A method for optimizing dynamic defense performance of active distribution network based on game theory

Abstract

The present invention discloses a method for optimizing the dynamic defense performance of an active distribution network based on game theory, the purpose of which is to optimize the active defense performance of the active distribution network by solving the refined Bayesian Nash equilibrium. Traditional defense methods for active distribution networks are mostly static defense. The method proposed in the present invention combines the active distribution network with the dynamic game of incomplete information, regards the grid destroyer and the grid manager as participants in the game, constructs an attack and defense game model, and converts static defense into dynamic defense, which is closer to the actual operation of the grid. The method combines the power system model with the state fault diagnosis matrix to detect network attacks, and at the same time, takes into account the misjudgment and wrong judgment in the detection. The invention can effectively improve the dynamic defense capability of the active distribution network against network attacks.

Description

Technical Field

[0001] The present invention belongs to the technical field of active distribution networks and relates to dynamic defense performance optimization. More specifically, the present invention relates to a method for optimizing the dynamic defense performance of an active distribution network based on game theory. Background Art

[0002] At present, there are still defects in the development of my country's distribution network, and there are obvious problems of unbalanced development, gaps between rural and urban areas, gaps between the east and the west, and there is still a big gap with the international level. There are two main aspects: First, the grid structure is weak and the automation level is low. With the large demand and construction of my country's active distribution network in recent years, a large number of smart meters and ubiquitous services have been connected to the distribution network, resulting in a complex grid structure. Traditional defense strategies are difficult to support the current operation requirements. This requires starting with defense. This problem can be improved through dynamic defense performance optimization methods. Second, the basic data of the active distribution network is poor and the information control is backward. The control system pursues speed, accuracy and stability. The basic data is basically scattered in different systems. There may be defects in the coordination between the systems, and it is impossible to achieve a timely sharing state. At the same time, there may be attacks in data transmission, which will cause the control target of the system to be lost. The distribution network currently involves a wide range of areas, large investments, and complex measurement and control objects, which also requires a large number of devices to be monitored. However, due to economic and other restrictions, the actual measurement devices are far from meeting the standards, and due to the performance of the equipment itself, the environment in which the equipment is located, and other factors, the data collected by the active distribution network measurement terminal is subject to greater external interference, making the data availability low. At present, there is no sufficiently in-depth research in the field of dynamic defense performance optimization of active distribution networks based on game theory. In view of this, it is planned to select the optimal defense strategy based on the game situation between the attacker and the defender, and optimize the dynamic defense to solve the impact of unavailable, incomplete, and unavailable data.

[0003] Most network security research focuses on specific vulnerabilities or resisting specific attacks through specific defense algorithms, which basically belongs to static defense. However, in general, network attacks are uncertain and are in a dynamic state. In this case, we need to establish a dynamic defense mechanism to ensure network security. According to the principle of robust control of network control systems, when the impact of network attacks on system parameters is less than the upper limit of system dynamic disturbances, a simple robust control method can resist such network attacks; but when its impact on the system state exceeds the upper limit brought by the disturbance, a corresponding attack resistance method must be adopted to solve it. At present, the asymmetric phenomenon of network attack and defense is prevalent. Defenders must protect in all aspects, while attackers only need to target one point and exploit its vulnerabilities to attack. Due to the static characteristics of computer networks, attackers can pre-reconnaissance the target network, identify and discover vulnerabilities that can be exploited, and then carry out targeted attacks after obtaining sufficient target information. Defenders are often unable to defend and are in a passive situation. Therefore, it is necessary to conduct in-depth research on the security of active distribution network systems and establish corresponding dynamic defense strategies based on game theory to solve incomplete information dynamic games. Summary of the invention

[0004] The fundamental starting point of the present invention is to overcome the shortcomings of the prior art and propose a dynamic defense performance optimization method for active distribution networks based on game theory. Its purpose is to optimize the dynamic defense performance of network attack behaviors in active distribution networks by using refined Bayesian Nash equilibrium to ensure safe, reliable and efficient data transmission.

[0005] To achieve the above object, the present invention intends to adopt the following technical solutions:

[0006] The present invention provides a method for optimizing the dynamic defense performance of an active distribution network based on game theory, characterized in that the method comprises the following steps:

[0007] Step S1: constructing a mathematical model of the active distribution network power system;

[0008] Step S2: Judgment matrix M F Whether the trace of changes: Using the state fault diagnosis matrix M F Detect network attacks; if the matrix M F The trace of does not change, go to step S3, if the matrix M F The trace changes, and the process goes to step S4;

[0009] Step S3: Restore grid operation by black start;

[0010] Step S4: Construct an attack-defense game model and use the refined Bayesian Nash equilibrium strategy to achieve the active defense performance optimization goal of the active distribution network

[0011] Furthermore, the step S1 specifically includes: analyzing the data in the active distribution network according to its unique attributes, and constructing a mathematical model of the active distribution network power system as formula (1):

[0012] x k+1 =Ax k +Bu k +w k +E k h k (1)

[0013] Where A and B are coefficient matrices, x k is the system state vector, which includes parameters such as the voltage phase angle at the generator bus, the rotor angular frequency deviation at the generator bus, and the voltage phase angle at the load bus. k is the control input, which includes the mechanical power input and the power flow components of other nodes, w k is the process noise, E k Indicates network attack, h k Indicates a fault signal.

[0014] Furthermore, the step S2 is specifically as follows: based on the power system mathematical model formula (1), using the state fault diagnosis matrix M F Detect network attacks and state fault diagnosis matrix

[0015]

[0016] Where P k|k-1 represents the covariance, which is a variable that considers the relationship between the attack signal and the estimation error. Represents the estimated process noise covariance, which is white noise with zero mean, η' k-1 Represents the estimation error, which can be represented by the system state vector x k Subtract estimated state value Get, that is

[0017] Furthermore, the state fault diagnosis matrix M F The main function is to quickly detect network attacks and reflect the impact of attack signals on the diagonal elements of the matrix. Therefore, the trace of the judgment matrix (M F ) changes, network attacks can be detected.

[0018] Furthermore, the trace of the judgment matrix (M F) changes, if trace(M F ) does not change, the network attack detection is misjudged, the network attack by the power grid destroyer is successful, causing the physical equipment in the power grid to fail, and the process goes to step S3; if there is a change, the network attack signal E k The impact will be directly reflected in the trace (M F ), it means that a network attack has occurred at some nodes in the power grid. Go to step S4.

[0019] Furthermore, the step S3 specifically includes the following steps:

[0020] Step S31: Determine whether the network attack continues. The method may adopt the threshold division standard, that is, the threshold represents the boundary of normal network behavior, and the behavior exceeding the threshold is determined as a network attack. If the network attack continues, resulting in further expansion of the fault range, then proceed to step S32; otherwise, proceed to step S33;

[0021] Step S32: adopt network security blocking technology to achieve coordinated communication based on physical isolation to ensure network security;

[0022] Step S33: Black start recovery: After the equipment fails and stops operating, it is in a power outage state. The affected physical equipment in the power grid is restored through black start, the power grid resumes operation, and the network attack is re-detected;

[0023] Furthermore, the step S4 specifically includes the following steps:

[0024] Step S41: constructing an attack and defense game model of an active distribution network: based on a network attack with normal detection results, an attack and defense game model of an active distribution network G=(P, T, Φ, B, U) is constructed in combination with an incomplete information dynamic game;

[0025] Step S42: Calculate the expected benefits U of both the attacker and the defender ΦAi , U ΦDj , where Φ Aj , Φ Dj Represent the strategies selected by the attacker and the defender respectively;

[0026] Step S43: Calculate the posterior probability B1=P(T A |Φ A ), where T A , Φ A Represent the attacker type and attacker strategy respectively;

[0027] Step S44: Propose an optimal control strategy based on a nonlinear programming method, and calculate the optimal strategies for both the attacker and the defender. and

[0028] Step S45: Calculate and refine the Bayesian Nash equilibrium EQ to achieve the active defense performance optimization goal of the active distribution network.

[0029] Furthermore, the step S41 is specifically as follows: in a network attack, the grid manager can only observe the actions of the grid destroyer, but the type of the grid destroyer is unknown. However, the grid manager can use this to infer the type of the grid destroyer or modify the prior belief about the type of the grid destroyer, and then select a better defense strategy from the defender strategy set for defense. The grid destroyer launches an attack based on the strategy selected by the grid manager, and the two sides form a reciprocating cycle, which constitutes an incomplete information dynamic game of the active distribution network. Therefore, the grid destroyer and the grid manager are regarded as participants in the game, and an active distribution network attack and defense game model G = (P, T, Φ, B, U) is constructed. Where P = (P A ,P D ,P N ) represents the set of participants on both sides of the attack and defense, P A For the attacker, that is, the grid destroyer, P D For the defender, that is, the grid manager, P N It represents nature, assuming that both the attacker and the defender are rational participants, and both choose strategies based on the principle of maximizing their own benefits. A ,T D ) represents the set of attacking and defending types, T A ={T A1 ,T A2 ,···,T An} represents the set of attacker types, T A The type of is known to the attacker, but unknown to the defender, but the defender has a probability distribution for it, T D ={T D1 ,T D2 ,…,T Dm} indicates the defender type; Φ=(Φ A ,Φ D ) represents the strategy set of the attacking and defending parties, where Φ A ={Φ A1 ,Φ A2 ,…,Φ AM} represents the set of attacker strategies, Φ D ={Φ D1 ,Φ D2 ,…,Φ DN} represents the defender’s strategy set; B = (B0, B1) represents the attacker’s belief set, where B0 = P(T A ) represents the attacker’s initial belief about the defender’s type, B1=P(T A |Φ A) represents the updated belief. U=(U A ,U D ) represents the set of profit functions of both attackers and defenders, where U A =f A (T A ,Φ A ,Φ D ) represents the attacker's profit function, U D =f D (T A ,Φ A ,Φ D ) represents the defender’s profit function. The profit values ​​corresponding to different strategies selected by the attacker and defender are also different.

[0030] Furthermore, the step S42 is specifically as follows: considering that the attacking and defending parties cannot grasp all the information of the other party, there will be randomness, and a purely strategic Nash equilibrium solution may not exist, and the probability distributions corresponding to the strategies in the attacking and defending strategy set are defined as follows:

[0031]

[0032]

[0033] Where 0≤p Ai ≤1,0≤p Dj ≤1, i=1,2,…,M, j=1,2,…,N, and there is Combine the grid manager's own strategy, as well as the type and strategy of the grid destroyer, to calculate the expected benefits of both the attacker and the defender.

[0034] Furthermore, the step S43 is specifically as follows: based on the initial belief inference, the posterior probability B1=P(T A |Φ A ), adjust the inference of the type of power grid destroyer or attacker. The calculation formula of Bayes' rule is formula (2):

[0035]

[0036] Where P(Φ A |T A ) is the prior probability, P(T A |Φ A ) is the posterior probability.

[0037] Furthermore, the step S44 is specifically as follows:

[0038] The optimal control strategy is proposed based on nonlinear programming. The optimal control strategy can be expressed as formula (3):

[0039]

[0040]

[0041] Where e is the maximum system safety factor, and denote the corresponding unit row vectors, and They represent the expected returns of the attacker and the defender under Nash equilibrium. The purpose of this optimal control strategy is to maximize the system safety factor e while Φ A and Φ D The selected strategy is optimal.

[0042] Calculate the optimal attack strategy of the power grid destroyer, i.e. the attacker Optimal defense strategy for power grid managers as defenders Obtaining Subgame Perfect Nash Equilibrium

[0043] Furthermore, the step S45 is specifically as follows: according to the sub-game refined Nash equilibrium Find the defender's inference of the attacker type under Bayes' rule B2=P * (T A |Φ A ), if B1=P(T A |Φ A ) and B2=P * (T A |Φ A ) do not conflict, then the refined Bayesian Nash equilibrium According to game theory, the strategy in the refined Bayesian Nash equilibrium is the optimal choice for both parties in the game. As the optimal defense strategy for network managers, it ultimately achieves the goal of optimizing the active defense performance of active distribution networks.

[0044] Compared with the prior art, the present invention can achieve the following optimization effects:

[0045] The present invention is a method for optimizing the dynamic defense performance of an active distribution network based on game theory, which has been rarely studied in traditional technology. Traditional information security mainly discovers system threats through means such as vulnerability scanning, abnormal data (IP address, service process, etc.), intrusion detection, virus detection, etc., and then ensures the safe communication and operation of the system by means such as setting up firewalls, patching vulnerabilities, installing anti-virus software, and updating virus databases in a timely manner. For control systems, the characteristics of real-time dynamic changes require that the real-time and stable operation of the system must be placed in the first place. Therefore, the present invention analyzes and calculates the dynamic game of incomplete information, optimizes and selects the corresponding control method, and makes dynamic defense strategies in time to ensure the normal operation of the system. The present invention takes into account the situation of misjudgment and wrong judgment in the detection of network attacks. The game also takes into account the incompleteness of information of both the attacker and the defender, as well as the influence of the offensive and defensive behaviors on the selection of the opponent's strategy. Compared with the game of complete information and static information, it is more in line with the actual offensive and defensive scenarios and has better accuracy and applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 The present invention is a flow chart of the first embodiment of a method for optimizing dynamic defense performance of an active distribution network based on game theory.

[0047] Figure 2 The present invention is a flow chart of the second embodiment of a method for optimizing dynamic defense performance of an active distribution network based on game theory. DETAILED DESCRIPTION

[0048] The present invention is further described below in conjunction with the accompanying drawings and embodiments to help relevant technical personnel in the field have a more accurate, intuitive and in-depth understanding of the strategic design of the present invention.

[0049] Figure 1 FIG. 1 is a flow chart of a first embodiment of a method for optimizing dynamic defense performance of an active distribution network based on game theory according to the present invention. Figure 1 As shown, the method for optimizing the dynamic defense performance of an active distribution network based on game theory specifically includes:

[0050] Step S1: Analyze the data in the active distribution network according to its unique attributes and construct the mathematical model of the active distribution network power system as formula (1): k+1 =Ax k +Bu k +w k +E k h k (1) where A and B are coefficient matrices, x k is the system state vector, which includes parameters such as the voltage phase angle at the generator bus, the rotor angular frequency deviation at the generator bus, and the voltage phase angle at the load bus; u k is the control input, which includes the mechanical power input and the power flow components of other nodes, wk is the process noise, E k Indicates network attack, h k Indicates a fault signal.

[0051] Step S2: Judgment matrix M F Based on the mathematical model of the active distribution network power system (1), the state fault diagnosis matrix M F Detect network attacks and state fault diagnosis matrix

[0052] Where P k|k-1 represents the covariance, which is a variable that considers the relationship between the attack signal and the estimation error. Represents the estimated process noise covariance, which is white noise with zero mean, η' k-1 Represents the estimation error, which can be represented by the system state vector x k Subtract estimated state value Get, that is This state fault diagnosis matrix M F The main function is to quickly detect network attacks and reflect the impact of attack signals on the diagonal elements of the matrix. F Detection, judgment matrix trace (M F ) changes, if trace(M F ) does not change, the network attack detection is misjudged or misjudged, and the network attack by the power grid destroyer is successful, causing the physical equipment in the power grid to fail, and the process goes to step S3; otherwise, the process goes to step S4.

[0053] Step S3: Restore grid operation by black start;

[0054] Step S4: Construct an attack and defense game model, calculate the refined Bayesian Nash equilibrium EQ, and achieve the goal of optimizing the active defense performance of the active distribution network.

[0055] Furthermore, the step S3 specifically includes the following steps:

[0056] Step S31: Determine whether the network attack continues. The method may adopt the threshold division standard, that is, the threshold represents the boundary of normal network behavior, and the behavior exceeding the threshold is determined as a network attack. If the network attack continues, resulting in further expansion of the fault range, then proceed to step S32; otherwise, proceed to step S33;

[0057] Step S32: adopt network security blocking technology to achieve coordinated communication based on physical isolation to ensure network security;

[0058] Step S33: Black start recovery: After the equipment fails and stops operating, it is in a power outage state. The affected physical equipment in the power grid is restored through black start, the power grid resumes operation, and the network attack is re-detected;

[0059] Furthermore, the step S4 specifically includes the following steps:

[0060] Step S41: If trace(M F ) undergoes any changes, then an attack and defense game model for the active distribution network is constructed. In a network attack, the grid manager can only observe the actions of the grid destroyer, but does not know the type of the grid destroyer. However, this can be used to infer the type of the grid destroyer or to modify the prior belief about the type of the grid destroyer, and then select a better defense strategy from the defender strategy set for defense. The grid destroyer then launches an attack based on the strategy selected by the grid manager, and the two sides form a reciprocating cycle, which constitutes an incomplete information dynamic game for the active distribution network. Therefore, the grid destroyer and the grid manager are regarded as participants in the game, and an attack and defense game model for the active distribution network G=(P,T,Φ,B,U) is constructed. Among them, P=(P A ,P D ,P N ) represents the set of participants on both sides of the attack and defense, P A For the attacker, that is, the grid destroyer, P D For the defender, that is, the grid manager, P N It represents nature, assuming that both the attacker and the defender are rational participants, and both choose strategies based on the principle of maximizing their own benefits; T = (T A ,T D ) represents the set of attacking and defending types, T A ={T A1 ,T A2 ,…,T An} represents the set of attacker types, T A The type of is known to the attacker, but unknown to the defender, but the defender has a probability distribution for it, T D ={T D1 ,T D2 ,…,T Dm} indicates the defender type; Φ=(Φ A ,Φ D ) represents the strategy set of the attacking and defending parties, where Φ A ={Φ A1 ,Φ A2 ,…,Φ AM} represents the set of attacker strategies, Φ D ={Φ D1 ,Φ D2 ,…,Φ DN} represents the defender’s strategy set; B = (B0, B1) represents the attacker’s belief set, where B0 = P(T A ) represents the attacker’s initial belief about the defender’s type, It can be obtained from historical experience or from the average distribution probability, B1=P(T A |Φ A ) represents the updated belief; U = (U A ,U D ) represents the set of profit functions of both attackers and defenders, where U A =f A (T A ,Φ A ,Φ D ) represents the attacker's profit function, U D =f D (T A ,Φ A ,Φ D ) represents the defender's profit function. The profit values ​​corresponding to different strategies selected by the attacker and defender are also different.

[0061] Step S42: Calculate the expected benefits of both the attacker and the defender where Φ Aj , Φ Dj They represent the strategy selected by the attacker and the strategy selected by the defender respectively. Considering that the attacker and the defender cannot grasp all the information of each other, there will be randomness, and a purely strategic Nash equilibrium solution may not exist. The probability distribution corresponding to the strategy set of the attacker and the defender is defined as:

[0062]

[0063]

[0064] Where 0≤p Ai ≤1,0≤p Dj ≤1, i=1,2,…,M, j=1,2,…,N, and there is Combine the grid manager's own strategy, as well as the type and strategy of the grid destroyer, to calculate the expected benefits of both the attacker and the defender. and get Specifically, according to the strategy of the grid saboteurs Φ A ={Φ A1 ,Φ A2 ,…,Φ AM} and grid managers' strategiesΦ D ={Φ D1 ,Φ D2 ,…,Φ DN}, generate a Cartesian set Accordingly, all attack and defense strategy pairs (Φ Ai ,Φ Dj ) all satisfy (Φ Ai ,Φ Dj )∈Φ A *Φ D .

[0065] When different strategies are used in the power grid to fight, different profit values ​​will be generated. Each strategy is visited in turn in the form of traversal to obtain the profit function U of the attacker and the defender. A , U D , the specific benefits can be expressed as follows:

[0066] The attacker's payoff function

[0067]

[0068] The defender's payoff function

[0069]

[0070] Combining the strategies of both the attacker and the defender, the probability p corresponding to the centralized strategy A ={p A1 ,p A2 ,…,p AM} and p D ={p D1 ,p D2 ,…,p DN}, the expected benefits of both attackers and defenders can be calculated

[0071] The attacker’s expected payoff is

[0072]

[0073] The defender’s expected payoff is

[0074]

[0075] Step S43: Calculate the posterior probability B1=P(T A |Φ A ), where T A , Φ A Represent the attacker type and attacker strategy respectively. Based on the initial belief inference, the posterior probability B1=P(T A |Φ A ), adjust the inference of the type of power grid destroyer or attacker. The Bayesian rule calculation formula is formula (2):

[0076]

[0077] Where P(Φ A |T A ) is the prior probability, P(T A |Φ A ) is the posterior probability.

[0078] Step S44: Propose an optimal control strategy based on a nonlinear programming method, and calculate the optimal strategies for both the attacker and the defender. and

[0079] The optimal control strategy is proposed based on nonlinear programming. Specifically, the optimal control strategy can be expressed as formula (3):

[0080]

[0081]

[0082] Where e is the maximum system safety factor, and denote the corresponding unit row vectors, and They represent the expected returns of the attacker and the defender under Nash equilibrium. The purpose of this optimal control strategy is to maximize the system safety factor e while Φ A and Φ D The selected strategy is optimal.

[0083] Calculate the optimal attack strategy of the power grid destroyer, i.e. the attacker Optimal defense strategy for power grid managers as defenders For standard nonlinear programming problems, the optimal attack strategy of a grid saboteurs can usually be calculated using Newton's method. and the optimal defense strategy for grid managers Get the subgame perfect Nash equilibrium

[0084] Step S45: Calculate and refine the Bayesian Nash equilibrium EQ to achieve the active defense performance optimization goal of the active distribution network. Find the defender's inference of the attacker type under Bayes' rule B2=P * (T A |Φ A ), if B1=P(T A |Φ A ) and B2=P * (T A |Φ A ) do not conflict, then the refined Bayesian Nash equilibrium According to game theory, the strategy in the refined Bayesian Nash equilibrium is the optimal choice for both parties in the game. As the optimal defense strategy for network managers, it ultimately achieves the goal of optimizing the active defense performance of active distribution networks.

[0085] The present invention mainly constructs a game model to solve the refined Bayesian Nash equilibrium, so as to solve the network attack problem occurring in the operation of the active distribution network, realize the safe, reliable and efficient transmission of data, and achieve the goal of optimizing dynamic defense performance.

[0086] The above is a detailed description of the embodiments of the present invention in conjunction with the accompanying drawings. It is obvious that the specific implementation of the present invention is not limited by the above-mentioned methods. It should be pointed out that relevant technical personnel can make other improvements without departing from the technical principles of the present invention, and these improvements should be regarded as the protection scope of the present invention.

Claims

1. A method for optimizing the dynamic defense performance of active distribution networks based on game theory, characterized in that: The following steps are involved: Step S1: constructing a mathematical model of the active distribution network power system; Step S2: Judgment matrix M F Whether the trace of changes: Using the state fault diagnosis matrix M F Detect network attacks; if the matrix M F The trace of does not change, go to step S3, if the matrix M F The trace changes, and the process goes to step S4; Step S3: Restore grid operation by black start; Step S4: construct an attack and defense game model and use the refined Bayesian Nash equilibrium strategy to achieve the active defense performance optimization goal of the active distribution network; The step S4 specifically comprises the following steps: Step S41: constructing an attack and defense game model of an active distribution network: based on a network attack with normal detection results, an attack and defense game model of an active distribution network G=(P, T, Φ, B, U) is constructed in combination with an incomplete information dynamic game; Step S42: Calculate the expected benefits of both the attacker and the defender where Φ Aj , Φ Dj Represent the strategies selected by the attacker and the defender respectively; Step S43: Calculate the posterior probability B1=P(T A Φ A ), where T A , Φ A Represent the attacker type and attacker strategy respectively; Step S44: Propose an optimal control strategy based on a nonlinear programming method, and calculate the optimal strategies for both the attacker and the defender. and Step S45: Calculate and refine the Bayesian Nash equilibrium EQ to achieve the active defense performance optimization goal of the active distribution network; The active distribution network attack and defense game model G=(P,T,Φ,B,U), where P=(P A ,P D ,P N ) represents the set of participants on both sides of the attack and defense, P A For the attacker, that is, the grid destroyer, P D For the defender, that is, the grid manager, P N It represents nature, assuming that both the attacker and the defender are rational participants, and both choose strategies based on the principle of maximizing their own benefits; T = (T A ,T D ) represents the set of attacking and defending types, T A ={T A1 ,T A2 ,···,T An } represents the set of attacker types, T A The type of is known to the attacker, but unknown to the defender, but the defender has a probability distribution for it, T D ={T D1 ,T D2 ,…,T Dm } indicates the defender type; Φ=(Φ A ,Φ D ) represents the strategy set of the attacking and defending parties, where Φ A ={Φ A1 ,Φ A2 ,…,Φ AM } represents the set of attacker strategies, Φ D ={Φ D1 ,Φ D2 ,…,Φ DN } represents the defender’s strategy set; B = (B0, B1) represents the attacker’s belief set, where B0 = P(T A ) represents the attacker’s initial belief about the defender’s type, B1=P(T A |Φ A ) represents the updated belief; U = (U A ,U D ) represents the set of profit functions of the attacker and the defender, where U A =f A (T A ,Φ A ,Φ D ) represents the attacker's profit function, U D =f D (T A ,Φ A ,Φ D ) represents the defender’s profit function. The profit values ​​corresponding to different strategies selected by the attacker and defender are also different.

2. According to claim 1, a method for optimizing the dynamic defense performance of an active distribution network based on game theory is characterized in that: The mathematical model of the active distribution network power system is as follows: x k+1 =Ax k +Bu k +w k +E k h k (1) Where A and B are coefficient matrices, x k is the system state vector, which includes parameters such as the voltage phase angle at the generator bus, the rotor angular frequency deviation at the generator bus, and the voltage phase angle at the load bus. k is the control input, which includes the mechanical power input and the power flow components of other nodes, w k is the process noise, E k Indicates network attack, h k Indicates a fault signal.

3. According to the game theory-based method for optimizing the dynamic defense performance of active distribution networks in claim 1, it is characterized in that: The state fault diagnosis matrix Where P k|k-1 represents the covariance, which is a variable that considers the relationship between the attack signal and the estimation error. Represents the estimated process noise covariance, which is white noise with zero mean, η' k-1 Represents the estimation error, which can be represented by the system state vector x k Subtract estimated state value Get, that is 4. According to claim 3, a method for optimizing the dynamic defense performance of an active distribution network based on game theory is characterized in that: The state fault diagnosis matrix M F The main function is to quickly detect network attacks and reflect the impact of attack signals on the diagonal elements of the matrix. Therefore, the trace of the judgment matrix (M F ) changes, network attacks can be detected.

5. According to claim 4, a method for optimizing the dynamic defense performance of an active distribution network based on game theory is characterized in that: The trace of the judgment matrix (M F ) changes, if trace(M F ) does not change, the network attack detection is misjudged, the network attack by the power grid destroyer is successful, causing the physical equipment in the power grid to fail, and the process goes to step S3; if there is a change, the network attack signal E k The impact will be directly reflected in the trace (M F ), it means that a network attack has occurred at some nodes in the power grid, and the process goes to step S4.

6. According to the game theory-based method for optimizing the dynamic defense performance of active distribution networks in claim 1, it is characterized in that: The step S3 specifically comprises the following steps: Step S31: Determine whether the network attack continues. The method may adopt the threshold division standard, that is, the threshold represents the boundary of normal network behavior, and the behavior exceeding the threshold is determined as a network attack. If the network attack continues, resulting in further expansion of the fault range, then proceed to step S32; otherwise, proceed to step S33; Step S32: adopt network security blocking technology to achieve coordinated communication based on physical isolation to ensure network security, and then proceed to step S33; Step S33: Black start recovery: After the equipment fails and stops operating, it is in a power outage state. The affected physical equipment in the power grid is restored through black start, the power grid resumes operation, and the network attack is re-detected.

7. According to claim 1, a method for optimizing the dynamic defense performance of an active distribution network based on game theory is characterized in that: The step S42 is specifically as follows: considering that the attacking and defending parties cannot grasp all the information of the other party, there will be randomness, and a purely strategic Nash equilibrium solution may not exist, and the probability distribution corresponding to the strategies in the strategic concentration of the attacking and defending parties is defined as follows: Where 0≤p Ai ≤1,0≤p Dj ≤1, i=1,2,…,M, j=1,2,…,N, and there is Combine the grid manager's own strategy, as well as the type and strategy of the grid destroyer, to calculate the expected benefits of both the attacker and the defender.

8. According to the game theory-based method for optimizing the dynamic defense performance of active distribution networks in claim 1, it is characterized in that: The step S43 is specifically as follows: based on the initial belief inference, the posterior probability B1=P(T A |Φ A ), adjust the inference of the type of power grid destroyer or attacker; the Bayesian rule calculation formula is formula (2): Where P(Φ A T A ) is the prior probability, P(T A Φ A ) is the posterior probability.

9. The method for optimizing the dynamic defense performance of an active distribution network based on game theory according to claim 1 is characterized in that: The step S44 specifically includes: The optimal control strategy is proposed based on nonlinear programming. The optimal control strategy can be expressed as formula (3): max e=p A iΦ A (p D j) T -U ΦAi +p A iΦ D (p D j) T -U ΦDj (3) Where e is the maximum system safety factor, and denote the corresponding unit row vectors, and They represent the expected returns of the attacker and defender under Nash equilibrium respectively; Calculate the optimal attack strategy of the power grid destroyer, i.e. the attacker Optimal defense strategy for power grid managers and defenders Obtaining Subgame Perfect Nash Equilibrium 10. The method for optimizing the dynamic defense performance of an active distribution network based on game theory according to claim 1, characterized in that: The step S45 is specifically as follows: refining the Nash equilibrium according to the sub-game Find the defender's inference of the attacker type under Bayes' rule B2=P * (T A Φ A ), if B1=P(T A Φ A ) and B2=P * (T A Φ A ) do not conflict, then the refined Bayesian Nash equilibrium According to game theory, the strategy in the refined Bayesian Nash equilibrium is the optimal choice for both parties in the game. As the optimal defense strategy for network managers, it ultimately achieves the goal of optimizing the active defense performance of active distribution networks.

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