Microgrid event-triggered resilience control method oriented to fdi and communication latency

Abstract

This invention provides a microgrid event-triggered resilient control method for FDI and communication delay, comprising the following steps: obtaining the lagging neighbor current at the current moment affected by communication delay and false data injection attacks, and reconstructing the neighbor current at the current moment by performing Kalman filtering estimation and forward extrapolation using the fourth-order Runge-Kutta method by the delay compensation module; reconstructing the trusted neighbor current at the current moment by solving the optimal neighbor trust weight based on the neighbor current at the current moment by the signal game module; pre-setting a dynamic event triggering mechanism, restoring communication between the local and neighbor only when the triggering conditions of the dynamic event triggering mechanism are met, and updating the neighbor communication current at the current moment according to the trusted neighbor current; otherwise, using a zero-order hold to retain the neighbor communication current at the previous communication triggering moment; after triggering the neighbor communication current update, calculating the control quantity of distributed secondary control based on the neighbor communication current at the current moment.

Description

Technical Field

[0001] This invention belongs to the field of distributed control technology for microgrids, specifically relating to an event-triggered resilient control method for microgrids that addresses FDI and communication latency. Background Technology

[0002] DC microgrids, as a key carrier for absorbing new energy sources, provide an important pathway for the construction of new power systems. To coordinate the operating states of multiple distributed generation (DG) sources, microgrids utilize distributed consensus protocols to achieve system control solely through information exchange between adjacent DGs, thus eliminating dependence on a central controller. However, this control method is highly dependent on communication networks. Communication delays lead to lag in system response, while periodic communication wastes communication resources. Furthermore, malicious attacks on the control system can cause system crashes.

[0003] False data injection (FDI) attacks are a typical threat targeting the communication layer of microgrids. They tamper with transmitted information between nodes, causing the consensus protocol to converge to an incorrect equilibrium point without damaging physical equipment. These attacks are characterized by their high stealth and persistence. Extensive research has been conducted on defenses against FDI attacks, with current research including model-based methods. Another approach involves resilient compensation against such attacks.

[0004] These methods can all defend against FDI attacks to some extent. However, most existing studies assume that communication is normal, while communication delays are inevitable in real networks. The coupling of delays and attacks will further deteriorate the system's control performance.

[0005] Event-triggered control (ETC) effectively reduces communication overhead in distributed control, thus avoiding unnecessary communication redundancy, and is therefore widely used in microgrids. Static event-triggered control can significantly reduce the number of communications, but this method relies on a fixed threshold for judgment, triggering communication only when the threshold condition is met. Therefore, it is difficult to adapt to dynamic changes in the system, and the trigger response sensitivity is weak when the system changes. Dynamic event-triggered control introduces internal dynamic variables, causing the threshold to change with the system, which not only ensures control performance but also further optimizes the communication frequency. However, existing event-triggered methods mostly assume ideal communication and rarely integrate the event-triggered mechanism with communication attacks and delay compensation, resulting in a difficulty in simultaneously achieving communication efficiency and communication security. Summary of the Invention

[0006] To overcome the problem that existing event-triggered methods often rely on ideal communication, making it difficult to balance communication efficiency and security, this invention provides a microgrid event-triggered elastic control method oriented towards FDI and communication delay. It alleviates information lag through delay compensation based on state prediction, suppresses the impact of FDI attacks through a game theory-based elastic trust mechanism, and achieves on-demand communication through a dynamic event-triggered mechanism based on internal dynamic variables. By coordinating these three aspects, it reduces communication overhead while ensuring control accuracy, thereby improving the elastic control capability of DC microgrids in environments where communication delay and FDI attacks coexist.

[0007] According to one aspect of the present invention, a microgrid event-triggered resilient control method for FDI and communication delay is provided, comprising the following steps:

[0008] Obtain the current of the current neighbor affected by communication delay and false data injection attack, perform Kalman filter estimation and forward extrapolation using the fourth-order Runge-Kutta method to reconstruct the current of the current neighbor.

[0009] The optimal neighbor trust weight is calculated based on the current neighbor current, and the current of the trusted neighbor is reconstructed at the current moment.

[0010] A preset dynamic event triggering mechanism is used. Communication between the local device and its neighbors is restored only when the triggering conditions of the dynamic event triggering mechanism are met. The neighbor communication current is updated according to the current trusted neighbor current. Otherwise, the neighbor communication current at the previous communication triggering time is used with a zero-order hold.

[0011] After triggering the neighbor communication current update, the control quantity of the distributed secondary control is calculated based on the neighbor communication current at the current moment.

[0012] As a further technical solution, Kalman filtering estimation is performed, the steps of which include:

[0013] The converter output stage is approximated as a second-order continuous state-space model, and the discrete state transition matrix is ​​obtained by forward Euler discretization with a step size h; wherein, the state vector of the second-order continuous state-space model includes current components and auxiliary state components.

[0014] At each sampling time, a Kalman filter is performed on the state vector containing the lag neighbor current. The Kalman filter includes a prediction step and an update step. In the prediction step, the state prediction value and error covariance matrix at the lag time are obtained by using the discrete state transition matrix based on the state estimate value at the previous time. In the update step, the Kalman gain is calculated by combining the error covariance matrix with the measurement noise covariance matrix, and the state prediction value at the lag time is corrected based on the Kalman gain and the measurement value of the lag neighbor current to obtain the preferred predicted state at the lag time.

[0015] As a further technical solution, the fourth-order Runge-Kutta method is used for forward extrapolation, and the steps include:

[0016] After obtaining the preferred predicted state at the lag time, the fourth-order Runge-Kutta method is used to integrate it forward along the continuous model for a time delay interval. The time delay interval is divided into several sub-steps for iterative extrapolation to obtain the state vector at the current time. The current component is taken as the predicted neighbor current at the current time.

[0017] Perform global deviation correction on the predicted neighbor currents at each current moment;

[0018] Apply a first-order low-pass filter to the predicted neighbor current at the current time after global bias correction to obtain the reconstructed neighbor current at the current time.

[0019] As a further technical solution, the optimal neighbor trust weight is calculated based on the current neighbor current, and the current trusted neighbor current is reconstructed. The steps include:

[0020] Based on the local current and neighbor current at the current moment, the consistency loss at the current moment is calculated, and the attack strength at the current moment is calculated according to the preset attack identification method.

[0021] Substitute the consistency loss and attack intensity at the current moment into the preset defender cost function that takes into account both attack risk cost and consistency loss cost, and solve for the optimal trust weight that minimizes the value of the defender cost function.

[0022] The current trusted neighbor current is obtained by fusing the current of the current neighbor and the current value of the previous trusted neighbor based on the optimal neighbor trust weight.

[0023] As a further technical solution, the attack identification method is configured to use neighbor deviation as a measure of attack strength and determine the attack strength gain based on whether the neighbor current changes continuously in the same direction.

[0024] As a further technical solution, the defender cost function that takes into account both the attack risk cost and the consistency loss cost is a weighted sum of the attack risk cost and the consistency loss cost. The attack risk cost is obtained by multiplying the square of the attack intensity by the trust weight, and the consistency loss cost is obtained by multiplying the square of the consistency loss by the difference between one and the trust weight.

[0025] As a further technical solution, the dynamic event triggering mechanism is configured as follows:

[0026] A consistency error term is constructed using the difference between the neighbor's trusted current and the local current, and a dynamic trigger threshold is constructed that combines the consistency error term with dynamic variables.

[0027] The triggering condition of the dynamic event triggering mechanism is met when the cumulative measurement error norm since the last trigger exceeds the dynamic triggering threshold at the current moment.

[0028] As a further technical solution, the measurement error norm is defined as the sum of the squares of the measurement errors of two neighbor currents; wherein, the neighbor current measurement error is defined as the difference between the current of the trusted neighbor at the current moment and the current of the neighbor communication at the corresponding previous communication trigger moment.

[0029] According to another aspect of this specification, a microgrid event-triggered resilient control system oriented towards FDI and communication delay is provided, for implementing a microgrid event-triggered resilient control method oriented towards FDI and communication delay, comprising:

[0030] The delay compensation module is used to obtain the lagging neighbor current at the current moment, which is affected by communication delay and false data injection attacks. It then performs Kalman filtering estimation and forward extrapolation using the fourth-order Runge-Kutta method to reconstruct the neighbor current at the current moment. The signal game module is used to solve for the optimal neighbor trust weight based on the neighbor current at the current moment and reconstruct the trusted neighbor current at the current moment. The communication update module is used to execute the judgment of the preset dynamic event triggering mechanism. Only when the triggering conditions of the dynamic event triggering mechanism are met, the communication between the local and the neighbor is restored, and the neighbor communication current at the current moment is updated based on the trusted neighbor current. Otherwise, the neighbor communication current at the previous communication triggering moment is used with a zero-order hold. The secondary control elastic update module is used to calculate the control quantity of the distributed secondary control based on the neighbor communication current at the current moment after triggering the neighbor communication current update.

[0031] According to another aspect of this specification, an electronic device is provided, including a memory and a processor, the memory storing program instructions executed by the processor, the processor invoking the program instructions to execute a microgrid event-triggered resilient control method oriented towards FDI and communication delay.

[0032] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0033] 1. A time delay compensation scheme based on Kalman filtering and fourth-order RK state extrapolation is designed to estimate the state and correct the deviation of the delayed neighbor current, and reconstruct the real-time value of the neighbor current from the time delay signal, which effectively alleviates the information delay caused by communication delay.

[0034] 2. To address the challenge of lacking trusted references under full-link FDI attacks, the adoption of neighbor signals is modeled as an attack-defense trust game. By solving for the optimal trust weights, the attacked signals are reconstructed with weights, thus suppressing the impact of attacks without relying on external references.

[0035] 3. Construct a dynamic event triggering mechanism based on internal dynamic variables, so that the triggering threshold changes adaptively with the system state, realizing an automatic balance between elastic control and communication frequency. While ensuring control accuracy, it significantly reduces communication overhead and achieves a unity of communication saving and attack suppression. Attached Figure Description

[0036] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0037] Figure 1 This is a diagram of the microgrid structure in an embodiment of the present invention;

[0038] Figure 2 This is a diagram illustrating the control objectives and problem statements in an embodiment of the present invention;

[0039] Figure 3 A flowchart illustrating the microgrid event-triggered resilient control method for FDI and communication latency provided in an embodiment of the present invention;

[0040] Figure 4 This is a schematic diagram of the delay compensation principle in an embodiment of the present invention;

[0041] Figure 5 This is a diagram of the FDI resilient trust mechanism in an embodiment of the present invention;

[0042] Figure 6 This is a dynamic event triggering control diagram in an embodiment of the present invention;

[0043] Figure 7 This is a flowchart of the controller in an embodiment of the present invention;

[0044] Figure 8 A schematic diagram of the structure of a microgrid event-triggered resilient control system for FDI and communication delay provided in an embodiment of the present invention;

[0045] Figure 9 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0046] It should be noted that:

[0047] The terms “comprising” and “having”, and any variations thereof, in the specification, claims, and drawings of this invention are intended to cover a non-exclusive inclusion, such as a process, method, system, product, or apparatus that includes a series of steps or units, not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0048] The block diagrams shown in the accompanying drawings are merely functional entities and do not necessarily correspond to physically independent entities. That is, these functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices. The flowcharts shown in the accompanying drawings are merely illustrative and do not necessarily include all content and operations / steps, nor do they necessarily have to be performed in the described order. For example, some operations / steps can be decomposed, while others can be combined or partially combined; therefore, the actual execution order may change depending on the specific circumstances.

[0049] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. In addition, the technical features of the various embodiments or individual embodiments provided by the present invention can be arbitrarily combined to form new technical solutions. Such combinations are not bound by the order of steps and / or structural composition patterns, but must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0050] This invention primarily utilizes state prediction delay compensation theory, game theory-based elastic trust mechanisms, and dynamic event-triggered control strategies to improve the resilience and communication efficiency of distributed secondary control in DC microgrids under conditions where communication delays and FDI attacks coexist. It proposes an event-triggered elastic control method for microgrids that considers both FDI attacks and communication delays. This invention fully leverages the advantages of Kalman filtering and fourth-order RK state extrapolation in delay compensation by estimating the state of lag information and reconstructing the real-time current through forward extrapolation. For FDI attacks, an elastic trust mechanism based on attack-defense game theory is designed to suppress the impact of attacks by solving for the optimal trust weights. For communication resource optimization, a dynamic event-triggered mechanism based on internal dynamic variables is adopted, coordinating delay compensation, attack defense, and event triggering. The control effect obtained through this invention is more efficient, suppressing the impact of communication delays and FDI attacks on control, and significantly reducing communication overhead.

[0051] The method provided by this invention can be implemented using computer simulation software technology. The microgrid structure diagram in the embodiments of this invention is as follows: Figure 1 As shown.

[0052] In this embodiment of the invention, the steps for modeling a DC microgrid and constructing a distributed secondary control protocol include:

[0053] Step S1.1: This DC microgrid topology model consists of several distributed generation (DG) sources, all of which converge to the same common DC bus and are connected in parallel to a load. At the communication layer, communication between DGs adopts a ring structure.

[0054] Step S1.2: The electrical dynamics of each DG are characterized by the state equations of the filtering stage, including the relationship between the filter inductor, filter capacitor, input voltage, inductor current and duty cycle.

[0055] Specifically, define L i For filter inductance; C i For filtering capacitors, The input voltage of the converter; v i To control the input voltage; I i For output current; d is the inductor current; i Duty cycle;

[0056] For a single converter, the expression for the electrical dynamics of the i-th DG is:

[0057] .

[0058] Step S1.3: Adopt droop control at the primary control layer to achieve initial system regulation and maintain initial stability in the absence of communication.

[0059] Specifically, define r d，i Let i be the droop coefficient of the i-th converter; i v is the output current of the i-th converter; d，i V is the droop control output of the i-th converter; nom This is the reference voltage.

[0060] The control of DC microgrids revolves around two tasks: voltage regulation and power balancing. For droop control, its main function is to achieve initial system regulation in the absence of communication, in order to maintain initial system stability.

[0061] .

[0062] Step S1.4: Adopt a dual closed-loop PI structure with voltage outer loop and current inner loop cascaded in the local control layer.

[0063] Specifically, define K pv K iv For outer loop parameters; K pi K ii For inner loop parameters; i ref，i The reference current for the inner current loop, v ref，i s1 is the reference voltage of the outer voltage loop; s2 is the Laplace operator;

[0064] To ensure accurate voltage tracking and current constraint, each DG is equipped with a dual closed-loop PI structure with a cascaded outer voltage loop and an inner current loop: the outer loop generates a current command based on the difference between the reference voltage and the measured terminal voltage, and the inner loop drives the duty cycle based on the difference between the current command and the measured inductor current.

[0065] .

[0066] Step 1.5: Construct a distributed secondary control protocol based on a consensus protocol.

[0067] Specifically, information exchange between DGs is accomplished through a communication network. In this invention, the communication network adopts a ring communication structure. The network is described by an undirected graph G=(υ,ε), where the node set υ={1,2,…,N} corresponds to each DG, N is the number of DGs in the microgrid, and the edge set ε represents the link connection relationship. When there is a communication link between nodes i and j, we denote (i,j)∈ε.

[0068] Based on this, define the adjacency matrix A=[a ij ]∈R (N×N) , with degree matrix D=diag(Σ j a ij ), where a ij The graph Laplace matrix is ​​expressed as the difference between the two. .

[0069] Define k v and k i To control the gain; G ii For voltage recovery weighting, c i This is the power distribution factor.

[0070] The distributed secondary control based on the consensus protocol consists of two channels: voltage recovery and current sharing. Voltage recovery is used to offset the steady-state voltage deviation of droop control, while current sharing drives each unit to share the current proportionally through the exchange of current information between neighbors, as shown below:

[0071] .

[0072] Therefore, the reference voltage for the i-th DG is:

[0073] .

[0074] The above derivation applies to ideal communication. In actual control processes, time delays are common between information communications. Let's assume that the current information sent from node j to node i takes a time delay τ. d If the information is received from the back end, then the neighbor information actually used in the consistency iteration should be represented as follows: ,in For communication delay τ d The current.

[0075] Besides latency, communication channels are also susceptible to cyberattacks. To comprehensively analyze the impact of FDI attacks on secondary control, this paper constructs three types of FDI attack models.

[0076] Define the attack start time as t a x j (t) represents the actual signal of neighbor node j, and y ij (t) represents the signal indicating an attack:

[0077] 1) Bounded FDI attack:

[0078] Define t f b is the moment when the bias climbs to saturation. f b is the steady-state amplitude of the bias. max The upper limit of the bias is set, and sat[-] represents the saturation function.

[0079] Inject bias from time t a The amplitude increases continuously, but is constrained by the maximum amplitude. Its signal model is as follows:

[0080] .

[0081] 2) Unbounded FDI attack:

[0082] Define α as the growth rate of the bias.

[0083] The injected bias accumulates continuously without an upper bound, causing the attacked signal to deviate infinitely from the true value over time. Its signal model is as follows:

[0084] .

[0085] 3) Unbounded noisy FDI attack:

[0086] Define n(t) as the original noise, n f (t) represents the filtered noise component, λ n This represents the filter bandwidth.

[0087] Random noise is further superimposed on the unbounded FDI attack, making the attack more covert while maintaining the trend shift. Its signal model is as follows:

[0088] ;

[0089] .

[0090] Based on the above model, the following assumptions are made for subsequent derivations:

[0091] Assumption 1: The communication graph G is an undirected connected graph with a positive semi-definite Laplace matrix L. Except for a single zero eigenvalue, all other eigenvalues ​​are positive. Let its smallest non-zero eigenvalue be λ2>0.

[0092] Assumption 2: The communication delay is bounded, that is, there exists a constant τ. max Make 0≤τ d ≤τ max .

[0093] The control objectives and problem statements in the embodiments of the present invention are shown in the diagram below. Figure 2 As shown.

[0094] In the aforementioned communication environment where latency and attacks coexist, traditional distributed secondary control is difficult to maintain stability for the following reasons: 1) Communication latency causes neighbor states to lag behind the true state, thereby disrupting the convergence state; 2) FDI attacks inject false information into the channel, causing consistency iteration to tend towards an incorrect equilibrium point, and the coupling of latency and attacks will further increase the difficulty of control; 3) Reducing the communication frequency may help suppress the impact of attacks, but it may sacrifice control performance.

[0095] Therefore, the objective of this invention is to design a distributed resilient secondary control method that enables the system to simultaneously achieve the following objectives even under the combined effects of communication latency and FDI attacks:

[0096] 1) Voltage Regulation: The output voltage of each DG converges to the reference value, i.e. .

[0097] 2) Current distribution: The current is distributed proportionally to each DG, i.e. .

[0098] 3) Attack resilience: Under FDI attack, the injected bias can be identified and resisted, so that the deviation of voltage and current is always bounded and recoverable.

[0099] 4) Communication savings: The number of event triggers is reduced, enabling on-demand communication and eliminating Zeno behaviors that may occur when events are triggered.

[0100] Furthermore, such as Figure 3 As shown, the microgrid event-triggered resilient control method for FDI and communication delay provided by the present invention includes the following steps:

[0101] Step 1: Obtain the current of the current neighbor affected by communication delay and false data injection attack, perform Kalman filter estimation and forward extrapolation using the fourth-order Runge-Kutta method to reconstruct the current of the current neighbor.

[0102] Step 2: Calculate the optimal neighbor trust weight based on the current neighbor current and reconstruct the current of the trusted neighbor at the current moment;

[0103] Step 3: Preset dynamic event triggering mechanism. Only when the triggering conditions of the dynamic event triggering mechanism are met will communication between the local and the neighbor be restored, and the neighbor communication current at the current time will be updated according to the trusted neighbor current at the current time. Otherwise, the neighbor communication current at the previous communication triggering time will be used with a zero-order hold.

[0104] Step 4: After triggering the neighbor communication current update, calculate the control quantity of the distributed secondary control based on the neighbor communication current at the current moment.

[0105] Step 1 involves performing Kalman filter estimation, which includes the following steps:

[0106] Step 1.1.1: Approximate the converter output stage as a second-order continuous state-space model, and perform forward Euler discretization with a step size h to obtain the discrete state transition matrix; wherein, the state vector of the second-order continuous state-space model includes current components and auxiliary state components.

[0107] Step 1.1.2: Perform a Kalman filter on the state vector containing the lag neighbor current at each sampling time. The Kalman filter includes a prediction step and an update step. In the prediction step, based on the state estimate of the previous time step, the discrete state transition matrix is ​​used to advance and obtain the state prediction value and error covariance matrix at the lag time. In the update step, the Kalman gain is calculated using the error covariance matrix combined with the measurement noise covariance matrix, and the state prediction value at the lag time is corrected based on the Kalman gain and the measured value of the lag neighbor current to obtain the preferred predicted state at the lag time.

[0108] In step 1, the fourth-order Runge-Kutta method is used to push forward outwards. The steps include:

[0109] Step 1.2.1: After obtaining the preferred predicted state at the lag time, integrate it forward along the continuous model by a time delay interval using the fourth-order Runge-Kutta method. Divide the time delay interval into several sub-steps for iterative extrapolation to obtain the state vector at the current time. Take the current component as the predicted neighbor current at the current time.

[0110] Step 1.2.2: Perform global deviation correction on the predicted neighbor currents at each current moment;

[0111] Step 1.2.3: Apply a first-order low-pass filter to the predicted neighbor current at the current time after global bias correction to obtain the reconstructed neighbor current at the current time.

[0112] Specifically, the time delay compensation principle diagram of step 1 in this embodiment of the invention is as follows: Figure 4 As shown.

[0113] Due to the time delay introduced by the communication link, the neighbor currents obtained by the consensus operation are lagging information. To compensate for the time delay, this paper constructs a predictive compensator based on Kalman filtering and state extrapolation for each DG. The core of this method is to first estimate the state of the lagging information, and then dynamically advance the estimated state according to the DG system to reconstruct the neighbor current at the current moment.

[0114] In step 1.1.1, R is defined. L C is the load resistor, C is the filter capacitor, and a is the load resistor. c This is the attenuation coefficient for the auxiliary state, used to describe the dynamic characteristics of the current change rate, and is set to 50.

[0115] The converter output stage can be approximated as a second-order continuous state-space model, with states x = [x1, x2]. T Where x1 represents the current component and x2 is the auxiliary state component, the DG system matrix is:

[0116] .

[0117] definition For identity matrix, To discretize the step size, perform forward Euler discretization with step size h to obtain the discrete state transition matrix:

[0118] .

[0119] In step 1.1.2, F is defined as the state transition matrix; P is the estimation error covariance matrix; P - Here, Q is the prediction error covariance matrix; Q is the process noise covariance. This is the state estimate. This is the predicted state value.

[0120] At each sampling moment, the delay compensation module performs a one-step Kalman filter on the lagging neighbor current at the current moment, which is affected by communication delay and spoofing attacks:

[0121] The prediction step advances the state and error covariance based on the state estimate from the previous time step:

[0122] .

[0123] Define H = [1, 0] as the measurement matrix, R as the measurement noise variance, and K as the Kalman gain; d This is the actual measured value of the current; The element in the first row and first column of the prior covariance matrix, The element in the 2nd row and 1st column of the verification covariance matrix, For new information covariance, For the prior estimate of the first state, For measurement matrix

[0124] The update step uses hysteresis information as a reference to calculate the gain and correct the state:

[0125] .

[0126] In step 1.2.1, κ is defined as the slope coefficient ( ); The value after processing by the fourth-order RK method. This is the value before processing by the fourth-order RK method.

[0127] After obtaining the state estimate at the lag time, the compensator uses the fourth-order RK method to integrate the state forward along the continuous model for a time delay interval τ to predict the current of the neighboring current.

[0128] Divide τ into n s Each sub-step has a step size Δt = τ / n s Each slope term is defined according to standard RK4, and the iteration format is as follows:

[0129] .

[0130] Define N as the number of DGs, p i This is the predicted neighbor current value before global bias correction. After n... s The first component of the state after step extrapolation is taken as the predicted current.

[0131] In step 1.2.2, to eliminate the bias introduced by the extrapolation process, the following global bias correction is made to the predicted current values ​​of each neighbor: This is the global average deviation. This is the predicted value of the i-th node after bias correction.

[0132] .

[0133] Define α f These are the filter coefficients. To compensate for the current.

[0134] Finally, in step 1.2.3, the delayed neighbor current is obtained after first-order low-pass filtering:

[0135] .

[0136] In step 2, the optimal neighbor trust weight is calculated based on the current neighbor current, and the current of the trusted neighbor is reconstructed. The steps include:

[0137] Step 2.1: Based on the local current and neighbor current at the current moment, solve for the consistency loss at the current moment, and solve for the attack strength at the current moment according to the preset attack identification method.

[0138] Step 2.2: Substitute the consistency loss and attack intensity at the current moment into the preset defender cost function that takes into account both attack risk cost and consistency loss cost, and solve for the optimal trust weight that minimizes the value of the defender cost function.

[0139] Step 2.3: Based on the optimal neighbor trust weight, fuse the current of the current neighbor at the current moment with the current value of the previous trusted neighbor to obtain the current of the trusted neighbor at the current moment.

[0140] Specifically, the FDI resilient trust mechanism diagram provided in step 2 of this embodiment is as follows: Figure 5 As shown.

[0141] Assume the attacked signal is y(t) = i(t) + b(t), where i is the real signal and b is an unknown injected bias. Under the condition of a full-link attack and no trusted reference, this paper does not reconstruct the injected bias, but models the problem of accepting neighbor signals as a trust decision game of the defender. By solving for the optimal trust weight, an equilibrium is achieved between resisting the attack and maintaining consistency.

[0142] Define i self For the local weighted current, i nbr,k The received current (after time delay compensation) of the k-th neighbor is indicated by the superscript "". "Indicates the value at the previous moment. g k For attack gain, g is the value when neighbor signals change continuously in the same direction. k =2, otherwise g k =1,d k Distance from neighbors.

[0143] As the consistency objective indicates, the weighted currents of each DG tend to be consistent in steady state. Therefore, step 2.1 provides an attack identification method configured to use neighbor deviation as a measure of attack strength and determine the attack strength gain based on whether the neighbor current changes continuously in the same direction. Mathematically, this is expressed as:

[0144] ;

[0145] ;

[0146] .

[0147] Furthermore, based on game theory, a trust decision-making game method is constructed, in which the defender chooses the trust weight w for the neighbor's signal. k For each ∈[0,1], there are two types of competition costs: trusting the attacked signal will introduce bias (attack risk cost), while distrusting the neighbor will result in the loss of consistent coordination ability (consistency loss cost).

[0148] In step 2.2, the defender cost function, which balances attack risk cost and consistency loss cost, is a weighted sum of attack risk cost and consistency loss cost, wherein the attack risk cost is determined by the attack intensity (d). k The consistency loss cost is obtained by multiplying the square of the consistency loss by the trust weight, and the consistency loss cost is obtained by multiplying the square of the consistency loss by the difference between one and the trust weight.

[0149] Define R atk As an attack risk weight, R cons For consistency requirement weights, δ k The consensus error is based on the previous confidence value. The constructed defender cost function is... The mathematical representation of is:

[0150] .

[0151] The equilibrium strategy in this game is the trust weight that minimizes the defender's cost, for w. k Minimize the optimal trust weight:

[0152] .

[0153] Therefore, we can conclude that d k The larger the size, the more likely it is to be an attack. The smaller the value, the less the defender trusts the signal; δ k The larger the building, the more cooperation from its neighbors is needed. The larger.

[0154] Finally, step 2.3 performs trust-weighted reconstruction, fusing the neighbor received signal (the neighbor current obtained in step 1) with the trusted neighbor current value from the previous time step using the optimal trust weight to obtain the trusted neighbor current at the current time step, which is then used in the consensus process.

[0155] .

[0156] Under normal circumstances, the signal is received directly from the neighbor; when attacked, it reverts to the previous trusted value, thereby suppressing the impact of the attack without relying on external references.

[0157] In step 3, the dynamic event triggering mechanism is configured as follows:

[0158] Step 3.1: Construct a consistency error term based on the difference between the neighbor's trusted current and the local current, and construct a dynamic trigger threshold that combines the consistency error term with the dynamic variables;

[0159] Step 3.2: When the cumulative measurement error norm since the last trigger exceeds the dynamic trigger threshold at the current moment, the triggering condition of the dynamic event triggering mechanism is met.

[0160] Specifically, the dynamic event triggering control diagram provided in step 3 of this embodiment of the invention is as follows: Figure 6 As shown.

[0161] To reduce the frequency of neighbor communication, a dynamic event triggering mechanism is designed. The maintained neighbor state is updated only when the triggering condition is met; otherwise, a zero-order hold (ZOH) is used to retain the value at the previous triggering time.

[0162] In step 3, the measurement error norm is defined as the sum of the squares of the two neighbor current measurement errors; whereby the neighbor current measurement error is defined as the difference between the current of the trusted neighbor at the current moment and the current of the neighbor communication at the corresponding previous communication trigger moment.

[0163] Define the current local current as The currents of its two neighbors are (Include ,and ), The neighbor current communication value held at the last trigger time is defined as the measurement error since the last trigger. and measurement error norm for:

[0164] .

[0165] In step 3.1, 'a' is defined as the neighbor coupling weight, and a consistency error term is constructed using the difference between the neighbor's current and the current of the current itself. Mathematically, this is expressed as:

[0166] .

[0167] Secondly, a dynamic variable θ that decays over time is introduced, allowing the threshold to be adjusted adaptively:

[0168] Define m>0 as the decay rate of the dynamic variable threshold; It is the derivative of the dynamic variable θ.

[0169] .

[0170] Define σ>0 as the static triggering coefficient. The triggering threshold is determined by combining the consistency error term and the dynamic variables. The definition is as follows:

[0171] .

[0172] Neighbor currents are updated only at the trigger moment after being sampled by the event, thus enabling on-demand communication.

[0173] The controller flowchart in this embodiment of the invention is as follows: Figure 7 As shown.

[0174] Based on the above three stages, the specific control flow of the elastic secondary control proposed in this paper is as follows:

[0175] 1) Neighbor current signals are affected by communication delays and FDI attacks, which alters the original convergence process;

[0176] 2) The time delay compensation module performs Kalman filtering estimation on the lagging neighbor current and pushes the state forward outward with fourth-order RK to reconstruct the current at the current moment in order to eliminate the effect of time delay;

[0177] 3) Use signal game theory to determine the communication information, solve for the optimal trust weight, and then output the reliable current;

[0178] 4) The dynamic event triggering module determines whether to update communication based on the current neighbor status. If not, it uses the value from the previous triggering moment through ZOH, thereby reducing the number of communication times.

[0179] 5) Generate secondary control correction quantities using the processed current and voltage signals;

[0180] 6) Based on droop control, a reference voltage is generated, and then the PWM duty cycle is obtained through dual-loop PI control to realize the signal control cycle.

[0181] Through a flexible control framework that combines time delay compensation, FDI elastic trust mechanism and dynamic event triggering, stable operation of DC microgrids is achieved in environments where communication delay and FDI attacks coexist. Communication is only performed on demand when triggering conditions are met, providing an effective technical solution for flexible control of DC microgrids in scenarios with non-ideal communication and limited communication resources.

[0182] The implementation of the various embodiments of this invention is based on programmed processing through a system with processor functionality. Therefore, in practical engineering, the technical solutions and functions of the various embodiments of this invention are encapsulated into various modules. Based on this reality, and building upon the above embodiments, the embodiments of this invention provide a microgrid event-triggered resilient control system oriented towards FDI and communication delay. This system is used to execute the microgrid event-triggered resilient control method oriented towards FDI and communication delay in the above method embodiments.

[0183] See Figure 8 The system includes: a delay compensation module, used to obtain the current lagging neighbor current affected by communication delay and false data injection attacks, and perform Kalman filtering estimation and forward extrapolation using the fourth-order Runge-Kutta method to reconstruct the current neighbor current at the current moment; a signal game module, used to solve for the optimal neighbor trust weight based on the current neighbor current at the current moment, and reconstruct the current trustworthy neighbor current at the current moment; a communication update module, used to execute a preset dynamic event triggering mechanism judgment, and only when the triggering conditions of the dynamic event triggering mechanism are met, to restore communication between the local and neighbor, and update the current neighbor communication current based on the current trustworthy neighbor current, otherwise to use the neighbor communication current at the previous communication triggering moment using a zero-order hold; and a secondary control elastic update module, used to calculate the control quantity of distributed secondary control based on the current neighbor communication current after triggering the neighbor communication current update.

[0184] It should be noted that the system embodiments provided by the present invention are used not only to implement the methods in the above method embodiments, but also to implement the methods in other method embodiments provided by the present invention. The only difference is that corresponding functional modules are set. The principle is basically the same as that of the above system embodiments provided by the present invention. As long as those skilled in the art can improve the modules in the above system embodiments by referring to the specific technical solutions in other method embodiments and combining technical features to obtain corresponding technical means and technical solutions composed of these technical means, on the basis of the above system embodiments, and on the premise of ensuring the practicality of the technical solutions, they can obtain corresponding system-like embodiments for implementing the methods in other method-like embodiments.

[0185] The method in this embodiment of the invention is implemented using an electronic device; therefore, it is necessary to introduce the relevant electronic device. For this purpose, embodiments of the present invention provide an electronic device, such as... Figure 9 As shown, the electronic device includes: at least one processor, a communication interface, at least one memory, and a communication bus, wherein the at least one processor, the communication interface, and the at least one memory communicate with each other via the communication bus. The at least one processor invokes logical instructions stored in the at least one memory to execute all or part of the steps of the methods provided in the foregoing method embodiments.

[0186] Furthermore, when the logical instructions in at least one of the aforementioned memories are implemented as software functional units and sold or used as independent products, they are stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, is embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (a personal computer, server, or network device) to execute all or part of the steps of the methods described in the various method embodiments of the present invention. The aforementioned storage medium includes: USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks—various media for storing program code.

[0187] The system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, located in one place, or distributed across multiple network units. The purpose of this embodiment is achieved by selecting some or all of the modules according to actual needs. Those skilled in the art will understand and implement this without any inventive effort.

[0188] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention 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.

[0189] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. 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 illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0190] 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.

[0191] 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.

[0192] In summary, the present invention provides an event-triggered elastic control method for microgrids that takes into account FDI attacks and communication delays. It is applicable to solving problems such as low communication efficiency in distributed secondary control of DC microgrids and difficulty in ensuring system stability under non-ideal communication conditions where communication delays and FDI attacks coexist. First, a time delay compensation scheme combining Kalman filtering and fourth-order Runge-Kutta (RK) state extrapolation is designed. This scheme estimates the state of lagging neighbor currents and extrapolates them forward along the system's dynamic model. Global deviation correction is then used to reconstruct the real-time values ​​of neighbor currents from the time delay signal. Second, addressing the challenge of no reliable reference under full-link FDI attacks, the adoption of neighbor signals is modeled as an attack-defense trust game. The attacked signal is reconstructed by solving for the optimal trust weight, thereby suppressing the attack's impact. Third, a dynamic event triggering mechanism based on internal dynamic variables is constructed, enabling the triggering threshold to adaptively change with the system state, achieving an automatic balance between resilient control and communication frequency. Finally, time delay compensation, the FDI resilient trust mechanism, and dynamic event triggering are designed collaboratively to unify communication savings and attack suppression. This invention effectively suppresses the impact of communication delays and FDI attacks, significantly reducing communication overhead while ensuring control accuracy, providing technical support for resilient control of DC microgrids under non-ideal communication environments.

[0193] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the technical solutions of the embodiments of the present invention.

Claims

1. A microgrid event-triggered resilient control method for FDI and communication delay, characterized in that, Includes the following steps: Obtain the current of the current neighbor affected by communication delay and false data injection attack, perform Kalman filter estimation and forward extrapolation using the fourth-order Runge-Kutta method to reconstruct the current of the current neighbor. The optimal neighbor trust weight is calculated based on the current neighbor current, and the current of the trusted neighbor is reconstructed at the current moment. A preset dynamic event triggering mechanism is used. Communication between the local device and its neighbors is restored only when the triggering conditions of the dynamic event triggering mechanism are met. The neighbor communication current is updated according to the current trusted neighbor current. Otherwise, the neighbor communication current at the previous communication triggering time is used with a zero-order hold. After triggering the neighbor communication current update, the control quantity of the distributed secondary control is calculated based on the neighbor communication current at the current moment.

2. The microgrid event-triggered resilient control method for FDI and communication delay as described in claim 1, characterized in that, The steps for performing Kalman filter estimation include: The converter output stage is approximated as a second-order continuous state-space model, and the discrete state transition matrix is ​​obtained by forward Euler discretization with a step size h; wherein, the state vector of the second-order continuous state-space model includes current components and auxiliary state components. At each sampling time, a Kalman filter is performed on the state vector containing the lag neighbor current. The Kalman filter includes a prediction step and an update step. In the prediction step, the state prediction value and error covariance matrix at the lag time are obtained by using the discrete state transition matrix based on the state estimate value at the previous time. In the update step, the Kalman gain is calculated by combining the error covariance matrix with the measurement noise covariance matrix, and the state prediction value at the lag time is corrected based on the Kalman gain and the measurement value of the lag neighbor current to obtain the preferred predicted state at the lag time.

3. The microgrid event-triggered resilient control method for FDI and communication delay as described in claim 2, characterized in that, The forward extrapolation using the fourth-order Runge-Kutta method includes the following steps: After obtaining the preferred predicted state at the lag time, the fourth-order Runge-Kutta method is used to integrate it forward along the continuous model for a time delay interval. The time delay interval is divided into several sub-steps for iterative extrapolation to obtain the state vector at the current time. The current component is taken as the predicted neighbor current at the current time. Perform global deviation correction on the predicted neighbor currents at each current moment; Apply a first-order low-pass filter to the predicted neighbor current at the current time after global bias correction to obtain the reconstructed neighbor current at the current time.

4. The microgrid event-triggered resilient control method for FDI and communication delay as described in claim 2, characterized in that, The optimal neighbor trust weight is calculated based on the current neighbor current, and the current of the trusted neighbor is reconstructed. The steps include: Based on the local current and neighbor current at the current moment, the consistency loss at the current moment is calculated, and the attack strength at the current moment is calculated according to the preset attack identification method. Substitute the consistency loss and attack intensity at the current moment into the preset defender cost function that takes into account both attack risk cost and consistency loss cost, and solve for the optimal trust weight that minimizes the value of the defender cost function. The current trusted neighbor current is obtained by fusing the current of the current neighbor and the current value of the previous trusted neighbor based on the optimal neighbor trust weight.

5. The microgrid event-triggered resilient control method for FDI and communication delay as described in claim 4, characterized in that, The attack identification method is configured to use neighbor deviation as a measure of attack strength and determine the attack strength gain based on whether the neighbor current changes continuously in the same direction.

6. The microgrid event-triggered resilient control method for FDI and communication delay as described in claim 4, characterized in that, The defender cost function that takes into account both attack risk cost and consistency loss cost is a weighted sum of attack risk cost and consistency loss cost. The attack risk cost is obtained by multiplying the square of the attack intensity by the trust weight, and the consistency loss cost is obtained by multiplying the square of the consistency loss by the difference between one and the trust weight.

7. The microgrid event-triggered resilient control method for FDI and communication delay as described in claim 1, characterized in that, The dynamic event triggering mechanism is configured as follows: A consistency error term is constructed using the difference between the neighbor's trusted current and the local current, and a dynamic trigger threshold is constructed that combines the consistency error term with dynamic variables. The triggering condition of the dynamic event triggering mechanism is met when the cumulative measurement error norm since the last trigger exceeds the dynamic triggering threshold at the current moment.

8. The microgrid event-triggered resilient control method for FDI and communication delay as described in claim 7, characterized in that, The measurement error norm is defined as the sum of the squares of the two neighbor current measurement errors; wherein, the neighbor current measurement error is defined as the difference between the current of the trusted neighbor at the current moment and the current of the neighbor communication at the corresponding previous communication trigger moment.

9. A microgrid event-triggered resilient control system oriented towards FDI and communication delay, used to implement the microgrid event-triggered resilient control method oriented towards FDI and communication delay as described in any one of claims 1 to 8, characterized in that, include: The delay compensation module is used to obtain the current of the lagging neighbor at the current moment affected by communication delay and false data injection attacks, and to perform Kalman filter estimation and forward extrapolation using the fourth-order Runge-Kutta method to reconstruct the current of the neighbor at the current moment. The signal game module is used to solve for the optimal neighbor trust weight based on the current neighbor current and reconstruct the current of the trusted neighbor at the current moment. The communication update module is used to perform a preset dynamic event triggering mechanism judgment. It restores communication between the local and neighbor only when the triggering conditions of the dynamic event triggering mechanism are met, and updates the neighbor communication current at the current time according to the trusted neighbor current at the current time. Otherwise, it uses a zero-order hold to carry over the neighbor communication current at the previous communication triggering time. The secondary control elastic update module is used to calculate the control quantity of distributed secondary control based on the current neighbor communication current after triggering the neighbor communication current update.

10. An electronic device, characterized in that, The system includes a memory and a processor, wherein the memory stores program instructions that are executed by the processor, and the processor invokes the program instructions to execute the microgrid event-triggered resilient control method for FDI and communication delay as described in any one of claims 1 to 8.

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