CN113282881B - Electric power information physical system robustness analysis method based on reachable matrix - Google Patents

Electric power information physical system robustness analysis method based on reachable matrix Download PDF

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CN113282881B
CN113282881B CN202110257711.7A CN202110257711A CN113282881B CN 113282881 B CN113282881 B CN 113282881B CN 202110257711 A CN202110257711 A CN 202110257711A CN 113282881 B CN113282881 B CN 113282881B
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葛愿
徐正伟
陈其工
余诺
林其友
杨树全
范晓东
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Anhui Polytechnic University
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Abstract

The invention discloses a power information physical system robustness analysis method based on a reachable matrix, which comprises the following steps: inputting an adjacency matrix Ep of the power network, an adjacency matrix Ec of the information network, and a dependency matrix Epc between the power network and the information network; determining an attack node in the power network, wherein the attack node is a starting point of fault propagation, deleting fault nodes which appear in an adjacent matrix Ep and an adjacent matrix Ec after the fault propagation based on a dependent matrix Epc, and outputting the adjacent matrix Ep, the adjacent matrix Ec and the dependent matrix Epc; updating the dependency matrix Epc, and forming an attacked widened adjacent matrix based on the adjacent matrix Ep, the adjacent matrix Ec and the updated dependency matrix Epc; and calculating the system robustness index after the attack based on the extended adjacency matrix. The modeling complexity of the mutual coupling network can be reduced, the structural characteristic change and the dynamics rule of network connection in the system are clearly and intuitively displayed, the complexity of an attack graph is reduced, and the understanding and analysis of safety personnel are facilitated.

Description

Electric power information physical system robustness analysis method based on reachable matrix
Technical Field
The invention belongs to the technical field of smart grids, and particularly relates to a power information physical system robustness analysis method based on a reachability matrix.
Background
Conventional primary grid-based Power systems have gradually evolved into systems in which the Power grid and the information grid coexist and are tightly integrated, i.e., power Cyber-physical systems (PCPS). The PCPS introduces advanced information communication technology, and deepens the integration of an information system and a power system, and simultaneously makes the system face serious safety test, wherein the robustness of the system is a primary problem. This is because the information system must sweep the power system when it is subject to a hacking network attack failure, and the power system failure will cause the relevant information devices to lose power supply and to generate an information communication failure, which in turn will cause the relevant power devices to be undetectable or uncontrolled, thereby causing the failure to be propagated in cascade due to the coupling relationship between the power system and the information system, so that the system robustness is drastically reduced until the whole system is paralyzed.
Historically, several more significant power outages were caused by such fault cascade propagation. Such as a north american blackout accident in 2003, a Luo Mada blackout in 2004, a power failure caused by a south China ice disaster in 2008, and a taiwan blackout accident of 8.15 in 2017. Therefore, the research on the failure cascade ship mechanism and the robustness analysis of the power system has important significance.
At present, the academic community generally adopts a graph theory method to study the robustness of an electric power information physical system, firstly establishes respective mathematical models of a physical network and an information network in the system based on the graph theory, then excavates a coupling relation between the two networks, establishes a dependent network model of the whole system, and analyzes the system robustness based on a seepage theory. However, the modeling simulation analysis method based on graph theory is not easy to show structural characteristics and dynamics rules of the complex network.
Disclosure of Invention
The invention provides a method for analyzing robustness of a power information physical system based on a reachable matrix, which aims to improve the problems.
The invention is realized in such a way that the robustness analysis method of the power information physical system based on the reachable matrix comprises the following steps:
s1, inputting an adjacency matrix Ep of a power network, an adjacency matrix Ec of an information network, and a dependence matrix Epc between the power network and the information network;
s2, determining an attack node in the power network, wherein the attack node is a starting point of fault propagation, deleting fault nodes in an adjacent matrix Ep and an adjacent matrix Ec after the fault propagation based on a dependent matrix Epc between the power network and an information network, and outputting the adjacent matrix Ep, the adjacent matrix Ec and the dependent matrix Epc;
s3, updating the dependency matrix Epc, and forming an attacked enlarged adjacent matrix based on the adjacent matrix Ep, the adjacent matrix Ec and the updated dependency matrix Epc;
s4, calculating a system robustness index P after the attack based on the extended adjacency matrix.
Further, the step S2 specifically includes the following steps:
s21, deleting rows and columns of attack nodes in an adjacent matrix Ep;
s22, determining a maximum connected matrix I in an adjacent matrix Ep, detecting whether rows and columns which do not belong to the maximum connected matrix I exist in the adjacent matrix Ep, deleting the rows and columns which do not belong to the maximum connected matrix I in the adjacent matrix Ep if the detected result is yes, executing a step S23, and directly executing the step S23 if the detected result is no;
s23, judging nodes which are dependent on the adjacent matrix Ep in the adjacent matrix Ec and delete rows and columns of the adjacent matrix Ep based on the dependent matrix Epc, and deleting the rows and columns of the dependent nodes in the adjacent matrix Ec;
s24, determining a maximum connected matrix II in the adjacent matrix Ec, detecting whether rows and columns which do not belong to the maximum connected matrix II exist in the adjacent matrix Ec, deleting the rows and columns which do not belong to the maximum connected matrix II in the adjacent matrix Ec if the detected result is yes, executing a step S25, and outputting adjacent matrix Ep and adjacent matrix Ec if the detected result is no;
s25, judging nodes which are dependent on the adjacent matrix Ec in the adjacent matrix Ep and delete rows and columns of the adjacent matrix Ec based on the dependent matrix Epc, and deleting rows and columns of the dependent nodes in the adjacent matrix Ep;
s26, determining a maximum connected matrix I in the adjacent matrix Ep, detecting whether rows and columns which do not belong to the maximum connected matrix I exist in the adjacent matrix Ep, deleting the rows and columns which do not belong to the maximum connected matrix I in the adjacent matrix Ep if the detected result is yes, executing step S23, and outputting adjacent matrix Ep and adjacent matrix Ec if the detected result is no.
Further, the calculation formula of the system robustness index P is specifically as follows:
Figure GDA0003166792840000031
wherein N 'is the order of the widened adjacent matrix after being attacked, N' S The sum of the degrees of all nodes in the enlarged adjacent matrix after being attacked is N, the order of the enlarged adjacent matrix before being attacked is N' S Is the sum of the degrees of all nodes in the extended adjacency matrix before attack.
Further, after step S4, the method further includes:
s5, taking the adjacent matrix Ep, the adjacent matrix Ec and the dependent matrix Epc as inputs of the next attack;
s6, arranging all nodes in the power network from large to small according to degrees, wherein the arrangement sequence of the nodes is the attack sequence of the nodes;
and S7, acquiring an attack sequence of the nodes contained in the adjacency matrix Ep, and executing the current attack by taking the node which is attacked first as the current attack node, namely executing the step S2.
Further, the extended adjacency matrix E is defined as follows:
Figure GDA0003166792840000032
where Ep is the adjacency matrix of the power network, ec is the adjacency matrix of the information network, epc is the dependency matrix between the power network and the information network, ecp is the transposed matrix of the dependency matrix Epc.
The robustness analysis method of the power information physical system based on the reachable matrix can not only reduce modeling complexity of the mutual coupling network, but also clearly and intuitively show structural characteristic changes and dynamics rules of network connection in the system, reduces complexity of an attack graph, and facilitates understanding and analysis of security personnel.
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FIG. 1 is a flow chart of a method for robustness analysis of a power information physical system based on a reachability matrix provided by an embodiment of the invention;
fig. 2 is an exemplary diagram of a power information physical system according to an embodiment of the present invention;
fig. 3 is a comparison chart of robustness analysis of different attack strategies provided by the embodiment of the present invention to the PCPS model provided by the present invention.
Detailed Description
The following detailed description of the embodiments of the invention, given by way of example only, is presented in the accompanying drawings to aid in a more complete, accurate, and thorough understanding of the inventive concepts and aspects of the invention by those skilled in the art.
S0, establishing a network model of a power information physical system, wherein the power information physical system is called as a system for short in the invention and comprises a power network subsystem and an information network subsystem, so that the network model of the power information physical system is formed by a power network model and a communication network model, and the construction of the power network model and the communication network model is described in detail below;
power grid network model: drawing out large-scale equipment such as power plants, transformer substations, converter stations and the like in power networksLike power nodes in a power grid network model, high voltage power lines are abstracted to edges between nodes in the power grid network model. Modeling a power grid as a network graph G P ＝(V P ,E P ) Wherein V is P ＝V P (G)＝{v p1 ,v p2 ,...,v pn }，V P Representing a set of nodes of a power network, E P Is an adjacency matrix of the power network, n is the number of nodes in the power network, wherein the adjacency matrix E of the power network P Can be expressed as:
Figure GDA0003166792840000051
the internal nodes of the power network are connected together by connecting edges to represent the connection relation between the internal nodes, when the association relation exists between the nodes in the network, the connection relation is 1, otherwise, the connection relation is 0, so that an adjacent matrix Ep of the power network is formed, and the connection relation is represented as follows:
Figure GDA0003166792840000052
communication network model: the method comprises the steps of abstracting equipment such as a router and a switch into communication nodes in a communication network model, abstracting communication lines such as cables and optical fibers into edges among the nodes in the communication network model, identifying all the edges as undirected edges, combining a plurality of lines in the same direction into one edge, eliminating multiple edges and self-loops, and ignoring the problems of capacity of the equipment and the lines, old and new nodes, node failure caused by overlarge load in the failure process and the like. Modeling a communication network as a network graph G C ＝(V C ,E C ) Wherein V is C ＝V C (G)＝{v c1 ,v c2 ,...,v cm }，V C Representing a set of nodes of a communication network, E C Is an adjacency matrix of the communication network, m is the number of nodes in the communication network, wherein,
Figure GDA0003166792840000053
wherein the internal nodes of the communication network are connected together by connecting edges to represent the connection relationship between the internal nodes, when the association relationship exists between the nodes in the network, the connection relationship is 1, otherwise, the connection relationship is 0, so that an adjacency matrix Ec of the communication network is formed, and the adjacency matrix Ec is represented as follows:
Figure GDA0003166792840000054
for the dependency relationship between the nodes of the power network and the communication network, a dependency matrix E can be used PC (E CP ) Representing the dependency matrix E CP Is a dependent matrix E PC Is a transposed matrix of (a), a dependent matrix E PC Can be expressed as:
Figure GDA0003166792840000061
abstracting the association relation between the power network and the information network nodes as edges in the network, wherein the association relation is 1 when the association relation exists between the network nodes, and otherwise, the association relation is 0, so that an inter-network dependency matrix is defined for the network nodes, and the inter-network dependency matrix is expressed as follows:
Figure GDA0003166792840000062
fig. 1 is a flowchart of a method for robustness analysis of an electric power information physical system based on a reachability matrix, which specifically includes the following steps:
s1, inputting an adjacency matrix Ep of a power network, an adjacency matrix Ec of an information network and a dependency matrix Epc between the power network and the information network;
s2, determining an attack node in the power network, wherein the attack node is a starting point of fault propagation, deleting fault nodes in an adjacent matrix Ep and an adjacent matrix Ec after fault propagation based on a dependent matrix Epc between the power network and an information network, and outputting the adjacent matrix Ep, the adjacent matrix Ec and the dependent matrix Epc, wherein the implementation method specifically comprises the following steps of:
s21, deleting rows and columns of attack nodes in an adjacent matrix Ep;
s22, determining a maximum connected matrix I in an adjacent matrix Ep, detecting whether rows and columns which do not belong to the maximum connected matrix I exist in the adjacent matrix Ep, deleting the rows and columns which do not belong to the maximum connected matrix I in the adjacent matrix Ep if the detected result is yes, executing a step S23, and directly executing the step S23 if the detected result is no;
s23, judging nodes which are dependent on the adjacent matrix Ep in the adjacent matrix Ec and delete rows and columns of the adjacent matrix Ep based on the dependent matrix Epc, and deleting the rows and columns of the dependent nodes in the adjacent matrix Ec;
s24, determining a maximum connected matrix II in the adjacent matrix Ec, detecting whether rows and columns which do not belong to the maximum connected matrix II exist in the adjacent matrix Ec, deleting the rows and columns which do not belong to the maximum connected matrix II in the adjacent matrix Ec if the detected result is yes, executing a step S25, and outputting adjacent matrix Ep and adjacent matrix Ec if the detected result is no;
s25, judging nodes which are dependent on the adjacent matrix Ec in the adjacent matrix Ep and delete rows and columns of the adjacent matrix Ec based on the dependent matrix Epc, and deleting rows and columns of the dependent nodes in the adjacent matrix Ep;
s26, determining a maximum connected matrix I in the adjacent matrix Ep, detecting whether rows and columns which do not belong to the maximum connected matrix I exist in the adjacent matrix Ep, deleting the rows and columns which do not belong to the maximum connected matrix I in the adjacent matrix Ep if the detected result is yes, executing step S23, and outputting adjacent matrix Ep and adjacent matrix Ec if the detected result is no.
S3, updating the dependency matrix Epc, and forming an attacked enlarged adjacent matrix based on the adjacent matrix Ep, the adjacent matrix Ec and the updated dependency matrix Epc;
the invention uniformly models the power information physical system into a network graph G= (V) by introducing the widening adjacency matrix E P ,V C E), wherein the extended adjacency matrix E is defined as follows:
Figure GDA0003166792840000071
by adopting the adjacency matrix to represent the network structure information of the system and directly establishing a system network model by using the adjacency matrix, the modeling complexity of the mutual coupling network can be reduced, and the understanding and analysis are convenient.
S4, calculating a system robustness index P after the attack based on the extended adjacency matrix, wherein a calculation formula of the system robustness index P is specifically as follows:
Figure GDA0003166792840000072
wherein N 'is the order of the widened adjacent matrix after being attacked, N' S The sum of the degrees of all nodes in the enlarged adjacent matrix after being attacked is N, the order of the enlarged adjacent matrix before being attacked is N' S The node degree is the sum of the degrees of all nodes in the extended adjacency matrix before being attacked, and is the number of other nodes connected with the node.
Fig. 2 is an example diagram of a power information physical system, in fig. 2 (a), a power network (hollow nodes) and an information network (solid nodes) are interdependent networks, wherein each node in the power network uniquely corresponds to one node in the information network, and vice versa.
When node 5 of the power network is attacked, the node and the edge connected with the node are all deleted, and node 11 in the information network which is dependent on the node is also deleted, at this time, the power network is split into three clusters, namely three relatively independent and non-communicated parts, as shown in fig. 2 (b).
At this time, the largest cluster (1, 2, 3) in the power network can know that the node No. 1, the node No. 2 and the node No. 3 are valid, the rest of the nodes are invalid, and the node No. 4 and the node No. 6 are invalid, so that the node No. 10 in the information network is invalid, and meanwhile, the node No. 12 and the largest cluster (7, 8) in the information network are out of connection, as shown in fig. 2 (c).
The maximum cluster (1, 2, 3) in the power network continues to split under the influence of the splitting cluster of the information network, and the final system is stable, and the maximum cluster of the stable system is (1, 2,7, 8) at the moment, as shown in fig. 2 (d).
Constructing an in-grid adjacency matrix E from the initial dependent network model in FIG. 2 (a) P Adjacency matrix E in information network C And inter-network dependency matrix E PC (E CP ) For ease of calculation and understanding, each column of the matrix is labeled with the same number as its node number, with the following result:
Figure GDA0003166792840000081
Figure GDA0003166792840000082
Figure GDA0003166792840000091
when the fifth node of the power grid is attacked, the adjacency matrix E of the fifth node of the power grid is deleted P Corresponding rows and columns and their power grid adjacency matrix E is determined P The rows and columns not belonging to the maximum connected matrix are deleted, and the result is as follows:
Figure GDA0003166792840000092
at this time, the number sets (4, 5, 6) are deleted in the rows and columns corresponding to the power grid adjacent matrix, and pass through the coupling network matrix E PC Judging the failure number set (10, 11, 12) dependent on the information network adjacent matrix, deleting the information network failure number in the adjacent matrix E C Corresponding rows and columns and their information network adjacency matrix E is determined C The result of deleting rows and columns not belonging to the maximum connected matrix is as follows:
Figure GDA0003166792840000093
at this time, braidingNumber 9 is deleted in the corresponding row and column of the information network adjacency matrix through the coupling network dependency matrix E PC Judging that the number 3 is dependent on the adjacent matrix in the power grid, deleting the number 3 from the adjacent matrix E P The corresponding rows and columns result as follows:
Figure GDA0003166792840000094
at this time, the power network and the information network adjacency matrix reach a stable state, no longer split, and the system widening adjacency matrix is output as follows:
Figure GDA0003166792840000101
from the evolution process of the system network and the system augmentation adjacency matrix, the interactive influence process of the information network and the power network is analyzed, the obtained results are the same, and the robustness indexes are all
Figure GDA0003166792840000102
Wherein the maximum connected part of the matrix (i.e. the maximum connected matrix) needs to be obtained by means of the reachable matrix in the present invention. Definition of the reachability matrix refers to describing the degree that can be achieved between nodes of the graph through a certain length of path in matrix form. The method for calculating the reachable matrix is as follows:
B＝(A+I) n ＝I+A+A 2 +……+A n
in the above formula, I represents an identity matrix, a represents an adjacency matrix of the graph, B represents an reachable matrix of the graph, n represents the total number of nodes of the system, and the reachable matrix represents whether at least one chain exists between any two nodes in the graph and whether a loop exists at the node.
The adjacency matrix of the graph is obtained by the node connection relation:
Figure GDA0003166792840000103
the reachable matrix of the graph can be found according to the above:
Figure GDA0003166792840000104
as can be seen from the definition of the reachable matrix and the graph thereof, in the reachable matrix, the number of the rows and columns 0 of the maximum connected part is the smallest (the number of the nodes in the maximum connected subgraph is the largest), so that the maximum connected part of the adjacent matrix a can be extracted, and the rows and columns which do not belong to the maximum connected part in the adjacent matrix a of the graph are deleted, so that the maximum connected matrix C of the matrix can be obtained.
Figure GDA0003166792840000105
The matrix C is the maximum connected matrix corresponding to the corresponding maximum connected subgraph, so that the maximum connected matrix is feasible according to the reachable matrix, namely the reachable matrix is shown to have feasibility in the aspect of robustness analysis of the electric power information physical system.
The invention takes the system as an attack object, takes random attack, node degree attack, node importance attack and node betweenness attack as attack strategies, and analyzes the robustness of the system by observing the change condition of the PCPS augmentation adjacency matrix. The attack strategy is subdivided as follows:
1) Random attack strategy: randomly selecting a certain number of nodes from the attack object network, and sequentially deleting corresponding rows and columns of the nodes in the subnet adjacent matrix according to the selection sequence; 2) Node degree attack strategy: sequencing all nodes in the attack object network from high degree to low degree (random damage is carried out when the degrees are the same), and sequentially deleting the corresponding rows and columns of the nodes in the subnet adjacency matrix; 3) Node importance attack policy: and calculating and sequencing the importance of all nodes in the attack object network. Sequentially deleting corresponding rows and columns of the nodes in the subnet adjacent matrix according to the order of the importance from high to low; 4) Node betting attack strategy: and calculating and sequencing the betweenness of all the nodes in the attack object network, and sequentially deleting the corresponding rows and columns of the nodes in the subnet adjacency matrix according to the order of the betweenness of the nodes from high to low.
The robustness analysis index P is found by the aforementioned power information physical system robustness assessment algorithm. In each attack, if the maximum communication matrix of the system changes, the attack is successful, otherwise, if the maximum communication matrix of the system does not change, the attack is invalid, and the attack times are not counted. And drawing a robustness change function curve of the power information physical system under several different fault modes by taking the attack times as an abscissa and taking a robustness analysis index P as an ordinate.
The invention takes IEEE118 node standard model as an example to construct the power network of the simulation experiment of the invention, sets corresponding communication nodes for 54 power supply nodes to form the communication network, connects the power supply nodes and the communication nodes according to a one-to-one correspondence, namely 54 communication nodes exist, and the connection mode among the communication nodes is regarded as adjacent power supply units according to the principle of nearby, namely if the 54 power supply units are connected through only one connecting line or one transformer substation, at the moment, the corresponding communication nodes are connected through the connecting line. An incomplete symmetric dependency network with 118 power nodes and 54 communication nodes is constructed from the power network, communication network topology and dependency relationship, from modeling the PCPS as a set of power network, communication network and dependency edges.
The PCPS robustness analysis index, the PCPS robustness evaluation algorithm and the attack strategy provided by the invention carry out robustness analysis on the established PCPS model, the simulation result is shown in figure 3, and the experimental result shows that the method has feasibility.
According to the method, simulation under different faults is carried out on the dependent network model based on the adjacency matrix, the robustness of the PCPS network is analyzed through the robustness of the power information physical system based on the reachable matrix, and the result shows that the reachable matrix has feasibility in the aspect of the robustness analysis of the power information physical system, so that the complexity of an attack graph is reduced, and the analysis and understanding are facilitated.
While the invention has been described above with reference to the accompanying drawings, it will be apparent that the invention is not limited to the above embodiments, but is capable of being modified or applied directly to other applications without modification, as long as various insubstantial modifications of the method concept and technical solution of the invention are adopted, all within the scope of the invention.

Claims (2)

1. The method for analyzing the robustness of the power information physical system based on the reachable matrix is characterized by comprising the following steps of:
s1, inputting an adjacency matrix Ep of a power network, an adjacency matrix Ec of an information network, and a dependence matrix Epc between the power network and the information network;
s2, determining an attack node in the power network, wherein the attack node is a starting point of fault propagation, deleting fault nodes in an adjacent matrix Ep and an adjacent matrix Ec after the fault propagation based on a dependent matrix Epc between the power network and an information network, and outputting the adjacent matrix Ep, the adjacent matrix Ec and the dependent matrix Epc;
s3, updating the dependency matrix Epc, and forming an attacked enlarged adjacent matrix based on the adjacent matrix Ep, the adjacent matrix Ec and the updated dependency matrix Epc;
s4, calculating a system robustness index P after the attack based on the extended adjacency matrix;
the step S2 specifically includes the following steps:
s21, deleting rows and columns of attack nodes in an adjacent matrix Ep;
s22, determining a maximum connected matrix I in an adjacent matrix Ep, detecting whether rows and columns which do not belong to the maximum connected matrix I exist in the adjacent matrix Ep, deleting the rows and columns which do not belong to the maximum connected matrix I in the adjacent matrix Ep if the detected result is yes, executing a step S23, and directly executing the step S23 if the detected result is no;
s23, judging nodes which are dependent on the adjacent matrix Ep in the adjacent matrix Ec and delete rows and columns of the adjacent matrix Ep based on the dependent matrix Epc, and deleting the rows and columns of the dependent nodes in the adjacent matrix Ec;
s24, determining a maximum connected matrix II in the adjacent matrix Ec, detecting whether rows and columns which do not belong to the maximum connected matrix II exist in the adjacent matrix Ec, deleting the rows and columns which do not belong to the maximum connected matrix II in the adjacent matrix Ec if the detected result is yes, executing a step S25, and outputting adjacent matrix Ep and adjacent matrix Ec if the detected result is no;
s25, judging nodes which are dependent on the adjacent matrix Ec in the adjacent matrix Ep and delete rows and columns of the adjacent matrix Ec based on the dependent matrix Epc, and deleting rows and columns of the dependent nodes in the adjacent matrix Ep;
s26, determining a maximum connected matrix I in an adjacent matrix Ep, detecting whether rows and columns which do not belong to the maximum connected matrix I exist in the adjacent matrix Ep, if so, deleting the rows and columns which do not belong to the maximum connected matrix I in the adjacent matrix Ep, executing step S23, and if not, outputting adjacent matrix Ep and adjacent matrix Ec;
after step S4, the method further comprises:
s5, taking the adjacent matrix Ep, the adjacent matrix Ec and the dependent matrix Epc as inputs of the next attack;
s6, arranging all nodes in the power network from large to small according to degrees, wherein the arrangement sequence of the nodes is the attack sequence of the nodes;
s7, acquiring an attack sequence of nodes contained in an adjacency matrix Ep, taking the node which is attacked first as a current attack node, and executing the current attack, namely executing the step S2;
the extended adjacency matrix E is defined as follows:
Figure FDA0004174581270000021
wherein, ep is the adjacent matrix of the power network, ec is the adjacent matrix of the information network, epc is the dependent matrix between the power network and the information network, ecp is the transposed matrix of the dependent matrix Epc;
calculating a reachable matrix based on the adjacent matrix E, wherein the maximum communication part of the reachable matrix has the maximum number of nodes in the rows and the columns, extracting the maximum communication part of the adjacent matrix E, deleting the rows and the columns which do not belong to the maximum communication part in the adjacent matrix E, and obtaining the maximum communication matrix of the matrix; the adjacency matrix E is adjacency matrix Ep or adjacency matrix Ec.
2. The method for analyzing the robustness of the power information physical system based on the reachable matrix according to claim 1, wherein a calculation formula of the system robustness index P is specifically as follows:
Figure FDA0004174581270000022
wherein N 'is the order of the widened adjacent matrix after being attacked, N' s The sum of the degrees of all nodes in the enlarged adjacent matrix after being attacked is N, the order of the enlarged adjacent matrix before being attacked is N' s Is the sum of the degrees of all nodes in the extended adjacency matrix before attack.
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