CN110350522B - Electric power system fragile line identification method based on weighted H index - Google Patents

Electric power system fragile line identification method based on weighted H index Download PDF

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CN110350522B
CN110350522B CN201910618551.7A CN201910618551A CN110350522B CN 110350522 B CN110350522 B CN 110350522B CN 201910618551 A CN201910618551 A CN 201910618551A CN 110350522 B CN110350522 B CN 110350522B
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范文礼
张乔
刘志刚
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Southwest Jiaotong University
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Abstract

The invention discloses a method for identifying a fragile line of an electric power system based on a weighted H index, which comprises the following specific steps: 1. establishing a secondary correlation network of the power system by considering the topological structure characteristics and the running state characteristics of the power system network; 2. considering the weight of edges and the node strength in the correlation network, improving the classic H index to obtain a weighted H index; 3. and (4) sequencing the power transmission lines according to the weighted H index obtained in the step (2) to complete the identification of the fragile lines. The invention takes the correlation network into consideration to improve the classic H index, expands the calculation range of the index from the integer field to the real number field, and can more accurately identify the fragile line in the system.

Description

Electric power system fragile line identification method based on weighted H index
Technical Field
The invention relates to a fragile line identification method in power grid vulnerability analysis, in particular to a power system fragile line identification method based on a weighted H index.
Background
In recent years, a blackout accident occurs. Although these accidents occur less frequently, each accident, without exception, can have catastrophic effects on society. About one quarter of the users were powered off due to brazilian blackout accident in 3 months of 2018. Due to an overload trip of a bus breaker, the sending end converter station loses the alternating current power supply, and bipolar shutdown is caused. In addition, the grid structure of the Brazilian power grid is unreasonable, so that the key AC/DC channels from north to south are affected, and finally cascading failure is caused. It can be seen from the accident process that some key lines in the system play a role in promoting the spread of the power failure range. Therefore, the searching of the fragile lines can effectively prevent and block the occurrence of cascading failures, and has important value for improving the safe operation level of the power grid.
Scholars at home and abroad make great efforts in the identification or search work of fragile lines of power systems, and the main achievements can be roughly divided into two categories. The first category is power system state analysis based on reduction theory. The method uses load flow calculation as a core and utilizes a deterministic or probabilistic method to describe the propagation process of the cascading failure of the power grid. And identifying the fragile line by combining an entropy theory, a risk assessment theory and Monte Carlo simulation. The method mainly considers the aspects of line power flow transfer and distribution characteristics, node voltage deviation, virtual injection power disturbance, system load loss and the like under the power grid disturbance. The second type is an identification method based on complex network theory. Complex network theory proposes many network properties (such as small-world characteristics and non-scale characteristics) and component statistical properties (such as degree, betweenness, clustering coefficient, etc.) to analyze the dynamic behavior of the network. In combination with the electrical characteristics of the grid, electrical distances, electrical betweenness, tidal current betweenness and power betweenness are successively proposed for identifying vulnerable lines in the system. In addition, an identification method based on K-kernel decomposition, a structure hole theory and a PageRank algorithm is proposed successively. The method fully utilizes the physical properties and static parameters of the power grid and the characteristics of power transfer and the like under disturbance, and can help the staff of the power system to know and master weak links in the system in time; however, the occurrence of blackout accidents is established on the dynamic characteristic of the system responding to power transfer and transmission capacity change after the key elements of the power grid fail. Therefore, the identification of the fragile line needs to further consider the system power transmission change characteristics after the grid fault and the correlation problem between the power transmission branches.
Disclosure of Invention
In order to provide a high-accuracy and high-effectiveness power grid fragile line identification method, the fragile line is identified by considering power transmission conversion correlation among power transmission branches based on a weighted H index.
Therefore, the invention provides a method for identifying a fragile line of a power system based on a weighted H index, which comprises the following specific steps:
step 1: the method comprises the following steps of considering the topological structure characteristics and the running state characteristics of a power system network, and establishing a secondary correlation network of the power system, wherein the specific construction method comprises the following steps:
1.1 calculating the reference load flow of the power system and recording the capacity margin M of each linej；
1.2, sequentially switching off each branch in the power grid based on the N-1 load flow calculation, and obtaining a power increment matrix delta P by taking the load flow increment of other branches caused by switching off the branches as a side weight;
1.3, judging whether the branch power exceeds the limit, if not, turning to the step 1.4; otherwise, retaining the element values corresponding to the out-of-limit branches in the matrix delta P, then disconnecting the out-of-limit branches, calculating the system power flow again, and updating the power increment matrix delta P according to the second power flow increment;
1.4, dividing each element in the power increment matrix Δ P by the capacity margin of the corresponding branch to obtain an improved correlation matrix R, specifically:
Figure BDA0002124766040000021
wherein Δ rijThe influence of the disconnection of the line i on the line j is represented by the following equation:
Figure BDA0002124766040000022
in the formula MjIndicating capacity margin, Δ P, of line jijThe power increment of the line j after the line i is disconnected is shown, n represents the total number of lines in the system, and correlation is carried out under the condition that the influence of the transmission line on the system is not consideredAll diagonal elements in the property matrix R are set to 0; and then, taking the power grid branch as a node, and taking the elements in the matrix R as edge weights, and constructing a new network, namely a secondary correlation network of the power system.
Step 2: considering the weight of edges and node strength in a correlation network, improving the classic H index to obtain a weighted H index, defining the weighted H index by adopting relative node strength, wherein the defined node weighted H index is as follows:
Figure BDA0002124766040000023
Figure BDA0002124766040000024
Figure BDA0002124766040000025
in the formula, WHiRepresenting the weighted H-index of the node i,
Figure BDA0002124766040000026
for weighted H-index calculation of the operator, wijRepresenting the edge weight, S, pointing from node i to node jj|iRepresenting the strength, S, of node j relative to node ijRepresenting the strength, Γ, of node jiRepresents the set of all neighboring nodes pointed to by node i, α, β represent adjustment factors; WHiThe larger the node, the more vulnerable its corresponding leg.
Computing a weighted H-index WH for a node iiThe algorithm is specifically as follows:
2.1 initializing relevant network parameters;
2.2 initializing node i weighting the H index value, let WHiThen calculating the relative node strength of all the adjacent nodes of the node i;
2.3 sorting all adjacent nodes of the node i in the order of their relative node strengths from small to large to form a sequence S ═ S1|i,S2|i,…,SM|iM is the number of sequences S; counting the edge weight value W ═ W corresponding to the sequence Si1,wi2,…,wiM}；
2.4 pairs of each value W in the sequence WikAll values in the calculated sequence greater than wikAnd SUMWkThen WHik＝min{Sk|i,SUMWkGet through all W in the sequence WikWeighted H index WH of node ii＝max{WHik|k∈M}。
And step 3: and (4) sequencing the power transmission lines according to the weighted H index obtained in the step (2) to complete the identification of the fragile lines. The method specifically comprises the following steps: and calculating the weighted H index of each line in the topological structure of the node system, and sequencing the lines in a descending order according to the weighted H indexes, thereby determining the fragile line (namely the key line) of the power system.
The invention has the beneficial effects that:
(1) the structural topological characteristic and the operating state characteristic of the power system network are considered at the same time, and compared with the electric power system state analysis fragile line identification method based on the reduction theory, the method has better identification accuracy and effectiveness;
(2) the invention adopts the improved H index, fully considers the depth and the breadth of the weak line influence, and deeply describes the dynamic characteristic of the cascading failure of the power grid.
(3) The method can provide a new idea for guiding the evolution of the power network and searching for a strategy for inhibiting the propagation of the cascading failure, and has important significance for the planning and safe and stable operation of the power system.
Drawings
Fig. 1 is a mapping diagram of physical wiring and correlation network of a power grid.
FIG. 2 is a diagram of node A and its neighboring nodes.
Fig. 3 is a schematic diagram of nodes B and C and their neighboring nodes.
Fig. 4 is a diagram of a bidirectional weighting network topology.
Fig. 5 is a flow chart of a line deliberate attack.
Fig. 6 is an IEEE39 node system diagram.
FIG. 7 is a graph comparing the discrimination of the weighted H-index and the classical H-index.
Detailed Description
The invention is explained in further detail below with reference to the drawings.
The invention provides a method for identifying a fragile line of a power system based on a weighted H index, which is based on the weighted H index, and the fragile line is identified by considering the power transmission conversion correlation among power transmission branches.
The specific implementation mode is as follows:
step 1: modeling of secondary correlation network of power system
In order to consider the topological structure characteristics of a power grid and the state characteristics of system operation, a method for establishing a power system and establishing a secondary correlation network is provided based on secondary cascading failures, and specifically comprises the following steps:
1.1 calculating the system reference load flow and recording the capacity margin M of each linej；
1.2, sequentially switching off each branch in the power grid based on the N-1 load flow calculation, and obtaining a power increment matrix delta P by taking the load flow increment of other branches caused by switching off the branches as a side weight;
1.3, judging whether the branch power exceeds the limit, if not, turning to the step 1.4; otherwise, retaining the element values corresponding to the out-of-limit branches in the matrix delta P, then disconnecting the out-of-limit branches, calculating the system power flow again, and updating the power increment matrix delta P according to the second power flow increment;
1.4, dividing each element in the power increment matrix Δ P by the capacity margin of the corresponding branch to obtain an improved correlation matrix R, specifically:
Figure BDA0002124766040000041
wherein Δ rijThe influence of the disconnection of the line i on the line j is represented by the following equation:
Figure BDA0002124766040000042
in the formula MjIndicating capacity margin, Δ P, of line jijRepresenting the power increment of the line j after the line i is disconnected, wherein n represents the total number of lines in the system, and all diagonal elements in the correlation matrix R are set to be 0 under the condition that the influence of the transmission line on the correlation matrix R is not considered; and then, taking the power grid branch as a node, and taking the elements in the matrix R as edge weights, and constructing a new network, namely a secondary correlation network of the original power grid.
The secondary correlation network is used for subsequent fragile transmission line identification, and the establishment process is shown in fig. 1.
Step 2: and improving the classic H index to obtain a weighted H index.
The classic H index was proposed by Jorge Hirsch in 2005, and its purpose was to quantify the research results of researchers as independent individuals, and was widely used in academia. Its original definition as the H index of a scientist means that there are H published Np papers cited at least H times each, while the remaining Np-H papers are cited less than H times each.
From the perspective of a complex network, the H-index can identify the impact of nodes in an unweighted network. As shown in fig. 2, node a has 4 neighboring nodes with node strengths of 2,3,4 and 5, respectively. Then node A has 4 neighboring node strengths ≧ 2,3 neighboring node strengths ≧ 3, but no 4 neighboring node strengths ≧ 4, according to the definition of the H-index, HA＝3。
In fact, most networks in real life are weighting networks, different edge weights assume different roles and functions, and the edge weights are not all integers. When the concept of the H index is expanded into the correlation network established in the text, the classical H index only considers the influence of adjacent nodes, neglects the importance of the edge weight, and has integral calculation results, and obviously has small difference of the calculation results. In the case shown in fig. 3, the H indices of nodes B and C are both 3, and the influence of the two nodes cannot be compared. Therefore, the patent provides a weighted H index calculation method considering the strength of the adjacent nodes and the edge weight, and the node identification discrimination is improved, so that the method is suitable for identifying the node influence in the correlation network.
The correlation network established in the step 1 is a bidirectional weighting network, improves the traditional H index, and considers the weight of edges and the node strength in the correlation network. In addition, in an electrical power system, a failure of a target branch may cause a power violation for other branches, represented as w in the correlation networkijA value of greater than 1 increases the risk of cascading failure of the system. Therefore, the relative node strength is used to define a weighted H-index, which is defined as:
Figure BDA0002124766040000051
Figure BDA0002124766040000052
Figure BDA0002124766040000053
in the formula, WHiRepresenting the weighted H-index of the node i,
Figure BDA0002124766040000054
for weighted H-index calculation of the operator, wijRepresenting the edge weight, S, pointing from node i to node jj|iRepresenting the strength, S, of node j relative to node ijRepresenting the strength, Γ, of node jiRepresents the set of all neighboring nodes pointed to by node i, α, β represent adjustment factors; WHiThe larger the node, the more vulnerable its corresponding leg.
In order to calculate the value of WH, a weighted H index WH of a computing node i is providediThe algorithm of (2) is shown in table 1.
TABLE 1 weighted H-index calculation method
Figure BDA0002124766040000055
Figure BDA0002124766040000061
Specifically, the algorithm can be divided into the following steps:
2.1 initializing relevant network parameters;
2.2 initializing node i weighting the H index value, let WHiThen calculating the relative node strength of all the adjacent nodes of the node i;
2.3 sorting all adjacent nodes of the node i in the order of their relative node strengths from small to large to form a sequence S ═ S1|i,S2|i,…,SM|iM is the number of sequences S; counting the edge weight value W ═ W corresponding to the sequence Si1,wi2,…,wiM}；
2.4 pairs of each value W in the sequence WikAll values in the calculated sequence greater than wikAnd SUMWkThen WHik＝min{Sk|i,SUMWkGet through all W in the sequence WikWeighted H index WH of node ii＝max{WHik|k∈M}。
The weighted H-indices of nodes B and C are calculated in a weighted network as shown in fig. 3 using the above algorithm, the process of which is shown in table 2. As can be seen from Table 2, the weighted H index of the node B is max { WH by the weighted H index calculationTBi3.5, the weighted H index of node C is max { WHTCi2.9, the H index values of the two nodes are obviously different, and the effectiveness of the index is shown.
TABLE 2 weighted H-index calculation procedure
Figure BDA0002124766040000062
In a dependency network, node out-degree represents the sameThe node influence on other nodes, and the node in degree represents the influence of other nodes on the node. In the bidirectional weighting network shown in fig. 4, Γ 12,3,5, 6. Thus defining the node strength SiWhen we only consider the impact on other nodes. In the correlation network, the node out degree represents the influence of the node on other nodes, and reflects the influence of the node in the network to a certain extent. The more the node out-degree number is, the wider the influence range of the node is reflected, and the larger the node out-degree weight is, the deeper the influence of the node on the adjacent node is reflected. The weighted H index defined by the formula (3) fully combines the depth and the breadth of the influence of the node in the system, and deeply describes the influence of the node, and reflects the vulnerability of the original network branch in the cascading failure process.
And step 3: identifying vulnerable lines using weighted H-indices
The power transmission lines are sorted according to the weighted H index obtained in the step 2, and the nodes with higher weighted H indexes in the correlation network correspond to the power transmission lines which can be more fragile in the original power grid; the weighted H index indexes of the lines in the power network are arranged from large to small, the larger the weighted H index of the line is, the larger the influence of the line on the system after the line is attacked is, and the more serious the load loss condition of the system is.
The vulnerability attack research of the line can be used for identifying faults seriously influencing the system, an AC OPA model is adopted to carry out static deliberate attack on the line according to the sequence of branch numbers, the load loss condition of the system after each line is attacked is counted, the attack process is simulated for 10000 times as shown in figure 5, and two vulnerability indexes of VaR (risk value, MW) and CVaR (risk condition value, MW) are calculated according to the load loss statistic condition of the system to evaluate the power failure risk; VaR represents the maximum possible load loss of the system for a certain period of time at a given confidence level σ; CVaR represents the average of the conditions when the loss exceeds VaR at a given confidence; in the present invention, σ is set to 0.95.
The analysis is carried out by taking an IEEE-39 node system as an example, the topological structure of the system is shown in figure 6, and the system comprises 39 nodes and 46 branches. According to the method, the weighted H index value of each line is calculated, and the lines are sorted in a descending order according to the weighted H index value, so that the key line of the system is determined. If the line with a large weighted H index value is damaged, a large-scale power failure accident is likely to be caused.
To evaluate the performance of the weighted H-index method, table 3 lists the vulnerability results of the top 5 lines identified by the weighted H-index (α ═ 0.5, β ═ 0.5) compared to the randomly selected top 5 lines.
TABLE 3 Fragile line identification result ordering for IEEE-39 node systems
Figure BDA0002124766040000071
Comparison
Figure BDA0002124766040000074
And
Figure BDA0002124766040000075
these two indices represent the average risk of blackouts caused by the most vulnerable transmission lines; it can be seen that caused by the weakest transmission line
Figure BDA0002124766040000072
And
Figure BDA0002124766040000073
the weighted H index method is obviously higher than the random selection method; this indicates that the weighted H-index method is accurate and efficient at identifying vulnerable links.
In addition, fig. 7 compares the discrimination degrees of the weighted H index and the classical H index, and as shown in fig. 7, within the circled range, the classical H index value remains unchanged, that is, the vulnerability of the lines is the same, and the discrimination of the vulnerability of the lines by the classical H index does not have the discrimination degree. On the contrary, the weighted H-index values decrease in sequence as the ranking of the lines increases, with good discrimination for each line. This demonstrates the effectiveness of this patent for classical H index improvement.
The fragile line identification algorithm provided by the invention considers the structural characteristics and the state characteristics of the line and adopts an improved H index decomposition method to identify the fragile line. The identification results are all weak links in the system, and show larger load loss than randomly selected lines in the process of deliberate attack. In addition, compared with the classic H index, the weighted H index has higher discrimination. Therefore, the method has important significance for searching the fragile line of the power system, blocking the strategy of the cascading failure and improving the safe operation level of the system.

Claims (2)

1. A method for identifying a fragile line of an electric power system based on a weighted H index is characterized by comprising the following steps:
step 1: considering the topological structure characteristics and the operating state characteristics of the power system network, establishing a secondary correlation network of the power system, specifically:
1.1 calculating the reference load flow of the power system and recording the capacity margin M of each linej；
1.2, sequentially switching off each branch in the power grid based on the N-1 load flow calculation, and obtaining a power increment matrix delta P by taking the load flow increment of other branches caused by switching off the branches as a side weight;
1.3, judging whether the branch power exceeds the limit, if not, turning to the step 1.4; otherwise, retaining the element values corresponding to the out-of-limit branches in the matrix delta P, then disconnecting the out-of-limit branches, calculating the system power flow again, and updating the power increment matrix delta P according to the second power flow increment;
1.4, dividing each element in the power increment matrix Δ P by the capacity margin of the corresponding branch to obtain an improved correlation matrix R, specifically:
Figure FDA0003523298250000011
wherein Δ rijThe influence of the disconnection of the line i on the line j is represented by the following equation:
Figure FDA0003523298250000012
in the formula MjIndicating capacity margin, Δ P, of line jijRepresenting the power increment of the line j after the line i is disconnected, wherein n represents the total number of lines in the system, and all diagonal elements in the correlation matrix R are set to be 0 under the condition that the influence of the transmission line on the correlation matrix R is not considered; then, taking the power grid branch as a node, and taking the elements in the matrix R as edge weights, and constructing a new network, namely a secondary correlation network of the power system;
step 2: considering the weight of edges and the node strength in the correlation network, improving the classic H index to obtain a weighted H index;
defining a weighted H index by using the relative node strength, wherein the weighted H index of the node is defined as:
Figure FDA0003523298250000013
Figure FDA0003523298250000014
Figure FDA0003523298250000015
in the formula, WHiRepresenting the weighted H-index of the node i,
Figure FDA0003523298250000021
for weighted H-index calculation of the operator, wijRepresenting the edge weight, S, pointing from node i to node jj|iRepresenting the strength, S, of node j relative to node ijRepresenting the strength, Γ, of node jiRepresents the set of all neighboring nodes pointed to by node i, α, β represent adjustment factors; WHiThe larger the node, the more fragile its corresponding leg is;
of computing node iWeighted H-index WHiThe algorithm is specifically as follows:
2.1 initializing relevant network parameters;
2.2 initializing node i weighting the H index value, let WHiThen calculating the relative node strength of all the adjacent nodes of the node i;
2.3 sorting all adjacent nodes of the node i in the order of their relative node strengths from small to large to form a sequence S ═ S1|i,S2|i,…,SM|iM is the number of sequences S; counting the edge weight value W ═ W corresponding to the sequence Si1,wi2,…,wiM}；
2.4 pairs of each value W in the sequence WikAll values in the calculated sequence greater than wikAnd SUMWkThen WHik＝min{Sk|i,SUMWkGet through all W in the sequence WikWeighted H index WH of node ii＝max{WHik|k∈M}；
And step 3: and (4) sequencing the power transmission lines according to the weighted H index obtained in the step (2) to complete the identification of the fragile lines.
2. The method as claimed in claim 1, wherein the step 3 is specifically to calculate a weighted H index of each line in the node system topology, and sort the lines in descending order according to the weighted H index, so as to determine the vulnerable line of the power system.
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