Method and system for identifying multi-dimensional dynamic elasticity of key coupling nodes of power distribution cyber physical system

Abstract

The application relates to the technical field of smart power grids, and is a multi-dimensional dynamic elasticity identification method and system for a key coupling node of a power distribution information physical system. The system comprises a key node screening unit, a unified CPDS model is constructed, and a candidate key node set is preliminarily screened based on structural controllability and structural observability; a fuzzy scene generation unit is used to construct a dynamic fuzzy disaster scene set by using a Markov chain Monte Carlo method, and a set containing a large number of dynamic fuzzy disaster scenes is generated; an elasticity function construction unit; a node calculation output unit; the application proposes a new CPDS key coupling node accurate identification method which is fused with structural controllability, structural observability, dynamic fuzzy disaster scenes, reverse reinforcement learning and Shapley value comprehensive calculation, so that the accuracy, fairness and adaptability of system elasticity analysis and decision-making are improved, and the fast response and recovery capability of the power grid to disasters or attack disturbances is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of smart grid, and particularly relates to a multi-dimensional dynamic elasticity identification method and system for a key coupling node of a power distribution information physical system. BACKGROUND

[0002] With the rapid development of global energy transformation and information technology, smart grid has become the core direction of modernization of power systems. As an important part of smart grid, CPDS realizes real-time monitoring, optimal scheduling and rapid fault recovery of the power distribution system by deeply integrating power networks (physical layer) and communication networks (information layer). CPDS not only improves the operation efficiency of the power system, but also enhances the adaptability of the system to external disturbances through information-physical coupling. However, with the increasing frequency and intensity of extreme weather events (such as typhoons, snow disasters) and network attacks (such as malicious data injection, denial of service attacks), the existing CPDS key node identification methods are mostly based on static topology structure or single index analysis, which is difficult to accurately reflect the true importance of nodes in multiple types and uncertain disaster environments. In addition, traditional methods often ignore the influence of the synergistic effect between different nodes on the overall system elasticity, resulting in the identification results may not be comprehensive and fair.

[0003] In CPDS, the power network and the communication network realize the interaction of information and energy through coupling nodes. These coupling nodes (such as sensors, controllers or communication routers) play a key role in system operation, responsible for transmitting state information, executing control instructions and coordinating the collaborative work of physical and information layers. However, once the key coupling nodes fail due to failure or attack, it may cause a significant decline in system performance, even trigger a cascading failure, seriously threatening the stability and reliability of power supply. Therefore, accurately identifying the key coupling nodes is an important prerequisite for improving the elasticity of CPDS.

[0004] The present application discloses a multi-dimensional dynamic elasticity identification method for key coupling nodes of a power distribution information physical system (CPDS) to address the shortcomings of existing CPDS key node identification methods. Current methods are mostly based on static topology structure or single index, which is difficult to accurately reflect the true importance of nodes in dynamic disaster environments and node synergistic effect. To solve this problem, the present application first integrates multi-dimensional structure analysis and data-driven expert experience weight, and innovatively uses the Shapley value in cooperative game theory to accurately identify key coupling nodes, significantly improving the dynamicity, accuracy and decision fairness of system elasticity evaluation, with outstanding theoretical and engineering value. SUMMARY

[0005] The application provides a multi-dimensional dynamic elasticity identification method and system for a key coupling node of a power distribution cyber-physical system.

[0006] To solve the above problems, one of the technical solutions of the application is implemented in the following way: a multi-dimensional dynamic elasticity identification method for a key coupling node of a power distribution cyber-physical system, comprising the following steps:

[0007] A unified CPDS model is constructed, and a candidate key node set is preliminarily screened based on structural controllability and structural observability; wherein the unified CPDS model comprises a power network and a communication network;

[0008] A dynamic fuzzy disaster scenario set is constructed by using a Markov chain Monte Carlo method, and a set containing a large number of dynamic fuzzy disaster scenarios is generated;

[0009] A dynamic weighted elasticity function is constructed by adaptively learning and optimizing the weight of each disaster scenario from expert experience through reverse reinforcement learning;

[0010] Based on each preliminarily screened candidate key node and each dynamic fuzzy disaster scenario, a weighted elasticity function of a fusion scenario is calculated, the Shapley value of each candidate key node is calculated, the nodes are sorted according to the Shapley value, and the sorted nodes are output.

[0011] The above-mentioned construction of the unified CPDS model comprises:

[0012] The unified CPDS model is an interconnected network system comprising a power network and a communication network; wherein the power network is the physical layer, defined as , wherein, represents the node set of the power network, is the edge set in the power network, represents the power network; the communication network is the information layer, defined as , represents the node set of the communication network, is the edge set in the communication network, represents the communication network;

[0013] The power network and the communication network are fused into a unified coupling adjacency matrix A CPDS , which represents the function as follows:

[0014] ,

[0015] wherein, A PPFor the internal connection matrix of the power network, A CC For the internal connection matrix of the communication network, A PC This represents the information flow dependency from the power grid to the communication network. A CP This represents the control flow dependency from the communication network to the power network;

[0016] Wherein, if a CPDS contains N P Power network nodes and N C If there are 10 communication network nodes, then the set of candidate key nodes is... N=N P +N C .

[0017] The aforementioned structural controllability includes:

[0018] The state equation for structural controllability is:

[0019] ,

[0020] in, This represents the state vector of a power network node. u ( t ) represents the input control vector; A This is the adjacency matrix of the power network; B The input control matrix is ​​determined by the communication node. The state equation for structural controllability represents the rate of change of the state of a power network node over time.

[0021] Maximum matching determines the minimum set of driving nodes. D min The formula is defined as:

[0022] ,

[0023] in, N A set of candidate key nodes; This represents the maximum number of matched edges.

[0024] The impact index of node failure is defined as follows:

[0025] ,

[0026] in, C i For nodes i Failure impact indicators; For nodes iThe number of uncontrollable nodes after failure increases; A set of nodes representing the power network; N A set of candidate critical nodes.

[0027] The above structural observability, including:

[0028] The observation system state satisfies the output model:

[0029] ,

[0030] Wherein, The state vector of the power network node; C The measurement output matrix; The output measurement vector;

[0031] The minimum sensor placement method based on network topology, the power network observation node set O min The power network observation node set O min Satisfy the following observability conditions:

[0032] ,

[0033] Wherein, O The set of measurement nodes; C The measurement output matrix; A The power network adjacency matrix; σ ( A ) The eigenvalue set of matrix A ; The eigenvalue of matrix A ; I The unit matrix; N A set of candidate critical nodes;

[0034] The node failure observation impact index is defined as:

[0035] ,

[0036] Wherein, O i The failure observation impact index of node i ; The number of unobservable nodes after node i Failure increases; N A set of candidate critical nodes; A set of nodes representing the power network;

[0037] The comprehensive importance index is defined as:

[0038] ,

[0039] wherein, α、β is a weight coefficient; C i is a failure impact indicator of a node i ; O i is an observed failure impact indicator of a node i ; I i is a comprehensive importance indicator of a node i .

[0040] The above utilizes the Markov chain Monte Carlo method to construct a dynamic fuzzy disaster scenario set, to generate a set containing a large number of dynamic fuzzy disaster scenarios, including:

[0041] According to historical data and expert experience, the transition probability between different disaster types and their intensity is defined; wherein, the disaster types include natural disasters and man-made attacks; wherein, each disaster type defines its intensity as a continuous variable x , a generalized Gaussian intensity fuzzy membership function is defined:

[0042] ,

[0043] In the formula, x is the disaster intensity, m is the intensity mean, σ is the standard deviation, k is the shape parameter;

[0044] Using the MCMC method, the initial disaster state is randomly sampled from the defined intensity fuzzy membership function;

[0045] Based on the transition probability and the time step, a series of continuous, fuzzy characteristic disaster scenario sequences are generated from the initial disaster state;

[0046] For each generated disaster scenario, its comprehensive fuzzy membership in multiple dimensions is calculated, and the cascading effect it may trigger is simulated; wherein, the disaster scenario set is defined, each characteristic disaster scenario S j is represented as:

[0047] ,

[0048] In the formula, is the disaster type, is the intensity vector, is the impact area / range, is the potential cascading effect it triggers; is the comprehensive fuzzy membership of the characteristic scenario;

[0049] Based on the comprehensive fuzzy membership, a set of a large number of dynamic fuzzy disaster scenarios is generated, as shown in the following formula:

[0050] S dynamic ={ S j,t},

[0051] In the formula, S j,t represents the first disaster scenario at time t ; j S dynamic is a set of a large number of dynamic fuzzy disaster scenarios.

[0052] The above-mentioned weights of each disaster scenario are self-adaptively learned and optimized from expert experience through inverse reinforcement learning, including:

[0053] A trajectory database containing CPDS full life cycle operation state, expert decision and system response is constructed, wherein the data structure in the trajectory database includes state s n , action a n , reward r n ; wherein for each expert experience trajectory :

[0054] The reward function is inversely derived from the expert trajectory using inverse reinforcement learning based on the maximum entropy principle, wherein the reward function is as follows:

[0055] ,

[0056] In the formula, f ( s,a ) is a feature vector corresponding to the state-action pair; is a weight vector to be learned; T is a vector transpose;

[0057] Find so that the feature expectation of the expert trajectory matches the feature expectation of all strategies, and the weight vector is calculated through an iterative algorithm, while the entropy of the strategy is maximized, wherein the entropy of the strategy is maximized as shown in the following formula:

[0058] ,

[0059] wherein, is the trajectory probability under the reward function ;​D expert It is an expert trajectory database; It is a regularization parameter; It represents the expert trajectory database D expert A specific expert trajectory in the dataset; K is the total number of expert trajectories; L is the length or time steps of each trajectory; It represents the trajectory τ The prior probability distribution; max w This represents a maximization operation, which involves finding the weight vector that maximizes the objective function. ;

[0060] Based on the learned reward function Assessment experts in characteristic disaster scenarios S j The expected reward for taking the optimal action:

[0061] ,

[0062] In the formula, max a In the current characteristic disaster scenario S j Next, iterate through all possible actions a and calculate the expected reward value for each action a; V( S j () represents a characteristic disaster scenario S j Under these circumstances, the maximum expected reward that can be obtained by taking the optimal action;

[0063] Extract weights related to disaster scenario characteristics from the reward function. :

[0064] ,

[0065] In the formula, For each characteristic disaster scenario S j Extract its key features; use softmax normalization to ensure that the sum of all scene weights is 1; w T This represents the transpose of the weight vector w, which transposes the weight vector from a column vector to a row vector.

[0066] The above iterative algorithm includes the following iterative process:

[0067] Strategy evaluation: for the current reward function Standard reinforcement learning algorithms are used to compute the optimal policy. ;

[0068] Reward function update: The weight vector of the reward function is updated using the gradient ascent method. The gradient ascent method is shown in the following equation:

[0069] ,

[0070] In the formula, η is the learning rate; For optimal strategy The resulting behavioral characteristics are expected; The expected actual behavioral characteristics in the expert experience database;

[0071] Convergence criterion: Repeat the policy evaluation and reward function update steps until... Convergence or reaching the maximum number of iterations.

[0072] The above calculation of the weighted elasticity function of the fused scenario, based on each initially selected candidate key node and each dynamically fuzzy disaster scenario, includes:

[0073] CPDS elasticity index E j Quantification: for each characteristic disaster scenario The elasticity of the system E j This can be obtained through simulation and measured using comprehensive indicators:

[0074] ,

[0075] The elasticity of a physical system can be quantified as:

[0076] ,

[0077] Among them, Lost Load( t )for t The amount of load loss at any given time, System recovery time; The normalized time base is used; Total Annual Load is the total electrical energy supplied or consumed by the system under normal operating conditions within one year.

[0078] The resilience of a communication system can be quantified as follows:

[0079] ,

[0080] Among them, Communication Interruption Rate ( t )for tThe communication interruption rate at any given time; Total Communication Needs refers to the system's communication interruption rate at a given time reference. Within, the total amount of communication services required to ensure the normal operation of the power system;

[0081] The impact of cyber-physical cascade failures is quantified by the amount of physical load loss caused by information failures or the amount of communication interruption caused by physical failures in the simulation.

[0082] : These are weighting coefficients used to balance different elasticity dimensions;

[0083] Weighted elasticity function for fusion scenarios v ( K ), defined as follows:

[0084] ,

[0085] In the formula, the alliance K It refers to a set consisting of one or more nodes; E j ( K ) is the first j Elasticity values ​​under various disaster scenarios; This represents the total number of dynamically blurred disaster scenarios; The first one obtained by inverse reinforcement learning j The weight of each disaster scenario.

[0086] The above process calculates the Shapley value for each candidate key node, sorts the nodes based on their Shapley values, and outputs the results, including:

[0087] Determine the set of nodes to be evaluated N This refers to the initial set of candidate key nodes;

[0088] Enumerate all possible node alliances K ;

[0089] For each node i∈N Iterate through all cases that do not contain i subset of K⊆N∖{i} ;

[0090] compute nodes i In each league K Marginal contribution ;

[0091] According to the Shapley value formula, by weighted summing of all marginal contributions, the node value is obtained. i Shapley value Among them, nodes iShapley value The calculation formula is:

[0092] ,

[0093] Wherein: N is a candidate key node set; n= ∣ N ∣ is the total number of nodes in the set N ; alliance K is a set composed of one or more nodes; K ∣ is the number of nodes in the alliance K ; represents the marginal contribution brought by the node i Joining the alliance, that is, the increment of the weighted elasticity function value of the overall system after the node joins; K

[0094] According to the calculated Shapley value of the node i , all nodes are arranged in descending order, and the arranged key coupling nodes are output.

[0095] The second technical scheme of the application is realized by the following way: a multi-dimensional dynamic elasticity identification system of power distribution information physical system key coupling nodes, the multi-dimensional dynamic elasticity identification system of power distribution information physical system key coupling nodes uses the multi-dimensional dynamic elasticity identification method of power distribution information physical system key coupling nodes, comprising:

[0096] A key node screening unit constructs a unified CPDS model and preliminarily screens a candidate key node set based on structural controllability and structural observability; wherein the unified CPDS model includes a power network and a communication network;

[0097] A fuzzy scenario generation unit constructs a dynamic fuzzy disaster scenario set using a Markov chain Monte Carlo method, and generates a set containing a large number of dynamic fuzzy disaster scenarios;

[0098] An elasticity function construction unit constructs a dynamic weighted elasticity function by adaptively learning and optimizing the weights of each disaster scenario from expert experience through reverse reinforcement learning;

[0099] A node calculation output unit calculates the weighted elasticity function of the fusion scene based on each preliminarily screened candidate key node and each dynamic fuzzy disaster scenario, calculates the Shapley value of each candidate key node, and sorts and outputs the nodes according to the Shapley value.

[0100] ​​The application discloses a new CPDS key coupling node accurate identification method fusing controllability and observability of structure, dynamic fuzzy disaster scene, reverse reinforcement learning and Shapley value comprehensive calculation, so as to improve the accuracy, fairness and adaptability of system elasticity analysis and decision-making, and improve the fast response and recovery ability of the power grid to disaster or attack disturbance. BRIEF DESCRIPTION OF DRAWINGS

[0101] The specific embodiments of the application will be further described in detail below with reference to the accompanying drawings.

[0102] Figure 1 The method flowchart of the embodiment 1 of the application.

[0103] Figure 2 The schematic diagram of the CPDS unified network model in the embodiment 1 of the application.

[0104] Figure 3 The schematic diagram of the CPDS modeling and preliminary key node identification process in the embodiment 1 of the application.

[0105] Figure 4 The schematic diagram of the dynamic fuzzy disaster scene construction and reverse reinforcement learning weight optimization process in the embodiment 1 of the application.

[0106] Figure 5 The schematic diagram of the weighted elasticity function and Shapley value calculation process in the embodiment 1 of the application.

[0107] Figure 6 The schematic diagram of the system structure framework in the embodiment 2 of the application. DETAILED DESCRIPTION

[0108] The application is not limited by the following embodiments, and the specific implementation can be determined according to the technical scheme of the application and the actual situation.

[0109] Embodiment 1: as shown in the following table, the embodiment of the application discloses a multi-dimensional dynamic elasticity identification method of a key coupling node of a power distribution cyber physical system, which comprises the following steps: Figure 1 Step S101, a unified CPDS model is constructed, and a candidate key node set is preliminarily screened based on controllability and observability of structure; wherein the unified CPDS model comprises a power network and a communication network; thus, a key node set which has a significant influence on the system operation state is preliminarily screened out, so as to reduce the key node candidate set and improve the accuracy of the preliminary screening.

[0110]

[0111] ​Step S102, a dynamic fuzzy disaster scenario set is constructed by using a Markov chain Monte Carlo method, and a set containing a large number of dynamic fuzzy disaster scenarios is generated; thus, by constructing a quantitative analysis model of the dynamic fuzzy disaster scenario, the uncertainty characteristics of the actual disaster are reflected.

[0112] Step S103, a dynamic weighted resilience function is constructed by adaptively learning and optimizing the weight of each disaster scenario from expert experience through inverse reinforcement learning; thus, by using the disaster scenario weight dynamic optimization method based on inverse reinforcement learning, the accuracy of the importance estimation of the disaster scenario is improved in a data-driven manner, and the problem of difficulty in determining the disaster scenario in the insufficient multi-factor fusion is solved.

[0113] Step S104, based on each preliminary screened candidate key node and each dynamic fuzzy disaster scenario, the weighted resilience function of the fusion scenario is calculated, the Shapley value of each candidate key node is calculated, the nodes are sorted and output according to the Shapley value; thus, by introducing the Shapley value analysis method in the cooperative game theory, the marginal contribution of the node under the multi-node cooperation is quantified fairly and accurately, and the limitation of the node cooperative contribution is fully considered.

[0114] As shown in Figure 2 , in the above step S101, the unified CPDS model is constructed, including:

[0115] The unified CPDS model is an interconnected network system composed of a power network (bus, substation) and a communication network (sensor, controller, communication router); wherein, the power network is the physical layer, defined as , wherein, represents the node set of the power network, is the edge set in the power network, represents the power network; the communication network is the information layer, defined as , represents the node set of the communication network, is the edge set in the communication network, represents the communication network;

[0116] The power network and the communication network are fused into a unified coupling adjacency matrix A CPDS , which represents the function as follows:

[0117] ,

[0118] , wherein, A PP is the internal connection matrix of the power network, A CC is the internal connection matrix of the communication network,A PC represents the information flow dependency from the power network to the communication network, A CP represents the control flow dependency from the communication network to the power network; the matrix elements can represent the connection strength, bandwidth, dependency degree, etc. weighted values, and this deep coupling model can capture the cascading effect between information and physical failures;

[0119] wherein, if a CPDS contains N P power network nodes and N C communication network nodes, then the candidate critical node set N=N P +N C .

[0120] As shown in Figure 3 , the structural controllability in the above step S101 is based on the maximum matching Hopcroft-Karp algorithm to calculate the minimum drive node set in the network to determine the minimum control input nodes required to achieve complete controllability of the network, and record the influence degree on the system controllable state when the node fails; wherein, the structural controllability includes:

[0121] The state equation of the structural controllability is:

[0122] ,

[0123] wherein, is the state vector of the power network node; u ( t ) is the input control vector; A is the power network adjacency matrix; B is the input control matrix determined by the communication node drive; is the state equation of the structural controllability, which represents the rate of change of the power network node state over time;

[0124] The maximum matching determines the minimum drive node set D min , the formula is defined as:

[0125] ,

[0126] wherein, N is the candidate critical node set; is the maximum matching edge number;

[0127] The node failure influence index is defined as:

[0128] ,

[0129] wherein, C i is the failure impact indicator of node i ; is the number of uncontrollable nodes increased after the failure of node i ; denotes the node set of the power network; N is the candidate critical node set.

[0130] As shown in Figure 3 , in the step S101, the structural observability is determined based on the minimum sensor placement method of the network topology to determine the minimum measurement nodes required for the network to achieve complete observation, and the loss degree of the network state observation performance after the node failure is recorded; wherein, the structural observability includes:

[0131] The observation system state satisfies the output model:

[0132] ,

[0133] wherein, is the state vector of the node of the power network; C is the measurement output matrix; is the output measurement vector;

[0134] Based on the minimum sensor placement method of the network topology, the observation node set of the power network O min is calculated, and the observation node set of the power network O min satisfies the following observability condition:

[0135] ,

[0136] wherein, O is the measurement node set; C is the measurement output matrix; A is the adjacent matrix of the power network; σ ( A ) is the eigenvalue set of the matrix A ; is the eigenvalue of the matrix A ; I is the unit matrix; N is the candidate critical node set;

[0137] The node failure observation impact indicator is defined as:

[0138] ,

[0139] wherein, O i is the nodei failure observation influence index of node failure observation influence index of node i failure observation influence index of node N candidate critical node set node set of power network

[0140] The comprehensive importance index is defined as:

[0141] ,

[0142] wherein, α、β is a weight coefficient; C i failure influence index of node i O i failure observation influence index of node i I i comprehensive importance index of node i

[0143] The above-mentioned structural controllability and structural observability are two structural indexes. Through analyzing the structural controllability (i.e. the importance of the node to the control of the whole system) and the structural observability (i.e. the importance of the node to the monitoring of the state of the whole system) of the node, the preliminary critical nodes affecting the operation control and state observation of the system are quickly screened out. The above-mentioned two indexes are integrated, the critical nodes with the greatest influence on the "system operation control" and "state observation" are preliminarily identified, and the dynamic fuzzy disaster scenario is established to further improve the accuracy and scene adaptability of the node analysis and consider the complex disaster characteristics in the actual operation.

[0144] As shown in Figure 4 , in the step S102, the Markov chain Monte Carlo method is used to construct a dynamic fuzzy disaster scenario set, a set containing a large number of dynamic fuzzy disaster scenarios is generated, including:

[0145] According to historical data and expert experience, the transition probability between different disaster types and their intensities is defined; wherein, the disaster types include natural disasters and man-made attacks; wherein, the intensity of each disaster type is defined as a continuous variable x , a generalized Gaussian intensity fuzzy membership function is defined:

[0146] ,

[0147] In the formula, x is the disaster intensity, m is the mean intensity, σ is the standard deviation, k is the shape parameter;​​​k The "fatness" of the membership function can be adjusted to represent the fuzzy boundary of different intensity levels more flexibly (e.g., when k = 2, it is a Gaussian function, and when k = 1, it is an exponential function);

[0148] Using the MCMC method, the initial disaster state is randomly sampled from the defined intensity fuzzy membership function; wherein Markov Chain Monte Carlo (MCMC) sampling: combining the intensity fuzzy membership function and the historical disaster frequency, the MCMC method is used to generate more representative dynamic fuzzy disaster scenarios, which not only considers the static characteristics of the scene, but also simulates the evolution process of the disaster; for example, the wind speed gradually increases, or secondary disasters are triggered after an earthquake;

[0149] Based on the transition probability and time step, a series of continuous, fuzzy characteristic disaster scene sequences are iteratively generated from the initial disaster state;

[0150] For each generated disaster scenario, the comprehensive fuzzy membership degree in multiple dimensions is calculated, and the cascading effect it may trigger is simulated; wherein a set of disaster scenarios is defined, S j is represented as:

[0151] ,

[0152] In the formula, is the disaster type (such as wind disaster), is the intensity vector (such as wind speed I j , wind, duration I j , duration), is the affected area / range, is the potential cascading effect it triggers (such as wind disaster leading to line icing, communication interruption); and is the comprehensive fuzzy membership degree of the feature scene, which can be obtained by the product (multiplying the membership degree of each dimension) or weighted average (weighted average of the membership degree of each dimension).

[0153] Based on the comprehensive fuzzy membership degree, a set containing a large number of dynamic fuzzy disaster scenarios is generated, as shown in the following formula:

[0154] S dynamic ={ S j,t ​},

[0155] wherein, S j,t represents the time t of the j disaster scenario; S dynamic is a set containing a large number of dynamic fuzzy disaster scenarios.

[0156] wherein, natural disasters: for example, wind disaster (wind speed, duration, impact range), earthquake (magnitude, intensity, focal depth), flood (water level, flow, flooded area), ice and snow disaster (icing thickness, duration); man-made attacks: for example, network attack (attack traffic, attack target, duration, attack type), physical destruction (destruction target, destruction degree), malicious software (infection range, damage function).

[0157] As can be seen from the above, each characteristic disaster scenario contains disaster type comprehensive fuzzy membership T j , intensity vector comprehensive fuzzy membership I j , impact range comprehensive fuzzy membership D j , potential cascading effect comprehensive fuzzy membership C j and the comprehensive fuzzy membership of the characteristic scene ; therefore, the comprehensive fuzzy membership is an important part of describing the characteristics of each characteristic disaster scenario itself; the final set containing a large number of dynamic fuzzy disaster scenarios S dynamic is generated based on the comprehensive fuzzy membership , which means that the value of the comprehensive fuzzy membership will be used as the basis for generating and screening scenarios to join the final set containing a large number of dynamic fuzzy disaster scenarios S dynamic , that is, first calculate the comprehensive fuzzy membership of each possible disaster scenario , and then based on these calculation results to build a set containing a large number of dynamic fuzzy disaster scenarios S dynamic .

[0158] Specifically, considering cascading failures means that when generating scenarios, not only the impact of a single disaster is considered, but also the potential cascading failure effects it may trigger. For example, when a windstorm reaches a certain intensity, it may cause physical breaks in power lines, leading to the interruption of related communication equipment and creating a vicious cycle of information and physical disruption. This cascading effect can be simulated using a pre-set rule base or a probabilistic model learned from historical data.

[0159] like Figure 4 As shown, in step S103 above, the weights of each disaster scenario are adaptively learned and optimized from expert experience through inverse reinforcement learning, including:

[0160] Construct a trajectory database that includes the entire lifecycle operation status of CPDS, expert decisions, and system responses. The data structure within the trajectory database... Including status s n ,action a n ,award r n Among them, for each expert experience trajectory :in, n Representing the entire time span, it refers to a set or sequence that starts at time step t=0, passes through t=1, 2, ..., until the last time step t= n All states, actions, and rewards;

[0161] The reward function is derived from the expert trajectory using inverse reinforcement learning based on the maximum entropy principle, where the reward function is as follows:

[0162] ,

[0163] In the formula, f ( s,a ) is the feature vector corresponding to the state-action (e.g., power outage load, communication interruption, number of damaged nodes, intensity of the current disaster scenario, etc.); It is the weight vector that needs to be learned; T This is the transpose of a vector; the feature vector here needs to contain information related to the disaster scenario so that the reward function can reflect the expert's preference for different disaster scenarios.

[0164] turn up To ensure that the feature expectations of the expert trajectory match the feature expectations of all policies, a weight vector is calculated using an iterative algorithm. Simultaneously, the entropy of the policy is maximized, where the entropy of the policy is maximized as shown in the following formula:

[0165] ,

[0166] where, is the trajectory probability under the reward function ; D expert is the expert trajectory database; is the regularization parameter; is a specific expert trajectory in the expert trajectory database D expert ; K is the total number of expert trajectories; L is the length or time step number of each trajectory; is the prior probability distribution of the trajectory τ ; when using the maximum entropy principle, it is usually assumed to be a uniform distribution if there is no specific prior information; max w represents a maximization operation, that is, finding the weight vector that can maximize the objective function;

[0167] Based on the learned reward function , the expected reward obtained by the expert taking the optimal action in the characteristic disaster scenario S j is evaluated:

[0168] ,

[0169] where max a is the current characteristic disaster scenario S j , traverse all possible actions a, and calculate the expected reward value for each action a, and finally select the action that can maximize the expected reward from all these results; V( S j ) represents the maximum expected reward that can be obtained by taking the optimal action in the characteristic disaster scenario S j ;

[0170] The weights related to the characteristics of the disaster scenario are extracted from the reward function :

[0171] ,

[0172] where, is the key feature of each characteristic disaster scenario S j (including its type, intensity, impact range, etc.); using softmax normalization ensures that the sum of all scenario weights is 1; w T represents the transpose of the weight vector w, which transposes the weight vector from a column vector to a row vector, so as to be multiplied with the feature vector Matrix multiplication operation is performed. In this way, the learned can be directly mapped to the importance of each disaster scenario, thereby adaptively generating the weights of the disaster scenario set ; this means that disaster scenarios that cause higher system risk and greater recovery difficulty in the eyes of experts will obtain higher weights.

[0173] wherein the state s n : contains physical state (node voltage, line flow, load, switch state, generator output, list of damaged equipment), information state (communication link bandwidth, delay, packet loss rate, communication device state), and current dynamic fuzzy disaster scenario information (disaster type, intensity, impact range, cascading failure situation).

[0174] action a n : the decision taken by the expert or operation and maintenance system in the state s n , for example: physical side: line reconstruction, load shedding, distributed power grid / grid, backup power supply, repair team scheduling, reinforcement measures; information side: communication routing adjustment, redundant link switching, network topology reconstruction, bandwidth allocation optimization.

[0175] reward r n : the immediate return brought by the expert action in the state s n , which is observable, but the reward function behind it is implicit; for example, the amount of power outage load reduction, the amount of recovery time reduction, the degree of system function retention, etc.; for example, the reward at a certain moment t can be defined as:

[0176] ,

[0177] wherein is the restored power load, is the amount of power outage time reduction, is the amount of communication loss reduction, k 1 , k 2 , k 3 is the weight coefficient.

[0178] As shown in Figure 4 , the above iterative algorithm includes the following iterative process:

[0179] Policy evaluation: for the current reward function , using standard reinforcement learning algorithms (e.g. Q-learning, SARS A, or policy iteration based on dynamic programming) to compute the optimal policy ;

[0180] Reward function update: update the weight vector of the reward function using gradient ascent ; where the gradient ascent is given by

[0181] ,

[0182] where η is the learning rate; is the behavior feature expectation generated by the optimal policy ; and is the actual behavior feature expectation in the expert experience database; this step aims to reduce the gap between the model policy and the expert policy in terms of behavior features; the weight of the reward function is adjusted by gradient ascent so that the trajectory features generated by the model policy are closer to those of the expert;

[0183] Convergence judgment: repeat the steps of policy evaluation and reward function update until convergence or the maximum number of iterations is reached.

[0184] As shown in Figure 5 , in the step S104, a weighted resilience function of the fusion scene (system resilience evaluation E j The functional loss and recovery ability of the physical system and information system under each characteristic disaster scene need to be considered comprehensively), including:

[0185] CPDS resilience index E j quantification: for each characteristic disaster scene , the resilience E j of the system can be obtained through simulation and measured by a comprehensive index:

[0186] ,

[0187] is the resilience of the physical system, which can be quantified as:

[0188] ,

[0189] where Lost Load( t ) is the lost load at time t, t ​The system recovery time measures the power outage losses and recovery speed. As a normalized time reference, this is typically... Taking one year (i.e. 8760 hours), the denominator directly represents the total annual load or total annual communication demand; Total Annual Load is the total electrical energy supplied or consumed by the system in a year under normal operating conditions, and is a benchmark value for measuring the annual service scale of the system.

[0190] The resilience of a communication system can be quantified as follows:

[0191] ,

[0192] Among them, Communication Interruption Rate ( t )for t The communication interruption rate at any given time measures the availability and reliability of information transmission; Total Communication Needs refers to the system's communication needs at a normalized time reference. Within, the total amount of communication services required to ensure the normal operation of the power system;

[0193] The impact of cyber-physical cascade failure is a negative indicator, representing the additional losses caused by the cascade effect. It can be quantified by the amount of physical load loss caused by information failure or the amount of communication interruption caused by physical failure in the simulation.

[0194] : These are weighting coefficients used to balance different elasticity dimensions;

[0195] Weighted elasticity function for fusion scenarios v ( K ), defined as follows:

[0196] ,

[0197] In the formula, the alliance K It refers to a set consisting of one or more nodes; E j ( K ) is the first j Elasticity values ​​under various disaster scenarios; This represents the total number of dynamically blurred disaster scenarios; The first one obtained by inverse reinforcement learning j The weighting of each disaster scenario ensures that the resilience assessment fully considers the true importance of different disaster scenarios.

[0198] Among them, the alliance KA Coalition refers to a set of one or more nodes that work together to harden a system (e.g., simultaneously strengthening the nodes physically, adding redundancy, or deploying backup power). When a subset of nodes is hardened, its resilience under different disaster scenarios is assessed. E j ( K This will improve.

[0199] like Figure 5 As shown, in step S104 above, the Shapley value of each candidate key node is calculated, the nodes are sorted according to the Shapley value and output, and thus the Shapley value is used to fairly allocate the contribution of each node to the overall system resilience. v (K) His contributions include:

[0200] Determine the set of nodes to be evaluated. N This refers to the initial set of candidate key nodes;

[0201] Enumerate all possible node alliances K For each consortium K, its nodes are assumed to have received some degree of protection or hardening. The performance of CPDS in consortium K after the nodes have been hardened is simulated under all dynamic fuzzy disaster scenarios, and its weighted resilience value is calculated. v ( K );

[0202] For each node i∈N Iterate through all cases that do not contain i subset of K⊆N∖{i} ;

[0203] compute nodes i In each league K Marginal contribution ;

[0204] According to the Shapley value formula, by weighted summing of all marginal contributions, the node value is obtained. i Shapley value Among them, nodes i Shapley value The calculation formula is:

[0205] ,

[0206] in: N It is a set of candidate key nodes; n= | N | is a set N Total number of nodes in the alliance; K It refers to a set consisting of one or more nodes; |K | is the number of nodes in the coalition K ; represents the marginal contribution of a node i joining the coalition, i.e., the increment of the weighted resilience function value of the system as a whole after the node joins; K

[0207] According to the calculated Shapley value of the node i , all nodes are arranged in descending order, and the arranged key coupling nodes are output. The larger the Shapley value of the node, the greater the contribution of the node to the overall resilience of the system, and therefore the node is identified as a more critical coupling node. These nodes are the objects that should be prioritized for reinforcement or protection in the CPDS resilience improvement strategy.

[0208] In addition, the above reinforcement effect simulation is also included: assuming that the probability of failure of the reinforced node in the disaster is reduced, or its recovery time is shortened, or its physical / communication capacity is improved, and the specific effect can be quantified through a preset model or historical data.

[0209] In summary, the present application proposes a new CPDS key coupling node accurate identification method that integrates structure controllability, structure observability, dynamic fuzzy disaster scenario, reverse reinforcement learning and Shapley value comprehensive calculation, to improve the accuracy, fairness and adaptability of system resilience analysis and decision-making, and to improve the rapid response and recovery capability of the power grid to disaster or attack disturbance.

[0210] Embodiment 2: As shown in Figure 6 , the embodiment of the present application discloses a multi-dimensional dynamic resilience identification system for key coupling nodes of a power distribution cyber physical system, which uses a multi-dimensional dynamic resilience identification method for key coupling nodes of a power distribution cyber physical system, comprising:

[0211] A key node screening unit constructs a unified CPDS model and preliminarily screens a candidate key node set based on structure controllability and structure observability; wherein the unified CPDS model includes a power network and a communication network;

[0212] A fuzzy scenario generation unit constructs a dynamic fuzzy disaster scenario set using a Markov chain Monte Carlo method to generate a set containing a large number of dynamic fuzzy disaster scenarios;

[0213] An elasticity function construction unit adaptively learns and optimizes the weights of each disaster scenario from expert experience through reverse reinforcement learning to construct a dynamic weighted resilience function;

[0214] ​​​The node calculates an output unit, based on each preliminary screened candidate key node and each dynamic fuzzy disaster scene, calculates a weighted resilience function of a fusion scene, calculates a Shapley value of each candidate key node, sorts and outputs the nodes according to the Shapley value.

Claims

1. A multi-dimensional dynamic elastic identification method for key coupled nodes in a power distribution cyber-physical system, characterized in that, Includes the following steps: A unified CPDS model is constructed, and a preliminary set of candidate key nodes is selected based on structural controllability and structural observability; the unified CPDS model includes power networks and communication networks. A set of dynamic fuzzy disaster scenarios is constructed using the Markov chain Monte Carlo method, generating a set containing a large number of dynamic fuzzy disaster scenarios; By using inverse reinforcement learning, the weights of each disaster scenario are adaptively learned and optimized from expert experience, and a dynamic weighted elasticity function is constructed. Based on each initially selected candidate key node and each dynamic fuzzy disaster scenario, the weighted elasticity function of the fused scenario is calculated, the Shapley value of each candidate key node is calculated, and the nodes are sorted and output according to the Shapley value.

2. The multi-dimensional dynamic elastic identification method for key coupled nodes in a power distribution cyber-physical system according to claim 1, characterized in that, The construction of the unified CPDS model includes: The unified CPDS model is an interconnected network system consisting of power networks and communication networks; whereby the power network is the physical layer, defined as follows: In the formula, Represents the set of nodes in a power network. For edge sets in a power network, This refers to the power grid; the communication network, also known as the information layer, is defined as follows: , Represents the set of nodes in a communication network. For the edge set in the communication network, Indicates a communication network; Integrate power grids and communication networks into a unified coupled adjacency matrix. A CPDS The function is represented as follows: ， In the formula, A PP For the internal connection matrix of the power network, A CC For the internal connection matrix of the communication network, A PC This represents the information flow dependency from the power grid to the communication network. A CP This represents the control flow dependency from the communication network to the power network; Wherein, if a CPDS contains N P Power network nodes and N C If there are 10 communication network nodes, then the set of candidate key nodes is... N=N P +N C .

3. The multi-dimensional dynamic elastic identification method for key coupled nodes in a power distribution cyber-physical system according to claim 1, characterized in that, The structural controllability includes: The state equation for structural controllability is: ， in, This represents the state vector of a power network node. For input control vectors; A This is the adjacency matrix of the power network; B The input control matrix is ​​determined by the communication node. The state equation for structural controllability represents the rate of change of the state of a power network node over time. Maximum matching determines the minimum set of driving nodes. D min The formula is defined as: ， in, N A set of candidate key nodes; This represents the maximum number of matched edges. The impact index of node failure is defined as follows: ， in, C i For nodes i Failure impact indicators; For nodes i The number of uncontrollable nodes that increase after failure; Represents the set of nodes in a power network; N This is the set of candidate key nodes.

4. The multi-dimensional dynamic elastic identification method for key coupled nodes in a power distribution cyber-physical system according to claim 2 or 3, characterized in that, The structural observability includes: The observed system state satisfies the output model: ， in, This represents the state vector of a power network node. C For measurement output matrix; To output the measurement vector; A minimum sensor placement method based on network topology is used to calculate the power network observation node set. O min Power network observation node set O min The following observability conditions must be met: ， in, O For the set of measurement nodes; C For measurement output matrix; A This is the adjacency matrix of the power network; For matrix A The set of eigenvalues; For matrix A eigenvalues; I It is the identity matrix; N A set of candidate key nodes; The impact index of node failure observation is defined as follows: ， in, O i For nodes i Failure observation impact indicators; For nodes i The number of unobservable nodes added after a failure; N A set of candidate key nodes; Represents the set of nodes in a power network; The overall importance index is defined as follows: ， in, These are the weighting coefficients; C i For nodes i Failure impact indicators; O i For nodes i Failure observation impact indicators; I i For nodes i The comprehensive importance indicator.

5. The multi-dimensional dynamic elastic identification method for key coupled nodes in a power distribution cyber-physical system according to claim 1, characterized in that, The method of using Markov chain Monte Carlo to construct a set of dynamic fuzzy disaster scenarios generates a set containing a large number of dynamic fuzzy disaster scenarios, including: Based on historical data and expert experience, the transition probabilities between different disaster types and their intensities are defined; where disaster types include natural disasters and man-made attacks; and where the intensity of each disaster type is defined as a continuous variable. x Define the generalized Gaussian intensity fuzzy membership function: ， In the formula, x As for the intensity of the disaster, m The average intensity Standard deviation, k For shape parameters; The initial disaster state is randomly sampled from the defined intensity fuzzy membership function using the MCMC method; Based on the transition probability and time step, a series of continuous disaster scenario sequences with fuzzy features are generated iteratively from the initial disaster state; For each generated disaster scenario, its comprehensive fuzzy membership degree across multiple dimensions is calculated, and its potential cascading effects are simulated; whereby, a disaster scenario set is defined. Each characteristic disaster scenario S j Represented as: ， In the formula, As a type of disaster, For intensity vectors, To the area / scope of impact, The potential cascading effects it may trigger; The comprehensive fuzzy membership degree of this characteristic disaster scenario; Based on the comprehensive fuzzy membership degree, a set containing a large number of dynamic fuzzy disaster scenarios is generated, as shown in the following formula: ， In the formula, S j,t Indicates time t The j One disaster scenario; S dynamic It is a collection containing a large number of dynamic and blurred disaster scenarios.

6. The multi-dimensional dynamic elastic identification method for key coupled nodes in a power distribution cyber-physical system according to claim 1, characterized in that, The method of adaptively learning and optimizing the weights of each disaster scenario from expert experience through inverse reinforcement learning includes: Construct a trajectory database that includes the entire lifecycle operation status of CPDS, expert decisions, and system responses. The data structure within the trajectory database... Including status s n ,action a n ,award r n Among them, for each expert experience trajectory : The reward function is derived from the expert trajectory using inverse reinforcement learning based on the maximum entropy principle, where the reward function is as follows: ， In the formula, f ( s,a ) is the feature vector corresponding to the state-action sequence; It is the weight vector that needs to be learned; T Transpose of a vector; turn up To ensure that the feature expectations of the expert trajectory match the feature expectations of all policies, a weight vector is calculated using an iterative algorithm. Simultaneously, the entropy of the policy is maximized, where the entropy of the policy is maximized as shown in the following formula: ， in, In the reward function The probability of the trajectory below; D expert It is an expert trajectory database; It is a regularization parameter; It represents the expert trajectory database D expert A specific expert trajectory in the dataset; K is the total number of expert trajectories; L is the length or time steps of each trajectory; It represents the trajectory The prior probability distribution; max w This represents a maximization operation, which involves finding the weight vector that maximizes the objective function. ; Based on the learned reward function Assessment experts in characteristic disaster scenarios S j The expected reward for taking the optimal action: ， In the formula, max a In the current characteristic disaster scenario S j Next, iterate through all possible actions a and calculate the expected reward value for each action a; V( S j () represents a characteristic disaster scenario S j Under these circumstances, the maximum expected reward that can be obtained by taking the optimal action; Extract weights related to disaster scenario characteristics from the reward function. : ， In the formula, For each characteristic disaster scenario S j Extract its key features; use softmax normalization to ensure that the sum of all scene weights is 1; Represents the weight vector The transpose of 1 transforms the weight vector from a column vector to a row vector.

7. The multi-dimensional dynamic elastic identification method for key coupled nodes in a power distribution cyber-physical system according to claim 6, characterized in that, The iterative algorithm includes the following iterative process: Strategy evaluation: for the current reward function Standard reinforcement learning algorithms are used to compute the optimal policy. ; Reward function update: The weight vector of the reward function is updated using the gradient ascent method. The gradient ascent method is shown in the following equation: ， In the formula, The learning rate; For optimal strategy The resulting behavioral characteristics are expected; The expected actual behavioral characteristics in the expert experience database; Convergence criterion: Repeat the policy evaluation and reward function update steps until... Convergence or reaching the maximum number of iterations.

8. The multi-dimensional dynamic elastic identification method for key coupled nodes in a power distribution cyber-physical system according to claim 1, characterized in that, The step of calculating the weighted elasticity function of the fused scenario based on each initially selected candidate key node and each dynamically fuzzy disaster scenario includes: CPDS elasticity index E j Quantification: for each characteristic disaster scenario The system's elasticity index E j This can be obtained through simulation and measured using comprehensive indicators: ， The elasticity of a physical system can be quantified as: ， Among them, Lost Load( t )for The amount of load loss at any given time, System recovery time; The normalized time base is used; Total Annual Load is the total electrical energy supplied or consumed by the system under normal operating conditions within one year. The resilience of a communication system can be quantified as follows: ， Among them, Communication Interruption Rate ( t )for t The communication interruption rate at any given time; Total Communication Needs refers to the system's communication interruption rate at a given time reference. Within, the total amount of communication services required to ensure the normal operation of the power system; The impact of cyber-physical cascade failures is quantified by the amount of physical load loss caused by information failures or the amount of communication interruption caused by physical failures in the simulation. : These are weighting coefficients used to balance different elasticity dimensions; Weighted elasticity function for fusion scenarios v ( K ), defined as follows: ， In the formula, the alliance K It refers to a set consisting of one or more nodes; E j ( K ) is the first j Elasticity values ​​under various disaster scenarios; This represents the total number of dynamically blurred disaster scenarios; The first one obtained by inverse reinforcement learning j The weight of each disaster scenario.

9. The multi-dimensional dynamic elastic identification method for key coupled nodes in a power distribution cyber-physical system according to claim 8, characterized in that, The process of calculating the Shapley value for each candidate key node, sorting the nodes based on the Shapley values, and outputting the results includes: Determine the set of nodes to be evaluated. N This refers to the initial set of candidate key nodes; Enumerate all possible node alliances K ; For each node i∈N Iterate through all cases that do not contain i subset of K⊆N∖{i} ; compute nodes i In each league K Marginal contribution ; According to the Shapley value formula, by weighted summing of all marginal contributions, the node value is obtained. i Shapley value Among them, nodes i Shapley value The calculation formula is: ， in: N It is a set of candidate key nodes; n= | N | is a set N Total number of nodes in the alliance; K It refers to a set consisting of one or more nodes; | K | is an alliance K The number of nodes in; Represents a node i Join the alliance K The marginal contribution it brings is the increment of the weighted elasticity function value of the overall system elasticity after the node is added; Based on the calculated nodes i Shapley value Sort all nodes in descending order and output the key coupled nodes after sorting.

10. A multi-dimensional dynamic resilience identification system for key coupled nodes in a power distribution cyber-physical system, wherein the multi-dimensional dynamic resilience identification system for key coupled nodes in a power distribution cyber-physical system uses the multi-dimensional dynamic resilience identification method for key coupled nodes in a power distribution cyber-physical system as described in any one of claims 1 to 9, characterized in that, include: The key node screening unit constructs a unified CPDS model and initially screens a set of candidate key nodes based on structural controllability and structural observability; the unified CPDS model includes power networks and communication networks. The fuzzy scene generation unit uses the Markov chain Monte Carlo method to construct a dynamic fuzzy disaster scene set, generating a set containing a large number of dynamic fuzzy disaster scenes; The elasticity function construction unit adaptively learns and optimizes the weights of various disaster scenarios from expert experience through inverse reinforcement learning, and constructs a dynamically weighted elasticity function. The node computation output unit calculates the weighted elasticity function of the fused scenario based on each initially selected candidate key node and each dynamic fuzzy disaster scenario, calculates the Shapley value of each candidate key node, sorts the nodes according to the Shapley value, and outputs the results.

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