Iterative estimation method and device for composite cascade fault propagation influence range

Abstract

The invention relates to the technical field of smart power grids, in particular to an iterative estimation method and device for a composite cascade fault propagation influence range, which can solve the problems of how to optimize resource configuration, strengthen protection and monitoring of key nodes and take prevention and control measures before large-scale propagation of faults to a certain extent. And the problem of influence of power failure on economy and society is reduced. The method comprises the following steps: abstracting an interaction relationship of nodes in the smart power grid as G = (Gp, Gc, Ec-p, Ep-c); wherein Gp (P, Ep) is a physical network, P is a physical node set, Gc (C, Ec) is an information network, and C is an information node set; based on the network state information at the current moment, the state transition probability of each node is calculated by decoupling the time and space dependency relationship and utilizing the Markov property; according to the state transition probability of each node, iteratively obtaining the probability distribution of each node state in the next time slice and the average number of affected nodes in the whole network, and obtaining an estimation result of the composite cascade fault propagation influence range.

Description

Technical Field

[0001] The present application relates to the field of smart grid technology, and in particular to a method and device for iteratively estimating the impact range of compound cascading fault propagation. Background Art

[0002] Smart grids couple the physical network that provides electricity with the information network that provides control functions, thereby greatly improving the reliability of the grid. The information network can intelligently monitor and control the grid, optimize the operation and management of the grid, help reduce the cost of grid construction and operation, and improve the economic benefits and resource utilization efficiency of the grid. However, the high degree of dependence between nodes also makes smart grids more sensitive to faults. Failures of a few nodes may spread over a large area, forming cascading failures.

[0003] Existing methods can analyze the propagation of a single fault type, but it is difficult to analyze compound cascading faults that exist in both physical and information networks. In recent years, network security incidents have gradually increased, and information networks are becoming an attack entry point for power grids. Compound cascading faults are very likely to become the main type of fault in the future. Estimating the propagation range of cascading faults will help power grid operators better understand the weak links of the power grid.

[0004] Therefore, it is urgent to provide a new prediction method to optimize resource allocation, strengthen the protection and monitoring of key nodes, take preventive and control measures before the fault occurs on a large scale, and reduce the impact of power outages on the economy and society. Summary of the invention

[0005] In order to solve the problem of how to optimize resource allocation, strengthen the protection and monitoring of key nodes, take prevention and control measures before large-scale propagation of faults, and reduce the impact of power outages on the economy and society, the present application provides an iterative estimation method and device for the impact range of compound cascading fault propagation.

[0006] The embodiment of the present application is implemented as follows:

[0007] In a first aspect, the present application provides a method and device for iteratively estimating the impact range of compound cascading fault propagation, including:

[0008] The interaction relationship of nodes in the smart grid is abstracted as G = (G p , G c , E c→p , E p→c );

[0009] Among them, G p (P,E p ) is the physical network, P is the set of physical nodes, G c (C,Ec ) is an information network, c is a set of information nodes;

[0010] Based on the current network status information, the state transition probability of each node is calculated by decoupling the time and space dependencies and using the Markov property.

[0011] According to the state transition probability of each node, the probability distribution of each node state in the next time slice and the average number of affected nodes in the entire network are iteratively obtained to obtain the estimated result of the impact range of the compound cascading fault propagation.

[0012] In a possible implementation, the time of the initial state of the network state information is recorded as t=0, and and It is called the initial screenshot of this system.

[0013] In one possible implementation, given the initial screenshot, the state transition of the system can be given by the following time-recursive master equation:

[0014]

[0015]

[0016] At any time t, the estimated number of physical nodes in the power grid that can still work normally is

[0017]

[0018] In a possible implementation, the propagation process of the composite cascading fault is decoupled in an asynchronous iterative manner, that is, the fault propagation in the information network and the physical network is performed alternately in each time step.

[0019] In one possible implementation, in the calculation of information networks, the propagation within a time step is divided into two stages, namely, time

[0020] In one possible implementation, the state correlation between adjacent nodes is considered and the state of their neighbors is enumerated using the total probability formula. Node c i The probability of infection in a neighborhood in a time slice and the probability that the neighborhood is in the maximum connected component

[0021] in, is the average probability that any node is not in the maximum connected component, q k，t-1 is the excess distribution; in the transition probability, the time dependence is included in I i (t) and LCC i(t), while the spatial dependence is given by the joint conditional probability describe.

[0022] In one possible implementation, the decomposition is performed based on conditional probability, using intermediate variables as well as The state transition probability is written as follows:

[0023] Node c i exist The probability of losing all power (transferring to offline state) is:

[0024]

[0025] Node c i exist The probability of remaining in the normal state (susceptible state) is:

[0026]

[0027] Node c i exist The probability of being infected (transferring from susceptible state to infected state) is:

[0028]

[0029] Node c i exist The probability of not being in the maximum connected component (transferring to the offline state) is:

[0030]

[0031] In one possible implementation, in the computation of the physical network, similar to the computation in the information network, the neighborhood states are enumerated using the total probability formula for derivation;

[0032] Physical node p i The probability of not losing control (i.e. the information nodes that the node depends on are still in a susceptible state) is:

[0033]

[0034] Physical node p i The probability of not being overloaded (i.e. the current load is less than or equal to the maximum threshold) is:

[0035]

[0036] In one possible implementation, a physical node p i The load of is the original load plus the load transferred through load balancing after the neighbor fails, that is,

[0037]

[0038] The load that a physical node distributes to its neighbors when it changes from a normal state to a faulty state is calculated as follows:

[0039]

[0040] In a second aspect, the present application provides an iterative estimation device for a composite cascading fault propagation impact range, comprising:

[0041] The network input module is used to abstract the interaction relationship of nodes in the smart grid as G = (G p , G c , E c→p , E p→c );

[0042] The probability calculation module is used to calculate the state transition probability of each node based on the current network state information by decoupling the time and space dependencies and using the Markov property;

[0043] The iterative estimation module is used to iteratively obtain the probability distribution of each node state in the next time slice according to the state transition probability of each node, as well as the average number of nodes affected in the entire network, and obtain the estimated result of the impact range of the composite cascading fault propagation.

[0044] The technical solution provided by this application can at least achieve the following beneficial effects:

[0045] The iterative estimation method of the impact range of compound cascading fault propagation provided by this application is

[0046] By taking the smart grid topology information into account and expressing it in the form of an adjacency matrix, the accuracy loss caused by the estimation based on the state mean is avoided, making the result closer to the true value and making the method universal.

[0047] By decoupling the spatial factors (i.e., the communication relationship between nodes in the information network, the load balancing relationship between nodes in the physical network) and the temporal factors (i.e., the order of load balancing and virus propagation) on which the propagation of compound cascading failures depends through the method of probability analysis, the dynamic process is made to have local Markov properties, so that its development process can be deduced.

[0048] By combining the mutual influence between information network nodes by adding edge distribution terms, the accuracy loss caused by assuming independent node states in traditional estimation is avoided.

[0049] By constructing an iterative deduction algorithm, given any starting state and network topology information, the expected impact range of compound cascading failures in the network at any time and the failure probability of each node can be output through iterative deduction. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, a brief introduction will be given below to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0051] Figure 1 It is a flowchart of an iterative estimation method for the impact range of compound cascading fault propagation shown in an exemplary embodiment of the present application;

[0052] Figure 2 It is a flowchart of an iterative estimation algorithm for information propagation influence range shown in an exemplary embodiment of the present application;

[0053] Figure 3 It is a structural schematic diagram of an iterative estimation device for the impact range of compound cascading fault propagation shown in an exemplary embodiment of the present application;

[0054] Figure 4 It is a schematic diagram of a composite cascading fault propagation process in a smart grid shown in an exemplary embodiment of the present application.

[0055] Reference numerals:

[0056] 1. Network input module; 2. Probability calculation module; 3. Iterative estimation module. DETAILED DESCRIPTION

[0057] In order to make the purpose, implementation mode and advantages of the present application clearer, the exemplary implementation mode of the present application will be clearly and completely described below in conjunction with the drawings in the exemplary embodiments of the present application. Obviously, the described exemplary embodiments are only part of the embodiments of the present application, not all of the embodiments. It should be understood that the specific embodiments described here are only used to explain the present application and are not used to limit the present application.

[0058] It should be noted that the brief description of terms in this application is only for the convenience of understanding the embodiments described below, and is not intended to limit the embodiments of this application. Unless otherwise specified, these terms should be understood according to their ordinary and common meanings.

[0059] The terms "first", "second", "third", etc. in the specification and claims of this application and the above drawings are used to distinguish similar or similar objects or entities, and do not necessarily mean to limit a specific order or sequence, unless otherwise noted. It should be understood that the terms used in this way can be interchangeable under appropriate circumstances.

[0060] The terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover but not exclude inclusion, for example, a product or device comprising a list of components is not necessarily limited to all the components expressly listed but may include other components not expressly listed or inherent to such product or device.

[0061] Before explaining the iterative estimation method for the impact range of compound cascading fault propagation provided in the embodiment of the present application, the application scenario and implementation environment of the embodiment of the present application are first introduced.

[0062] Smart grids couple the physical network that provides electricity with the information network that provides control functions, thereby greatly improving the reliability of the grid. The information network can intelligently monitor and control the grid, optimize the operation and management of the grid, help reduce the cost of grid construction and operation, and improve the economic benefits and resource utilization efficiency of the grid. However, the high degree of dependence between nodes also makes smart grids more sensitive to faults. Failures of a few nodes may spread over a large area, forming cascading failures.

[0063] Existing methods can analyze the propagation of a single fault type, but it is difficult to analyze compound cascading faults that exist in both physical and information networks. In recent years, network security incidents have gradually increased, and information networks are becoming an attack entry point for power grids. Compound cascading faults are very likely to become the main type of fault in the future. Estimating the propagation range of cascading faults will help power grid operators better understand the weak links of the power grid.

[0064] Therefore, it is urgent to provide a new prediction method to optimize resource allocation, strengthen the protection and monitoring of key nodes, take preventive and control measures before the fault occurs on a large scale, and reduce the impact of power outages on the economy and society.

[0065] Based on this, the present application provides an iterative estimation method and device for the impact range of compound cascade fault propagation. First, the management agency describes the topological structure of the smart grid as an adjacency matrix of dimension (the smart grid is modeled as a coupling of a physical network and an information network, and the number of nodes in the physical network and the information network are both ); then, at the initial stage of propagation, the propagation intensity of the virus in the information network and the current impact range are obtained through short-term observation; on this basis, the local Markov property of the fault propagation process is utilized to decouple the spatial and temporal factors on which the fault propagation depends, and the impact range of the physical fault of the power grid at any time is calculated based on the recursive expression under the condition that the infection of the corresponding information network propagates simultaneously.

[0066] Next, the technical solution of the present application and how the technical solution of the present application solves the above-mentioned technical problems will be described in detail through embodiments and in combination with the accompanying drawings. The embodiments may be combined with each other, and the same or similar concepts or processes may not be repeated in some embodiments. Obviously, the described embodiments are part of the embodiments of the present application, not all of them.

[0067] Figure 1 It is a flowchart of an iterative estimation method for the impact range of compound cascading fault propagation shown in an exemplary embodiment of the present application.

[0068] In an exemplary embodiment, Figure 1 As shown, a method for iteratively estimating the impact range of compound cascading fault propagation is provided. In this embodiment, the method may include the following steps:

[0069] Step 100: Abstract the interaction relationship of nodes in the smart grid as G = (G p , G c , E c→p , E p→c ).

[0070] Among them, G p (P,E p ) is the physical network, P is the set of physical nodes, G c (C,E c ) is an information network, and C is a set of information nodes.

[0071] Step 200: Based on the network status information at the current moment, the state transition probability of each node is calculated by decoupling the time and space dependencies and using the Markov property.

[0072] Step 300: Iteratively obtain the probability distribution of each node state in the next time slice and the average number of nodes affected in the entire network according to the state transition probability of each node, and obtain an estimation result of the impact range of the composite cascading fault propagation.

[0073] In a possible implementation, the estimation method first abstracts the interaction relationship of nodes in the smart grid into a graph G = (G p , G c , E c→p , E p→c ), where G p (P,E p ) is the physical network, P is the set of physical nodes, G c (C,E c ) is an information network, and C is a set of information nodes.

[0074] Then, based on the network status information at the current moment (called a network screenshot), by decoupling the time and space dependencies, the state transition probability of each node is calculated using the Markov property, and based on this, the probability distribution of the state of each node in the next time slice and the average number of affected nodes in the entire network are iteratively obtained to estimate the impact range of the propagation of compound cascading faults.

[0075] In a possible implementation, the specific implementation is as follows:

[0076] Define the scope of impact of compound cascading failure propagation:

[0077] Without loss of generality, the time when the network initial state is observed is recorded as t = 0, and It is called the initial screenshot of this system.

[0078] Given the initial screenshot, the state transition of the system can be given by the following time-recursive master equation:

[0079]

[0080]

[0081] At any time t, the estimated number of physical nodes in the power grid that can still work normally is:

[0082]

[0083] Iterative calculation of transition probability and impact range

[0084] The present invention decouples the propagation process of the composite cascading fault by adopting an asynchronous iteration mode, that is, the fault propagation in the information network and the physical network is performed alternately in each time step.

[0085] First, the calculation in the information network divides the propagation within a time step into two stages, namely, time Considering the state correlation between adjacent nodes, the total probability formula is used to enumerate the states of their neighbors. Node c i The probability of infection in a neighborhood in a time slice and the probability that the neighborhood is in the maximum connected component

[0086] in:

[0087] is the average probability that any node is not in the maximum connected component, q k，t-1 It is the excess degree distribution.

[0088] In the transition probability, the time dependence is included in I i (t) and LCC i (t), while the spatial dependence is given by the joint conditional probability In order to avoid the prediction accuracy deviation caused by the assumption that the node states are independent of each other in the traditional method, the present invention decomposes based on conditional probability and uses intermediate variables as well as The one-step state transition probability is written as follows:

[0089] That is, node c i exist The probability of losing all power (transferring to offline state) is:

[0090]

[0091] Node c i exist The probability of remaining in the normal state (susceptible state) is:

[0092]

[0093] Node c i exist The probability of being infected (transferring from susceptible state to infected state) is:

[0094]

[0095] Node c i exist The probability of not being in the maximum connected component (transferring to the offline state) is:

[0096]

[0097] Only equations (5), (6), and (7) are needed to fully describe the state changes of a node during the simultaneous propagation of positive and negative information.

[0098] The above formula shows that, given the initial state, the dynamic process of virus propagation has dependencies in both time and space, that is, node c i Status Determined by the state of the previous time slice Neighbor node status (in space) And the propagation action of neighbor nodes in the current time slice (infected or not in the maximum connected component). Among them, the propagation action is composed of the transition probability in each time slice t Description, where s, r∈{0, 1, -1}, the specific calculation method is as follows:

[0099]

[0100] in, Indicates that at a fixed node c j After node c is in state w i The probability of the state migrating from u to v in time slice t is calculated as follows:

[0101]

[0102] Next is the calculation in the physical network. The method is similar to the calculation in the information network. The neighborhood state is enumerated using the total probability formula for derivation.

[0103] Physical node p i The probability of not losing control (i.e. the information node that the node depends on is still in a susceptible state) is

[0104]

[0105] Physical node p i The probability of not being overloaded (i.e., the current load is less than or equal to the maximum threshold) is

[0106]

[0107] A physical node p i The load of is the original load plus the load transferred through load balancing after the neighbor fails, that is,

[0108]

[0109] The load that a physical node distributes to its neighbors when it changes from a normal state to a faulty state is calculated as follows:

[0110]

[0111] The degree distribution of the last updated information network:

[0112]

[0113] in,

[0114] In order to solve the real-time impact range of compound cascading failures, the following six transition probability matrices are defined as intermediate variables:

[0115]

[0116] Figure 2 It is a flowchart of an iterative estimation algorithm for the information propagation influence range shown in an exemplary embodiment of the present application.

[0117] Based on the above definition, an iterative estimation algorithm is proposed for smart grids with arbitrary topology G = (G p , G c , E c→p , E p→c ), and any initial network screenshots on it Iteratively estimate the composite cascading failure at any time t e (t e >0) for the network G=(G p , G c , E c→p , E p→c ), the specific implementation process of the iterative algorithm is as follows Figure 2 shown.

[0118] In the above-mentioned iterative estimation method of the impact range of compound cascading fault propagation, by taking into account the smart grid topology information and expressing it in the form of an adjacency matrix, the accuracy loss caused by the estimation based on the state mean is avoided, making the result closer to the true value and making the method universal.

[0119] By decoupling the spatial factors (i.e., the communication relationship between nodes in the information network, the load balancing relationship between nodes in the physical network) and the temporal factors (i.e., the order of load balancing and virus propagation) on which the propagation of compound cascading failures depends through the method of probability analysis, the dynamic process is made to have local Markov properties, so that its development process can be deduced.

[0120] By combining the mutual influence between information network nodes by adding edge distribution terms, the accuracy loss caused by assuming independent node states in traditional estimation is avoided.

[0121] By constructing an iterative deduction algorithm, given any starting state and network topology information, the expected impact range of compound cascading failures in the network at any time and the failure probability of each node can be output through iterative deduction.

[0122] It should be understood that, although the various steps in the flowcharts involved in the above-mentioned embodiments are displayed in sequence according to the instructions, these steps are not necessarily executed in sequence according to the order of the instructions. Unless there is a clear explanation in this article, the execution of these steps is not strictly limited in order, and these steps can be executed in other orders. Moreover, at least a portion of the steps in the flowcharts involved in the above-mentioned embodiments may include multiple steps or multiple stages, and these steps or stages are not necessarily executed at the same time, but can be executed at different times, and the execution order of these steps or stages is not necessarily to be carried out in sequence, but can be executed in turn or alternately with other steps or at least a portion of the steps or stages in other steps.

[0123] Corresponding to the aforementioned embodiment of the iterative estimation method for the impact range of compound cascading fault propagation, and adopting the same technical concept, the present application also provides an embodiment of the iterative estimation device for the impact range of compound cascading fault propagation.

[0124] Figure 3 It is a structural schematic diagram of an iterative estimation device for the impact range of compound cascading fault propagation shown in an exemplary embodiment of the present application.

[0125] In an exemplary embodiment, Figure 3 As shown, the iterative estimation device for the impact range of the composite cascading fault propagation includes:

[0126] The network input module 1 is used to abstract the interaction relationship of nodes in the smart grid as G = (G p , G c , E c→p , E p→c );

[0127] Probability calculation module 2 is used to calculate the state transition probability of each node based on the network state information at the current moment by decoupling the time and space dependencies and using the Markov property;

[0128] Iterative estimation module 3 is used to iteratively obtain the probability distribution of each node state in the next time slice according to the state transition probability of each node, as well as the average number of nodes affected in the entire network, and obtain the estimated result of the impact range of the composite cascading fault propagation

[0129] For the specific definition of the iterative estimation device for the impact range of compound cascade fault propagation, please refer to the definition of the iterative estimation method for the impact range of compound cascade fault propagation, which will not be repeated here. Each module in the above-mentioned iterative estimation device for the impact range of compound cascade fault propagation can be implemented in whole or in part by software, hardware and a combination thereof. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.

[0130] It can be seen that:

[0131] The estimation of this application is highly real-time: the traditional estimation method belongs to steady-state analysis, which can only estimate the final state of the smart grid system after the fault propagation ends, and lacks the understanding of the fault propagation process. The algorithm proposed in this invention can estimate the state of the smart grid system at any time and the failure probability of each node at any time through iterative deduction.

[0132] The estimation of the present application is highly accurate: the algorithm proposed in the present invention estimates the impact of the entire propagation process using conditional probability and marginal probability distribution, rather than using expectation, thereby improving the accuracy of the estimation.

[0133] The algorithm of the present application has a wide range of applications: from the perspective of applicable networks, due to the introduction of network topology, the algorithm is applicable to heterogeneous scenarios with various topologies and various parameters; from the perspective of algorithm execution, the lower space and time complexity makes the algorithm suitable for deployment on a variety of computing platforms.

[0134] Figure 4 It is a schematic diagram of a composite cascading fault propagation process in a smart grid shown in an exemplary embodiment of the present application.

[0135] To verify this application, a pre-estimation experiment was conducted, in which the composite cascade fault propagation in the smart grid is as follows Figure 4 As shown, a physical node may lose control of an information node or become overloaded, an information node may lose power to the physical node, become infected, or become separated from a large number of connected components, and failures from multiple causes propagate simultaneously on the network, causing node states to change over time.

[0136] Assume that the time at which the impact range is to be estimated is t e =1, such as Figure 2 As shown. Figure 2 The smart grid G(G p , G c , E c→p , E p→c ) as an example, its physical node set is P(p 1 , p2 , p 3 , p 4 , p 5 , p 6 ), the information node set is C = {c 1 , c 2 , c 3 , c 4 , c 5 , c 6}, here we assume it is an unweighted graph. Screenshot of the initial network Based on the initial network screenshot and node load properties, t is calculated using an iterative method. e =1 when the edge distribution of physical node status Finally, we find E(|N(t=1)|)=3. e >1, multiple iterations can be performed according to the algorithm.

[0137] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0138] The above-described embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the attached claims.

Claims

1. An iterative estimation method for the impact range of compound cascading fault propagation, characterized in that: include: The interaction relationship of nodes in the smart grid is abstracted as G = (G p , G c , F c→p , E p→c ); Among them, G p (P,E p ) is the physical network, P is the set of physical nodes, G c (C,E c ) is an information network, C is a set of information nodes; Based on the current network status information, the state transition probability of each node is calculated by decoupling the time and space dependencies and using the Markov property. According to the state transition probability of each node, the probability distribution of each node state in the next time slice and the average number of affected nodes in the entire network are iteratively obtained to obtain the estimated result of the impact range of the compound cascading fault propagation.

2. The iterative estimation method for the impact range of compound cascading fault propagation according to claim 1, characterized in that: The time of the initial state of the network state information is recorded as t=0, and and It is called the initial screenshot of this system.

3. The iterative estimation method for the impact range of compound cascading fault propagation according to claim 2, characterized in that: Given the initial screenshot, the state transition of the system can be given by the following time-recursive master equation: At any time t, the estimated number of physical nodes in the power grid that can still work normally is 4. The iterative estimation method for the impact range of compound cascading fault propagation according to claim 1, characterized in that: The propagation process of compound cascading faults is decoupled in an asynchronous iterative manner, that is, fault propagation in the information network and the physical network is performed alternately in each time step.

5. The iterative estimation method for the impact range of compound cascading fault propagation according to claim 1, characterized in that: In the calculation of information networks, the propagation within a time step is divided into two stages, namely time 6. The iterative estimation method for the impact range of compound cascading fault propagation according to claim 5, characterized in that: Considering the state correlation between adjacent nodes, the total probability formula is used to enumerate the states of their neighbors. Node c i The probability of infection in a neighborhood in a time slice and the probability that the neighborhood is in the maximum connected component in, is the average probability that any node is not in the maximum connected component, q k，t-1 is the excess distribution; in the transition probability, the time dependence is included in I i (t) and LCC i (t), while the spatial dependence is given by the joint conditional probability describe.

7. The iterative estimation method for the impact range of compound cascading fault propagation according to claim 5, characterized in that: Decomposition based on conditional probability, with the help of intermediate variables as well as The state transition probability is written as follows: Node c i exist The probability of losing all power (transferring to offline state) is: Node c i exist The probability of remaining in the normal state (susceptible state) is: Node c i exist The probability of being infected (transferring from susceptible state to infected state) is: Node c i exist The probability of not being in the maximum connected component (transferring to the offline state) is:

8. The iterative estimation method for the impact range of compound cascading fault propagation according to claim 1, characterized in that: In the computation of physical networks, similar to the computation in information networks, the neighborhood states are enumerated using the total probability formula for derivation; Physical node p i The probability of not losing control (i.e. the information nodes that the node depends on are still in a susceptible state) is: Physical node p i The probability of not being overloaded (i.e. the current load is less than or equal to the maximum threshold) is:

9. The iterative estimation method for the impact range of compound cascading fault propagation according to claim 8, characterized in that: A physical node p i The load of is the original load plus the load transferred through load balancing after the neighbor fails, that is, The load that a physical node distributes to its neighbors when it changes from a normal state to a faulty state is calculated as follows:

10. An iterative estimation device for the impact range of compound cascading fault propagation, characterized in that: include: The network input module is used to abstract the interaction relationship of nodes in the smart grid as G = (G p , G c , E c→p , E p→c ); The probability calculation module is used to calculate the state transition probability of each node based on the current network state information by decoupling the time and space dependencies and using the Markov property; The iterative estimation module is used to iteratively obtain the probability distribution of each node state in the next time slice and the average number of nodes affected in the entire network according to the state transition probability of each node, and obtain the estimated result of the impact range of the composite cascading fault propagation.

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