CN101938124A - Matrix analysis method of power system network topology - Google Patents

Abstract

The invention relates to a matrix analysis method of power system network topology, which still utilizes the advantages of a matrix method to obtain a full-access matrix by two matrix multiply operations and improves matrix analysis speed. The matrix analysis method comprises the following steps of: optimizing and numbering nodes according to the number of closed switches connected with the nodes from big to small and optimizing and numbering a bus according to the number of branch circuits connected with the bus from big to small, thereby reducing the matrix multiply operand; and preserving values of a communication matrix and the full-access matrix by directly using adjacency matrixes without needing a special sandwich matrix in order to save a half of a computer storage space and reduce matrix assignment operation. Compared with the traditional matrix method, the matrix analysis method has smaller calculation amount and the more obvious efficiency the more top points.

Description

A kind of matrix analysis method of power system network topology

Technical field

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

Background technology

The network topology analysis of electric power system is a very important module in Utilities Electric Co.'s EMS and the distribution management system, and its effect is that the physical model of electric power system is converted into the required Mathematical Modeling of network analysis.The physical model of electric power system has been described the relation that all primary equipments of electric power system link together by node, and equipment comprises generator, load, circuit, transformer, capacitor, reactor, circuit breaker, isolating switch etc.For electric power system is analyzed, must form the circuit model of reflection bus and branch road relation by the network topology analysis.

The network topology analysis comprises bus analysis and electric island analysis two parts, and the bus analysis is the synthetic bus of a set of node that connects together by Closing Switch, and it is that a bus that connects together by branch road assembles electric island that electric island is analyzed.Though this two parts analytic target difference, method is identical, all belongs to the method that connected graph is analyzed in the graph theory.As the network topology analytical method of electric power system connected graph analytical method, mainly contain two kinds of analytical methods of search method and matrix method at present.Search method is to carry out network topology by the method for search node and adjacent node annexation to analyze, simple, the understanding easily of search method principle, but it is loaded down with trivial details to programme; Matrix method is that connection relation between nodes is expressed as adjacency matrix, then it is carried out the method that topological analysis is carried out in matrix operation, and the matrix method programming is fairly simple, but memory demand and amount of calculation are all very big.In existing matrix method, the matrix multiple number of times is n-1 time when connecting matrix to adopt the matrix involution to demand perfection, and the matrix multiple number of times is log when connecting matrix to adopt quadratic method to demand perfection ₂(n-1), amount of calculation is all very big.

Summary of the invention

For overcoming the deficiency of above-mentioned matrix method, purpose of the present invention is exactly to propose a kind of network topology analytical method that the matrix method programming is simple relatively but also can save calculator memory and operation time that not only had.

For achieving the above object, the present invention proposes a kind of matrix analysis method of power system network topology, promptly based on the network topology analytical method of the accurate quadratic method of adjacency matrix, concrete step is:

Step 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.

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

Step 3: connect the Closing Switch number according to each node and carry out the node optimization numbering by order from big to small.

Step 4: form about the adjacency matrix of node by the Closing Switch annexation.

Step 5: call the accurate quadratic method module of matrix, generate the full matrix of connecting.

Step 6: matrix is connected in the analysis of line scanning method entirely, obtains all buses in the current electric pressure.

Step 7: current electric pressure KV=KV+1 is set.

Step 8: judge whether KV counts KVS greater than total electric pressure, if KV is greater than KVS then enter into the electric island of step 9 beginning and analyze; If KV is not more than KVS, then turn back to step 3, proceed the bus analysis of new electric pressure.

Step 9: form bus branch road contingency table according to branch road two end nodes.

Step 10: carry out bus optimization numbering by order from big to small according to each bus institute chord way.

Step 11: form the adjacency matrix of reflection bus by the branch road annexation.

Step 12: call the accurate quadratic method module of matrix, generate the full matrix of connecting.

Step 13: matrix is connected in the analysis of line scanning method entirely, obtains all electric islands.

The step that the present invention connects matrix formation module entirely is:

Step 1: the inferior number variable l=1 that matrix square is set.

Step 2: current line i=1 is set.

Step 3: be provided with as prostatitis j=1.

Step 4: judgment matrix element a _IjWhether be 0, if a _IjBe not 0, then go to step 10.

Step 5: k=1 is set.

Step 6: judge a _IkAnd a _JkWhether all be 1,, then go to step 8 if the two is not all to be 1.

Step 7: make a _Ij=1, a _Ji=1, go to step 10.

Step 8: make k=k+1.

Step 9: judge that k whether greater than number of vertex n, if k is not more than n, then turns back to step 6.

Step 10: make j=j+1.

Step 11: whether judge j greater than n,, then turn back to step 4 if j is not more than n.

Step 12: make i=i+1.

Step 13: whether judge i greater than n,, then turn back to step 3 if i is not more than n.

Step 14: make l=l+1.

Step 15: judge that whether l is greater than 2.If l greater than 2, finishes; Otherwise, turn back to step 2.

The present invention adopts the analysis of line scanning method to connect matrix entirely, and step is:

Step 1: the Group[of record node group number] the array zero clearing, present node i=1, group number m=0.

Step 2: judge Group[i] whether be 0, if be 0, then enter into the node grouping situation that step 3 begins to analyze present node i place group; If be not 0, then enter into step 7, continue to analyze the grouping situation of next node.

Step 3: group number m=m+1, row j=i+1.

Step 4: establish Group[i]=m.

Step 5: judge the full matrix element t that connects _IjWhether be 1,, then make Group[j if be 1]=m.

Step 6: make j=j+1.

Step 7: whether judge j greater than n,, then turn back to step 5 if j is not more than n.

Step 8: make i=i+1.

Step 9: whether judge i greater than n, if i greater than n, finishes; Otherwise, turn back to step 2.

For bus analysis, Group[i] female wire size of value representation node i; Analyze Group[i for electric island] the electric island number of value representation bus i.

The accurate quadratic method of matrix of the present invention whenever calculates an element a based on matrix square in the matrix multiple process _IjNew value, at once upgrade this matrix element a with this new value _IjAnd symmetry elements a _Ji, concrete computing formula is as follows:

Because adjacency matrix and connection matrix all are symmetrical matrixes, the computing that square can be expressed as matrix two row elements of matrix, the matrix multiple process is:

$a_{\mathrm{ij}}^{\left(k\right)}=a_{\mathrm{ij}}^{(k-1)}+\underset{k=1}{\overset{n}{\mathrm{\Σ}}}(a_{\mathrm{ik}}^{(k-1)}\·a_{\mathrm{jk}}^{(k-1)})---\left(1\right)$

K represents the result of the k time computing in the formula bracket.

The matrix symmetry elements are:

$a_{\mathrm{ji}}^{\left(k\right)}=a_{\mathrm{ij}}^{\left(k\right)}---\left(2\right)$

Because the element of adjacency matrix is a Boolean quantity, so the matrix multiple computing is logical operation.In order to accelerate analysis speed, when the concrete programming of application formula (1) realizes, only need matrix element a _Ij=0 carries out computing, as long as and judge and have one group of a _IkAnd a _Jk Be 1 simultaneously, can obtain a _IjNew value be 1, a _JiNew value be 1.

The formation method of adjacency matrix of the present invention is as follows:

The summit of node as figure, Closing Switch is as the limit of figure when bus is analyzed.The diagonal entry assignment 1 of adjacency matrix, the element assignment 1 that has the limit to get in touch between the summit, the element assignment 0 that does not have the limit to get in touch between the summit.

The summit of bus as figure, branch road is as the limit of figure when analyzing on electric island, and the diagonal entry assignment 1 of adjacency matrix has the element assignment 1 of limit contact between the summit, do not have the element assignment 0 of limit contact between the summit.

Node optimization numbering of the present invention is numbered node by the descending order of the Closing Switch number that node connected, and bus optimization numbering is numbered bus by the descending order of way that bus connected.An ascending order of way carried out that the node optimization method for numbering serial is just in time opposite by node connects when this found the solution with sparse matrix.

The invention has the beneficial effects as follows: compare with existing matrix method,

1,, have matrix method clear concept, programming characteristic of simple, but arithmetic speed is more faster than existing matrix method because the present invention has still utilized the advantage of matrix method.

2, the present invention only needs twice matrix multiplication operation just can be connected matrix entirely, has improved the speed of matrix analysis.Carrying out the connected graph analysis with a network diagram that n summit arranged is example.Adopting the calculation times of adjacency matrix under the multiplication algorithm worst case is n-1 time, and adopting the demand perfection calculation times of connection matrix of quadratic method is log ₂(n-1) inferior, and calculation times is 2 times when adopting methods analyst of the present invention.This shows that amount of calculation of the present invention is less than existing matrix method, the summit is many more, and efficient is obvious more.

3, the present invention adopts and to connect the descending order of Closing Switch number by node and carry out node optimization and number, and by the descending order of way of propping up that bus connected bus is optimized numbering, has reduced the matrix multiplication operation amount.

4, the present invention directly preserves connection matrix and the full value of connecting with adjacency matrix, does not need special intermediary matrix, can save the Computer Storage space of half, has also reduced the matrix assignment operation.

Description of drawings

5 in the total accompanying drawing of the present invention.Wherein:

Fig. 1 is the flow chart of the inventive method.

Fig. 2 is the flow chart of the accurate square module of adjacency matrix in the inventive method.

Fig. 3 is the flow chart that the line scanning method is communicated with the sheet analysis module in the inventive method.

Fig. 4 is the network diagram of the inventive method embodiment.

Fig. 5 is the inventive method embodiment topological diagram.

Among Fig. 4,1, 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.

Embodiment

Below in conjunction with accompanying drawing the present invention is further described.Fig. 4 is the physical model of a simple power system network, 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.It is as follows according to the flow process of Fig. 1～shown in Figure 3 the physical model of simple network shown in Figure 4 to be carried out the step that network topology analyzes:

Step 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.

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

Step 3: connect the Closing Switch number according to each node and carry out the node optimization numbering.Be optimized numbering by the descending order of Closing Switch number that node connected.The new node of numbering result: electric pressure KV1 is identical with old node.

Step 4: form about the adjacency matrix A of node by the Closing Switch annexation ₁:

The 1st electric pressure carried out the bus analysis, only consider switch element when bus is analyzed, do not consider other elements.The summit of node as figure, Closing Switch forms the adjacency matrix A of reflection summit by the switch annexation as the limit of figure ₁, the diagonal of a matrix element is 1 all, and it is 1 that the off diagonal element of limit contact is arranged between the summit, and not having the off diagonal element of limit contact between the summit is 0.There is switch to get in touch and all closed as 1.1 of: nodes and node 1.3, node 1.5, node 1.6, so adjacency matrix A ₁The off diagonal element a of the 1st row ₁₃, a ₁₅, a ₁₆ Be 1, all the other all are 0; 1.6 of nodes have switch to get in touch with node 1.1, node 1.8, but the switch between node 1.6 and the node 1.8 is that off-state is not as the limit of figure, so adjacency matrix A ₁The off diagonal element a of the 6th row ₆₁Be 1, all the other all are 0.

$A_1=\left[\begin{array}{cccccccc}1& 0& 1& 0& 1& 1& 0& 0\\ 0& 1& 1& 1& 0& 0& 0& 0\\ 1& 1& 1& 0& 0& 0& 0& 0\\ 0& 1& 0& 1& 0& 0& 1& 0\\ 1& 0& 0& 0& 1& 0& 0& 0\\ 1& 0& 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 1& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 0& 0& 1\end{array}\right]$

Step 5: to adjacency matrix A ₁Call the accurate quadratic method module of matrix, it is as follows to generate full connection matrix:

${\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="HSA00000204030000021.png,HSA00000204030000031.png"\; state="\{\{state\}\}">T</figure-callout>}}_1=\left[\begin{array}{cccccccc}1& 1& 1& 1& 1& 1& 1& 0\\ 1& 1& 1& 1& 1& 1& 1& 0\\ 1& 1& 1& 1& 1& 1& 1& 0\\ 1& 1& 1& 1& 1& 1& 1& 0\\ 1& 1& 1& 1& 1& 1& 1& 0\\ 1& 1& 1& 1& 1& 1& 1& 0\\ 1& 1& 1& 1& 1& 1& 1& 0\\ 0& 0& 0& 0& 0& 0& 0& 1\end{array}\right]$

Step 6: matrix is connected in the analysis of line scanning method entirely, obtains all buses in the current electric pressure:

With the line scanning method to full connection matrix T ₁The 1st line scanning the time, can draw: node 1.1, node 1.2, node 1.3, node 1.4, node 1.5, node 1.6, node 1.7 belong to same connection sheet, their female wire size all is 1, and promptly bus 1 comprises node 1.1, node 1.2, node 1.3, node 1.4, node 1.5, node 1.6, node 1.7 totally 7 nodes; To full connection matrix T ₁Eighth row when scanning, find that node 1.8 belongs to one and is communicated with sheet, its female wire size is 2,2 of buses of expression comprise node 1.8.

Step 7: current electric pressure KV=KV+1 is set.

Step 8: judge that KV is whether several 4 greater than total electric pressure, if KV is greater than 4 then enter into the electric island of step 9 beginning and analyze; If KV is not more than 4, then turn back to step 3, proceed the bus analysis of new electric pressure.

The topological analysis that all 4 electric pressures are carried out obtaining after the bus analysis the results are shown in Table 1.

The bus analysis result of table 1 Fig. 4 embodiment

Step 9: form bus branch road contingency table according to branch road two end nodes.

Step 10: carry out bus optimization numbering according to each bus institute chord way.A descending order of way was carried out bus optimization numbering by bus connected, and new, one's old mother's line table of comparisons sees Table 2 and accompanying drawing 5, among Fig. 5 in the circle numeral be one's old mother's wire size, the interior numeral of square frame is new female wire size.

New, the one's old mother's line table of comparisons of table 2 Fig. 5 embodiment

The new female wire size of one's old mother's wire size

1 3

2 4

3 1

4 5

5 6

6 2

Step 11: form the adjacency matrix of the new female wire size of reflection by the branch road annexation.

Obtain network model according to the bus analysis result, the summit of bus as figure, branch road is as the limit of figure, form the adjacency matrix A of reflection bus by the branch road annexation, the diagonal of a matrix element all is 1, it is 1 that the off diagonal element of limit contact is arranged between the summit, and not having the off diagonal element of limit contact between the summit is 0.As: bus 1 has branch road to get in touch with bus 3, so the off-diagonal element a of adjacency matrix A the 1st row ₁₃Be 1; Bus 1 does not have branch road to get in touch with bus 2, so the off-diagonal element a of the 1st row ₁₂Be 0.

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

Step 12: adjacency matrix A is called the accurate quadratic method module of matrix, and it is as follows to generate full connection matrix:

$T=\left[\begin{array}{cccccc}1& 0& 1& 0& 0& 1\\ 0& 1& 0& 1& 1& 0\\ 1& 0& 1& 0& 0& 1\\ 0& 1& 0& 1& 1& 0\\ 0& 1& 0& 1& 1& 0\\ 1& 0& 1& 0& 0& 1\end{array}\right]$

Step 13: matrix is connected in the analysis of line scanning method entirely, obtains all electric islands:

During to the 1st line scanning of full connection matrix T, can draw: bus 1, bus 3, bus 6 belong to same connection sheet with the line scanning method, and their electric island number all is 1, and promptly electric island 1 comprises bus 1, bus 3, bus 6 totally 3 buses; During to the 2nd line scanning of full connection matrix T, can draw: bus 2, bus 4, bus 5 belong to same connection sheet, and their electric island number all is 2, and promptly electric island 2 comprises bus 2, bus 4, bus 5 totally 3 buses.

Female wire size changes one's old mother's wire size into, can draw the topological analysis result and be: the electric island of bus 1, bus 3, bus No. 5 is 1, and promptly electric island 1 comprises bus 1, bus 3, bus 5; The electric island of bus 2, bus 4, bus No. 6 is 2, and promptly electric island 2 comprises bus 2, bus 4, bus 6.

Fig. 5 is the topological diagram that adopts after the present invention carries out the network topology analysis.

The present invention can adopt any programming language and programmed environment to realize, as C language, C++, FORTRAN, Delphi etc.Development environment can adopt Visual C++, Borland C++Builder, Visual FORTRAN etc.Applied environment: a module that can be used as real-time systems such as EMS and distribution management system is used, and the power system analysis software that also can be used as an off-line uses.

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

This electrical network is a large-scale power grid, scale was at that time: 187 at factory station, 715 of 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 and series reactor branch roads.

The topological analysis result forms 957 of buses, 49 on electric island.Wherein 1 is the island of living, and the bus number 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, and bus is analyzed 0.297s consuming time, and 1.313s consuming time is analyzed on electric island, the 1.610s that is about total consuming time of topological analysis.

The present invention and adjacency matrix relatively see Table 3 from multiplication algorithm and quadratic method, and visible the inventive method and existing matrix method compare, and the matrix multiplication number of times obviously reduces, and computational speed significantly improves.

Table 3 the present invention and existing method are relatively

Claims (3)

1. the matrix analysis method of a power system network topology is characterized in that:

Concrete step is:

Step 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;

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

Step 3: connect the Closing Switch number according to each node and carry out the node optimization numbering by order from big to small;

Step 4: form about the adjacency matrix of node by the Closing Switch annexation;

Step 5: call the accurate quadratic method module of matrix, generate the full matrix of connecting;

Step 6: matrix is connected in the analysis of line scanning method entirely, obtains all buses in the current electric pressure;

Step 7: current electric pressure KV=KV+1 is set;

Step 8: judge whether KV counts KVS greater than total electric pressure, if KV is greater than KVS then enter into the electric island of step 9 beginning and analyze; If KV is not more than KVS, then turn back to step 3, proceed the bus analysis of new electric pressure;

Step 9: form bus branch road contingency table according to branch road two end nodes;

Step 10: carry out bus optimization numbering by order from big to small according to each bus institute chord way;

Step 11: form the adjacency matrix of reflection bus by the branch road annexation;

Step 12: call the accurate quadratic method module of matrix, generate the full matrix of connecting;

Step 13: matrix is connected in the analysis of line scanning method entirely, obtains all electric islands.

2. the matrix analysis method of a kind of power system network topology as claimed in claim 1, its feature

Be:

The step that described full connection matrix forms module is:

Step 1: the inferior number variable l=1 that matrix square is set;

Step 2: current line i=1 is set;

Step 3: be provided with as prostatitis j=1;

Step 4: judgment matrix element a _IjWhether be 0, if a _IjBe not 0, then go to step 10;

Step 5: k=1 is set;

Step 6: judge a _IkAnd a _JkWhether all be 1,, then go to step 8 if the two is not all to be 1;

Step 7: make a _Ij=1, a _Ji=1, go to step 10;

Step 8: make k=k+1;

Step 9: judge that k whether greater than number of vertex n, if k is not more than n, then turns back to step 6;

Step 10: make j=j+1;

Step 11: whether judge j greater than n,, then turn back to step 4 if j is not more than n;

Step 12: make i=i+1;

Step 13: whether judge i greater than n,, then turn back to step 3 if i is not more than n;

Step 14: make l=l+1;

Step 15: judge that whether l is greater than 2; If l greater than 2, finishes; Otherwise, turn back to step 2.

3. the matrix analysis method of a kind of power system network topology as claimed in claim 1 is characterized in that:

Matrix is connected in the analysis of described employing line scanning method entirely, and step is:

Step 1: the Group[of record node group number] the array zero clearing, present node i=1, group number m=0;

Step 2: judge Group[i] whether be 0, if be 0, then enter into the node grouping situation that step 3 begins to analyze present node i place group; If be not 0, then enter into step 7, continue to analyze the grouping situation of next node;

Step 3: group number m=m+1, row j=i+1;

Step 4: establish Group[i]=m;

Step 5: judge the full matrix element t that connects _IjWhether be 1,, then make Group[j if be 1]=m;

Step 6: make j=j+1;

Step 7: whether judge j greater than n,, then turn back to step 5 if j is not more than n;

Step 8: make i=i+1;

Step 9: whether judge i greater than n, if i greater than n, finishes; Otherwise, turn back to step 2.

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