CN-121984728-A - Intelligent power grid elastic distributed optimization algorithm based on event triggering under malicious attack

Abstract

The invention discloses an event-triggered intelligent power grid elastic distributed optimization algorithm under malicious attack, which aims to solve the problems of network constraint and attack interference in intelligent power grid optimization, reduce communication overhead and guarantee control effect. The algorithm firstly gives a convex and continuous and tiny cost function, determines an optimization target as a normal and trusted node cooperation minimized cost function average, then performs dual-mode triggering condition judgment, trusted neighbor set screening and algorithm state updating through initializing node states, gives a transfer matrix, a backward product and properties thereof and a convex optimal set, and finally verifies algorithm convergence through simulation. The intelligent power grid intelligent power system has the advantages of being high in anti-attack elasticity and communication efficiency, being suitable for the scenes of intelligent power grid new energy consumption, demand side response and the like, guaranteeing the reliable and optimal operation of the power grid, and having good engineering application value.

Inventors

• LIU DAN
• HU TAO
• YI HUI
• CHEN JUN
• LI LIWEI

Assignees

• 南京工业大学

Dates

Publication Date

20260505

Application Date

20260119

Claims (1)

1. 1. The intelligent power grid elastic distributed optimization algorithm based on event triggering under malicious attack is characterized by comprising the following steps of: constructing a cost optimization model of the intelligent power grid, wherein the mathematical expression is as follows: Where f i (x) represents the local cost function of node i, x represents the global variable, and assuming f i (x) is a continuously differentiable convex function, each set of optimal points arg min f i (x) for f i (x) is non-empty, bounded and closed; In order to realize robustness to the attack, worst case is considered, namely the attacked node falsifies a local cost function and masqueraded normal node follows a preset iteration rule, and the traditional gradient descent algorithm based on consistency is not applicable to the scene because of difficulty in distinguishing the behavior modes of the hostile node and the normal node, and the problem is converted into that all the normal nodes and the trusted nodes cooperatively minimize the average value of the cost function, wherein the expression is as follows: Wherein V h and V r represent a normal node set and a trusted node set, respectively, |v h |＝n 1 ,|V r |＝n 2 ,n 1 and n 2 represent the cardinalities of the normal node set and the trusted node set, respectively; Optimizing the intelligent power grid is one of core tasks for realizing efficient operation, and needs to consider the problems of reducing communication constraint, namely reducing redundant transmission and saving network bandwidth, resisting attack interference, namely resisting malicious attack from tampering power data and control instructions in an information physical fusion environment, and constructing an intelligent power grid elastic distributed optimization algorithm based on event triggering under malicious attack, wherein the intelligent power grid elastic distributed optimization algorithm comprises the following specific steps: In the algorithm, x i (0) represents the initial state of node i, T i in represents the set of trusted neighboring nodes, Representing the state maximum of the trusted neighbors with themselves, Representing the minimum value of the state of the trusted neighbors and themselves, ri (k) represents the set of neighbors whose states are within the range of the trusted extremum, Representing the gradient of the function f i (x i (k)), Representing the triggering state at the last moment, c 1 、c 2 is a dynamic parameter, epsilon is a small positive number, lambda represents an exponential decay coefficient, alpha k represents an iteration step, R i (k) represents the cardinal number of R i (k), x i (k) represents the node i state at the moment k, and if the neighbor j triggers communication at the current iteration, the node i state at the moment k Otherwise the first set of parameters is selected, For convergence and optimality, a transfer matrix and its properties, and a backward product and its properties are given, and the specific steps are as follows: First a transfer matrix is given in the form that for all k there is a transfer matrix Wherein n 0 ＝n 1 +n 2 , such that: In the formula, And has the following properties, (1) Γ (k) is a row random matrix, (2) Γ ij (k) noteq0 if and only if (j, i) ∈e 1 { (i, i) }; (3) d M ＝max{|N i in |}; Wherein E 1 is the edge set of the subgraph, All directed edges between the trusted nodes and all directed edges with the trusted nodes as the starting point and the normal nodes as the ending point; Secondly, the following form of backward product is given: In the formula, Phi (k+1, t+1) represents the backward product (t≤k+1), satisfies phi (k, k) =Γ (k), Is an identity matrix with the size of n 0 ×n 0 , under the elastic distributed optimization algorithm, Has the following properties: (1) For all t, n 2 columns in the matrix Φ (t+n 0 -l, t) are grouped in the sense of a component Lower bound constraint in which Is a vector with all elements being 1; (2) For Φ (k+1, t+1), it holds that Wherein ψ T (t) is a random vector (element sum 1) dependent on t; (3) For any Φ (k+1, t+1), there are (4) For any fixed t, there are n 2 non-zero elements in ψ (t) that are written The lower bound constraint that there are n 2 non-zero elements i e {1,., n 0 } such that Finally, the following convex optimal set is given, and a function set is given for evaluating the set to which the final value of the elastic distributed optimization algorithm belongs: where I {.cndot } is an index function that, for any given μ and v, Is a set of effective functions, and further defines Y (μ, v) =U g(x)∈C(μ,v) argmin x∈R g (x), if And v=n 2 , then Y (μ, v) is a convex set; The distributed optimization algorithm based on dynamic event triggering verifies convergence and optimality, and controls the intelligent power grid, and the specific steps are as follows: For the following The structure is as follows: the limit is taken from the two sides: Wherein < > represents the inner product of two vectors, the vectors The limit of (2) is a vector with all elements equal to a constant, using Representation, set up The three-step deduction is obtained according to the matrix norm limitation, the series convergence of the error upper bound and the fractional estimation, From the above limit forms, we find: Recording device In order to obtain a sequence by the above formula, For the local variable sequence derived from the limit form for node i (i.e. V h ∪V r ), when V=n 2 , and The elastic distributed optimization algorithm converges and the final solution belongs to Y (μ, v), i.e

Description

Intelligent power grid elastic distributed optimization algorithm based on event triggering under malicious attack Technical Field The invention relates to an optimization algorithm for a smart grid, in particular to an event-triggering-based smart grid elastic distributed optimization algorithm under malicious attack. Background The intelligent power grid is a power system which integrates advanced sensing, communication, calculation and control technologies and realizes intelligent management of all links of power production, transmission, distribution and consumption. The intelligent power grid can efficiently integrate traditional energy and new energy, improves reliability, economy and flexibility of a power system, and can solve core problems in a plurality of power fields such as energy transformation, power supply and demand balance, power grid safety and the like. Optimizing the intelligent power grid is one of core tasks for realizing efficient operation of the intelligent power grid, state sensing and control decision-making of the intelligent power grid depending on sensing, communication and computing equipment needs to be considered, double risks of information safety and physical safety exist, and based on the idea, researchers develop a great deal of research on the intelligent power grid optimization problem under the network information safety and acquire a series of achievements. Disclosure of Invention The invention aims to provide an event triggering-based intelligent power grid elastic distributed optimization algorithm under malicious attack, which effectively solves the distributed optimization problem in the intelligent power grid under the malicious attack and improves the utilization rate of network resources. The intelligent power grid elastic distributed optimization algorithm based on event triggering under malicious attack comprises the following steps: the intelligent power grid cost optimization problem is characterized by the following mathematical expression: Where f i (x) represents the local cost function of node i, x represents the global variable, and assuming f i (x) is a continuously differentiable convex function, each set of optimal points arg min f i (x) for f i (x) is non-empty, bounded and closed. Considering that an attacker can control the attacked node and tamper the state of the attacked node at will, in order to realize robustness to the attack, the attacked node tamper a local cost function of the attacker, and disguise a normal node to follow a preset iteration rule, because the behavior modes of the hostile node and the normal node are difficult to distinguish, the traditional gradient descent algorithm based on consistency is not applicable to the scene any more, at the moment, the problem is converted into the mean value of the cost function of all the normal nodes and the trusted node to be minimized in a synergic way, and the expression is as follows: V h and V r respectively represent a normal node set and a trusted node set, V h|＝n1,|Vr|＝n2,n1 and n 2 respectively represent the base numbers of the normal node set and the trusted node set, and optimizing the intelligent power grid is one of core tasks for realizing efficient operation of the intelligent power grid, and problems of communication constraint reduction, attack interference resistance and the like need to be considered. Reducing communication constraint refers to reducing redundant transmission and saving network bandwidth, and resisting attack interference refers to resisting tampering of malicious attacks on power data and control instructions in an information physical fusion environment. In order to solve the problems, an event-triggered intelligent power grid elastic distributed optimization algorithm under malicious attack is constructed, and the method specifically comprises the following steps: In the algorithm, x i (0) represents the initial state of node i, T iin represents the set of trusted neighboring nodes, Representing the state maximum of the trusted neighbors with themselves,Representing the minimum value of the state of the trusted neighbors and the trusted neighbors, R i (k) represents the neighbor set of which the state is in the range of the trusted extremum,Representing the gradient of the function f i(xi (k)),Representing the triggering state at the last moment, c 1、c2 is a dynamic parameter, epsilon is a small positive number, lambda represents an exponential decay coefficient, alpha k represents an iteration step, R i (k) represents the cardinal number of R i (k), x i (k) represents the node i state at the moment k, and if the neighbor j triggers communication at the current iteration, the node i state at the moment kOtherwise the first set of parameters is selected, For the convergence and optimality parts, the transfer matrix and its properties, and the product of the postterms and its properties are designed as follows: the transfer matrix is first designed in