store and expire the battle array mode (as the initial value of connection matrix) storage; Wherein full battle array storage mode adopts one 2 dimension group when programming; But when design is asked for the full-mesh matrix function through matrix multiple; 2 dimension groups of variable size can't pass to function through function parameters; The 2 dimension groups that can only transmit fixed size have reduced the flexibility of function, or the mode of employing global variable is stored the full battle array of adjacency matrix." cohesion " and the encapsulation of data of function stressed in programming, reduces the coupling with other module as far as possible.Adopt the mode of global variable to store " cohesion " that data then reduce function, the coupling of increase and other module, the independence and the readability of reduction function are unfavorable for the transplanting of program.The adjacency matrix of the inventive method only adopts sparse mode to store, and adopts 1 dimension group during programming, and when design was asked for the full-mesh matrix function through matrix multiple, 1 dimension group of variable size can pass to function through parameter easily.It is thus clear that the inventive method and existing algorithm are relatively, when the full-mesh matrix function is asked in design, be superior to the ZL201110249362.0 method aspect the readability of the encapsulation of " cohesion " of function, data, program and the transplantability.

Claims (1)

1. matrix method network topology analytical method may further comprise the steps:

Steps A 1: node switch contingency table, node branch road contingency table, informational table of nodes, the bus information table of the establishment electrical network of analyzing;

Steps A 2: the current electric pressure sign KV=1 that will carry out the bus analysis is set, the analysis of beginning bus;

Steps A 3: connect the close switch number according to each node and carry out the node optimization numbering by order from big to small;

Steps A 4: form the adjacency matrix of reflection node through the close switch annexation;

Steps A 5: call the local multiplication of matrix and confirm the connected graph module, obtain all buses in the current electric pressure;

Steps A 6: electric pressure sign KV=KV+1 is set, prepares to analyze next electric pressure;

Steps A 7: judge whether KV counts KVS greater than total electric pressure, if KV is greater than KVS then enter into the electric island of steps A 8 beginning and analyze; If KV is not more than KVS, then turn back to steps A 3, proceed the bus analysis of new electric pressure;

Steps A 8: form bus branch road contingency table according to branch road two end nodes;

Steps A 9: carry out bus optimization numbering by order from big to small according to each bus institute chord way;

Steps A 10: form the adjacency matrix of reflection bus through the branch road annexation;

Steps A 11: call the local multiplication of matrix and confirm the connected graph module, obtain all electric islands;

It is characterized in that: steps A 5 confirms that with the local multiplication of steps A 11 described matrixes the step of connected graph module is following:

Step B1: two array AR that form that adjacency matrix press that sparse matrix stores and array AC;

Step B2: be communicated with the array Group zero clearing of figure number under the expression node;

Step B3: connection figure number k=0 is set, current line i=1 is set;

Step B4: judge that whether Group [i] is 0, if be not 0, then goes to step B20;

Step B5: it is capable to utilize array AR and AC to form the i of initial connection matrix;

Step B6: connection figure number k=k+1 is set;

Step B7: make Group [i]=k;

Step B8: the sign change=0 of connection matrix element variation is set, is provided with as prostatitis j=i+1;

Step B9: judge whether j counts n greater than node, if j greater than n, then goes to step B19;

Step B10: judgment matrix element t _IjWhether be 0, if t _IjBe not 0, then go to step B16;

Step B11: make l=AR _j

Step B12: judge that whether l is less than AR _J+1If l is not less than AR _J+1, then go to step B16;

Step B13: make m=AC _l

Step B14: judge t _ImWhether be 1, if t _ImBe not 1, then make l=l+1, go to step B12;

Step B 15: make t _Ij=1, change=1;

Step B16: judgment matrix element t _IjWhether be 1, if t _IjBe not 1, then go to step B18;

Step B17: make Group [j]=k;

Step B18: make j=j+1, go to step B9;

Step B19: judge whether change equals 1,, then forward step B8 to if change equals 1;

Step B20: make i=i+1;

Step B21: judge whether i counts n greater than node,, then go to step B4 if i is not more than n; Otherwise, finish.

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