Micro-grid network attack influence quantitative evaluation method based on reachability analysis

Abstract

The invention discloses a microgrid network attack influence quantitative evaluation method based on reachability analysis, and the method comprises the steps: considering the internal complex dynamics and line dynamics of an inverter, and building a nonlinear mathematical model of a microgrid; constructing a network attack model with variable amplitude by using a modeling method based on a sino polyhedron, and adding the established network attack model as a disturbance input item into the nonlinear mathematical model of the micro-grid; on the basis of a reachability analysis theory, aiming at the problem that the number of the chirnol polyhedron generators is increased along with an iteration index, designing a clustering method-based chirnol polyhedron generator adaptive merging strategy to improve a reachability set calculation algorithm; and calculating a reachable set of the micro-grid under the influence of different types of network attacks by applying an improved reachable set calculation algorithm. According to the method, the influence of the network attack on the inverter control and the operation performance of the micro-grid is quantitatively analyzed according to the reachable set result, and important guidance is provided for ensuring the safe and stable operation of the micro-grid.

Description

Technical Field

[0001] The present invention relates to the technical field of power system security assessment, and in particular to a method for quantitatively assessing the impact of microgrid network attacks based on reachability analysis. Background Art

[0002] As a key link in the new power system, microgrids can enhance the distribution network's ability to absorb new energy, ensure continuous power supply to critical loads in the event of a grid failure, and effectively solve electricity problems in scenarios far away from the main power supply center, such as islands, remote areas, and ships. They are of great significance to improving energy utilization efficiency, enhancing power supply reliability, and promoting sustainable energy development.

[0003] In terms of operational mechanisms, microgrids deeply integrate measurement and communication systems. Leveraging their powerful data collection and transmission capabilities, they tightly connect distributed power sources with diverse characteristics, such as wind, solar, and storage, enabling precise coordinated control. Microgrids are therefore typical power cyber-physical systems that integrate computing, communication, and control technologies. However, this heavy reliance on communication networks also poses a serious threat to microgrid cybersecurity. Hackers can precisely target communication and control terminals and exploit carefully crafted false data injection attacks to compromise the integrity and availability of measurement data. This not only disrupts the microgrid's real-time monitoring and decision-making systems but can also trigger a chain reaction, leading to a range of serious consequences, including malfunctioning power equipment, abnormal output from renewable energy sources, and load power outages, seriously threatening the stable operation and reliable power supply of the microgrid. Therefore, understanding the impact mechanisms of cyberattacks and assessing the vulnerabilities of microgrids under various operating conditions are crucial for developing effective security measures and ensuring microgrid resilience.

[0004] Existing research analyzing the impact of cyberattacks on the secure and stable operation of microgrids typically relies on time-domain simulation. This method qualitatively predicts the impact of attacks on microgrid synchronization stability through simulations, but lacks theoretical support, making in-depth quantitative analysis difficult. To achieve quantitative assessment, some studies have introduced Monte Carlo simulations and established evaluation metrics to quantify the impact of cyberattacks on microgrid operational reliability. However, this method requires multiple simulations, is computationally intensive, and cumbersome, and it fails to fully cover all possible operating scenarios. Furthermore, the Lyapunov method has been used to analyze inter-inverter synchronization errors. While this method explores microgrid stability by constructing Lyapunov functions and combining them with linear matrix inequalities, it remains limited to qualitative analysis and fails to clearly reveal the quantitative impact mechanisms of cyberattacks. Some studies have attempted to quantitatively analyze the impact of cyberattacks by establishing detailed models of distributed energy resources. After linearizing the models, they use eigenvalue calculations to assess changes in microgrid stability under attacks. However, this method, based on the small-disturbance assumption of linearized models, fails to fully capture the nonlinear characteristics of the inverter, resulting in inaccurate analysis results. Furthermore, these studies typically assume that attack signals have fixed amplitudes, whereas real-world attacks are often uncertain and time-varying. Some studies have attempted to generate multiple curves using time-domain simulations to examine the impact of attacks with varying amplitudes. However, this approach is not only complex and cumbersome, but also fails to cover all potential attack scenarios, limiting the comprehensiveness of the analysis.

[0005] In summary, current research methods have shortcomings in theoretical depth, computational efficiency, and comprehensive analysis, and there is still a lack of a quantitative assessment method for the impact of cyber attacks on microgrids. Summary of the Invention

[0006] The purpose of the present invention is to overcome the shortcomings and deficiencies of the existing technology and provide a method for quantitatively evaluating the impact of microgrid network attacks based on reachability analysis. The impact of network attacks on inverter control and microgrid operation performance is quantitatively analyzed based on the reachable set results, providing important guidance for ensuring the safe and stable operation of the microgrid.

[0007] To achieve the above objectives, the present invention provides a technical solution: a method for quantitatively assessing the impact of microgrid network attacks based on reachability analysis, comprising the following steps:

[0008] Step 1: Considering the complex dynamics inside the inverter and the line dynamics, a nonlinear mathematical model of the microgrid is established;

[0009] Step 2: Considering the uncertainty in cyber attacks, a cyber attack model with variable amplitude is constructed using a modeling method based on Qino polyhedrons. The established cyber attack model is then added as a disturbance input to the nonlinear mathematical model of the microgrid.

[0010] Step 3: To effectively analyze the nonlinear mathematical model of the microgrid, an improved reachable set calculation algorithm is designed based on reachability analysis theory. The nonlinear mathematical model is converted into a linear abstract model. Taking into account the linearization error, the reachable set of the microgrid is obtained by combining the solution results of the linear abstract model. The improvement of the reachable set calculation algorithm is as follows: to address the problem that the number of Chino polyhedron generators increases exponentially with iterations, an adaptive Chino polyhedron generator merging strategy based on clustering is designed. Generators with similar directions are merged and replaced to reduce the number of generators. This ensures the accuracy of the reachable set calculation while constraining the complexity of the set representation.

[0011] Step 4: Apply the improved reachable set calculation algorithm to calculate the reachable set of the microgrid under the influence of different types of network attacks, and predict the dynamic trajectory of the microgrid state based on the reachable set results, so as to quantitatively analyze the impact of network attacks on the operating performance of the microgrid.

[0012] Furthermore, in step 1, the microgrid includes distributed energy sources based on inverters, transmission lines and power loads, including N nodes, N i Inverter, N g transmission lines and N l An electrical load.

[0013] Furthermore, in step 1, first, in order to capture the complex internal operating characteristics of distributed energy, the dynamics of the voltage outer loop-current inner loop controller are considered, and a detailed nonlinear mathematical model of the inverter is accurately established; secondly, the coupling effect of the inductor-capacitor-inductor filter on the inverter export line is further combined to construct a dynamic model of the filter between the inverter and the terminal bus. In addition, considering the dynamic characteristics of the transmission line and the nonlinear load, the transmission network model and the power load model are constructed respectively; finally, by integrating the nonlinear models of the inverter, filter, transmission line and power load, a nonlinear mathematical model of the microgrid is constructed.

[0014] Furthermore, the detailed nonlinear mathematical model of the inverter includes: a power controller model, a voltage controller model, and a current controller model based on droop control; a nonlinear mathematical model of the microgrid is constructed in the form of a differential-algebraic equation system by combining a filter dynamic model, a transmission network model, and a power load model;

[0015] By integrating the state variables and algebraic variables in the nonlinear mathematical model of the microgrid, the vector matrix of the state variables is defined Vector matrix of algebraic variables in j=1,2,...,N g , k=1,2,...,N l , n=1,2,...,N; is the set of real numbers; δ vi 、P vi , Q vi and ω vi are the power angle, active power, reactive power and angular frequency of the i-th inverter respectively; φ vdi and φ vqi Represents the internal state quantity of the voltage controller; γ vdi and γ vqi Represents the internal state of the current controller; i fdi and i fqi They represent the d-axis and q-axis components of the current at the inverter output respectively; v cdi and v cqi Represent the d-axis and q-axis components of the voltage at the filter capacitor respectively; i cqi and i cqi Respectively represent the d-axis and q-axis components of the current at the filter outlet; i gdj and i gqj They represent the d-axis and q-axis components of the transmission line current respectively; i ldk and i lqk They represent the d-axis and q-axis components of the load current respectively; and They represent the d-axis and q-axis components of the voltage reference value of the voltage controller respectively; and They represent the d-axis and q-axis components of the current command value of the current controller respectively; and Represent the d-axis and q-axis components of the inverter output voltage reference value respectively; V n Represents the node voltage of the microgrid; the nonlinear mathematical model of the microgrid is expressed as:

[0016]

[0017] Where t is the time variable; is the derivative of the state variable vector matrix x(t); f(·) and g(·) are the set of nonlinear differential equations and algebraic equations that characterize the continuous dynamic characteristics of the microgrid, respectively; u(t) represents the set of input variables of the microgrid.

[0018] Furthermore, in step 2, considering the impact of the uncertainty of network attacks, a network attack model with variable amplitude is constructed using a modeling method based on Qino polyhedron, and the established network attack model is added as a disturbance input item to the nonlinear mathematical model of the microgrid, thereby reflecting the impact of uncertain network attacks on the microgrid.

[0019] Furthermore, the network attack model with variable amplitude constructed based on the Qino polyhedron modeling method is expressed as:

[0020]

[0021] Where U c Indicates the magnitude of network attack; represents the center value of the Chino polyhedron; β m is the proportional coefficient; l m is the generator of the Chino polyhedron; N c is the number of generators of the Zeno polyhedron; m is a variable used to record the change in the number of generators of the Zeno polyhedron during the modeling process;

[0022] By setting the center value and generator of the Chino polyhedron, a network attack model with arbitrary amplitude and variation range can be established. Considering the impact of network attacks on the droop control of the inverter in the microgrid, the model is added to the nonlinear mathematical model of the microgrid. The nonlinear mathematical model of the microgrid is transformed into:

[0023]

[0024] Where x c (t), y c (t) and u c (t) are the state variable vector, algebraic variable vector and input variable set of the microgrid considering the impact of cyber attacks, is x c The derivative value of (t).

[0025] Furthermore, in step 3, an improved reachable set calculation algorithm is designed based on the reachability analysis theory, and the nonlinear mathematical model of the microgrid in the form of a nonlinear differential-algebraic equation is converted into a linear abstract model through Taylor expansion. Taking into account the linearization error, the reachable set of the nonlinear mathematical model of the microgrid is obtained by combining the solution results of the linear abstract model.

[0026] Furthermore, the reachability analysis theory examines the dynamic behavior of high-dimensional nonlinear systems by calculating a conservative set containing all possible operating trajectories. By evaluating whether the states in the conservative set fluctuate significantly or show unstable trends, and whether the set boundaries exceed safety limits, the severity of the impact of injected cyber attacks on the microgrid is quantitatively assessed.

[0027] Considering the difficulty of directly solving nonlinear differential-algebraic equations, it is necessary to perform Taylor expansion at the linearization point, abstractly approximate the nonlinear mathematical model in the form of differential-algebraic equations into a linear differential equation model, and then use the reachable set calculation algorithm applicable to the linear differential equation model for calculation. In order to compensate for the linearization error caused by the abstract approximation, it is necessary to make an initial assumption about the linearization error, and the assumption must satisfy Where L is the initial assumption value of the linearization error, L d and L a are the Lagrangian remainders obtained by Taylor expansion, and B and E are the coefficient matrices of the linear differential equation model. The initial assumed value of the linearization error is added to the uncertain input term, and the reachable set determined by the uncertain input term is calculated. This is combined with the reachable set of the linear differential equation model to obtain the reachable set result of the nonlinear mathematical model in the form of a differential-algebraic equation. On this basis, in order to ensure the reliability of the linearization error compensation, the calculated true error must be compared with the initial assumed value of the linearization error. The true error should be within the range of the initial assumed value, otherwise the initial assumed value needs to be amplified and recalculated.

[0028] In the process of reachable set calculation, in order to alleviate the dimensionality curse problem caused by the exponential growth of the number of generators with iterations, an adaptive merging strategy for the generators of the Chino polyhedron based on the clustering method is designed. After each linear transformation, the generators with similar directions are clustered to address the generator direction redundancy problem and replaced with the minimum enclosing generator to constrain the complexity of the set. The adaptive merging strategy for the generators of the Chino polyhedron based on the clustering method is as follows: for the Chino polyhedron in the p-dimensional state space, its generator set is G = {g1, g2, ..., g q ,...,g p}, where g q is the qth generator, q=1,2,...,p; first normalize all the generators of the Chino polyhedron and calculate the unit vector of each generator Then the cosine similarity of the preset angle ≥ 0.95 is used as the threshold s min , if there are two generators and The unit vectors are satisfy Then determine the generator and The generators with similar directions are defined as the same cluster, and the same cluster generators are aggregated into the minimum enclosing main direction. To compensate for the regional shrinkage caused by the merger, the covariance weighted method is used to reconstruct the generator vector, and an expansion coefficient of 1.05-1.10 is introduced to ensure conservatism. The threshold adaptive rule is designed in combination with the dynamic characteristics of the microgrid, and the merger threshold s is dynamically adjusted according to the volume expansion rate of the Chino polyhedron. min ,When a volume surge caused by a fault transient is detected, the ,direction discrimination accuracy is automatically improved by raising the threshold to 0.98 to prevent the ,generalization of the critical safety margin;

[0029] After solving the nonlinear mathematical model in the form of differential-algebraic equations using the designed adaptive merging strategy of Chino polyhedron generators based on clustering method, the reachable set result at each moment is obtained. On this basis, the convex hull operation CH(·) is applied to calculate the reachable set within the specified calculation step Δt. The specific calculation process is: In the formula They are the reachable sets at time t1 and time t2 respectively. Finally, the reachable sets within each calculation step are combined to obtain the reachable sets within the specified time range [t0,t end ] reachable set within where t0, t end The start and end times are specified respectively.

[0030] Furthermore, in step 4, based on the established nonlinear mathematical model of the microgrid, the improved reachable set calculation algorithm designed in step 3 is used to calculate the reachable sets of the microgrid affected by different types of network attacks, and the obtained reachable sets are used to quantitatively analyze the impact of network attacks on each inverter in the microgrid and the overall operating status of the microgrid.

[0031] Furthermore, for the calculation of reachable sets of microgrids under various operating conditions, the operating conditions are divided into normal operation, attack introduction, fault occurrence and post-fault state. Time is used as the switching condition, and the corresponding reachable sets are converted and calculated between the nonlinear mathematical models of the microgrid under different operating conditions. Finally, the reachable sets under multiple operating conditions are merged through the union operation to obtain the reachable set results that can fully capture the changes in the internal state of the microgrid under different operating conditions. According to the reachable set results, the vulnerability of the microgrid under different attack scenarios and operating conditions can be evaluated, providing important guidance for ensuring the safe and stable operation of the microgrid.

[0032] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0033] 1. The model studied in this paper retains the original nonlinear characteristics of the microgrid and fully captures the internal complex operating characteristics of inverter-based distributed energy, providing a more reliable basis for in-depth analysis of the stability and security issues of the microgrid when it is attacked by a network.

[0034] 2. The present invention takes into account the impact of the uncertainty of network attacks, and uses a modeling method based on Chino polyhedron to construct a network attack model with variable amplitude. The established network attack model is added as a disturbance input item to the nonlinear mathematical model of the microgrid, reflecting the impact of uncertain network attacks on the operating performance of the microgrid, and providing a convenient and effective modeling method for quantitatively considering the impact of network attacks with different variation ranges on the operating status.

[0035] 3. To address the problem that the number of Chino polyhedron generators increases exponentially with iterations, the present invention designs an adaptive merging strategy for Chino polyhedron generators based on a clustering method, merges and replaces generators with similar directions, appropriately reduces the number of generators, and while ensuring the calculation accuracy of the reachable set, constrains the complexity of the set representation and improves the calculation efficiency of the reachable set.

[0036] 4. This invention utilizes an improved reachable set calculation algorithm to effectively predict the range of microgrid operating states under different operating conditions and different types of cyberattacks. By calculating a conservative set encompassing all possible operating trajectories, it examines the dynamic behavior of high-dimensional nonlinear systems. By assessing whether the states within the conservative set exhibit significant fluctuations or unstable trends, and whether the set boundaries exceed safety limits, it quantitatively assesses the severity of the impact of an injected cyberattack on the microgrid.

[0037] 5. The improved reachable set calculation algorithm adopted in the present invention can directly process the characteristics of complex systems without manual intervention to simplify the nonlinear part of the model, and can effectively deal with the nonlinear, random and uncertain characteristics inherent in actual systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 Flowchart of the method of the present invention.

[0039] Figure 2 This is a structural diagram of a microgrid according to an embodiment of the present invention.

[0040] Figure 3 This is a flow chart of microgrid reachability analysis according to an embodiment of the present invention. DETAILED DESCRIPTION

[0041] The present invention will be described in further detail below with reference to the embodiments and drawings, but the embodiments of the present invention are not limited thereto.

[0042] like Figure 1 As shown, this embodiment discloses a method for quantitatively evaluating the impact of microgrid network attacks based on reachability analysis, the details of which are as follows:

[0043] Step 1: Considering the complex dynamics inside the inverter and the line dynamics, a nonlinear mathematical model of the microgrid is established as follows:

[0044] like Figure 2 As shown in the figure, the microgrid consists of distributed energy, inverters, filters, transmission lines, power loads, collection and communication systems, etc. The microgrid contains N nodes, N i Inverter, N g transmission lines and N lpower loads. First, in order to capture the complex operating characteristics of distributed energy, the voltage outer loop-current inner loop controller dynamics are considered to accurately establish a detailed nonlinear mathematical model of the inverter; secondly, the coupling effect of the inductor-capacitor-inductor filter on the inverter export line is further combined to construct a dynamic model of the filter between the inverter and the terminal bus. In addition, considering the dynamic characteristics of the transmission line and the nonlinear load, the transmission network model and the power load model are constructed respectively; finally, by integrating the nonlinear models of the inverter, filter, transmission line and power load, a nonlinear mathematical model of the microgrid is systematically constructed. The modeling process specifically includes the following steps:

[0045] 1) Construct an inverter model, which specifically includes a power controller model based on droop control, a voltage controller model, and a current controller model;

[0046] 2) Build a dynamic model of the filter at the inverter outlet, which mainly consists of the inductor current dynamic model and the capacitor voltage dynamic model;

[0047] 3) Considering the dynamics of resistance and inductance on the transmission line, establish a transmission network model;

[0048] 4) Consider the resistance and inductance dynamics in the power load and establish a power load model;

[0049] 5) By integrating the nonlinear models of various parts such as inverters, filters, transmission lines and power loads, a nonlinear mathematical model of the microgrid is constructed in the form of a set of differential-algebraic equations.

[0050] By integrating the state variables and algebraic variables in the nonlinear mathematical model of the microgrid, the vector matrix of the state variables is defined Vector matrix of algebraic variables where i=1,2,...,N i ,j=1,2,...,N g , k=1,2,...,N l , n=1,2,...,N; is the set of real numbers; δ vi 、P vi , Q vi and ω vi are the power angle, active power, reactive power and angular frequency of the i-th inverter respectively; φ vdi and φ vqi Represents the internal state quantity of the voltage controller; γ vdi and γ vqi Represents the internal state of the current controller; i fdi and i fqi They represent the d-axis and q-axis components of the current at the inverter output respectively; v cdi and vcqi Represent the d-axis and q-axis components of the voltage at the filter capacitor respectively; i cqi and i cqi Respectively represent the d-axis and q-axis components of the current at the filter outlet; i gdj and i gqj They represent the d-axis and q-axis components of the transmission line current respectively; i ldk and i lqk They represent the d-axis and q-axis components of the load current respectively; and They represent the d-axis and q-axis components of the voltage reference value of the voltage controller respectively; and They represent the d-axis and q-axis components of the current command value of the current controller respectively; and Represent the d-axis and q-axis components of the inverter output voltage reference value respectively; V n Represents the node voltage of the microgrid. The nonlinear mathematical model of the microgrid is expressed as:

[0051]

[0052] Where t is the time variable; is the derivative of the state variable vector matrix x(t); f(·) and g(·) are the set of nonlinear differential equations and algebraic equations that characterize the continuous dynamic characteristics of the microgrid, respectively; u(t) represents the set of input variables of the microgrid.

[0053] Step 2: Considering the impact of the uncertainty of cyber attacks, a cyber attack model with variable amplitude is constructed using a modeling method based on Qino polyhedrons. The established cyber attack model is added as a disturbance input to the nonlinear mathematical model of the microgrid to reflect the impact of uncertain cyber attacks on the microgrid. The specific implementation method is as follows:

[0054] Based on the modeling method of Qino polyhedron, the network attack model with variable amplitude is expressed as follows:

[0055]

[0056] Where U c Indicates the magnitude of network attack; represents the center value of the Chino polyhedron; β m is the proportional coefficient; l m is the generator of the Chino polyhedron; N c is the number of generators of the Zeno polyhedron; m is a variable used to record the change in the number of generators of the Zeno polyhedron during the modeling process;

[0057] By setting the center value and generator of the Chino polyhedron, a network attack model with arbitrary amplitude and variation range can be established. Consider the network attack on the inverter droop control signal The specific network attack types can be: disturbance-type virtual data injection attack and proportional-type virtual data injection attack. Disturbance-type virtual data injection attacks include step attacks, sine attacks, etc. The attacked signal is expressed as:

[0058]

[0059] Where, is the droop control signal affected by the perturbation-type virtual data injection attack, Δy d The attack component is injected into the perturbation virtual data with uncertainty, t is the time variable, t c Time injected into the attack;

[0060] Under the influence of proportional virtual data injection attack, the attacked signal can be converted into:

[0061]

[0062] Where, is the droop control signal affected by the proportional virtual data injection attack, k fp The proportional coefficient for proportional virtual data injection attacks;

[0063] Considering the impact of cyber attacks on the droop control of the inverter in the microgrid, the cyber attack model is added to the nonlinear mathematical model of the microgrid. The nonlinear mathematical model of the microgrid is transformed into:

[0064]

[0065] Where x c (t), y c (t) and u c (t) are the state variable vector, algebraic variable vector and input variable set of the microgrid considering the impact of cyber attacks, is x c The derivative value of (t).

[0066] Step 3: Based on the reachability analysis theory, an improved reachable set calculation algorithm is designed. The nonlinear mathematical model of the microgrid in the form of nonlinear differential-algebraic equations is converted into a linear abstract model through Taylor expansion. Taking into account the linearization error, the reachable set of the nonlinear mathematical model of the microgrid is obtained by combining the solution results of the linear abstract model. The specific improvement of the reachable set calculation algorithm is as follows: in order to solve the problem that the number of Chino polyhedron generators increases exponentially with iterations, an adaptive merging strategy of Chino polyhedron generators based on clustering method is designed to merge and replace generators with similar directions, appropriately reduce the number of generators, and ensure the accuracy of reachable set calculation while constraining the complexity of set representation. The improved reachable set calculation algorithm process can be achieved through Figure 3 The specific implementation method is as follows:

[0067] 1) In order to alleviate the dimensionality curse problem caused by the exponential growth of the number of generators with iterations, an adaptive merging strategy for the generators of the Chino polyhedron based on the clustering method is designed. After each linear transformation, the generators with similar directions are clustered to address the problem of generator direction redundancy after the linear transformation, and replaced with the minimum enclosing generator to constrain the complexity. The adaptive merging strategy for the generators of the Chino polyhedron based on the clustering method is as follows: for the Chino polyhedron in the p-dimensional state space, its generator set is G = {g1, g2, ..., g q ,...,g p}, where g q is the qth generator, q=1,2,...,p. First, normalize all the generators of the Chino polyhedron and calculate the unit vector of each generator Then the cosine similarity of the preset angle ≥ 0.95 is used as the threshold s min If there are two generators and The unit vectors are satisfy Then determine the generator and The generators with similar directions are defined as the same cluster, and the same cluster generators are aggregated into the minimum enclosing main direction. To compensate for the regional shrinkage caused by merging, the covariance weighting method is used to reconstruct the generator vector, and an expansion coefficient of 1.05-1.10 is introduced to ensure conservatism. Furthermore, a threshold adaptive rule is designed based on the dynamic characteristics of the microgrid, and the merging threshold s is dynamically adjusted according to the volume expansion rate of the Chino polyhedron. min ,When a volume surge caused by a fault transient is detected, the ,direction discrimination accuracy is automatically improved by raising the threshold to 0.98 to prevent the over-generalization of the ,critical safety margin;

[0068] 2) Apply the designed adaptive merging strategy of Chino polyhedron generators based on clustering method to calculate the reachable set of the nonlinear mathematical model of the microgrid. In the calculation step Δt=[t1,t2] with t1 as the starting time and t2 as the ending time, the reachable set at time t1 is calculated. Starting from the linearization point, the calculation steps of the reachable set of the nonlinear mathematical model are as follows: Considering the difficulty of directly solving the nonlinear differential-algebraic equation model, it is necessary to calculate the reachable set of the nonlinear mathematical model by Perform Taylor expansion to approximate the nonlinear mathematical model in the form of nonlinear differential-algebraic equations into a linear model: In the formula and are matrices consisting of linearization points of state variables, algebraic variables and input variables, respectively. is the new state variable vector of the linear model, for The derivative value of is a disturbance term that includes linearization error and uncertain input, A c =A-BE -1 D is the linear model coefficient matrix, A, B, D and E are the Jacobian matrix coefficients of the set of nonlinear differential equations and algebraic equations obtained by linearization operations respectively;

[0069] Due to the unknown linearization error, in order to proceed with the calculation, an initial assumption must be made about this error and the assumption must satisfy The subsequent error is scaled by a scalar factor, where L is the initial assumed value of the linearization error and L d and L a is the Lagrangian residual obtained by Taylor expansion, B and E are the coefficient matrices of the linear differential equation model. The solution of the nonlinear mathematical model of the microgrid at time t2 is Where A set determined by the disturbance term. To ensure the reliability of error compensation, the true error must be calculated based on the above solution and compared with the initial assumption value. The true error should be within the range of the initial assumption value, otherwise the initial assumption value needs to be amplified and recalculated;

[0070] According to the above calculation, the reachable set within the calculation step length Δt is obtained by calculating the convex hull CH()

[0071] 3) Combine the reachable sets within each calculation step to obtain the specified time range [t0,t end ] reachable set within where t0, t end The start and end times are specified respectively.

[0072] Step 4: Based on the established nonlinear mathematical model of the microgrid, the improved reachable set calculation algorithm designed in step 3 is used to calculate the reachable sets of the microgrid affected by different types of cyber attacks. The obtained reachable sets are then used to quantitatively analyze the impact of cyber attacks on the operating status of each inverter in the microgrid and the entire microgrid. The specific implementation method is as follows:

[0073] The reachable sets of a microgrid are calculated under various operating conditions, including normal operation, attack introduction, fault occurrence, and post-fault state. Using time as the switching condition, the nonlinear mathematical model of the microgrid under different operating conditions is switched and the corresponding reachable sets are calculated. Finally, the reachable sets under multiple operating conditions are combined through a set union operation to obtain a reachable set that fully captures the changes in the microgrid's internal state under different operating conditions. This reachable set result can be used to assess the vulnerability of the microgrid under different attack scenarios and operating conditions, providing important guidance for ensuring the safe and stable operation of the microgrid.

[0074] The above description is merely a specific embodiment of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of this application. Therefore, the scope of protection of this application should be based on the scope of protection of the claims.

Claims

1. A quantitative assessment method for the impact of microgrid network attacks based on reachability analysis, characterized by: The following steps are involved: Step 1: Considering the complex dynamics inside the inverter and the line dynamics, a nonlinear mathematical model of the microgrid is established; Step 2: Considering the uncertainty in cyber attacks, a cyber attack model with variable amplitude is constructed using a modeling method based on Qino polyhedrons. The established cyber attack model is then added as a disturbance input to the nonlinear mathematical model of the microgrid. Step 3: To effectively analyze the nonlinear mathematical model of the microgrid, an improved reachable set calculation algorithm is designed based on reachability analysis theory. The nonlinear mathematical model is converted into a linear abstract model. Taking into account the linearization error, the reachable set of the microgrid is obtained by combining the solution results of the linear abstract model. The improvement of the reachable set calculation algorithm is as follows: to address the problem that the number of Chino polyhedron generators increases exponentially with iterations, an adaptive Chino polyhedron generator merging strategy based on clustering is designed. Generators with similar directions are merged and replaced to reduce the number of generators. This ensures the accuracy of the reachable set calculation while constraining the complexity of the set representation. Step 4: Apply the improved reachable set calculation algorithm to calculate the reachable set of the microgrid under the influence of different types of network attacks, and predict the dynamic trajectory of the microgrid state based on the reachable set results, so as to quantitatively analyze the impact of network attacks on the operating performance of the microgrid.

2. The microgrid network attack impact quantitative assessment method based on reachability analysis according to claim 1 is characterized in that: In step 1, the microgrid includes distributed energy sources based on inverters, transmission lines and power loads, including N nodes, N i Inverter, N g transmission lines and N l An electrical load.

3. The microgrid network attack impact quantitative assessment method based on reachability analysis according to claim 2 is characterized in that: In step 1, first, in order to capture the complex operating characteristics of distributed energy, the dynamics of the voltage outer loop and current inner loop controller are considered, and a detailed nonlinear mathematical model of the inverter is accurately established; secondly, the coupling effect of the inductor-capacitor-inductor filter on the inverter export line is further combined to construct a dynamic model of the filter between the inverter and the terminal bus. In addition, considering the dynamic characteristics of the transmission line and nonlinear load, the transmission network model and the power load model are constructed respectively; finally, by integrating the nonlinear models of the inverter, filter, transmission line and power load, a nonlinear mathematical model of the microgrid is constructed.

4. The microgrid network attack impact quantitative assessment method based on reachability analysis according to claim 3 is characterized in that: The detailed nonlinear mathematical model of the inverter includes: a power controller model based on droop control, a voltage controller model, and a current controller model; a nonlinear mathematical model of the microgrid is constructed in the form of a differential-algebraic equation system by combining a filter dynamic model, a transmission network model, and a power load model; By integrating the state variables and algebraic variables in the nonlinear mathematical model of the microgrid, the vector matrix of the state variables is defined Vector matrix of algebraic variables where i = 1, 2, ... N i ,j=1,2,...,N g , k=1,2,...,N l , n=1,2,...,N; is the set of real numbers; δ vi 、P vi , Q vi and ω vi are the power angle, active power, reactive power and angular frequency of the i-th inverter respectively; φ vdi and φ vqi Represents the internal state quantity of the voltage controller; γ vdi and γ vqi Represents the internal state of the current controller; i fdi and i fqi They represent the d-axis and q-axis components of the current at the inverter output respectively; v cdi and v cqi Represent the d-axis and q-axis components of the voltage at the filter capacitor respectively; i cqi and i cqi Respectively represent the d-axis and q-axis components of the current at the filter outlet; i gdj and i gqj They represent the d-axis and q-axis components of the transmission line current respectively; i ldk and i lqk They represent the d-axis and q-axis components of the load current respectively; and They represent the d-axis and q-axis components of the voltage reference value of the voltage controller respectively; and They represent the d-axis and q-axis components of the current command value of the current controller respectively; and Represent the d-axis and q-axis components of the inverter output voltage reference value respectively; V n Represents the node voltage of the microgrid; the nonlinear mathematical model of the microgrid is expressed as: Where t is the time variable; is the derivative of the state variable vector matrix x(t); f(·) and g(·) are the set of nonlinear differential equations and algebraic equations that characterize the continuous dynamic characteristics of the microgrid, respectively; u(t) represents the set of input variables of the microgrid.

5. The microgrid network attack impact quantitative assessment method based on reachability analysis according to claim 1 is characterized in that: In step 2, considering the impact of the uncertainty of network attacks, a network attack model with variable amplitude is constructed using the modeling method based on Qino polyhedron. The established network attack model is added as a disturbance input item to the nonlinear mathematical model of the microgrid, thereby reflecting the impact of uncertain network attacks on the microgrid.

6. The microgrid network attack impact quantitative assessment method based on reachability analysis according to claim 5 is characterized in that: The network attack model with variable amplitude constructed based on the modeling method of Qino polyhedron is expressed as: Where U c Indicates the magnitude of network attack; represents the center value of the Chino polyhedron; β m is the proportional coefficient; l m is the generator of the Chino polyhedron; N c is the number of generators of the Zeno polyhedron; m is a variable used to record the change in the number of generators of the Zeno polyhedron during the modeling process; By setting the center value and generator of the Chino polyhedron, a network attack model with arbitrary amplitude and variation range can be established. Considering the impact of network attacks on the droop control of the inverter in the microgrid, the model is added to the nonlinear mathematical model of the microgrid. The nonlinear mathematical model of the microgrid is transformed into: Where x c (t), y c (t) and u c (t) are the state variable vector, algebraic variable vector and input variable set of the microgrid considering the impact of cyber attacks, is x c The derivative value of (t).

7. The microgrid network attack impact quantitative assessment method based on reachability analysis according to claim 1 is characterized in that: In step 3, an improved reachable set calculation algorithm is designed based on the reachability analysis theory. The nonlinear mathematical model of the microgrid in the form of nonlinear differential-algebraic equations is converted into a linear abstract model through Taylor expansion. Taking the linearization error into consideration, the reachable set of the nonlinear mathematical model of the microgrid is obtained by combining the solution results of the linear abstract model.

8. The microgrid network attack impact quantitative assessment method based on reachability analysis according to claim 7 is characterized in that: The reachability analysis theory examines the dynamic behavior of high-dimensional nonlinear systems by calculating a conservative set containing all possible operating trajectories. By evaluating whether the states in the conservative set fluctuate significantly or show unstable trends, and whether the set boundaries exceed safety limits, the severity of the impact of injected cyber attacks on the microgrid is quantitatively assessed. Considering the difficulty of directly solving nonlinear differential-algebraic equations, it is necessary to perform Taylor expansion at the linearization point, abstractly approximate the nonlinear mathematical model in the form of differential-algebraic equations into a linear differential equation model, and then use the reachable set calculation algorithm applicable to the linear differential equation model for calculation. In order to compensate for the linearization error caused by the abstract approximation, it is necessary to make an initial assumption about the linearization error, and the assumption must satisfy Where L is the initial assumption value of the linearization error, L d and L a are the Lagrangian remainders obtained by Taylor expansion, and B and E are the coefficient matrices of the linear differential equation model. The initial assumed value of the linearization error is added to the uncertain input term, and the reachable set determined by the uncertain input term is calculated. This is combined with the reachable set of the linear differential equation model to obtain the reachable set result of the nonlinear mathematical model in the form of a differential-algebraic equation. On this basis, in order to ensure the reliability of the linearization error compensation, the calculated true error must be compared with the initial assumed value of the linearization error. The true error should be within the range of the initial assumed value, otherwise the initial assumed value needs to be amplified and recalculated. In the process of reachable set calculation, in order to alleviate the dimensionality curse problem caused by the exponential growth of the number of generators with iterations, an adaptive merging strategy for the generators of the Chino polyhedron based on the clustering method is designed. After each linear transformation, the generators with similar directions are clustered to address the generator direction redundancy problem and replaced with the minimum enclosing generator to constrain the complexity of the set. The adaptive merging strategy for the generators of the Chino polyhedron based on the clustering method is as follows: for the Chino polyhedron in the p-dimensional state space, its generator set is G = {g1, g2, ..., g q ,...,g p }, where g q is the qth generator, q=1,2,...,p; first normalize all the generators of the Chino polyhedron and calculate the unit vector of each generator Then the cosine similarity of the preset angle ≥ 0.95 is used as the threshold s min , if there are two generators and The unit vectors are satisfy Then determine the generator and The generators with similar directions are defined as the same cluster, and the same cluster generators are aggregated into the minimum enclosing main direction. To compensate for the regional shrinkage caused by the merger, the covariance weighted method is used to reconstruct the generator vector, and an expansion coefficient of 1.05-1.10 is introduced to ensure conservatism. The threshold adaptive rule is designed in combination with the dynamic characteristics of the microgrid, and the merger threshold s is dynamically adjusted according to the volume expansion rate of the Chino polyhedron. min ,When a volume surge caused by a fault transient is detected, the ,direction discrimination accuracy is automatically improved by raising the threshold to 0.98 to prevent the ,generalization of the critical safety margin; After solving the nonlinear mathematical model in the form of differential-algebraic equations using the designed adaptive merging strategy of Chino polyhedron generators based on clustering method, the reachable set result at each moment is obtained. On this basis, the convex hull operation CH(·) is applied to calculate the reachable set within the specified calculation step Δt. The specific calculation process is: In the formula They are the reachable sets at time t1 and time t2 respectively. Finally, the reachable sets within each calculation step are combined to obtain the reachable sets within the specified time range [t0,t end ] reachable set within where t0, t end The start and end times are specified respectively.

9. The microgrid network attack impact quantitative assessment method based on reachability analysis according to claim 1 is characterized in that: In step 4, based on the established nonlinear mathematical model of the microgrid, the improved reachable set calculation algorithm designed in step 3 is used to calculate the reachable sets of the microgrid affected by different types of network attacks, and the obtained reachable sets are used to quantitatively analyze the impact of network attacks on each inverter in the microgrid and the overall operating status of the microgrid.

10. The microgrid network attack impact quantitative assessment method based on reachability analysis according to claim 9 is characterized in that: For the calculation of reachable sets of microgrids under various operating conditions, the operating conditions are divided into normal operation, attack introduction, fault occurrence and post-fault state. Time is used as the switching condition to convert and calculate the corresponding reachable sets between the nonlinear mathematical models of the microgrid under different operating conditions. Finally, the reachable sets under multiple operating conditions are merged through the union operation to obtain the reachable set results that can fully capture the changes in the internal state of the microgrid under different operating conditions. Based on the reachable set results, the vulnerability of the microgrid under different attack scenarios and operating conditions can be evaluated, providing important guidance for ensuring the safe and stable operation of the microgrid.

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