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

Abstract

The invention discloses a method for identifying weak lines in a power system. The vulnerability analysis of power systems has always been based on differential algebraic equations. When analyzing the vulnerability of large-scale power systems, there will be a combinatorial explosion problem, which consumes a lot of computing time. In view of the above problems, the present invention proposes an identification method using weighted line betweenness as a fragile line index, and defines the weighted line betweenness of a line as the shortest electrical path between the generator and the load in the network. Load sum, and take the method of improving the betweenness index of the line in the power network to the highest betweenness index of all adjacent lines. This method can better identify vulnerable lines in the power network, especially those lines that bear little power but have a significant impact on system vulnerability because of their special position in the grid structure.

Description

A Method for Identification of Vulnerable Lines in Large Power System

technical field

The invention belongs to the technical field of power system security defense, and in particular relates to a method for identifying vulnerable lines in a power system.

Background technique

In recent years, frequent blackouts in power systems have drawn people's attention to large-scale cascading failures and the vulnerability of power systems. The vulnerability analysis of the power system has been established on the basis of differential equations, that is, through the establishment of detailed mathematical models for each component in the system, the dynamic analysis of the system is carried out in the form of time domain simulation. With the continuous expansion of the scale of the power system, this analysis method increasingly shows its limitations: ① pay too much attention to the individual dynamic characteristics of each component, while ignoring the overall behavior of the system; ② detailed mathematical models need to consume a lot of computing time; ③ N- X vulnerability analysis encounters the problem of combinatorial explosion in large-scale power grids. Therefore, it is urgent to develop new system analysis methods to study the vulnerability of complex power systems.

In recent years, the study of complex networks has opened up a new direction for power system vulnerability analysis. Scholars have used complex network theory to analyze the vulnerability of power networks: Meng Zhongwei et al. verified that the power grids in the two large regions of China and the United States belong to small-world networks, and qualitatively analyzed the impact of small-world network characteristics on chain collapse; Ding Ming analyzed the impact of the overall structure of the power grid on cascading collapses from the topological structure of the power grid, and pointed out that contact nodes with high betweenness and degree not only ensure the connectivity of the power grid, but also contribute to the propagation of faults.

Related literature: (1) Meng Zhongwei, Lu Zongxiang, Song Jingyan. Comparative analysis of small-world topology models of China and the United States [J]. Electric Power System Automation, 2004, 28(15): 21-24. (2) Ding Ming, Han Ping Ping. Vulnerability assessment of large power grid based on small-world topology model[J]. Chinese Journal of Electrical Engineering, 2005, 25 (Supplement): 118-122.

Contents of the invention

The object of the present invention is to provide a method for identifying vulnerable lines in a power system to address the above problems.

It includes the following steps:

(1) The connection weight matrix {E _ij } and the generator weight matrix {W _i } are obtained by simplifying the actual grid data of the power network;

(2) According to the connection weight matrix {E _ij }, the Floyed algorithm is used to calculate the shortest electrical distance matrix {L _ij } of the entire network;

(3) Use the Floyed algorithm to calculate the shortest electrical path set S _L between all generators and loads;

(4) According to the shortest electrical path set S _L , calculate the preliminary weighted line betweenness B _LWeighted (m, n) for each line;

(5) Correct the betweenness of the line with weight to obtain the final betweenness of the line with weight B _LWeighted (m, n)';

(6) Using the bubble sorting method, those lines with a particularly high betweenness B _LWeighted ′ of the weighted lines are fragile lines.

The steps of the actual grid data simplification method of the power network are as follows:

(1) Consider all wiring except wiring in power plants and substations. The network model in the present invention is used for the vulnerability analysis of the actual system, so it is required to have higher modeling precision to the physical system;

(2) All nodes in the network are divided into three sets: generator node set S _G , load node set S _L , substation node set S _T ;

(3) All power lines are simplified as undirected weighted edges, and the weight of the line is defined as the reactance value of the line;

(4) Merge the transmission lines paralleled on the same pole, ignoring the parallel capacitor branch, so that the model becomes a simple diagram;

(5) The weight W _i of the generator is defined as the active power output of the generator i in the current operating mode.

The shortest electrical path is defined as the shortest electrical path between any two points in the network as the path with the smallest sum of weights along the lines among all paths between two points; the shortest electrical distance is defined as the sum of the weights of the lines along the shortest electrical path.

The calculation method of the described preliminary weighted line betweenness B _LWeighted (m, n) is according to the following formula:

${\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; LWeighted</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}$

Where S _w represents the set of generator serial numbers passing through the shortest electrical path of the line (m, n).

The correction method of the final weighted line betweenness B _LWeighted (m, n)' is according to the following formula:

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

Where (m, i) and (j, n) denote all lines connected to node m and node n, respectively.

The invention can identify the vulnerable lines in the power network, especially those lines that bear little power but have a significant impact on system vulnerability because of their special positions in the grid structure. Compared with the vulnerability analysis method based on time-domain simulation, this method can greatly reduce the calculation amount and speed up the calculation speed.

Description of drawings

Fig. 1 is a schematic diagram of problems existing in calculating the shortest electrical path;

Figure 2 is a schematic diagram of an example power grid;

Fig. 3 is the rotor speed deviation curve of generator 32 at different faults;

Fig. 4 is the line betweenness curve with weight;

Figure 5 is a schematic diagram of the backbone grid of the central China-Sichuan-Chongqing power grid.

Detailed ways

From the perspective of complex network, the invention uses weighted line betweenness as a vulnerability index to identify vulnerable lines in the power network.

Using the idea of complex network to study the characteristics of power grid, firstly simplify the power grid into a topology model, the principle is:

(1) Consider all wiring except wiring in power plants and substations. The network model in the present invention is used for the vulnerability analysis of the actual system, so it is required to have higher modeling precision for the physical system.

(2) All nodes in the network are divided into three sets: generator node set S _G , load node set S _L , substation node set S _T , respectively NG _, N _L and _NT .

(3) All power lines (transmission lines, transformer branches) are simplified as undirected and entitled edges. The weight of a line is defined as the reactance value of the line. And define the shortest electrical path between any two points in the network as the path with the smallest weight sum of the lines along the line among all paths between two points. The weight sum of the lines along the shortest electrical path is the shortest electrical distance.

(4) Merge the transmission lines on the same pole, ignoring the parallel capacitive branch (eliminating self-loop and multiple lines), so that the model becomes a simple diagram.

(5) The weight w _i of the generator is defined as the active power output of the generator i in the current operating mode.

After simplification, the power grid becomes a sparsely connected graph with n nodes and k lines, represented by n×n order connection weight matrix {E _ij } and n×1 order weight matrix {W _i }.

The line betweenness _BL in complex network theory refers to the number of times a line is passed by the shortest path between all nodes in the network. In addition to the network topology, the distribution and output of generators also have a significant impact on system stability in actual power systems. Therefore, the weighted line betweenness B _LWeighted is defined here. If the line (m, n) is passed by the shortest electrical path between generator i and load j, the line needs to bear the load W _i brought by generator i. Define the weighted line betweenness B _LWeighted (m, n) of the line (m, n) as the sum of the loads it bears because it is passed by the shortest electrical distance between the generator and the load in the network, as shown in formula (1) .

${\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; LWeighted</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Where S _w represents the set of generator serial numbers passing through the shortest electrical path of the line (m, n).

This method may bypass some important lines when calculating the shortest electrical distance, as shown in Figure 1. If path (1,3,4) is shorter than path (1,2,4), then all shortest electrical paths from node 1 to node 4 will go through (1,3,4) and bypass path (1 , 2, 4), resulting in the betweenness of weighted lines of lines (1, 2) and lines (2, 4) being much lower than those of lines (1, 3) and lines (3, 4). However, in the actual system, the three-phase ground fault of any line (1, 2) and line (1, 3) will cause a large amount of power to be injected into the fault point, resulting in the interruption of the transmission channel from left to right, that is It is said that the impact of the two faults on the system is similar. Therefore, the method of increasing the betweenness index of the line in the power network to the highest betweenness index of all adjacent lines before the correction is used to make up for this defect, as shown in formula (2).

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

Where (m, i) and (j, n) denote all lines connected to node m and node n, respectively.

Based on the above analysis, the implementation steps for identifying vulnerable lines are given as follows:

(1) Simplify the actual grid data of the power network according to the simplification principle above, and obtain the connection weight matrix {E _ij } and the generator weight matrix {W _i }.

(2) According to the connection weight matrix {E _ij }, use the Floyed algorithm to calculate the shortest electrical distance matrix {L _ij } of the entire network.

(3) Use the Floyed algorithm to find the shortest electrical path set _SL between all generators and loads.

(4) Use formula (1) to process the shortest electrical path set _SL , and calculate the initial weighted line betweenness B _LWeighted (m, n) for each line.

(5) Use formula (2) to correct the weighted line betweenness obtained in step 3 to obtain the final weighted line betweenness B _LWeighted (m, n)'.

(6) Using the bubble sorting method, those lines with a particularly high betweenness B _LWeighted ′ of the weighted lines are fragile lines.

The following is a simple example to illustrate the specific identification steps. The example power grid is shown in Figure 2. There are 4 load nodes and 2 generator nodes in the power grid. The weight of all lines in the figure is 1, and the weight of generator G ₁ $W_{G_1}=20,$ Generator G ₄ weights $W_{G_{}}$${{}_4}_{}=30.$ The specific calculation process is shown in Table 1.

Table 1 Example of identification steps step 1 Model the network slightly step 2 Compute {L _ij } slightly step 3 Find the shortest path set S _L between all generators and loads 1-2-3-6-7-8-91-2-3-6-7-8-101-2-3-6-11-121-2-3-6-11-134-5-3- 6-7-8-94-5-3-6-7-8-104-5-3-6-11-124-5-3-6-11-13 step According to the formula (1) to calculate all _B1-2 ＝ _80B7-8 ＝ _100B2-3 ＝ _80B8-9 ＝ _50B3-5 ＝ _120B8-10 ＝50 4 Preliminary weighted line betweenness of the line B _3-6 = 200 B _6-11 = 100B _3-7 = 0 B _11-12 = 50B _6-7 = 100 B _11-13 = 50B _4-5 = 120 step 5 According to formula (2) to correct and get the final weighted line betweenness B _1-2 = 80 B _7-8 = 100B _2-3 = 200 B _8-9 = _{100B 3-5} = 200 B _8-10 = 100B _3-6 = 200 B _6-11 = 200B _3-7 = 200 B _11-12 = 100B _6-7 = 200 B _11-13 = 100B _4-5 = 120 step 6 According to the vulnerability ranking of the weighted line betweenness B _LWeighted ′, the first 6 lines in the vulnerability ranking are determined to be vulnerable lines B _2-3 = 200 B _7-8 = 100B _3-5 = 200 B _8-9 = 100B _3-6 = 200 B _8-10 = 100B _3-7 = 200 B _11-12 = 100B _6-7 = 200 B _11-13 = 100B _6-11 = 200 B _1-2 = 80B _4-5 = 120

The effectiveness and characteristics of the present invention are further illustrated below by implementing examples.

Example 1

This method is used to identify vulnerable lines in the IEEE 39 example, and 13 vulnerable lines are selected with the betweenness of weighted lines exceeding 6000. Then use PST 2.0 software for time domain verification. Set a three-phase grounding short-circuit fault at the bus outlet with higher voltage at both ends of the line at 0.1 second, and clear the fault at 0.225 seconds (because the IEEE 39 node system is relatively strong, the fault within 100ms has little effect on the stability of the system , so extend the fault time to 125ms), and record the generator speed deviation curves of all 10 generators within 10 seconds. Except for those generators directly connected to the faulty line, if the generator speed deviation is not large and can finally return to the stable speed of the system, it is determined that this line is a non-fragile line, as shown by the dotted line in Figure 3; if If the generator speed deviation is too large and cannot return to the stable speed of the system in the end, it is determined that this line is a fragile line, as shown by the solid line in Figure 3.

After time-domain verification, 4 lines are confirmed as vulnerable lines, and the results are listed in Table 2; the lines with weighted line betweenness ranking 13 and above are all non-vulnerable lines after time-domain verification.

Table 2 Vulnerable lines in IEEE 39-node systems line name Weighted line betweenness Betweenness sorting with weighted lines Line active power (per unit value) Line Active Power Sorting 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

It can be seen that except for the line L _21-22 , the active power transmitted by the other three lines is medium in the whole network. The common feature of these fragile lines is that they are all located on important transmission channels, and their faults will directly cause the interruption of transmission channels, resulting in power shortages in some areas, resulting in power angle instability of the system. For example, a three-phase ground short-circuit fault occurs on the line L _15-16 or line L _16-17 , which causes the power of the generators 33, 34, 35, and 36 to be unable to be sent out, causing a large amount of power shortage in the rest of the system, and finally causing the power angle loss of the system. stable. Therefore, when analyzing the vulnerable lines of the power network, we should not only rely on the power borne by the lines, but also consider the position of the lines in the entire network.

Example 2

The betweenness of each line with weight is obtained by identifying the vulnerable lines of Central China-Sichuan-Chongqing power grid. Arrange the 3142 lines from left to right in accordance with the value of the weighted lines, as shown in Figure 4. There is an inflection point in the curve at about 10000 between weighted lines. The betweenness value of the weighted line on the left side of the inflection point increases slowly; while on the right side of the inflection point, the betweenness value of the weighted line on the left side increases much faster. This shows that there are a small number of lines with a high betweenness value between weighted lines in the network. Conservatively select lines with weighted line betweenness greater than 10,000 as fragile lines, a total of 571 lines.

Then use the PSASP6.2 power system comprehensive analysis application program for time domain verification. Set a three-phase grounding short-circuit fault at the bus outlet with higher voltage at both ends of the line at 0.1 second, and clear the fault at 0.4 second (because the Central China-Sichuan-Chongqing power grid is relatively strong, the fault within 100ms has little effect on the stability of the system , so the fault time is extended to 300ms), and the speed deviation curves of all 316 generators are recorded within 10 seconds. Implementation example 1 of the judgment principle of vulnerable lines.

After time-domain simulation verification, 153 of the 571 lines are vulnerable lines; and the lines with weighted line betweenness less than 10000 are verified to be non-vulnerable lines.

Accompanying drawing 5 is the trunk map of the power grid in this large area, and 7 lines appear in the trunk map (indicated by thick lines in the figure) among the top 10 lines with weighted line betweenness. Node 1 in the figure is the Three Gorges left substation, node 5 is the Douli substation, node 7 is the left substation, and node 8 is the Jiangling substation. On the whole, these high betweenness lines and nodes are all on the channel of Sichuan-Chongqing Power Grid to Central China Power Grid, which normally transmits 1520MW. If a serious fault occurs on these lines (three-phase ground short-circuit fault), the transmission channel will be interrupted, causing a large power shortage in the receiving end system (Central China Power Grid), and eventually leading to instability of the Central China Power Grid.

In the test, it was also found that the voltage level of 30 of the 153 vulnerable lines was less than or equal to 220kV. This is quite contrary to common belief, because the power delivered by 220kV lines is much less than that of 500kV lines. Through analysis, it is found that most of these lines are located on the power transmission channels in the densely populated areas of generator nodes. This shows that when judging the vulnerable lines of the power network, we should not only rely on the power transmitted by the lines, but also consider the power of the lines in the overall structure of the power grid. where you are. This example also shows that the method can identify those lines that do not transmit much power, but have a significant impact on the system due to their special position in the entire grid structure.

Claims (5)

1. A method for identifying weak lines in a power system, characterized in that it comprises the steps of: (1) The connection weight matrix {E _ij } and the generator weight matrix {W _i } are obtained by simplifying the actual grid data of the power network; (2) According to the connection weight matrix {E _ij }, the Floyed algorithm is used to calculate the shortest electrical distance matrix {L _ij } of the entire network; (3) Use the Floyed algorithm to calculate the shortest electrical path set S _L between all generators and loads; (4) According to the shortest electrical path set S _L , calculate the preliminary weighted line betweenness B _LWeighted (m, n) for each line; (5) Correct the betweenness of the line with weight to obtain the final betweenness of the line with weight B _LWeighted (m, n)'; (6) Using the bubble sorting method, those lines with a particularly high betweenness B _LWeighted ′ of the weighted lines are fragile lines. 2. A method for identifying vulnerable lines in a power system according to claim 1, wherein the steps of the power network simplification method are as follows: (1) Consider all wiring except wiring in power plants and substations. The network model in the present invention is used for the vulnerability analysis of the actual system, so it is required to have higher modeling precision to the physical system; (2) All nodes in the network are divided into three sets: generator node set S _G , load node set S _L , substation node set S _T ; (3) All power lines are simplified as undirected weighted edges, and the weight of the line is defined as the reactance value of the line; (4) Merge the transmission lines paralleled on the same pole, ignoring the parallel capacitor branch, so that the model becomes a simple diagram; (5) Generator weight Wi is defined as the active power output of generator i in the current operating mode. 3. A method for identifying vulnerable lines in a power system according to claim 1, wherein the shortest electrical path is the path with the smallest sum of line weights among all paths between any two points in the power network; The shortest electrical distance mentioned above is the sum of the weights of the lines along the shortest electrical path. 4. A method for identifying vulnerable lines in a power system according to claim 1, characterized in that: the preliminary weighted line betweenness B _LWeighted (m, n) is calculated using the following formula: ${\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; LWeighted</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; S</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}$ Where S _w represents the set of generator serial numbers passing through the shortest electrical path of the line (m, n). 5. A method for identifying vulnerable lines in a power system according to claim 1, characterized in that: said final weighted line betweenness B _LWeighted (m, n)' is corrected according to the following formula: B _LWeighted (m, n)'=MAX(B _LWeighted (m, i), B _LWeighted (j, n)) Where (m, i) and (j, n) denote all lines connected to node m and node n, respectively.

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