Distributed elastic control method and system for alternating-current micro-grid

Abstract

The invention relates to a distributed elastic control method and system for an alternating-current micro-grid, and belongs to the technical field of micro-grid control. Comprising the following steps: respectively constructing elastic secondary voltage, frequency and active power distribution controllers; constructing a first Lyapunov function, and analyzing a first stability condition of the elastic quadratic voltage controller by using the first Lyapunov function; analyzing a second stability condition of the elastic quadratic frequency controller by using the first Lyapunov function; constructing a second Lyapunov function, and analyzing a third stability condition of the elastic secondary active power distribution controller by using the second Lyapunov function; according to the first stable condition, the second stable condition and the third stable condition, respective control gain parameters of the elastic secondary voltage controller, the elastic secondary frequency controller and the elastic secondary active power distribution controller are adjusted, and respective control signals are obtained. According to the method, the vulnerability of secondary control in the face of network attacks is reduced, and the capacity of the micro-grid for resisting hybrid attacks is enhanced.

Description

Technical Field

[0001] The present invention relates to the field of microgrid control technology, and in particular to an AC microgrid distributed elastic control method and system. Background Art

[0002] In recent years, microgrids have gradually become the focus of academic research due to their outstanding capabilities in the integration of distributed generation and energy storage equipment, especially in terms of flexible operating characteristics and efficient energy utilization efficiency. AC microgrids have attracted great attention from many engineers and researchers due to their high efficiency and good compatibility with traditional power grids. However, the complex dynamic characteristics inherent in islanded AC microgrid systems pose major challenges to their precise and stable control. In addition, the control architecture of islanded microgrids needs to take into account multiple requirements, which vary significantly in impact degree and time scale, such as the need to maintain the voltage and frequency of each generator set at rated values, reasonably distribute loads, and optimize operating costs. To meet these challenges, researchers usually adopt a hierarchical control framework to achieve efficient and precise control of multiple generator sets.

[0003] Typically, the hierarchical control architecture consists of a primary control layer, a secondary control layer, and a tertiary control layer. As the basic layer, the primary control layer is responsible for adjusting the three-phase voltage amplitude and frequency output by the generator set, and using the droop control principle to achieve reasonable power distribution. However, due to the voltage and frequency deviations caused by the droop characteristics and load disturbances, it is difficult for the primary control to accurately adjust these parameters to their rated values. To this end, researchers have proposed a distributed secondary control strategy based on multi-agent theory to optimize the operation of microgrids. Distributed secondary control uses communication networks to achieve real-time information exchange between distributed generators, thereby achieving consistent control of each variable.

[0004] However, the communication network that distributed secondary control relies on is vulnerable to potential network threats. Fraud attacks and denial of service (DoS) attacks are two major common network threats in microgrids. Fraud attacks convey false and misleading information by manipulating the data transmitted in the network. In terms of defending against fraud attacks, existing technologies mainly use detection-compensation mechanisms and elastic controller strategies. DoS attacks hinder and block communication channels, interfere with information transmission, and make the communication network unable to operate normally. At present, most strategies to defend against DoS attacks are elastic control schemes.

[0005] In the existing technology, most of the research on fraud attacks focuses on continuous-time attack models, while less attention is paid to discrete forms of fraud attacks. In actual operating environments, attackers usually choose discrete covert fraud attacks to evade detection algorithms because these attacks are highly concealed and difficult to quickly identify. In addition, the existing technology mainly focuses on response strategies for a single type of attack. However, in real-world scenarios, attackers usually use multiple forms of attacks to infiltrate communication networks, undermine the stability of the system in multiple ways, and weaken its detection algorithms for specific types of attacks. This covert hybrid attack may cause significant interference to the secondary control system of the microgrid, ultimately leading to instability of the entire system. Summary of the invention

[0006] To this end, the technical problem to be solved by the present invention is to overcome the vulnerability of the distributed secondary control in the prior art when facing network attacks, and the shortcomings of the prior art in dealing with hybrid attacks.

[0007] In a first aspect, in order to solve the above technical problems, the present invention provides a distributed elastic control method of an AC microgrid, comprising:

[0008] S1, constructing an elastic secondary voltage controller, an elastic secondary frequency controller and an elastic secondary active power distribution controller of an AC microgrid; the expressions of the elastic secondary voltage controller, the elastic secondary frequency controller and the elastic secondary active power distribution controller are respectively:

[0009]

[0010] in, is the intensity of secondary voltage control, is the strength of the secondary frequency control, is the strength of the secondary active power distribution controller, S i is the set of neighbor nodes, a ij There is a communication channel between the i-th node and the j-th node, V odi (t) is the d-axis component of the three-phase output voltage of the i-th node, b i There is a communication channel between the i-th node and the leader node, V rated is the rated voltage, ω i (t) is the frequency of the ith node, ω rated is the rated frequency, m pi is the droop coefficient in the droop characteristic, P i (t) is the active power of the ith node, i and j are the node numbers;

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

[0012]

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

[0014] S3, analyzing a second stability condition of the elastic quadratic frequency controller using the first Lyapunov function;

[0015] S4. Construct a second Lyapunov function, and use the second Lyapunov function 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 is the sum of the errors in active power sharing between neighboring nodes;

[0018] S5. According to the first stable condition, the second stable condition and the third stable 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 respective control signals;

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

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

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

[0022]

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

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

[0025]

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

[0027]

[0028] is a constant, the expression is:

[0029]

[0030] in, is the secondary voltage control strength, η v is a positive number, λ max (·) means taking the maximum eigenvalue of the matrix, F is a positive definite matrix, λ min (·) means taking the minimum eigenvalue of the matrix, max(·) means taking the maximum value, κ ij ∈[0,1], and m max are different constants, and N is the total number of nodes.

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

[0032]

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

[0034]

[0035] is a constant, the expression is:

[0036]

[0037] in, is the strength of the secondary frequency control, η ω is a positive number, λ max (·) means taking the maximum eigenvalue of the matrix, F is a positive definite matrix, λ min (·) means taking the minimum eigenvalue of the matrix, max(·) means taking the maximum value, κ ij ∈[0,1], and m 1max are different constants, and N is the total number of nodes.

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

[0039]

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

[0041]

[0042] is a constant, the expression is:

[0043]

[0044] in, is the strength of the secondary active power distribution controller, η p is a positive number, λ max (·) means taking the maximum eigenvalue of the matrix, λ 2min (·) means taking the second smallest eigenvalue of the matrix, L is the matrix, λ min (·) means taking the minimum eigenvalue of the matrix, max(·) means taking the maximum value, κ ij ∈[0,1], and m 2max are different constants, and N is the total number of nodes.

[0045] In one embodiment of the present invention, the S1 includes introducing a virtual leader when constructing the elastic secondary voltage controller and the elastic secondary frequency controller, and the output voltage and output frequency of the virtual leader are kept constant; the virtual leader communicates with other nodes.

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

[0047]

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

[0049] In a second aspect, in order to solve the above technical problems, the present invention provides an AC microgrid distributed elastic control system, comprising:

[0050] The controller construction module is used to construct an elastic secondary voltage controller, an elastic secondary frequency controller and an elastic secondary active power distribution controller of an AC microgrid; the expressions of the elastic secondary voltage controller, the elastic secondary frequency controller and the elastic secondary active power distribution controller are respectively:

[0051]

[0052] in, is the secondary voltage control intensity, is the strength of the secondary frequency control, is the strength of the secondary active power distribution controller, S i is the set of neighbor nodes, a ij There is a communication channel between the i-th node and the j-th node, V odi (t) is the d-axis component of the three-phase output voltage of the i-th node, b i There is a communication channel between the i-th node and the leader node, V rated is the rated voltage, ωi (t) is the frequency of the ith node, ω rated is the rated frequency, m pi is the droop coefficient in the droop characteristic, P i (t) is the active power of the ith node, 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 quadratic voltage controller using the first Lyapunov function; the expression of the first Lyapunov equation is:

[0054]

[0055] Among them, e v is the difference between the output voltage amplitude and the rated voltage, F is a positive definite matrix, and T is the matrix transposition symbol; the first Lyapunov function is used to analyze the second stability condition of the elastic quadratic frequency controller; a second Lyapunov function is constructed, and the second Lyapunov function is used to analyze the third stability condition of the elastic quadratic active power distribution controller; the expression of the second Lyapunov function is:

[0056]

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

[0058] A control parameter adjustment module, 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 stable condition, the second stable condition and the third stable condition to obtain respective control signals;

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

[0060] In a third aspect, in order to solve the above-mentioned technical problems, the present invention provides an islanded microgrid, including the above-mentioned AC microgrid distributed elastic control system.

[0061] The above technical solution of the present invention has the following beneficial effects compared with the prior art:

[0062] (1) The distributed elastic control method and system of an AC microgrid described in the present invention significantly enhances the ability of the microgrid to resist hybrid network attacks by constructing elastic secondary voltage control, secondary frequency control and secondary active power distribution control, thereby improving the robustness and reliability of the system. At the same time, by establishing the first and second Lyapunov functions, the stability conditions of these controllers are deeply analyzed, and then simple inequalities are derived. These inequalities provide a clear reference standard for the selection of secondary controller parameters to maintain the stability of the microgrid under a hybrid attack environment. In addition, by realizing information sharing and joint control between adjacent nodes, the collaborative working ability of distributed power sources within the microgrid is further enhanced. This collaborative mechanism effectively improves the overall operating efficiency and reliability of the system. The present invention not only significantly reduces the problems that may arise when distributed secondary control encounters network attacks, but also improves the defense capability of the microgrid against hybrid attacks, ensuring the safe and stable operation of the microgrid.

[0063] (2) The present invention cleverly solves the dimensional inconsistency problem faced by the system matrix in the case of network attacks by introducing a series of extended diagonal matrices based on random variables. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] In order to make the content of the present invention more clearly understood, the present invention is further described in detail below according to specific embodiments of the present invention in conjunction with the accompanying drawings, wherein

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

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

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

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

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

[0070] Figure 6 An output voltage diagram of a distributed power generation unit under a flexible controller in a preferred embodiment of the present invention;

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

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

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

[0074] Embodiment 1

[0075] Reference Figure 1 As shown, the present invention provides an AC microgrid distributed elastic control method, comprising:

[0076] S1, construct the elastic secondary voltage controller, elastic secondary frequency controller and elastic secondary active power distribution controller of the AC microgrid; the expressions of the elastic secondary voltage controller, the elastic secondary frequency controller and the elastic secondary active power distribution controller are:

[0077]

[0078] in, is the secondary voltage control intensity, is the strength of the secondary frequency control, is the strength of the secondary active power distribution controller, S i is the set of neighbor nodes, a ij There is a communication channel between the i-th node and the j-th node, V obi (t) is the d-axis of the three-phase output voltage of the i-th node, b i There is a communication channel between the i-th node and the leader node, V rated is the rated voltage, ω i (t) is the frequency of the ith node, ω rated is the rated frequency, m pi is the droop coefficient in the droop characteristic, P i (t) is the active power of the ith node, i and j are the node numbers;

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

[0080]

[0081] Among them, e vis the difference between the output voltage amplitude and the rated voltage, F is a positive definite matrix, and T is the matrix transpose sign;

[0082] S3, analyzing the second stability condition of the elastic quadratic frequency controller using the first Lyapunov function;

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

[0084]

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

[0086] S5. According to the first stable condition, the second stable condition and the third stable 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 respective control signals;

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

[0088] An AC microgrid distributed elastic control method provided by an embodiment of the present invention significantly improves the robustness and reliability of the microgrid in the face of hybrid attacks by designing elastic secondary voltage, frequency and active power distribution controllers. At the same time, the stability conditions of the three types of controllers are deeply analyzed by using the constructed first Lyapunov function and the second Lyapunov function, thereby deriving a set of simple inequalities. These inequalities provide clear guidelines for the selection of secondary controller parameters to maintain the stability of the microgrid under a hybrid attack environment. In addition, this embodiment further enhances the collaborative operation capability of each distributed power source in the microgrid through information exchange and collaborative control between neighboring nodes. This synergy improves the operating efficiency and reliability of the entire system. Therefore, this embodiment not only effectively reduces the vulnerability of distributed secondary control in the face of network attacks, but also enhances the ability of the microgrid to resist hybrid attacks, providing a strong guarantee for the safe and stable operation of the microgrid.

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

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

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

[0092]

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

[0094]

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

[0096] In this embodiment, in order to achieve the consistency control of the voltage and frequency of each generator set and the reasonable distribution of active power, secondary control needs to be introduced. Due to the droop characteristics of the generator set, it is difficult to meet the requirements by primary control alone, and secondary control can further optimize the various indicators of the microgrid. In addition, in order to realize the information exchange between the generator sets, a communication network needs to be introduced to support the implementation of secondary control.

[0097] Specifically, in the communication network, it is assumed that each generator set is used as a node. This embodiment relates to a network structure of an isolated island microgrid, specifically an undirected graph The collection Represents the nodes in the microgrid communication topology, the set Contains edges representing communication connections. Define the neighbor node set S i =(j|(χ j , χ i )∈ε N ), i = 1, 2, ..., N in order to obtain the neighbors of the i-th node. Adjacency matrix A N =(a ij ) N×N (i, j = 1, 2, ..., N) describes the flow of information interaction between distributed generators in the microgrid, where a ij =a ji >0, i≠j means there is a communication channel between the i-th node and the j-th node, and a ij =a ji = 0, i≠j means that there is no such channel, and it is assumed that a ii = 0. In this embodiment, the entire communication topology graph is strongly connected, and thus 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 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 of the output voltage amplitude is simplified to V odi →V rated In order to effectively control the voltage and frequency of the entire microgrid, this embodiment introduces a virtual leader DGO, whose output voltage is kept constant at V rated , the output frequency remains constant at ω rated To represent the communication connection between the virtual leader DGO and other nodes, the 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 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 microgrids, distributed secondary control is usually performed by drooping the V iref Used in adjusting the operating state of the main control. Based on the input-output feedback linearization method, the state equation of the power generation unit is processed by input-output feedback linearization. Based on formula (1), it can be obtained:

[0100]

[0101] Where: u vi (t),u ωi (t) and u pi (t) are auxiliary variables, which represent the outputs of the secondary voltage control, secondary frequency control, and secondary active power distribution control of the i-th node. Therefore, V ref and ω ref can be re-expressed as:

[0102]

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

[0104]

[0105] in: Indicates the secondary voltage control strength.

[0106] The distributed secondary voltage controller (3) needs to exchange information about neighbor 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 spoofing attacks on the information exchanged between neighbor nodes.

[0107] Specifically, a DoS attack can destroy the entire communication network in a distributed secondary control, thereby preventing the controller from operating effectively. D ={σ 1 , σ 2 , …, σ h , ...}, Used to describe the moment when a DoS attack occurs, time series ξ I ={∈ 1 ,∈ 2 ,…,∈ h , …} is used to represent the duration of each attack. It is worth noting that there is still a period of normal communication between two adjacent attacks, so that the time interval between adjacent attacks satisfies σ h+1 -σ h >∈ h In addition, the definition represents the time interval of normal communication in the interval [s, t), and represents the time interval of message blocking during the DoS attack, which is also in the interval [s, t). Obviously, and Therefore, it is necessary to define the following function r(t) to represent the situation where a DoS attack occurs on the secondary controller. The mathematical expression of the function r(t) is:

[0108]

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

[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 that satisfies 0<ρ<1 so that the following inequality holds:

[0112]

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

[0114] Furthermore, the pulse fraud attack is a pulse tampering of the information operation of the neighboring nodes in the distributed secondary controller. In this embodiment, the sequence of pulse fraud attack moments is defined as F ={t 1 , t 2 ,…,t k ,…},in: and Considering that the fraud attack is random at the pulse time, define the random variable μ ij (where i, j = 1, 2, ..., N) to indicate whether the communication channel from the jth node to the ith node is under attack. Specifically, μ ij =1, i≠j means the communication channel is attacked, and μ ij =0, i≠j means the channel is not attacked. In addition, μ ij =0, i=j. The probability distribution of this random variable follows the Bernoulli distribution, which is described as:

[0115]

[0116] Where: ij ∈[0, 1], i≠j and κii =0.

[0117] Furthermore, a matrix μ associated with the random variable is defined, and the expectation of the matrix can be expressed as the following matrix Ξ:

[0118]

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

[0120]

[0121] Where: δ(·) is the Dirac pulse function, u vi (t) At the pulse fraud attack time t k 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 ={t 1 ,…,t k , …}, the average pulse fraud attack occurs at an interval of at least T a (T a is a time interval), so there exists at least one positive integer N 0 satisfy:

[0124]

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

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

[0127]

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

[0129] Therefore, the distributed secondary voltage controller is attacked by DoS and pulse fraud attacks can be written as:

[0130]

[0131] In the face of DoS attacks and pulse fraud attacks, the overall communication network of the microgrid shows significant instability, which leads to great interference in the voltage regulation of the secondary control. Therefore, it is necessary to explore in depth how to make the secondary control still stabilize the voltage well under these complex attack backgrounds. First, a systematic overview of the control objectives of the secondary voltage controller under hybrid attack scenarios is given.

[0132] Definition 2: The goal of distributed secondary voltage control under mixed attack is to make the output three-phase voltage amplitude V of the i-th distributed generation unit odi The desired value is gradually adjusted to its rated value V rated .

[0133]

[0134] Due to e vi =V odi -V rated , the control objective is described as:

[0135]

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

[0137]

[0138] in:

[0139] for Combining equation (2) and equation (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 the matrix H = L + B. Therefore, the controller (8) can be integrated as follows when not under attack:

[0142]

[0143] Furthermore, for t = tk , as well as You can get:

[0144]

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

[0146]

[0147] Similarly, it is necessary to integrate equation (11) of each distributed generation unit into a comprehensive structure, thereby introducing an extended matrix. The expression of the extended matrix is:

[0148]

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

[0150] In this embodiment, in order to deal with the problem of inconsistent dimensions of the system matrix caused by network attacks, a series of extended diagonal matrices are innovatively introduced. This method cleverly solves the problem of inconsistent dimensions that the system matrix may face in the case of network attacks.

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

[0152]

[0153] Furthermore, since at least one of the values ​​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 that satisfies N×N satisfy:

[0154] FH+H T F=I N×N ;

[0155] Where: I N×N Represents the identity matrix of dimension N.

[0156] In order to further analyze the stability of the microgrid system, this embodiment designs a Lyapunov equation W(t) (i.e., the first Lyapunov function), which is expressed as follows:

[0157]

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

[0159]

[0160] for Directly get:

[0161]

[0162] For t∈[t k ,t k+1 ), You can get:

[0163]

[0164] For t = t k , Formula (13) can be written as:

[0165]

[0166] Further, analyzing each part of equation (16), we get the following inequality:

[0167]

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

[0169]

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

[0171]

[0172] in: From this, we further get:

[0173]

[0174] in:

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

[0176]

[0177] in:

[0178] For further analysis, the time interval [t k , t k+1 ), Number of DoS attacks:

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

[0180]

[0181] (2) At time [t k , t k+1 ), A DoS attack occurs in That means So we can get:

[0182]

[0183] (3) At time [t k , t k+1 ), There are h DoS attacks in So we get:

[0184]

[0185] From formula (19), for [0, t1 ), we can get

[0186]

[0187] Similarly, for [t 1 , t 2 ), we can get:

[0188]

[0189] Finally, for [t k , t k+1 ), You can get:

[0190]

[0191] Furthermore, according to Definition 1 and Assumption 1, we can finally get:

[0192]

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

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

[0195]

[0196] in: It indicates the strength of secondary frequency control. Obviously, the exchange process of information such as voltage, frequency and active power between distributed generation units (DG) is usually carried out simultaneously. Therefore, when an attacker targets a communication link, all information exchanged between nodes will be compromised.

[0197] Furthermore, the control objectives of the secondary frequency controller under the background of mixed attacks are explained. Firstly, the relevant definitions and assumptions are given.

[0198] Definition 3: The target of distributed secondary frequency control under hybrid attack 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] Definition ωi =ω i -ω rated , thus the control objective can be further transformed into:

[0201]

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

[0203]

[0204] in: is the attack signal, which is a nonlinear function related to eωi, δ(·) is the Dirac pulse function, u ωi (t) At the pulse fraud attack time t k is right continuous, that is

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

[0206]

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

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

[0209] In this embodiment, for the active power allocation problem in secondary control under mixed attack, the distributed secondary active power allocation controller is designed as follows:

[0210]

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

[0212] Furthermore, the control objectives of the secondary active power distribution controller under the background of hybrid attacks are explained. First, the relevant definitions and assumptions are given:

[0213] Definition 4: The goal of the distributed secondary active power distribution controller under mixed attack is to accurately distribute the output active power P in proportion to the droop coefficient of each distributed power source, that is:

[0214]

[0215] definition Its control objectives can be further converted into:

[0216]

[0217] Similarly, the active power distribution controller subjected to DoS attack and pulse spoofing attack can be expressed as:

[0218]

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

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

[0221]

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

[0223] Furthermore, we 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 get and e p =LPm Then, we select the Lyapunov function (i.e., the second Lyapunov function) as

[0224] for

[0225]

[0226] For t∈[t k , t k+1 ), You can get:

[0227]

[0228] For t = t k , You can get:

[0229]

[0230] in:

[0231]

[0232] η p is a positive number.

[0233] Therefore, we can get:

[0234]

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

[0236]

[0237] in:

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

[0239] Based on the above analysis, we can draw the following conclusions:

[0240] (1) If both Assumption 1 and Assumption 2 are true, then the elastic quadratic voltage controller (3) under DoS attack and pulse fraud attack only needs to meet the condition (i.e., the first stability condition):

[0241]

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

[0243] (2) If both Assumption 1 and Assumption 3 are true, then the resilient quadratic frequency controller (21) under DoS attack and pulse fraud attack only needs to satisfy the condition (i.e., the second stability condition):

[0244]

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

[0246] (3) If both Assumption 1 and Assumption 4 are valid, then the elastic secondary active power distribution controller (23) under DoS attack and pulse fraud attack only needs to meet the condition (i.e., the third stability condition):

[0247]

[0248] This ensures that each distributed generation unit can achieve accurate total active power distribution according to the droop coefficient.

[0249] This embodiment targets hybrid network attack scenarios, covering pulse fraud attacks and denial of service attacks (DoS). In communication networks, attackers usually carry out attacks through information exchange between adjacent nodes, and hybrid attack methods are more likely to be used by attackers due to their concealment and destructiveness. For pulse fraud attacks, this embodiment assumes that each interaction channel is independent and random. To this end, 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 way. In addition, a distributed elastic secondary control scheme proposed in this embodiment can be used to achieve voltage and frequency recovery and reasonable allocation of active power. Based on the Lyapunov stability analysis method, a secondary controller parameter selection criterion that can maintain the stability of the microgrid under hybrid attacks is given.

[0250] Furthermore, in order to verify the effectiveness of the control method provided by the embodiment of the present invention, a specific microgrid simulation example is 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 in the figure, the entire AC microgrid consists of four power generation units, represented by DG1, DG2, DG3 and DG4 (DG0 represents the virtual leader). d1 , L d1 , L d1 and L d1Represents an inductor; Z 1 , Z 2 , Z 3 and Z 4 Represents the combination of resistance and reactance; Z L1 , Z L2 , Z L3 and Z L4 Represents the impedance of the inductor. The rated voltage amplitude of the AC microgrid is 311V and the rated frequency is 50Hz, so 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] The DoS attacks in the simulation experiments were all launched randomly and followed the conditions outlined in Assumption 1. Under DoS attacks, the proportion of normal communication time of the communication network in the secondary control layer is ρ = 0.7. The average attack interval of the pulse fraud attack is T a = 0.05s, the probability of successfully destroying each communication channel in each attack is κ ij =0.2(i≠j). The total duration of this experiment is 7 seconds. In the interval [0,1s], only a simple primary control is used, and a secondary control is introduced after 1 second. The pulse deception attack in the simulation experiment satisfies Definition 1. The attack signal of the pulse deception attack is as follows:

[0255]

[0256] Step 2: Setup Obviously, it does not satisfy conditions (25), (26) and (27). Tests are carried out in the test island AC microgrid. Figure 3 is the output voltage of the distributed generation unit under the unoptimized secondary controller, Figure 4 is the output frequency of the distributed generation unit under the non-optimized secondary controller, Figure 5 It is the output active power of the distributed generation unit under the unoptimized secondary controller. It can be seen from the three figures that under the control of the unoptimized secondary controller, after being attacked by DoS and pulse fraud, it is impossible to maintain the voltage and frequency of the microgrid output in a stable state, and it is also impossible to achieve accurate distribution of active power.

[0257] Step 3: According to conditions (25), (26) and (27), we can calculate Substitute the controller gains into the elastic quadratic controller and test it in the test AC microgrid. Figure 6is the output voltage of the distributed generation unit under the flexible controller, Figure 7 is the output frequency of the distributed generation unit under the flexible controller, Figure 8 It is the output active power of the distributed generation unit under the elastic controller. From these three figures, it can be seen that under the action of the proposed elastic secondary controller, the microgrid can resist the mixed attack of DoS attack and pulse fraud attack, achieve the output voltage and frequency of each generation unit tending to be consistent with its rated value, and also achieve accurate distribution of active power.

[0258] Embodiment 2

[0259] Based on the same inventive concept, this embodiment provides an AC microgrid distributed elastic control system, and its principle of solving the problem is similar to the AC microgrid distributed elastic control method provided in Example 1, and the repeated parts are not repeated here.

[0260] This embodiment provides an AC microgrid distributed elastic control system, including:

[0261] The controller building module is used to build a flexible secondary voltage controller, a flexible secondary frequency controller and a flexible secondary active power distribution controller of the AC microgrid; the expressions of the flexible secondary voltage controller, the flexible secondary frequency controller and the flexible secondary active power distribution controller are:

[0262]

[0263] in, is the secondary voltage control intensity, is the strength of the secondary frequency control, is the strength of the secondary active power distribution controller, S i is the set of neighbor nodes, a ij There is a communication channel between the i-th node and the j-th node, V odi (t) is the d-axis component of the three-phase output voltage of the i-th node, b i There is a communication channel between the i-th node and the leader node, V rated is the rated voltage, ω i (t) is the frequency of the ith node, ω rated is the rated frequency, m pi is the droop coefficient in the droop characteristic, P i (t) is the active power of the ith node, i and j are the node numbers;

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

[0265]

[0266] Among them, e v is the difference between the output voltage amplitude and the rated voltage, F is a positive definite matrix, and T is the matrix transpose symbol; the first Lyapunov function is used to analyze the second stability condition of the elastic quadratic frequency controller; the 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 of the second Lyapunov function is:

[0267]

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

[0269] A control parameter adjustment module, 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 stable condition, the second stable condition and the third stable condition to obtain respective control signals;

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

[0271] Embodiment 3

[0272] This embodiment provides an islanded microgrid, including an AC microgrid distributed elastic control system provided in the second embodiment.

[0273] The isolated microgrid provided in this embodiment has enhanced capability of resisting network attacks.

[0274] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0275] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0276] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0277] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0278] Obviously, the above embodiments are merely examples for clear explanation and are not intended to limit the implementation methods. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation methods here. The obvious changes or modifications derived from these are still within the protection scope of the invention.

Claims

1. A distributed elastic control method for an AC microgrid, characterized in that: include: S1, constructing an elastic secondary voltage controller, an elastic secondary frequency controller and an elastic secondary active power distribution controller of an AC microgrid; the expressions of the elastic secondary voltage controller, the elastic secondary frequency controller and the elastic secondary active power distribution controller are respectively: in, is the intensity of secondary voltage control, is the strength of the secondary frequency control, is the strength of the secondary active power distribution controller, S i is the set of neighbor nodes, a ij There is a communication channel between the i-th node and the j-th node, V odi (t) is the d-axis component of the three-phase output voltage of the i-th node, b i There is a communication channel between the i-th node and the leader node, V rated is the rated voltage, ω i (t) is the frequency of the i-th node, ω rated is the rated frequency, m pi is the droop coefficient in the droop characteristic, P i (t) is the active power of the ith node, i and j are the node numbers; S2. Construct a first Lyapunov function, and use the first Lyapunov function to analyze a first stability condition of the elastic quadratic voltage controller; the expression of the first Lyapunov equation is: Among them, e v is the difference between the output voltage amplitude and the rated voltage, F is a positive definite matrix, and T is the matrix transpose sign; S3, analyzing a second stability condition of the elastic quadratic frequency controller using the first Lyapunov function; S4. Construct a second Lyapunov function, and use the second Lyapunov function to analyze the third stability condition of the elastic secondary active power distribution controller; the expression of the second Lyapunov function is: Among them, e p is the sum of the errors in active power sharing between neighboring nodes; S5. According to the first stable condition, the second stable condition and the third stable 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 respective control signals; S6. Control the operating state of each distributed power generation unit in the AC microgrid according to the control signal.

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

3. The AC microgrid distributed elastic control method according to claim 2, characterized in that: The expression of the expansion matrix is: in, All are matrices of different dimensions; for The elements on the main diagonal of ; for The elements on the main diagonal of ; for The elements on the main diagonal of i1 , l i2 , l iN for The elements on the main diagonal of i1 , μ i2 , μ iN for The elements on the main diagonal of ; for The elements on the main diagonal of ; diag(·) is the symbol for a diagonal matrix, is the real matrix symbol, and N is the total number of nodes.

4. The AC microgrid distributed elastic control method according to claim 1, characterized in that: The first stable condition obtained by S2 is: Where ρ is a constant between 0 and 1, T a is the time interval; is a constant, the expression is: is a constant, the expression is: in, is the secondary voltage control strength, η v is a positive number, λ max (·) means taking the maximum eigenvalue of the matrix, F is a positive definite matrix, λ min (·) means taking the minimum eigenvalue of the matrix, max(·) means taking the maximum value, κ ij ∈[0,1], and m max are different constants, and N is the total number of nodes.

5. The AC microgrid distributed elastic control method according to claim 1, characterized in that: The second stable condition obtained by S3 is: Where ρ is a constant between 0 and 1, T a is the time interval, is a constant, the expression is: is a constant, the expression is: in, is the strength of the secondary frequency control, η ω is a positive number, λ max (·) means taking the maximum eigenvalue of the matrix, F is a positive definite matrix, λ min (·) means taking the minimum eigenvalue of the matrix, max(·) means taking the maximum value, κ ij ∈[0,1], and m 1max are different constants, and N is the total number of nodes.

6. The AC microgrid distributed elastic control method according to claim 1, characterized in that: The third stable condition obtained in S4 is: Where ρ is a constant between 0 and 1, T a is the time interval; is a constant, the expression is: is a constant, the expression is: in, is the strength of the secondary active power distribution controller, η p is a positive number, λ max (·) means taking the maximum eigenvalue of the matrix, λ 2min (·) means taking the second smallest eigenvalue of the matrix, L is the matrix, λ min (·) means taking the minimum eigenvalue of the matrix, max(·) means taking the maximum value, κ ij ∈[0,1], and m 2max are different constants, and N is the total number of nodes.

7. A distributed elastic control method for AC microgrid according to claim 1 or 2, characterized in that: When constructing the elastic secondary voltage controller and the elastic secondary frequency controller, S1 includes introducing a virtual leader, and the output voltage and output frequency of the virtual leader are kept constant; the virtual leader communicates with other nodes.

8. The AC microgrid distributed elastic control method according to claim 1, characterized in that: Before constructing the elastic secondary voltage controller, the elastic secondary frequency controller and the elastic secondary active power distribution controller, the S1 includes performing input-output feedback linearization processing on the power generation unit state equation; constructing the elastic secondary voltage controller, the elastic secondary frequency controller and the elastic secondary active power distribution controller according to the processed power generation unit state equation; wherein the processed power generation unit state equation is: Among them, V odi is the d-axis component of the ith third-phase output voltage, n qi and m pi are the droop coefficients in the droop characteristics, ω i is the frequency of the ith generating unit, Q i is the reactive power after first-order low-pass filtering, P i is the active power after first-order low-pass filtering; 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; V i ref and are the reference voltage value and reference frequency value, and i is the node number.

9. An AC microgrid distributed elastic control system, characterized in that: include: The controller construction module is used to construct an elastic secondary voltage controller, an elastic secondary frequency controller and an elastic secondary active power distribution controller of an AC microgrid; the expressions of the elastic secondary voltage controller, the elastic secondary frequency controller and the elastic secondary active power distribution controller are respectively: in, is the secondary voltage control intensity, is the strength of the secondary frequency control, is the strength of the secondary active power distribution controller, S i is the set of neighbor nodes, a ij There is a communication channel between the i-th node and the j-th node, V odi (t) is the d-axis component of the three-phase output voltage of the i-th node, b i There is a communication channel between the i-th node and the leader node, V rated is the rated voltage, ω i (t) is the frequency of the i-th node, ω rated is the rated frequency, m pi is the droop coefficient in the droop characteristic, P i (t) is the active power of the ith node, i and j are the node numbers; The stability condition acquisition module is used to construct a first Lyapunov function and analyze the first stability condition of the elastic quadratic voltage controller using the first Lyapunov function; the expression of the first Lyapunov equation is: Among them, e v is the difference between the output voltage amplitude and the rated voltage, F is a positive definite matrix, and T is the matrix transposition symbol; the first Lyapunov function is used to analyze the second stability condition of the elastic quadratic frequency controller; a second Lyapunov function is constructed, and the second Lyapunov function is used to analyze the third stability condition of the elastic quadratic active power distribution controller; the expression of the second Lyapunov function is: Among them, e p is the sum of the errors in active power sharing between neighboring nodes; A control parameter adjustment module, 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 stable condition, the second stable condition and the third stable condition to obtain respective control signals; The control module is used to control the operating state of each distributed power generation unit in the AC microgrid according to the control signal.

10. An islanded microgrid, characterized in that: It includes an AC microgrid distributed elastic control system as described in claim 9.

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