Security assessment method for power cyber-physical systems considering wind power and cascading failures

Abstract

This invention discloses a security assessment method for a power cyber-physical system (FPS) considering wind power and cascading failures. The method includes: constructing a mathematical model of the PFS; launching a network attack against the PFS; designing a wind power stochastic model based on the Markov-Monte Carlo method after a cascading failure occurs; obtaining the active and reactive power injections of each node in the power system based on the wind power at each simulation moment of the cascading failure, and calculating the voltage at each node and the power flow of the transmission lines using an improved linearized AC power flow calculation method; updating the operating temperature of the transmission lines based on the power flow of the transmission lines at each simulation moment, and calculating the probability of transmission line disconnection; and proposing a cascading failure security assessment index that simultaneously considers wind turbine output and load fluctuations, based on entropy theory. This index can analyze the impact of transmission line disconnection on the subsequent evolution of cascading failures and assess the dynamic security of the system during the cascading failure process.

Description

Technical Field

[0001] This invention relates to the technical field of risk assessment for power cyber-physical systems, and in particular to a method for safety assessment of power cyber-physical systems that takes into account wind power and cascading failures. Background Technology

[0002] Modern power systems exhibit a trend of gradually increasing total load, rising penetration of renewable energy, and continuously improving informatization levels. While this improves the operational efficiency of the power system, it also exposes the system to new security risks. Specifically, the increasing power load and the pursuit of economic benefits are pushing the system closer to its operational safety boundaries, making initial faults more likely to trigger and evolve into complex chain reactions. The increasing proportion of renewable energy rapidly depletes the power system's flexible adjustment resources. Its intermittent, random, and fluctuating characteristics make system regulation more difficult, further reducing the system's recovery capability after a fault. On the other hand, the widespread integration of information technology equipment is gradually transforming traditional power systems into cyber-physical systems. While this enhances the monitoring and control capabilities of the power system, it also increases the system's digital attack surface. Therefore, constructing a security assessment mechanism for cyber-physical systems that can comprehensively consider the impact of renewable energy access and potential cascading faults is crucial for ensuring the stable operation and long-term development of the power system.

[0003] Traditional power system security assessment methods can be broadly categorized into static security assessment and transient security assessment. Static security assessment evaluates system security by analyzing whether key state variables can remain within safe zones after a anticipated fault occurs. This method focuses on analyzing the system's state at a specific moment after a fault occurs, without considering the subsequent fault evolution process, thus limiting its reliability. In contrast, transient security assessment focuses on the dynamic response of the power system after a disturbance, assessing its security by analyzing whether the system can recover stable operation after a disturbance. However, this method suffers from modeling difficulties and high computational costs, making it difficult to implement online in large-scale power systems. To overcome the limitations of traditional methods, some scholars have proposed machine learning-based security assessment methods. This method transforms the judgment of power system security into a classification problem, overcoming the technical bottleneck of excessive computation time in traditional security assessment methods. Since power outages are extremely rare in power systems, the above methods often rely on simulation data to train the model, making their effectiveness uncertain.

[0004] Furthermore, traditional security assessment methods only take the power system as the research object, without considering the interaction mechanism between the information-side communication and control system and the physical-side power system, nor the impact of the access of new energy units in the power system. As a result, the results often fail to reflect the true security status of the power information physical system. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a power cyber-physical system security assessment method that takes into account wind power and cascading failures. This method can dynamically assess the security of the power system during cascading failures, analyze the risk of the failure continuing to spread in the future, and the possibility that the system has recovered to stability.

[0006] To achieve the above objectives, the technical solution provided by this invention is: a security assessment method for power cyber-physical systems considering wind power and cascading failures, comprising the following steps:

[0007] S1: Construct a mathematical model of the power cyber-physical system, including the communication and control system on the information side and the power system on the physical side, and connect some nodes in the power system on the physical side to wind turbines;

[0008] S2: Launch a cyberattack against the power cyber-physical system as the initial condition for a cascading failure;

[0009] S3: After a cascading failure occurs, a wind power stochastic model based on the Markov-Monte Carlo method is designed to simulate the dynamic fluctuations of wind power over the time scale of cascading failure evolution.

[0010] S4: Based on the wind power at each cascading fault simulation moment, obtain the active and reactive power injections at each node in the power system. Calculate the voltage at each node and the power flow of the transmission lines using an improved linearized AC power flow calculation method. The improvement of this linearized AC power flow calculation method lies in linearizing the trigonometric terms related to the node voltage phase angle and the quadratic terms related to the node voltage amplitude in the nonlinear AC power flow equation. This involves two steps: First, approximate the node voltage phase angle using the DC power flow method, converting the trigonometric terms related to the node voltage phase angle into constants; second, perform a Taylor expansion of the power flow equation at the node's rated voltage and retain the linear terms, eliminating the quadratic terms related to the node voltage amplitude.

[0011] S5: Update the operating temperature of the transmission line according to the power flow of the transmission line at each simulation moment, calculate the probability of the transmission line disconnection using the fault probability model of the transmission line, wherein the fault probability model considers the probability of the transmission line disconnection due to overheating and the transmission power exceeding the relay protection setting value; use Monte Carlo sampling to obtain faulty components and remove them from the power system, and update the parameters of the power system.

[0012] S6: Based on entropy theory, a cascading fault safety assessment index is proposed that simultaneously considers wind turbine output and load fluctuations. This index, combined with the transmission line fault probability model and branch interruption power flow entropy weight, can analyze the impact of transmission line disconnection on the subsequent evolution of cascading faults and assess the dynamic safety of the power system during the cascading fault process. The branch interruption power flow entropy weight is used to reflect the magnitude of the impact of a disconnected transmission line on the power flow distribution of the power system. When there are no more transmission lines that can be disconnected in three consecutive simulation steps, the cascading fault evolution ends; otherwise, return to step S3.

[0013] Furthermore, in step S1, the power cyber-physical system is a multidimensional heterogeneous complex system composed of an information-side communication and control system and a physical-side power system. The communication and control system includes three subsystems: a measurement system, a communication system, and a control system. The measurement system is responsible for converting the physical state quantities of the power system into measurement signals. The communication system is the intermediary for signal transmission between different information devices, responsible for uploading measurement signals to the control system and transmitting control commands to the corresponding terminal devices. The control system generates control commands based on the collected measurement signals and control objectives. The power system is responsible for the production, transmission, and consumption of electrical energy and consists of generators, transmission lines, transformers, and various terminal devices. Its physical characteristics can be described by the power balance equation.

[0014] Furthermore, in step S2, the information devices in the power information physical system communicate with each other via Modbus, DNP3, and IEC 61850 protocols. Before launching a network attack, the attacker needs to perform network sniffing to find the transmission path of data packets and gain the trust of the target host through deception. The attacker uses the attacking host as a relay node for data packet transmission. After intercepting and cracking the transmitted data packets through decryption algorithms, the attacker can tamper with the data packets and transmit them to the target host, ultimately leading to incorrect decisions or malfunctions of the information devices, further causing initial faults in the power system and triggering a chain of faults.

[0015] Furthermore, in step S3, the wind power stochastic model consists of two parts: a wind speed stochastic model and a wind power characteristic function; the wind speed stochastic model is modeled using a Markov process, and the state space of the wind speed is set to S = {v1, v2, ..., v...}. d,...,v m-1 ,v m}, where v d This represents the median of the d-th wind speed interval. The wind speed variation exhibits Markov properties, where for equal time intervals t1, t2, ..., t... n+1 The following formula holds true:

[0016]

[0017] In the formula, Represents conditional probability, t1, t2, ..., t n+1 The random variable representing wind speed at any given time is: The above formula shows that t n+1 The wind speed at any given moment is only related to t n It is related to the wind speed at that moment, and to t. n Previous moments are irrelevant; the dynamic changes in wind speed can be represented by the state transition matrix T = {p} kl} m×m Analysis, matrix element p kl This represents the change in wind speed from v within a unit time interval. k Change to v l The probability, and has By performing maximum likelihood estimation on historical wind speed data, p can be obtained. kl =m kl / m l , where m k m represents the number of samples where the wind speed falls within the k-th wind speed interval. kl This represents the number of samples where the wind speed falls within the k-th and l-th wind speed intervals at two different times; after obtaining the wind speed state transition matrix T, we can determine the wind speed based on t. n Calculation of actual wind speed vector at time t n+1 Probability of wind speed values ​​at any given time

[0018]

[0019] In the formula, The wind speed vector representing the one-hot encoded wind speed. The index of an element with a value of 1 represents t. n Index of the wind speed range in which the actual wind speed falls at any given time. This represents the probability that the wind speed falls within each wind speed range. Monte Carlo sampling was performed, and the median of the wind speed range was used as t. n+1 The actual wind speed at that moment;

[0020] The wind power characteristic function is described by the following formula:

[0021]

[0022] In the formula, P w V represents the actual active power output of the wind turbine. in Represents the cut-in wind speed, v o V represents the rated wind speed. c V represents the cut-out wind speed. w P represents the actual wind speed of the wind turbine. wn This represents the rated active power output of the wind turbine unit; by using the wind power characteristic function and combining it with the wind speed at the current moment, the real-time wind power output of each unit can be calculated.

[0023] Furthermore, in step S4, when solving the power flow equations, the nonlinear terms related to the quadratic terms of node voltage phase angle and node voltage magnitude in the original power flow equations are linearized to obtain an improved linearized AC power flow calculation method; the topology of the power system can be represented by an undirected graph G =<U,L> This can be represented as follows: where U represents the set of power nodes and L represents the set of transmission lines; depending on the node type, U can be further represented as {U...} pq U pv U s Upq, Upv, and Us represent the pq node, pv node, and slack node, respectively; the power balance equation of the power system is expressed by the following equation:

[0024]

[0025] P ij =|V i | 2 g ij -|V i ||V j |(g ij cos(θ i -θ j )-b ij sin(θ i -θ j (6)

[0026] Q ij =-|V i | 2 b ij -|V i ||V j |(b ij cos(θ i -θ j )-g ij sin(θ i -θ j (7)

[0027] In the formula, P i Qi P represents the active and reactive power injected into power node i, respectively. ij Q ij P represents the active and reactive power flowing from node i to node j, respectively. ri Q ri V represents the active and reactive power flowing from node r to node i, respectively. i ,θ i G represents the voltage magnitude and phase angle at node i, respectively. ij 、b ij and represent the real and imaginary parts of the nodal admittance matrix elements, respectively; the nodal voltage phase angle is calculated using the branch power flow method, and the result is substituted into the original power flow equation, which can transform the trigonometric function terms about the phase angle difference between the two ends of the line into constants; the voltage magnitude of any power node i is expressed as Where V ni This represents the rated voltage amplitude of node i. This represents the voltage offset of power node i; in actual power system operation, the degree to which the node voltage amplitude deviates from the rated value is small. Will Substitute into the branch power flow expression and ignore about The quadratic term yields the following linearized power flow equations:

[0028]

[0029] By solving the mathematical programming problems simultaneously (4), (5), (8), and (9), the voltage magnitude and phase angle of all nodes in the power system can be obtained.

[0030] Furthermore, in step S5, based on the heat generation and dissipation balance of the transmission line at various times, the temperature change of the transmission line during the cascading fault process is calculated, and a functional relationship between the line break probability and the operating temperature is established, i.e., the fault probability model; wherein, the change ΔT of the operating temperature of the transmission line z within one simulation time step is calculated by the following formula:

[0031]

[0032] In the formula, M represents the mass of the transmission line, c represents the heat capacity of the transmission line, and P... zt h represents the active power transmitted by transmission line z at time t. c A represents the convective heat transfer coefficient of the transmission line. c T represents the surface area of ​​a power transmission line. ct T represents the operating temperature of the transmission line at time t. aThe ambient temperature is represented by ε, and σ represents the emissivity of the conductor and the Stephen-Boltzmann constant, respectively. Considering the probability of latent faults in the transmission line, the probability of line breakage is p. trip With operating temperature T c The relationship is:

[0033]

[0034] In the formula, p0 represents the probability of a hidden fault in the transmission line, and T u T represents the long-term maximum allowable operating temperature of the transmission line. m P represents the maximum operating temperature that a transmission line can withstand. max The power setting value of the relay protection device is used; during the cascading fault process, Monte Carlo sampling is performed on all possible disconnected transmission lines at each simulation time to determine the actual disconnected transmission line, and the topology and parameters of the power system are updated.

[0035] Furthermore, in step S6, due to fluctuations in the load and wind turbine output in the power system, the power system has multiple possible power distribution states at each moment. Let the load factor sequence be [0, 0.1, 0.2, ..., 2.5], and the branch interruption power flow entropy weight H of transmission line z be... z Calculated by the following formula:

[0036]

[0037] In the formula, D represents the total number of power system state samples extracted at a certain moment, and each sample contains the power distribution in the power system after the transmission line z is disconnected. d (i') The power vector representing the i'th sample; This indicates that when the power distribution of the power system is P d (j') At that time, the load factor is the proportion of transmission lines with a load factor in the k-th interval [0.1(k-1), 0.1k] to the total number of transmission lines in the power system; the load factor is the ratio of the actual power flow of the transmission line to the maximum long-term allowable power flow. The cascading failure safety assessment index S1 of the power system is calculated by the following formula:

[0038]

[0039] In the formula, N l P represents the total number of transmission lines in the power system. z The active power flow transmitted to transmission line z. This is the per-unit value of the operating temperature of the transmission line z, with the base value being the long-term maximum allowable operating temperature T of the transmission line. u .

[0040] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0041] 1. This invention establishes a mathematical model of the power cyber-physical system, which can be used to study the role and impact of network attacks in the evolution of cascading failures.

[0042] 2. This invention designs a wind power stochasticity model based on the Markov-Monte Carlo method, which can simulate the dynamic fluctuation of wind power over the time scale of cascading failures.

[0043] 3. This invention proposes an improved linearized AC power flow calculation method, which not only maintains a calculation accuracy close to that of the Newton-Raphson method, but also significantly improves the calculation efficiency and does not have the problem of non-convergence.

[0044] 4. Based on the physical characteristics of transmission lines, this invention establishes a transmission line fault probability model that considers thermal stability and power flow overload.

[0045] 5. Based on entropy theory, this invention proposes a cascading fault safety assessment index that considers the output of new energy sources and load fluctuations. Combined with the power flow entropy weight of the branch interruption of the transmission line, the impact of transmission line disconnection on the evolution of cascading faults and system safety can be analyzed. Attached Figure Description

[0046] Figure 1 This is an architecture diagram of a power cyber-physical system.

[0047] Figure 2 This is a flowchart for the security assessment of power cyber-physical systems. Detailed Implementation

[0048] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0049] This embodiment discloses a security assessment method for a power cyber-physical system that considers wind power and cascading failures. The architecture of the power cyber-physical system is as follows: Figure 1 As shown, the security assessment process for power cyber-physical systems is as follows: Figure 2 As shown, the specific steps include:

[0050] 1) Construct a mathematical model of the power cyber-physical system, including the communication and control system on the information side and the power system on the physical side, with some nodes in the physical power system connected to wind turbines. The power cyber-physical system is a multidimensional, heterogeneous, and complex system composed of the communication and control system on the information side and the power system on the physical side, such as... Figure 1As shown. The communication and control system comprises three subsystems: a measurement system, a communication system, and a control system. The measurement system converts the physical state quantities of the power system into measurement signals. The communication system acts as an intermediary for signal transmission between different information devices, responsible for uploading measurement signals to the control system and transmitting control commands to the corresponding terminal devices. The control system generates control commands based on the collected measurement signals and control objectives. The power system is responsible for the production, transmission, and consumption of electrical energy, and consists of generators, transmission lines, transformers, and various terminal devices. Its physical characteristics can be described by a power balance equation.

[0051] 2) Initialize the wind speed state vectors of each wind farm and the cascading failure simulation time t=0. Launch a network attack against the power cyber-physical system as the initial condition for the occurrence of cascading failures. Before launching the network attack, the attacker needs to perform network sniffing to find the transmission path of data packets and gain the trust of the target host through deception, using the attacking host as a relay node for data packet transmission. After intercepting and cracking the transmitted data packets through decryption algorithms, the attacker can tamper with them and transmit them to the target host, ultimately leading to incorrect decisions or malfunctions of the information equipment. Errors in the operation of the communication and control system cause initial faults in the power system, such as the tripping of circuit breakers on both sides of the transmission line, which further triggers cascading failures.

[0052] 3) Update simulation time t ← t+1. Obtain the wind speed state vector for each wind farm at the current time t. Calculate the active power output P of each wind farm. wt The randomness of wind speed can be modeled using a Markov process. Let the state space of wind speed be S = {v1, v2, ..., v...}. d ,...,v m-1 ,v m}, where v d This represents the median of the d-th wind speed interval. Wind speed variation exhibits the Markov property, where for equal time intervals t1, t2, ..., t... n+1 The following formula holds true:

[0053]

[0054] In the formula, Represents conditional probability, t1, t2, ..., t n+1 The random variable representing wind speed at any given time is: The above formula shows that t n+1 The wind speed at any given moment is only related to t n It is related to the wind speed at that moment, and to t. n Previous moments are irrelevant; the dynamic changes in wind speed can be represented by the state transition matrix T = {p} kl} m×m Analysis, matrix element pkl This represents the change in wind speed from v within a unit time interval. k Change to v l The probability, and has By performing maximum likelihood estimation on historical wind speed data, p can be obtained. kl =m kl / m l , where m k m represents the number of samples where the wind speed falls within the k-th wind speed interval. kl This represents the number of samples where the wind speed falls within the k-th and l-th wind speed intervals at two different times; after obtaining the wind speed state transition matrix T, we can determine the wind speed based on t. n Calculation of actual wind speed vector at time t n+1 Probability of wind speed values ​​at any given time

[0055]

[0056] In the formula, The wind speed vector representing the one-hot encoded wind speed. The index of an element with a value of 1 represents t. n Index of the wind speed range in which the actual wind speed falls at any given time. This represents the probability that the wind speed falls within each wind speed range. Monte Carlo sampling was performed, and the median of the wind speed range was used as t. n+1 The actual wind speed at that moment;

[0057] The wind power characteristic function is described by the following formula:

[0058]

[0059] In the formula, P w V represents the actual active power output of the wind turbine. in Represents the cut-in wind speed, v o V represents the rated wind speed. c V represents the cut-out wind speed. w P represents the actual wind speed of the wind turbine. wn This represents the rated active power output of the wind turbine unit; by using the wind power characteristic function and combining it with the wind speed at the current moment, the real-time wind power output of each unit can be calculated.

[0060] 4) Measurement devices in the power information physical system record the current measurement data of all substations and transmission lines and upload it to the control center. During this process, attackers can tamper with the measurement data uploaded by the information system, thereby misleading the control center's decisions. Based on the measurement data of the current system status, the control center generates recovery control commands, including generator power adjustment, wind farm power adjustment, and load reduction commands, and transmits them to the corresponding power nodes.

[0061] 5) Perform power flow calculations to obtain the voltage magnitude, phase angle, and power transmitted through transmission lines at each node. The topology of a power system can be represented by an undirected graph G =<U,L> Let U represent the set of power nodes and L represent the set of transmission lines. Depending on the node type, U can be further represented as {U...} pq U pv U s}, U pq U pv U s These represent the pq node, pv node, and slack node, respectively. The power balance equation of the power system can be expressed by the following equation:

[0062]

[0063] P ij =|V i | 2 g ij -|V i ||V j |(g ij cos(θ i -θ j )-b ij sin(θ i -θ j (6)

[0064] Q ij =-|V i | 2 b ij -|V i ||V j |(b ij cos(θ i -θ j )-g ij sin(θ i -θ j (7)

[0065] In the formula, P i Q i P represents the active and reactive power injected into power node i, respectively. ij Q ij P represents the active and reactive power flowing from node i to node j, respectively. ri Q ri V represents the active and reactive power flowing from node r to node i, respectively. i ,θ i G represents the voltage magnitude and phase angle at node i, respectively. ij 、b ijand represent the real and imaginary parts of the nodal admittance matrix elements, respectively; the nodal voltage phase angle is calculated using the branch power flow method, and the result is substituted into the original power flow equation, which can transform the trigonometric function terms about the phase angle difference between the two ends of the line into constants; the voltage magnitude of any power node i is expressed as Where V ni This represents the rated voltage amplitude of node i. This represents the voltage offset of power node i; in actual power system operation, the degree to which the node voltage amplitude deviates from the rated value is very small, typically... Will Substitute into the branch power flow expression and ignore about The quadratic term yields the following linearized power flow equations:

[0066]

[0067] By solving the mathematical programming problems simultaneously (4)-(5) and (8)-(9), the voltage magnitude and phase angle of all nodes in the power system can be obtained.

[0068] 6) Update the operating temperature of the transmission lines and calculate the probability of disconnection for all transmission lines in the power system. Use Monte Carlo sampling to identify disconnected transmission lines. Based on the heat generation and dissipation balance of the transmission lines at various times, calculate the temperature change of the transmission lines within one simulation time step of a cascading fault, and establish a functional relationship between the probability of line disconnection and the operating temperature, i.e., the fault probability model. The change in operating temperature ΔT of transmission line z within one simulation time step can be calculated by the following formula:

[0069]

[0070] In the formula, M represents the mass of the transmission line, c represents the heat capacity of the transmission line, and P... zt h represents the active power transmitted by transmission line z at time t. c A represents the convective heat transfer coefficient of the transmission line. c T represents the surface area of ​​a power transmission line. ct T represents the operating temperature of the transmission line at time t. a Let represent the ambient temperature, and ε and σ represent the emissivity of the conductor and the Stephen-Boltzmann constant, respectively. Considering the probability of latent faults in the transmission line, the probability of line breakage, p... trip With operating temperature T c The relationship is:

[0071]

[0072] In the formula, p0 represents the probability of a hidden fault in the transmission line, and T u T represents the long-term maximum allowable operating temperature of the transmission line.m P represents the maximum operating temperature that a transmission line can withstand. max This refers to the power setting value of the relay protection device.

[0073] 7) Based on entropy theory, a cascading fault safety assessment index that simultaneously considers wind turbine output and load fluctuations is proposed. This index, combined with the transmission line fault probability model and branch interruption power flow entropy weight, can analyze the impact of transmission line disconnection on the subsequent evolution of cascading faults and assess the dynamic safety of the power system during cascading faults. The branch interruption power flow entropy weight reflects the magnitude of the impact of a disconnected transmission line on the power flow distribution of the power system. The cascading fault evolution ends when there are no more transmission lines that can be disconnected in three consecutive simulation steps; otherwise, it returns to step 3). The power system cascading fault safety assessment index considers the transmission line disconnection probability and combines it with the branch interruption power flow entropy weight to analyze the impact of transmission line disconnection on the system, enabling dynamic assessment of the cascading fault risk of the power cyber-physical system. Since the load and wind turbine output in the power system fluctuate, the system has multiple possible power distribution states at each moment. Assuming the load rate sequence is [0, 0.1, 0.2, ..., 2.5], the branch interruption power flow entropy of transmission line z is calculated by the following formula:

[0074]

[0075] In the formula, D represents the total number of power system state samples extracted at a certain moment, and each sample contains the power distribution in the power system after the transmission line z is disconnected. d (i') The power vector representing the i'th sample; This indicates that when the power distribution of the power system is P d (j') At that time, the load factor is the proportion of transmission lines with a load factor in the k-th interval [0.1(k-1), 0.1k] to the total number of transmission lines in the power system; the load factor is the ratio of the actual power flow of the transmission line to the maximum long-term allowable power flow. The cascading failure safety assessment index S1 of the power system is calculated by the following formula:

[0076]

[0077] In the formula, N l P represents the total number of transmission lines in the power system. z The active power flow transmitted to transmission line z. This is the per-unit value of the operating temperature of the transmission line z, with the base value being the long-term maximum allowable operating temperature T of the transmission line. u .

[0078] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be considered as equivalent replacement methods and are included in the scope of protection of the present invention.

Claims

1. A method for security assessment of power cyber-physical systems considering wind power and cascading failures, characterized in that, Includes the following steps: S1: Construct a mathematical model of the power cyber-physical system, including the communication and control system on the information side and the power system on the physical side, and connect some nodes in the power system on the physical side to wind turbines; S2: Launch a cyberattack against the power cyber-physical system as the initial condition for a cascading failure; S3: After a cascading failure occurs, a wind power stochastic model based on the Markov-Monte Carlo method is designed to simulate the dynamic fluctuations of wind power over the time scale of cascading failure evolution. S4: Based on the wind power at each cascading fault simulation moment, obtain the active and reactive power injections at each node in the power system. Calculate the voltage at each node and the power flow of the transmission lines using an improved linearized AC power flow calculation method. The improvement of this linearized AC power flow calculation method lies in linearizing the trigonometric terms related to the node voltage phase angle and the quadratic terms related to the node voltage amplitude in the nonlinear AC power flow equation. This involves two steps: First, approximate the node voltage phase angle using the DC power flow method, converting the trigonometric terms related to the node voltage phase angle into constants; second, perform a Taylor expansion of the power flow equation at the node's rated voltage and retain the linear terms, eliminating the quadratic terms related to the node voltage amplitude. S5: Update the operating temperature of the transmission line according to the power flow of the transmission line at each simulation moment, calculate the probability of the transmission line disconnection using the fault probability model of the transmission line, wherein the fault probability model considers the probability of the transmission line disconnection due to overheating and the transmission power exceeding the relay protection setting value; use Monte Carlo sampling to obtain faulty components and remove them from the power system, and update the parameters of the power system. S6: Based on entropy theory, a cascading fault safety assessment index is proposed that simultaneously considers wind turbine output and load fluctuations. This index, combined with the transmission line fault probability model and branch interruption power flow entropy weight, can analyze the impact of transmission line disconnection on the subsequent evolution of cascading faults and assess the dynamic safety of the power system during the cascading fault process. The branch interruption power flow entropy weight is used to reflect the magnitude of the impact of a disconnected transmission line on the power flow distribution of the power system. When there are no more transmission lines that can be disconnected in three consecutive simulation steps, the cascading fault evolution ends; otherwise, return to step S3.

2. The power cyber-physical system security assessment method considering wind power and cascading failures according to claim 1, characterized in that, In step S1, the power cyber-physical system is a multidimensional heterogeneous complex system composed of a communication and control system on the information side and a power system on the physical side. The communication and control system includes three subsystems: a measurement system, a communication system, and a control system. The measurement system is responsible for converting the physical state quantities of the power system into measurement signals. The communication system is the intermediary for signal transmission between different information devices, responsible for uploading measurement signals to the control system and transmitting control commands to the corresponding terminal devices. The control system generates control commands based on the collected measurement signals and control objectives. The power system is responsible for the production, transmission, and consumption of electrical energy and consists of generators, transmission lines, transformers, and various terminal devices. Its physical characteristics can be described by the power balance equation.

3. The power cyber-physical system security assessment method considering wind power and cascading failures according to claim 1, characterized in that, In step S2, the information devices in the power information physical system communicate with each other via Modbus, DNP3, and IEC61850 protocols. Before launching a network attack, the attacker needs to sniff the network to find the transmission path of data packets and gain the trust of the target host through deception. The attacker uses the attacking host as a relay node for data packet transmission. After intercepting and cracking the transmitted data packets through decryption algorithms, the attacker can tamper with the data packets and transmit them to the target host, ultimately leading to incorrect decisions or malfunctions of the information devices, further causing initial faults in the power system and triggering a chain of faults.

4. The power cyber-physical system security assessment method considering wind power and cascading failures according to claim 1, characterized in that, In step S3, the wind power stochastic model consists of two parts: a wind speed stochastic model and a wind power characteristic function. The wind speed stochastic model is modeled using a Markov process, and the state space of the wind speed is set to S = {v1, v2, ..., v...}. d ,...,v m-1 ,v m }, where v d This represents the median of the d-th wind speed interval. The wind speed variation exhibits Markov properties, where for equal time intervals t1, t2, ..., t... n+1 The following formula holds true: In the formula, Represents conditional probability, t1, t2, ..., t n+1 The random variable representing wind speed at any given time is: The above formula shows that t n+1 The wind speed at any given moment is only related to t n It is related to the wind speed at that moment, and to t. n Previous moments are irrelevant; the dynamic changes in wind speed can be represented by the state transition matrix T = {p} kl } m×m Analysis, matrix element p kl This represents the change in wind speed from v within a unit time interval. k Change to v l The probability, and has By performing maximum likelihood estimation on historical wind speed data, p can be obtained. kl =m kl / m l , where m l m represents the number of samples where the wind speed falls within the l-th wind speed interval. kl This represents the number of samples where the wind speed falls within the k-th and l-th wind speed intervals at two different times; after obtaining the wind speed state transition matrix T, we can determine the wind speed based on t. n Calculation of actual wind speed vector at time t n+1 Probability of wind speed values ​​at any given time In the formula, The wind speed vector representing the one-hot encoded wind speed. The index of an element with a value of 1 represents t. n Index of the wind speed range in which the actual wind speed falls at any given time. This represents the probability that the wind speed falls within each wind speed range. Monte Carlo sampling was performed, and the median of the wind speed range was used as t. n+1 The actual wind speed at that moment; The wind power characteristic function is described by the following formula: In the formula, P w V represents the actual active power output of the wind turbine. in Represents the cut-in wind speed, v o V represents the rated wind speed. c V represents the cut-out wind speed. w P represents the actual wind speed of the wind turbine. wn This represents the rated active power output of the wind turbine unit; by using the wind power characteristic function and combining it with the wind speed at the current moment, the real-time wind power output of each unit can be calculated.

5. The power cyber-physical system security assessment method considering wind power and cascading failures according to claim 1, characterized in that, In step S4, when solving the power flow equations, the nonlinear terms related to the quadratic terms of node voltage phase angle and node voltage magnitude in the original power flow equations are linearized to obtain an improved linearized AC power flow calculation method; the topology of the power system can be represented by an undirected graph G =<U,L> This can be represented as follows: where U represents the set of power nodes and L represents the set of transmission lines; depending on the node type, U can be further represented as {U...} pq U pv U s }, U pq U pv U s These represent the pq node, pv node, and slack node, respectively; the power balance equation of the power system is expressed by the following equation: P ij =|V i | 2 g ij -|V i ||V j |(g ij cos(θ i -θ j )-b ij sin(θ i -θ j )) (6) Q ij =-|V i | 2 b ij -|V i ||V j |(b ij cos(θ i -θ j )-g ij sin(θ i -θ j )) (7) In the formula, P i Q i P represents the active and reactive power injected into power node i, respectively. ij Q ij P represents the active and reactive power flowing from node i to node j, respectively. ri Q ri V represents the active and reactive power flowing from node r to node i, respectively. i ,θ i G represents the voltage magnitude and phase angle at node i, respectively. ij 、b ij and represent the real and imaginary parts of the nodal admittance matrix elements, respectively; the nodal voltage phase angle is calculated using the branch power flow method, and the result is substituted into the original power flow equation, which can transform the trigonometric function terms about the phase angle difference between the two ends of the line into constants; the voltage magnitude of any power node i is expressed as Where V ni This represents the rated voltage amplitude of node i. This represents the voltage offset of power node i; in actual power system operation, the degree to which the node voltage amplitude deviates from the rated value is small. Will Substitute into the branch power flow expression and ignore about The quadratic term yields the following linearized power flow equations: By solving the mathematical programming problems simultaneously (4), (5), (8), and (9), the voltage magnitude and phase angle of all nodes in the power system can be obtained.

6. The power cyber-physical system security assessment method considering wind power and cascading failures according to claim 1, characterized in that, In step S5, based on the heat generation and dissipation balance of the transmission line at various times, the temperature change of the transmission line during the cascading fault process is calculated, and a functional relationship between the line break probability and the operating temperature is established, i.e., the fault probability model; wherein, the change ΔT of the operating temperature of the transmission line z within one simulation time step is calculated by the following formula: In the formula, M represents the mass of the transmission line, c represents the heat capacity of the transmission line, and P... zt h represents the active power transmitted by transmission line z at time t. c A represents the convective heat transfer coefficient of the transmission line. c T represents the surface area of ​​a power transmission line. ct T represents the operating temperature of the transmission line at time t. a The ambient temperature is represented by ε, and σ represents the emissivity of the conductor and the Stephen-Boltzmann constant, respectively. Considering the probability of latent faults in the transmission line, the probability of line breakage is p. trip With operating temperature T c The relationship is: In the formula, p0 represents the probability of a hidden fault in the transmission line, and T u T represents the long-term maximum allowable operating temperature of the transmission line. m P represents the maximum operating temperature that a transmission line can withstand. max The power setting value of the relay protection device is used; during the cascading fault process, Monte Carlo sampling is performed on all possible disconnected transmission lines at each simulation time to determine the actual disconnected transmission line, and the topology and parameters of the power system are updated.

7. The method for security assessment of power cyber-physical systems considering wind power and cascading failures according to claim 1, characterized in that, In step S6, due to fluctuations in the load and wind turbine output in the power system, the power system has multiple possible power distribution states at each moment. Let the load factor sequence be [0, 0.1, 0.2, ..., 2.5], and the branch interruption power flow entropy weight H of transmission line z be... z Calculated by the following formula: In the formula, D represents the total number of power system state samples extracted at a certain moment. Each sample contains the power distribution in the power system after the transmission line z is disconnected. The power vector representing the i'th sample; This indicates that when the power distribution of the power system is At that time, the load factor is the proportion of transmission lines with a load factor in the k-th interval [0.1(k-1), 0.1k] to the total number of transmission lines in the power system; the load factor is the ratio of the actual power flow of the transmission line to the maximum long-term allowable power flow. The cascading failure safety assessment index S1 of the power system is calculated by the following formula: In the formula, N l P represents the total number of transmission lines in the power system. z The active power flow transmitted to transmission line z. This is the per-unit value of the operating temperature of the transmission line z, with the base value being the long-term maximum allowable operating temperature T of the transmission line. u .

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