A Distributed Resilient Control Method and System for AC Microgrids

Abstract

This invention relates to a distributed resilient control method and system for AC microgrids, belonging to the field of microgrid control technology. It includes: constructing resilient secondary voltage, frequency, and active power distribution controllers respectively; constructing a first Lyapunov function and using it to analyze the first stability condition of the resilient secondary voltage controller; using the first Lyapunov function to analyze the second stability condition of the resilient secondary frequency controller; constructing a second Lyapunov function and using it to analyze the third stability condition of the resilient secondary active power distribution controller; and adjusting the control gain parameters of the resilient secondary voltage controller, resilient secondary frequency controller, and resilient secondary active power distribution controller according to the first, second, and third stability conditions to obtain their respective control signals. This invention reduces the vulnerability of secondary control to network attacks and enhances the microgrid's ability to resist hybrid attacks.

Description

Technical Field

[0001] This invention relates to the field of microgrid control technology, and in particular to a distributed resilient control method and system for AC microgrids. Background Technology

[0002] In recent years, microgrids have gradually become a focus of academic research due to their excellent capabilities in the integration of distributed generation and energy storage devices, especially demonstrating significant advantages in flexible operation and high energy efficiency. AC microgrids, with their high efficiency and good compatibility with traditional power grids, have attracted considerable attention from engineers and researchers. However, the inherently complex dynamic characteristics of islanded AC microgrid systems pose significant challenges to their precise and stable control. Furthermore, the control architecture of islanded microgrids needs to accommodate multiple requirements that differ significantly in their impact and time scale, such as maintaining the voltage and frequency of each generator unit at rated values, rationally allocating loads, and optimizing operating costs. To address these challenges, researchers typically employ hierarchical control frameworks to achieve efficient and precise control of multiple generator units.

[0003] Typically, a hierarchical control architecture consists of a first-level control layer, a second-level control layer, and a third-level control layer. The first-level control layer, as the foundational layer, is responsible for regulating the amplitude and frequency of the three-phase voltage output from the generator set and achieving reasonable power distribution using the droop control principle. However, due to droop characteristics and voltage and frequency deviations caused by load disturbances, the first-level control layer struggles to precisely adjust these parameters to their rated values. To address this, researchers have proposed a distributed secondary control strategy based on multi-agent theory to optimize microgrid operation. Distributed secondary control utilizes a communication network to achieve real-time information exchange between distributed generators, thereby enabling consistent control of all variables.

[0004] However, the communication network upon which distributed secondary control relies is vulnerable to potential network threats. Fraud attacks and denial-of-service (DoS) attacks are two common and major network threats in microgrids. Fraud attacks manipulate data transmitted over the network to convey false and misleading information. Existing technologies for mitigating fraud attacks primarily employ detection-compensation mechanisms and resilient controller strategies. DoS attacks, on the other hand, disrupt and block communication channels, interfering with information transmission and rendering the communication network inoperable. Currently, most strategies for mitigating DoS attacks are resilient control schemes.

[0005] In current research, most studies on fraud attacks focus on continuous-time attack models, with less attention paid to discrete forms of fraud attacks. In real-world environments, attackers typically choose discrete, covert fraud attacks to evade detection algorithms because these attacks are highly stealthy and difficult to identify quickly. Furthermore, existing technologies primarily concentrate on countermeasures against single attack types. However, in real-world scenarios, attackers often employ multiple attack methods to penetrate communication networks, disrupting system stability in various ways and weakening detection algorithms against specific attack types. Such covert, hybrid attacks can cause significant disruption to the secondary control system of a microgrid, ultimately leading to system instability. Summary of the Invention

[0006] Therefore, the technical problem to be solved by the present invention is to overcome the vulnerability of distributed secondary control in the face of network attacks, and the shortcomings of the existing technology in dealing with hybrid attacks.

[0007] In a first aspect, to solve the above-mentioned technical problems, the present invention provides a distributed resilient control method for AC microgrids, comprising:

[0008] S1. Constructing a flexible secondary voltage controller, a flexible secondary frequency controller, and a flexible secondary active power distribution controller for an AC microgrid; the expressions for the flexible secondary voltage controller, the flexible secondary frequency controller, and the flexible secondary active power distribution controller are as follows:

[0009]

[0010] in, The intensity is controlled by the secondary voltage. The intensity is controlled by a secondary frequency. For the strength of the secondary active power distribution controller, S i Let a be the set of neighboring nodes. ij For the existence of a communication channel between the i-th node and the j-th node, V odi (t) represents the d-axis component of the three-phase output voltage at the i-th node, b i For the i-th node to have a communication channel with the leader node, V rated For the rated voltage, ω i (t) represents the frequency of the i-th node, ω rated For the rated frequency, m pi P is the droop coefficient in the droop characteristic. i (t) represents the active power of the i-th node, where i and j are the node numbers;

[0011] S2. Construct the first Lyapunov function, and use the first Lyapunov function to analyze the first stability condition of the elastic secondary voltage controller; the expression of the first Lyapunov equation is:

[0012]

[0013] Among them, e v The difference between the output voltage amplitude and the rated voltage is represented by F, where F is a positive definite matrix and T is the matrix transpose sign.

[0014] S3. Analyze the second stability condition of the elastic quadratic frequency controller using the first Lyapunov function;

[0015] S4. Construct a second Lyapunov function and use it to analyze the third stability condition of the elastic secondary active power distribution controller; the expression of the second Lyapunov function is:

[0016]

[0017] Among them, e p This is the sum of errors in active power sharing among neighboring nodes;

[0018] S5. Based on the first stability condition, the second stability condition, and the third stability condition, adjust the control gain parameters of the elastic secondary voltage controller, the elastic secondary frequency controller, and the elastic secondary active power distribution controller to obtain their respective control signals;

[0019] S6. Control the operating status of each distributed generation unit in the AC microgrid according to the control signal.

[0020] In one embodiment of the present invention, after S1 constructs the flexible secondary voltage controller, the flexible secondary frequency controller and the flexible secondary active power distribution controller, it further includes introducing an extended matrix to integrate the output voltage error of each distributed generation unit into a comprehensive structure.

[0021] In one embodiment of the present invention, the expression for the extended matrix is:

[0022]

[0023] in, All of them are matrices of different dimensions; for Elements on the main diagonal; for Elements on the main diagonal; for Elements on the main diagonal; l i1 li2 l iN for Elements on the main diagonal; μ i1 μ i2 μ iN for Elements on the main diagonal; for The elements on the main diagonal; diag(·) is the symbol for a diagonal matrix. is a real matrix symbol, and N is the total number of nodes.

[0024] In one embodiment of the present invention, the first stability condition obtained by S2 is:

[0025]

[0026] Where ρ is a constant between 0 and 1, and T a For time intervals; For a constant, the expression is:

[0027]

[0028] For a constant, the expression is:

[0029]

[0030] in, For the secondary voltage control strength, η v λ is a positive number. max (·) denotes taking the largest eigenvalue of the matrix, where F is a positive definite matrix and λ min (·) represents taking the minimum eigenvalue of the matrix, and max(·) represents taking the maximum eigenvalue. ij ∈[0,1], and m max Let N be a different constant, where N is the total number of nodes.

[0031] In one embodiment of the present invention, the second stability condition obtained by S3 is:

[0032]

[0033] Where ρ is a constant between 0 and 1, and T a For time intervals, For a constant, the expression is:

[0034]

[0035] For a constant, the expression is:

[0036]

[0037] in, For the intensity of the second-order frequency control, η ω λ is a positive number. max (·) denotes taking the largest eigenvalue of the matrix, where F is a positive definite matrix and λ min (·) represents taking the minimum eigenvalue of the matrix, and max(·) represents taking the maximum eigenvalue. ij ∈[0,1], and m 1max Let N be a different constant, where N is the total number of nodes.

[0038] In one embodiment of the present invention, the third stability condition obtained by S4 is:

[0039]

[0040] Where ρ is a constant between 0 and 1, and T a For time intervals; For a constant, the expression is:

[0041]

[0042] For a constant, the expression is:

[0043]

[0044] in, For the strength of the secondary active power distribution controller, η p λ is a positive number. max (·) represents taking the largest eigenvalue of the matrix, λ 2min (·) denotes taking the second smallest eigenvalue of the matrix, where L is the matrix and λ is the eigenvalue. min (·) represents taking the minimum eigenvalue of the matrix, and max(·) represents taking the maximum eigenvalue. ij ∈[0,1], and m 2max Let N be a different constant, where N is the total number of nodes.

[0045] In one embodiment of the present invention, when constructing the resilient secondary voltage controller and the resilient secondary frequency controller in S1, a virtual leader is introduced, wherein the output voltage and output frequency of the virtual leader remain constant; the virtual leader communicates with other nodes.

[0046] In one embodiment of the present invention, before constructing the flexible secondary voltage controller, the flexible secondary frequency controller, and the flexible secondary active power distribution controller, step S1 includes performing input-output feedback linearization processing on the state equation of the power generation unit; the flexible secondary voltage controller, the flexible secondary frequency controller, and the flexible secondary active power distribution controller are constructed based on the processed state equation of the power generation unit; wherein the processed state equation of the power generation unit is:

[0047]

[0048] Among them, V odi Let n be the d-axis component of the i-th third-phase output voltage. qi and m pi All are droop coefficients in the droop characteristic, ω i Let Q be the frequency of the i-th power generation unit. i P is the reactive power value after a first-order low-pass filter. i The active power value after a first-order low-pass filter; u vi (t), u ωi (t) and u pi (t) represent the outputs of the secondary voltage control, secondary frequency control, and secondary active power distribution control of the i-th node, respectively; and Here, i represents the reference voltage and reference frequency values, and i is the node number.

[0049] Secondly, to solve the above-mentioned technical problems, the present invention provides a distributed resilient control system for AC microgrids, comprising:

[0050] The controller construction module is used to construct a flexible secondary voltage controller, a flexible secondary frequency controller, and a flexible secondary active power distribution controller for an AC microgrid; the expressions for the flexible secondary voltage controller, the flexible secondary frequency controller, and the flexible secondary active power distribution controller are as follows:

[0051]

[0052] in, For secondary voltage control intensity, The intensity is controlled by a secondary frequency. For the strength of the secondary active power distribution controller, S i Let a be the set of neighboring nodes. ij For the existence of a communication channel between the i-th node and the j-th node, V odi (t) represents the d-axis component of the three-phase output voltage at the i-th node, b i For the i-th node to have a communication channel with the leader node, V rated For the rated voltage, ωi (t) represents the frequency of the i-th node, ω rated For the rated frequency, m pi P is the droop coefficient in the droop characteristic. i (t) represents the active power of the i-th node, where i and j are the node numbers;

[0053] The stability condition acquisition module is used to construct a first Lyapunov function and analyze the first stability condition of the elastic secondary voltage controller using the first Lyapunov function; the expression of the first Lyapunov equation is:

[0054]

[0055] Among them, e v Let F be the difference between the output voltage amplitude and the rated voltage, T be the matrix transpose, and F be a positive definite matrix. The second stability condition of the elastic quadratic frequency controller is analyzed using the first Lyapunov function. A second Lyapunov function is constructed, and the third stability condition of the elastic quadratic active power distribution controller is analyzed using the second Lyapunov function. The expression for the second Lyapunov function is:

[0056]

[0057] Among them, e p This is the sum of errors in active power sharing among neighboring nodes;

[0058] The control parameter adjustment module is used to adjust the control gain parameters of the elastic secondary voltage controller, the elastic secondary frequency controller, and the elastic secondary active power distribution controller according to the first stability condition, the second stability condition, and the third stability condition, so as to obtain their respective control signals;

[0059] The control module is used to control the operating status of each distributed generation unit in the AC microgrid according to the control signal.

[0060] Thirdly, to solve the above-mentioned technical problems, the present invention provides an islanded microgrid, including the aforementioned distributed resilient control system for an AC microgrid.

[0061] Compared with the prior art, the above-described technical solution of the present invention has the following advantages:

[0062] (1) The distributed resilient control method and system for AC microgrids described in this invention significantly enhances the microgrid's ability to resist hybrid network attacks by constructing resilient secondary voltage control, secondary frequency control, and secondary active power distribution control, thereby improving the system's robustness and reliability. Simultaneously, by establishing first and second Lyapunov functions, the stability conditions of these controllers are analyzed in depth, leading to the derivation of simple inequalities. These inequalities provide clear reference standards for selecting secondary controller parameters to maintain microgrid stability under hybrid attack environments. Furthermore, by realizing information sharing and joint control between adjacent nodes, the collaborative working capability of distributed power sources within the microgrid is further strengthened. This collaborative mechanism effectively improves the overall operating efficiency and reliability of the system. This invention not only significantly reduces the problems that may arise in distributed secondary control when encountering network attacks but also improves the microgrid's defense capability against hybrid attacks, ensuring the safe and stable operation of the microgrid.

[0063] (2) This invention cleverly solves the problem of inconsistent dimensions of the system matrix under network attack by introducing a series of extended diagonal matrices based on random variables. Attached Figure Description

[0064] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein...

[0065] Figure 1 This is a flowchart of a distributed resilient control method for an AC microgrid in a preferred embodiment of the present invention;

[0066] Figure 2 This is a test AC microgrid structure diagram in a preferred embodiment of the present invention;

[0067] Figure 3 This is an output voltage diagram of a distributed generation unit under an unoptimized secondary controller in a preferred embodiment of the present invention.

[0068] Figure 4 This is the output frequency diagram of the distributed generation unit under an unoptimized secondary controller in a preferred embodiment of the present invention.

[0069] Figure 5 This is a diagram of the output active power of a distributed generation unit under an unoptimized secondary controller in a preferred embodiment of the present invention.

[0070] Figure 6 This is a diagram showing the output voltage of a distributed generation unit under a flexible controller in a preferred embodiment of the present invention.

[0071] Figure 7This is the output frequency diagram of the distributed generation unit under the flexible controller in a preferred embodiment of the present invention;

[0072] Figure 8 This is a diagram showing the output active power of a distributed generation unit under a flexible controller in a preferred embodiment of the present invention. Detailed Implementation

[0073] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0074] Example 1

[0075] Reference Figure 1 As shown, the present invention provides a distributed resilient control method for AC microgrids, comprising:

[0076] S1. Constructing a flexible secondary voltage controller, a flexible secondary frequency controller, and a flexible secondary active power distribution controller for an AC microgrid; the expressions for the flexible secondary voltage controller, the flexible secondary frequency controller, and the flexible secondary active power distribution controller are as follows:

[0077]

[0078] in, For secondary voltage control intensity, The intensity is controlled by a secondary frequency. For the strength of the secondary active power distribution controller, S i Let a be the set of neighboring nodes. ij For the existence of a communication channel between the i-th node and the j-th node, V obi (t) represents the d-axis of the three-phase output voltage at the i-th node, and b i For the i-th node to have a communication channel with the leader node, V rated For the rated voltage, ω i (t) represents the frequency of the i-th node, ω rated For the rated frequency, m pi P is the droop coefficient in the droop characteristic. i (t) represents the active power of the i-th node, where i and j are the node numbers;

[0079] S2. Construct the first Lyapunov function and use it to analyze the first stability condition of the elastic secondary voltage controller; the expression of the first Lyapunov equation is:

[0080]

[0081] Among them, e vThe difference between the output voltage amplitude and the rated voltage is represented by F, where F is a positive definite matrix and T is the matrix transpose sign.

[0082] S3. Analyze the second stability condition of the elastic quadratic frequency controller using the first Lyapunov function.

[0083] S4. Construct the second Lyapunov function and use it to analyze the third stability condition of the elastic quadratic active power distribution controller; the expression of the second Lyapunov function is:

[0084]

[0085] Among them, e p This is the sum of errors in active power sharing among neighboring nodes;

[0086] S5. Based on the first stability condition, the second stability condition, and the third stability condition, adjust the control gain parameters of the elastic secondary voltage controller, the elastic secondary frequency controller, and the elastic secondary active power distribution controller to obtain their respective control signals.

[0087] S6. Control the operating status of each distributed generation unit in the AC microgrid according to the control signal.

[0088] This invention provides a distributed resilient control method for AC microgrids. By designing resilient secondary voltage, frequency, and active power distribution controllers, it significantly improves the robustness and reliability of the microgrid in the face of mixed attacks. Simultaneously, using constructed first and second Lyapunov functions, the stability conditions of three types of controllers are analyzed in depth, leading to a set of simple inequalities. These inequalities provide clear guidelines for selecting secondary controller parameters to maintain microgrid stability under mixed attack environments. Furthermore, this embodiment further enhances the collaborative operation capability of various distributed power sources in the microgrid through information exchange and cooperative control among neighboring nodes. This collaborative effect improves the overall system operating efficiency and reliability. Therefore, this embodiment not only effectively reduces the vulnerability of distributed secondary control to network attacks but also enhances the microgrid's ability to resist mixed attacks, providing a strong guarantee for the safe and stable operation of the microgrid.

[0089] In this embodiment, for ease of description, the meanings of the relevant characters are explained as follows:

[0090] μ is a random variable. Indicate its mathematical expectation; Represents the set of non-negative integers; Represent an n-dimensional vector; Let λ represent an n×n real matrix; max(L) represents the largest eigenvalue of matrix L; λ min (L) represents the smallest eigenvalue of matrix L, λ 2min (L) denotes the second smallest eigenvalue of matrix L; ||z|| denotes the Euclidean norm of vector z; sign(·) denotes the sign function; A T This represents the transpose of matrix A.

[0091] Specifically, considering a distributed generation unit in a microgrid with a purely inductive line impedance environment, its droop characteristic generally satisfies the following relationship:

[0092]

[0093] Where: V odi and V oqi It is the output voltage V of the i-th third phase. oi The d-axis and q-axis components, and satisfying N represents the total number of nodes. ω i It is the frequency of the i-th generating unit (DG). and These are the reference voltage and reference frequency values. pi and n qi It is the droop coefficient in the droop characteristic. Q i and P i It is reactive power measured instantaneously. and active power After first-order low-pass filtering The instantaneous value can be calculated using the following formula:

[0094]

[0095] Among them: I odi and I ogi It is the dq component of the output current.

[0096] In this embodiment, secondary control is required to achieve consistent voltage and frequency control and reasonable active power allocation among the generator sets. Due to the droop characteristics of the generator sets, primary control alone is insufficient to meet the requirements; secondary control can further optimize various indicators of the microgrid. Furthermore, a communication network is needed to support the implementation of secondary control in order to enable information exchange between the generator sets.

[0097] Specifically, in the communication network, each generator set is assumed to be a node. This embodiment relates to a network structure of an islanded microgrid, specifically an undirected graph. The set Represents the set of nodes in a microgrid communication topology. It contains edges representing communication connections. Define the set S of neighbor nodes. i =(j|(χ) j , χ i )∈ε N Let i = 1, 2, ..., N, to easily obtain the neighbors of the i-th node. The adjacency matrix A is... N =(a ij ) N×N (i, j = 1, 2, ..., N) describes the flow of information exchange between distributed generators within a microgrid, where a ij =a ji >0, i≠j indicates that there is a communication channel between the i-th node and the j-th node, while a ij =a ji =0, i≠j indicates that such a channel does not exist, and assume a ii =0. In this embodiment, the entire communication topology is strongly connected, and therefore an irreducible symmetric Laplace matrix L is obtained, where l ij =-a ij i≠j and

[0098] This embodiment aims to adjust the output voltage amplitude V. oi Up to rated voltage V rated And stabilize the output frequency ω i At its rated value ω rated .because And V oqi =0, the control target for the output voltage amplitude is simplified to V odi →V rated To effectively control the voltage and frequency of the entire microgrid, this embodiment introduces a virtual leader (DGO) whose output voltage remains constant at V. rated The output frequency remains constant at ω. rated To represent the communication connections between the virtual leader DGO and other nodes, we define matrix B = diag(b 10 b 20 , ..., b N0 ), where if the i-th node can receive information from the virtual leader DGO, then b i0 >0; otherwise b i0 =0. At the same time, it is required that there is at least one b. i0 Satisfy b i0 >0 for i = 1, 2, ..., N, to ensure that the entire microgrid can receive information from the virtual leader DGO.

[0099] Specifically, in the control framework of a microgrid, distributed secondary control is typically achieved through the V of the droop controller. iref In use, the operating state of the main control is adjusted. Based on the input-output feedback linearization method, the state equation of the power generation unit is linearized by input-output feedback. Based on equation (1), we can obtain:

[0100]

[0101] Where: u vi (t), u ωi (t) and u pi (t) are auxiliary variables, representing the outputs of the secondary voltage control, secondary frequency control, and secondary active power distribution control at the i-th node, respectively. Therefore, V in the droop controller ref and ω ref It can be rephrased as:

[0102]

[0103] Furthermore, the distributed secondary elastic controller in this embodiment is designed as follows:

[0104]

[0105] in: This indicates the secondary voltage control strength.

[0106] The distributed secondary voltage controller (3) needs to exchange information about neighboring nodes through a communication network. However, the addition of this network exposes the system to potential network attack risks, including DoS attacks against the entire controller network and deception attacks that disrupt the exchange of information between neighboring nodes.

[0107] Specifically, a DoS attack disrupts the entire communication network in a distributed secondary control system, thereby preventing the controller from operating effectively. In this embodiment, a time series ξ is defined. D ={σ1, σ2, ..., σ h , ...}, Used to describe the timing of a DoS attack, time series ξ I = {∈1, ∈2, ..., ∈ h , ...} are used to represent the duration of each attack. It is worth noting that there will still be a period of normal communication between two adjacent attacks, thus the time interval between adjacent attacks satisfies σ. h+1 -σ h >∈ h Furthermore, the definition This represents the time interval for normal communication within the interval [s, t), while This represents the time interval of message blocking during a DoS attack, also within the interval [s, t). Clearly, and Therefore, we need to define the following function r(t) to represent the situation where the secondary controller is under a DoS attack. The mathematical expression of the function r(t) is:

[0108]

[0109] in: yes abbreviation, and Clearly, r(t) = 0 indicates a DoS attack has occurred, while r(t) = 1 indicates no DoS attack has occurred and the communication channel remains open. Therefore, the secondary voltage controller under a DoS attack is described as follows:

[0110]

[0111] Furthermore, in this embodiment, it is assumed that under a DoS attack, the entire communication network of the system will still maintain normal communication for a certain period of time. Therefore, there exists a constant ρ satisfying 0 < ρ < 1 such that the following inequality holds:

[0112]

[0113] in: This represents the time of normal communication within the time interval (0, t).

[0114] Furthermore, a pulse spoofing attack involves pulse-like tampering with the information operations of neighboring nodes in the distributed secondary controller. In this embodiment, the sequence ξ of the pulse spoofing attack time is defined. F ={t1, t2, ..., t k ,…},in: and Considering that the timing of the fraud attack is random, a random variable μ is defined. ij (where i, j = 1, 2, ..., N) represents whether the communication channel from the j-th node to the i-th node is under attack. Specifically, μ ij =1, i≠j indicates that the communication channel is under attack, while μ ij =0, i≠j indicates that the channel has not been attacked. Furthermore, μ ij =0, i=j. The probability distribution of this random variable follows a Bernoulli distribution, described as:

[0115]

[0116] Wherein: κ ij ∈[0,1], i≠j and κ ii =0.

[0117] Furthermore, we define a matrix μ associated with this random variable, and the expectation of this matrix can be represented as the following matrix Ξ:

[0118]

[0119] Furthermore, let ψ ij (i, j = 1, 2, ..., N) represents the pulse spoofing attack signal on the information exchange channel from the j-th node to the i-th node, which is related to e vj (t)=V odj (t)-V rated The relevant nonlinear functions. Therefore, the controller (3) under a pulse fraud attack can be expressed as:

[0120]

[0121] Where: δ(·) is the Dirac impulse function, u vi (t) at time t of the pulse fraud attack k It is right-continuous, that is...

[0122] Furthermore, in order to clearly illustrate the technical solution of this embodiment, the relevant definitions and assumptions are explained as follows.

[0123] Definition 1: In the pulse time series ξ F ={t1, ...,t} k In the sequence , ..., the average interval between pulse fraud attacks is at least T. a (T a (where N is the time interval), thus there exists at least one positive integer N0 that satisfies:

[0124]

[0125] Where: N ξ (s, T) represents the number of times a burst spoofing attack occurs within the time interval (s, T).

[0126] Assumption 1: Nonlinear pulse fraud attack function for each interactive channel satisfy:

[0127]

[0128] in: It is a non-negative number, and N is the total number of nodes.

[0129] Therefore, the distributed secondary voltage controller can be defended against DoS attacks and pulse fraud attacks as follows:

[0130]

[0131] Under the threat of DoS and pulse spoofing attacks, the overall communication network of a microgrid exhibits significant instability, leading to substantial interference with voltage regulation in secondary control. Therefore, it is necessary to explore in depth how to ensure stable voltage regulation in secondary control under these complex attack scenarios. First, a systematic overview of the control objectives of the secondary voltage controller in a hybrid attack scenario will be provided.

[0132] Definition 2: The objective of distributed secondary voltage control under hybrid attack is to maximize the output three-phase voltage amplitude V of the i-th distributed generation unit. odi The expected value is gradually adjusted to its nominal value V. rated .

[0133]

[0134] Because of e vi =V odi -V rated The control objective is described as follows:

[0135]

[0136] Based on the types of attacks occurring in different time periods, the i-th controller (6) can be integrated as follows:

[0137]

[0138] in:

[0139] for Combining equations (2) and (7), we can obtain:

[0140]

[0141] Furthermore, define e v =(e v1 e v2 , ..., e vN ) T V od =(V od1 V od2 , ..., V odN ) T And matrix H = L + B. Therefore, controller (8) can be integrated as follows when not under attack:

[0142]

[0143] Furthermore, for t=t k , as well as What can be obtained:

[0144]

[0145] Define the output voltage error of the i-th distributed generation unit. From equation (10), we can obtain:

[0146]

[0147] Similarly, equation (11) of each distributed generation unit needs to be integrated into a comprehensive structure, thereby introducing an extended matrix, the expression of which is:

[0148]

[0149] in: All of them are matrices of different dimensions; for Elements on the main diagonal; for Elements on the main diagonal; for Elements on the main diagonal; l i1 l i2 l iN for Elements on the main diagonal; μ i1 μ i2 μ iN for Elements on the main diagonal; for The elements on the main diagonal; diag(·) is the symbol for a diagonal matrix. is a real matrix symbol, and N is the total number of nodes.

[0150] In this embodiment, to address the issue of inconsistent system matrix dimensions caused by network attacks, a series of extended diagonal matrices are innovatively introduced. This method cleverly solves the problem of inconsistent system matrix dimensions that may be encountered under network attack conditions.

[0151] Furthermore, define ΔV od =(ΔV) od1 ΔV od2 , …, ΔV odN ) T Therefore, equation (11) can be derived as:

[0152]

[0153] Furthermore, since at least one of the Laplace matrix L and the diagonal matrix B is greater than 0, H is a positive definite matrix. Therefore, for the closed-loop system (9), there exists a positive definite matrix F.N×N satisfy:

[0154] FH+H T F = I N×N ;

[0155] Among them: I N×N This represents the identity matrix with dimension N.

[0156] To further analyze the stability of the microgrid system, this embodiment designs a Lyapunov equation W(t) (i.e., the first Lyapunov function), whose expression is:

[0157]

[0158] Furthermore, define Δe v =(Δe) v1 ,Δe v2 ,…,Δe vN )and Combining equations (7), (9), and (12), we obtain:

[0159]

[0160] for Directly obtained:

[0161]

[0162] For t∈[t k ,t k+1 ), We can obtain:

[0163]

[0164] For t = t k , Equation (13) is written as:

[0165]

[0166] Furthermore, analyzing each part of equation (16) yields the following inequality:

[0167]

[0168] Where: η v It is a positive number. At the same time, we can obtain:

[0169]

[0170] in: Considering the expected value of matrix (4), the expected value of equation (17) is:

[0171]

[0172] in: Therefore, we can further conclude that:

[0173]

[0174] in:

[0175] Based on the above analysis, combining equations (14), (15), and (18), we obtain:

[0176]

[0177] in:

[0178] For further analysis, the time interval [t] between two adjacent pulse fraud attacks is discussed below. k , t k+1 ), Number of DoS attacks in China:

[0179] (1) At time [t] k , t k+1 ), No DoS attack occurred, therefore:

[0180]

[0181] (2) At time [t] k , t k+1 ), A DoS attack occurred in [location], and the attack time was [time]. This means Therefore, we can conclude that:

[0182]

[0183] (3) At time [t] k , t k+1 ), h DoS attacks occurred, which means Therefore, we get:

[0184]

[0185] From equation (19), for [0, t1), we can obtain

[0186]

[0187] Similarly, for [t1, t2), we can obtain:

[0188]

[0189] Finally, for [t] k , t k+1 ), We can obtain:

[0190]

[0191] Furthermore, based on Definition 1 and Assumption 1, we can ultimately obtain:

[0192]

[0193] Based on the previous analysis, we can conclude that as long as the controller in equation (3) satisfies the condition... Then we can obtain Therefore, we can obtain lim t→∞ e v =0. According to Definition 2, the output three-phase voltage amplitude can asymptotically converge to V. rated .

[0194] In this embodiment, for the frequency recovery problem, the distributed secondary frequency controller is designed as follows:

[0195]

[0196] in: This indicates the strength of the secondary frequency control. Clearly, in distributed generation units (DGs), the exchange of information such as voltage, frequency, and active power typically occurs simultaneously. Therefore, when an attacker targets a communication link, all information exchanged between nodes is compromised.

[0197] Furthermore, the control objective of the secondary frequency controller under a hybrid attack scenario is elaborated. First, relevant definitions and assumptions are given.

[0198] Definition 3: The objective of distributed secondary frequency control under hybrid attacks is the frequency ω of the i-th distributed generation unit. i The expectation can be gradually adjusted to ω rated That is:

[0199]

[0200] Define e ωi =ω i -ω rated Therefore, this control objective can be further transformed into:

[0201]

[0202] Similar to the secondary voltage controller, the secondary frequency controller under DoS and pulse spoofing attacks can be written as:

[0203]

[0204] in: It is an attack signal, which is a nonlinear function related to eωi, where δ(·) is the Dirac impulse function, and u ωi (t) at time t of the pulse fraud attack k It is right-continuous, that is...

[0205] Assumption 3: Nonlinear pulse fraud attack function for each interactive channel satisfy:

[0206]

[0207] in: It is a non-negative number, and N is the number of nodes.

[0208] Furthermore, define η ω It is a positive number. From the previous analysis of the secondary voltage control, we can conclude that as long as the controller in equation (21) satisfies the condition... Then we can obtain lim t→∞ e ω =0. According to Definition 3, the output three-phase voltage amplitude can asymptotically converge to ω. rated .

[0209] In this embodiment, to address the active power allocation problem in secondary control under hybrid attacks, the distributed secondary active power allocation controller is designed as follows:

[0210]

[0211] in: This indicates the strength of the secondary active power distribution controller. Unlike voltage recovery and frequency regulation problems, active power distribution operates as a leaderless system. However, it is evident from the controller (23) that it still relies on information from neighboring nodes. Therefore, active power information transmitted through the interaction channel is vulnerable to DoS attacks and pulse spoofing attacks.

[0212] Furthermore, the control objective of the secondary active power distribution controller under a hybrid attack scenario is elaborated. First, relevant definitions and assumptions are given:

[0213] Definition 4: The objective of a distributed secondary active power distribution controller under a hybrid attack is to accurately and proportionally distribute the output active power P based on the droop coefficient of each distributed power source, i.e.:

[0214]

[0215] definition Its control objective can be further transformed into:

[0216]

[0217] Similarly, an active power distribution controller subjected to DoS attacks and pulse spoofing attacks can be represented as:

[0218]

[0219] in: It is an attack signal; it is a signal related to m. pj P j (t) is a related nonlinear function, δ(·) is a Dirac impulse function, u pi (t) in the pulse fraud attack t k The time interval is right-continuous, that is...

[0220] Assumption 4: Nonlinear pulse fraud attack function for each interactive channel satisfy:

[0221]

[0222] in: It is a non-negative number, and N is the number of nodes.

[0223] Furthermore, let's first define: P mi =m pi P i (t), e p =(e p1 e p2 , ..., e pN ) T P m =(P m1 P m2 , ..., P mN ) T Therefore, we can obtain and e p =LP m Then, the Lyapunov function (i.e., the second Lyapunov function) is chosen as...

[0224] for

[0225]

[0226] For t∈[t k , t k+1 ), We can obtain:

[0227]

[0228] For t = t k , We can obtain:

[0229]

[0230] in:

[0231]

[0232] η p It is a positive number.

[0233] Therefore, we can obtain:

[0234]

[0235] Referring to the proof of the stability of the distributed secondary voltage controller, we can further conclude that:

[0236]

[0237] in:

[0238] Therefore, as long as the following conditions are met The output active power P can be precisely distributed according to the droop coefficient of each generator set.

[0239] Based on the above analysis, the following conclusions can be drawn:

[0240] (1) If both assumption 1 and assumption 2 are true, then the resilient secondary voltage controller (3) under DoS attack and pulse fraud attack will be able to meet the following condition (i.e., the first stability condition):

[0241]

[0242] This ensures that the amplitude of the three-phase voltage of each distributed generation unit asymptotically matches its rated value V. rate d.

[0243] (2) If both assumptions 1 and 3 are true, then the resilient secondary frequency controller (21) under DoS attacks and pulse spoofing attacks will be able to meet the following condition (i.e., the second stability condition):

[0244]

[0245] This ensures that the output frequency of each distributed generation unit asymptotically matches its rated value ω. rated .

[0246] (3) If both assumptions 1 and 4 hold true, then the resilient secondary active power distribution controller (23) under DoS attacks and pulse spoofing attacks will be able to meet the following condition (i.e., the third stability condition):

[0247]

[0248] This ensures that each distributed generation unit can accurately allocate total active power based on the droop factor.

[0249] This embodiment addresses hybrid network attack scenarios, covering both spoofing and denial-of-service (DoS) attacks. In communication networks, attackers typically launch attacks through information exchange between adjacent nodes, while hybrid attack methods, due to their stealth and destructiveness, are more favored by attackers. For spoofing attacks, this embodiment assumes that the attack is independent and random for each interaction channel. Therefore, a series of extended diagonal matrices based on random variables are introduced to explore the impact of hybrid network attacks on the stability of AC microgrids in a more significant and effective manner. Furthermore, this embodiment proposes a distributed resilient secondary control scheme that can be used to achieve voltage and frequency recovery and rational allocation of active power. Based on Lyapunov stability analysis, the selection criteria for secondary controller parameters that can maintain microgrid stability under hybrid attacks are given.

[0250] Furthermore, to verify the effectiveness of the control method provided in the embodiments of the present invention, a specific microgrid simulation example was constructed for verification. The specific steps of the simulation example are as follows:

[0251] Step 1: The framework diagram of the isolated AC microgrid is as follows. Figure 2 As shown, the entire AC microgrid consists of four generating units, denoted as DG1, DG2, DG3, and DG4 (DG0 represents the virtual leader). L in the diagram... d1 L d1 L d1 and L d1 Z1, Z2, Z3, and Z4 represent combinations of resistance and reactance; Z L1 Z L2 Z L3and Z L4 This represents the impedance of the inductor. The rated voltage amplitude of this AC microgrid is 311V, and the rated frequency is 50Hz; therefore, the voltage amplitude of its virtual leader is 311V, and the rated frequency is 50Hz. Other specific parameters are shown in Table 1.

[0252] Table 1. Test AC Microgrid Parameters

[0253]

[0254] In the simulation experiments, all DoS attacks were initiated randomly and followed the conditions outlined in Assumption 1. Under a DoS attack, the normal communication time percentage of the secondary control layer's communication network was ρ = 0.7. The average attack interval for the pulse spoofing attack was T. a =0.05s, the probability of successfully destroying each communication channel during each attack is κ. ij =0.2 (i≠j). The total duration of this experiment is 7 seconds. Within the interval [0,1s], only a simple single-stage control is used, while a second-stage control is introduced after 1 second. The pulse deception attack in the simulation experiment satisfies Definition 1, and the attack signal for the pulse deception attack is shown below:

[0255]

[0256] Step 2: Settings Clearly, it does not meet conditions (25), (26), and (27). Testing was conducted in a test islanded AC microgrid. Figure 3 The output voltage of the distributed generation unit under an unoptimized secondary controller. Figure 4 The output frequency of the distributed generation unit under an unoptimized secondary controller. Figure 5 The figures show the output active power of a distributed generation unit under an unoptimized secondary controller. As can be seen from the three figures, under the control of the unoptimized secondary controller, after being subjected to DoS attacks and pulse spoofing attacks, it is unable to maintain the voltage and frequency of the microgrid output in a stable state, and also cannot achieve accurate distribution of active power.

[0257] Step 3: Based on conditions (25), (26) and (27), calculate the following: Substituting this into the controller gain, the result is applied to the flexible secondary controller, and then tested in a test AC microgrid. Figure 6 The output voltage of the distributed generation unit under the flexible controller. Figure 7 The output frequency of the distributed generation unit under the flexible controller. Figure 8The figure shows the output active power of the distributed generation unit under the flexible controller. These three figures demonstrate that, under the proposed flexible secondary controller, the microgrid can withstand mixed attacks of DoS and pulse fraud, achieving asymptotic consistency of the output voltage and frequency of each generation unit with its rated values, and also enabling precise allocation of active power.

[0258] Example 2

[0259] Based on the same inventive concept, this embodiment provides a distributed resilient control system for AC microgrids. The principle of solving the problem is similar to that of the distributed resilient control method for AC microgrids provided in Embodiment 1, and the repeated parts will not be described again.

[0260] This embodiment provides a distributed resilient control system for AC microgrids, including:

[0261] The controller construction module is used to construct the flexible secondary voltage controller, flexible secondary frequency controller, and flexible secondary active power distribution controller for AC microgrids; the expressions for the flexible secondary voltage controller, flexible secondary frequency controller, and flexible secondary active power distribution controller are as follows:

[0262]

[0263] in, For secondary voltage control intensity, The intensity is controlled by a secondary frequency. For the strength of the secondary active power distribution controller, S i Let a be the set of neighboring nodes. ij For the existence of a communication channel between the i-th node and the j-th node, V odi (t) represents the d-axis component of the three-phase output voltage at the i-th node, b i For the i-th node to have a communication channel with the leader node, V rated For the rated voltage, ω i (t) represents the frequency of the i-th node, ω rated For the rated frequency, m pi P is the droop coefficient in the droop characteristic. i (t) represents the active power of the i-th node, where i and j are the node numbers;

[0264] The stability condition acquisition module is used to construct the first Lyapunov function and analyze the first stability condition of the elastic secondary voltage controller using the first Lyapunov function; the expression of the first Lyapunov equation is:

[0265]

[0266] Among them, e vLet F be the difference between the output voltage amplitude and the rated voltage, T be the matrix transpose, and F be the positive definite matrix. The second stability condition of the elastic quadratic frequency controller is analyzed using the first Lyapunov function. A second Lyapunov function is constructed, and the third stability condition of the elastic quadratic active power distribution controller is analyzed using this function. The expression for the second Lyapunov function is:

[0267]

[0268] Among them, e p This is the sum of errors in active power sharing among neighboring nodes;

[0269] The control parameter adjustment module is used to adjust the control gain parameters of the elastic secondary voltage controller, the elastic secondary frequency controller, and the elastic secondary active power distribution controller according to the first stability condition, the second stability condition, and the third stability condition, so as to obtain their respective control signals.

[0270] The control module is used to control the operating status of each distributed generation unit in the AC microgrid according to the control signal.

[0271] Example 3

[0272] This embodiment provides an islanded microgrid, including the AC microgrid distributed resilient control system provided in Embodiment 2.

[0273] This embodiment provides an islanded microgrid that enhances the ability to resist network attacks.

[0274] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0275] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0276] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0277] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0278] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A distributed resilient control method for AC microgrids, characterized in that, include: S1. Constructing a flexible secondary voltage controller, a flexible secondary frequency controller, and a flexible secondary active power distribution controller for an AC microgrid; the expressions for the flexible secondary voltage controller, the flexible secondary frequency controller, and the flexible secondary active power distribution controller are as follows: ; ; ; in, The intensity is controlled by the secondary voltage. The intensity is controlled by a secondary frequency. The strength of the secondary active power distribution controller, For the set of neighboring nodes, For the first The node and the first There is a communication channel between the nodes. For the first The three-phase output voltage of each node Axial components, For the first Each node has a communication channel with the leader node. Rated voltage, For the first The frequency of each node For the rated frequency, This refers to the droop coefficient in the droop characteristic. For the first The active power of each node. and Number the nodes; S2. Construct the first Lyapunov function, and use the first Lyapunov function to analyze the first stability condition of the elastic secondary voltage controller; the expression of the first Lyapunov equation is: ； The expression for the first stability condition is: ; ; ; ; wherein, is the difference between the output voltage amplitude and the rated voltage, is a positive definite matrix, is the matrix transpose symbol; is a constant between 0 and 1, is the time interval, is the secondary voltage control strength, is a positive number, represents taking the maximum eigenvalue of the matrix, is a positive definite matrix, represents taking the minimum eigenvalue of the matrix, is taking the maximum value, , and are different constants, is the total number of nodes; S3. Analyze the second stability condition of the elastic quadratic frequency controller using the first Lyapunov function; the expression for the second stability condition is: ; ; ; ; in, The intensity is controlled by a secondary frequency. It is a positive number. It is a constant; S4. Construct a second Lyapunov function and use it to analyze the third stability condition of the elastic secondary active power distribution controller; the expression of the second Lyapunov function is: ; The expression for the third stability condition is: ; ; ; ; in, This is the sum of errors in active power sharing among neighboring nodes; The strength of the secondary active power distribution controller, It is a positive number. This indicates taking the second smallest eigenvalue of the matrix. For a matrix, It is a constant; S5. Based on the first stability condition, the second stability condition, and the third stability condition, adjust the control gain parameters of the elastic secondary voltage controller, the elastic secondary frequency controller, and the elastic secondary active power distribution controller to obtain their respective control signals; S6. Control the operating status of each distributed generation unit in the AC microgrid according to the control signal.

2. The distributed resilient control method for AC microgrids according to claim 1, characterized in that, After constructing the elastic secondary voltage controller, elastic secondary frequency controller, and elastic secondary active power distribution controller, S1 also includes introducing an extended matrix to integrate the output voltage error of each distributed generation unit into a comprehensive structure.

3. The distributed resilient control method for AC microgrids according to claim 2, characterized in that, The expression for the extended matrix is: ; ; ; ; ; ; in, , , , , , All of them are matrices of different dimensions; for Elements on the main diagonal; for Elements on the main diagonal; for Elements on the main diagonal; for Elements on the main diagonal; for Elements on the main diagonal; for Elements on the main diagonal; The symbol for a diagonal matrix is... For real matrix notation, This represents the total number of nodes.

4. A distributed resilient control method for AC microgrids according to claim 1 or 2, characterized in that, When constructing the resilient secondary voltage controller and the resilient secondary frequency controller, S1 includes introducing a virtual leader, whose output voltage and output frequency remain constant; the virtual leader communicates with other nodes.

5. The distributed resilient control method for AC microgrids according to claim 1, characterized in that, Before constructing the flexible secondary voltage controller, flexible secondary frequency controller, and flexible secondary active power distribution controller, step S1 includes performing input-output feedback linearization processing on the state equations of the power generation unit; the flexible secondary voltage controller, the flexible secondary frequency controller, and the flexible secondary active power distribution controller are constructed based on the processed state equations of the power generation unit; wherein the processed state equations of the power generation unit are: ; in, For the first The third phase output voltage Axial components, and All of these are droop coefficients in the droop characteristic. For the first The frequency of each power generation unit This is the reactive power value after a first-order low-pass filter. This is the active power value after a first-order low-pass filter. and They represent the first The outputs of secondary voltage control, secondary frequency control and secondary active power distribution control of each node; and For reference voltage and reference frequency values, Number the nodes.

6. A distributed resilient control system for an AC microgrid, used to implement the distributed resilient control method for an AC microgrid as described in any one of claims 1 to 5, characterized in that, include: The controller construction module is used to construct a flexible secondary voltage controller, a flexible secondary frequency controller, and a flexible secondary active power distribution controller for an AC microgrid; the expressions for the flexible secondary voltage controller, the flexible secondary frequency controller, and the flexible secondary active power distribution controller are as follows: ; ; ; in, For secondary voltage control intensity, The intensity is controlled by a secondary frequency. The strength of the secondary active power distribution controller, For the set of neighboring nodes, For the first The node and the first There is a communication channel between the nodes. For the first The three-phase output voltage of each node Axial components, For the first Each node has a communication channel with the leader node. Rated voltage, For the first The frequency of each node For the rated frequency, This refers to the droop coefficient in the droop characteristic. For the first The active power of each node. and Number the nodes; The stability condition acquisition module is used to construct a first Lyapunov function and analyze the first stability condition of the elastic secondary voltage controller using the first Lyapunov function; the expression of the first Lyapunov equation is: ； in, The difference between the output voltage amplitude and the rated voltage. It is a positive definite matrix. Let be the matrix transpose notation; analyze the second stability condition of the elastic quadratic frequency controller using the first Lyapunov function; construct the second Lyapunov function, and analyze the third stability condition of the elastic quadratic active power distribution controller using the second Lyapunov function; the expression of the second Lyapunov function is: ; in, This is the sum of errors in active power sharing among neighboring nodes; The control parameter adjustment module is used to adjust the control gain parameters of the elastic secondary voltage controller, the elastic secondary frequency controller, and the elastic secondary active power distribution controller according to the first stability condition, the second stability condition, and the third stability condition, so as to obtain their respective control signals; The control module is used to control the operating status of each distributed generation unit in the AC microgrid according to the control signal.

7. An islanded microgrid, characterized in that, Includes the AC microgrid distributed resilient control system described in claim 6.

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