Power system disaster risk scheduling optimization method combined with behavior cloning

Abstract

The invention discloses an electric power system disaster risk scheduling optimization method in combination with behavior cloning, and belongs to the technical field of electric power system scheduling optimization. In combination with a behavior cloning technology, expert experience is quickly learned in an initial stage, the scheduling efficiency is improved, and adaptive scheduling in a dynamic environment is realized through reinforcement learning of an optimization strategy; according to the method, the preliminary scheduling strategy is quickly generated by directly utilizing expert experience through a behavior cloning technology, and a foundation is laid for subsequent optimization. According to the method, the disaster risk is prevented in advance, the system stability is improved, the dependency relationship between equipment and the cascading failure propagation effect are quantified, the effectiveness and adaptability of the scheduling strategy are improved through the two-stage learning strategy, the stability and robustness of the scheduling optimization process are improved, and the equipment failure and the system risk are reduced.

Description

Technical Field

[0001] The invention belongs to the technical field of power system dispatch optimization, and specifically is a power system disaster risk dispatch optimization method combined with behavior cloning. Background Art

[0002] At present, disaster risk dispatch of power systems mainly relies on traditional rule-driven methods and model-based optimization methods. These methods usually assume that equipment failures are isolated events, ignoring the complex correlation between equipment and the cascading failure propagation effect. Under extreme climate conditions such as icing disasters, this simplified assumption is difficult to truly reflect the complexity of the system's dynamic response, resulting in insufficient effectiveness and reliability of dispatch strategies.

[0003] The existing technologies have the following main shortcomings: Ignoring the interdependence between equipment: Traditional scheduling methods do not fully consider the propagation effect of equipment failures and cannot accurately quantify the impact of cascading failures on the overall risk of the system. Insufficient response to extreme weather events: Existing scheduling technologies are usually unable to quickly respond to dynamically changing risk environments, especially when icing disasters occur, and it is difficult to generate efficient scheduling decisions in a timely manner. Lack of intelligent adaptive capabilities: Traditional methods rely more on static rules or optimization models, which are difficult to adapt to the complex and changing environment under icing disasters, and the scheduling strategies lack flexibility and adaptability. Low efficiency in the use of historical data: Traditional optimization methods fail to effectively combine expert experience and historical data, resulting in low efficiency in the generation of scheduling strategies and difficulty in completing optimization in a short period of time. Summary of the invention

[0004] Aiming at the shortcomings of the existing power system disaster dispatching technology under extreme weather conditions, the present invention proposes a disaster risk dispatching optimization method combining behavioral cloning and deep Q network (BC-DQN) algorithm. The following technical problems need to be solved: The existing dispatching strategy lacks consideration of the effect of chain failure propagation: The traditional dispatching method fails to fully quantify the dependency between devices and the impact of chain failure propagation on the overall reliability of the system. The present invention solves this problem by introducing a fault propagation model based on the adjacency matrix. Insufficient emergency dispatching efficiency and decision-making flexibility: Under extreme weather conditions such as icing disasters, the existing dispatching strategy has a slow response speed and lacks real-time optimization capabilities for dynamic environments. The present invention combines behavioral cloning technology to quickly learn expert experience in the initial stage to improve dispatching efficiency, and realizes adaptive dispatching in a dynamic environment through reinforcement learning optimization strategy. Insufficient utilization of expert experience: Traditional methods fail to fully mine and utilize historical expert dispatching data, resulting in poor initial performance of dispatching strategies in disaster emergency. The present invention directly utilizes expert experience through behavioral cloning technology to quickly generate preliminary dispatching strategies, laying the foundation for subsequent optimization. Stability issues of dispatching models under complex disaster scenarios: Existing methods are prone to problems of unstable training or slow convergence in high-dimensional complex environments. The present invention improves the stability and convergence speed of the scheduling optimization process by introducing experience replay and target network technology.

[0005] The technical solution of the present invention is as follows: a method for optimizing power system disaster risk dispatch combined with behavioral cloning, comprising the following steps:

[0006] S1 Establish risk model: P f =f(I,W,C), where P f The failure probability of each device is given by I, the amount of ice and snow accumulation, W, the wind speed, and C, the device characteristic parameters, which are used as the basic inputs for the failure probability;

[0007] S2 Establish a regression model for failure probability: Use historical data to fit the regression equation and predict the equipment failure probability P f , that is, P f =a0+a1I+a2W+a3C+a4I 2 +a5W 2 +a6C 2 +..., where a0,a1,...,a n is the regression coefficient, construct the objective function:

[0008]

[0009] By taking the partial derivative of L with respect to the regression coefficient to zero, we can obtain the optimal estimate of the regression coefficient.

[0010] S3 establishes a cascading failure model: using topological structures to describe fault propagation and recursively calculating the failure probability after propagation Among them, P i is the failure probability, A ij is an element in the adjacency matrix, is the probability before device j fails, is the new probability after device j fails, α is the propagation factor;

[0011] S4 Cascading Fault Propagation Path: Calculate the fault propagation index to assess system vulnerability and identify key equipment through the formula Analyze the cascading failure propagation path, where represents the updated failure probability of device i after fault propagation;

[0012] S5 Using BC-DQN to build a reinforcement learning model S t = {P f (t),C t ,L t ,O t ,P c}, where S t is the state space, P f (t) is the probability of equipment failure; L t is the load state; O t is the topological information; c Cascading failure effects;

[0013] S6 establishes the action space A t ={a1,a2,...,a M}, where a M is a specific dispatching action of the system, M is the size of the action space, which depends on the scale of the power grid and the control strategy;

[0014] S7 builds a return function Among them, λ1, λ2, λ3 are weight coefficients, is the sum of the failure probabilities of all devices, f l is the load imbalance, P c It is the impact degree of cascading failure.

[0015] Furthermore, in step S1, the amount of ice and snow accumulation Among them, P x (t') is the snowfall rate at time t', P m (t') is the melting rate of ice and snow.

[0016] Furthermore, P x (t') = f(T,H), where T is temperature and H is humidity.

[0017] Furthermore, Pm (t') = β·(T(t')-T f )·F w (t'), T(t') is the temperature at time t', T f The freezing temperature of ice and snow, usually set to 0℃, F w (t') is the wind speed at time t', and β is a constant representing the sensitivity of temperature and wind speed to the melting rate.

[0018] Furthermore, in step S3, the power system consists of N devices, and each device i corresponds to a failure probability P i , there is a dependency relationship between devices for power transmission, represented by the adjacency matrix A. If there is a dependency relationship between device i and device j, then A ij =1, otherwise A ij = 0, when device i fails, the failure probability of device j is P j Will be affected by P i impact.

[0019] The beneficial effects of the present invention are:

[0020] (1) Prevent disaster risks in advance and improve system stability: This invention combines historical expert data and environmental parameters and uses behavior cloning to quickly generate pre-disaster dispatch strategies, enabling the power system to perform preventive dispatch of potential risk areas and high-failure probability equipment before a disaster occurs. Compared with the prior art, this invention can optimize the equipment operating status before a disaster occurs, thereby reducing the probability of equipment failure and cascading failures.

[0021] (2) Quantifying the dependencies between devices and the cascading fault propagation effects: In view of the fact that the existing scheduling methods do not fully consider the correlation between devices and the fault propagation characteristics, the present invention establishes a fault propagation model based on the adjacency matrix, which can accurately describe the mutual influence between devices. By considering the failure probability and cascading effect of power equipment, the present invention optimizes the design of the scheduling scheme, so that the scheduling strategy can effectively reduce the system risk caused by cascading failures.

[0022] (3) The two-stage learning strategy improves the effectiveness and adaptability of the scheduling strategy: By combining behavioral cloning and deep Q-network, the present invention adopts a two-stage learning strategy to quickly acquire expert experience in the early stage and generate a preliminary pre-disaster scheduling strategy; then, the strategy is continuously optimized through reinforcement learning, so that the scheduling scheme can dynamically adapt to complex pre-disaster environmental changes. This framework that combines imitation and optimization significantly improves the effectiveness and flexibility of the scheduling strategy.

[0023] (4) Improved the stability and robustness of the scheduling optimization process: This invention adopts experience replay and target network technology to effectively solve the problems of unstable training and slow convergence that may occur in traditional reinforcement learning algorithms. By randomly extracting historical experience for training, the correlation between samples is reduced and the stability of training is improved; at the same time, the introduction of the target network avoids the oscillation phenomenon in the update process, significantly improving the robustness and convergence speed of the model.

[0024] (5) Reduced equipment failure and system risks: By comprehensively considering factors such as ice and snow accumulation, wind speed, and equipment carrying capacity, the present invention establishes a more accurate equipment failure probability model. Combined with dynamic scheduling optimization strategies, the present invention can effectively reduce the equipment failure rate, reduce the system risk caused by equipment failure, reduce equipment failures and their chain reactions during ice disasters, and optimize the operating status of the power system. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 Diagram of the two-stage learning framework of BC-DQN. DETAILED DESCRIPTION

[0026] It should be noted that in the description of the present invention, the terms "center", "up", "down", "left", "right", "vertical", "horizontal", "inside", "outside", "clockwise", "counterclockwise", etc. indicate directions or positional relationships based on the directions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operated in a specific direction.

[0027] In the present invention, unless otherwise clearly specified and limited, the terms "set", "install", "connect", "connect" and the like should be understood in a broad sense. For example, "fixed" can be a fixed connection, a detachable connection, or an integral connection; the connection can be a mechanical connection or an electrical connection; the connection can be a direct connection or an indirect connection through an intermediate medium, and can be the internal connection of two elements or the interaction relationship between two elements. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0028] Risk Model

[0029] Failure risk probability under icing conditions

[0030] The failure risk of power systems under icing disaster conditions is the result of the combined effect of multiple factors. The main factors considered include ice and snow accumulation, wind speed, and equipment load capacity. The following is a mathematical model for establishing the failure risk probability based on these factors.

[0031] Effects of ice and snow accumulation and wind speed on failure probability

[0032] Snow and ice accumulation I refers to the mass of snow and ice on the surface of power system equipment (such as power lines, transformers, etc.) at a specific location and time. Snow and ice accumulation directly affects the structural bearing capacity and operating status of the equipment, affecting the failure probability. In order to accurately calculate the snow and ice accumulation, meteorological data is usually relied on, especially factors such as temperature, humidity, precipitation and wind speed.

[0033] Assume that the failure probability P of each device (including power lines and transformers) is f It can be expressed by the amount of ice and snow accumulation I, wind speed W and equipment characteristic parameter C. The relationship between the failure probability and these factors is a nonlinear relationship, and the following regression model is established:

[0034] P f =f(I,W,C)

[0035] In the formula, I is the amount of ice and snow accumulation, in kg / m 2 , P x (t')=f(T,H),P x (t') is the snowfall rate at time t', in mm / h, T is the temperature, in °C, H is the humidity, in %, and the relationship between the two determines the possibility and intensity of snowfall; P m (t') = β·(T(t')-T f )·F w (t'), P m (t') is the melting rate of ice and snow, in mm / h, T(t') is the temperature at time t', in °C, T f The freezing temperature of ice and snow, usually set to 0℃, F w (t') is the wind speed at time t', in m / s. The greater the wind speed, the higher the melting rate of ice and snow. β is a constant, which is the sensitivity of temperature and wind to the melting rate. W is the wind speed, in m / s. The greater the wind speed, the greater the amount of ice and snow accumulation and the higher the probability of equipment failure. C is a parameter related to equipment characteristics, line length, and transformer capacity.

[0036] Regression Model for Failure Probability

[0037] After obtaining the amount of ice and snow accumulation I, a regression model is established to quantify the failure probability. The failure probability is not only affected by the amount of ice and snow accumulation I, but also by the wind speed W and equipment characteristics C. Polynomial regression is used to establish this relationship. Failure probability P f It is represented by the following polynomial regression model:

[0038] P f =a0+a1I+a2W+a3C+a4I 2 +a5W2 +a6C 2 +...

[0039] Where a0, a1, ..., a n The least squares method is used to estimate the regression coefficients and find the optimal regression coefficients by minimizing the sum of squares of the errors between the observed data and the model predictions.

[0040] Assume that there are N sets of historical data, each set of data includes the corresponding ice and snow accumulation I i , wind speed W i 、Equipment Characteristics C i and the actual failure probability P f,i , construct the objective function:

[0041]

[0042] By taking the partial derivative of L with respect to the regression coefficient to zero, the optimal estimate of the regression coefficient can be obtained.

[0043] Cascading failure model

[0044] Under icing disaster conditions, the failure of the power system may lead to a chain reaction, that is, the failure of one component will trigger the failure of other components, affecting the reliability of the entire system. In order to accurately describe this chain failure effect, a topological structure model of the power system is first established. Each device in the system can be regarded as a node, and the dependencies between devices (such as power transmission, load flow, etc.) can be represented by edges.

[0045] Power system topology and fault propagation model

[0046] The power system consists of N devices, and each device i has a corresponding failure probability P i , there is a dependency relationship between devices for power transmission, represented by the adjacency matrix A. If there is a dependency relationship between device i and device j, then A ij =1, otherwise A ij = 0. When device i fails, the failure probability of device j is P j Will be affected by P i The propagation model calculation formula is as follows:

[0047]

[0048] In the formula, is the probability before equipment j fails; is the new probability after device j fails; α is the propagation factor, which indicates the impact of the failure on adjacent devices; A ij is an element in the adjacency matrix, indicating whether there is a power transmission path between device i and device j.

[0049] Analysis of Cascading Failure Propagation Paths

[0050] In order to analyze the propagation path of faults in the power system, we model the power system as a directed graph, where each device corresponds to a node, and the power transmission dependency between devices is represented by the edges in the graph. When a device i fails, the fault will propagate along the power transmission path and may affect other devices connected to it. In order to quantify this propagation effect, the fault propagation index (Cascading Index) is defined, which measures the number of all affected devices in the system after the initial fault occurs. The fault propagation index is calculated as:

[0051]

[0052] Where P i new It represents the updated failure probability of device i after fault propagation, and evaluates the overall impact of the propagation range of different fault points on the system.

[0053] BC-DQN’s two-stage learning framework

[0054] The BC-DQN algorithm combines the advantages of behavior cloning (BC) and DQN, and adopts a two-stage learning strategy to accelerate the learning process. It quickly acquires the basic strategy by imitating the expert strategy in the initial stage, and then further optimizes the strategy through DQN reinforcement learning, accelerating strategy learning to improve the accuracy and robustness of system scheduling decisions.

[0055] Phase 1: Behavioral cloning

[0056] Behavior Cloning (BC) is a technique based on imitation learning, whereby agents learn how to make decisions in specific tasks by imitating the behavior of experts. Unlike traditional reinforcement learning methods, behavior cloning does not require agents to interact with the environment multiple times, but instead directly learns from historical data by observing and imitating the decision trajectories of experts. In particular, in this study, behavior cloning is used for the dispatching task of the power system, and the agent learns preliminary dispatching strategies by imitating the decision-making behavior of experts in emergency dispatching.

[0057] In the behavior cloning stage, the agent does not interact with the environment, but relies on the historical decision data provided by the expert, which includes the actions taken by the expert in each state. The expert's decision data can be regarded as a set of state-action pairs (s t ,a t ), where s t is the state of the agent at time t, a t For experts in the statet The agent learns the mapping from states to actions by minimizing the difference between the predicted action and the actual action of the expert.

[0058] The learning process of behavior cloning can be regarded as a supervised learning problem, the goal is to train the decision model of the agent by minimizing the loss function. Commonly used loss functions are cross entropy loss or mean square error loss, the goal is to minimize the gap between the action predicted by the agent and the action actually selected by the expert:

[0059]

[0060] In the formula, a t For experts in the state t The actual action below, is the action predicted by the agent through the model, and N is the number of samples. By minimizing the loss function, the agent can use historical data to make preliminary scheduling of the scheduling strategy before interacting with the environment. In the behavior cloning stage, the learning of the agent is based on supervised learning, which completely relies on historical expert data without direct interaction with the environment, helping the agent to quickly establish a set of preliminary scheduling decision rules, laying the foundation for the reinforcement learning stage.

[0061] Phase 2: DQN reinforcement learning

[0062] After the behavior cloning phase is completed, BC-DQN enters the reinforcement learning phase. At this point, the agent begins to interact with the environment and continuously optimizes the scheduling strategy through the Q-value update mechanism of DQN. In this phase, the agent continuously tries and adjusts in the environment through a combination of exploration and utilization to optimize scheduling decisions. The goal of the agent is to maximize long-term rewards, which is achieved through Q-value updates.

[0063] The Q value update formula is as follows:

[0064]

[0065] In the formula, α is the learning rate, γ is the discount factor, is the next state s t+1 The maximum Q value of all possible actions under the condition of . This enables the agent to extract different samples from multiple historical experiences, reduce the correlation caused by the order of samples, and improve the stability of training.

[0066] Experience Replay and Target Network

[0067] In order to improve the stability of training and accelerate convergence, BC-DQN adopts experience replay and target network technology.

[0068] In terms of experience replay, in traditional Q-learning, the agent's experience is learned sequentially, which may cause the correlation between samples to affect the training effect. Experience replay effectively reduces the correlation between data and enhances the stability of training by storing the agent's experience in a pool and randomly extracting batches of samples from it for training.

[0069] In the target network, DQN uses two networks to update the Q value: one is the current network, which is used to generate the Q value; the other is the target network, which is used to calculate the target Q value. The parameters of the target network are not updated in each training step, but are updated every several steps. This strategy avoids drastic fluctuations in the Q value update process and improves the stability of the model.

[0070] Through these two technologies, BC-DQN can maintain high stability during training and accelerate the convergence of the model, thereby effectively solving the problems of high dimensionality, complexity and instability in power system scheduling.

[0071] Reinforcement learning model construction

[0072] State Space

[0073] Define the state space S t These include the operating status of power equipment, load status, equipment failure probability, influencing factors of the icing environment (ice and snow accumulation, wind speed, etc.) and the impact of cascading failures.

[0074] S t = {P f (t),C t ,L t ,O t ,P c}

[0075] Where P f (t) is the probability of equipment failure; L t is the load state; O t is the topological information; c Cascading failure effects.

[0076] Action Space

[0077] Assume that each device can take two actions (enable or disable)

[0078] A t ={a1,a2,...,a M}

[0079] In the formula, a M is a specific dispatching action of the system, and M is the size of the action space, which depends on the scale of the power grid and the control strategy.

[0080] Reward Function

[0081]

[0082] In the formula, λ1, λ2, and λ3 are weight coefficients that adjust the influence of various factors; is the sum of the failure probabilities of all devices; f l is the load imbalance; P c It is the impact degree of cascading failure.

[0083] With the frequent occurrence of extreme weather events, the risks faced by the power system are increasing, especially in natural disasters such as icing in ice and snow disasters. Icing refers to the condensation of water vapor on the surface of power equipment under low temperature conditions to form an ice layer, which increases the load on the equipment and even causes equipment failure. Power equipment such as lines and transformers are prone to failure in icing disasters, and because the equipment is interconnected, failures often trigger a chain reaction, exacerbating the risk of the system and seriously threatening the safe and stable operation of the power system.

[0084] In this situation, how to accurately assess the failure risk of equipment and conduct efficient power system dispatch becomes a key issue in dealing with icing disasters. Especially in extreme weather such as icing disasters, the risk dispatch of the power system must not only consider the status of the equipment, but also dynamically assess the impact of various risk factors on system stability. The goal of power system dispatch is to make reasonable dispatch decisions based on the failure probability of equipment, the dependencies between equipment, and possible chain reactions, so as to minimize the overall risk of the system.

[0085] To solve these problems, imitation learning, including the behavior cloning method, provides an effective solution. Behavior cloning enables intelligent agents to imitate the behavior of experts and quickly generate reasonable emergency dispatch strategies without real-time feedback by learning the dispatch decisions of experts in the face of disasters. This method not only accelerates the learning process, but also responds quickly when disasters occur, reduces dependence on real-time exploration and feedback, and improves decision-making efficiency.

[0086] The reinforcement learning method combined with the deep Q network (DQN) further improves the decision-making ability of the intelligent agent. Based on behavioral cloning, DQN can further optimize the dispatching strategy through reinforcement learning, so that the intelligent agent can continuously adjust its decision-making according to real-time environmental changes, and improve the emergency response capability of the power system in complex disaster scenarios. Through this combined method, the intelligent agent can have a good dispatching strategy in the early stage, and on this basis, optimize the decision-making through interactive learning, thereby improving the adaptability and robustness of the system.

[0087] This invention proposes a two-stage risk dispatching method based on imitation learning (behavioral cloning) and deep Q network (DQN), focusing on optimizing the emergency dispatching decision of the power system in icing disasters. First, behavioral cloning training is carried out by imitating expert experience to construct a preliminary dispatching strategy, and then the strategy is further optimized through reinforcement learning to adapt to the dynamic environment under icing disasters. It can effectively enhance the ability of the power system to respond to disasters, accelerate the convergence process of the dispatching strategy, improve the accuracy and efficiency of dispatching decisions, and provide an innovative solution for the power system to respond to extreme weather events.

[0088] The above is only a specific implementation of the present invention, but the protection scope of the present invention is not limited thereto. Any modification, equivalent replacement and improvement made by any person skilled in the art within the technical scope disclosed by the present invention and within the spirit and principle of the present invention shall be covered within the protection scope of the present invention. At the same time, the contents not described in detail in this specification belong to the prior art known to those skilled in the art.

[0089] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device.

Claims

1. A method for optimizing power system disaster risk dispatch combined with behavioral cloning, characterized in that: The following steps are involved: S1 Establish risk model: P f =f(I,W,C), where P f The failure probability of each device is given by I, the amount of ice and snow accumulation, W, the wind speed, and C, the device characteristic parameters, which are used as the basic inputs for the failure probability; S2 Establish a regression model for failure probability: Use historical data to fit the regression equation and predict the equipment failure probability P f , that is, P f =a0+a1I+a2W+a3C+a4I 2 +a5W 2 +a6C 2 +..., where a0,a1,...,a n is the regression coefficient, and the objective function is constructed: By taking the partial derivative of L with respect to the regression coefficient to zero, we can obtain the optimal estimate of the regression coefficient. S3 establishes a cascading failure model: using topological structures to describe fault propagation and recursively calculating the failure probability after propagation Among them, P i is the failure probability, A ij is an element in the adjacency matrix, is the probability before device j fails, is the new probability after device j fails, α is the propagation factor; S4 Cascading Fault Propagation Path: Calculate the fault propagation index to assess system vulnerability and identify key equipment through the formula Analyze the cascading failure propagation path, where P i new represents the updated failure probability of device i after fault propagation; S5 Using BC-DQN to build a reinforcement learning model S t = {P f (t),C t ,L t ,O t ,P c }, where S t is the state space, P f (t) is the probability of equipment failure; L t is the load state; O t is the topological information; c Cascading failure effects; S6 establishes the action space A t ={a1,a2,...,a M }, where a M is a specific dispatching action of the system, M is the size of the action space, which depends on the scale of the power grid and the control strategy; S7 builds a return function Among them, λ1, λ2, λ3 are weight coefficients, is the sum of the failure probabilities of all devices, f l is the load imbalance, P c It is the impact degree of cascading failure.

2. The method for optimizing power system disaster risk dispatch combined with behavioral cloning according to claim 1 is characterized in that: In step S1, the amount of ice and snow accumulation Among them, P x (t') is the snowfall rate at time t', P m (t') is the melting rate of ice and snow.

3. The method for optimizing power system disaster risk dispatch combined with behavioral cloning according to claim 2 is characterized in that: P x (t') = f(T,H), where T is temperature and H is humidity.

4. The method for optimizing power system disaster risk dispatch combined with behavioral cloning according to claim 2 is characterized in that: P m (t') = β·(T(t')-T f )·F w (t'), T(t') is the temperature at time t', T f The freezing temperature of ice and snow, usually set to 0℃, F w (t') is the wind speed at time t', and β is a constant representing the sensitivity of temperature and wind speed to the melting rate.

5. The method for optimizing power system disaster risk dispatch combined with behavioral cloning according to claim 1 is characterized in that: In step S3, the power system consists of N devices, and each device i corresponds to a failure probability P i , there is a dependency relationship between devices for power transmission, represented by the adjacency matrix A. If there is a dependency relationship between device i and device j, then A ij =1, otherwise A ij = 0, when device i fails, the failure probability of device j is P j Will be affected by P i impact.

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