CN113722868A - Multi-index power grid node vulnerability assessment method fusing structure hole characteristics - Google Patents

Multi-index power grid node vulnerability assessment method fusing structure hole characteristics Download PDF

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CN113722868A
CN113722868A CN202111029535.8A CN202111029535A CN113722868A CN 113722868 A CN113722868 A CN 113722868A CN 202111029535 A CN202111029535 A CN 202111029535A CN 113722868 A CN113722868 A CN 113722868A
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李利娟
丁钢伟
王远飞
李月
郑昕晖
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Abstract

A multi-index power grid node vulnerability assessment method fusing structural hole characteristics is characterized in that node degree and clustering coefficient indexes are selected by considering topological characteristics; selecting low-power risk factors, node voltage out-of-limit risks and node electrical betweenness indexes by considering electrical performance; selecting a loss load index in consideration of the cascading failure result; and selecting PageRank, LeaderRank and HITs indexes based on the sorting of the feature vectors, and comprehensively sorting the power grid nodes by 9 evaluation indexes from the four aspects. Constructing a power grid key node sorting algorithm considering the structural hole characteristics based on ListNet sorting learning, firstly randomly generating initial weight coefficient values of all node indexes, and obtaining initial scores of all nodes by using a scoring function h (x); and then substituting the index weight coefficient into a linear neural network model, updating the index weight coefficient by a gradient descent method, controlling circulation by using iteration times until the obtained index weight coefficient value reaches a stable state, outputting the weight coefficient value at the moment, and finally obtaining the scores of all nodes of the power grid according to a scoring function h (x) and sequencing.

Description

Multi-index power grid node vulnerability assessment method fusing structure hole characteristics
Technical Field
The invention relates to the field of safe and stable operation of a power system, in particular to a multi-index power grid node vulnerability assessment method fusing structure hole characteristics.
Background
With the increasing demand of electricity, the large-scale interconnection of power grids is continuously developed, and the power grids become one of the most complex networks in the world. In recent years, major power failure accidents frequently occurring around the world bring huge economic loss and serious influence to society. Often, a power failure accident is caused by a failure of one element in the grid system, which results in the power flowing through the element being transferred to other places, so that the rest of the series of elements in the system are overloaded and quit working, and finally, the grid is crashed. Therefore, the identification of the vulnerable node, namely the node which is easy to break down, in the power grid has important significance for ensuring the safe and stable operation of the power system.
At present, identification of some key nodes in a power grid is carried out mainly on the basis of a complex network theory, and the importance of the power grid nodes is evaluated by methods such as a small-world model, electric betweenness and degree in combination with characteristics of a power system. Meanwhile, the importance degree of the nodes is measured by introducing internet webpage algorithms such as PageRank, LeaderRank and HITs into a power grid. The comprehensive evaluation method overcomes the limitation of single index evaluation to a certain extent, but the selection of the indexes in the method lacks factors with structural hole characteristics and cannot completely reflect the actual vulnerability of the power grid.
Disclosure of Invention
At present, sequencing research on key nodes is almost focused on core nodes of a power grid, the nodes at the positions of structural holes are often ignored, and meanwhile, the selection of a single index for sequencing the power grid nodes has great limitation, so that the invention provides a multi-index power grid node vulnerability assessment method fusing structural hole characteristics.
The invention selects 9 indexes from four aspects of topological characteristics, electrical performance, cascading failure consequences and sorting based on characteristic vectors, and sorts the nodes of a power grid comprehensively by using index weight coefficients of all nodes obtained by neural network training and learning and based on a ListNet sorting learning algorithm, and the method comprises the following steps:
step 1: selecting a power grid node index; and respectively selecting 9 index values from the four aspects of topological characteristics, electrical performance, cascading failure consequences and feature vector-based sequencing as learning features.
1) Aspect of topological characteristics
Node degree: the degree is the total number of all edges on the node, can be used for measuring the connectivity of the node in the network, and can describe partial characteristics of the node of the structural hole;
clustering coefficient: one of the important weighting coefficients used for representing the clustering degree of the network nodes, and the positions of the structural hole nodes in the network are more special, so that the nodes with small clustering coefficients are more likely to become the structural hole nodes.
2) Aspect of electrical performance
Low power risk factor: reflecting the probability of power factor reduction in the power grid and the severity of risk consequences, and quantitatively measuring the operation state of the microgrid at a certain future moment;
node voltage out-of-limit risk index: reflecting the possibility and harm of overhigh bus voltage in the system after the power system fails;
node electrical permittivity: the ratio of the number of paths passing through the node to the total number of paths between the two nodes that are the most efficient or the shortest, among the most efficient or shortest paths between the two nodes in the network.
3) Consequences of cascading failures
Load loss: and defining the difference value between the initial value and the load after the load is cut off as the loss load quantity of the power system fault, wherein the loss load can be used for measuring the severity of the node after the fault occurs.
4) Ordering aspect based on feature vectors
PageRank index: the method comprises the steps that a PageRank algorithm is applied to carry out key node sequencing on a power grid on the basis of constructing a power grid directed graph, and nodes with higher PR scores can be presumed to be structure hole nodes more probably according to a PR algorithm principle;
LeaderRank index: the method is an improved algorithm of the PageRank algorithm, a background node is added in a network, the node and all nodes in the network are in bilateral contact to obtain a new network of nodes in strong connection, and then node sequencing is obtained according to PageRank calculation;
HITs index: the authority of the node and the pivot in the network information flow transmission are considered, and more electrical characteristics of the power grid are considered conveniently.
Step 2: learning the index values of the 9 nodes by a ListNet sorting learning algorithm to obtain weight coefficients, and performing comprehensive sorting on the final weight coefficient values obtained by the weight coefficients through cross validation.
In the above method for evaluating vulnerability of multi-index power grid nodes with fusion structure hole characteristics, the concrete model in step 2 is established:
step 2-1: inputting training data, randomly generating a weight coefficient of each index, and constructing a scoring function h (x), wherein the scoring function of the ith node is h (x)i)=<θi,xi>1,2,3,. eta., m, vector xi={x1,x2,...,x9Denotes 9 evaluation index values corresponding to one node, vector θi={θ12,...,θ9The weighting coefficients corresponding to the evaluation indexes of the nodes are obtained, m is the total node number of the power grid, and the score of the node i is h (x)i) Represents;
h(xi)=θi·xi,i=1,2,...m (1)
in the formula, thetaiIs a set of weight coefficients, x, for node ii9 evaluation index value sets corresponding to the node i;
step 2-2: measuring each of power grids by introducing Luce model through ListNet algorithmProbability P of node ordering modeh(x)Expressing any sorting mode of the power grid nodes as a probability value, and expressing the probability of the sequence by using the sorting probability of the top k items of the scoring function, as shown in formula (2):
Figure BDA0003244642700000041
in the formula, m represents the total node number of the power grid, and j represents the serial number of the node;
the nodes in the training data are ranked, labeled and scored, and a Luce model is applied to obtain the ranking probability P of the ranked and labeled scoresy
Figure BDA0003244642700000042
Where m represents the total number of nodes of the grid, yjAnd ykThe ranking label scores of the nodes j and k respectively;
step 2-3: respectively obtaining probability distribution of the sequences by scoring a scoring function h (x) and a sequencing annotation through a Luce model, and applying cross entropy to measure similarity construction loss function L (y, h (x)) of the probability distribution of the two types of sequences as follows:
Figure BDA0003244642700000043
step 2-4: optimizing index weight coefficients by a gradient descent method, and calculating the gradient delta theta of the loss function L (y, h (x)) to theta:
Figure BDA0003244642700000051
step 2-5: updating each index weight coefficient until the obtained weight coefficient value reaches a stable state, outputting the weight coefficient value theta' at the moment, and obtaining the final score of the node through a scoring function:
θ'=θ-η·Δθ (6)
in the formula, eta is the learning step length in the neural network; updating the weighting coefficients, the final scoring function is obtained by equation (1):
h(xi)=θ'i·xi,i=1,2,...,m (7)
and obtaining the final score of the nodes through the finally updated weight coefficient to realize the sequencing of the power grid nodes.
Drawings
FIG. 1 is a basic flow chart of a multi-index power grid node vulnerability assessment method fusing structure hole characteristics;
FIG. 2 is a power grid key node sorting algorithm based on ListNet sorting learning considering structural hole characteristics;
fig. 3 is a linear neural network model.
Detailed Description
The invention is further described below with reference to the figures and examples.
Referring to fig. 1, a multi-index power grid node vulnerability assessment method fusing structure hole characteristics includes the following steps:
step 1: selecting a power grid node vulnerability assessment index fused with the structural hole characteristics;
in order to enable the ordering of the power grid nodes to be more reasonable and incorporate indexes of structural hole characteristics, node degree and clustering coefficient indexes are selected by considering topological characteristics; selecting low-power risk factors, node voltage out-of-limit risks and node electrical betweenness indexes by considering electrical performance; selecting a loss load index in consideration of the cascading failure result; and selecting PageRank, LeaderRank and HITs indexes based on the sorting of the feature vectors, and comprehensively sorting the power grid nodes by 9 evaluation indexes from the four aspects.
Step 2: referring to fig. 2, the weight coefficient of each index is randomly given, and the score function is used to obtain the initial score of each node; then the weight coefficients are brought into a neural network model and updated by a gradient descent method; the scores of all nodes at the moment are obtained through cross validation until the output index weight coefficient reaches a stable state, so that a power grid key node sorting algorithm considering the structural hole characteristics based on ListNet sorting learning is constructed;
step 2-1: referring to fig. 2 and 3, training data is input, a weight coefficient of each index is randomly generated, a scoring function h (x) is constructed, and the scoring function of the ith node is h (x)i)=<θi,xi>1,2,3,. eta., m, vector xi={x1,x2,...,x9Denotes 9 evaluation index values corresponding to one node, vector θi={θ12,...,θ9The weighting coefficients corresponding to the evaluation indexes of the nodes are obtained, and m is the total number of the nodes of the power grid; the score of node i is determined by the value of its scoring function, which is h (x)i) Represents:
h(xi)=θi·xi,i=1,2,...m (1)
in the formula, thetaiIs a set of weight coefficients, x, for node ii9 evaluation index value sets corresponding to the node i;
step 2-2: measuring probability P of each node sequencing mode in power grid by introducing ListNet algorithm into Luce modelh(x)Expressing any sorting mode of the power grid nodes as a probability value, and expressing the probability of the sequence by using the sorting probability of the top k items of the scoring function, as shown in formula (2):
Figure BDA0003244642700000061
in the formula, m represents the total node number of the power grid, and j represents the serial number of the node;
the nodes in the training data are ranked, labeled and scored, and a Luce model is applied to obtain the ranking probability P of the ranked and labeled scoresy
Figure BDA0003244642700000071
Where m represents the total number of nodes of the grid, yjAnd ykThe ranking label scores of the nodes j and k respectively;
step 2-3: respectively obtaining probability distribution of the sequences by scoring a scoring function h (x) and a sequencing annotation through a Luce model, and applying cross entropy to measure similarity construction loss function L (y, h (x)) of the probability distribution of the two types of sequences as follows:
Figure BDA0003244642700000072
step 2-4: optimizing index weight coefficients by a gradient descent method, and calculating the gradient delta theta of the loss function L (y, h (x)) to theta:
Figure BDA0003244642700000073
step 2-5: updating each index weight coefficient until the obtained weight coefficient value reaches a stable state, outputting the weight coefficient value theta' at the moment, and obtaining the final score of the node through a scoring function:
θ'=θ-η·Δθ (6)
in the formula, eta is the learning step length in the neural network; updating the weighting coefficients, the final scoring function is obtained by equation (1):
h(xi)=θ'i·xi,i=1,2,...,m (7)
the scores of the nodes are obtained through the scoring function, the power grid nodes are sorted, and the specific flow of the power grid key node sorting algorithm considering the structural hole characteristics based on ListNet sorting learning is shown in Table 1.
Table 1 power grid key node sorting algorithm considering structure hole characteristics based on ListNet sorting learning
Figure BDA0003244642700000081
As can be seen from fig. 3 and table 1, the linear neural network in the algorithm has 9 index values of the grid nodes, a node sorting and labeling score value y, an iteration number T, and a learning step length η as inputs, and has a model weight coefficient θ obtained based on neural network training and learning as an output.
Examples
In order to verify the effectiveness of the proposed multi-index power grid node vulnerability assessment method fusing the structure hole characteristics, the embodiment selects an IEEE-118 node system as an example to complete simulation calculation on MATLAB software.
1) Selection of key nodes
Obtaining 9 index specific numerical values of each node of the IEEE-118 node system based on MATLAB, evaluating and scoring each node of the IEEE-118 node system by the multi-index power grid node vulnerability evaluation method of the fusion structure hole characteristics, selecting nodes with the top ten points of scoring as key nodes of the IEEE-118 node system, wherein the key node data of the IEEE-118 node system is shown in table 2.
TABLE 2 IEEE-118 node System Key node data
Figure BDA0003244642700000082
Figure BDA0003244642700000091
As can be seen from table 2, the highest score is 49 nodes by the total evaluation of 9 indexes, that is, 49 nodes are also the most critical nodes. In order to verify the effect of the comprehensive evaluation result and the single index ordering, the evaluation result is compared with a power grid node importance evaluation method of an electric leader rank (elr) algorithm and a power grid node importance evaluation method of an improved HITs algorithm, and the result is shown in table 3.
TABLE 3 IEEE-118 System first 10 key nodes three methods contrast value
Figure BDA0003244642700000092
As can be seen from table 3, the first ten key nodes of the IEEE-118 node system obtained by the three different methods are different, and the obtained key node sequences are different because the factors considered by the three methods are different, but the first ten key nodes obtained by the three methods all have nodes No. 12, 49, 80, 92 and 100, which indicates that the proposed multi-index power grid node vulnerability assessment method for the fusion structure hole feature has general applicability to the identification of the power grid key nodes.
2) Key node and common node comparison
For the obtained key nodes of the IEEE-118 node system, each index of the key node is analyzed in combination with table 2, and the comparison between the key node and each index mean of all nodes is shown in table 4.
TABLE 4 comparison of key nodes with the mean values of all nodes
Figure BDA0003244642700000101
As can be seen from table 4, the mean values of the node degree mean value, the electrical medium mean value, the loss load mean value, the LR value, the PR value, and the HITs value of the key nodes are larger than the mean values of all the nodes; the clustering coefficients of the key nodes are lower than the overall clustering coefficient, and the clustering coefficients can represent the aggregation degree of the nodes in the power grid, which shows that the clustering coefficient indexes have little influence on the result of the sequencing model; the low-power risk factor of the key nodes is lower than the average value of all the nodes, and the lower the index is, the more reactive loads exist in the key nodes of the power grid, so that the operation state and the power supply quality of the power grid are influenced, and therefore the nodes are more prone to faults in the power grid, and further cascading faults occur. The voltage out-of-limit risk index of the key node is lower than the average value of all nodes, the smaller the index value is, the more stable the node is, the less fault is easy to occur, namely the node is less important, and therefore the voltage out-of-limit risk index has little influence on the comprehensive score of the sequencing model.
For the key nodes of the IEEE-118 node system, data of most indexes of the key nodes are larger than those of other common nodes, so that the important positions of the key nodes in the whole node system are well illustrated, and meanwhile, the key nodes play an important role in a power grid, so that the key nodes are prone to faults in the actual power grid operation process, cascading faults are caused, the power grid is finally broken down, and a major power failure accident is caused. In order to prevent the occurrence of grid cascading failures, key nodes of a power grid are subjected to important protection, which is necessary for preventing a blackout accident of the power grid.

Claims (2)

1. A multi-index power grid node vulnerability assessment method fusing structure hole characteristics comprises the following steps:
step 1: selecting a power grid node vulnerability assessment index fused with the structural hole characteristics;
in order to enable the ordering of the power grid nodes to be more reasonable and incorporate indexes of structural hole characteristics, node degree and clustering coefficient indexes are selected by considering topological characteristics; selecting low-power risk factors, node voltage out-of-limit risks and node electrical betweenness indexes by considering electrical performance; selecting a loss load index in consideration of the cascading failure result; and selecting PageRank, LeaderRank and HITs indexes based on the sorting of the feature vectors, and comprehensively sorting the power grid nodes by 9 evaluation indexes from the four aspects.
Step 2: constructing a power grid key node sorting algorithm based on ListNet sorting learning and considering the characteristics of the structural holes;
randomly giving the weight coefficient of each index, and obtaining the initial score of each node by using a scoring function; substituting the index weight coefficients into a neural network model and updating each index weight coefficient by using a gradient descent method; and performing cross validation until the output index weight coefficient reaches a stable state to obtain the score of each node at the moment, thereby realizing the key node sorting algorithm of the power grid.
2. The method for evaluating the vulnerability of multi-index grid nodes fusing structure hole characteristics according to claim 1, wherein in step 2 of claim 1, a grid key node sorting algorithm considering structure hole characteristics based on ListNet sorting learning is constructed, and the steps are as follows:
step 2-1: randomly generating initial weight coefficient values of evaluation indexes of all nodes, and constructing a scoring function h (x), wherein the scoring function of the ith node is h (x)i)=<θi,xi>I 1,2,3, …, m, vector xi={x1,x2,...,x9Denotes 9 evaluation index values corresponding to one node, vector θi={θ12,...,θ9The weighting coefficients corresponding to all evaluation indexes of the nodes are obtained, m is the total node number of the power grid, the score of the node i is determined by the value of a scoring function of the node i, and h (x) is usedi) Represents:
h(xi)=θi·xi,i=1,2,…m (1)
in the formula, thetaiIs a set of weight coefficients, x, for node ii9 evaluation index value sets corresponding to the node i;
step 2-2: measuring probability P of each node sequencing mode in power grid by introducing ListNet algorithm into Luce modelh(x)Expressing any sorting mode of the power grid nodes as a probability value, and expressing the probability of the sequence by using the sorting probability of the top k items of the scoring function, as shown in formula (2):
Figure FDA0003244642690000021
in the formula, m represents the total node number of the power grid, and j represents the serial number of the node;
the nodes in the training data are ranked, labeled and scored, and a Luce model is applied to obtain the ranking probability P of the ranked and labeled scoresy
Figure FDA0003244642690000022
Where m represents the total number of nodes of the grid, yjAnd ykThe ranking label scores of the nodes j and k respectively;
step 2-3: respectively obtaining probability distribution of the sequences by scoring a scoring function h (x) and a sequencing annotation through a Luce model, and applying cross entropy to measure similarity construction loss function L (y, h (x)) of the probability distribution of the two types of sequences as follows:
Figure FDA0003244642690000023
step 2-4: optimizing index weight coefficients by a gradient descent method, and calculating the gradient delta theta of the loss function L (y, h (x)) to theta:
Figure FDA0003244642690000024
step 2-5: updating each index weight coefficient until the obtained weight coefficient value reaches a stable state, outputting the weight coefficient value theta' at the moment, and obtaining the final score of the node through a scoring function:
θ'=θ-η·Δθ (6)
in the formula, eta is the learning step length in the neural network; updating the weighting coefficients, the final scoring function is obtained by equation (1):
h(xi)=θ′i·xi,i=1,2,…,m (7)
and obtaining the final score of the nodes through the finally updated weight coefficient to realize the sequencing of the power grid nodes.
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