Intelligent power grid elastic distributed optimization algorithm based on event triggering under hostile attack

Abstract

The invention discloses a smart power grid elastic distributed optimization algorithm based on event triggering under a hostile attack, and aims to solve the problems of network constraint and attack interference in smart power grid optimization, reduce communication overhead and guarantee a control effect at the same time. According to the algorithm, firstly, a convex and continuous differentiable cost function is given, and an optimization target is determined as normal and credible node cooperation minimum cost function average; secondly, executing dual-mode trigger condition judgment, credible neighbor set screening and algorithm state updating by initializing a node state; giving a transfer matrix, a backward product and properties and a convex optimal set of the backward product, and finally verifying the convergence of the algorithm through simulation. The method has anti-attack elasticity and high communication efficiency, adapts to scenes of new energy consumption, demand side response and the like of the smart power grid, ensures reliable and optimized operation of the power grid, and has good engineering application value.

Description

Technical Field

[0001] This invention relates to an optimization algorithm for smart grids, specifically an event-triggered resilient distributed optimization algorithm for smart grids under malicious attacks. Background Technology

[0002] A smart grid is a power system that integrates advanced sensing, communication, computing, and control technologies to achieve intelligent management of all aspects of power production, transmission, distribution, and consumption. Smart grids can efficiently integrate traditional and new energy sources, improve the reliability, economy, and flexibility of the power system, and solve many core problems in the power sector, such as energy transition, power supply and demand balance, and grid security. Optimizing the smart grid is one of the core tasks for achieving its efficient operation. This requires considering that the smart grid relies on sensing, communication, and computing devices for state perception and control decisions, which presents dual risks to information security and physical security. Based on this idea, researchers have conducted extensive research on the optimization problem of smart grids under network information security, and have achieved a series of results. Summary of the Invention

[0003] The purpose of this invention is to propose an event-triggered resilient distributed optimization algorithm for smart grids under malicious attacks, which effectively solves the distributed optimization problem in smart grids under malicious attacks and improves network resource utilization.

[0004] The specific technical solution of this invention is as follows: A smart grid resilient distributed optimization algorithm based on event triggering under malicious attacks, comprising the following steps:

[0005] The mathematical expression for the smart grid cost optimization problem is as follows: In the formula, f i Let (x) denote the local cost function of node i, x denote the global variable, and assume f i (x) is a continuously differentiable convex function, and each f i The optimal set of points corresponding to (x) is arg min f i (x) is nonempty, bounded, and closed.

[0006] Considering that attackers can control compromised nodes and arbitrarily modify their states, to achieve robustness against such attacks, the worst-case scenario must be considered. A compromised node might alter its local cost function and simultaneously impersonate a normal node, following a pre-defined iteration rule. Since it's difficult to distinguish the behavior patterns of adversary and normal nodes, traditional consensus-based gradient descent algorithms are no longer applicable in this scenario. The problem then transforms into all normal and trusted nodes collaboratively minimizing the mean of their cost functions, as shown in the following expression: Where V h and V r Let |V| represent the normal node set and the trusted node set, respectively. h |=n1,|V r |=n2, where n1 and n2 represent the cardinality of the normal node set and the trusted node set, respectively; Optimizing the smart grid is one of the core tasks for its efficient operation, which requires consideration of issues such as reducing communication constraints and resisting attack interference. Reducing communication constraints refers to reducing redundant transmissions and saving network bandwidth; resisting attack interference refers to resisting malicious attacks that tamper with power data and control commands in a cyber-physical fusion environment.

[0007] To address the aforementioned issues, a smart grid resilient distributed optimization algorithm based on event triggering is constructed under malicious attacks. The specific steps are as follows: In the algorithm, x i (0) represents the initial state of node i, T i in Represents the set of trusted incoming neighbor nodes. This represents the maximum value of the trusted neighbor's state and the state of itself. R represents the minimum state of trusted neighbors and itself. i (k) represents the set of neighbors of a state within the range of credible extrema. Represents the function f i (x i The gradient of (k)). This represents the trigger state at the previous moment, where c1 and c2 are dynamic parameters, ε is a small positive number, λ represents the exponential decay coefficient, and α... k Represents the iteration step size, |R i (k)| represents R i The cardinality of (k), x i (k) represents the state of node i at time k. If neighbor j triggers communication in this iteration, then otherwise,

[0008] For the convergence and optimality aspects, the transition matrix and its properties, as well as the subsequent product and its properties, are designed. The specific steps are as follows: First, design a transition matrix of the following form: For all k, there exists Where n0 = n1 + n2, such that: In the formula, And it has the following properties, (1)Γ(k) is a row random matrix (2)Γ ij (k)≠0 if and only if (j, i)∈E1∪{(i, i)}; (3) d M =max{|N i in |}; Where E1 is the edge set of the subgraph. It includes two types of edges: all directed edges between trusted nodes, and all directed edges starting from trusted nodes and ending at normal nodes.

[0009] Furthermore, we design the product of the following terms in the form of: In the formula, Φ(k+1, t+1) represents the backward product (t≤k+1) satisfying Φ(k, k)=Γ(k), It is an identity matrix of size n0×n0. Under the elastic distributed optimization algorithm, It has the following properties: (1) For all t, the matrix Φ(t+n0-1, t) has n2 columns that are component-wise. Lower bound constraints, where It is a vector in which all elements are 1; (2) For Φ(k+1, t+1), the following holds true. Where ψ T (t) is a random vector that depends on t (the sum of its elements is 1); (3) For any Φ(k+1, t+1), we have (4) For any fixed t, n2 non-zero elements in ψ(t) are... The lower bound constraint states that there exist n² non-zero elements i∈{1, ..., n0} such that

[0010] Finally, the following convex optimal set is designed as the set to which the final value of the elastic distributed optimization algorithm belongs, and a set of functions is given: Where I{·} is the index function. For any given μ and ν, It is a set of valid functions, and thus Y(μ,ν)=U is defined. g(x)∈C(μ，ν) argmin x∈R g(x), if And if ν = n2, then Y(μ, ν) is a convex set;

[0011] The convergence and optimality of a distributed optimization algorithm based on a dynamic event-triggered communication mechanism are verified, and the algorithm is used to control a smart grid. The specific steps are as follows: for Construct the following form:

[0012] Taking the limit of both sides of the above equation, we get: In the formula, < and > represent the dot product of two vectors. The limit of a vector is a vector in which all elements are equal to a constant, expressed as: Indicate. Let. Based on the boundedness of matrix norm, the series convergence of the upper bound of error, and the partial estimation, the following three-step derivation can be obtained: Based on the above limit form, we obtain:

[0013] remember The sequence obtained by the above formula is... For node i (i∈V) h ∪V r The sequence of local variables obtained from the limit form. When ν = n2, and Then the elastic distributed optimization algorithm converges, and the final solution belongs to Y(μ, ν), that is... Attached Figure Description

[0014] Figure 1 This is a flowchart of a method according to an embodiment of the present invention;

[0015] Figure 2 This is a schematic diagram of a smart grid system according to an embodiment of the present invention;

[0016] Figure 3 This is a simulation diagram of a smart grid system according to an embodiment of the present invention;

[0017] Figure 4 This is a diagram illustrating the convergence process of the method proposed in this invention on a strongly connected directed graph in an embodiment.

[0018] Figure 5 This is a distribution diagram of the event-triggered communication triggering times using the method proposed in this invention in an embodiment.

[0019] Figure 6 The convergence rate diagram is shown for the method proposed in this invention in the example.

[0020] Figure 7 This is a comparison chart showing the optimality of the method proposed in this invention used in the embodiments; Detailed Implementation

[0021] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0022] like Figure 1 As shown, a smart grid resilient distributed optimization algorithm based on dynamic event triggering includes the following steps:

[0023] Step 1: System initialization, setting initial parameter values;

[0024] Step 2: Determine the triggering conditions for dual modes;

[0025] Step 3: Filtering the effective neighbor set;

[0026] Step 4: Algorithm state update;

[0027] Step 5: Threshold determination;

[0028] Step Six: An embodiment of the present invention is described below: The proposed resilient distributed optimization algorithm for smart grids based on dynamic event triggering was validated using the standard IEEE 39-bus power system. The IEEE 39-bus power system is divided into 10 regions. To better reflect the distributed structure of the simulation, the simulation data for each power system was placed in the IEEE database. The IEEE data port DOI for the data is 10.21227 / hnwa-7691. Considering the resilient distributed optimization algorithm for smart grids based on a dynamic event triggering communication mechanism, its corresponding local cost function is:

[0029]

[0030] The system parameter is: p i e i q i p represents the weighting coefficient, smoothing offset parameter, and local optimum reference value of a smart grid node, respectively. i The selection range is [0, 70], e i The selected range is [8, 20], q i The selection range is [50, 80].

[0031] The observation matrix parameters are as follows:

[0032] Figure 1 This is a flowchart of a method according to an embodiment of the present invention; Figure 2This is a schematic diagram of a smart grid system according to an embodiment of the present invention; Figure 3 This is a simulation diagram of a smart grid system according to an embodiment of the present invention; applying the proposed method, Figure 4 This diagram illustrates the convergence process of the proposed method in a strongly connected directed graph. Figure 5 Event-triggered communication trigger time distribution diagram, Figure 6 The convergence velocity graph is shown. Figure 7 These four figures show the optimality comparison. As can be seen from them, the proposed method performs well in circuit systems.

Claims

1. A smart grid resilient distributed optimization algorithm based on event triggering under malicious attacks, characterized in that, Includes the following steps: The mathematical expression for the smart grid cost optimization model is as follows: In the formula, f i Let (x) denote the local cost function of node i, x denote the global variable, and assume f i (x) is a continuously differentiable convex function, and each f i The optimal set of points corresponding to (x) is arg min f i (x) is non-empty, bounded, and closed; Considering that attackers can control compromised nodes and arbitrarily modify their states, to achieve robustness against such attacks, a worst-case scenario must be considered: compromised nodes may alter their local cost functions and disguise themselves as normal nodes following pre-defined iteration rules. Since it is difficult to distinguish the behavior patterns of adversary and normal nodes, traditional consensus-based gradient descent algorithms are no longer applicable in this scenario. The problem then transforms into: all normal and trusted nodes collaboratively minimizing the mean of their cost functions, as shown in the following expression: Where V h and V r Let |V| represent the normal node set and the trusted node set, respectively. h |=n1,|V r |=n2, where n1 and n2 represent the cardinality of the normal node set and the trusted node set, respectively; Optimizing the smart grid is one of the core tasks for its efficient operation. This requires considering issues such as reducing communication constraints and resisting attacks and interference. Reducing communication constraints refers to minimizing redundant transmissions and saving network bandwidth; resisting attacks and interference refers to protecting against malicious attacks that could tamper with power data and control commands in a cyber-physical system. To address these issues, an event-triggered, resilient distributed optimization algorithm for the smart grid under malicious attacks is constructed. The specific steps are as follows: In the algorithm, x i (0) represents the initial state of node i, T i in Represents the set of trusted incoming neighbor nodes. This represents the maximum value of the trusted neighbor's state and the state of itself. Let Ri(k) represent the minimum state of a trusted neighbor and itself, and let Ri(k) represent the set of neighbors whose states fall within the trusted extreme value range. Represents the function f i (x i The gradient of (k)). This represents the trigger state at the previous moment, where c1 and c2 are dynamic parameters, ε is a small positive number, λ represents the exponential decay coefficient, and α... k Represents the iteration step size, |R i (k)| represents R i The cardinality of (k), x i (k) represents the state of node i at time k. If neighbor j triggers communication in this iteration, then otherwise, Regarding convergence and optimality, the transition matrix and its properties, as well as the backward product and its properties, are given. The specific steps are as follows: First, we give a transition matrix of the following form: For all k, there exists Where n0 = n1 + n2, such that: In the formula, And it has the following properties, (1)Γ(k) is a row random matrix (2)Γ ij (k)≠0 and (j, i)∈E1∪{(i, i)}; (3) d M =max{|N i in |}; Where E1 is the edge set of the subgraph. It includes two types of edges: all directed edges between trusted nodes, and all directed edges starting from trusted nodes and ending at normal nodes; Next, the backward product is given in the following form: In the formula, Φ(k+1, t+1) represents the backward product (t≤k+1) satisfying Φ(k, k)=Γ(k), It is an identity matrix of size n0×n0. Under the elastic distributed optimization algorithm, It has the following properties: (1) For all t, the matrix Φ(t+n0-l, t) has n2 columns that are component-wise. Lower bound constraints, where It is a vector in which all elements are 1; (2) For Φ(k+1, t+1), the following holds true. Where ψ T (t) is a random vector that depends on t (the sum of its elements is 1); (3) For any Φ(k+1, t+1), we have (4) For any fixed t, n2 non-zero elements in ψ(t) are... The lower bound constraint states that there exist n² non-zero elements i∈{1, ..., n0} such that Finally, the following convex optimal set is given, which is the set to which the final value of the elastic distributed optimization algorithm belongs, and the set of functions is given: Where I{·} is the index function, for any given μ and v, It is a set of valid functions, and thus Y(μ,v)=U is defined. g(x)∈C(μ,v) argmin x∈R g(x), if And if v = n2, then Y(μ, v) is a convex set; The convergence and optimality of a distributed optimization algorithm triggered by dynamic events are verified to control the smart grid. The specific steps are as follows: for Construct the following form: Taking the limit of both sides of the above equation, we get: In the formula, < and > represent the inner product of two vectors, and the vectors are... The limit of a vector is a vector in which all elements are equal to a constant, expressed as: It means, set Based on the boundedness of matrix norm, the series convergence of the upper bound of error, and the partial estimation, the following three-step derivation can be obtained: Based on the above limit form, we obtain: remember The sequence obtained by the above formula is... For node i (i∈V) h ∪V r The sequence of local variables obtained from the limit form, when v = n2, and Then the elastic distributed optimization algorithm converges, and the final solution belongs to Y(μ, v), that is...

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